Kur Johnson, Jaes J. McAndrews, and Ko Soraäk Econozng on Lqudy wh Deferred Seleen Mechanss Real-e gross seleen (RTGS) syses such as he Federal Reserve s Fedwre Funds Servce enable parcpang banks o sele payens edaely and n he full aoun; however, he hgh level of lqudy nheren n he syses requres large nraday cred exensons. An exanaon of several deferred seleen echanss ha could poenally copleen RTGS syses consders a novel echans a recep-reacve gross seleen syse ha bases he seleen of a bank s payens on he value of s receps over a gven e, raher han on he bank s balance. The recep-reacve echans can poenally reduce nraday cred exensons sgnfcanly whle odesly delayng he average e of payen seleen; he echans also provdes good ncenves for banks o sub payens earler n he day. O 1. Inroducon n a ypcal day, he oal value of payens seled by he Federal Reserve s Fedwre Funds Servce exceeds $1.8 rllon. On average, cred exended o banks usng Fedwre s abou $30 bllon over he course of he day, whle he peak nraday aoun reaches $86 bllon. Gven hs hgh level of cred exensons, s worhwhle askng wheher payen seleens could be anaged wh a lower level of ousandng cred, hus allowng syse operaors o econoze on lqudy. 1 Fedwre operaes as a real-e gross seleen (RTGS) syse. RTGS syses ransfer he full aoun of payen orders beween coercal bank parcpans edaely upon recep, hus avodng shor-er deb oblgaons beween parcpans. Ths s a desrable feaure ha has proped any cenral banks worldwde o pleen hese syses over he pas decade. However, because payen ransfers beween parcpans are ade edaely n he full aoun, and because of he asynchronous ng of payens by parcpans, ananng he lqudy needs of RTGS syses can be cosly. Indeed, soe syse operaors have alered her RTGS syses n recen years o econoze on he funds needed o coplee seleens. Kur Johnson s an econos and Jaes J. McAndrews a vce presden a he Federal Reserve Bank of New York; Ko Soraäk s a payen syses polcy exper a he European Cenral Bank and a research vsor a he Federal Reserve Bank of New York. <kur.johnson@ny.frb.org> <jae.candrews@ny.frb.org> <ko.soraak@ecb.n> The auhors hank Rober Ashan, Lucnda Brckler, Dara Hun, Travs Nesh, wo anonyous referees, and senar parcpans a he Bank of England, he Federal Reserve Bank of New York, he 2001 Money Transfer Conference, he Frs Sulaor Conference a he Bank of Fnland, and he European Cenral Bank for helpful coens. They also hank Harry Lenonen and he Bank of Fnland for he use of he Bank of Fnland s Payen Syse Sulaor, and he Wholesale Produc Offce and Cred Rsk Manageen Funcon of he Federal Reserve Bank of New York for provdng he daa. The vews expressed are hose of he auhors and do no necessarly reflec he poson of he Federal Reserve Bank of New York, he Federal Reserve Syse, or he European Cenral Bank. FRBNY Econoc Polcy Revew / Deceber 2004 51
One way o reduce a syse s lqudy needs s by usng deferred seleen echanss such as neng. In neng syses, payen orders are deferred unl soe desgnaed e usually lae n he day when he parcpans exchange only he ne aouns hey owe or are owed. If all parcpans successfully sub hese ne aouns, he syse seles all he payens accuulaed durng he day wh he leas aoun of funds possble ha s, jus he ne aouns. To acheve hs econoy n funds use, a neng syse delays he seleen of payens so ha all orders rean pendng unl he ne seleen payens are copleed successfully. Ths delay feaure creaes dsnc lqudy and rsk anageen characerscs. Anoher ype of deferred seleen echans queues payens as hey ener he syse. Soe European RTGS syses use hese queue-augened RTGS syses, or hybrd syses. 2 Such syses save on lqudy as n a neng syse bu wh less delay han end-of-day neng poses. In hs arcle, we propose alernave ways of selng payens subed o he Fedwre Funds Servce ha would resul n lower nraday cred exensons. We analyze he effecs of copleenng an RTGS syse wh varous deferred seleen echanss by perforng sulaons on hsorcal Fedwre daa. Alhough ohers have suded he effecs of such odfcaons on payens syses, hs s he frs exanaon n he conex of Fedwre. One funcon of a payens syse desgn could be o nze he cobned cos of delayng payens and he rsk of exendng nraday cred o coercal banks ha s, he cred rsk ha a cenral bank assues by provdng nraday cred. We do no use an explc, objecve funcon o evaluae he varous alernaves o an RTGS syse because we do no know banks preferences regardng delays or specfc defaul rsks. We can, however, evaluae hose desgns ha reduce boh delays and cred exensons as preferable o ohers. In shor, soe odfcaons ay clearly be ore effecve han ohers bu none copares easly wh a pure RTGS syse, whch by defnon elnaes delays. Our resuls sugges ha, copared wh RTGS syses, alernave seleen desgns could sgnfcanly reduce cred exensons whle odesly delayng he average e of seleen of payens. Ths arcle s organzed as follows. In he nex secon, we dscuss he bascs of deferred seleen syses, and n Secon 3 we descrbe he syses used n our sulaons. In Secon 4, we descrbe he perforance ercs and resuls of he basc sulaons, and n Secon 5 we conduc a sensvy analyss of he resuls obaned fro alernave levels of queued payens. Secons 6 and 7 presen ore dealed analyses of lqudy use and he level of end-of-day queues. In Secon 8, we dscuss our resuls and he lkely behavoral responses by a bank parcpan o he avalably of he sulaed syses. We conclude wh a dscusson of our resuls n lgh of he prevous leraure. 2. Characerscs of Deferred Seleen As a baselne case, a pure RTGS syse s one n whch no payens are deferred for seleen all payens are released upon recep by he syse operaor as long as he parcpan has adequae funds o sele he payens. If no, he payen s rejeced. Deferred seleen can work n conjuncon wh RTGS syses. In pracce, deferred seleen echanss can operae n any ways, bu all requre ceran crera by whch payen orders are enered, ranked, and seled. In addon, crera for he end-of-day closng or he epyng of queues are requred n a queung syse. The enry creron n a deferred seleen echans deernes wheher payens are deferred or wheher hey are seled edaely by pure RTGS. Ths creron can be based eher on decsons ade by parcpang banks or on an auoac feaure creaed by prespecfed crera. In any European RTGS syses, deferen s auoac: Raher han rejec payen orders ourgh, he syses auoacally place payens n a queue f RTGS seleen of he payen would breach he cred l of he parcpan. The order creron defnes he rankng or orderng of payen essages ha are queued. Mos coneporary RTGS We propose a novel deferred seleen echans ha bases he seleen of queued payens on he value of ncong payens raher han on a parcpan s accoun balance. syses adhere o he frs-n, frs-ou (FIFO) prncple ha s, payens ha ener he queue earler have prory over payens ha ener he queue laer. The FIFO prncple s easy o pleen. Assung lqudy consrans, FIFO perfors reasonably well when a syse s saller payens are subed generally earler n he day. Because early, larger payens can obsruc FIFO-ordered queues, soe RTGS 52 Econozng on Lqudy
syses now have bypass-fifo algorhs ha allow parcpans o reorder and prorze queued payens. Soe, such as he CHAPS Clearng Copany n he Uned Kngdo, allow he parcpans o selec he order of he queued payens accordng o oher crera, for exaple, by he value of he payens. The seleen creron defnes he rules by whch payen essages are released fro he queue, rggerng he flow of oney fro he payer s accoun o he payee s accoun. Payens can be released fro he queue eher ndvdually or n groups. In os queung arrangeens, payens are released ndvdually, bu soe syses eploy grdlockresoluon algorhs ha allow ulple payens o be seled fro he queue sulaneously f he release of he payens on an ndvdual bass s no possble (see Bech and Soraäk [2001, 2002]). In prevously descrbed queung syses, he seleen creron has been based on he balance of he parcpan ha s, payens are released as soon as he parcpan s balance s hgh enough o cover he payen s seleen. The release of payens fro he queue can be based on oher crera as well. In hs arcle, we propose a novel deferred seleen echans ha bases he seleen of queued payens on he value of ncong payens raher han on a parcpan s accoun balance. The las poran eleen of he desgn of a queung syse s end-of-day close of queues, or how o epy he queue of payen orders a he close of busness. One ehod used n soe European syses s o sele all essages reanng n he queue afer a ceran lengh of e hrough an exchange of he ne aouns of he payens. An alernave ehod of closng queues s o reurn unreleased payens o banks before he RTGS syse closes so banks can redrec he unreleased essages o he RTGS syse. 3. Syse Desgns 3.1 Recep-Reacve Gross Seleen Syse In he recep-reacve gross seleen syse ha we sulae, a poron of banks payens s randoly seleced o be seled hrough RTGS, whle he reanng se of payens s placed n a queue for deferred seleen. Queued payen essages are ranked on a frs-n, frs-ou bass. For he release creron, a payen essage s release fro he queue s rggered by he arrval of ncong funds receved by he bank whn a specfed perod of e. In our sulaons, hs e perod s one calendar nue. 3 The syse wll release whn one nue as any payens fro he fron of he queue as possble o offse bu no exceed he aoun of ncong funds. In he sulaons, hs process connues hroughou he day unl 5:30 p.., when he queue closes. The exhb below shows he effecs of a recep-reacve queue on a bank s balance durng a nue n whch he bank boh sends and receves RTGS payens (see Appendx A for a dealed descrpon of hs queung syse). An poran desgn eleen of a queung syse s how o epy he queue of payen essages a he end of he day. In our sulaons, we randoly reassgn he unreleased payens a seleen e beween 5:30 p.. and 6:00 p.. Ths s our approxaon o reurnng, a 5:30 p.., he unreleased (ha s, unseled) payens o he banks ha subed he, wh he banks subsequenly resubng he payens hrough he RTGS syse over he nex half-hour. Ths feaure of our queue desgn was chosen for a nuber of reasons. The end-of-day reurn of he queued essages s conssen wh he basc desgn of queung syses used as adjuncs o RTGS syses. The recep-reacve queung syse Dynacs of a Bank s Balance under Recep-Reacve Gross Seleen Dollars In our sulaons, we desgn a syse n whch payens go hrough one of wo alernave channels deferred seleen or real-e gross seleen. These wo an channels recognze ha soe payens are ore e-crcal han ohers. Banks would lkely wan o sele her e-crcal payens hrough he edae RTGS channel whle he less e-crcal payens could go hrough he deferred seleen channel o save lqudy. The deferred seleen channel allows payens o ake one of hree possble pahs: a one-hour neng syse, a sx-hour neng syse, or a unque ype of syse ha we call a recep-reacve gross seleen (RRGS) syse. Incong recep of payen Bank s balance Ougong real-e gross seleen payens ade by bank End of nue -1 Release of queued payen essages Incong recep of payen Te Release of queued payen essages End of nue FRBNY Econoc Polcy Revew / Deceber 2004 53
s nended o encourage banks o sub o he queue hose payens ha can be seled wh ncong funds. If parcular payens canno be seled ha way, hen he banks would lkely sub he payens hrough he RTGS syse, whch s desgned o sele payens edaely wh avalable balances. Therefore, reurnng banks payens ha rean n he queue o he respecve banks near he end of he day s conssen wh he nended use of he recep-reacve queue and of he RTGS syse. 3.2 One-Hour and Sx-Hour Neng Syses We sulae he perforance of wo sple neng syses. In boh syses, a poron of all payens s seled by RTGS whle a copleenary se of payens s pu n a queue. The queued payens are cuulaed for a ceran perod of e, need, hen seled even f hey cause an overdraf n he banks accoun balances. In he frs sulaon, he payens are cuulaed, need, hen seled afer each hour of he operang day. In he second sulaon, cuulaed payens are need and seled afer sx hours. (See Table 1 for a suary of he sulaons.) 4. Sulaons of he Three Syses To gauge he usefulness of hese hree copleens o RTGS syses one-hour neng, sx-hour neng, and recep-reacve gross seleen we sulae her perforance usng a progra developed by he Bank of Fnland. The sulaor s descrbed n deal n Lenonen and Soraäk (2003). (See also he Bank of Fnland s webse: <hp://www.bof.f/sc/bof-pss>.) In he sulaons, we nally assue ha banks would sub half of all ndvdual payens o he queue for deferred seleen and he oher half of her payens o he RTGS syse. In he sulaons, we nclude all Fedwre funds ransfers for a randoly seleced se of en days beween Ocober 1999 and February 2000. We perfor a sensvy analyss (see Secon 5) and presen robusness checks o gauge he effecs resulng fro dfferen levels of parcpaon n he hree deferred seleen arrangeens. Usng hree days of daa, we reproduce he sulaons wh eher 20 percen or 80 percen of all payens assgned o he deferred seleen echans. The sulaons are conduced on hsorcal payen ransacons slar o he generalzed exaple below: Sender Accoun Nuber Recever Accoun Nuber Value Sen (Dollars) Sub Te (Hour:Mnues) Roung Flag 02100xxxx 02100yyyy 100.50 10:20 1 or 0 Table 1 Suary of Sulaed Syses Syse Enry Creron Order Creron Release Creron End-of-Day Close of Queue One-hour neng Sx-hour neng Recep-reacve gross seleen Randoly seleced 50 percen of payen orders. In conducng our sensvy analyss, we randoly seleced eher 20 percen or 50 percen of payens. No applcable Frs-n, frs-ou All payen orders for all banks n queues are need and released a one-hour nervals. All payen orders for all banks n queues are need and released a sx-hour nervals. A payen order a he fron of a bank s queue s released fro queue as receps for he bank, whn a calendar nue, exceed he value of he payen order o be released. All payen orders n queue are need a 6:30 p.., he end of he Fedwre day. Any payen orders reanng n queues a 5:30 p.. are randoly and unforly assgned and seled by real-e gross seleen over he nex hry nues. 54 Econozng on Lqudy
In hs exaple, Bank A (wh Aercan Bankng Assocaon accoun nuber 02100xxxx) sends Bank B (02100yyyy) $100.50 a 10:20 a.. hrough he Fedwre servce. If he roung flag s one, he payen s roued o he deferred seleen echans. If he flag s zero, he payen s roued o he RTGS syse. The roung flag randoly assgns a one or a zero accordng o a predeerned level of parcpaon n he deferred seleen echans (for exaple, 20 percen, 50 percen, or 80 percen of he day s payens have roung flags equal o one). For any gven day, several hundred housand ransacons are roued, one by one n he order of her e saps, o he seleen echans assgned. If roued o RTGS, a payen wll be seled edaely. If roued o he deferred seleen echans, seleen could be delayed. We repor he dealed resuls of hese sulaons n Appendx B. Our prary perforance ercs focus on he syse s pac on daylgh overdrafs and on he delay n he e of payen ha s, he dfference beween he e he payen was subed and he e was seled. 4.1 Daylgh Overdrafs and Delay Indcaors A bank ncurs a daylgh overdraf when s balance falls below $0. The Federal Reserve easures daylgh overdrafs ousandng a he end of each nue of he Fedwre operang day and repors he aggregae peak and average overdrafs for all banks. The aggregae peak overdraf occurs n a specfc nue n whch he aggregae overdraf has he hghes value of all he nues n he Fedwre operang day; he average overdraf s he su of all he banks overdrafs for all nues of he day dvded by he nuber of nues n he Fedwre operang day. We focus on he average overdraf because ha s he basc easure used by he Federal Reserve o calculae he fees charges banks for her cred use, whch s nheren n daylgh overdrafs (see Appendx C for a descrpon). The basc ndcaor of delay ha we consder s he average e of seleen across all payens and banks. I s he average e a whch payens sele where he e of acual seleen s weghed by he value of he payen. The delay sasc s a sandardzed ndcaor ha ay ake values beween zero and one. RTGS, wh s edae seleen, resuls n a zero-delay sasc. End-of-day neng resuls n a delay sasc equal o one. In coparson wh he average e of seleen sasc, he delay sasc ends o wegh ore heavly payens ha are enered early n he day, even f he payens are sall n value. We copare he hree sulaed queue-augened RTGS syses wh Fedwre s hsorcal perforance usng hese lqudy and delay ercs (Table 2). We fnd ha only he recep-reacve gross seleen syse reduces he use of overdraf lqudy by a sascally sgnfcan aoun. Whle he wo neng syses affec he average overdraf, neher of hese dfferences s sascally sgnfcan (see Appendx B). The one-hour neng echans shows no sascally sgnfcan change n he average overdraf relave o RTGS. Payens are delayed he leas under one-hour neng, wh he average e of seleen of payens ovng o 2:51 p.. fro he RTGS average e of 2:35 p.. For sx-hour neng, he decrease n overdrafs s hgher (alhough s no sascally dfferen fro no change), bu so s he delay n payens, as he average payen e oves o 3:46 p.. he laes e of all he alernaves. The recep-reacve gross seleen syse reduces average overdrafs by abou 14 percen he larges aoun aong he alernaves consdered here. The e of payen s 3:18 p.., slghly laer han for he one-hour neng alernave. The average e of seleen ncreases by seveny-one nues for sx-hour neng whle ncreases by fory-hree nues for he recepreacve queung syse a 65 percen dfference whle sxhour neng shows a 150 percen ncrease n he delay sasc when copared wh he recep-reacve syse. Our resuls sugges ha he recep-reacve syse perfors arkedly Table 2 Averages fro Sulaons wh 50 Percen Parcpaon Treaen Average Overdraf Percenage Change fro RTGS Peak Overdraf Percenage Change fro RTGS Average Te of Seleen Delay Sasc (Percen) Real-e gross seleen (RTGS) 20.29 66.28 14:35 0 One-hour neng 20.41 0.58 64.69-2.40 14:51 7.53 Sx-hour neng 19.45-4.10 60.15-9.25 15:46 34.35 Recep-reacve gross seleen 17.52-13.64 72.66 9.62 15:18 13.74 Source: Auhors calculaons, based on daa fro Federal Reserve Bank of New York, Fedwre Funds Servce. FRBNY Econoc Polcy Revew / Deceber 2004 55
beer n selng early-ornng and early-afernoon payens, as well as saller ones. The recep-reacve queung syse s ncrease n peak overdrafs, n conjuncon wh s decrease n average overdrafs, s a b puzzlng (Table 2). Why do peak overdrafs ncrease f payens rean n he queue unl suffcen receps arrve for he bank? The answer s relaed o he curren ng of payens on Fedwre. As descrbed n McAndrews and Rajan (2000), a hgh proporon of he value ransferred over Fedwre occurs n he lae afernoon. Durng ha perod, banks have a large nuber of payen receps, as well as payen ouflows. Under he recep-reacve gross seleen syse, he hgh level of receps ha occurs durng he lae afernoon (fro he 50 percen of payens ha connue o be seled hrough he RTGS syse) begns o rgger he release of a large nuber of queued payens. Tha process cascades Our resuls sugges ha he recepreacve syse perfors arkedly beer n selng early-ornng and early-afernoon payens, as well as saller ones. as he payens released fro he queue are receps for oher banks, whch rggers furher releases fro he queues. For any banks prarly large banks he ouflow fro he queue absorbs all of he bank s receps. Few, f any, of s receps a ha e of day add o s balance; nsead, he receps faclae he release of payens fro queues. The cobnaon of receps beng dedcaed o he release of payens fro he queue and he subsson of any RTGS payens a ha e of day drves any accouns deeply no overdraf. Saller banks, no havng he sae heavy ouflow of payens, enjoy sgnfcanly ore posve balances a ha e, as he cascade of payens occurs. On balance, hs process furher concenraes payen acvy n e, and reduces he use of overdrafs on average, even hough he peak overdraf s ncreased. Of course, we would expec ha banks would aler her behavor f hey expeced such a cascade of payens o be rggered. 5. Sensvy Analyss To es he robusness of our resuls, we exane wo sulaons n whch 20 percen and hen 80 percen of payens are randoly seleced for deferred payen. These sulaons were conduced on hree days of daa. Because an analyss of only hree days yelds such a sall saple, we do no consder sascal sgnfcance, bu sply repor averages. 4 One poenal proble wh a recep-reacve gross seleen syse s ha banks ay ake an excessve nuber of subssons o ha syse and very few o he RTGS syse. If all banks fnd convenen and econocal o sub payens o he queue for deferred seleen, hen a paucy of RTGS payens gh cause wdespread payen delays. 5 By varyng he nuber of payens subed for deferred seleen, we can evaluae how each of he alernave syses would perfor, assung dfferen behavoral paerns (see Table 3 for he resuls of hese sulaons). The nubers for he RTGS syse are calculaed usng only he hree days pernen o he alernae level sulaons and hus dffer fro hose n Table 2. These sulaons sugges ha our resuls are relavely robus a dfferen levels of parcpaon. The level of lqudy savngs and he lengh of delays n seleen ncrease as ore payens are subed o he queues. Of neres s he resul ha he RRGS syse anans coparable or hgher levels of lqudy savngs for a gven delay han does he sx-hour neng syse, a all levels of subsson o he queue. In addon, even wh 80 percen of payens subed o he queue, he RRGS syse poses an average seleen delay ha s no greaer han he delay wh sx-hour neng. However, he poran dfference s ha RRGS does hs wh uch greaer lqudy savngs han sxhour neng does. The delay sasc provdes soe evdence for why hs occurred. The average e akes o sele a payen for he 80 percen recep-reacve syse s one nue ore han he average e for sx-hour neng, suggesng ha he recep-reacve syse holds ore large payens n s queue unl he end of he day. The delay sasc for sx-hour neng s abou 2.5 es hgher han he sasc for he recep-reacve syse, ndcang ha he RRGS queue ouperfors he sx-hour neng syse n overdraf anageen. 56 Econozng on Lqudy
Table 3 Syse Averages Coparng Alernae Levels of Parcpaon Treaen Average Overdraf Percenage Change fro RTGS Peak Overdraf Percenage Change fro RTGS Average Te of Seleen Delay Sasc (Percen) Real-e gross seleen (RTGS) 20.52 68.49 14:32 0 One-hour neng 20 percen 20.37-0.74 67.16-1.93 14:37 2.52 50 percen 20.55 0.12 65.27-4.69 14:47 7.31 80 percen 19.83-3.38 64.66-5.59 14:53 9.93 Sx-hour neng 20 percen 20.53 0.04 64.42-5.94 15:01 13.97 50 percen 19.87-3.16 62.50-8.74 15:45 34.89 80 percen 17.32-15.59 50.77-25.87 16:28 55.44 Recep-reacve gross seleen 20 percen 20.88 1.75 71.47 4.36 14:48 3.35 50 percen 17.38-15.33 70.40 2.80 15:18 14.78 80 percen 11.49-44.05 55.92-12.52 16:29 22.50 Source: Auhors calculaons, based on daa fro Federal Reserve Bank of New York, Fedwre Funds Servce. 5.1 Lqudy To provde ore nsgh no he perforance of hese deferred seleen syses, we need o undersand how he echanss use lqudy hroughou he day. Whle our nal analyss focused on he echanss effecs on overdrafs and delays, we now look a four easures of lqudy, assess her levels n each syse, hen copare he levels wh hose found n he RTGS syse (see Appendx B for furher deals). The average funds ransfer sasc easures he average level of lqudy, or funds, ha us be ransferred fro an ndvdual accoun fro one nue o he nex, across he nues of he day, o coplee he payens for he day. For exaple, n he RTGS syse, he average funds ransfer for an accoun s $226,000 per nue. To ake hs ransfer, he bank us have suffcen funds n s accoun or receve suffcen funds fro oher banks. For any bank n he syse, he average funds ransfer ay ake values beween zero and he per-nue gross value of payens sen by he bank. In general, neng exhbs lower average lqudy usage over he day as ndcaed by he average funds ransfer easure copared wh an RTGS or RRGS syse. Once queued, payens us say n he queue unl he nex ne seleen e and do no cause any balance changes n he ner. Ths lqudy conservaon ncreases wh longer neng es and larger parcpaon n he neng syses (Table 4). If we look a he nue wh he hghes average funds ransfer, we oban he axu funds ransfer. Usng hs ndcaor, we see ha he neng syses deonsrae very hgh lqudy requreens durng her ne seleen perods up o $17 llon. These one-nue axus occur near he end of he day when he Federal Reserve s RTGS syse experences s usual peak n volue. The recepreacve gross seleen syse, however, produces lower The recep-reacve queue acs o sooh he lqudy usage across he payens syse parcpans and across he day. axu lqudy ouflows, deonsrang s ably o sooh he lqudy usage over e. Ths soohng a feaure of he ore dynac recep-reacve queung echans resuls n greaer average lqudy usage han he neng alernaves, bu also produces sgnfcanly saller axu requreens. The lower axu requreens are poran as s generally less cosly for banks o ake sall payens ha are dsrbued hroughou he day han o FRBNY Econoc Polcy Revew / Deceber 2004 57
Table 4 Lqudy, Correlaon, and Skewness Resuls Treaen Average Funds Transfer (Thousands of Dollars) Maxu Funds Transfer (Thousands of Dollars) Correlaon wh RTGS Balances (Percen) Skewness Real-e gross seleen (RTGS) 226 2,206 100.0 One-hour neng 20 percen 209 5,521 99.5 13.9 50 percen 170 10,808 98.0 18.8 80 percen 130 13,901 97.2 23.4 Sx-hour neng 20 percen 201 10,944 96.2 20.3 50 percen 145 12,122 90.5 23.2 80 percen 86 17,356 84.7 19.0 Recep-reacve gross seleen 20 percen 209 1,827 94.8 13.0 50 percen 165 1,975 86.6 26.2 80 percen 140 3,315 76.0 24.2 Source: Auhors calculaons, based on daa fro Federal Reserve Bank of New York, Fedwre Funds Servce. ake large payens. The soohng effec of he RRGS syse s hus a desrable feaure. The correlaon wh he RTGS easure represens he degree of correlaon and hence he exhbed ndependence beween he end-of-nue balances of RTGS and he oher sulaed syses. The one- and sx-hour neng echanss exhb a greaer correlaon beween her balances and he orgnal balances creaed by he RTGS syse, despe he neng syses lower average fgures of lqudy use. The lower correlaon for RRGS ndcaes ha, whle resuls n hgher balance ransfers han he neng syses hroughou he day, hese balances are crculaed ore rapdly, allowng earler seleen of payens and a greaer dvergence n he paern of balances fro he orgnal RTGS balances. The skewness easures he posve dfferences n a bank s balances fro an RTGS syse across he nues of he day. Ths easure s obaned by calculang he skewness of he balance dfferences beween RTGS and he sulaed syse. When copared wh he neng syses, he recep-reacve gross seleen syse s dsrbuon of he dfferences n balances s ore posvely skewed, suggesng ha ore parcpans anan posve balances and hence a reduced need for overdrafs on average. The recep-reacve queue acs o sooh he lqudy usage across he payens syse parcpans and across he day, generang larger balances and saller overdrafs fro he syse s lqudy. 6. End-of-Day Queue Analyss When lookng a he sulaed recep-reacve gross seleen syse, s poran o deerne how he endof-day selng of payens nfluenced our resuls. The RRGS syse closed a 5:30 p.. and he reanng payens were evenly dsbursed over he nex hry nues. Table 5 gves he percenages of all payens subed o he queue ha seled by 5:30 p.. In addon, he able presens he average value of payens n he queue a 5:30 p.. o offer a sense of he role ha sze played n he seleen of hese queued payens. The one-hour neng arrangeen que naurally yelds he bes resuls here because he payens n he queue only sar accuulang fro 4:30 p.. Because hs e of day experences he larges value payens (McAndrews and Rajan 2000), he average payen values are wce as hgh as hose produced by sx-hour neng and RRGS. The sx-hour neng syse shows ha payens enered as early as 12:30 p.. rean n he queue, whch resuls n a low percenage of seled queued payens by 5:30 p.. In ers of overall seleen by 5:30 p.., he RRGS syse perfors slarly o a one-hour neng syse a he 20 percen and 50 percen parcpaon levels and ore lke a sx-hour neng syse a he 80 percen level. Ths resul ndcaes ha when 80 percen of payens are deferred o RRGS, any never ge seled and are reurned o he banks ha sen he. 58 Econozng on Lqudy
Table 5 Queue Characerscs a 5:30 p.. Queued Payens Seled (Percen) Treaen Value Volue Average Payen Value n Queue (Thousands of Dollars) One-hour neng 20 percen 73 91 10,234 50 percen 69 90 10,653 80 percen 73 91 10,063 Sx-hour neng 20 percen 25 41 4,338 50 percen 26 40 4,291 80 percen 25 41 4,310 Recep-reacve gross seleen 20 percen 64 73 4,533 50 percen 72 80 4,890 80 percen 28 48 5,184 Source: Auhors calculaons, based on daa fro Federal Reserve Bank of New York, Fedwre Funds Servce. A feaure of he sulaed RRGS echans s ha he FIFO rule was srcly adhered o when selng queued payens. The FIFO rule resuls n suaons where large payens n fron of he queue block saller payens fro beng seled. The average value of queued payens a 5:30 p.. was consderably hgher for all levels of payens queued. The value of payens reanng n he queue rose as he parcpaon n he queue ncreased. A he 80 percen level, he average value of payens ha reaned queued was 50 percen hgher han he average value of payens n he orgnal RTGS syse ($3.45 llon). Ths resul suggess ha he perforance of RRGS syses could lkely be proved by usng a dfferen order creron, such as allowng saller payens o go frs, splng he large ransacons no several saller ones, or usng grdlock-resoluon echanss. 7. Dscusson of Sulaon Resuls and Lkely Behavoral Responses Neng has long been acknowledged as an effcen way o reduce he lqudy needs of a payens syse. Roberds (1993) shows ha he neng of payens acheves he heorecal nu of lqudy use for he seleen of a specfc se of payens. Anoher way o reduce lqudy needs s o use varous queung arrangeens n RTGS syses. Many sulaon sudes of he behavor of queueaugened RTGS syses have been conduced recenly. The research exanes he echancal reorderng of payens ha s possble wh a queung syse and hen copares hs feaure wh oher alernave desgns o see how each handles lqudy use and payen delays. Koponen and Soraäk (1998) and Lenonen and Soraäk (1999) use he sulaon approach o easure he lqudy savngs and seleen delays for a nuber of alernave queung, neng, and payen-splng echnques wh an RTGS syse usng daa fro he Bank of Fnland s RTGS syse. Boh sudes conclude ha queung syses can conrbue subsanal proveens copared wh pure neng syses. Bech and Soraäk (2001) analyze he effecs of a sulaneous seleen algorh based on FIFO o sele a subse of payens fro queues. A repor on RTGS syses by he Bank for Inernaonal Seleens (1997) dscusses how o sequence payens so ha ncong ransfers fro oher banks can be used o fund payens. A pure RTGS syse reles solely on he parcpans (n a decenralzed way) o e her payens n a anner ha bes ulzes her ncong funds. Our sulaon resuls show ha neng n conjuncon wh RTGS seleen s no very desrable. Neng every sx hours yelds relavely odes bu sascally nsgnfcan reducons n daylgh overdrafs (3.2 percen) copared wh a sgnfcan delay n payen ng (one hour and hreen nues n average seleen e). Copared wh one-hour neng, he seleen delays n sx-hour neng are uch greaer. The sulaed RRGS echans ouperfors he neng syses when boh lqudy savngs and payen delays are aken no accoun. The recep-reacve syse saves sgnfcan lqudy (13.6 percen) and resuls n relavely odes payen delays (fory-hree nues) when copared wh sx-hour neng. These resuls are n lne wh hose of he sudes ced above. 7.1 Bank Parcpaon and Rsk One queson o ask s wheher banks would acually use deferred payen echanss f hey were avalable. Our sulaons canno predc banks behavor. However, by relyng on how he echanss work n a sulaed envronen and applyng heorecal reasonng fro he odels of payen behavor, we can gan nsgh no he lkely endogenous responses o pleenng hese copleens o an RTGS syse. FRBNY Econoc Polcy Revew / Deceber 2004 59
Consder he neng syses, for exaple. The sulaon shows ha a neng syse ha seles payens each hour of he day, even f were o arac 50 percen of he payens on Fedwre, would no creae a sascally dfferen level of daylgh overdrafs. When we consder he parcpaon rsk n a neng syse, s unlkely ha banks would use such a facly. Parcpaon rsk s presen n any neng syses. In he operaon of os payens syses, f a bank eners payens no he syse, he bank s expeced and, n soe cases, oblgaed o sele hose payen orders. If he bank expecs any offseng payens o be enered, bu n fac only a few are, he bank ay face a larger-han-expeced seleen oblgaon. Neng syses end o be ore effecve n gaherng offseng payens as ore banks parcpae. Hence, a sar-up neng syse exposes poenal parcpans o rsk. If any banks parcpae, he bank wll have a sall expeced seleen oblgaon, bu f only few ohers do, he bank ay have a larger-han-expeced seleen oblgaon. If a payens syse were o offer a neng arrangeen n conjuncon wh an RTGS syse, banks ha choose o use he neng echans would face lqudy rsks. Those banks ha use he neng syse ay end he day needng ore lqudy han f hey had carefully anaged her payens srcly hrough an RTGS syse. RTGS syse parcpans lkely sub payens n ways ean o lessen her lqudy deands and rsks endogenously. As a resul, a neng servce gh fal o arac parcpaon when offered n conjuncon wh he curren Fedwre servce. Deferred seleen syses provde a eans o allow parcpans n an RTGS syse o ake soe payens conngen on he subsson of offseng payens by her counerpares. Allowng a parcpan s payen subsson sraegy o be conngen on he payen subssons of ohers reduces he rsk of loss assocaed wh akng payens and he rsk of havng one s counerpares fal o ake expeced offseng payens pror o defaulng. The reducon n ha rsk should lessen he ncenve o delay subng one s payens, a leas n he conngen, deferred seleen payen opon. We expec ha banks would face lower parcpaon rsk n he recep-reacve queung syse. The basc operaon of he queue s useful o a sngle bank n solaon, even f no oher banks use her opons o queue payens. Queung enables he bank o auoacally synchronze ougong payens wh s ncong payens. Ths s an poran advanage n encouragng use of he queue: Banks face no rsk of ncreasng her lqudy deands by usng he queue. They can always do a leas as well for heselves by usng he queue o anage her lqudy deands as hey would f hey had her own nhouse auoac queue anageen syse. How would he banks change he ng of her payens o he syse n he new envronen? Models of he ng of payens n an RTGS odel have been presened by Angeln (1998, 2000), Buckle and Capbell (2002), Kobayakawa (1997), and Kahn, McAndrews, and Roberds (2003). Soe of hese sudes consder he defaul rsk of counerpares and focus on he possbly of payen delays n an RTGS syse, parly because of he rsk of sendng he gross aoun of a payen o a counerpary n advance of recevng an offseng aoun fro ha counerpary. Because payens ade n an RTGS syse are no conngen on he subsson of By usng a recep-reacve queue, banks would no face any downsde rsk o her lqudy poson by he early enry of payen essages n he queue. payens by counerpares, banks could be relucan o sub payens n a ely fashon, and as a resul, he ng of all payens could be delayed (relave o he e ha a cenral planner would choose o have he payens sen). Buckle and Capbell (2002) consder requreens, chosen jonly by he parcpans, ha co parcpans o sub ceran percenages of her payens by ceran es of he day. Such a requreen s n effec n he U.K. payens syse, CHAPS, and, on he European level, gudelnes ssued by he European Bankng Federaon govern he ng of payens n he TARGET syse. Recen heorecal work by Bech and Garra (2003) analyzes he ncenves ha banks have n an RTGS syse n he case n whch here s no defaul rsk aong counerpares o coordnae he ng of payens. In her odel, banks wsh o coplee a se of payens whle econozng on her holdngs of overngh balances. Bech and Garra fnd ha banks are expeced o synchronze he ng of her payen subssons o ake bes advanage of ncong ransfers, whch allows all he banks o econoze on her holdngs of overngh balances. McAndrews and Rajan (2000) presen evdence conssen wh ha odel for he Fedwre syse. The recep-reacve queue echans can be a useful way for a bank o reduce s deand for cosly lqudy. In fac, we would also expec banks o ener ore of her day s acvy earler n he day, wh uch of placed n he queue. We expec hs o be he case because n os RTGS syses oday, 60 Econozng on Lqudy
a bank s only ehod of lqudy anageen s sply o delay payens. In conras, by usng a recep-reacve queue, banks would no face any downsde rsk o her lqudy poson by he early enry of payen essages n he queue because he aoun released fro he queue would always be less han he ncong payen aoun. In he Uned Saes, soe banks use he Clearng House Inerbank Payens Syse, whch has lqudy-savng feaures. The presence of such a syse could serve o sasfy banks deand for an alernave o RTGS. If ha s so, hen appendng lqudy-savng feaures o he exsng RTGS syse ay no lead o a grea deal of use of he lqudy-savng feaures. The prary reason why a recep-reacve syse would generae good ncenves for he early subsson of payens s ha he release of payens fro he queue s ndependen of he ng of a bank s own RTGS payens. Because an RRGS syse does no rely on a bank s balance, bu only a bank s receps o rgger he release of payens, he hsory of a bank s subsson of RTGS payens does no affec he release of s payens fro he queue. As a resul, here s no ncenve o delay akng RTGS payens o allow he release of queued payen essages. Ths suaon resuls n ncenves for earler enry of RTGS payens, whch would endogenously prove he crculaon of lqudy, releasng he queued essages of ohers n a vruous crcle. 6 Soe degree of ransparency of he queues gh also offer banks nforaon ha hey canno gan by usng nernal queues. Wh he use of such feaures, we would end o expec wdespread parcpaon of banks n queung echanss. In hs case, grdlock resoluon whch requres a cenral queue could be used o opze furher he queue s perforance. Fnally, cenralzed queung n general ay be benefcal for saller banks. Whle larger banks currenly e he enry of her payens no RTGS syses wh he ad of nernal queues, he operaon of he recep-reacve queue would gve ore banks he opon of auoaed payen seleen. 8. Concluson In hs arcle, we sulae deferred seleen echanss o undersand he lqudy plcaons of usng he echanss o copleen real-e gross seleen syses. Usng hsorcal daa on all payens ade over en days on he Fedwre Funds Servce, we sulae wo dfferen neng syses and a recep-reacve gross seleen syse. We fnd ha, unlke an RTGS syse, boh neng and RRGS queung syses nroduce delays o payens. However, boh neng and queung also have he poenal o reduce n soe cases, sgnfcanly daylgh overdrafs. These resuls appear o be robus o alernave assupons abou he level a whch banks are wllng o sub payens o a queue for deferred seleen. The recep-reacve gross seleen syse we exane s novel n ha releases payens fro he queue based on a bank s receps over a gven e raher han on s balance. The sulaons n hs arcle ndcae ha an RRGS syse reduces sgnfcanly ore overdrafs han a sx-hour neng syse would, wh consderably less delay n payens. Our consderaon of he recep-reacve gross seleen syse reveals ha ay provde good ncenves for banks o sub payens early o he queung syse, as he release of payens fro he queue s ndependen of he subsson of he bank s own RTGS payens. Ths feaure s lkely o encourage banks o qucken he ng of payens and o reduce he nuber of daylgh overdrafs. As a resul, such a syse gh prove o be a rue lqudy-savng copleen o an RTGS syse. Whle sulaons provde a good sarng pon for sudyng enhanceens o RTGS syses, our resuls sugges ha hese syses warran furher nvesgaon. For exaple, how banks would change her behavor when offered hese alernaves o payen seleen reans an open queson. Gong forward, a beer heorecal and eprcal undersandng of banks payen behavor would help nfor polcyakers consderng enhanceens o RTGS syses. FRBNY Econoc Polcy Revew / Deceber 2004 61
Appendx A: Dealed Dynacs of he Recep-Reacve Gross Seleen Syse In hs appendx, we explan he feaures of our proposed recep-reacve gross seleen desgn. A real-e gross seleen (RTGS) payen fro bank o bank j enered a ' e s p j. Slarly, a queued payen essage s q j ( r), wh denong he e of enry n he queue and r denong he essage s rank n he order of s enry. A bank s funds balance a e s denoed b. A seled payen s s j, where a seled payen s eher an RTGS payen or a queued payen essage ha has been released a e. The basc recep-reacve gross seleen desgn operaes as follows: By he end of nue, he payen essages { q ' j ( r) : j, ' <, r = 1, 2, k} are released fro he queue, where k s he axu rank ha sasfes nequaly A1: (A1) ( ) ( ' ( r) ). A he begnnng of each nue, he rank of queued payens s rese so ha he oldes queued payen s assgned rank one, he second-oldes, rank wo, and so on. (The acual algorh releases payens whn he nue as soon as suffcen receps arrve.) Inequaly A1 saes ha he frs k queued payen essages of he bank are released n nue when he value of he bank s receps n ha sae nue are greaer han or equal o he value of he k payen essages o be released. A bank s balance a he end of nue wll hen be equal o: (A2) ( 1) < b = 1 b j 1 ( 1) < j s j k r = 1 j q j ( p ) + j ( 1) < j s j ( ) k r= 1 j ( q' j ( r) ). Equaon A2 saes ha a bank begns a nue wh s balance of he prevous nue, and s balance decreases n he nue by any RTGS payens akes and ncreases by he ne aoun of s receps, less any release of payens fro s queue. By nequaly A1, he ne aoun of s receps us be a leas as large as he aoun ha s released fro he queue. If a bank s queued payens were nuerous and fnely dvsble so ha he receps are approxaely equal o he aoun released fro he queue hen he bank s balance would be approxaely equal o s prevous balance nus s 1 ougong RTGS payens: b b ( ). ( 1) < j In a heorecal l o he use of hs queung syse, banks could place n he queue all payens whose value hey expec o be offse by ncong payens. Banks real-e payens would equal he aoun of ne payen ouflows ha hey would expec durng he day equvalen o he ullaeral ne deb of a ne seleen syse. If expecaons were fully realzed and banks held suffcen balances o fund her payens, he aoun of balances held would equal he aoun of seleen payens ha he banks would need f hey seled payens n a ullaeral ne seleen syse. A he sae e, banks would have he advanages of real-e release of payens and he assocaed release of payens fro he queue hroughou he day. Ths s he essenal heorecal benef of hs desgn. No praccal pleenaon of hs syse s lkely o acheve he heorecal axu n lqudy savngs. In fac, he praccal pleenaon of hs queung syse s an poran aspec of he echans. One poran eleen s ha he recep-reacve syse reles on soe funds flowng aong parcpans o rgger he release of queued payen essages. If all banks were o queue all her payens, all payens would rean queued. In such a case, he syse operaor could consder usng a grdlock-resoluon echans o break he logja and release soe payens fro he queue, as n Bech and Soraäk (2001, 2002). p j 62 Econozng on Lqudy
Appendx B: Sulaon Resuls and Analyss To gauge he effecs of soe of he lqudy enhanceens descrbed n our arcle, we esed varous feaures of hese possble enhanceens usng a sulaon progra developed by he Bank of Fnland. The sulaon progra s a verson of he one descrbed n Lenonen and Soraäk (1999) and Koponen and Soraäk (1998). (A ore n-deph descrpon can be found a he Bank of Fnland s webse: <hp:// www.bof.f/sc/bof-pss>.) The sulaons frs generaed baselne oupu daa for boh real-e gross seleen (RTGS) and ne seleen syses. Furher sulaons exaned an alernave enhanceen ha releases gross payens agans he aggregae aoun of ncong funds whn each nue recep-reacve gross seleen (RRGS). We randoly seleced 20 percen, 50 percen, or 80 percen of all Fedwre Funds Servce payens and placed hose payens eher no a queue for deferred seleen or no a neng syse. Those payens no enered no he queue or neng syse were seled by he RTGS syse. Wh he excepon of he changes n seleen e posed by he queung or neng arrangeens, we assued no behavoral changes n Fedwre ha would affec he ng of payen enry. The bulk of our analyss was perfored wh en days of daa, drecng 50 percen of payens o he deferred seleen echanss. The 20 percen and 80 percen sulaons esed he nework effec assocaed wh varyng degrees of parcpaon n hese queung and neng arrangeens. The 80 percen sulaons were parcularly e consung, so he 20 percen and 80 percen sensvy analyses were perfored on only hree days of daa. Because hese sulaons focus on reducng boh he Federal Reserve s rsk exposure n granng nraday cred and he lqudy use by banks, we seleced sascs ha assess hese areas. The analyss nvolves average and peak overdrafs and seleen delays. Daa The sulaons were perfored usng en ypcal days of funds ransfer acvy daa fro he Fedwre Funds Servce (Table B1). The days were randoly seleced fro he perod Ocober 1999 hrough February 2000. We ncluded all ransacon ypes bu elnaed payen ransfers of less han $100. The ransacon daa only ncluded aser accouns. Subordnae accoun nubers were changed o her relaed aser accoun nubers before sulaon. A unfor rando-nuber generaor was used o selec he 50 percen of payens o be queued n each reaen. The res of he payens were auoacally processed by he RTGS syse accordng o her hsorcal ng durng he sulaons. Whle no drecly nvolved n he sulaons, Naonal Book-Enry Syse (NBES) secures ransacon daa were used for he overdraf analyss presened laer. Table B1 Suary Sascs for Fedwre Funds Daa Dae Nuber of Payens Su of Payens Nuber of Banks Average Value (Mllons of Dollars) Sandard Devaon of Payen Value (Mllons of Dollars) Su of Openng Balances 1/6/2000 369,094 1,181.34 6,289 3.20 28.66 10.03 1/26/2000 373,685 1,318.44 6,191 3.53 31.84 15.61 2/23/2000 406,644 1,421.39 6,339 3.50 31.47 16.90 2/24/2000 404,356 1,470.65 6,293 3.64 32.55 16.42 10/1/1999 541,075 1,840.46 6,767 3.40 32.85 21.50 10/8/1999 406,628 1,377.19 6,400 3.39 31.23 12.76 11/4/1999 373,811 1,329.56 6,228 3.56 32.23 15.38 11/10/1999 395,304 1,354.38 6,159 3.43 31.42 10.87 12/6/1999 400,689 1,394.28 6,234 3.48 30.95 10.88 12/16/1999 413,024 1,383.84 6,295 3.35 30.53 12.71 Source: Auhors calculaons, based on daa fro Federal Reserve Bank of New York, Fedwre Funds Servce. FRBNY Econoc Polcy Revew / Deceber 2004 63
Appendx B: Sulaon Resuls and Analyss (Connued) Analycal Fraework In he followng dscusson, le represen a seleen of a payen order a e fro o j. The balance a he end of any nue,, s equal o he prevous balance plus he dfference beween he cuulave value of ougong and ncong payens: = 12,,, D. (B1) = ( s j ) + ( s j ), b 1 b where = 12,,, M. Overdrafs ( 1) < Overdraf calculaons are based on end-of-nue balances. For overdraf accounng purposes, a bank s balance s affeced by several servces. We aep o exrac he Fedwre Funds Servce s conrbuon o he bank s balance, and hence s overdraf, fro he bank s oher non-fedwre funds ransacons usng a ehod ha cs he Federal Reserve s overdraf accounng procedures. 7 Ths nvolves a coparson of he Fedwre funds and NBES balances o deerne he applcable balance, b, appled n he followng forulas. The analyss assues ha sae-day NBES and non-fedwre funds acves rean unchanged (see Appendx C for furher elaboraon). Governen-sponsored enerprses, he Clearng House Inerbank Payens Syse, Federal Reserve Syse banks, and governen agency accouns were ncluded n he sulaons, bu reoved pror o analyss. The overdraf durng he day for any nue,, and bank,, equals he absolue value of a negave balance or zero. (B2) OD = n( 0, b ). The average connuous overdraf s (B3) Average OD = ---------------------------, 1081, ha s, he su of overdrafs for each bank durng he day dvded by he nuber of nues Fedwre s open (egheen hours and one nue). 8 Peak overdraf s (B4) Peak OD ax = 0, OD. s j j ( 1) < j OD Delay and Te Sascs The seleen delay for each payen s calculaed as he e dfference beween payen orgnaon by he sendng bank and he fnal and rrevocable seleen of he payen. The wo sascs ha we use o easure he delay posed by he queung and neng arrangeens n our proposed desgn are he delay sasc and he average e of seleen. The delay sasc for he syse s calculaed as: jj,, ( ' ) s ' j (B5) Delay = --------------------------------------------------. ', ( T ' ) j, j In he noaon for he delay sasc, we capure, for each seled payen, boh s enry e, denoed by ', and s release e, denoed by. The delay sasc easures n he nueraor he value of he seled payens ulpled by he e hey spen delayed n he queue. In he denonaor, he value of seled payens s ulpled by he e ha payens could have been queued, had her seleen been delayed unl he queue s closed. The delay sasc s a sandardzed ndcaor ha ay ake values beween zero and one. In an RTGS syse, for exaple, payens spend no e n he queue, and '=, resulng n a delay sasc equal o zero. In an end-of-day neng syse, he seleen of payens s delayed unl end of day, and =T, resulng n a delay sasc equal o one. The delay sasc places greaer ephass han he average e of seleen on he seleen of boh early-ornng and early-afernoon payens, as well as on saller payens. Early-ornng or early-afernoon payens carry ore wegh han her nonal value because he delay sasc repeaedly couns hese payens for every nue ha hey rean unseled. The average e of seleen (ATOS) s he average e weghed by he value of he payens seled a each nue,. s j j (B6) ATOS = -----------------------------------------. These sascs are calculaed for all applcable reaens. In addon, we ran a sascal es on he average connuous overdraf sasc o provde added confraon of a T s j = 0 s j j 64 Econozng on Lqudy
Appendx B: Sulaon Resuls and Analyss (Connued) scenaro s overdraf savngs or loss. Because he sae payen daa are used for each sulaon reaen, he sascs for each reaen can be vewed as dfferen varables of he sae group. Furherore, he sall, en-day saple sze and unequal varances across reaens sugges ha a sandard paraerc sascal analyss s napproprae. Therefore, we use he nonparaerc Wlcoxon ached-pars sgned-rank es o deerne wheher a sascal dfference n average connuous overdraf exss beween he dependen groups or reaens. All reaens are copared wh he baselne perforance of he RTGS syse. When a reaen shows a nonal ncrease or decrease n average connuous overdraf when copared wh each of hese wo reaens, we conduc a one-sded es o deerne wheher a sascally sgnfcan ncrease or decrease can be found versus he null hypohess ha here s no sascal dfference. All ess were conduced a he 5 percen level. sulaons. The sensvy analyss average and sensvy analyss sandard devaon fgures represen aggregae sascs calculaed usng he hree days n our 20 percen and 80 percen sensvy analyss sulaons: January 6, 2000; January 26, 2000; and Noveber 4, 1999. Real-Te Gross Seleen The RTGS sulaon provdes a benchark for he analyss of he alernave queung and neng arrangeens (Table B2). In hs sulaon, 100 percen of he payens are seled edaely by he RTGS syse. The delay sasc for RTGS s zero by defnon and he average e of seleen equals he e when an average dollar was subed o he syse. One-Hour Ne Seleen Treaens and Resuls To properly copare aggregae sascs fro he sensvy analyss wh he 50 percen sulaons, we added wo lnes for he RTGS sulaon resuls, as well as for all 50 percen Ne seleen of queued payens occurred every hour, and he ne aouns were seled edaely hereafer hrough he RTGS syse (Table B3). Accouns had unled lqudy avalable. A 18:30, reanng queued ransfers were need and he ne balances were ransferred beween banks. Table B2 Real-Te Gross Seleen Sulaons Dae Average Overdraf Peak Overdraf Te of Peak Overdraf Average Te of Seleen Delay Sasc (Percen) 1/6/2000 19.87 65.54 15:31 14:28 0 1/26/2000 20.57 70.73 15:49 14:32 0 2/23/2000 19.51 68.60 15:54 14:31 0 2/24/2000 21.01 67.58 15:55 14:41 0 10/1/1999 20.22 67.58 14:23 14:39 0 10/8/1999 19.69 59.68 14:01 14:39 0 11/4/1999 21.14 69.20 14:38 14:37 0 11/10/1999 22.91 75.58 15:54 14:35 0 12/6/1999 19.67 59.10 15:47 14:43 0 12/16/1999 18.28 59.20 15:53 14:33 0 Average 20.29 66.28 15:22 14:35 0 Sandard devaon 1.23 5.47 0:44 0:04 0 Average for hree days 20.52 68.49 15:19 14:32 0 Sandard devaon for hree days 0.64 2.67 0:36 0:04 0 Source: Auhors calculaons, based on daa fro Federal Reserve Bank of New York, Fedwre Funds Servce. Noe: The fgures for he average for hree days and he sandard devaon for hree days are calculaed for he days for whch he sensvy analyss sulaons were conduced. FRBNY Econoc Polcy Revew / Deceber 2004 65
Appendx B: Sulaon Resuls and Analyss (Connued) One-hour ne seleen acually ncreases he average overdraf by 0.6 percen, alhough he dfference s no sascally dfferen fro he RTGS overdraf. One-hour ne seleen, lke sx-hour ne seleen, lowers he peak overdraf slghly whle generang a 7.5 percenage pon addon n he delay ndcaor. As expeced, he average e of seleen s delayed by weny-one nues when copared wh he RTGS average e of seleen a logcal resul of delayng 50 percen of he payens for up o an hour. Sx-Hour Ne Seleen Ne seleen of queued payens occurred every sx hours (6:30, 12:30, and 18:30), and he ne aouns were seled edaely hereafer hrough he RTGS syse (Table B4). Accouns had unled lqudy avalable. A 18:30, reanng queued ransfers were need and he ne balances were ransferred beween banks. The average and sandard devaon fgures represen hose sascs for he hree days Table B3 One-Hour Ne Seleen Sulaons wh Alernae Levels of Parcpaon Dae Average Overdraf Percenage Change fro Real-Te Gross Seleen Peak Overdraf Percenage Change fro Real-Te Gross Seleen Te of Peak Overdraf Average Te of Seleen Delay Sasc (Percen) 20 percen 1/6/2000 19.86 0.0 63.78-2.7 15:31 14:33 2.49 1/26/2000 20.24-1.6 70.62-0.2 14:55 14:36 2.26 11/4/1999 21.01-0.6 67.09-3.0 14:38 14:43 2.82 Average 20.37-0.7 67.16-1.9 15:01 14:37 2.52 Sandard devaon 0.58 0.8 3.42 1.6 00:27 0:04 0.28 50 percen 1/6/2000 20.02 0.8 59.08-9.9 15:31 14:43 7.24 1/26/2000 20.36-1.0 68.94-2.5 14:53 14:46 6.86 2/23/2000 19.48-0.2 66.53-3.0 15:54 14:46 7.03 2/24/2000 21.36 1.6 68.30 1.1 16:10 14:55 7.38 10/1/1999 20.27 0.2 64.18-5.0 15:10 14:54 7.72 10/8/1999 19.96 1.4 59.80 0.2 14:01 14:54 7.72 11/4/1999 21.27 0.6 67.80-2.0 15:23 14:52 7.84 11/10/1999 23.49 2.5 76.83 1.6 16:31 14:50 7.54 12/6/1999 19.65-0.1 57.01-3.5 16:07 14:58 8.00 12/16/1999 18.21-0.4 58.43-1.3 16:22 14:49 7.97 Average 20.41 0.6 64.69-2.4 15:36 14:51 7.53 Sandard devaon 1.41 1.1 6.19 3.3 0:46 0:04 0.39 Average for hree days 20.55 0.1 65.27-4.7 15:15 14:47 7.31 Sandard devaon for hree days 0.64 1.0 5.39 4.4 0:20 0:04 0.49 80 percen 1/6/2000 19.06-4.1 56.36-14.0 15:31 14:49 9.94 1/26/2000 19.77-3.9 69.67-1.5 15:49 14:51 9.31 11/4/1999 20.66-2.3 67.93-1.8 15:31 14:59 10.55 Average 19.83-3.4 64.66-5.6 15:37 14:53 9.93 Sandard devaon 0.80 1.0 7.24 7.1 00:10 0:05 0.62 Source: Auhors calculaons, based on daa fro Federal Reserve Bank of New York, Fedwre Funds Servce. Noe: The fgures for he average for hree days and he sandard devaon for hree days are calculaed for he days for whch he sensvy analyss sulaons were conduced. 66 Econozng on Lqudy
Appendx B: Sulaon Resuls and Analyss (Connued) nvolved n our 20 percen and 80 percen sulaons: January 6, 2000; January 26, 2000; and Noveber 4, 1999. Sx-hour ne seleen produced a odes 3.2 percen reducon n average overdraf, alhough, once agan, he dfference s no sascally sgnfcan. However, hs reaen produced he lowes overall peak overdraf. The 35 percen delay sasc s roughly fve es ha of one-hour ne seleen and, as we wll see, s nearly hree es ha of RRGS. The average e of seleen was one hour and hreen nues laer han n RTGS. Recep-Reacve Gross Seleen The gross aoun of payens receved durng each nue provded he avalable lqudy for release fro he queue (Table B5). The payens subjec o deferral were held n he queue f hey were no offse by ncong payens n ha nue. The avalable lqudy fro ncong payens reses o zero a he sar of a new nue and does no accuulae pas ha nue. Payens seled on a frs n, frs ou (FIFO) bass when a bank receved suffcen ncong funds. Queued Table B4 Sx-Hour Ne Seleen Sulaons wh Alernae Levels of Parcpaon Dae Average Overdraf Percenage Change fro Real-Te Gross Seleen Peak Overdraf Percenage Change fro Real-Te Gross Seleen Te of Peak Overdraf Average Te of Seleen Delay Sasc (Percen) 20 percen 1/6/2000 20.53 3.4 63.55-3.0 15:31 14:56 13.30 1/26/2000 19.63-4.6 65.27-7.7 14:55 15:01 14.04 11/4/1999 21.43 1.4 64.44-6.9 14:38 15:07 14.59 Average 20.53 0.0 64.42-5.9 15:01 15:01 13.97 Sandard devaon 0.90 4.1 0.86 2.5 00:27 0:05 0.65 50 percen 1/6/2000 20.47 3.0 69.99 6.8 15:39 15:42 34.56 1/26/2000 19.27-6.3 60.67-14.2 14:53 15:44 34.70 2/23/2000 19.58 0.4 65.72-4.2 15:54 15:42 33.56 2/24/2000 18.83-10.4 58.67-13.2 16:45 15:48 33.64 10/1/1999 17.83-11.8 59.59-11.8 14:25 15:45 32.83 10/8/1999 20.14 2.3 56.63-5.1 16:14 15:51 35.88 11/4/1999 19.88-5.9 56.85-17.8 16:36 15:49 35.41 11/10/1999 22.92 0.1 70.41-6.9 16:31 15:45 34.00 12/6/1999 19.43-1.2 55.01-6.9 16:06 15:51 34.56 12/16/1999 16.19-11.5 47.92-19.1 15:53 15:44 34.38 Average 19.45-4.1 60.15-9.3 15:53 15:46 34.35 Sandard devaon 1.75 5.8 6.95 7.7 0:44 0:03 0.90 Average for hree days 19.87-3.2 62.50-8.7 15:42 15:45 34.89 Sandard devaon for hree days 0.60 5.3 6.76 13.3 0:51 0:03 0.46 80 percen 1/6/2000 18.15-8.7 51.37-21.6 14:23 16:25 54.70 1/26/2000 16.20-21.2 50.26-28.9 15:57 16:29 55.94 11/4/1999 17.62-16.6 50.67-26.8 16:06 16:31 55.67 Average 17.32-15.6 50.77-25.9 15:29 16:28 55.44 Sandard devaon 1.01 6.4 0.56 3.8 00:57 0:03 0.65 Source: Auhors calculaons, based on daa fro Federal Reserve Bank of New York, Fedwre Funds Servce. Noe: The fgures for he average for hree days and he sandard devaon for hree days are calculaed for he days for whch he sensvy analyss sulaons were conduced. FRBNY Econoc Polcy Revew / Deceber 2004 67
Appendx B: Sulaon Resuls and Analyss (Connued) payen essages were ransferred o RTGS for seleen. The nondeferred payens were seled edaely by he RTGS syse and dd no affec he ncong funds accounng. Sarng a 17:30, he reanng queued payens were spread evenly over he nex hry nues and seled by he RTGS syse. In su, recep-reacve gross seleen offers a sgnfcan overdraf reducon coupled wh an ncrease n he peak overdraf. The RRGS produced sascally sgnfcan lower average connuous overdrafs han dd he RTGS reaen. Indcaors of Lqudy Use Overdraf calculaons use only he negave balances and herefore easure only he lower end dsrbuon of balances accordng o a cuoff pon of zero. Whle hs s useful fro a rsk anageen sandpon, we calculae furher sascs regardng he perforance of hese syses by analyzng he n ers of her lqudy usage. Each sulaon resrucures he ng of he orgnal RTGS payens by changng he release sequence of he payens. By dong so, he dfferen Table B5 Recep-Reacve Gross Seleen Sulaons wh Alernae Levels of Parcpaon Dae Average Overdraf Percenage Change fro Real-Te Gross Seleen Peak Overdraf Percenage Change fro Real-Te Gross Seleen Te of Peak Overdraf Average Te of Seleen Delay Sasc (Percen) 20 percen 1/6/2000 21.41 7.8 76.52 16.8 15:45 14:44 3.51 1/26/2000 20.20-1.8 67.91-4.0 14:55 14:46 3.01 11/4/1999 21.04-0.5 69.98 1.1 15:24 14:55 3.53 Average 20.88 1.7 71.47 4.4 15:21 14:48 3.35 Sandard devaon 0.62 5.2 4.49 10.8 00:25 0:05 0.30 50 percen 1/6/2000 19.18-3.4 78.12 19.2 16:52 15:19 15.61 1/26/2000 15.06-26.8 60.52-14.4 16:48 15:13 12.32 2/23/2000 15.90-18.5 68.51-0.1 16:38 15:15 13.38 2/24/2000 17.24-18.0 70.92 4.9 16:53 15:18 12.81 10/1/1999 14.18-29.9 64.44-4.6 16:48 15:22 14.06 10/8/1999 19.05-3.2 76.50 28.2 16:46 15:22 14.78 11/4/1999 17.89-15.4 72.58 4.9 16:51 15:24 16.42 11/10/1999 21.97-4.1 89.96 19.0 16:23 15:17 13.56 12/6/1999 20.82 5.8 78.78 33.3 16:50 15:18 11.03 12/16/1999 13.89-24.0 66.23 11.9 16:55 15:14 13.42 Average 17.52-13.6 72.66 9.6 16:46 15:18 13.74 Sandard devaon 2.77 11.9 8.55 14.9 0:09 0:03 1.58 Average for hree days 17.38-15.3 70.40 2.8 16:50 15:18 14.78 Sandard devaon for hree days 2.11 11.7 9.00 16.9 0:02 0:05 2.17 80 percen 1/6/2000 12.59-36.7 67.76 3.4 17:12 16:29 19.02 1/26/2000 8.61-58.1 45.93-35.1 17:05 16:29 23.11 11/4/1999 13.28-37.2 66.07-4.5 17:02 16:29 25.35 Average 11.49-44.0 59.92-12.5 17:06 16:29 22.50 Sandard devaon 2.52 12.3 12.15 20.3 00:05 0:00 3.21 Source: Auhors calculaons, based on daa fro Federal Reserve Bank of New York, Fedwre Funds Servce. Noe: The fgures for he average for hree days and he sandard devaon for hree days are calculaed for he days for whch he sensvy analyss sulaons were conduced. 68 Econozng on Lqudy
Appendx B: Sulaon Resuls and Analyss (Connued) syses generae dfferen lqudy levels and balance dsrbuons han he orgnal RTGS syse. When evaluang he dfferen sulaons eporal resrucurng of he orgnal RTGS payens, he approaches presened here aep o ndcae effcency of lqudy use boh above and below zero, provdng a beer overall vew of each sulaon s effec on lqudy usage. We do hs ndrecly by easurng boh he degree of dfference n he sulaon balances when copared wh RTGS balances and he drecon of ha dfference. Our frs lqudy calculaon easures he average absolue change n balances ha occurs per nue for each bank. In effec, hs calculaon gves he aoun of oney ha an average bank would have o ove, eher n or ou of s accoun, for any gven nue of he day. A lqudy-usage easure calculaes he exen o whch he balance us flucuae n order o sele he payens. An RTGS syse requres he os lqudy. To easure lqudy, we frs calculaed he absolue value of a bank s change n balance fro one nue o he nex and sued hs aoun across all banks for a gven nue. We dd hs for all 1,080 dfference perods, sued he resuls, and dvded by 1080, N, wh N beng he nuber of banks. The b used n he lqudy equaons s he su of each bank s end-of-nue balance across he hree days subjec o he alernave levels of payen subsson sulaons. Average funds ransfer = ----------------------- 1, 081 N 1. 1, 080 N b 1 1 b ( b b ) < 0 = 2 = 1 Our second easure s he axu funds ransfer across he nues: Maxu funds ransfer = N ax b 1 b = 1 b 1 b ( ) < 0. Our hrd easure of lqudy use n he syses s an ndrec one. We calculaed he degree of dfference n he balances by easurng he ndependence exhbed beween he end-of-nue balances of RTGS and he sulaed syse. Our ndependence calculaon produced Pearson correlaon coeffcens for each nue and sued he across he 1,081 nues of he Fedwre day. We hen dvded by 1,081 o ge he average per nue. For RTGS, he correlaon of s end-of-nue balances wh self s one. For he sulaed syses, hs nuber s he correlaon beween end-of-nue balances n he sulaed syse and hose n he RTGS syse. Lower nubers deonsrae ore ndependence fro he orgnal RTGS payen dsrbuon. The b SIM, and b RTGS,, respecvely, represen he collecon of he pernen sulaed balances and he RTGS balances n nue. The balances ncluded n hs collecon are he su of each bank s end-ofnue balance across he hree days subjec o he alernave levels of payen subsson sulaons. 1, 081 Correlaon wh RTGS = ------------- 1. 1, 081 corr b ( SIM, b RTGS, ) = 1 Our fourh easure, he skewness of he dfference n balances, gauges he degree of posve change n balances posed by he sulaed syse on he orgnal RTGS payens. The dfference n balances beween he sulaed syse and RTGS s calculaed for each bank and nue. A skewness sasc s generaed for each nue and he average for he day s hen calculaed. The b SIM, and b RTGS,, respecvely, represen he su of each bank s sulaed and RTGS end-of-nue balances across he hree days subjec o he alernave levels of payen subsson sulaons. 1, 081 Skewness = ------------- 1. 1, 081 skewness b ( SIM, b RTGS, ) = 1 FRBNY Econoc Polcy Revew / Deceber 2004 69
Appendx C: Funds Overdraf Accounng Procedure An explanaon of daylgh overdrafs can be found n Colean (2002). When deernng a bank s balance, he Federal Reserve s Daylgh Overdraf Reporng and Prcng Syse (DORPS) accouns for several funds creds and debs ha we could no observe. These funds are no processed on he Fedwre Funds Servce and are posed o he DORPS syse hrough oher eans. We call hese posngs exraneous funds and nclude such funds prarly fro checks, he Auoaed Clearng House nework, reurn checks, currency and cons, savngs bonds, and accoun defcency creds and debs. Exraneous funds play a ajor role n a bank s balance anageen. To crcuven hs proble, we had o eploy he followng ehod: We had access o he followng nforaon: he DORPS oal end-of-nue balances, Naonal Book-Enry Syse (NBES) ransacon daa, and Fedwre funds daa. Snce he DORPS balance daa conan he openng balance for Fedwre funds and he NBES has an openng balance of zero, end-ofnue balances were consruced fro he ransacon daa. The followng forulas descrbe he end-of-nue balance suaon for each bank a a parcular nue : (C1) Toalbal = NBESbal + FedwreFundsbal + XFundsbal. The exraneous funds balance was exraced accordng o he followng forula: The RTGS exraneous funds and NBES balances were hen held consan. The Bank of Fnland sulaor used he openng balance o creae new Fedwre funds balances, FedwreFundsbal *. The Fedwre funds balance was hen consruced usng he RTGS exraneous funds balance: (C3) Fundsbal = NBESbal + Fundsbal *. The new funds balance, n conjuncon wh he RTGS bookenry secures balance, resuled n a new oal balance: (C4) Toalbal * = NBESbal + Fundsbal. We hen copared he hree coponens n equaon C4 o deerne each bank s applcable funds overdraf, FundsOD, accordng o he followng DORPS accounng prncples: If Fundsbal 0, hen FundsOD = 0. If Fundsbal < 0 and NBESbal < 0, hen FundsOD = Fundsbal. If Fundsbal < 0 and NBESbal 0 : If Toalbal * 0, hen FundsOD = Toalbal *. Oherwse, FundsOD = 0. FundsOD = OD n Appendx B for each bank. (C2) XFundsbal = Toalbal NBESbal FedwreFundsbal. 70 Econozng on Lqudy
Endnoes 1. On average, overngh deposs ade by coercal banks are worh abou $15 bllon. 2. See McAndrews and Trundle (2001) for a descrpon of several new desgns ha have been pu no use n varous large payen syses and for a dscusson of soe specfc polcy ssues ha are assocaed wh he novel desgns. 3. We choose one calendar nue as our e perod because banks daylgh overdrafs are calculaed as of he end of each calendar nue. By choosng a one-nue perod whn whch receps can be se agans he release of payens fro he queue, we preven he release of hose payens fro causng an overdraf a he end of he nue. 4. A sngle day s sulaon for he recep-reacve syse wh 80 percen of payens placed n he queue requred ore han wo onhs o coplee, usng he sngle copuer we eployed for he sulaons. 5. In such a case, a grdlock-resoluon ehod of selng payens fro queues gh be useful. See Bech and Soraäk (2001) for a dscusson. 6. These and oher behavoral responses of queung syses are dscussed n McAndrews and Trundle (2001) and Roberds (1999). 7. These are acves unrelaed o he daly Fedwre Funds Servce and hey are posed o he Daylgh Overdraf Reporng and Prcng Syse a parcular es. These nclude he Auoaed Clearng House nework, checks, currency and cons, and savngs bonds. 8. Effecve May 16, 2004, he Federal Reserve Banks expanded he operang hours of he Fedwre Funds Servce fro egheen hours o weny-one-and-a-half hours. The new hours begn a 9:00 p.. Easern Te (ET) on he precedng calendar day (wh a cycle dae of he followng calendar day) and end a 6:30 p.. ET, regardless of he Bank s locaon or e zone. FRBNY Econoc Polcy Revew / Deceber 2004 71
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