The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Financial Fragility and the Exchange Rate Regime Roberto Chang and Andres Velasco Federal Reserve Bank of Atlanta Working Paper 97-16 November 1997 Abstract: We study financial fragility, exchange rate crises, and monetary policy in an open economy version of a Diamond-Dybvig model. The banking system, the exchange rate regime, and central bank credit policy are seen as parts of a mechanism intended to maximize social welfare; if the mechanism fails, banking crises and speculative attacks become possible. We compare currency boards, fixed rates, and flexible rates with and without a lender of last resort. A currency board cannot implement a socially optimal allocation; in addition, bank runs are possible under a currency board. A fixed exchange rate system may implement the social optimum but is more prone to bank runs and exchange rate crises than a currency board. A flexible rate system implements the social optimum and eliminates runs, provided the exchange rate and central bank lending policies are appropriately designed. JEL classification: F3, E5, G2 Key words: exchange rates, financial crises, central bank policy The views expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors’ responsibility. Please address questions regarding content to Roberto Chang, Research Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, NW, Atlanta, Georgia 30303-2713, 404/521-8057, roberto.chang@atl.frb.org, or Andres Velasco, Department of Economics, New York University, 269 Mercer Street, New York, New York 10003, 212/998-8958, velasco@fasecon.econ.nyu.edu. Questions regarding subscriptions to the Federal Reserve Bank of Atlanta working paper series should be addressed to the Public Affairs Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, NW, Atlanta, Georgia 30303-2713, 404/521-8020. The full text of this paper may be downloaded (in PDF format) from the Atlanta Fed’s World-Wide Web site at http://www.frbatlanta.org/publica/work_papers/. Ilqdqfldo Iudjlolw| dqg wkh H{fkdqjh Udwh Uhjlph Urehuwr Fkdqj Dqguhv Yhodvfr Rfwrehu 4<<: 41 Lqwurgxfwlrq Wkh 4<<7 Ph{lfdq fulvlv dqg wkh 4<<: Wkdl fulvlv duh wkh odwhvw h{dpsohv ri dq djh0 rog suhglfdphqw= zhdn qdqfldo v|vwhpv hdvlo| xqghuplqh {hg h{fkdqjh udwhv1 Iudjloh edqnv suhyhqw wkh prqhwdu| dxwkrulw| iurp xvlqj wljkw prqh| dqg kljk lqwhuhvw udwhv wr ghihqg wkh shj> edqn uxqv pd| lpso| d vkliw rxw ri grphvwlf prqh| dqg wrzdug iruhljq dvvhwv> edqnuxsw edqnv pd| uhtxluh prqh|0qdqfhg edlorxwv1 Lq doo fdvhv/ wkh qhw hhfw lv uhvhuyh hurvlrq dqg d olnho| froodsvh ri wkh {hg h{fkdqjh udwh1 Vxfk olqnv duh eruqh rxw e| pruh wkdq dqhfgrwdo hylghqfh iurp Ph{lfr dqg Wkdlodqg1 Lq wkhlu dqdo|vlv ri d odujh qxpehu ri edqnlqj dqg fxuuhqf| fulvhv/ Ndplqvn| dqg Uhlqkduw ^6` qg wkdw wkh rffxuuhqfh ri wkh iruphu khosv suhglfw wkh hphujhqfh ri wkh odwwhu1 Lq d vlplodu yhlq/ Vdfkv/ Wruqhoo dqg Yhodvfr ^<` qg wkdw d zhdn edqnlqj v|vwhp +sur{lhg e| d suhylrxv ohqglqj errp, lv wkh ehvw suhglfwru ri zkhwkhu d frxqwu| zdv klw e| wkh Whtxlod hhfw lq hduo| 4<<81 Wkhvh srolf| h{shulhqfhv kdyh jlyhq qhz xujhqf| wr wkh txhvwlrq ri zkdw h{0 fkdqjh udwh duudqjhphqwv khos olplw wkh gdqjhuv dvvrfldwhg zlwk qdqfldo iudjlolw|1 Li {hg h{fkdqjh udwh v|vwhpv duh yxoqhudeoh/ grhv dgrswlqj d fxuuhqf| erdug khosB Ru vkrxog frxqwulhv pryh lq wkh rwkhu gluhfwlrq dqg dgrsw h{leoh udwhvB Lqghhg/ qdqfldo frqvlghudwlrqv fdq kdyh vxfk zhljkw wkdw Fdoyr ^4` kdv dujxhg wkdw zh qhhg d qhz wkhru| ri h{fkdqjh udwh uhjlph fkrlfh edvhg rq qdqfldo vwuxf0 wxuh udwkhu wkdq/ dv lv frqyhqwlrqdo/ wkh ghjuhh ri sulfh uljlglw| ru wkh vrxufh ri vwrfkdvwlf vkrfnv1 Ixuwkhupruh/ iru d jlyhq h{fkdqjh udwh uhjlph/ zkdw duh wkh surshu frpsoh0 phqwdu| prqhwdu| dqg vfdo srolflhvB Kdylqj wkh Fhqwudo Edqn vhuyh dv wkh ohqghu ri odvw uhvruw lv d frpprq duudqjhphqw1 Exw wklv lv kdug wr gr xqghu {hg h{fkdqjh udwhv dqg fdslwdo prelolw|/ dqg lpsrvvleoh xqghu d fxuuhqf| erdug1 Iru lqvwdqfh/ Dujhqwlqd*v vwulfw frqyhuwlelolw| odz suhyhqwv wkh Fhqwudo Edqn iurp lvvxlqj grphvwlf fuhglw wr wurxeohg edqnv> wklv pd| kdyh rshqhg wkh zd| wr d 5 edqn sdqlf lq 4<<81 Jlyhq wklv orvv ri prqhwdu| lqghshqghqfh/ lw lv vrphwlphv vxjjhvwhg wkdw jryhuqphqwv vkrxog lqvwhdg xvh vfdo srolf| +wkdw lv/ wkhlu srzhuv ri wd{dwlrq, wr exlog d zdu fkhvw wr eh vshqw dw wlphv ri edqn wurxeoh1 Txhvwlrqv dovr dulvh derxw wkh surshu pdqdjhphqw ri wkh qdqfldo v|vwhp1 Lv lqfuhdvlqj uhvhuyh uhtxluhphqwv rq edqnv +dv Dujhqwlqd kdv grqh, sduw ri wkh vrox0 wlrqB Duh iruhljq fxuuhqf| ghsrvlwv lq wkh grphvwlf edqnlqj v|vwhp gh0vwdelol}lqjB Revhuyhuv vxfk dv Vdfkv ^;` fhuwdlqo| wklqn vr1 Lq wklv sdshu zh ghyhors d irupdo iudphzrun lq zklfk vxfk fodlpv fdq eh dqdo|}hg dqg hydoxdwhg1 Rxu dssurdfk lv qryho lq wkdw lw vwduwv iurp wkh plfur0 irxqgdwlrqv ri d frxqwu|*v qdqfldo v|vwhp1 Pruh vshflfdoo|/ zh vwxg| frpphu0 fldo edqnlqj/ Fhqwudo Edqn srolflhv/ dqg h{fkdqjh udwh uhjlphv dv phfkdqlvpv zkrvh sxusrvh lv wr lpsohphqw vrfldoo| ghvludeoh doorfdwlrqv lq dq hfrqrp| zlwk lqfrpsohwh qdqfldo pdunhwv1 Jlyhq wkdw edqnlqj iudjlolw| lv d fruh lvvxh/ zh irfxv rq d prqhwdu|/4 rshq hfrqrp| yhuvlrq ri wkh ehqfkpdun prgho e| Gldprqg dqg G|eylj ^5`1 Lq wkdw prgho edqnv duh hvvhqwldoo| pdwxulw| wudqviruphuv wkdw wdnh oltxlg ghsrvlwv dqg lqyhvw sduw ri wkh surfhhgv lq looltxlg dvvhwv1 Lq grlqj vr wkh| srro ulvn dqg Pruh suhflvho|/ prqh| hqwhuv wkh xwlolw| ixqfwlrq1 Lq dgglwlrq/ iru prvw ri wkh sdshu edqn ghsrvlwv duh dvvxphg wr eh ghqrplqdwhg lq grphvwlf fxuuhqf|1 4 6 hqkdqfh zhoiduh/ exw dovr fuhdwh wkh srvvlelolw| ri vhoi0ixooolqj edqn uxqv1 Zh hpehg wklv edqnlqj vwru| lq d jhqhudo htxloleulxp pdfurhfrqrplf prgho zklfk fdq rshudwh xqghu d ydulhw| ri h{fkdqjh udwh dqg prqhwdu| duudqjhphqwv ru uhjlphv1 Zh frqvlghu fxuuhqf| erdugv/ {hg h{fkdqjh udwhv zlwk Fhqwudo Edqn fuhglw wr frpphufldo edqnv/ dqg h{leoh h{fkdqjh udwhv1 Zkhq dssursuldwh zh dqdo|}h wkh ixqfwlrqlqj ri wkhvh uhjlphv zlwk dqg zlwkrxw d ohqghu ri odvw uhvruw1 Zh fdq dovr vwxg| wkh hhfwv ri d ydulhw| ri suhfdxwlrqdu| phdvxuhv/ lqfoxglqj kljk uhvhuyh uhtxluhphqwv/ zdu fkhvwv dqg iruhljq fxuuhqf| ghsrvlwv1 Lq doo fdvhv zh lqyhvwljdwh zkhwkhu vhoi0ixooolqj uxqv rq wkh edqn dqg2ru wkh fxuuhqf| fdq rffxu lq htxloleulxp1 Rxu pdlq uhvxowv duh= 41 D fxuuhqf| erdug/ zklfk e| ghvljq plplfv wkh rshudwlrq ri d qrq0prqhwdu| hfrqrp|/ lv yxoqhudeoh wr vhoi0ixooolqj edqn uxqv exw +suhglfwdeo|, qrw wr fxuuhqf| fulvhv1 51 D {hg h{fkdqjh udwh uhjlph zlwk olplwhg Fhqwudo Edqn fuhglw wr frpphu0 fldo edqnv |lhogv kljkhu zhoiduh wkdq d fxuuhqf| erdug iru wkh uhdvrqv vwuhvvhg e| Iulhgpdq ^8` qhduo| kdoi d fhqwxu| djr= vlqfh +xs wr d srlqw, dgglwlrqdo dw prqh| udlvhv xwlolw| dqg frvwv qrwklqj wr surgxfh/ lw lv rswlpdo wr lvvxh lw lq srvl0 wlyh txdqwlwlhv1 Krzhyhu/ wklv uhjlph lv pruh surqh wr edqn uxqv wkdq d fxuuhqf| 7 erdug1 Wkh lqwxlwlrq lv wkdw/ zlwk {hg h{fkdqjh udwhv/ wkh oldelolwlhv ri wkh edqn0 lqj v|vwhp dv d zkroh duh/ lpsolflwo|/ reoljdwlrqv lq lqwhuqdwlrqdo fxuuhqf|1 Khqfh edqn uxqv duh srvvleoh wr wkh h{whqw wkdw wkh edqnlqj v|vwhp*v lpsolflw oldelolwlhv duh juhdwhu wkdq lwv lqwhuqdwlrqdoo| oltxlg dvvhwv1 Zh vkrz wkdw wkh jds ehwzhhq wkh wzr lv juhdwhu zkhq Fhqwudo Edqn fuhglw wr wkh edqnlqj v|vwhp lv srvlwlyh/ zklfk lpsolhv wkdw edqn uxqv duh pruh olnho|1 61 Lqwurgxflqj xqolplwhg grphvwlf fuhglw wr wkh edqnlqj v|vwhp dw wlphv ri wurxeoh +wkdw lv/ d ohqghu ri odvw uhvruw, lqwr d {hg h{fkdqjh udwh v|vwhp suhfoxghv vhoi0ixooolqj edqn uxqv rqo| dw wkh frvw ri fuhdwlqj d edodqfh ri sd|phqwv fulvlv +wkh fhqwudo edqn uxqv rxw ri uhvhuyhv, li dqg zkhq wkh edqn lv uxq rq1 Li d edodqfh ri sd|phqwv fulvlv rffxuv/ wkh fruuhvsrqglqj uhdo doorfdwlrqv +dqg wkhuhiruh zhoiduh, duh wkh vdph dv wkh| zrxog eh lq wkh hyhqw ri d edqn uxq1 71 Erwk d srolf| ri kljk edqn uhvhuyhv dqg rqh ri odujh lqwhuqdwlrqdo uhvhuyhv +wkh zdu fkhvw dssurdfk, fdq holplqdwh wkh edg +uxq, htxloleulxp/ exw rqo| dw wkh frvw ri lqgxflqj d zruvh doorfdwlrq dqg khqfh orzhulqj zhoiduh +uhodwlyh wr wkh jrrg htxloleulxp zlwkrxw wkhvh srolflhv,1 Zkhwkhu hlwkhu srolf| lv ghvludeoh ghshqgv rq djhqwv* ulvn dyhuvlrq/ dqg rq wkh suredelolw| wkh hfrqrp| zrxog odqg lq wkh edg htxloleulxp zkhq rqh lv ihdvleoh1 Pruhryhu/ zh vkrz wkdw d srolf| ri kljk edqn uhvhuyhv xqdpeljxrxvo| grplqdwhv rqh ri odujh lqwhuqdwlrqdo uhvhuyhv1 8 Wkh lqwxlwlrq lv wkdw lqfuhdvlqj wkh lqwhuqdwlrqdo oltxlglw| ri wkh edqnlqj v|vwhp kdv d vrfldo rssruwxqlw| frvw1 Xqghu d srolf| ri kljk uhvhuyh uhtxluhphqwv/ edqnv lqwhuqdol}h wklv frvw> xqghu wkh zdu fkhvw dssurdfk/ wkh| gr qrw1 81 Wkh frpelqdwlrq ri h{leoh h{fkdqjh udwhv dqg d ohqghu ri odvw uhvruw grp0 lqdwhv doo rwkhu srolf| uhjlphv/ iru lw fdq lpsohphqw wkh suhihuuhg uhdo doorfdwlrq zkloh uxolqj rxw vhoi0ixooolqj edqn uxqv1 Wkh lqwxlwlrq iru wklv odvw uhvxow lv vlp0 soh1 Dq htxloleulxp edqn uxq rffxuv li dqg rqo| li hdfk edqn ghsrvlwru h{shfwv rwkhuv zloo uxq dqg h{kdxvw wkh dydlodeoh uhvrxufhv1 Xqghu d {hg udwhv uhjlph/ wkrvh zkr uxq wr wkh edqn zlwkgudz grphvwlf fxuuhqf|/ zklfk lq wxuq wkh| xvh wr ex| grooduv dw wkh Fhqwudo Edqn1 Li rqh ghsrvlwru h{shfwv wklv vhtxhqfh ri dfwlrqv zloo fdxvh wkh Fhqwudo Edqn wr uxq rxw ri grooduv/ wkhq lw lv d ehvw uhvsrqvh iru khu wr uxq dv zhoo/ dqg wkh shvvlplvwlf h{shfwdwlrqv ehfrph vhoi0ixooolqj1 Rq wkh rwkhu kdqg/ xqghu d h{leoh udwhv uhjlph soxv d ohqghu ri odvw uhvruw wkhuh lv dozd|v hqrxjk grphvwlf fxuuhqf| dw wkh frpphufldo edqn wr vdwlvi| wkrvh zkr uxq1 Exw vlqfh wkh Fhqwudo Edqn lv qr orqjhu frpshoohg wr vhoo doo wkh dydlodeoh uhvhuyhv +lq0 foxglqj wkh looltxlg lqyhvwphqwv,/ wkrvh zkr uxq idfh d ghsuhfldwlrq/ zkloh wkrvh zkr gr qrw uxq nqrz wkdw wkhuh zloo vwloo eh grooduv dydlodeoh zkhq wkh| ghvluh wr zlwkgudz wkhp dw d odwhu gdwh1 Khqfh/ uxqqlqj wr wkh edqn lv qr orqjhu d ehvw uhvsrqvh/ shvvlplvwlf h{shfwdwlrqv duh qrw vhoi0ixooolqj/ dqg wkh ghsuhfldwlrq grhv 9 qrw kdsshq lq htxloleulxp1 91 Lqwurgxflqj groodu0ghqrplqdwhg edqn ghsrvlwv pdnhv qr glhuhqfh wr wkh ihdvleoh htxloleuld lq wkh fdvhv ri d fxuuhqf| erdug dqg ri d {hg h{fkdqjh udwh zlwk olplwhg grphvwlf fuhglw1 Exw wkh Fhqwudo Edqn fdq qr orqjhu vhuyh dv d ohqghu ri odvw uhvruw1 Wkdw phdqv wkdw wkh ehqhwv ri d h{leoh h{fkdqjh udwh uhjlph ydqlvk li ghsrvlwv duh groodul}hg/ dqg zhoiduh lv frqvhtxhqwo| uhgxfhg1 Wkh sdshu lv rujdql}hg dv iroorzv1 Vhfwlrq 5 ghvfulehv wkh hfrqrplf hqylurq0 phqw1 Vhfwlrq 6 vwxglhv d fxuuhqf| erdug/ zkloh 7 dqdo|}hv wkh fdvh ri d {hg h{fkdqjh udwh zlwk olplwhg grphvwlf fuhglw1 Wkh hhfwv ri kljk uhvhuyh uhtxluh0 phqwv dqg zdu fkhvwv duh frqvlghuhg lq 81 Vhfwlrq 9 frqwdlqv wkh dqdo|vlv ri h{leoh h{fkdqjh udwhv1 Vhfwlrq : frqvlghuv groodul}hg edqn ghsrvlwv/ zkloh ; frqfoxghv1 51 Wkh Hfrqrplf Hqylurqphqw Zh zloo vwxg| d vpdoo rshq hfrqrp| srsxodwhg e| d odujh qxpehu ri h{ dqwh lghqwlfdo djhqwv1 Wkhuh duh wkuhh shulrgv lqgh{hg e| | ' fc c 21 Hdfk djhqw lv eruq dw | ' f zlwk d txdqwlw| e : f ri dq hqgrzphqw jrrg1 Wkh hqgrzphqw jrrg fdq eh lqyhvwhg dw krph lq d orqj whup frqvwdqw uhwxuqv whfkqrorj| zkrvh |lhog shu xqlw lqyhvwhg lv o xqlwv ri frqvxpswlrq lq shulrg 4/ dqg - : : xqlwv ri frqvxpswlrq lq shulrg 51 Dowhuqdwlyho|/ wkh hqgrzphqw fdq eh lqyhvwhg lq wkh zruog pdunhw/ zkhuh rqh xqlw lqyhvwhg dw | ' f |lhogv rqh xqlw ri d iruhljq fxuuhqf| +grooduv, lq hlwkhu shulrg 4 ru shulrg 51 Wkh sulfh ri frqvxpswlrq lq wkh zruog pdunhw lv {hg dqg qrupdol}hg dw rqh groodu1 Dw | ' hdfk grphvwlf djhqw glvfryhuv khu w|sh1 Zlwk suredelolw| b vkh lv lpsdwlhqw dqg ghulyhv xwlolw| rqo| iurp shulrg 4 frqvxpswlrq1 Zlwk suredelolw| E b vkh wxuqv rxw wr eh sdwlhqw1 Sdwlhqw djhqwv ghulyh xwlolw| iurp wkh uhdo ydoxh ri kroglqjv ri d grphvwlf fxuuhqf| +shvrv, lq shulrg 4 dqg iurp frqvxpswlrq lq shulrg 51 Shvrv duh frvwohvvo| fuhdwhg dqg2ru ghvwur|hg e| d Fhqwudo Edqn1 Vrph lqyhvwphqw lq qrwdwlrq zloo khos irupdol}lqj wkh deryh dvvxpswlrqv1 Ohw % ghqrwh wkh w|slfdo djhqw*v frqvxpswlrq lq shulrg 4 li vkh wxuqv rxw wr eh lpsdwlhqw1 Ohw dqg + ghqrwh/ uhvshfwlyho|/ wkh txdqwlw| ri shvrv dftxluhg lq shulrg 4 dqg khu shulrg 5 frqvxpswlrq li vkh wxuqv rxw wr eh sdwlhqw1 Ilqdoo|/ ohw .| wkh shvr sulfh ri frqvxpswlrq lq shulrg | ' c 2/ zklfk pxvw htxdo wkh h{fkdqjh udwh1 Wkhq wkh h{shfwhg xwlolw| ri wkh uhsuhvhqwdwlyh djhqw fdq eh uhsuhvhqwhg e|= +514, b}E% n E b}EE*.2 n + ; Qrwh wkdw uhdo prqh| edodqfhv duh phdvxuhg e| wkh txdqwlw| ri grooduv rewdlqhg dw wkh hqg ri shulrg 4 gh dwhg e| wkh sulfh ri frqvxpswlrq lq shulrg 51 Wklv lv wkh qdwxudo dvvxpswlrq/ vlqfh sdwlhqw djhqwv zloo krog vxfk edodqfhv xqwlo wkh hqg ri shulrg 51 Wkh ixqfwlrq } E lv vprrwk/ vwulfwo| lqfuhdvlqj/ vwulfwo| frqfdyh/ dqg vdwlvhv Lqdgd frqglwlrqv1 Dvvxph dovr wkdw E lv vprrwk/ vwulfwo| frqfdyh/ dqg vdwlvhv Ef ' fc Ef ' 4c dqg E6 ' f iru vrph 6 : f1 Wklv ghqhv 6 dv wkh vdwldwlrq ohyho ri prqh|1 Wzr ixuwkhu dvvxpswlrqv frpsohwh wkh ghvfulswlrq ri wkh hfrqrplf hqylurq0 phqw1 Dv lq frqyhqwlrqdo lq prghov ri wklv w|sh/ dqg sduwlfxoduo| lq ^5`/ wkh uhdol}dwlrq ri hdfk djhqw*v w|sh lv sulydwh lqirupdwlrq wr wkdw djhqw1 Zh zloo dovr dvvxph wkdw grphvwlf uhvlghqwv +lqfoxglqj wkh Fhqwudo Edqn, fdq lqyhvw exw qrw eruurz lq wkh zruog pdunhw1 Wklv lv d qdwxudo dvvxpswlrq li zh duh wr vwxg| fxuuhqf| fulvhv +wkh vdph dvvxpswlrq/ iru lqvwdqfh/ lv pdgh lq ^7`,/ iru vxfk d fulvlv lv e| ghqlwlrq d vlwxdwlrq ri h{wuhph vfduflw| ri iruhljq h{fkdqjh/ dqg vxfk h{wuhph looltxlglw| frxog qrw rffxu li vroyhqw grphvwlf uhvlghqwv frxog eruurz deurdg doo wkh| ghvluhg dw wkh zruog udwh ri lqwhuhvw1 Wklv vhwxs lv vlplodu wr wkh fodvvlf Gldprqg0G|eylj irupxodwlrq lq ^5`/ vlqfh wkhuh lv xqfhuwdlqw| derxw wkh wlplqj ri frqvxpswlrq/ dqg dovr d sdwwhuq ri dvvhw < uhwxuqv vxfk wkdw djhqwv zrxog suhihu wr lqyhvw lq wkh zruog pdunhw li wkh| nqhz wkh| zhuh lpsdwlhqw/ dqg lq wkh looltxlg whfkqrorj| li wkh| nqhz wkh| zhuh sd0 wlhqw1 D qhz ihdwxuh ri wkh prgho lv wkdw djhqwv duh dvvxphg wr ghpdqg grphvwlf fxuuhqf|1 Vlqfh rqo| wkh grphvwlf Fhqwudo Edqn fdq sulqw shvrv/ wkh dqdo|vlv ri wklv prgho pxvw lqfoxgh dq dvvxpswlrq rq wkh h{fkdqjh udwh 0 prqhwdu| uhjlph/ wkdw lv/ d vshflfdwlrq ri wkh zd| shvrv duh lvvxhg dqg h{fkdqjhg iru grooduv1 Wkh dqdo|vlv ri dowhuqdwlyh uhjlphv lv wkh vxemhfw ri rxu hqvxlqj glvfxvvlrq1 61 D Fxuuhqf| Erdug Wklv vhfwlrq dqdo|}hv uhjlphv lq zklfk wkh Fhqwudo Edqn iroorzv d yhu| vlpsoh uxoh= lw vwdqgv uhdg| wr h{fkdqjh grooduv iru shvrv dw d {hg h{fkdqjh udwh dqg/ lq dgglwlrq/ lw lv frpplwwhg qrw wr fuhdwh ru ghvwur| shvrv lq dq| rwkhu zd|1 Lq rwkhu zrugv/ wkh Fhqwudo Edqn ixqfwlrqv dv d fxuuhqf| erdug1 Xqghu d fxuuhqf| erdug wkh dprxqw ri edvh prqh| lq flufxodwlrq lv h{dfwo| htxdo wr wkh iruhljq uhvhuyhv ri wkh Fhqwudo Edqn1 Khqfh wkhuh fdqqrw eh d edodqfh ri sd|phqwv fulvlv1 Jlyhq d fxuuhqf| erdug uhjlph/ wkh sulydwh vhfwru fdq eh rujdql}hg lq ydulrxv zd|v1 Zh zloo h{dplqh wzr ri wkhp/ rqh uhvhpeolqj dxwdun| dqg dqrwkhu uhvhp0 eolqj d edqnlqj v|vwhp1 Xqghu sodxvleoh frqglwlrqv/ d edqnlqj v|vwhp pd| eh 43 Sduhwr vxshulru wr dxwdun|1 Krzhyhu/ lw pd| dovr eh vxemhfw wr edqn uxqv1 6141 Dxwdun| xqghu d Fxuuhqf| Erdug Xqghu dxwdun| hdfk sulydwh djhqw dfwv lq lvrodwlrq iurp wkh rwkhuv/ lqwhudfwlqj rqo| zlwk wkh Fhqwudo Edqn dqg wkh uhvw ri wkh zruog1 Zh vkdoo dvvxph zlwkrxw orvv ri jhqhudolw| wkdw wkh fxuuhqf| erdug jxdudqwhhv wkdw wkh h{fkdqjh udwh zloo eh rqh shvr iru hdfk groodu1 Wkhq/ wkh w|slfdo djhqw pxvw fkrrvh krz wr glylgh klv shulrg 3 hqgrzphqw ehwzhhq wkh orqj whup whfkqrorj| dqg wkh zruog dvvhw/ krz pxfk ri wkh orqj whup dvvhw wr oltxlgdwh lq shulrg 4/ dqg krz pxfk wr frqvxph dqg wr ghyrwh wr shvr kroglqjv lq hdfk shulrg frqwlqjhqw rq klv w|sh uhdol}dwlrq1 Irupdoo|/ hdfk djhqw pd{lpl}hv 514/ jlyhq .2 ' c vxemhfw wr= +614, &nK e +615, % K n o& +616, K n o, +617, + n -E& , +618, ,& 44 +619, &c Kc %c +c c , f zkhuh K ghqrwhv lqyhvwphqw lq wkh zruog pdunhw/ & lqyhvwphqw lq wkh orqj whup dvvhw/ dqg , oltxlgdwlrq ri wkh orqj whup dvvhw lq shulrg 4 li wkh djhqw wxuqv rxw wr eh sdwlhqw1 Htxdwlrq 614 lv wkh shulrg 3 frqvwudlqw rq lqyhvwphqw1 Htxdwlrq 615 vd|v wkdw/ li wkh djhqw wxuqv rxw wr eh lpsdwlhqw/ vkh frqvxphv lq shulrg 4 wkh oltxlgdwlrq ydoxh ri khu lqyhvwphqwv1 Rq wkh rwkhu kdqg/ 616 vd|v wkdw li vkh wxuqv rxw wr eh sdwlhqw vkh pxvw ghflgh lq shulrg 4 wkh txdqwlw| ri shvrv wr dftxluh dqg/ fruuhvsrqglqjo|/ krz pxfk ri wkh orqj whup dvvhw wr oltxlgdwh1 Wkh ydoxh ri wkh uhpdlqlqj orqj whup lqyhvwphqw soxv khu shvr kroglqjv lq wkh odvw shulrg ghwhuplqhv khu frqvxpswlrq wkhq> wklv lv doo uh hfwhg lq 6171 Htxdwlrq 618 vd|v wkdw oltxlgdwlrq fdqqrw h{fhhg wkh lqyhvwphqw lq wkh orqj whup +looltxlg, whfkqrorj|/ dqg 619 frqwdlqv wkh reylrxv qrqqhjdwlylw| frqvwudlqwv1 Lw vkrxog eh fohdu wkdw xqghu dxwdun| wkh djhqw idfhv lglrv|qfudwlf xqfhuwdlqw|1 Wklv glvwruwv wkh doorfdwlrq ri lqyhvwphqw dqg uhvxowv lq frvwo| oltxlgdwlrq ri wkh orqj whup dvvhw1 Wklv vlwxdwlrq fdq eh lpsuryhg xsrq li djhqwv fdq srro wkhlu uhvrxufhv lq vrph nlqg ri lqvxudqfh vfkhph/ dv zh zloo vhh qh{w1 45 6151 D Edqnlqj V|vwhp Qrz vxssrvh wkdw djhqwv dfw froohfwlyho|> wkhlu frdolwlrq zloo eh fdoohg d edqn +lq idfw/ d frpphufldo edqn, iru uhdvrqv wkdw zloo eh fohdu vkruwo|1 Wkh remhfwlyh ri wkh edqn lv wr srro wkh uhvrxufhv ri wkh hfrqrp| lq rughu wr pd{lpl}h wkh zhoiduh ri lwv uhsuhvhqwlyh phpehu1 Lghdoo| wklv zrxog uhtxluh dvvljqlqj frqvxpswlrq dqg shvr kroglqjv wr hdfk djhqw frqwlqjhqw rq wkh uhdol}dwlrq ri khu w|sh1 Lq fkrrvlqj vxfk d frqwlqjhqw doorfdwlrq/ wkh edqn lv uhvwulfwhg qrw rqo| e| uhvrxufh ihdvlelolw| frqvwudlqwv exw dovr e| idfw wkdw w|sh uhdol}dwlrqv duh sulydwh lqirupdwlrq1 Wklv lpsolhv wkdw wkh edqn pxvw qg vrph zd| ri holflwlqj vxfk lqirupdwlrq1 H{dplqlqj wkh edqn*v rswlrqv lv juhdwo| vlpsolhg dsso|lqj wkh Uhyhodwlrq Sulqflsoh/5 zklfk lpsolhv wkdw dwwhqwlrq fdq eh uhvwulfwhg wr ihdvleoh w|sh frq0 wlqjhqw doorfdwlrqv wkdw jlyh qr djhqw dq lqfhqwlyh wr plvuhsuhvhqw khu w|sh1 Wr h{suhvv wkh odvw frqglwlrq fruuhfwo|/ lw lv qhfhvvdu| wr pdnh d pruh suhflvh dvvxps0 wlrq zkdw wkh edqn fdq dqg fdqqrw revhuyh1 Wkh vlpsohvw dvvxpswlrq/ zklfk zloo eh pdlqwdlqhg khuhrq/ lv wkdw wkh frpphufldo edqn fdq revhuyh hdfk djhqw*v wudqv0 dfwlrqv zlwk wkh grphvwlf edqnlqj v|vwhp +wkh edqn lwvhoi dqg wkh Fhqwudo Edqn,/ 5 Wkh Uhyhodwlrq Sulqflsoh dssolhg wr wkh edqn*v sureohp lv wkdw wkh Ed|hvldq Qdvk htxloleuld ri dq| jdph wkdw wkh ghsrvlwruv pd| sod| fdq eh uhsolfdwhg e| wkh wuxwkixo htxloleuld ri d jdph lq zklfk hdfk ghsrvlwru lv dvnhg wr uhsruw khu w|shv1 Vhh ^9` iru dq h{fhoohqw lqwurgxfwlrq wr wkh Uhyhodwlrq Sulqflsoh1 46 zkloh frqvxpswlrq dqg zruog wudqvdfwlrqv fdqqrw eh prqlwruhg1 Wkh deryh glvfxvvlrq lpsolhv wkdw wkh edqn zloo fkrrvh dq doorfdwlrq wkdw pd{lpl}hv 514/ zlwk .2 ' c vxemhfw wr 614 dqg +61:, b% n E b K n o, +61;, E b+ E b n -E& , +61<, E n + % +6143, ,& +6144, &c Kc %c +c c , f Wkh deryh sureohp zloo eh ghqrwhg e| S4/ dqg lwv vroxwlrq ghqrwhg e| wloghv1 Htxdwlrq 61: lv wkh ihdvlelolw| frqvwudlqw lq shulrg 41 Wkh vroxwlrq ri S4 dvvljqv shvrv wr hdfk sdwlhqw> wklv lv % xqlwv ri frqvxpswlrq wr hdfk lpsdwlhqw dqg qdqfhg e| oltxlgdwlqj wkh vkruw whup dvvhw/ Kc dqg srvvleo| vrph sruwlrq ri wkh orqj whup dvvhw1 Qrwh wkdw 61: lqfrusrudwhv wkh dvvxpswlrq wkdw wkh edqn fdq dftxluh shvrv iurp wkh Fhqwudo Edqn dw dq h{fkdqjh udwh ri rqh1 Wr xqghuvwdqg 61;/ lw lv hdvlhvw wr dvvxph wkdw wkh edqn uhtxluhv sdwlhqw djhqwv wr uhwxuq lq shulrg 5 wkh shvrv wkh| zhuh jlyhq lq shulrg 41 Wkh edqn wkhq uhvhoov wkh shvrv 47 wr wkh Fhqwudo Edqn/ dqg lq dgglwlrq lw oltxlgdwhv wkh uhpdlqghu ri wkh orqj whup lqyhvwphqw1 Wkh surfhhgv iurp wkhvh rshudwlrqv duh xvhg wr qdqfh wkh shulrg 5 frqvxpswlrq ri wkh sdwlhqw1 Ilqdoo|/ htxdwlrqv 6143 dqg 6144 duh vhoi h{sodqdwru|1 Htxdwlrq 61< lv wkh lqfhqwlyh frpsdwlelolw| ru wuxwk whoolqj frqvwudlqw iru sdwlhqw djhqwv1 Li d sdwlhqw shvrv lq wkh uvw shulrg dqg djhqw uhsruwv khu w|sh krqhvwo| vkh zloo uhfhlyh k l n + 1 Li vkh olhv vkh zloo rqo| eh frqvxph + lq wkh vhfrqg/ zkrvh ydoxh lv } E jlyhq % xqlwv ri frqvxpswlrq lq shulrg 4> jlyhq rxu dvvxpswlrqv/ wkh ehvw vkh fdq gr wkhq lv wr h{fkdqjh wkhp iru % grooduv/ zklfk fdq eh xvhg lq shulrg 5 wr ex| % xqlwv ri frqvxpswlrq1 Wkh ydoxh ri o|lqj lv wkhq } E % c zklfk 61< uhtxluhv qrw wr eh odujhu wkdq wkh ydoxh ri whoolqj wkh wuxwk1 S4 lv d vwdqgdug pd{lpl}dwlrq sureohp dqg lwv dqdo|vlv |lhogv xvhixo surshuwlhv ri wkh vroxwlrq1 Lw fdq eh vkrzq wkdw , ' f wkdw lv/ wkhuh lv qr oltxlgdwlrq lq shulrg 4 ri wkh orqj whup lqyhvwphqw1 Wklv vkrxog eh reylrxv/ vlqfh wkh edqn idfhv qr djjuhjdwh xqfhuwdlqw|/ dqg oltxlgdwlqj wkh orqj whup dvvhw lq shulrg 4 lv frvwo|1 Jlyhq wklv idfw/ lw fdq eh vkrzq wkdw wkh ydoxh ri S4 lv vxshulru wr wkh ydoxh ri wkh dxwdunlf vroxwlrq1 Wklv dovr vkrxog eh lqwxlwlyh/ vlqfh wkh edqn srrov uhvrxufhv wr suhyhqw wkh lqh!flhqw oltxlgdwlrq ri wkh orqj whup dvvhw> lq frqwudvw/ wkh orqj whup dvvhw pxvw eh oltxlgdwhg zlwk srvlwlyh suredelolw| lq dxwdun|1 48 Wkh rwkhu ihdwxuhv ri wkh vroxwlrq iroorz iurp pdujlqdo rswlpdolw| frqglwlrqv1 Wkh rswlpdo txdqwlw| ri shvrv wr jlyh sdwlhqw djhqwv lv ghwhuplqhg e| '-:f E +6145, Htxdwlrq 6145 vd|v wkdw wkh pdujlqdo xwlolw| ri jlylqj shvrv wr wkh sdwlhqw pxvw htxdo wkh pdujlqdo frvw ri shvrv wr wkh edqn/ zklfk lv - / dqg lpsolhv wkdw lv ohvv wkdq 61 Jlyhq wklv uhvxow/ wkh fkrlfhv ri % dqg + pxvw vdwlvi| wkh iroorzlqj htxdwlrq/ zklfk fdq eh wkrxjkw ri dv d wudqvirupdwlrq fxuyh= -b % n E b + ' e- E- E b +6146, Wkh qdo rswlpdolw| frqglwlrq lv wkdw wkh vrfldo lqglhuhqfh fxuyh eh wdqjhqw wr wkh deryh wudqvirupdwlrq fxuyh= % bb} E k l' n + E b E b} +6147, k l n + 1 +Qrwh wkdw/ vlqfh - : dqg } E lv frqfdyh/ 6147 ru } E % ' -} E jxdudqwhhv wkdw wkh lqfhqwlyh frqvwudlqw 61< grhv qrw elqg1, Htxdwlrqv 6145/ 6146/ dqg 6147 frpsohwho| ghwhuplqh wkh rswlpdo doorfdwlrq 49 ri frqvxpswlrq dqg shvr kroglqjv e| wkh wzr w|shv1 Qh{w zh glvfxvv krz wklv doorfdwlrq fdq eh lpsohphqwhg lq d ghfhqwudol}hg idvklrq1 6161 Ghpdqg ghsrvlwv dqg edqn uxqv Wkh suhylrxv vxevhfwlrq lghqwlhg wkh vroxwlrq ri S4 dv wkh ehvw doorfdwlrq wkdw wkh edqn fdq lq sulqflsoh dfklhyh jlyhq wkh hqylurqphqw/ lqfoxglqj wkh h{lvwhqfh ri d fxuuhqf| erdug1 Wkh qh{w txhvwlrq lv krz wkdw doorfdwlrq zloo eh lpsohphqwhg lq sudfwlfh dqg/ pruh jhqhudoo|/ krz wkh edqnlqj v|vwhp pd| wu| wr dffrpsolvk dq| jlyhq remhfwlyh1 Wr dqvzhu vxfk txhvwlrqv/ zh vkdoo dvvxph wkdw wkh frpphu0 fldo edqn dqg lwv ghsrvlwruv hvwdeolvk d sduwlfxodu frqwudfw1 Dovr/ zh vkdoo dvvxph wkdw wkh Fhqwudo Edqn dqg wkh frpphufldo edqn djuhh rq surfhgxuhv derxw krz grooduv dqg shvrv zloo eh h{fkdqjhg dqg/ srvvleo|/ d ohqglqj0eruurzlqj uhodwlrq0 vkls1 Wkh frqwudfw ehwzhhq wkh edqn dqg lwv ghsrvlwruv dqg wkh rshudwlqj uxohv ri wkh edqnlqj v|vwhp/ lqfoxglqj Fhqwudo Edqn srolf|/ lv zkdw zh fdoo d uhjlph1 Zh vkdoo vhh wkdw hdfk uhjlph lqgxfhv d jdph sod|hg e| wkh ghsrvlwruv1 Wkh dqdo|vlv ri d uhjlph wkhq uhgxfhv wr wkh dqdo|vlv ri wkh htxloleuld ri wkh lqgxfhg jdph1 Rqh qdwxudo zd| lq zklfk wkh edqn fdq lpsohphqw wkh vroxwlrq ri S4 lv yld ghpdqg ghsrvlwv1 Ghpdqg ghsrvlwv duh frqwudfwv wkdw vwlsxodwh wkdw hdfk djhqw pxvw wxuq ryhu khu hqgrzphqw wr wkh edqn lq shulrg 31 Wkh edqn lqyhvwv K lq 4: wkh zruog oltxlg dvvhw dqg & lq wkh orqj whup whfkqrorj|1 Lq uhwxuq/ wkh djhqw lv surplvhg vrph sd|phqwv iurp wkh edqn lq shulrgv 4 dqg 5/ ghshqglqj rq khu uhsruwhg w|sh1 Zh vkdoo lpsrvh vrph dgglwlrqdo dvvxpswlrqv rq wkh sureohp1 Iluvw/ zh zloo dvvxph wkdw doo sd|phqwv iurp wkh edqn wr lwv ghsrvlwruv duh ghqrplqdwhg dqg duh jlyhq lq shvrv1 Wklv lpsolhv wkdw wkh djhqw lv hqwlwohg wr zlwkgudz hlwkhu % shvrv lq shulrg 4 dqg + shvrv lq shulrg 5/ ghshqglqj shvrv lq shulrg 4/ ru rq wkh uhsruw ri khu w|sh1 Dovr/ lq rughu wr ex| frqvxpswlrq lq wkh zruog pdunhw/ wkh djhqw pxvw jr wr wkh Fhqwudo Edqn wr h{fkdqjh shvrv lqwr grooduv1 Wkh vhfrqg dvvxpswlrq lv wkdw erwk wkh edqn dqg wkh Fhqwudo Edqn pxvw uhvshfw vhtxhqwldo vhuylfh frqvwudlqwv1 Wkhvh frqvwudlqwv uhtxluh/ orrvho| vshdnlqj/ wkdw erwk wkh frpphufldo edqn dqg wkh Fhqwudo Edqn dwwhqg wkh uhtxhvwv ri ghsrvlwruv rq d uvw frph0uvw vhuyhg edvlv1 Wkh h{lvwhqfh ri vhtxhqwldo vhuylfh frqvwudlqwv fdq eh mxvwlhg e| pruh sulplwlyh ihdwxuhv ri wkh hqylurqphqw/ dv vxjjhvwhg e| ^43`1 Zh zloo dvvxph wkdw lq shulrg 4 ghsrvlwruv duulyh wr wkh edqn lq udqgrp rughu1 Xsrq duulydo/ hdfk djhqw uhsruwv khu w|sh uhdol}dwlrq dqg zlwkgudzv hlwkhu % ru shvrv/ dvvxplqj wkh edqn lv vwloo rshq1 Li wkh djhqw zlwkgudzv % shvrv vkh pxvw h{fkdqjh wkhp iru grooduv lq shulrg 4 dw wkh Fhqwudo Edqn> wr gr wklv/ vkh 4; zdonv wr wkh Fhqwudo Edqn wr mrlq d olqh zdlwlqj wkhuh1 Lq frqwudvw/ li wkh shvrv vkh pxvw krog wkhp xqwlo shulrg 51 djhqw zlwkgudzv Wkh frpphufldo edqn vhuylfhv uhtxhvwhg zlwkgudzdov vhtxhqwldoo|/ dv orqj dv lw kdv dvvhwv wr oltxlgdwh/ lq zkrvh fdvh lw oltxlgdwhv wkhp dv qhhghg wr rewdlq grooduv/ zklfk lw h{fkdqjhv iru shvrv dw wkh Fhqwudo Edqn1 Li wkh edqn h{kdxvwv lwv dvvhwv/ lw forvhv dqg glvdsshduv1 Diwhu doo ghsrvlwruv kdyh ylvlwhg wkh edqn/ wkh Fhqwudo Edqn vwduwv vhoolqj grooduv/ dw dq h{fkdqjh udwh ri xqlw|/ wr wkh ghsrvlwruv wkdw kdyh zlwkgudzq % shvrv1 Zh zloo dvvxph wkdw wkh Fhqwudo Edqn forvhv li lw uxqv rxw ri grooduv +wklv fdqqrw kdsshq xqghu d fxuuhqf| erdug/ exw zloo kdsshq lq rwkhu uhjlphv,1 Ilqdoo|/ li wkh edqn glg qrw forvh lq shulrg 4/ lq shulrg 5 wkh edqn oltxlgdwhv doo ri lwv uhpdlqlqj lqyhvwphqwv dqg vhoov wkh uhvxowlqj groodu surfhhgv wr wkh Fhqwudo shvrv soxv dq| surwv wr djhqwv wkdw uhsruwhg wr eh sdwlhqw Edqn1 Lw sd|v + lq shulrg 41 Wkhvh djhqwv h{fkdqjh wkh shvrv wkxv dffxpxodwhg iru grooduv dw wkh Fhqwudo Edqn/ zklfk wkh| xvh wr ex| frqvxpswlrq1 Wkh uhjlph mxvw ghvfulehg lv/ lq vkruw/ d ghpdqg ghsrvlw v|vwhp zlwk d fxu0 uhqf| erdug1 Jlyhq wklv uhjlph/ wkh frqvxphuv duh hqjdjhg lq dq +dqrq|prxv, jdph1 Wkh rxwfrphv ri wklv uhjlph duh wkhq jlyhq e| wkh htxloleuld ri wkh jdph1 Dq htxloleulxp lv d ghvfulswlrq ri wkh vwudwhjlhv ri hdfk ghsrvlwruv dqg djjuhjdwh 4< rxwfrphv vxfk wkdw wkh djjuhjdwh rxwfrphv duh lpsolhg e| wkh ghsrvlwruv* vwudwh0 jlhv dqg hdfk ghsrvlwru vwudwhj| lv rswlpdo iru khu jlyhq wkh djjuhjdwh rxwfrphv16 Wkh iroorzlqj fdq qrz eh suryhq= Sursrvlwlrq 6141 Wkhuh lv dq krqhvw htxloleulxp1 Lq wklv htxloleulxp/ lq shulrg Wkh edqn grhv 4 lpsdwlhqw ghsrvlwruv uhwluh % shvrv dqg sdwlhqw rqhv uhwluh 1 wr sdwlhqw ghsrvlwruv lq wkh vhfrqg shulrg1 Wkh Fhqwudo qrw idlo/ dqg sd|v + grooduv/ zklfk lw xvhv wr uhghhp wkh prqh| Edqn hqgv shulrg 4 zlwk E b vxsso| lq shulrg 51 Surri1 +Vnhwfk, Xqghu wkh k|srwkhvl}hg ehkdylru lw lv hdv| wr fkhfn wkdw wkh frpphufldo edqn grhv qrw idlo/ dqg wkdw wkh Fhqwudo Edqn dffxpxodwhv E b grooduv lq shulrg 41 Rqo| rswlpdo ehkdylru e| ghsrvlwruv qhhgv wr eh fkhfnhg1 Lpsdwlhqw ghsrvlwruv jhw % xqlwv ri frqvxpswlrq li wkh| whoo wkhlu w|sh> li wkh| olh/ shvrv lq shulrg 4/ zklfk wkh| pxvw fduu| wr shulrg 5 zkhq shvrv zloo wkh| jhw eh ri qr xvh iru wkhp1 Khqfh lw lv rswlpdo iru wkh lpsdwlhqw qrw wr olh1 Sdwlhqw shvrv lq shulrg 4 dqg + pruh shvrv li wkh| ehkdyh krqhvwo|1 w|shv jhw Vlqfh wkh| fdq h{fkdqjh shvrv dw dq h{fkdqjh udwh ri rqh/ wkh ydoxh ri krqhvw| 6 Wklv ghvfulswlrq lv lqwhqwlrqdoo| ydjxh1 Wklv lv ehfdxvh zh kdyh dvvxphg d odujh qxpehu ri ghsrvlwruv/ zkr kdyh phdvxuh }hur1 Jlyhq wklv/ wkh htxloleulxp ghqlwlrq pxvw hqvxuh wkdw ghsrvlwruv dvvxph wkdw wkhlu lpsdfw rq djjuhjdwh rxwfrphv lv qhjoljleoh1 Lq vxfk fdvh wkh dssursuldwh htxloleulxp frqfhsw lv wkdw ri ^:`1 53 k l n + 1 Li wkh| olh/ wkh| rewdlq % lv } E shvrv lq shulrg 4/ zklfk wkh| pxvw frqyhuw wr grooduv1 Khqfh wkh| fdq frqvxph % lq shulrg 5/ dqg wkh ydoxh ri o|lqj lv }E %1 Vlqfh } E lv lqfuhdvlqj/ 61< hqvxuhv wkdw wkh sdwlhqw gr qrw olh hlwkhu1 Wkh deryh Sursrvlwlrq fodulhv wkh uroh ri d edqnlqj v|vwhp lq d fxuuhqf| erdug uhjlph +dqg/ lq idfw/ lq prvw rwkhu uhjlphv,1 D edqnlqj v|vwhp pd| lpsohphqw dq doorfdwlrq wkdw lpsuryhv xsrq zkdw djhqwv fdq dfklhyh lq lvrodwlrq1 Krzhyhu/ wkh edqnlqj v|vwhp pd| dwwdlq vxfk lpsuryhphqw rqo| e| kroglqj ohvv lqwhuqdwlrqdoo| oltxlg dvvhwv wkdq lwv lpsolflw oldelolwlhv1 Frqvhtxhqwo|/ wkh edqnlqj v|vwhp pd| eh vxemhfw wr d uxq1 Lq sduwlfxodu/ vxssrvh wkdw +6148, % : K n o& Lq vxfk fdvh/ d uxq hphujhv lq htxloleulxp= Sursrvlwlrq 6151 Li 6148 krogv/ wkhuh lv dq htxloleulxp lq zklfk doo djhqwv fodlp wr eh lpsdwlhqw dqg wkh edqn idlov lq shulrg 41 Li 6148 grhv qrw krog/ wkhuh fdqqrw eh htxloleulxp edqn uxqv 1 Surri1 Iluvw zh suryh vx!flhqf|1 Vxssrvh wkdw hyhu| ghsrvlwru fodlpv wr eh lpsdwlhqw zkdwhyhu khu w|sh1 Wkhq/ 6148 lpsolhv wkdw wkh edqn idlov lq shulrg 4 diwhu oltxlgdwlqj doo lqyhvwphqwv1 Wkh Fhqwudo Edqn grhv qrw idlo/ exw forvhv diwhu 54 vhoolqj K n o& grooduv1 Lpsdwlhqw ghsrvlwruv duh reylrxvo| ehkdylqj rswlpdoo|1 Wr fkhfn wkdw lw lv rswlpdo iru hdfk sdwlhqw djhqw wr fodlp wr eh lpsdwlhqw li hyhu|erg| hovh grhv wkh vdph/ lw lv hqrxjk wr frqvlghu wkh rswlrqv rshq wr wkrvh oxfn| sdwlhqw djhqwv wkdw lq wkh duulyh wr wkh edqn hduo| hqrxjk wr kdyh d fkrlfh ri zlwkgudzlqj % ru uvw shulrg1 Lq wkh srvlwhg htxloleulxp/ wkh edqn forvhv lq shulrg 4/ dqg khqfh qr ixuwkhu sd|phqwv zloo eh jlyhq lq shulrg 51 Dovr/ wkh Fhqwudo Edqn zloo krog qr grooduv lq shulrg 5/ dqg khqfh wkh uhdo ydoxh ri shvrv wkhq zloo eh }hur1 Lw iroorzv lv zruwkohvv iru erwk w|shv/ frquplqj wkh rswlpdolw| ri wkdw d zlwkgudzdo ri fodlplqj lpsdwlhqfh1 Wr suryh qhfhvvlw|/ vxssrvh wkdw d qxpehu Ob ri ghsrvlwruv fodlp wr eh lpsdwlhqw lq shulrg 41 Fohduo| lw lv hqrxjk wr uhvwulfw dwwhqwlrq wr wkh fdvh lq zklfk Ob : b1 Zh vkdoo dujxh e| frqwudglfwlrq dqg vkrz wkdw li 6148 grhv qrw krog wkh edqn lv deoh wr sd| dw ohdvw + wr krqhvw sdwlhqw w|shv lq shulrg 5/ zklfk lpsolhv wkdw lw fdqqrw eh rswlpdo iru wkh sdwlhqw wr olh1 Ohw O, ghqrwh wkh dprxqw ri oltxlgdwlrq ri wkh orqj whup dvvhw> lw lv ghqhg ' K n oO, Xvlqj wklv dqg b ' K/ rqh frqfoxghv e| Ob % n Ob % n E b Qrz/ lw lv hdv| wr fkhfn wkdw wkh edqn zloo eh deoh wr wkdw oO, ' EOb bE % n -E& O,* Ob + sd| + wr wkh Ob uhsruwhgo| sdwlhqw ghsrvlwruv li 55 Wklv lqhtxdolw| zloo krog/ iurp wkh ghqlwlrq ri + dqg wkh odvw htxdwlrq iru O,c li Exw wkh odwwhu lv htxlydohqw wr wkh idloxuh ri 6148 1 Wkh surri o& E bE % lv frpsohwh1 Wkh sursrvlwlrq vwdwhv wkdw 6148 lv qrw rqo| vx!flhqw exw dovr qhfhvvdu| iru wkh h{lvwhqfh ri d edqn uxq1 Qrz/ 6148 lv d frqglwlrq rq wkh vroxwlrq ri S41 Rqh pd| zlvk wr ghvfuleh frqglwlrqv rq wkh ixqgdphqwdo sdudphwhuv ri wkh hfrqrp| duh dvvrfldwhg zlwk wkh srvvlelolw| ri edqn uxqv1 Vxfk frqglwlrqv fdq lq idfw eh fkdudfwhul}hg dv iroorzv1 D olwwoh pdqlsxodwlrq vkrzv wkdw 6148 lv htxlydohqw wr= +6149, % : eo n E oE b % o? E ob Xvlqj wkh deryh idfw/ lw fdq eh vkrzq wkdw d qhfhvvdu| dqg vx!flhqw frqglwlrq iru wkh h{lvwhqfh ri d edqn uxq lv= n -Ee b Sursrvlwlrq 6161 Ohw +o? ' E - %o? *E b Wkhq/ d edqn uxq lv srvvleoh li dqg rqo| li +614:, n +o? } E %o? : -} EE 56 Surri1 Wkh frqglwlrqv deryh hqvxuh wkdw 6149 krogv1 Zh frqfoxgh wkdw= Fruroodu| 6171 Htxloleulxp edqn uxqv pd| rffxu lq d fxuuhqf| erdug uhjlph1 Wkh surri lv hdv| dqg ohiw wr wkh uhdghu1 6171 Vxppdu| Xqghu d fxuuhqf| erdug/ wkhuh fdq eh qr dwwdfnv rq Fhqwudo Edqn uhvhuyhv1 D edqnlqj v|vwhp rshudwlqj zlwk ghpdqg ghsrvlwv fdq hphujh dqg lpsuryh xsrq dxwdun|1 Krzhyhu/ wklv duudqjhphqw pd| eh surqh wr uxqv1 Lq idfw/ vlqfh lq d fxuuhqf| erdug doo prqhwdu| kroglqjv pxvw eh edfnhg e| uhdo uhvhuyhv +lq wklv fdvh/ kroglqjv ri wkh oltxlg dvvhw,/ wklv fdvh lv txlwh dqdorjrxv wr wkh ruljlqdo Gldprqg0G|eylj vhwxs lq ^5`1 Erwk krqhvw dqg uxq htxloleuld zhuh srvvleoh lq wkdw frqwh{w/ dqg wkh vdph lv wuxh khuh1 71 Il{hg H{fkdqjh Udwhv dqg Fhqwudo Edqn Fuhglw Xqghu d fxuuhqf| erdug/ hdfk shvr lq flufxodwlrq lv edfnhg e| d groodu lq wkh Fhqwudo Edqn*v ydxow1 Wklv lpsolhv wkdw/ lq shulrg 4 shvrv duh fuhdwhg dw d srvlwlyh frvw/ zklfk lv htxdo wr wkh rssruwxqlw| frvw ri wkh Fhqwudo Edqn*v uhvhuyh kroglqjv1 57 Krzhyhu/ sulqwlqj shvrv lv iuhh iru wkh Fhqwudo Edqn1 Wklv vxjjhvwv wkdw wkh fxuuhqf| erdug lv lqh!flhqw dqg wkdw d ehwwhu doorfdwlrq pd| eh dwwdlqdeoh1 Wklv vhfwlrq vwduwv e| vkrzlqj wkdw wkh deryh frqmhfwxuh lv wuxh/ dqg wkdw d uhjlph lq zklfk wkh Fhqwudo Edqn jlyhv srvlwlyh fuhglw wr wkh frpphufldo edqn pd| dwwdlq d ehwwhu doorfdwlrq wkdq xqghu d fxuuhqf| erdug1 Wklv uhjlph fdq eh ghfhqwudol}hg/ dv zlwk wkh fxuuhqf| erdug/ zlwk d ghpdqg ghsrvlw v|vwhp1 Dv zlwk d fxuuhqf| erdug/ edqn uxqv duh srvvleoh1 Lq dgglwlrq/ qrz edodqfh ri sd|phqwv fulvhv ehfrph srvvleoh1 Zkhwkhu edqn uxqv ru edodqfh ri sd|phqwv fulvhv duh revhuyhg ghshqgv rq wkh vshflf duudqjhphqwv ehwzhhq wkh Fhqwudo Edqn dqg frpphufldo edqnv1 Krzhyhu/ erwk fdq eh fdxvhg e| wkh lqwhuqdwlrqdo looltxlglw| ri wkh edqnlqj v|vwhp dv d zkroh1 Ilqdoo|/ wklv vhfwlrq vkrzv wkdw wkh lqwhuqdwlrqdo oltxlglw| ri wkh edqnlqj v|v0 whp lv ohvv xqghu d {hg h{fkdqjh udwh v|vwhp zlwk Fhqwudo Edqn fuhglw wkdq xqghu d fxuuhqf| erdug1 Dv d uhvxow/ frqyhqwlrqdo {hg h{fkdqjh udwh v|vwhpv duh pruh surqh wr uxqv wkdq fxuuhqf| erdug v|vwhpv1 7141 Wkh Rswlpdo Vxsso| ri Fhqwudo Edqn Fuhglw Wr dqdo|}h d {hg h{fkdqjh udwh uhjlph zlwk Fhqwudo Edqn fuhglw lw lv khosixo wr vwduw e| vwxg|lqj d vrfldo rswlpxp sureohp1 Frqvlghu zkdw wkh edqn dqg 58 wkh Fhqwudo Edqn fdq lghdoo| dfklhyh li wkh| dfwhg wrjhwkhu/ dvvxplqj wkdw wkh h{fkdqjh udwh zloo eh {hg dw rqh1 Wkh Uhyhodwlrq Sulqflsoh dssolhv wr wklv vrfldo sureohp/ dqg wkh rswlrqv rshq duh jlyhq e| doo ihdvleoh lqfhqwlyh frpsdwleoh door0 fdwlrqv1 Khqfh wkh vrfldo rswlpxp pxvw pd{lpl}h 514 +zlwk .2 ' , vxemhfw wr 614 dqg +714, b% K +715, E b + -& +716, %c +c c &c K f dqg wkh lqfhqwlyh frpsdwlelolw| frqglwlrq 61<1 Zh vkdoo fdoo wklv sureohp S5 dqg lwv vroxwlrqv zloo eh lghqwlhg zlwk d edu1 Lq vhwwlqj xs S5/ zh kdyh dvvxphg wkdw shvrv fdq eh surylghg dw qr frvw wr vdwlvi| wkh shvr ghpdqgv ri wkh sdwlhqw w|shv1 Zh kdyh dovr dvvxphg wkdw wkh h{fkdqjh udwh lq shulrg 5 lv rqh1 Zh vkdoo vhh wkdw erwk dvvxpswlrqv wxuq rxw wr eh mxvwlhg/ lq wkh vhqvh wkdw wkh uhvxowlqj doorfdwlrq fdq eh lpsohphqwhg1 59 Wkh vroxwlrq ri S5 fdq eh lqwxlwlyho| xqghuvwrrg dv iroorzv1 Iluvw/ vlqfh surylg0 lqj shvrv lv hhfwlyho| judwlv/ wkh rswlpdo doorfdwlrq hqvxuhv wkdw wkh uhdo txdqwlw| ri shvrv lv wkh vdwldwlrq ohyho= 7 ' E6 ' f E +717, Vhfrqg/ wkh wudqvirupdwlrq fxuyh lv qrz jlyhq e| +718, -b7 % n E b7 + ' e- Qrwh wkh glhuhqfh zlwk wkh wudqvirupdwlrq fxuyh xqghu d fxuuhqf| erdug/ jlyhq e| 6146= lq d {hg h{fkdqjh udwh v|vwhp zlwk rswlpdo surylvlrq ri shvrv/ wkh zklfk lv wkh rssruwxqlw| frvw ri surylglqj hfrqrp| vdyhv E- E b/ shvrv iru wkh sdwlhqw w|shv wr krog ehwzhhq shulrgv 4 dqg 51 Wkh qdo rswlpdolw| frqglwlrq lv wkdw +719, k l 7 n +7 } E7 % ' -} E zklfk vd|v wkdw wkh vrfldo pdujlqdo udwh ri vxevwlwxwlrq pxvw htxdo wkh vorsh ri wkh wudqvirupdwlrq fxuyh1 Wkh wkuhh frqglwlrqv 717/ 718/ dqg 719 fkdudfwhul}h wkh 5: vrfldo rswlpxp1 Qrz zh vkdoo suryh wkdw wkh rswlpdo doorfdwlrq fdq eh ghfhqwudol}hg lq d {hg h{fkdqjh udwh v|vwhp zlwk Fhqwudo Edqn fuhglw1 Vxssrvh qrz wkdw wkh frpphufldo edqn dfwv lqghshqghqwo| ri wkh Fhqwudo Edqn dqg pd{lpl}hv wkh zhoiduh ri wkh uhsuhvhqwdwlyh ghsrvlwru1 Dvvxph dovr wkdw shvrv fdq eh h{fkdqjhg iru grooduv dw d xqlw| h{fkdqjh udwh1 Ilqdoo|/ vxssrvh wkdw wkh Fhqwudo Edqn rhuv wr ohqg shvrv wr wkh frpphufldo edqn lq shulrg 4/ wr eh uhsdlg zlwkrxw lqwhuhvw lq shulrg 51 Wkh Uhyhodwlrq Sulqflsoh dssolhv rqfh pruh dqg lpsolhv wkdw wkh edqn*v sureohp lv wr pd{lpl}h 514/ zlwk .2 ' c vxemhfw wr 614/ dqg +71:, b% n E b K n +71;, E b+ E b n -& +71<, %c +c c &c Kc f dqg wkh lqfhqwlyh frpsdwlelolw| frqvwudlqw 61</ zkhuh ghqrwhv wkh edqn*v eru0 urzlqj iurp wkh Fhqwudo Edqn1 Dv vwdwhg/ wkhuh lv d gl!fxow| zlwk wklv dujxphqw/ lq wkdw wkh frpphufldo edqn zloo fkrrvh wr lqyhvw doo ri wkh hfrqrp|*v hqgrzphqw lq wkh orqj whup dvvhw 5; dqg eruurz iurp wkh Fhqwudo Edqn doo lw qhhgv wr vhuylfh zlwkgudzdov lq shulrg 41 Wklv lv hdvlo| fruuhfwhg/ krzhyhu/ li zh dvvxph wkdw wkh frpphufldo edqn pxvw uhvshfw d nlqg ri uhvhuyh uhtxluhphqw= +7143, b% K Zlwk wkh uhvhuyh uhtxluhphqw/ wkh edqn*v sureohp lv wr pd{lpl}h 514 vxemhfw wr 614/ 71:/ 71;/ 71</ 61</ dqg 71431 Wkh vroxwlrq ri wklv sureohp fdq eh hdvlo| vhhq wr frlqflgh zlwk wkh vrfldo rswlpxp ghvfulehg deryh1 Vrph ihdwxuhv ri wkh vrfldo rswlpxp duh zruwk qrwlqj1 Lw fdq eh fkhfnhg wkdw wkh vroxwlrq uhvxowv lq d Sduhwr lpsuryhphqw ryhu wkh fxuuhqf| erdug doorfdwlrq ghulyhg iurp S41 Wklv lpsolhv/ lq sduwlfxodu/ wkdw % 7:% G lpsdwlhqw djhqwv duh hqwlwohg wr pruh frqvxpswlrq lq shulrg 4 wkdq lq d fxuuhqf| erdug17 Odvwo|/ wkh rswlpdo vxsso| ri fuhglw iurp wkh Fhqwudo Edqn wr wkh frpphufldo edqnv lv 7 ' E b 7 ' E b6 Wkdw lv/ wkh dprxqw wkh Fhqwudo Edqn ohqgv wr wkh edqn vkrxog eh mxvw hqrxjk wr fryhu wkh ghpdqg iru shvrv ri sdwlhqw djhqwv lq shulrg 41 Zkhwkhu | A |h dv zhoo ghshqgv rq wkh vkdsh ri wkh " +=, ixqfwlrq1 Ryhudoo lqfrphkdv ulvhq +wkh wudqvirupdwlrq fxuyh kdv pryhg dzd| iurp wkh ruljlq,/ zklfk zrxog whqg wr lqfuhdvh | i uhodwlyh wr |h1 Exw " P A " P / zklfk/ fhwhulv sdulexv/ zrxog whqg wr uhgxfh | uhodwlyh wr |h1 7 5< Vxppdul}lqj/ lq d {hg h{fkdqjh udwh v|vwhp zlwk d uhvhuyh uhtxluhphqw dqg rswlpdo Fhqwudo Edqn fuhglw wkh frpphufldo edqn zloo wu| wr lpsohphqw d vrfldoo| rswlpdo doorfdwlrq1 Qh{w zh vkdoo vwxg| krz wklv lpsohphqwdwlrq pd| rffxu yld d ghpdqg ghsrvlw v|vwhp1 7151 Ghpdqg Ghsrvlwv dqg Edqn Uxqv Dv zlwk wkh fxuuhqf| erdug/ d ghpdqg ghsrvlw lq d {hg h{fkdqjh udwh uhjlph lv d frqwudfw wkdw uhtxluhv ghsrvlwruv wr vxuuhqghu wkhlu shulrg 3 hqgrzphqwv wr wkh edqn1 Wkh edqn lqyhvwv 7K lq wkh vkruw whup dvvhw dqg &7 lq wkh orqj whup whfkqrorj|1 Lq uhwxuq/ ghsrvlwruv jhw d surplvh ri zlwkgudzlqj/ dw wkhlu rzq glvfuhwlrq/ hlwkhu 7 shvrv lq shulrg 4 dqg +7 shvrv lq shulrg 51 Qrwh wkdw zh % 7 shvrv lq shulrg 4 ru pdlqwdlq wkh dvvxpswlrq wkdw ghsrvlwv duh ghqrplqdwhg lq shvrv1 Zh vkdoo dovr pdlqwdlq rxu dvvxpswlrqv rq vhtxhqwldo vhuylfh1 Wkh pdlq gli0 ihuhqfh zlwk wkh fxuuhqf| erdug fdvh lv wkdw qrz wkh h{lvwhqfh ri Fhqwudo Edqn fuhglw pdnhv lw qhfhvvdu| wr ghvfuleh wkh fuhglw duudqjhphqwv ehwzhhq wkh Fhqwudo Edqn dqg wkh frpphufldo edqn1 Zh vkdoo h{dplqh vrph dowhuqdwlyhv lq wxuq/ dqg dujxh wkdw wkh pdlq glhuhqfh wkh| pdnh lv zkhwkhu wkhuh pd| eh edqn uxqv ru edodqfh ri sd|phqwv fulvhv1 63 7161 D Uhjlph zlwk Olplwhg Grphvwlf Fuhglw dqg qr Edodqfh ri Sd|0 phqwv Fulvhv 7 grooduv wr wkh frpphufldo edqn Vxssrvh wkdw wkh Fhqwudo Edqn rhuv wr ohqg lq shulrg 4 dw qr lqwhuhvw/ exw lw uhvwulfwv wkh frpphufldo edqn wr xvh wklv olqh ri fuhglw rqo| iru zlwkgudzdov ri wkh uhsruwhgo| sdwlhqw w|shv1 Wkh uhdvrq iru wklv uxoh lv wkdw wkh Fhqwudo Edqn zdqwv wr ghihqg lwv uhvhuyhv1 Dq djhqw zkr uhsruwv wkdw vkh lv lpsdwlhqw zloo wu| wr vhoo wkh shvrv vkh zlwkgudzv zlwklq wkh shulrg wr wkh Fhqwudo Edqn1 Khqfh/ uhtxlulqj wkh frpphufldo edqn wr xvh wkh fuhglw olqh rqo| iru sdwlhqw zlwkgudzdov hqvxuhv wkdw wkh Fhqwudo Edqn grhv qrw uxq rxw ri grooduv dqg wkdw d edodqfh ri sd|phqwv fulvlv lv wkhuhiruh qrw srvvleoh1 Jlyhq wklv nlqg ri duudqjhphqw/ lq shulrg 4 wkh frpphufldo edqn vhuylfhv 7 e| eruurzlqj iurp wkh Fhqwudo Edqn/ dqg zlwkgudzdov zlwkgudzdov ri vl}h 7 Wkh frpphufldo edqn lv dvvxphg wr forvh li lw ri vl}h % 7 e| oltxlgdwlqj 7K ru & oltxlgdwhv doo ri lwv dvvhwv1 Lq shulrg 5/ li wkh frpphufldo edqn glg qrw forvh/ lw oltxlgdwhv wkh uhvw ri lwv dvvhwv1 Lw xvhv wkh surfhhgv wr uhsd| wkh ordq iurp wkh 7 soxv dq| surwv wr hdfk uhsruwhgo| sdwlhqw Fhqwudo Edqn> qdoo|/ lw sd|v +7 ghsrvlwru1 Dv lq wkh fxuuhqf| erdug fdvh/ wklv prgxv rshudqgl lqgxfhv dq dqrq|prxv 64 jdph sod|hg e| wkh ghsrvlwruv1 Qrz lw fdq eh vkrzq wkdw= Sursrvlwlrq 7141 Wkhuh lv dq krqhvw htxloleulxp zkrvh rxwfrph lv wkh vrfldoo| rswlpdo doorfdwlrq1 Lq wklv htxloleulxp/ qhlwkhu wkh edqn qru wkh Fhqwudo Edqn forvh1 Surri1 Li doo djhqwv uhsruw wkhlu w|shv krqhvwo|/ lq shulrg 4 wkh edqn vhuylfhv 7 e| eruurzlqj iurp zlwkgudzdov ri b7 % e| oltxlgdwlqj wkh zruog dvvhw dqg E b 7 ' E b 7 wkh Fhqwudo Edqn1 Wklv lv ihdvleoh iru wkh edqn/ jlyhq 7143 dqg Qrz/ 71; hqvxuhv wkdw wkh edqn fdq uhsd| wkh Fhqwudo Edqn*v ordq dqg vhuylfh ghsrvlwv lq shulrg 51 Khqfh wkh edqn grhv qrw forvh1 Lq shulrg 4/ wkh Fhqwudo Edqn uhfhlyhv 7K grooduv iurp wkh edqn/ zklfk duh +mxvw, hqrxjk wr dwwhqg wkh ghpdqgv ri wkh lpsdwlhqw w|shv1 Lq shulrg 5/ wkh Fhqwudo Edqn uhfhlyhv -&7 grooduv iurp wkh edqn/ zklfk lv hqrxjk wr vdwlvi| wkh ghpdqg iru grooduv ri wkh sdwlhqw w|shv1 Wkh uhvw ri wkh surri lv reylrxv dqg ohiw wr wkh uhdghu1 Khqfh wklv v|vwhp pd| lpsohphqw wkh rswlpdo doorfdwlrq1 Krzhyhu/ Sursrvlwlrq 7151 Dvvxph wkdw +7144, % 7 : 7K n o&7 65 Wkhq wkhuh lv dq htxloleulxp lq zklfk doo ghsrvlwruv fodlp wr eh lpsdwlhqw dqg wkh edqn idlov lq shulrg 41 Frqyhuvho|/ li 7144 grhv qrw krog wkhuh fdqqrw eh dq htxloleulxp zlwk d edqn uxq1 Surri1 Iluvw zh suryh wkh vx!flhqf| ri 71441 Vxssrvh doo frqvxphuv dwwhpsw wr zlwkgudz % 7 Wkhq/ jlyhq wkh dvvxpswlrq wkdw wkh edqn fdqqrw xvh wkh Fhqwudo Edqn fuhglw olqh wr vhuylfh lpsdwlhqw zlwkgudzdov/ 7144 lpsolhv wkdw wkh edqn idlov lq shulrg 41 Xqghu wkh vdph frqglwlrqv/ wkhuh lv qr Fhqwudo Edqn ohqglqj lq shulrg 41 Lq shulrg 4/ wkh Fhqwudo Edqn uhfhlyhv 7K n o&7 grooduv iurp wkh edqn1 Wklv lv mxvw hqrxjk wr vhoo grooduv wr wkh ghsrvlwruv wkdw krog shvrv1 Khqfh wkh Fhqwudo Edqn grhv qrw forvh lq shulrg 41 Lpsdwlhqw ghsrvlwruv duh reylrxvo| ehkdylqj rswlpdoo|1 Wr fkhfn wkdw lw lv rswlpdo iru hdfk sdwlhqw djhqw wr fodlp wr eh lpsdwlhqw li hyhu|erg| hovh grhv wkh vdph/ rqh qhhg rqo| fkhfn wkh rswlpdo dfwlrqv ri d sdwlhqw ghsrvlwru wkdw duulyhv 7 Li vkh zlwkgudzv wr wkh edqn hduo| hqrxjk wr kdyh dq rswlrq wr zlwkgudz % 7 ru 1 % 7c kh fdq rewdlq % 7 grooduv iurp wkh Fhqwudo Edqn/ zklfk kh fdq xvh lq shulrg 5 7 shvrv kh pxvw krog wkhp wr ex| % 7 xqlwv ri frqvxpswlrq1 Li vkh zlwkgudzv xqwlo shulrg 51 Exw lq shulrg 5 shvrv zloo kdyh qr ydoxh ehfdxvh wkh Fhqwudo Edqn zloo kdyh qr grooduv zlwk zklfk wr uhghhp shvrv1 Khqfh wkh sdwlhqw djhqwv zloo olh 66 derxw wkhlu w|sh1 Wkh surri ri wkh qhfhvvlw| ri 7144 lv dqdorjrxv wr wkdw ri wkh qhfhvvlw| ri 6148 lq d fxuuhqf| erdug1 Wkh ghwdlov duh ohiw wr wkh uhdghu1 Wkh frqglwlrq 7144 lv reylrxvo| dqdorjrxv wr 61481 Qrz/ lw wxuqv rxw wkdw= Sursrvlwlrq 7161 Li 6148 lv vdwlvhg/ vr lv 71441 Wkh frqyhuvh lv qrw wuxh1 Surri1 Xvlqj 614/ 7144 fdq eh uhzulwwhq dv % 7 : eo*E E ob Xvlqj wkh ghqlwlrq ri %o? jlyhq lq 6149/ wklv lv htxlydohqw wr % 7 n E oE b*E 7:% wkh sursrvlwlrq iroorzv lpphgldwho|1 bE o : %o? Vlqfh % Khqfh/ li uxqv duh srvvleoh lq d fxuuhqf| erdug wkh| duh dovr srvvleoh lq d {hg h{fkdqjhu udwh uhjlph/ exw wkh frqyhuvhu lv qrw wuxh1 Wkhuh lv d vhqvh/ wkhuhiruh/ lq zklfk d {hg h{fkdqjh udwh uhjlph lv pruh frqgxflyh wr d edqn uxq wkdq d fxuuhqf| erdug1 Rq wkh rwkhu kdqg/ wkh {hg h{fkdqjh udwh uhjlph fdq lpsohphqw dq doorfdwlrq +li wkh jrrg htxloleulxp rewdlqv, wkdw lpsuryhv xsrq wkh ehvw fxuuhqf| erdugv fdq dwwdlq1 Wkh txhvwlrq ri zklfk uhjlph lv wr eh suhihuuhg lv vxewoh1 Li sdudphwhu ydoxhv duh vxfk wkdw d uxq htxloleulxp fdq rffxu xqghu d fxuuhqf| erdug +wkdw lv/ li 6148 lv vdwlvhg,/ wkhq vkliwlqj wr d {hg h{fkdqjh udwh zlwk grphvwlf fuhglw pd| lpsuryh wkh ihdwxuhv ri wkh jrrg +krqhvw, htxloleulxp zlwkrxw fkdqjlqj wkh qxpehu ri 67 htxloleuld wkdw duh ihdvleoh1 Lq wklv fdvh d fxuuhqf| erdug lv fohduo| lqihulru1 Li/ rq wkh rwkhu kdqg/ rqo| rqh htxloleulxp +wkh krqhvw rqh, h{lvwv xqghu d fxuuhqf| erdug/ prylqj wr d {hg h{fkdqjh udwh zlwk olplwhg grphvwlf fuhglw pd| +djdlq/ iru vrph sdudphwhu ydoxhv, rshq xs wkh srvvlelolw| ri d qhz/ edg htxloleulxp1 Lq wklv fdvh/ zklfk uhjlph lv suhihuuhg ghshqgv rq dq dvvhvvphqw ri wkh olnholkrrg wkdw wkh hfrqrp| zrxog odqg lq wkh edg htxloleulxp li rqh lv ihdvleoh1 Xqiruwxqdwho|/ rxu dqdo|vlv +dv zhoo dv h{lvwlqj hfrqrplf wkhru|, lv qrw lqirupdwlyh rq krz dq htxloleulxp zloo eh vhohfwhg zkhq wkhuh duh pdq| ri wkhp1 7171 Il{hg H{fkdqjh Udwhv Zlwk d Ohqghu ri Odvw Uhvruw Lq wkh suhfhglqj vxevhfwlrq wkh Fhqwudo Edqn glg qrw dfw dv d ohqghu ri odvw uhvruw lq wkh vhqvh wkdw/ li wkhuh zdv d edqn uxq/ wkh Fhqwudo Edqn glg qrw h{whqg fuhglw wr wkh frpphufldo edqn1 Zh vkdoo qrz h{dplqh wkh frqvhtxhqfhv ri gursslqj wkdw dvvxpswlrq1 Krzhyhu/ zh vkdoo vwloo dvvxph wkdw wkh Fhqwudo Edqn wulhv wr pdlqwdlq d {hg h{fkdqjh udwh uhjlph lq wkh vhqvh wkdw lw zloo ghihqg wkh shvr xqwlo lw lv lpsrvvleoh iru wkh hfrqrp| wr rewdlq pruh grooduv1 Vxfk d uhjlph lv ehvw irupdol}hg dv iroorzv1 Lq dgglwlrq wr wkh olqh ri fuhglw ri 7 wkh Fhqwudo Edqn rhuv wr ohqg dq xqolplwhg txdqwlw| ri shvrv wr wkh frpphufldo c edqn lq fdvh pruh wkdq b fxvwrphuv fodlp wr eh lpsdwlhqw1 Li vxfk hphujhqf| 68 fuhglw lv xvhg/ wkrxjk/ zh dvvxph wkdw wkh Fhqwudo Edqn rewdlqv frqwuro ryhu wkh orqj whup dvvhw lq shulrg 4/ dqg oltxlgdwhv wkh dvvhw dv qhhghg wr vhoo grooduv wr djhqwv fodlplqj lpsdwlhqfh1 Lq shulrg 4/ wkh frpphufldo edqn sd|v uhsruwhgo| sdwlhqw w|shv e| eruurzlqj iurp wkh qrupdo olqh ri fuhglw/ dqg lw sd|v zlwkgudzdov ri wkh lpsdwlhqw e| olt0 xlgdwlqj wkh zruog dvvhw uvw/ dqg wkhq gudzlqj rq wkh hphujhqf| fuhglw1 Ehfdxvh hphujhqf| fuhglw lv xqolplwhg/ wkh edqn grhv qrw forvh1 Wkh Fhqwudo Edqn vhoov grooduv dw dq xqlw| h{fkdqjh udwh/ xvlqj uvw wkh grooduv rewdlqhg iurp wkh edqn/ dqg wkhq oltxlgdwlqj wkh orqj whup dvvhw1 Li wkh orqj whup dvvhw lv frpsohwho| oltxlgdwhg lq shulrg 4/ zh vd| wkdw wkhuh lv d edodqfh ri sd|phqwv fulvlv1 Xqghu wkhvh dvvxpswlrqv rqh fdq vkrz wkdw li doo ghsrvlwruv dfw krqhvwo| wkh vrfldo rswlpxp lv lpsohphqwhg= Sursrvlwlrq 7171 Wkh {hg h{fkdqjh udwh v|vwhp zlwk d ohqghu ri odvw uhvruw kdv dq krqhvw htxloleulxp1 Wkh surri lv vlplodu wr suhylrxv rqhv dqg ohiw wr wkh uhdghu1 Qrz/ wkh vdph frqglwlrqv xqghu zklfk wkhuh zdv d edqn uxq lq wkh suhylrxv uhjlph lpso| wkdw wkhuh lv d edodqfh ri sd|phqwv fulvlv zlwk d ohqghu ri odvw uhvruw= Sursrvlwlrq 7181 Li 7144 krogv/ wkhuh lv dq htxloleulxp lq zklfk doo ghsrvlwruv 69 fodlp wr eh lpsdwlhqw dqg wkh Fhqwudo Edqn lv xqdeoh wr vhuylfh doo groodu ghpdqgv lq shulrg 41 Surri1 Li doo ghsrvlwruv fodlp wr eh lpsdwlhqw/ wkh| doo duulyh wr wkh Fhqwudo Edqn zlwk % 7 shvrv lq shulrg 41 Wkh Fhqwudo Edqn rewdlqv 7K grooduv iurp wkh edqn/ dqg o&7 iurp oltxlgdwlqj wkh orqj whup dvvhw1 Jlyhq 7144/ wkh Fhqwudo Edqn uxqv rxw ri grooduv dqg forvhv1 Fohduo|/ wkh edqn grhv qrw forvh lq shulrg 41 Vlqfh doo ghsrvlwv duh sdlg lq wkh uvw shulrg/ wkh edqn kdv qr ixuwkhu oldelolwlhv ylv d ylv ghsrvlwruv lq shulrg 518 Lw uhpdlqv wr fkhfn wkdw hdfk ghsrvlwru lv dfwlqj rswlpdoo|1 Wklv lv hdv| dqg ohiw wr wkh uhdghu1 Rqh frqfoxvlrq iurp wkh dqdo|vlv lv wkdw/ zlwk {hg h{fkdqjh udwhv/ zkhwkhu wkh hhfwv ri lqwhuqdwlrqdo looltxlglw| ohdg wr edqn uxqv ru edodqfh ri sd|phqwv fulvhv ghshqg rq wkh fuhglw duudqjhphqwv ehwzhhq wkh Fhqwudo Edqn dqg wkh frp0 phufldo edqn1 Krzhyhu/ wkh urrw vrxufh ri qdqfldo iudjlolw| lv wkh vdph1 Wkh vrfldoo| rswlpdo doorfdwlrq lpsolhv wkdw lqyhvwphqw lq wkh zruog oltxlg dvvhw lv ohvv wkdq wkh lpsolflw vkruw whup groodu oldelolwlhv ri wkh edqnlqj v|vwhp1 Wklv kdv ehhq 8 Wkh edqn kdv qr uhvrxufhv wr uhsd| lwv ghew wr wkh Fhqwudo Edqn lq shulrg 5 exw wklv lv qrw lpsruwdqw/ vlqfh e| wkhq wkh Fhqwudo Edqn kdv ehfrph edqnuxsw1 Dowhuqdwlyho|/ rqh fdq dvvxph wkdw wkh ghew lv fdqfhoohg zkhq wkh Fhqwudo Edqn idlov wr uhwxuq wkh orqj whup dvvhw wr wkh frpphufldo edqn1 6: lghqwlhg ehiruh dv d srwhqwldo sureohp xqghu {hg udwhv1 Krzhyhu/ rxu dqdo|vlv frqwudvwv zlwk suhylrxv rqhv lq vkrzlqj wkdw lqwhuqdwlrqdo looltxlglw| kdv ehqhwv dv zhoo dv frvwv= zkhq wkh v|vwhp lv lqwhuqdwlrqdoo| looltxlg dv lq wkh h{dpsoh ri wklv vhfwlrq/ wkh jrrg htxloleulxp lv dvvrfldwhg zlwk d uhdo doorfdwlrq zklfk lv suhihuuhg wr wkh doorfdwlrq wkdw zrxog suhydlo xqghu d fxuuhqf| erdug1 Wkh dqdo|vlv ri wklv vxevhfwlrq dvvxphv wkdw wkh Fhqwudo Edqn jkwv d ghydox0 dwlrq olnh d grj1 Wklv lv lpsolhg/ lq sduwlfxodu/ lq wkh dvvxpswlrq wkdw wkh Fhqwudo Edqn vwrsv vhoolqj grooduv lq wkh uvw shulrg rqo| diwhu wkh orqj whup dvvhw kdv ehhq oltxlgdwhg1 Rqh pd| dvn zkdw zrxog kdsshq zlwk d ohvv frpplwwhg Fhqwudo Edqn1 Iru h{dpsoh/ wkh Fhqwudo Edqn surfhgxuh pd| fdoo iru vwrsslqj wkh vdoh ri grooduv ehiruh wkh orqj whup dvvhw kdv ehhq h{kdxvwhg1 Vxfk d uxoh/ lq idfw/ zrxog dprxqw wr d uxoh iru zkhq wr ghydoxh wkh shvr dqg/ khqfh/ ehvw ghod|hg xqwlo h{leoh h{fkdqjh udwhv duh frqvlghuhg1 Ehiruh wkdw/ zh vkdoo vwxg| vrph srolf| phdvxuhv wkdw pd| eh xvhg wr suhyhqw uxqv xqghu {hg udwhv1 81 Qduurz Edqnlqj yhuvxv Odujh Lqwhuqdwlrqdo Uhvhuyhv Jlyhq wkh srvvlelolw| ri edqn uxqv dqg edodqfh ri sd|phqwv fulvhv zlwk {hg udwhv/ vrph revhuyhuv kdyh vxjjhvwhg wkdw frpphufldo edqnv vkrxog eh uhtxluhg 6; wr krog hqrxjk oltxlglw| wr fryhu doo ri wkhlu ghpdqgdeoh ghew1 Lq wklv vhfwlrq zh vkdoo vkrz wkdw wklv srvlwlrq/ zklfk kdv ehhq whuphg qduurz edqnlqj/ fdq lq idfw holplqdwh htxloleulxp uxqv/ exw dw wkh frvw ri lpsohphqwlqj dq lqh!flhqw doorfdwlrq1 Zh vkdoo dovr vwxg| d uhjlph lq zklfk wkh jryhuqphqw lpsrvhv d wd{0wudqvihu vfkhph wr qdqfh dq hphujhqf| groodu ixqg wr eh xvhg wr jkw uxqv1 Dv glv0 fxvvhg lq wkh lqwurgxfwlrq/ wklv srolf| kdv ehhq dgyrfdwhg lq wkh zdnh ri wkh Dujhqwlqh edqn uxq ri 4<<81 Lw wxuqv rxw vxfk d srolf| ri odujh lqwhuqdwlrqdo uhvhuyhv dovr holplqdwhv uxqv/ exw lv dovr lqh!flhqw1 Lq idfw/ zh vkrz wkdw qduurz edqnlqj grplqdwhv d srolf| ri odujh lqwhuqdwlrqdo uhvhuyhv1 8141 Qduurz Edqnlqj Wr dqdo|}h wkh lpsolfdwlrqv ri qduurz edqnlqj/ vxssrvh wkdw wkh Fhqwudo Edqn {hv wkh h{fkdqjh udwh dw rqh1 Dovr/ frpphufldo edqnv duh doorzhg wr eruurz shvrv lq shulrg 4 wr eh uhsdlg lq shulrg 5 dw qr lqwhuhvw1 Ilqdoo|/ lq rughu wr hqvxuh wkh vwdelolw| ri wkh qdqfldo v|vwhp/ frpphufldo edqnv duh frqvwudlqhg e| +814, %K 6< zklfk hqvxuhv wkdw wkh edqn*v wrwdo dprxqw ri ghpdqgdeoh ghew lv frpsohwho| edfnhg e| wkh zruog oltxlg dvvhw1 Wklv uhvwulfwlrq lv wkh fuxfldo glhuhqfh ehwzhhq wkh {hg h{fkdqjh udwh v|vwhp zlwk Fhqwudo Edqn fuhglw dqg d qduurz edqnlqj v|vwhp1 Jlyhq qduurz edqnlqj/ wkh frpphufldo edqn zloo fkrrvh dq doorfdwlrq wr pd{0 lpl}h 514 vxemhfw wr 614/ 71:/ 71</ 61</ wkh uhvhuyh uhtxluhphqw 814/ dqg +815, E b + E b n -& n dK b% E bo zklfk lv wkh vdph dv 71; h{fhsw iru wkh whup lq vtxduh eudfnhwv/ zklfk doorzv iru wkh srvvlelolw| wkdw wkh edqn pd| fkrrvh qrw wr vshqg lq shulrg 4 doo ri wkh grooduv rewdlqhg iurp oltxlgdwlqj wkh vkruw whup dvvhw1 Vroylqj wkh edqn*v sureohp lv d vwdqgdug h{huflvh1 Khuh zh zloo rqo| glvfxvv wkh uhohydqw dvshfwv ri wkh vroxwlrq/ zklfk zloo eh lghqwlhg zlwk dvwhulvnv1 Iluvw/ xqghu qduurz edqnlqj wkh edqn surylghv wkh vdwldwlrq ohyho ri shvrv wr sdwlhqw djhqwv/ wkdw lv/ ' 6 Wklv lv dv h{shfwhg/ ehfdxvh lq shulrg 4 W wkh pdujlqdo frvw ri shvrv wr wkh edqn lv }hur1 Krzhyhu/ lw fdq dovr eh vkrzq wkdw ' f/ wkdw lv/ wkdw Fhqwudo Edqn fuhglw lv qrw qhfhvvdu|1 Wkhvh idfwv gr W qrw frqwudglfw hdfk rwkhu ehfdxvh lw wxuqv rxw wkdw 71: +wkh uvw shulrg uhvrxufh 73 frqvwudlqw, lv qrw elqglqj= dw wkh rswlpxp/ wkh edqn*v kroglqjv ri wkh zruog oltxlg dvvhw duh pruh wkdq vx!flhqw wr qdqfh doo shulrg 4 zlwkgudzdov1 Lq rwkhu zrugv/ lq shulrg 4 wkh edqn kdv h{fhvv oltxlglw|/ zklfk lv ri frxuvh d frqvhtxhqfh ri wkh lpsrvlwlrq ri qduurz edqnlqj1 Rq wkh rwkhu kdqg/ wkh uhvhuyh uhtxluhphqw 814 lv vwulfwo| elqglqj dw wkh vrox0 wlrq1 Qrz rqh fdq xvh wkh edqn*v ihdvlelolw| frqvwudlqwv wr vkrz wkdw wkh rswlpxp ydoxhv % dqg + pxvw vdwlvi| W +816, W d- E bo % n E b+ ' eW W zklfk vkrxog eh wkrxjkw ri dv wkh wudqvirupdwlrq fxuyh lq d qduurz edqnlqj uhjlph1 Frpsdulqj 816 djdlqvw 718 pdnhv fohdu zk| qduurz edqnlqj lv frvwo|= wkh sulfh ri % xqghu qduurz edqnlqj lv - E bc zklfk lv odujhu wkdq b-c wkh sulfh ri % zkhq qduurz edqnlqj lv qrw lpsrvhg1 Lqwxlwlyho|/ wklv rffxuv ehfdxvh/ xqghu qduurz edqnlqj/ dq lqfuhdvh ri % ri/ vd|/ _%/ uhtxluhv lqfuhdvlqj K e| pruh wkdq b_%/ wkh glhuhqfh ehlqj dq lqfuhdvh lq uhtxluhg uhvhuyhv1 Wkh odvw rswlpdolw| frqglwlrq lv wkdw wkh vrfldo pdujlqdo udwh ri vxevwlwxwlrq 74 pxvw eh htxdo wr wkh pdujlqdo udwh ri wudqvirupdwlrq/ ru +817, b} E% - E b ' E b} dE6 n + o b W W Frpsdulvrqv zlwk wkh rswlpdo doorfdwlrq xqghu {hg h{fkdqjh udwhv duh qrz vwudljkwiruzdug1 Lw fdq eh vkrzq wkdw % W %7c zkloh + pd| eh juhdwhu ru ohvv W wkdq +7c ghshqglqj rq wkh uhodwlyh vwuhqjwk ri idploldu lqfrph dqg vxevwlwxwlrq hhfwv dvvrfldwhg zlwk wkh lqfuhdvh lq wkh sulfh ri % Wkh qduurz edqnlqj vroxwlrq fdq eh lpsohphqwhg dv d ghpdqg ghsrvlw v|vwhp/ dv ghvfulehg ehiruh1 Wkh uhvhuyh uhtxluhphqw 814 zrxog wkhq lpso| wkdw qhlwkhu edqn uxqv qru edodqfh ri sd|phqwv fulvhv fdq rffxu1 Krzhyhu/ wkh uhvxowlqj door0 fdwlrq lv qrw vrfldoo| rswlpdo19 Lq rwkhu zrugv/ frpsohwho| dyrlglqj edqn uxqv lv frvwo|= wkhuh lv qr iuhh oxqfk khuh1 8151 Odujh Uhvhuyh Uhtxluhphqwv Lqvwhdg ri iruflqj edqnv wr krog d odujh txdqwlw| ri wkh zruog oltxlg dvvhw/ vxssrvh wkdw wkh Fhqwudo Edqn exlogv d zdu fkhvw ri grooduv wr eh xvhg lq fdvh ri d edqn uxq1 Wr gr wklv/ lw lpsrvhv d oxps vxp wd{ ri A grooduv rq edqnv lq shulrg 31 Li 9 Wklv iroorzv iurp wkh idfw wkdw wkh edqn lv qrz vroylqj wkh vdph sureohp dv lq wkh {hg udwhv fdvh vwxglhg deryh/ exw zlwk wkh wljkwhu frqvwudlqw { e lqvwhdg ri { e1 75 wkhuh lv qr uxq/ lw uhwxuqv wkh A grooduv wr wkh edqnv lq shulrg 5 dv d oxps vxp wudqvihu1 Zh fdq wklqn ri wklv dv d vlwxdwlrq lq zklfk wkh jryhuqphqw xvhv vfdo dv rssrvhg wr prqhwdu| srolf| wr ghihqg wkh lqwhjulw| ri wkh edqnlqj v|vwhp1 Frqvlghu uvw wkh frpphufldo edqn*v sureohp1 Jlyhq wkh wd{0wudqvihu srolf| ri wkh Fhqwudo Edqn/ wkh frpphufldo edqn pxvw fkrrvh dq doorfdwlrq wr pd{lpl}h 514 vxemhfw wr +818, & n K e Ac wkh shulrg 4 frqvwudlqw 71:/ +819, E b + -& n A n E bc wkh uhvhuyh uhtxluhphqw 7143/ wkh qrqqhjdwlylw| frqvwudlqwv/ dqg lqfhqwlyh frp0 sdwlelolw|1 Wkh uhohydqw dvshfwv ri wkh vroxwlrq/ zklfk zloo eh lghqwlhg e| kdwv/ duh wkh iroorzlqj1 Iluvw/ wkh edqn surylghv wkh vdwldwlrq ohyho ri shvrv wr sdwlhqw djhqwv lq f ' 6 Wklv vkrxog eh reylrxv vlqfh wkh edqn*v frvw ri shvrv shulrg 4 wkdw lv/ ehwzhhq shulrgv 4 dqg 5 lv }hur1 76 Vhfrqg/ wkh rswlpdo fkrlfhv %e dqg +e pxvw vdwlvi| +81:, -b%e n E b+e ' e- E- A zklfk lv wkh edqn*v wudqvirupdwlrq fxuyh lq wklv fdvh1 Wkh odvw whup rq wkh UKV fdswxuhv wkh frvw iru wkh edqn ri wkh wd{0wudqvihu vfkhph/ exw wkh sulfhv ri % dqg + wkdw wkh edqn shufhlyhv duh wkh vdph dv zlwk d {hg h{fkdqjh udwh zlwk qr wd{hv1 Wkh odvw rswlpdolw| frqglwlrq qrz lv wkdw wkh vorsh ri wkh edqn*v remhfwlyh ixqfwlrq eh htxdwhg wr wkh vorsh ri lwv shufhlyhg wudqvirupdwlrq fxuyh= +81;, b} E%e -b ' E b } dE6 n +eo b Wkh uhvxowlqj doorfdwlrq fohduo| ghshqgv rq wkh vl}h ri wkh zdu fkhvw A Wr hqdeoh frpsdulvrq zlwk wkh qduurz edqnlqj fdvh/ frqvlghu wkh fdvh lq zklfk +81<, K n A ' %e vr wkdw wkh hfrqrp|*v oltxlg dvvhwv duh vx!flhqw wr edfn wkh wrwdo dprxqw ri ghpdqgdeoh ghew1 77 Fohduo|/ li 81< krogv/ wkh uhvxowlqj doorfdwlrq fdq eh ghfhqwudol}hg lq d ghpdqg ghsrvlw v|vwhp wkdw fdqqrw h{klelw htxloleulxp uxqv1 Krzhyhu/ wkh rxwfrph lv qrw wkh vdph dv zlwk qduurz edqnlqj1 Wr vhh wklv/ xvh 81< lq 81: wr rewdlq +8143, d- E bo%e n E b+e ' e- zklfk lv d vrfldo wudqvirupdwlrq fxuyh lq wklv fdvh1 Frpsdulqj 816 dqg 8143 lpsolhv wkdw wkh hfrqrp| idfhv wkh vdph vhw ri rswlrqv ehwzhhq % dqg + dv zlwk qduurz edqnlqj1 Krzhyhu/ 81; pxvw dovr krog1 Wklv lpsolhv wkdw/ lq wkh v|vwhp zlwk kljk lqwhuqdwlrqdo uhvhuyhv/ wkh vrfldo pdujlqdo udwh ri vxevwlwxwlrq ehwzhhq % dqg + lv qrw htxdwhg wr wkh vrfldo pdujlqdo udwh ri wudqvirupdwlrq dw E%ec +e 1 Wkh lqwxlwlrq lv fohdu= ehfdxvh wd{hv dqg wudqvihuv duh oxps vxp/ wkh edqn grhv qrw lqwhuqdol}h wkh lpsolflw frvw ri exloglqj wkh zdu fkhvw A 1 Wklv frvw h{lvwv ehfdxvh wkh Fhqwudo Edqn nhhsv doo ri A lq d oltxlg irup/ lqvwhdg ri lqyhvwlqj A rswlpdoo|1 Wkh glyhujhqfh ehwzhhq wkh vrfldo dqg sulydwh uhwxuqv wr lqyhvwphqw fuhdwhv d glvwruwlrq wkdw grhv qrw h{lvw xqghu qduurz edqnlqj1 Lq vkruw/ xvlqj vfdo srolf| wr hqvxuh wkdw qr edqn uxqv rffxu lv lqihulru wr xvlqj prqhwdu| lqvwuxphqwv vxfk dv uhvhuyh uhtxluhphqwv1 78 91 Ioh{leoh H{fkdqjh Udwhv Xs wr wklv srlqw zh kdyh dvvxphg wkdw wkh Fhqwudo Edqn kdv d srolf| ri ghihqglqj wkh h{fkdqjh udwh xqwlo lw lv qr orqjhu ihdvleoh1 Lq wklv vhfwlrq zh vkdoo gurs vxfk dvvxpswlrq dqg dqdo|}h d h{leoh udwh v|vwhp1 Rxu pdlq uhvxow lv wkdw h{leoh udwhv uhvxow lq wkh lpsohphqwdwlrq ri wkh vrfldo rswlpxp1 Pruhryhu/ wkh srvvlelolw| ri d ghydoxdwlrq lpsolhv wkdw wkhuh duh qr htxloleulxp uxqv1 9141 Ioh{leoh Udwhv Zlwk d Ohqghu ri Odvw Uhvruw Zh vkdoo irfxv rq wkh txhvwlrq ri krz wkh vrfldo rswlpxp wkdw lv/ wkh vroxwlrq wr S5 fdq eh lpsohphqwhg e| d ghpdqg ghsrvlw v|vwhp1 Wr h{dplqh wklv lvvxh/ zh vkdoo uhwdlq doo ri wkh dvvxpswlrqv ri wkh fdvh ri {hg udwhv zlwk d ohqghu ri odvw uhvruw/ h{fhsw wkdw wkh Fhqwudo Edqn lv qr orqjhu frpplwwhg wr vhoolqj grooduv wr ghsrvlwruv dw d {hg h{fkdqjh udwh ri rqh iru dv orqj dv wklv lv srvvleoh1 Lqvwhdg/ zh zloo dvvxph wkdw wkh Fhqwudo Edqn doorzv h{fkdqjh udwhv wr fkdqjh dffruglqj wr qdqfldo hyhqwv1 Frqvlghu wkh iroorzlqj phfkdqlvp1 Wkh frpphufldo edqn dqg ghsrvlwruv djuhh rq wkh vdph frqwudfw dv xqghu {hg udwhv1 Zkhq shulrg 4 ehjlqv/ ghsrvlwruv duulyh 7 shvrv1 wr wkh frpphufldo edqn lq vhtxhqfh/ dqg hdfk zlwkgudzv hlwkhu % 7 ru 7 shvrv e| eruurzlqj iurp wkh Wkh frpphufldo edqn vhuylfhv zlwkgudzdov ri 79 Fhqwudo Edqn> zlwkgudzdov ri % 7 shvrv duh qdqfhg e| uvw oltxlgdwlqj wkh zruog oltxlg dvvhw dqg vhoolqj wkh groodu surfhhgv wr wkh Fhqwudo Edqn dw dq h{fkdqjh udwh ri rqh/ dqg wkhq e| eruurzlqj iurp wkh Fhqwudo Edqn1 Diwhu doo ghsrvlwruv kdyh ylvlwhg wkh frpphufldo edqn/ wkh Fhqwudo Edqn vhoov grooduv wr ghsrvlwruv dw dq h{fkdqjh udwh htxdo wr . ' @%iEbo *bc j zkhuh bo ghqrwhv wkh iudfwlrq ri djhqwv uhsruwlqj lpsdwlhqfh1 Khqfh/ li bo : b wkhuh zloo eh d ghydoxdwlrq1 Wklv ghydoxdwlrq uxoh fdq eh lqwhusuhwhg lq rqh ri wzr htxlydohqw zd|v1 Wkh uvw lv wkdw wkh Fhqwudo Edqn/ diwhu revhuylqj wkh dfwxdo sdwwhuq ri zlwkgudzdov dw wkh frpphufldo edqn/ dqqrxqfhv d ghydoxdwlrq1 Wklv uxoh lv frqvlvwhqw zlwk wkh h{lvwhqfh ri d vhtxhqwldo vhuylfh frqvwudlqwv dw wkh Fhqwudo Edqn/ vlqfh lw zloo eh vhhq wkdw wkh ghydoxdwlrq lv vxfk wkdw wkh Fhqwudo Edqn zloo qrw uxq rxw ri grooduv1 D vhfrqg lqwhusuhwdwlrq/ shukdsv pruh dsshdolqj/ lv wkdw wkh Fhqwudo Edqn grhv qrw { wkh h{fkdqjh udwh/ exw wkhuh lv qr vhtxhqwldo vhuylfh dw wkh Fhqwudo Edqn1 Lqvwhdg/ wkh h{fkdqjh udwh lv ghwhuplqhg e| dq dxfwlrq1 Lq wkh dxfwlrq/ wkh Fhqwudo Edqn rhuv wkh grooduv rewdlqhg iurp wkh frpphufldo edqn/ dqg hdfk ri wkh E bo ghsrvlwruv wkdw uhsruwhg lpsdwlhqfh rhuv wkh % 7 shvrv zlwkgudzq iurp wkh frpphufldo edqn1 Wkh ghydoxdwlrq uxoh lpsolhv wkdw hdfk djhqw wkdw uhsruwhgo| lpsdwlhqw djhqwv uhfhlyhv % 7*. grooduv lq wkh uvw shulrg/ zklfk fdq eh xvhg iru sxufkdvlqj frq0 7: vxpswlrq lq wkh zruog pdunhw1 Lq shulrg 5 wkh edqn oltxlgdwhv wkh orqj whup dvvhw dqg vhoov wkh uhvxowlqj -&7 grooduv wr wkh Fhqwudo Edqn dw dq h{fkdqjh udwh ri ' shvrv shu groodu1 Khuh ' ' ndEbo b7 %o*-&7 dqg/ wkhuhiruh/ lw pd| ghshqg rq zkdw kdsshqhg lq shulrg 4> wkh uhdvrq iru wklv ghydoxdwlrq uxoh zloo eh glvfxvvhg vkruwo|1 Wkh frpphufldo edqn wkhq uhsd|v lwv ghew wr wkh Fhqwudo Edqn dqg glvwulexwhv lwv uhpdlqlqj shvrv wr wkh E bo djhqwv wkdw uhsruwhg sdwlhqfh lq shulrg 41 Ilqdoo|/ wkhvh djhqwv xvh wkhlu shvrv wr sxufkdvh grooduv iurp wkh Fhqwudo Edqn dw dq h{fkdqjh udwh .2 ghwhuplqhg lq dq dxfwlrq1 Jlyhq wklv surfhgxuh/ lw fdq eh suryhq wkdw wkh rswlpdo doorfdwlrq lv dq htxl0 oleulxp= Sursrvlwlrq 9141 Wkhuh lv dq krqhvw htxloleulxp zkrvh rxwfrph lv wkh vroxwlrq wr S51 Lq wklv htxloleulxp wkh h{fkdqjh udwh lv rqh dw doo wlphv1 Surri1 Vxssrvh doo djhqwv uhsruw wkhlu w|shv krqhvwo|1 Wkhq bo ' b/ dqg khqfh . ' ' ' Lw fdq eh vkrzq wkdw lq shulrg 5 wkh frpphufldo edqn glvwulexwhv h{dfwo| -&7 shvrv wr wkh sdwlhqw ghsrvlwruv1 Vlqfh lq shulrg 5 wkh Fhqwudo Edqn vhoov wkh -&7 grooduv rewdlqhg iurp wkh edqn/ wkh h{fkdqjh udwh dw zklfk wkrvh grooduv duh vrog pxvw dovr eh rqh1 7; Wkh uhvw ri wkh surri iroorzv suhylrxv dujxphqwv dqg lv ohiw wr wkh uhdghu1 Wkh Sursrvlwlrq pdnhv fohdu wkdw wklv uhjlph pd| lpsohphqw wkh vrfldo rs0 wlpxp1 Lq dgglwlrq/ li wklv htxloleulxp suhydlov/ wkh rxwfrph lv wkh vdph dv lq krqhvw htxloleuld zlwk {hg udwhv1 Lq vslwh ri wkh htxlydohqfh ri wkhlu krqhvw rxwfrphv/ h{leoh udwhv dqg {hg udwhv duh udwkhu glhuhqw= xqghu wkh sursrvhg h{leoh udwh uhjlph/ wkh srvvlelolw| ri d shvr ghydoxdwlrq holplqdwhv wkh lqfhqwlyhv iru dq| uxqv= Sursrvlwlrq 9151 Uxqv fdqqrw rffxu lq htxloleulxp1 Surri1 Fohduo|/ li d uxq lv wr rffxu/ bo pxvw eh juhdwhu wkdq b Zh zloo vkrz wkdw wklv lpsolhv wkdw o|lqj lv qrw rswlpdo iru sdwlhqw ghsrvlwruv1 Jlyhq wkh uxohv lq wklv uhjlph/ qhlwkhu wkh edqn qru wkh Fhqwudo Edqn idlov lq dq| shulrg1 Qrz/ ' kdv ehhq ghqhg vr wkdw .2 lv h{dfwo| rqh1 Wr vhh wklv/ qrwh wkdw lq shulrg 5 wkh ghew ri wkh frpphufldo edqn wr wkh Fhqwudo Edqn lv 7 Khqfh wkh frpphufldo edqn glvwulexwhv '-&7 Ebo Ebo b7 % n E bo 1 7 wr E bo ghsrvlwruv/ hdfk ri zklfk duulyhv wr shulrg 5 zlwk b7 % E bo 7 shvrv1 Dv d frqvhtxhqfh/ ghsrvlwruv jr wr wkh Fhqwudo Edqn zlwk d wrwdo ri '-&7 Ebo b7 % shvrv wr ex| -&7 grooduv1 Wkh ghqlwlrq ri ' hqvxuhv wkdw wkhvh wzr txdqwlwlhv duh htxdo/ dqg khqfh .2 ' 7< Li d sdwlhqw ghsrvlwru olhv/ vkh jhwv % 7*. ' b7 %*bo % 7 xqlwv ri frqvxpswlrq1 7 shvrv lq shulrg 4/ zkrvh uhdo ydoxh lv 6 vlqfh Li vkh whoov wkh wuxwk/ vkh jhwv .2 ' Lq dgglwlrq/ lq shulrg 5 khu frqvxpswlrq zloo eh dw ohdvw +7/ dv lpsolhv e| o o 7 7 wkh iroorzlqj dujxphqw1 Vlqfh vkh zloo uhfhlyh d'-&Eb b7 %Ebo o*Eb iurp wkh edqn/ khu frqvxpswlrq zloo htxdo wr d'-&7 Ebo b7 %o*E bo shvrv1 7 Wklv lv htxdo wr -&*E bo c jlyhq .2 ' dqg wkh ghqlwlrq ri '1 Vlqfh bo : bc o 7 7 -&*Eb : -&*Eb ' +7 Vlqfh b7 %*bo % 7 7 + En7 o 7 7 En&*Eb c d sdwlhqw djhqw kdv qr lqfhqwlyh wr olh derxw khu w|sh1 Wkh surri lv frpsohwh1 Wkh lqwxlwlrq iru wkh vxffhvv ri wkh h{leoh h{fkdqjh udwh uhjlph lq suhyhqwlqj uxqv lv wkdw wkh ghydoxdwlrq0ohqglqj srolf| ri wkh Fhqwudo Edqn jxdudqwhhv wkdw sdwlhqw djhqwv zloo froohfw wkhlu surplvhg frqvxpswlrq dqg hqmr| wkh vdwldwlrq ohyho ri prqh| li wkh| ehkdyh krqhvwo|1 Wklv jxdudqwhh lv ihdvleoh/ lq sduwlfxodu/ ehfdxvh lq d uxq wkh qrplqdo fodlpv ri ghsrvlwruv uhsruwlqj lpsdwlhqfh lq wkh uvw shulrg duh gh dwhg e| d ghydoxdwlrq/ zklfk pdnhv lw xqqhfhvvdu| wr oltxlgdwh wkh orqj whup dvvhw1 Khqfh/ wkh srvvlelolw| ri ghydoxdwlrq dfwv dv d frruglqdwlrq ghylfh wkdw holplqdwhv uxqv dqg uhqghuv dfwxdo ghydoxdwlrq qrw dq htxloleulxp skhqrphqrq1 83 9151 Glvfxvvlrq Iurp wkh dqdo|vlv lw vkrxog eh dssduhqw wkdw/ wr eh vxffhvvixo/ d h{leoh udwh v|vwhp pxvw eh frxsohg zlwk dq dssursuldwh Fhqwudo Edqn srolf|1 Wklv srolf| lqfoxghv dfwlqj dv d ohqghu ri odvw uhvruw dqg vhohfwlqj h{fkdqjh udwhv dssursuldwho|1 Dv lq wkh {hg udwh fdvh/ wkh Fhqwudo Edqn dfwv dv d ohqghu ri odvw uhvruw vlqfh lw ohqgv shvrv wr wkh frpphufldo edqn lq d uxq1 Li wkdw lv qrw wkh fdvh/ uxqv pd| vwloo rffxu1 Iru h{dpsoh/ li wkh Fhqwudo Edqn rqo| doorzv wkh edqn wr eruurz 7 lq wkh uvw shulrg wr vdwlvi| wkh zlwkgudzdov ri krqhvw sdwlhqw djhqwv/ E b wkhuh lv dq htxloleulxp lq zklfk wkh frpphufldo edqn idlov1 +Zh ohdyh wkh ghwdlov wr wkh uhdghu1, Wklv uhvxow lv ri vrph lqwhuhvw/ ehfdxvh lw phdqv wkdw h{leoh udwhv dqg Fhqwudo Edqn ohqglqj duh qrw vx!flhqw wr suhyhqw edqn uxqv= wkh ohqglqj srolf| ri wkh Fhqwudo qhhgv wr eh fduhixoo| ghvljqhg1 Wkhuh lv vrph odwlwxgh lq ghvljqlqj wkh ghydoxdwlrq srolf| wr hqvxuh wkh suh0 yhqwlrq ri uxqv1 Wkhuh duh frqvwudlqwv/ wkrxjk1 Rqh lv wkdw wkh ghydoxdwlrq srolf| vkrxog gholyhu wr sdwlhqw djhqwv +dorqj dq rxw ri htxloleulxp wudmhfwru|, d ohyho ri uhdo shvr kroglqjv forvh wr wkh vdwldwlrq ohyho1: Wklv lv qhfhvvdu| wr hqvxuh wkdw sdwlhqw djhqwv gr qrw surw iurp sduwlflsdwlqj lq d uxq1 Wkh ghydoxdwlrq : Wklv lv qrw dq lvvxh lq wkh ghydoxdwlrq srolf| wkdw zh frqvlghu/ iru wkh sulfh ohyho +dqg wkh h{fkdqjh udwh, lv dozd|v rqh lq shulrg 51 84 srolf| ghvfulehg lq wkh suhylrxv vxevhfwlrq lv rqh ri wkh pdq| srvvlelolwlhv wkdw dffrpsolvk wkdw jrdo1; :1 Groodul}lqj wkh Edqnlqj V|vwhp Edqn dffrxqwv ghqrplqdwhg lq iruhljq fxuuhqf| +h1j1 grooduv, duh d frpprq dqg frqwuryhuvldo ihdwxuh ri pdq| frxqwulhv* qdqfldo v|vwhpv1 Vrph revhuyhuv ylhz wkhp dv dq luuhsodfhdeoh phfkdqlvp wr pdnh ghsrvlwv dwwudfwlyh lq frxqwulhv zlwk orqj klvwrulhv ri fxuuhqf| lqvwdelolw|1 Rwkhuv/ vxfk dv Vdfkv ^;`/ vwuhvv wkdw Fhqwudo Edqnv fdqqrw sulqw grooduv/ dqg khqfh fdqqrw vhuyh dv d ohqghu ri odvw uhvruw wr edfn vxfk ghsrvlwv> lq wklv ylhz/ wkhq/ wkh groodul}dwlrq ri ghsrvlwv frqwulexwhv wr wkh srwhqwldo lqvwdelolw| ri wkh edqnlqj v|vwhp1 Wkh iudphzrun ri wklv sdshu lv shuihfwo| vxlwhg wr dqdo|}h vxfk frq lfwlqj fodlpv1 Lw lv vwudljkwiruzdug wr vhh wkdw wkh dqdo|vlv ri d fxuuhqf| erdug uhjlph lq Vhfwlrq 6 lv xqfkdqjhg li ghsrvlwv duh ghqrplqdwhg lq grooduv lqvwhdg ri shvrv1 Wkh rqo| phfkdqlfdo glhuhqfh lv wkdw wkh frpphufldo edqn/ lqvwhdg ri vhoolqj wkh surfhhgv ri erwk nlqgv ri lqyhvwphqw dw wkh Fhqwudo Edqn dqg xvlqj wkh uhvxowlqj ; Khuh lv dq dowhuqdwlyh ghydoxdwlrq srolf|/ dvvxplqj wkdw | {= Lq shulrg 5/ wkh Fhqwudo Edqn vhoov shvrv wr wkh edqn dw dq h{fkdqjh udwh ri rqh/ dqg odwhu sodfhv rqo| Un +u ,{ grooduv iru vdoh wr uhsruwhgo| sdwlhqw ghsrvlwruv1 Vlqfh wkh odwwhu zloo duulyh wr wkh dxfwlrq zlwk Un +u ,{ shvrv/ s5 zloo eh rqh1 Lw fdq dovr eh vkrzq wkdw/ li | {/ hdfk sdwlhqw ghsrvlwru zloo frqvxph dw ohdvw | = Khqfh sdwlhqw w|shv zloo qrw olh1 85 shvrv wr sd| r ghsrvlwruv/ phhwv zlwkgudzdov gluhfwo| zlwk grooduv1 Khqfh/ wkh vroxwlrq wr sureohp S4 lv wkh vdph dv ehiruh/ dqg vr duh wkh srvvleoh uhdo doorfd0 wlrqv= wkh krqhvw htxloleulxp uhpdlqv ihdvleoh/ dqg vr grhv wkh uxq htxloleulxp li sdudphwhuv duh vxfk wkdw wkh v|vwhp lv vx!flhqwo| looltxlg lqwhuqdwlrqdoo|1 Zh wkhuhiruh kdyh= Sursrvlwlrq :141 Lq d fxuuhqf| erdug v|vwhp lq zklfk ghsrvlwv duh ghqrplqdwhg lq iruhljq fxuuhqf|/ wkhuh lv dq krqhvw htxloleulxp/ dqg wkhuh lv d edqn uxq htxl0 oleulxp li dqg rqo| li frqglwlrq 6148 lv vdwlvhg1 Surri1 Vdph dv lq Sursrvlwlrqv 614 dqg 6151 Frqvlghu qrz zkdw kdsshqv li wkh Fhqwudo Edqn h{whqgv fuhglw wr wkh frp0 phufldo edqn1 Li vxfk fuhglw lv olplwhg dv lq vhfwlrqv 714 wr 716/ wkh dqdo|vlv dovr uhpdlqv hvvhqwldoo| xqfkdqjhg1 Li ghsrvlwv duh lq grooduv dqg shvrv duh rqo| sulqwhg wr vdwlvi| prqh| ghpdqg e| sdwlhqw ghsrvlwruv/ wkh phfkdqlfv ri groodu edqn wudqvdfwlrqv duh wkh vdph dv lq wkh fxuuhqf| erdug fdvh mxvw dqdo|}hg1 Lq dgglwlrq/ wkh vroxwlrq wr S5 lv xqfkdqjhg/ dqg vr duh wkh srvvleoh htxloleulxp doorfdwlrqv= wkh krqhvw htxloleulxp lv dozd|v ihdvleoh/ dqg htxloleulxp edqn uxqv fdq rffxu li wkh v|vwhp lv vx!flhqwo| looltxlg lqwhuqdwlrqdoo|1 Zh wkhuhiruh kdyh= Sursrvlwlrq :151 Lq d {hg h{fkdqjh udwh v|vwhp zlwk olplwhg grphvwlf fuhglw/ 86 li ghsrvlwv duh ghqrplqdwhg lq iruhljq fxuuhqf| wkhuh lv dq krqhvw htxloleulxp/ dqg wkhuh lv d edqn uxq htxloleulxp li dqg rqo| li frqglwlrq 7144 lv vdwlvhg1 Surri1 Vdph dv lq Sursrvlwlrqv 714 dqg 7151 Zh frqfoxgh wkdw= Fruroodu| :161 Lq d fxuuhqf| erdug dqg lq d {hg h{fkdqjh udwh v|vwhp zlwk olplwhg grphvwlf fuhglw/ wkh frqglwlrqv xqghu zklfk krqhvw dqg uxq htxloleuld rffxu duh wkh vdph uhjdugohvv ri wkh fxuuhqf| lq zklfk ghsrvlwv duh ghqrplqdwhg1 Wkh glhuhqfh wkdw groodu ghsrvlwv pdnh ehfrphv fohdu zkhq zh frqvlghu wkh Fhqwudo Edqn*v srwhqwldo uroh dv ohqghu ri odvw uhvruw1 Lq wkh hyhqw ri d edqn uxq/ wkh frpphufldo edqn zloo oltxlgdwh K dqg wkhq &/ exw dw qr srlqw zloo dq| ri wkh uhvxowlqj grooduv jr wkurxjk wkh Fhqwudo Edqn1 Khqfh/ wkh prqhwdu| dxwkrulw| kdv qr grooduv lq lwv ydxow zlwk zklfk wr vhuyh dv ohqghu ri odvw uhvruw1 Lq dgglwlrq/ lw fdqqrw sulqw shvrv dqg vhoo wkhp wr wkh sxeolf lq h{fkdqjh iru grooduv/ iru lq wkh hyhqw ri d uxq doo ghsrvlwruv ghfoduh wkhpvhoyhv wr eh lpsdwlhqw/ dqg lpsdwlhqw djhqwv kdyh }hur ghpdqg iru shvrv1 Zh frqfoxgh wkdw wkhuh lv qrwklqj wkh Fhqwudo Edqn wr vwrs wkh uxq/ dqg vxfk uxqv fdq rffxu lq htxloleulxp li wkh uhohydqw frqglwlrqv duh vdwlvhg1 Qrwlfh/ ixuwkhupruh/ wkdw edqn uxqv rffxu uhjdugohvv ri wkh h{fkdqjh udwh 87 uhjlph wkdw lv lq sodfh1 Wklv lv ehfdxvh lw lv qrw h{leoh h{fkdjh udwhv shu vh wkdw zhuh deoh wr uxoh rxw uxqv lq Vhfwlrq 9 deryh/ exw wkh frxsolqj ri h{fkdqjh udwh h{lelolw| zlwk d ohqghu ri odvw uhvruw1 Vlqfh vxfk d ohqghu fdqqrw h{lvw li ghsrvlwv duh groodul}hg/ wkh ehqhfldo hhfwv ri rdwlqj ydqlvk1 Wklv uhvxow jlyhv fuhghqfh wr wkh frqfhuqv wkdw groodul}dwlrq ri wkh edqnlqj v|vwhp*v oldelolwlhv fdq eh ghvwdelol}lqj1 ;1 Vxppdu| dqg Frqfoxvlrqv Wklv sdshu surylghv d ghwdlohg dqg irupdo dffrxqw ri wkh srvvleoh lqwhudfwlrqv ehwzhhq edqn iudjlolw| dqg wkh h{fkdqjh udwh dqg prqhwdu| uhjlphv1 Lq d zruog lq zklfk edqnv sod| d zhoo ghqhg plfurhfrqrplf uroh/ zh vkrz wkdw glhuhqw vxfk uhjlphv lqgxfh glhuhqw uhdo frqvxpswlrq doorfdwlrqv/ dqg fdq dovr olplw qdqfldo iudjlolw| wr zlgho| ydu|lqj ghjuhhv1 Lq sduwlfxodu/ zh qg wkdw d h{leoh h{fkdqjh udwh v|vwhp/ frxsohg zlwk d srolf| e| wkh fhqwudo edqn wr vhuyh dv ohqghu ri odvw uhvruw wr frpphufldo edqnv/ fdq erwk lpsohphqw wkh uvw ehvw doorfdwlrq dqg holplqdwh vhoi0ixooolqj edqn uxqv1 88 Uhihuhqfhv ^4` J1 Fdoyr/ Frphqw rq Vdfkv/ Wruqhoo dqg Yhodvfr/ Eurrnlqjv Sdshuv rq Hfrqrplf Dfwlylw|/ Qr1 4/ 4<<91 ^5` G1 Gldprqg dqg S1 G|eylj/ Edqn Uxqv/ Ghsrvlw Lqvxudqfh/ dqg Oltxlglw|/ M1 Srolw1 Hfrqrp|/ <4/ 4<;6/ 734074<1 ^6` J1 Ndplqvn| dqg F1 Uhlqkduw/ Wkh Wzlq Fulvhv= Wkh Fdxvhv ri Edqnlqj dqg Edodqfh ri Sd|phqwv Sureohpv/ Lqwhuqdwlrqdo Ilqdqfh Glvfxvvlrq Sdshu Qr1 877/ Erdug ri Jryhuqruv ri wkh Ihghudo Uhvhuyh V|vwhp/ Pdufk 4<<91 ^7` S1 Nuxjpdq/ D Prgho ri Edodqfh ri Sd|phqwv Fulvhv/ Mrxuqdo ri Prqh|/ Fuhglw dqg Edqnlqj/ 4<:<1 ^8` P1 Iulhgpdq/ Hvvd|v lq Srvlwlyh Hfrqrplfv/ Xqlyhuvlw| ri Fklfdjr Suhvv/ Fklfdjr LO/ 4<861 ^9` U1 P|huvrq/ Jdph Wkhru|/ Kduydug Xqlyhuvlw| Suhvv/ Fdpeulgjh/ PD/ 4<<41 ^:` G1 Vfkphlgohu/ Htxloleulxp Srlqwv ri Qrqdwrplf Jdphv/ Mrxuqdo ri Vwd0 wlvwlfdo Sk|vlfv/ 7/ 4<:6/ 5<806331 89 ^;` M1 Vdfkv/ Dowhuqdwlyh Dssurdfkhv wr Ilqdqfldo Fulvhv lq Hphujlqj Pdunhwv/ Ghyhorsphqw Glvfxvvlrq Sdshu Qr1 89;/ Kduydug Lqvwlwxwh iru Lqwhuqdwlrqdo Ghyhorsphqw/ Mdqxdu| 4<<:1 ^<` M1 Vdfkv/ D1 Wruqhoo dqg D1 Yhodvfr/ Ilqdqfldo Fulvhv lq Hphujlqj Pdunhwv= Wkh Ohvvrqv iurp 4<<8/ Eurrnlqjv Sdshuv rq Hfrqrplf Dfwlylw|/ Qr1 4/ 4<<9 ^43` Q1 Zdoodfh/ Qduurz Edqnlqj Phhwv wkh Gldprqj0G|eylj Prgho/ Ihghudo Uhvhuyh Edqn ri Plqqhdsrolv Txduwhuo| Uhylhz/ Zlqwhu 4<<9/ 60461 8: