WORKING PAPER NO. 184
EFFICIENT PRICING OF
LARGE VALUE INTERBANK
PAYMENT SYSTEMS
BY CORNELIA HOLTHAUSEN
AND JEAN-CHARLES ROCHET
October 2002
E U R O P E A N C E N T R A L B A N K
WORKING PAPER SERIES
CORE Metadata, citation and similar papers at core.ac.uk
WORKING PAPER NO. 184
EFFICIENT PRICING OF
LARGE VALUE INTERBANK
PAYMENT SYSTEMS
1BY CORNELIA HOLTHAUSEN
2AND JEAN-CHARLES ROCHET
3October 2002
1 We are grateful to Charles Goodhart, Diana Hancock, Tom Kokkola, Jamie McAndrews, Dieter Reichwein, Juha Tarkka, and seminar participants at Toulouse University, the Bank of England, the European Central Bank, the Danish National Bank, the Finnish Central Bank,
E U R O P E A N C E N T R A L B A N K
© European Central Bank, 2002
Address Kaiserstrasse 29
D-60311 Frankfurt am Main Germany
Postal address Postfach 16 03 19
D-60066 Frankfurt am Main Germany Telephone +49 69 1344 0 Internet http://www.ecb.int Fax +49 69 1344 6000 Telex 411 144 ecb d
All rights reserved.
Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged. The views expressed in this paper do not necessarily reflect those of the European Central Bank.
Contents
Abstract 4
Non-technical summary 5
1 Introduction 7
2 The model 9
3 Optimal pricing for a monopoly LVPS 11
3.1 Discrete distribution of types 11
3.2 Continuous distribution of types 13
4 Optimal pricing in a mixed duopoly 15
5 Competition between national RTGSs 19
5.1 Efficient pricing with by-passing 20
5.2 By-passing is deterred 21
6 Concluding remarks 23
Appendix: proofs 24
References 29
Devwudfw
Wklv sdshu vwxglhv wkh h!flhqw sulflqj ri odujh0ydoxh sd|phqw v|vwhpv lq wkh suhvhqfh ri xqrevhuydeoh khwhurjhqhlw| derxw edqnv* ixwxuh sd|phqw yroxphv1 Lw lv vkrzq wkdw wkh rswlpdo sulflqj vfkhph iru d sxeolf prqrsro| v|vwhp lqyroyhv txdqwlw| glvfrxqwv lq wkh irup ri d ghfuhdvlqj pdujlqdo ihh1 Wklv lv dovr wuxh zkhq wkh sxeolf v|vwhp frpshwhv zlwk d sulydwh v|vwhp fkdudfwhul}hg e| d orzhu pdujlqdo frvw1 Krzhyhu lq wklv fdvh/rswlpdo pdujlqdo ihhv lq wkh sxeolf v|vwhp duh orzhu wkdq lwv pdujlqdo frvw/dqg {hg ihhv kdyh wr eh ohylhg1 Zh dovr vwxg| wkh fdvh ri frpshwlwlrq ehwzhhq vhyhudo sxeolf v|vwhpv1 Wkh vwuxfwxuh ri wkh rswlpdo wdul ghshqgv rq wkh zloolqjqhvv ri Fhqwudo Edqnv wr doorz e|0sdvv1
MHO Frghv= J5;/H8;/G75/G76
Qrq0Whfkqlfdo Vxppdu|
Odujh0ydoxh sd|phqw v|vwhpv duh fkdudfwhul}hg e| odujh hfrqrplhv ri vfdoh= lq rughu wr surylgh sd|phqw vhuylfhv/odujh {hg frvw dulvh uhodwhg wr wkh vhwwlqj0xs dqg pdlqwdlqh0 qdqfh ri wkh v|vwhp1 Frqwudulo|/hdfk lqglylgxdo sd|phqw jhqhudwhv yhu| vpdoo frvwv1 Vxfk vfdoh hfrqrplhv suhvhqw d sureohp iru h!flhqw sulflqj1 Vwdqgdug hfrqrplf wkhru| uhtxluhv wkdw wkh sulfh ri hdfk xqlw sxufkdvhg vkrxog htxdo lwv pdujlqdo frvw +pdujlqdo frvw sulflqj,1 Lq wkh suhvhqfh ri {hg frvw/krzhyhu/pdujlqdo frvw sulflqj zrxog fuhdwh d ghflw ehfdxvh wkh {hg frvw frxog qrw eh uhfryhuhg1 Wkhuhiruh/li frvw uhfryhu| lv d uhtxluhphqw/d glhuhqw sulflqj uxoh qhhgv wr eh irxqg1 Wkh jrdo ri wklv sdshu lv wr qg wkh rswlpdo/zhoiduh0pd{lpl}lqj sulflqj uxoh iru d odujh0ydoxh sd|phqw v|vwhp1
Wkhuh duh vhyhudo srvvlelolwlhv iru sulflqj vfkhphv wkdw dfklhyh frvw uhfryhu|1 Wkh uvw zrxog eh d vlpsoh olqhdu wdul/lq zklfk hdfk sd|phqw lv sulfhg dw wkh dyhudjh frvw1 Wkdw lv/wkh {hg frvw zrxog eh glylghg dqg vsolw dprqj wkh wrwdo qxpehu ri sd|phqwv pdgh1 Wkh gudzedfn ri vxfk d vfkhph lv wkdw iru kljk {hg frvwv/wkh pdujlqdo ihh zrxog qhhg wr eh vxevwdqwldoo| deryh wkh pdujlqdo frvw1 Wklv zrxog glvfrxudjh edqnv wr xqghuwdnh d odujh qxpehu ri sd|phqwv1 Exw zlwk d orz sd|phqw yroxph/lw zloo eh hyhq pruh gl!fxow wr uhfryhu frvwv1 D vhfrqg srvvlelolw| lv wr dsso| d {hg ihh rqo|/dqg qr fkdujh rq hdfk lqglylgxdo sd|phqw1 Wklv wdul kdv wkh dgydqwdjh ri ehlqj yhu| vlpsoh/dqg ri |lhoglqj d kljk sd|phqw yroxph iru edqnv zkr sduwlflsdwh lq wkh v|vwhp1 Krzhyhu/lw pd| eh srolw0 lfdoo| xqghvludeoh/dqg lw zloo glvfrxudjh edqnv zlwk d orz h{shfwhg yroxph ri sd|phqwv wr sduwlflsdwh lq wkh v|vwhp1
D ehwwhu vroxwlrq pljkw eh wr ghvljq d sulflqj vfkhph wkdw frpelqhv wkh dgydqwdjhv ri wkhvh dowhuqdwlyhv1 Wklv fdq eh dfklhyhg e| kdylqj d sulflqj vfkhph lq zklfk pdujlqdo ihhv ydu| zlwk wkh sd|phqw yroxph ri hdfk lqglylgxdo edqn1 Vxfk d qrq0olqhdu sulflqj vfkhph frxog/lq lwv vlpsohvw irup/wdnh wkh irup ri d wzr0sduw wdul/l1h1 d frpelqdwlrq ri d {hg ihh dqg d frqvwdqw pdujlqdo ihh1 D pruh dgydqfhg vfkhph frxog frqvlvw ri d eorfn wdul/ru ri d phqx ri wzr0sduw wdulv1 Lqghhg/wklv sdshu vkrzv wkdw h!flhqf| jhqhudoo| uhtxluhv wkdw pdujlqdo ihhv ghfuhdvh zlwk wkh sd|phqw yroxph ri hdfk v|vwhp sduwlflsdqw1 Lq wklv zd|/d kljk {hg ihh lv dyrlghg/dqg dw wkh vdph wlph/edqnv zlwk d odujh sd|phqw ghpdqg zloo qrw eh glvfrxudjhg iurp urxwlqj wkhvh sd|phqwv wkurxjk wkh v|vwhp1
Wkh sdshu vwduwv iurp d vlwxdwlrq lq zklfk wkhuh lv rqo| rqh sxeolf odujh ydoxh sd|phqw v|vwhp1 Wkh ihh vwuxfwxuh lv fkrvhq zlwk wkh dlp wr pd{lpl}h wkh djjuhjdwh zhoiduh ri wkh v|vwhp sduwlflsdqwv/xqghu wkh frqvwudlqw wkdw wkh sd|phqw v|vwhp euhdnv hyhq1 Lw lv vkrzq wkdw wkh rswlpdo wdul lpsolhv wkdw orz sd|phqw yroxphv duh sulfhg deryh pdujlqdo frvw/wkh kljkhu yroxphv duh sulfhg dw pdujlqdo frvw/dqg wkdw wkhuh lv qr {hg ihh1 Wkh rswlpdo glvwruwlrq ri orzhu sd|phqw yroxphv/l1h1 lwv glyhujhqfh iurp pdujlqdo frvw sulflqj/uhvxowv iurp wkh iroorzlqj wudgh0r= rq wkh rqh kdqg/d orz glvwruwlrq lv pruh h!flhqw dqg hqfrxudjhv d kljk sd|phqw yroxph1 Rq wkh rwkhu kdqg/d kljk glvwruwlrq/ l1h1 d kljk pdujlqdo sulfh/pdnhv frvw uhfryhu| hdvlhu1
Lq wkh uhpdlqlqj sduw ri wkh sdshu/d gxrsro| vlwxdwlrq lv vwxglhg lq zklfk d sxeolf sd|phqw v|vwhp frh{lvwv zlwk dqrwkhu v|vwhp1 Iluvw/zh dvvxph wkdw wkh sxeolf v|vwhp frpshwhv zlwk d sulydwh qrq0surw sd|phqw v|vwhp1 Khuh/lw lv dvvxphg wkdw wkh sulydwh v|vwhp kdv orzhu pdujlqdo frvwv dqg lv wkhuhiruh deoh wr dwwudfw wkrvh edqnv zlwk wkh kljkhvw sd|phqw yroxph1 Wkhq/zh wdnh wkh fdvh ri wzr qdwlrqdo sd|phqw v|vwhpv frp0 shwlqj djdlqvw hdfk rwkhu e| doorzlqj edqnv wr e|0sdvv wkhlu qdwlrqdo v|vwhp dqg xvh wkh iruhljq v|vwhp lqvwhdg1 Lw lv vkrzq wkdw wkh sulflqj vfkhph uhpdlqv ghjuhvvlyh1 Krzhyhu/ frpshwlwlrq iru edqnv zlwk d kljk sd|phqw yroxph pd| uhtxluh wkdw kljk yroxphv duh vxevlgl}hg dw wkh pdujlq/lq rughu wr hqvxuh wkdw wkhvh edqnv uhpdlq lq wkh qdwlrqdo sxeolf v|vwhp1
4 Lqwurgxfwlrq
Wklv sdshu dqdo|}hv wkh h!flhqw sulflqj ri odujh0ydoxh sd|phqw v|vwhpv1 Wkhvh v|vwhpv/ zklfk duh xvhg e| edqnv dqg odujh qdqfldo vhuylfh surylghuv wr fkdqqho sd|phqwv wr hdfk rwkhu/kdyh fkdqjhg vxevwdqwldoo| ryhu wkh odvw ghfdgh1 Lq sduwlfxodu/wkh yroxphv wudqv0 ihuuhg lq wkhvh v|vwhpv kdyh lqfuhdvhg gudpdwlfdoo|/pdlqo| ehfdxvh ri jurzlqj qdqfldo lqwhjudwlrq/qhz qdqfldo surgxfwv dqg whfkqrorjlfdo ghyhorsphqwv1 Wklv wuhqg udlvhg frqfhuqv dprqj uhjxodwruv ehfdxvh ri lwv srwhqwldo lpsolfdwlrqv iru v|vwhplf vwdelolw|/dqg ohg wr d qxpehu ri uhjxodwru| lqlwldwlyhv zlwk wkh dlp wr uhgxfh ulvn0h{srvxuhv ehwzhhq sduwlflsdqwv +vhh Edqn iru Lqwhuqdwlrqdo Vhwwohphqwv 4<<3,1 Wkhvh lqfoxghg wkh surprwlrq ri uhdo0wlph jurvv vhwwohphqw +UWJV, v|vwhpv/zklfk uhsodfhg qhwwlqj v|vwhpv lq pdq| frxqwulhv1
Lq Hxursh/wkh dgyhqw ri Hfrqrplf dqg Prqhwdu| Xqlrq sod|hg dq htxdoo| lpsruwdqw uroh iru wkh ghyhorsphqw ri odujh ydoxh sd|phqw v|vwhpv1 Iru d orqj wlph/rqh ru vhyhudo sd|phqw v|vwhpv h{lvwhg lq hdfk frxqwu|/doo rujdql}hg glhuhqwo|1 Prvw furvv0erughu wudqvdfwlrqv zhuh grqh yld fruuhvsrqghqw edqnv1 Lq rughu wr idflolwdwh wkh lpsohphqwdwlrq ri wkh vlqjoh prqhwdu| srolf| lq Hxursh/lw zdv ghflghg lq 4<<8 wr exlog d Hxurshdq zlgh sd|phqw v|vwhp/WDUJHW7/frqqhfwlqj qdwlrqdo UWJV v|vwhpv ri doo HX phpehu vwdwhv18
Wkhvh qdwlrqdo frpsrqhqwv ri WDUJHW zhuh kduprql}hg rqo| wr vrph ghjuhh/h1j1 lq whupv ri rshudwlqj krxuv1 Vlqfh wkh xvh ri WDUJHW lv frpsxovru| iru vhwwohphqw ri HFE prqhwdu| srolf| rshudwlrqv/doo edqnv zlvklqj wr rewdlq oltxlglw| iurp wkh fhqwudo edqn duh uhtxluhg wr sduwlflsdwh gluhfwo| ru lqgluhfwo| lq WDUJHW1
Ehfdxvh prqhwdu| srolf| wudqvdfwlrqv ri wkh Hxurshdq Fhqwudo Edqn duh frqgxfwhg xvlqj WDUJHW/doo edqnv zlvklqj wr rewdlq oltxlglw| iurp wkh Fhqwudo Edqn duh uhtxluhg wr kdyh dq dffrxqw lq WDUJHW1
Qdwxudoo|/WDUJHW grhv qrw surylgh wkh rqo| zd| wr pdnh odujh ydoxh lqwhuedqn sd|phqwv lq Hxursh1 Elodwhudo djuhhphqwv ehwzhhq edqnv dqg fruuhvsrqghqw edqnlqj duudqjhphqwv frqwlqxh wr h{lvw1 Ixuwkhupruh/d ihz/sulydwho| uxq/qhwwlqj dqg k|eulg v|vwhpv duh lq sodfh/prvwo| rshudwlqj dw grphvwlf ohyhov1 Wkh eljjhvw ri wkhvh v|vwhpv lv HXUR4/d qhw v|vwhp wkdw rhuv pdlqo| furvv0erughu sd|phqw vhuylfhv1 HXUR4 lv uxq e| wkh Hxur Edqnlqj Dvvrfldwlrq +HED,1 Lq rughu wr xvh HXUR4/d edqn pxvw eh phpehu ri wkh HED dqg ixoo fhuwdlq uhtxluhphqwv vxfk dv jrrg fuhglw udwlqj dqg d plqlpxp
7Wklv lv dq dfurq|p iru Wudqv0Hxurshdq Dxwrpdwhg Uhdo0wlph Jurvv vhwwohphqw H{suhvv Wudqvihu1 8vhh HFE +5334,1
edodqfh vkhhw vl}h1
Wkh dlp ri wklv sdshu lv wr fkdudfwhul}h wkh h!flhqw sulflqj vwuxfwxuh iru d sxeolf sd|phqw v|vwhp/ghshqglqj rq wkh w|sh ri frpshwlwlrq lw idfhv1 Wklv txhvwlrq lv uhohydqw qrw rqo| iru wkh Hxurshdq fdvh glvfxvvhg deryh/exw htxdoo| zhoo iru wkh XV/zkhuh d sxeolf UWJV v|vwhp/Ihgzluh/h{lvwv vlgh e| vlgh zlwk FKLSV/d sulydwh v|vwhp91 Vr
idu/wkh olwhudwxuh rq sd|phqw v|vwhpv zdv prvwo| frqfhuqhg zlwk lvvxhv ri v|vwhplf ulvn1 Iru lqvwdqfh/Iuhl{dv dqg Sduljl +4<<9, dqg dovr Ndkq dqg Urehugv +4<<;, dqdo|}h wkh wudgh0r ehwzhhq d pruh h!flhqw oltxlglw| pdqdjhphqw lq UWJV v|vwhpv yhuvxv kljkhu v|vwhplf ulvn lq qhwwlqj v|vwhpv1 Ihz sdshuv kdyh dgguhvvhg wkh fr0h{lvwhqfh ri sulydwh dqg sxeolf v|vwhpv1 H{fhswlrqv duh Urfkhw dqg Wluroh +4<<9,/zkr dujxh lq idyru ri d forvh fr0rshudwlrq lq wkh frqwuroolqj ri ulvn0h{srvxuhv lq erwk v|vwhpv/dqg Krowkdxvhq dqg Uûqgh +5334, zkr dqdo|}h dffhvv uhjxodwlrq wr qhwwlqj v|vwhpv1
Wr rxu nqrzohgjh/wkhuh h{lvwv qr wkhruhwlfdo vwxg| vr idu rq wkh sulflqj ri odujh ydoxh sd|phqw vhuylfhv1 Wkhuh duh/krzhyhu/d ihz hpslulfdo vwxglhv rq wkh sulflqj ri Ihgzluh +wkh XV htxlydohqw wr WDUJHW,1 Kdqfrfn hw do +4<<<, dqdo|}h wkh sulflqj rq lqwhuedqn wudqvdfwlrqv e| whvwlqj iru vfdoh hfrqrplhv lq sd|phqwv surfhvvlqj1 PfDqguhzv +4<<;, hv0 wlpdwhv ghpdqg hodvwlflwlhv iru Ihgzluh sd|phqw vhuylfhv1 Wkh prghoolqj dssurdfk wdnhq lq wklv sdshu lv forvho| frqqhfwhg wr wkh olwhudwxuh rq qdwxudo prqrsrolhv dqg Udpvh| sulf0 lqj +vhh h1j1 Eùv 4<<7,1 Lw lv dovr uhodwhg wr lvvxhv ri frpshwlwlrq lq whohfrppxqlfdwlrqv dqg rwkhu qhwzrun lqgxvwulhv +vhh h1j1 Odrqw dqg Wluroh 5333,1
Lq Vhfwlrq 5 ri wklv sdshu/zh ghyhors d vlpsoh prgho ri d edqnlqj lqgxvwu| zkhuh edqnv pdnh sd|phqwv wkurxjk d odujh ydoxh sd|phqw v|vwhp1 Vhfwlrq 6 dqdo|}hv wkh ehqfkpdun fdvh ri d sxeolf prqrsro| sd|phqw v|vwhp1 Wkh rswlpdo sulflqj vfkhph lv wkh rqh wkdw pd{lpl}hv djjuhjdwh vxusoxv ri wkh edqnlqj lqgxvwu| xqghu wkh frqvwudlqw wkdw wkh sxeolf sd|phqw v|vwhp euhdnv hyhq1 Lq vhfwlrq 7/wkh pruh lqwhuhvwlqj fdvh ri d pl{hg gxrsro| lv vwxglhg/lq zklfk edqnv duh iuhh wr fkrrvh zkhwkhu wr urxwh wkh sd|phqwv wkurxjk d sxeolf ru d sulydwh sd|phqw v|vwhp1
Dv qrwhg deryh/qdwlrqdo UWJV v|vwhpv lq wkh HX duh qrw ixoo| kduprql}hg1 Lq sduwlfxodu/wkh ihh vwuxfwxuh iru sd|phqwv zlwklq d frxqwu| glhuv dfurvv v|vwhpv1 Wklv ohdgv wr d vlwxdwlrq zkhuh wkhvh v|vwhpv frpshwh iru sd|phqwv/ehfdxvh odujhu edqnv wkdw duh lqfrusrudwhg lq vhyhudo frxqwulhv pd| eh deoh wr fkrrvh zklfk qdwlrqdo v|vwhp wr xvh
9FKLSV iru pdq| |hduv rshudwhg dv d qhw vhwwohphqw v|vwhp1 Vlqfh 5334/lw kdv uhylvhg lwv rshudwlrqdo iudphzrun dqg lv qrz ehwwhu ghvfulehg dv d k|eulg v|vwhp1
wr urxwh sd|phqwv1: Wr fdswxuh vxfk dq hqylurqphqw/lq Vhfwlrq 8 ri wklv sdshu zh vwxg|
wkh rswlpdo sulflqj zkhq wzr sxeolf v|vwhpv frpshwh iru fxvwrphuv1
5 Wkh Prgho
Zh prgho d shuihfwo| frpshwlwlyh edqnlqj lqgxvwu| ryhu d {hg shulrg ri wlph +vd| d prqwk ru d txduwhu, xvhg dv wkh lqyrlfh shulrg e| wkh odujh ydoxh lqwhuedqn sd|phqw v|vwhp +lq vkruw/OYSV,1
Hdfk edqn kdv d ghpdqg iru pdnlqj sd|phqwv ryhu wkh OYSV/ghqrwhg ^1 Sd|phqwv duh ri wkh vdph vl}h1 Wkh sd|phqw ghpdqg ghshqgv rq wkh wdul A E^ wkdw lv fkdujhg e| wkh OYSV1 Lq sduwlfxodu/zh dvvxph wkdw hdfk sd|phqw jhqhudwhv vrph udqgrp prqhwdu| ydoxh 6 wr wkh edqn1 Wklv ydoxh lv lqwhusuhwhg dv wkh prqhwdu| vxusoxv wkdw lv jhqhudwhg e| urxwlqj wkh sd|phqw wkurxjk wkh OYSV lqvwhdg ri ghod|lqj lw dqg exqgolqj lw zlwk rwkhu sd|phqwv/ru lqvwhdg ri qglqj dowhuqdwlyh zd|v wr vhqg sd|phqwv/iru lqvwdqfh e| xvlqj d fruuhvsrqghqw edqn1 Qrwlfh wkdw wkh uhdol}dwlrq ri 6/ 6/zloo glhu iru hdfk sd|phqw dqg hdfk edqn/exw wkh glvwulexwlrq lv wkh vdph1
Hdfk sd|phqw zloo eh xqghuwdnhq li dqg rqo| li lwv prqhwdu| ydoxh lv dw ohdvw dv kljk dv wkh pdujlqdo ihh fkdujhg e| wkh OYSV/ AE^/wkdw lv li 6 AE^1 Dvvxplqj wkdw wkh
wlph shulrg lv odujh hqrxjk vr wkdw wkh odz ri odujh qxpehuv fdq eh dssolhg/wkh sd|phqw ghpdqg ^ lv wkhq wkh sursruwlrq ri srwhqwldo sd|phqwv wkdw zloo eh urxwhg rq wkh OYSV e| d jlyhq edqn/ ^ 'Sured d6 AE^o1 Wklv ghpdqg ixqfwlrq ri wkh edqn zloo eh
ghqrwhg (ER/dqg lwv lqyhuvh E^1
Wkh xwlolw| ixqfwlrq ri wkh edqn lv wkhq e| ghqlwlrq E^ ' ^
f Er_r
dqg lqglylgxdo vxusoxv iru d edqn +dqg lwv fxvwrphuv, lv wkhq htxdo wr E^ A E^1;
:Lq idfw/edqnv duh dovr deoh wr xvh rwkhu UWJV v|vwhpv frqqhfwhg wr WDUJHW e| uhprwh dffhvv1
Krzhyhu/wklv srvvlelolw| lv qrw zlgho| xvhg/dqg lw lv glvuhjdughg lq wkh prghoolqj1
;Lq wkh vhtxho/zh zloo qrw dqdo|}h wkh uhsduwlwlrq ri wkh vxusoxv ehwzhhq wkh edqn dqg lwv fxvwrphuv1 Wkh rqo| dvvxpswlrq wkdw zh qhhg lv wkdw t lv fkrvhq vr dv wr pd{lpl}h wklv vxusoxv/zklfk lv wkh fdvh li edqnv duh shuihfwo| frpshwlwlyh +wklv lv rxu dvvxpswlrq, exw dovr li edqnv duh pxwxdov zkr dfw lq wkh ehvw lqwhuhvw ri wkhlu fxvwrphuv ru dw wkh rwkhu h{wuhph li edqnv duh prqrsrolvwlf dqg h{wudfw doo wkh frqvxphuv* vxusoxv1 Wkh fdvh zkhuh wkh edqnv dqg wkh frqvxphuv vkduh wklv vxusoxv lq {hg sursruwlrqv lv dovr frpsdwleoh zlwk rxu dqdo|vlv1
Edqnv zloo w|slfdoo| glhu lq wkhlu sd|phqw ghpdqgv1 Wr prgho wklv/zh dvvxph wkdw wkh glvwulexwlrqv ri prqhwdu| ydoxhv dfurvv edqnv duh lghqwlfdo xs wr d wudqvodwlrq
6 ' w n 0c
zkhuh w lv dq xqrevhuydeoh khwhurjhqhlw| sdudphwhu wkdw fkdudfwhul}hv wkh edqn +wkh w|sh ri wkh edqn, dqg wkh 0v duh lqghshqghqwo| dqg lghqwlfdoo| glvwulexwhg dfurvv edqnv1 Iru lqvwdqfh/ w frxog eh uhodwhg wr wkh edqn*v vl}h/lwv h!flhqf|/ru wr lwv hqjdjhphqw lq d fhuwdlq w|sh ri qdqfldo dfwlylw|1
Wklv olqhdu vwuxfwxuh lpsolhv d vlpsoh sdudphwul}dwlrq ri edqnv* ghpdqg dqg xwlolw| ixqfwlrqv=
(Ewc A ' Sured dw n 0 Ao ' (Efc A wc
dqg
Ewc ^ ' ^
f iw n (
3Efc rj_r ' w^ n Efc ^
Wkdw lv/d edqn*v xwlolw| ghshqgv olqhduo| rq lwv w|sh1 Wkh dgydqwdjh ri wklv sdudphwul}d0 wlrq lv wkdw lw vdwlvhv wkh idploldu vlqjoh furvvlqj surshuw| vlqfh
Y2
YwY^ : f +4,
Wklv lpsolhv wkdw/lqghshqghqwo| ri wkh sulflqj vwuxfwxuh/wkh yroxph ri wudqvdfwlrqv ^Ew fkrvhq e| d edqn ri w|sh w zloo eh lqfuhdvlqj zlwk w Wkh dgglwlyh sdudphwul}dwlrq ri khwhurjhqhlw| lv rqo| pdgh iru frqyhqlhqfh= doo rxu uhvxowv jr wkurxjk xqghu wkh pruh jhqhudo vlqjoh furvvlqj surshuw|1
Dv lv xvxdo lq wkh qrqolqhdu sulflqj olwhudwxuh/zh dvvxph wkdw wkh ydoxh ri w lv sulydwho| revhuyhg e| hdfk edqn/dqg wkdw wkh Fhqwudo Edqn rqo| nqrzv wkh vwdwlvwlfdo glvwulexwlrq ri w dprqj edqnv1 Wkh sureohp ri ghwhuplqlqj wkh h!flhqw sulflqj vfkhgxoh zrxog eh wulyldo li wkh lqglylgxdo edqnv* sd|phqw ghpdqg zhuh shuihfwo| revhuydeoh1 Lq wkdw fdvh/ wkh ehvw wdul zrxog eh uvw ehvw rswlpdo dqg zrxog frqvlvw ri d pdujlqdo ihh htxdo wr wkh pdujlqdo frvw dqg d shuvrqdol}hg {hg ihh wkdw zrxog ghshqg rq wkh vxusoxv rewdlqhg e| hdfk edqn<1 Lq wkh pruh uhdolvwlf fdvh zkhuh wdulv fdqqrw eh frqglwlrqhg rq wc wkh
vhfrqg ehvw vfkhgxoh lqyroyhv yroxph edvhg sulflqj/dv zh qrz dqdo|}h lq ghwdlo1
<Lq idfw wkhuh zrxog eh dq lqqlw| ri Sduhwr rswlpdo wdulv/hdfk dvvrfldwhg wr d glhuhqw vkdulqj ri {hg frvwv dprqj edqnv1 Qrw rqo| vxfk d glvfulplqdwru| wdul zrxog eh srolwlfdoo| gl!fxow wr lpsoh0 phqw/exw lw zrxog uhtxluh wkdw wkh Fhqwudo Edqn srvvhvvhv yhu| suhflvh lqirupdwlrq rq fkdudfwhulvwlfv wkdw lqglylgxdo edqnv fdq hdvlo| dowhu1
6 Rswlpdo Sulflqj iru d Prqrsro| OYSV
Lq wklv vhfwlrq/zh ghulyh wkh +vhfrqg ehvw, rswlpdo sulflqj uxoh iru d sxeolf OYSV zkhq lw grhv qrw idfh dq| frpshwlwlrq/hlwkhu lq wkh vdph frxqwu| e| d sulydwho| uxq OYSV +wklv lv vwxglhg lq Vhfwlrq 7, ru lq d qhljkerulqj frxqwu| e| d sxeolfo| uxq OYSV +wklv lv vwxglhg lq Vhfwlrq 8,1 Wkh sulflqj uxoh ghyhorshg khuh lv d sduwlfxodu fdvh ri Udpvh| sulflqj iru d sxeolf prqrsro| vxemhfw wr d exgjhw frqvwudlqw +vhh Eùv 4<<7,1
614 Glvfuhwh glvwulexwlrq ri w|shv
Wr ehjlq zlwk/zh dgrsw d vlpsoh glvfuhwh glvwulexwlrq ri edqnv* w|shv1 Zh dvvxph wkdw wkhuh duh rqo| wzr srvvleoh w|shv/ wu dqg wM/zkhuh wu wM1 D iudfwlrq s& ri edqnv lv ri
w|sh w&/ & 5 iuc Mj/dqg sun sM ' 1
Ghqrwh A E^ wkh wdul fkdujhg e| wkh Fhqwudo Edqn iru d yroxph ^ ri wudqvdfwlrqv1 Zlwkrxw orvv ri jhqhudolw|/wkh wdul A E^ lv vxssrvhg wr eh slhfhzlvh glhuhqwldeoh/dqg zkhqhyhu lw h{lvwv/lwv ghulydwlyh lv ghqrwhg e| AE^1 Vlqfh edqnv duh qrw reoljhg wr
sduwlflsdwh/zh uhtxluh A Ef ' f +lqglylgxdo udwlrqdolw| frqglwlrq,1 Qrwlfh wkdw wklv lv qrw lqfrpsdwleoh zlwk d {hg ihh A zklfk lv rqo| lqfxuuhg iru d vwulfwo| srvlwlyh wudqvdfwlrq ydoxh +vhh dovr irrwqrwh 44,1
Wkh lqgluhfw xwlolw| ixqfwlrq ri d edqn ri w|sh & lv ghqhg dv wkh pd{lpxp vxusoxv & rewdlqhg e| d edqn ri w|sh w&+ru lwv fxvwrphuv, zkhq wkh wdul fkdujhg e| wkh Fhqwudo
Edqn lv A 1 E| ghqlwlrq=
&' 4@ ^
&DfiEw&c ^& A E^&jc +5,
zkhuh wkh pd{lpxp iru d w|sh & edqn lv rewdlqhg iru d yroxph ^& ' ^Ew& dqg d sd|phqw
A&' A E^&Zkhqhyhu A lv glhuhqwldeoh dw ^Ew/wkh uvw rughu frqglwlrq lpsolhv=
^Ewc ^Ew ' AE^Ewc +6,
zkhuh ^ ghqrwhv wkh sduwldo ghulydwlyh ri zlwk uhvshfw wr ^1 Jlyhq wkdw wkhuh duh rqo|
wzr w|shv ri edqnv/wkh Fhqwudo Edqn sureohp fdq eh uhgxfhg wr qglqj wzr sdluv E^&c A&
wkdw vdwlvi| wkh djhqwv* lqfhqwlyh frpsdwlelolw| frqvwudlqwv=
EUM G M ' EwMc ^M AM EwMc ^u Au +7,
dqg lqglylgxdo udwlrqdolw| frqvwudlqwv/zklfk jxdudqwhh wkdw edqnv rewdlq wkhlu uhvhuydwlrq xwlolw| +zklfk zh qrupdol}hg wr 3,=
EU-M G M f +9,
EU-u G u f +:,
Wkh wrwdo yroxph ri wudqvdfwlrqv lq wkh OYSV lv ' ' su^un sM^M1 Wkh frvw ixqfwlrq
ri wkh OYSV lv ghqrwhg E'1 Zh zloo dgrsw wkh iroorzlqj vlpsoh vshflfdwlrq=
E' ' @ n S'c +;,
zkhuh @ ghqrwhv wkh {hg frvw/dqg wkh pdujlqdo frvw S lv wdnhq wr eh frqvwdqw1 Zh dvvxph wkdw wkh Fhqwudo Edqn lv frqvwudlqhg wr fkrrvlqj d wdul vwuxfwxuh wkdw vdwlvhv exgjhw edodqfh43=
&'ucM
s&A E^& ' E' +<,
Wkh fhqwudo edqn*v sureohp frqvlvwv ri qglqj wkh rswlpdo txdqwlwlhv iru erwk w|shv ri edqnv ^u dqg ^M/wrjhwkhu zlwk wdulv Au ' A E^u dqg AM ' A E^M vr wkdw djjuhjdwh
vxusoxv 7 lv pd{lpl}hg1 7 lv jlyhq e| 7 '
&'ucM
s&Ew&c ^& E' ' &'ucM
s&rEw&c ^& @
zkhuh zh kdyh ghqhg rEw&c ^& Ew&c ^& S^&1
Wkh Fhqwudo Edqn wkhuhiruh qhhgv wr pd{lpl}h &s&iEw&c ^& S^&j xqghu wkh frq0
vwudlqwv +6, 0 +:, dqg +<,1
Wkh vroxwlrq ri wklv sureohp lv jlyhq e| wkh iroorzlqj sursrvlwlrq1
Sursrvlwlrq 4 Iru d prqrsro| OYSV/ wkh vhfrqg ehvw rswlpdo wdul vdwlvhv AE^
M ' ^EwMc ^M ' S
AE^
u ' ^Ewuc ^u ' S n n bb ssM
u EwM wu
zkhuh b lv wkh Odjudqjh pxowlsolhu dvvrfldwhg zlwk wkh euhdn0hyhq frqvwudlqw +<,1
43Frvw uhfryhu| lv d vwdwxwru| uhtxluhphqw iru pdq| sd|phqw v|vwhpv/iru lqvwdqfh WDUJHW ru Ihg0 zluh1
Iurp Sursrvlwlrq 4/zh vhh wkdw/dv vrrq dv wkh euhdn0hyhq frqvwudlqw lv elqglqj +b : f,/wkh rswlpdo wdul lv yroxph0edvhg= wkh pdujlqdo sulfh A fkdujhg wr edqn
ghshqgv rq wkh wrwdo qxpehu ri sd|phqwv vhqw e| wkh edqn1 Lq sduwlfxodu/edqnv zlwk kljkhu yroxphv idfh d orzhu pdujlqdo sulfh/l1h1 wkh vfkhph lv ghjuhvvlyh1 Qrwlfh wkdw kljk w|sh edqnv wM/zkr fkrrvh txdqwlw| ^M/rewdlq pdujlqdo frvw sulflqj/zklfk lpsolhv
wkdw wkhlu wudqvdfwlrq yroxph lv qrw glvwruwhg1 Krzhyhu/orz w|sh edqnv wu sd| pdujlqdo
ihhv deryh pdujlqdo frvw/zklfk lpsolhv wkdw wkh| vhqg ohvv sd|phqwv wkdq zkdw zrxog eh h!flhqw +grzqzdug glvwruwlrq,1
Zkhq wkh {hg frvw ri wkh v|vwhp lv vpdoo/wkh euhdn0hyhq frqvwudlqw lv qrw elqglqj +b ' f, dqg wkh rswlpdo wdul lv uvw0ehvw h!flhqw= pdujlqdo ihhv htxdo pdujlqdo frvw iru doo w|shv1 Krzhyhu/lq wkh pruh uhdolvwlf fdvh zkhuh wkh {hg frvw lv kljk/wkh qhhg wr dfklhyh exgjhw edodqfh lqwurgxfhv sulfh glvwruwlrqv= pdujlqdo ihhv iru orz yroxphv duh vhw deryh pdujlqdo frvw/dw wkh plqlpxp ohyho wkdw ghwhuv kljk w|sh edqnv wr uhgxfh wkhlu wudqvdfwlrq yroxph1 Qrwlfh wkdw wkh surshuw| wkdw kljk wudqvdfwlrq yroxphv duh qrw glvwruwhg +qr glvwruwlrq dw wkh wrs,/lv d vwdqgdug uhvxow lq wkh dgyhuvh0vhohfwlrq olwhudwxuh1
Wklv vlpsoh wzr0w|sh fdvh looxvwudwhv wkh sureohp ri qglqj wkh rswlpdo sulflqj vfkhph dqg wkxv doorzv xv wr qg vrph hvvhqwldo fkdudfwhulvwlfv ri wkh rswlpdo wdul1 Vwloo/lw lv qrw vx!flhqw wr rewdlq d frpsohwh fkdudfwhul}dwlrq q ri wkh wdul vwuxfwxuh/vlqfh wkhuh lv dq lqqlw| ri ixqfwlrqv A E vdwlvi|lqj wkh frqglwlrqv ri Sursrvlwlrq 41 Lq sduwlfxodu/ zh duh qrw deoh wr ghwhuplqh xqltxho| wkh rswlpdo ydoxh ri wkh {hg ihh1 Pruhryhu lw lv lpsruwdqw wr fkhfn wkh urexvwqhvv ri wkh ihdwxuhv ri wkh vroxwlrq wr pruh jhqhudo glvwulexwlrqv ri xqrevhuydeoh khwhurjhqhlw|1 Wklv lv zk| zh qrz wxuq wr wkh fdvh ri d frqwlqxrxv glvwulexwlrq ri w|shv1
615 Frqwlqxrxv glvwulexwlrq ri w|shv
Zh qrz wdnh wkh glvwulexwlrq ri w|shv wr eh frqwlqxrxv zlwk ghqvlw| s dqg f1g1i1 8 rq d erxqghg vxssruw dwc 7wo1 Wkh ghqvlw| s lv vxssrvhg wr eh orj frqfdyh1 Xvlqj wklv glvwulexwlrq/doo djjuhjdwh yduldeohv qhhg wr eh uhghqhg1 Wkh wrwdo yroxph ri wudqvdfwlrqv ryhu doo edqnv lv qrz
' ' 7w
wf
zkhuh wf lv wkh sduwlflsdwlrq wkuhvkrog/ghqhg lpsolflwo| e| Ewf ' f1 Exgjhw edodqfh
ri wkh OYSV lv jlyhq e|
7w wf
A E^Ew_8Ew ' E'c +44,
zkhuh ' lv jlyhq e| +43, dqg ^E vdwlvhv +6,1
Dqdorjrxvo| wr wkh wzr0w|sh fdvh/wkh rswlpdo sulflqj iru d prqrsro| OYSV lv rewdlqhg e| fkrrvlqj wkh wdul A E dqg wkh edqnv* uhdfwlrq ixqfwlrq ^E wkdw pd{lpl}h djjuhjdwh vxusoxv=
7 ' 7w
wf
Ewc ^Ew_8 Ew E'c +45,
xqghu frqvwudlqwv +5, wr +;,/+43, dqg +44,/soxv wkh frqglwlrq wkdw ^E lv qrq0ghfuhdvlqj/ zklfk zh zloo rqo| fkhfn h{0srvw1 Vlqfh wklv sureohp lv vwdqgdug/zh lpphgldwho| vwdwh wkh irup ri wkh vroxwlrq +doo surriv duh lq wkh dsshqgl{,1
Sursrvlwlrq 5 Zkhq wkh glvwulexwlrq ri w|shv lv frqwlqxrxv/ wkh rswlpdo wdul iru d
prqrsro| OYSV lv fkdudfwhul}hg e| wkh devhqfh ri d {hg ihh44 EA ' f dqg d ghfuhdv0 lqj pdujlqdo ihh AE^1 Wklv pdujlqdo ihh dqg wkh wudqvdfwlrq yroxph ^Ew duh mrlqwo| ghwhuplqhg e| wzr htxdwlrqv=
AE^Ew ' S n b
n b 8
s Ew ' ^Ewc ^Ewc +46,
zkhuh b lv wkh Odjudqjh pxowlsolhu dvvrfldwhg wr wkh euhdn0hyhq frqvwudlqw +44,1
Dv lq wkh wzr0w|sh fdvh/zh rewdlq d qrq0olqhdu/ghjuhvvlyh sulflqj vfkhph1 Wkh pdujlqdo ihh lv deryh wkh pdujlqdo frvw/h{fhsw dw wkh wrs ri wkh glvwulexwlrq ri edqnv Ew ' 7w iru zklfk AE^E7w ' S +qr glvwruwlrq dw wkh wrs,1 Wkh lqfuhphqw lv sursruwlrqdo
wr wkh lqyhuvh kd}dug udwh 38
s zklfk lv ghfuhdvlqj lq w vlqfh s lv orj frqfdyh +iru d
surri vhh Edjqrol dqg Ehujvwurp 4<;<,1 Vlqfh ^E lv dq lqfuhdvlqj ixqfwlrq ri w/ AE^ 44Wkh {hg ihh +zklfk lv khuh rswlpdoo| vhw wr }hur, lv qrw wr eh frqixvhg zlwk wkh frqqhfwlrq ihh sdlg e| wkh edqn ghshqglqj rq wkh w|sh ri frqqhfwlrq lw uhtxluhv +vhh Kdqfrfn hw do1 +4<<<, irrwqrwh :,1 Qrwlfh wkdw W +3, @ 3 e| frqvwuxfwlrq +lqglylgxdo udwlrqdolw| frqglwlrq, exw wkdw W fdq d sulrul eh glvfrqwlqxrxv dw 3 li wkhuh lv d {hg ihh/zklfk zh fkdudfwhul}h e|
W W +3., @ olp t$3 tA3
lv ghfuhdvlqj zlwk uhvshfw wr ^1 Wklv lv looxvwudwhg lq jxuh 41 A lv dovr lqfuhdvlqj zlwk
uhvshfw wr b/wkh Odjudqjh pxowlsolhu dvvrfldwhg wr wkh euhdn0hyhq frqvwudlqw1 H{wuhph ydoxhv ri b fruuhvsrqg wr pdujlqdo frvw sulflqj +iru b ' f, dqg sulydwh prqrsro| sulflqj +iru b ' n4,1 Lq sudfwlfh/wkh rswlpdo A fdq eh dssur{lpdwhg e| d phqx ri wzr sduw wdulv1
T
F
7¶T
T
T
q
Iljxuh 4= Rswlpdo Sulflqj lq d Sxeolf Prqrsro|
Ohw xv qrz pryh wr wkh pruh ruljlqdo sureohp ri rswlpdoo| sulflqj d sxeolf OYSV wkdw kdv d sulydwh frpshwlwru1
7 Rswlpdo sulflqj lq d pl{hg gxrsro|
Diwhu wkh prqrsro| ehqfkpdun vroxwlrq fkdudfwhul}hg lq Vhfwlrq 6/zh frqvlghu qrz wkh pl{hg gxrsro| sureohp srvhg e| furvv erughu wudqvdfwlrqv zlwklq wkh HX/zklfk fdq eh urxwhg dowhuqdwlyho| rq WDUJHW ru lwv sulydwh frpshwlwru HXUR41 Vxfk d pl{hg gxrsro| vlwxdwlrq lv dovr suhvhqw lq wkh XV/zkhuh wkh Ihghudo Uhvhuyh uxqv wkh jurvv v|vwhp IHGZLUH/zkloh odujh frpphufldo edqnv uxq wkh k|eulg v|vwhp FKLSV1 Lq idfw/ wklv vlwxdwlrq h{lvwv dovr/iru qdwlrqdo wudqvdfwlrqv/lq doo wkh frxqwulhv +lqfoxglqj HX frxqwulhv, zkr kdyh lpsohphqwhg d qdwlrqdo UWJV/zkloh doorzlqj frpphufldo edqnv wr rujdql}h vlpxowdqhrxvo| d frpshwlqj sd|phqw v|vwhp145 Iru wkh prphqw zh irfxv rq wkh
pl{hg gxrsro| vlwxdwlrq/zklfk zh looxvwudwh e| furvv erughu wudqvdfwlrqv zlwklq wkh HX1
45Krzhyhu/dq dgglwlrqdo frpsoh{lw| dsshduv lq HPX frxqwulhv/jlyhq wkdw wkh edqnv wkdw duh lqfru0 srudwhg lq vhyhudo frxqwulhv fdq dovr urxwh wkhlu wudqvdfwlrqv rq wkh qdwlrqdo UWJVv ri wkhvh glhuhqw frxqwulhv= wklv lv dqdo|}hg lq Vhfwlrq 81
Qrwlfh wkdw d xqltxh sd|phqw v|vwhp zrxog suredeo| eh pruh frvw0hhfwlyh +dw ohdvw lq wkh vkruw uxq, gxh wr wkh surshuw| ri lqfuhdvlqj uhwxuqv wr vfdoh ri wkh sd|phqw whfkqrorj| +vhh Kdqfrfn hw do1/4<<</iru dq hpslulfdo whvw ri wklv surshuw|,1 Lw lv dovr fohdu wkdw wkh frh{lvwhqfh ri d sulydwh sd|phqw v|vwhp/riwhq rujdql}hg rq d qhw edvlv/lqfuhdvhv wkh srwhqwldo iru v|vwhplf ulvn +vhh iru lqvwdqfh Urfkhw dqg Wluroh/4<<9/dqg wkh uhihuhqfhv wkhuhlq iru glvfxvvlrqv ri v|vwhplf ulvn lvvxhv lq sd|phqw v|vwhpv,146 Krzhyhu/lw zrxog
eh h{wuhpho| gl!fxow iru dq| Fhqwudo Edqn wr reoljh frpphufldo edqnv wr urxwh doo wkhlu wudqvdfwlrqv rq d xqltxh v|vwhp1 Pruhryhu/iurp wkh srlqw ri ylhz ri orqj whup h!flhqf| wkh fr0h{lvwhqfh ri wzr v|vwhpv lv suredeo| d jrrg zd| wr surylgh lqfhqwlyhv iru frvw plqlpl}dwlrq dqg surprwh lqqrydwlrq +|dugvwlfn frpshwlwlrq,1
Zh prgho wkh sulydwh v|vwhp e| frqvlghulqj wkdw wkh eljjhvw ru prvw h!flhqw edqnv pryh doo wkhlu wudqvdfwlrqv wr d glhuhqw/sulydwh OYSV1 Zh eholhyh wklv dvvxpswlrq wr eh frqvlvwhqw zlwk wkh dfwxdo vlwxdwlrq/vlqfh phpehuv ri wkh sulydwh v|vwhpv whqg wr uhsuhvhqw wkh odujhvw edqnv ri wkhlu uhvshfwlyh frxqwulhv471
Wkh sulydwh OYSV lv dvvxphg wr eh fkdudfwhul}hg e| d frvw ixqfwlrq E' ' @n S'
zkhuh S S1 Wklv dvvxpswlrq uh hfwv hylghqfh iurp HX frxqwulhv vxjjhvwlqj wkdw wkh
pdujlqdo frvw iru furvv0erughu sd|phqw surfhvvlqj lv orzhu lq HXUR4 wkdq lq wkh sxeolf UWJV v|vwhpv1
Iru whfkqlfdo uhdvrqv zh zloo uhvwulfw rxuvhoyhv wr wkh fdvh ri glvfuhwh glvwulexwlrqv/dqg dvvxph wkdw wkhuh duh wkuhh w|shv ri edqnv/ wu w wM/zklfk rffxu zlwk iuhtxhqf|
s&/ & ' uc c M/zlwk sun s n sM ' 1 Vhyhudo frqjxudwlrqv pljkw rffxu/zkhuhe|
wkh wkuhh w|shv ri edqnv xvh rqh v|vwhp ru wkh rwkhu1 Iru wkh vdnh ri frqflvhqhvv/zh irfxv rq wkh prvw lqwhuhvwlqj uhjlph zkhuh wkh sulydwh v|vwhp lv xqghu wkh frqwuro ri wkh kljk w|sh edqnv rqo|/dqg wkh elqglqj sduwlflsdwlrq frqvwudlqw iru wkh Fhqwudo Edqn lv wr suhyhqw phglxp w|sh edqnv iurp dovr prylqj wkhlu wudqvdfwlrqv wr wkh sulydwh v|vwhp148
Zh dvvxph wkdw wkh sulydwh v|vwhp lv uxq olnh d pxwxdo uhsuhvhqwlqj wkh froohfwlyh
46Vrph sulydwh v|vwhpv kdyh uhfhqwo| dgrswhg d k|eulg vwuxfwxuh +vxfk dv FKLSV, dqg wkhuhe| uhgxfhg v|vwhplf ulvn1
47Vwloo/lq sudfwlfh hyhq wkh odujhvw edqnv xvh wkh sxeolfo| uxq UWJV iru urxwlqj vrph ri wkhlu wudqvdf0 wlrqv/uhodwhg iru h{dpsoh wr prqh| pdunhw dqg iruhljq h{fkdqjh rshudwlrqv1 Lw pd| eh wkh fdvh wkdw iru vxfk wudqvdfwlrqv/zklfk duh riwhq ri yhu| odujh ydoxh/lpphgldf| dqg ulvn frqvlghudwlrqv pd| grplqdwh sulflqj lvvxhv1 Wkhvh lvvxhv duh ohiw rxwvlgh wkh vfrsh ri wkh suhvhqw sdshu1
48Zkhq wklv frqvwudlqw lv qrw elqglqj/wkh vroxwlrq lv wkh vdph dv lq Vhfwlrq 6= wkh suhvhqfh ri d sulydwh frpshwlwru grhv qrw dhfw wkh sulflqj srolf| ri wkh Fhqwudo Edqn1 Wkhuh lv dovr d pruh frpsoh{ fdvh
lqwhuhvwv ri wkh phpehu edqnv dqg wkhlu fxvwrphuv/l1h1/wkdw wkh| fkrrvh d wdul A wkdw
pd{lpl}hv wkh djjuhjdwh vxusoxv jhqhudwhg e| wkh phpehu edqnv xqghu wkh euhdn hyhq frqvwudlqw
sMAM E'
Vlqfh wkhuh lv rqo| rqh w|sh xvlqj wkh sulydwh v|vwhp/ wkh wdul vwuxfwxuh lv vlpsoh= wkh v|vwhp qhhgv wr uhfryhu frvwv zlwk d sd|phqw yroxph ri ' ' sM^M1 Wklv lv dfklhyhg
zlwk dyhudjh frvw sulflqj= wkh {hg ihh lv vkduhg dprqj sduwlflsdqwv sursruwlrqdoo|/dqg pdujlqdo ihhv duh htxdo wr wkh pdujlqdo frvw1 Wkh wdul fkdujhg e| wkh sulydwh v|vwhp lv wkhuhiruh
AE^ ' s@
M n S^ +47,
Qrwlfh wkdw zlwk wklv sulflqj vwuxfwxuh/edqnv fkrrvh wkh wudqvdfwlrq yroxph ^ wkdw pd{lpl}hv vxusoxv
r
M 4@ ^ dEwMc ^ S^o +48,
Zh prgho wkh sxeolf v|vwhp dv d Vwdfnhoehuj ohdghu= zh dvvxph wkdw lw kdv wkh srzhu wr frpplw wr d wdul A E dqg lv deoh wr dqwlflsdwh wkh uhdfwlrq ri lwv sulydwh frpshwlwru1 Wkh remhfwlyh ri wkh sxeolf v|vwhp lv wkxv wr pd{lpl}h djjuhjdwh vxusoxv
4@
&'uccM
s&rEw&c ^&Ew&c
xqghu d frqglwlrq ri edodqfhg exgjhw/zklfk uhtxluhv
&'uc
s&A& @ n S &'uc
s&^&
Dv ehiruh/wkh Fhqwudo Edqn fdq ghvljq frpelqdwlrqv E^&c A& iru hdfk w|sh ri edqn
xvlqj lwv v|vwhp1 Wkh lqfhqwlyh frqvwudlqwv ri wkh edqnv sduwlflsdwlqj lq wkh sxeolf v|vwhp duh/vlplodu wr vhfwlrq 6/
Ew wu ^u u Ew wu ^c
zkhuh wkh Fhqwudo Edqn idfhv wzr elqglqj sduwlflsdwlrq frqvwudlqwv= wkdw ri orz w|shv/dqg wkh frqvwudlqw wkdw phglxp w|shv duh qrw dwwudfwhg e| wkh sulydwh v|vwhp1
dqg wkh sduwlflsdwlrq frqvwudlqwv u f dqg f1 Ixuwkhupruh/rqh qhhgv wr hqvxuh
wkdw edqnv ri w|sh w kdyh qr lqwhuhvw lq vzlwfklqj wr wkh sulydwh v|vwhp1 Wklv uhtxluhv
zkhuh 4@ ^ dEwc ^ A E^o ' r s@ M +49, zkhuh r /zklfk lv ghqhg dqdorjrxvo| wr +48,/ghqrwhv wkh zhoiduh wkh phglxp w|sh
zrxog kdyh rewdlqhg lq wkh sulydwh v|vwhp1 Wklv looxvwudwhv wkh glhuhqfh wr wkh deryh prqrsro| vlwxdwlrq dqdo|}hg lq vhfwlrq 6= qrz/wkhuh lv frpshwlwlrq iurp deryh zklfk uhtxluhv wkh lqwurgxfwlrq ri wkh dgglwlrqdo frqvwudlqw/ 1 Dv douhdg| glvfxvvhg/
zh irfxv rq wkh prvw lqwhuhvwlqj fdvh lq zklfk wklv lv wkh elqglqj sduwlflsdwlrq frqvwudlqw1 Wklv lv wkh fdvh iru
r s@
M : Ew wu ^ +4:,
Wkh rswlpdo sulflqj lv fkdudfwhul}hg e| wkh iroorzlqj sursrvlwlrq1
Sursrvlwlrq 6 Vxssrvh wkdw wkh kljkhvw w|shv wM sduwlflsdwh lq d sulydwh v|vwhp/ wkh w|shv w dqg wu lq wkh sxeolf v|vwhp/ dqg +4:, krogv1 Wkh rswlpdo pdujlqdo wdul lq wkh sxeolf OYSV lv wkhq jlyhq e|
AE^
' ^Ewc ^ ' S n bb ssu
Ew wu
AE^
u ' ^Ewuc ^u ' S
Wkhuhiruh/lq wkh fdvh ri d pl{hg gxrsro|/zh djdlq rewdlq d ghjuhvvlyh sulflqj vfkhph1 Frqwudu| wr wkh prqrsro| fdvh krzhyhu/lw lv qrz wkh orzhu w|sh zkr rewdlqv pdujlqdo frvw sulflqj/zkloh wkh kljkhu w|sh idfhv d glvwruwlrq1 Pruhryhu/wkh phglxp edqn w|shv +w,
idfh sulfhv wkdw duh ehorz pdujlqdo frvw1 Wklv sulflqj vfkhph uhvxowv iurp frpshwlwlrq iurp wkh sulydwh v|vwhp= wkh sulydwh v|vwhp kdv pdujlqdo ihhv S wkdw duh ehorz pdujlqdo
frvw ri wkh sxeolf v|vwhp/ S1 Lq rughu wr jlyh lqfhqwlyhv iru edqnv ri w|sh w wr xvh
wkh sxeolf v|vwhp/wkhuh pxvw eh d vxevlg| dw wkh pdujlq1 Iru wkh orz w|shv/pdujlqdo frvw sulflqj lv qrz dwwdlqdeoh1 Wklv lv ehfdxvh ri frqglwlrq +4:,/zklfk lpsolhv wkdw wkh phglxp w|shv gr qrw kdyh dq| lqfhqwlyhv wr fkrrvh wkh sd|phqw yroxph ri wkh orzhu w|shv/exw udwkhu pryh wr wkh sulydwh v|vwhp1 Wkhuhiruh/wkhuh lv qr qhhg wr glvwruw wkh orzhu w|sh*v pdujlqdo ihh xszdugv1
Wkh sulflqj vfkhph ri Sursrvlwlrq 6 qhfhvvdulo| lqyroyhv d srvlwlyh {hg ihh1 Lqghhg/ vlqfh pdujlqdo frvwv duh ehorz ru htxdo wr wkh pdujlqdo frvw S/exgjhw edodqfh fdq rqo| eh
dfklhyhg zlwk d {hg ihh/kljk hqrxjk wr uhfryhu qrw rqo| wkh {hg frvw exw dovr wkh vxe0 vlglhv wr phglxp vl}hg edqnv1 Wklv sulflqj vfkhph lv rqo| yldeoh li Ewuc ^uA E^u f lv
vwloo vdwlvhg/l1h1 li wkh orzhu w|sh*v sduwlflsdwlrq frqvwudlqw lv qrw ylrodwhg1 Lq sduwlfxodu/ wkhuh lv dq xsshu olplw wr wkh pd{lpdo {hg frvw @ wkdw fdq eh vxvwdlqhg zlwk wkh wdul vfkhgxoh ghyhorshg khuh1 Iru yhu| kljk @/+ru iru kljk b,/wkh Fhqwudo Edqn pljkw kdyh wr ghsduw iurp wkh frvw uhfryhu| sulqflsoh ru hovh uhod{ wkh lqfhqwlyh frqvwudlqwv e| doorzlqj wkh edqn w|shv w wr xvh wkh sulydwh v|vwhp1 Lq wkh pruh jhqhudo fdvh ri d frqwlqxrxv
glvwulexwlrq ri w|shv/wkh sdwwhuq ri wkh rswlpdo wdul lv pruh frpsoh{/lqyroylqj pdujlqdo sulfhv deryh pdujlqdo frvw iru orz yroxphv/dqg ehorz iru odujh yroxphv/frpelqhg zlwk d srvlwlyh {hg ihh1
8 Frpshwlwlrq Ehwzhhq Qdwlrqdo UWJVv
Zh qrz frqvlghu d glhuhqw w|sh ri frpshwlwlrq ehwzhhq OYSVv/qdpho| ehwzhhq wkh sxeolf v|vwhpv ri wzr glhuhqw frxqwulhv +ghqrwhg e| wkh lqgh{ ' c 2,1 Zh prgho wkh edqnlqj vhfwruv dqg wkh OYSVv ri wkh wzr frxqwulhv h{dfwo| dv ehiruh= lq erwk frxqwulhv/ wkhuh lv d sursruwlrq s
& / ' c 2/ri w|shv & ' iuc Mj1 Wkh frvw ixqfwlrqv ri wkh OYSV
lq frxqwu| duh jlyhq dv
' @n S'
zkhuh z1o1r1j1/zh dvvxph wkdw S S2 dqg @ : @21 Li doo edqnv zhuh xvlqj wkhlu rzq
qdwlrqdo OYSV/hdfk frxqwu| frxog fkrrvh d orfdoo| rswlpdo ihh vwuxfwxuh/dv jlyhq lq Sursrvlwlrq 4= A E^M ' ^EwMc ^M ' S A E^u ' ^Ewuc ^u ' S n n bb s M s u EwM wu
Glhuhqw fkdudfwhulvwlfv ri wkh edqnlqj vhfwruv +h1j1 d glhuhqw glvwulexwlrq ri edqn w|shv,/dqg glhuhqfhv lq wkh frvw vwuxfwxuhv ri wkh OYSV zrxog ohdg wr glhuhqw ihh vwuxfwxuhv dfurvv frxqwulhv1 Vxfk dq hqylurqphqw pd| fuhdwh lqfhqwlyhv iru edqnv wr e|0 sdvv wkhlu rzq v|vwhp dqg urxwh wkhlu sd|phqwv wkurxjk wkh v|vwhp ri d qhljkerulqj frxqwu| lqvwhdg1 Lq wkh deryh h{dpsoh/iru lqvwdqfh/iru wkh kljkhu w|shv wM wkh pdujlqdo
ihh lv orzhu lq frxqwu| 4 wkdq lq frxqwu| 51 Edqnv pd| eh lq d srvlwlrq wr fkrrvh zklfk ri wkh qdwlrqdo sd|phqw v|vwhpv wr xvh hlwkhu ehfdxvh wkh| kdyh vxevlgldulhv lq vhyhudo
frxqwulhv dqg wkhuhiruh dffhvv wr vhyhudo qdwlrqdo OYSV/ru ehfdxvh uhprwh dffhvv49 lv
srvvleoh1
Wkh srvvlelolw| ri e|0sdvvlqj udlvhv pdq| txhvwlrqv iru wkh ghvljq ri dq h!flhqw sulflqj vfkhph/vxfk dv zkhwkhu wkh glhuhqw v|vwhpv vkrxog fr0ruglqdwh wkhlu ihh vwuxfwxuhv lq rughu wr hlwkhu ghwhu ru wr hqfrxudjh e|0sdvvlqj/dqg zkhwkhu d xqlirup ihh vwuxfwxuh wkurxjkrxw wkh duhd frxog eh rswlpdo1 Wklv vhfwlrq wulhv wr dgguhvv vrph ri wkhvh lvvxhv1 Zh zloo dqdo|vh erwk fdvhv/uvw rqh zkhuh e|0sdvvlqj lv doorzhg/dqg d vhfrqg fdvh zkhuh wkh OYSVv dgmxvw wkhlu sulflqj lq rughu wr pdnh e|0sdvvlqj xqdwwudfwlyh wr edqnv1 D zhoiduh frpsdulvrq ri wkh wzr rxwfrphv zrxog ghwhuplqh zklfk lv wkh pruh ghvludeoh zd| wr jr1
Zh zloo irfxv rq wkh fdvh wkdw uhprwh dffhvv lv qrw srvvleoh1 Lqvwhdg/zh dvvxph wkdw rqo| vrph edqnv fdq e|0sdvv ehfdxvh wkh| kdyh eudqfkhv lq wkh rwkhu frxqwu|/wkrvh zlwk wkh kljkhu ghpdqg iru sd|phqwv1 Lw lv dvvxphg wkdw wkhuh lv d frvw wkdw qhhgv wr eh eruqh e| wkh edqnv zkr e|0sdvv1 Ixuwkhupruh/zh dvvxph iru vlpsolflw| wkdw d edqn qhhgv wr urxwh doo lwv sd|phqwv wkurxjk rqh vlqjoh v|vwhp/l1h1 lw fdqqrw vsolw sd|phqwv vr wkh| duh urxwhg wkurxjk wzr v|vwhpv dw wkh vdph wlph1 Ilqdoo|/zh uhtxluh wkdw wkh frvw0uhfryhu| frqvwudlqw kdv wr eh vdwlvhg iru hdfk lqglylgxdo OYSV1
814 H!flhqw sulflqj zlwk e|0sdvvlqj
Vxssrvh wkdw wkh frvw ri e|sdvv lv vx!flhqwo| orz vr lw lv zruwkzkloh iru edqnv ri w|sh wM
lq frxqwu| 5 wr xvh wkh OYSV lq frxqwu| 41 Wkh sureohp ri qglqj wkh h!flhqw sulflqj vwuxfwxuh iru wkdw OYSV lv ghulyhg dqdorjrxvo| wr wkh suhylrxv vhfwlrqv/wkh rqo| glhuhqfh ehlqj wkdw wkh ghpdqg iru d kljk sd|phqw yroxph lq frxqwu| 4 kdv qrz lqfuhdvhg1 Wkh rswlpdo pdujlqdo wdul lq frxqwu| 4 lv jlyhq lq wkh iroorzlqj sursrvlwlrq=
Sursrvlwlrq 7 Vxssrvh wkdw wM0edqnv iurp frxqwu| 5 e|0sdvv1 Wkh rswlpdo wdul lq frxqwu| 4 kdv wr vdwlvi| A E^M ' AE^M2 ' ^EwMc ^M ' S A E^u ' ^Ewuc ^u ' Sn n bb s Mn sM2 s u EwM wu
Wkh h!flhqw sulflqj lq frxqwu| 4 lv wkhuhiruh yhu| vlplodu wr wkh prqrsro| fdvh1 Lq frxqwu| 5/rq wkh rwkhu kdqg/wkhuh lv qrz rqo| rqh edqn w|sh zlwk d srvlwlyh sd|phqw
ghpdqg1 Wkhuhiruh/wkh OYSV fdq vlpso| dsso| dyhudjh frvw sulflqj dqg fkdujh d wdul A2E^ ' s@
u n S2^
Doorzlqj e|0sdvv kdv rqh dwwudfwlyh ihdwxuh= pruh edqnv xvh wkh v|vwhp zkhuh wkh pdujlqdo frvw ri vhqglqj sd|phqwv lv orzhvw +frxqwu| 4,1 Krzhyhu/dv xvxdo zh qhhg wr fkhfn zkhwkhu wkh sduwlflsdwlrq frqvwudlqw ri wkh wu0 w|shv lv vdwlvhg1 Wklv pljkw srvh
d sureohp khuh= ehfdxvh wkh qxpehu ri sduwlflsdqwv lq wkh OYSV ri frxqwu| 5 kdv qrz glplqlvkhg/wkh edqnv zlwk d orz sd|phqw ghpdqg kdyh wr ehdu wkh hqwluh {hg frvw ri uxqqlqj wkh v|vwhp/ @2/dprqj wkhpvhoyhv1 Wkhlu sduwlflsdwlrq frqvwudlqw pljkw wkhuhiruh
eh ylrodwhg/dqg wkh v|vwhp zrxog euhdn grzq1 Wkxv/wkhuh duh fdvhv zkhuh lw fdq eh mxvwlhg wr ghwhu e|0sdvv1 Wklv lv zkdw zh vwxg| qrz1
815 E|0sdvvlqj lv ghwhuuhg
Wkh dowhuqdwlyh wr doorzlqj e|0sdvv wr kdsshq lv wr fkdqjh wkh sulflqj vwuxfwxuh ri wkh qdwlrqdo OYSV lq rughu wr pdnh e|0sdvv qrqsurwdeoh iru edqnv1 Rqh srvvlelolw| khuh lv wr uhtxluh d ixoo kduprql}dwlrq ri wdulv1 Lq wkdw fdvh/d srvlwlyh frvw ri e|sdvv zrxog pdnh e|0sdvv xqdwwudfwlyh1 Krzhyhu/zh kdyh dujxhg deryh wkdw wklv vroxwlrq fdqqrw eh h!flhqw= sulfhv vkrxog ydu| dfurvv frxqwulhv dqg uh hfw glhuhqfhv lq wkh vwuxfwxuh ri edqnlqj vhfwruv dqg srvvleo| wkh xqghuo|lqj frvw sdudphwhuv ri hdfk OYSV1
D ohvv h{wuhph vlwxdwlrq lv rqh lq zklfk wkhuh duh sulfh glhuhqfhv dfurvv frxqwulhv exw wkh| duh olplwhg lq rughu wr ghwhu e|0sdvv1 Vlqfh lw lv wkh kljk w|sh edqnv wkdw duh pruh olnho| wr e|0sdvv/zh mxvw kdyh wr lqwurgxfh wkh dgglwlrqdo frqvwudlqw wkdw edqnv ri w|sh wM lq frxqwu| 5 suhihu wr xvh wkh krph frxqwu| OYSV=
2
M M
Zh irfxv rq wkh fdvh zkhuh wklv frqvwudlqw lv elqglqj1 Wkh dqdo|vlv dovr ghshqgv fuxfldoo| rq wkh ohyho ri /wkh frvw ri e|sdvv1 Zh irfxv rq wkh fdvh zkhuh lv uhodwlyho| orz +iru ghwdlov/vhh wkh surri lq wkh dsshqgl{,1 Ghqrwh e| b dqg b2 Odjudqjh pxowlslhuv
ri wkh euhdn hyhq frqvwudlqwv ri wkh wzr OYSV1 Iru wklv fdvh/zh rewdlq
lq frxqwu| 4 qhhgv wr vdwlvi|= A E^M ' ^EwMc ^M ' S A E^u ' ^Ewuc ^u ' S nbs Mn b2Esu2 n sM2 E n bsu EwM wuc dqg lq frxqwu| 5= A 2E^M2 ' ^EwMc ^M2 ' S2 n bb2 2 s2 u s2 MEwM wu A 2E^u2 ' ^Ewuc ^2u ' S2
Li e|0sdvv lv wr eh ghwhuuhg/ wkh sulflqj vfkhphv lq wkh wzr frxqwulhv wkhuhiruh kdyh wr kdyh glhuhqw ihdwxuhv1 Lq wkh frxqwu| zlwk wkh orzhu pdujlqdo frvw +l1h1 frxqwu| 4,/wkh rswlpdo wdul lv vlplodu wr wkh rqh ri wkh prqrsro| fdvh= lw lv ghjuhvvlyh/dqg rqo| edqnv zlwk d kljk sd|phqw yroxph sd| d pdujlqdo ihh htxdo wr pdujlqdo frvw1 Lq wkh frxqwu| idflqj wkh ulvn ri e|0sdvv +l1h1 frxqwu| 5,/rq wkh rwkhu kdqg/wkh pdujlqdo ihh iru wkh kljk sd|phqw yroxph qhhgv wr eh orzhuhg lq rughu wr pdnh e|0sdvv xqdwwudfwlyh1
Qrwlfh/krzhyhu/wkdw dovr khuh zh qhhg wr yhuli| zkhwkhu wkh orzhu w|sh*v sduwlfl0 sdwlrq frqvwudlqwv duh vdwlvhg= ehfdxvh pdujlqdo ihhv duh ehorz pdujlqdo frvw iru vrph w|shv/d {hg ihh lv qhhghg lq rughu wr dfklhyh exgjhw edodqfh1 Li wkh {hg ihh lv wrr kljk/ ru li wkh pdujlqdo vxevlg| iru wkh kljk w|shv lv wrr odujh/wkhq wkh v|vwhp lv qrw yldeoh1 Vwloo/ehfdxvh wkh kljk w|shv sduwlflsdwh lq wkh v|vwhp/exgjhw edodqfh lv hdvlhu wr vdwlvi| wkdq lq wkh fdvh zkhuh e|0sdvv lv doorzhg1
D mxgjhphqw zkhwkhu e|0sdvv vkrxog eh doorzhg ru qrw lv qrw srvvleoh lq jhqhudo whupv1 Wklv zloo ghshqg rq wkh vshflf sdudphwhuv ri wkh prgho1 Sursrvlwlrqv 7 dqg 8 lpso| wkdw lq erwk fdvhv pdujlqdo sulfhv qhhg wr eh glvwruwhg dzd| iurp pdujlqdo frvwv1 Wkh uhvxowlqj lqh!flhqw ohyhov ri sd|phqw ghpdqg ^& qhhg wr eh wdnhq lqwr dffrxqw lq wkh
zhoiduh dqdo|vlv1 Vwloo/e|0sdvvlqj kdv wkh dgydqwdjh wkdw pruh edqnv xvh wkh sd|phqw whfkqrorj| zlwk wkh orzhu pdujlqdo frvw1 E|sdvvlqj lq lwvhoi pljkw krzhyhu lqwurgxfh vrfldo zhoiduh frvw zklfk duh qrw srvvleoh wr fdswxuh lq d prgho olnh rxuv1 Rqh vxfk frvw frxog eh uhodwhg wr wkh srvvleoh euhdngrzq ri rqh ri wkh v|vwhpv lq fdvh ri e|0sdvv1 Wkhuhiruh/wkh rswlpdo wdul zloo ghshqg rq wkh zloolqjqhvv ri fhqwudo edqnv wr doorz wklv wr kdsshq/ru wr srvvleo| vxevlgl}h rqh ri wkh v|vwhpv1
9 Frqfoxglqj Uhpdunv
Zh kdyh dqdo|}hg wkh rswlpdo sulflqj lq d Odujh Ydoxh Sd|phqw V|vwhp zkhq ixoo frvw uhfryhu| lv uhtxluhg1 Zh kdyh vkrzq wkdw li wkh sd|phqw v|vwhp rshudwhv dv d prqrsro|/ wkhq wkh rswlpdo wdul lqyroyhv txdqwlw| glvfrxqwv/exw qr {hg ihh1 Wklv sduwlfxodu irup ri yroxph0edvhg sulflqj lv wkh rswlpdo zd| wr dfklhyh uhfryhu| ri {hg frvwv/jlyhq wkh lpsrvvlelolw| wr lpsohphqw shuvrqdol}hg wdulv1 Txdqwlw| glvfrxqwv duh lpsruwdqw wr hqvxuh wkdw edqnv zlwk d srwhqwldoo| kljk sd|phqw yroxph grq*w ghflgh wr orzhu wkh qxpehu ri sd|phqwv vhqw wkurxjk wkh sd|phqw v|vwhp1 Pruhryhu/wkh devhqfh ri d {hg ihh hqvxuhv sduwlflsdwlrq ri orz w|sh edqnv1
Wkh vlwxdwlrq fkdqjhv zkhq wkh sxeolf v|vwhp idfhv frpshwlwlrq iurp d sulydwh v|vwhp zklfk/ehfdxvh ri orzhu pdujlqdo frvwv/lv deoh wr dwwudfw wkh edqnv zlwk wkh kljkhvw sd|phqw ghpdqg1 Wkh rswlpdo sulflqj vfkhph ri wkh sxeolf v|vwhp wkhq qhhgv wr eh dgmxvwhg1 Wklv sdshu vkrzv wkdw wkh sxeolf v|vwhp qhhgv wr ghfuhdvh lwv pdujlqdo ihhv ehorz pdujlqdo frvwv lq rughu wr nhhs d vx!flhqw yroxph ri wudqvdfwlrqv> dv d uhvxow/{hg ihhv kdyh wr eh lqwurgxfhg1
Zh dovr dqdo|}h wkh vlwxdwlrq zkhuh wzr qdwlrqdo sxeolf sd|phqw v|vwhpv frpshwh iru wkh grphvwlf wudqvdfwlrqv ri odujh edqnv zkr kdyh eudqfkhv lq erwk frxqwulhv dqg duh deoh wr urxwh wkhlu sd|phqwv wkurxjk hlwkhu v|vwhp1 Zh fkdudfwhul}h wkh rswlpdo wdulv dqg vkrz wkdw wkh| ghshqg rq zkhwkhu vxfk d e|0sdvv lv ghwhuuhg ru qrw1 Zkhq lw lv qrw/wkh rswlpdo wdulv h{klelw wkh vdph txdolwdwlyh surshuwlhv dv lq wkh prqrsro| fdvh= pdujlqdo ihhv duh deryh pdujlqdo frvwv1 Li e|0sdvv lv wr eh ghwhuuhg rq wkh frqwudu|/wkh ihdwxuhv ri wkh rswlpdo wdulv duh vlplodu wr wkh fdvh ri frpshwlwlrq e| d sulydwh v|vwhp= wkh frxqwu| wkdw lv vxemhfw wr wkh ulvn ri e|0sdvv kdv wr ghfuhdvh lwv pdujlqdo ihhv ehorz pdujlqdo frvwv/zkloh wkh rssrvlwh lv wuxh iru wkh rwkhu frxqwu|1
Rqh lpsruwdqw olplwdwlrq ri rxu dqdo|vlv lv wkdw zh kdyh frqvlghuhg krprjhqrxv sd|0 phqwv/vr wkdw yroxph lv wkh yduldeoh wkdw fdq eh xvhg wr glhuhqwldwh sulfhv1 Lw zrxog eh lpsruwdqw wr lqwurgxfh khwhurjhqhrxv sd|phqwv/vr dv wr wdnh lqwr dffrxqw rwkhu fkdu0 dfwhulvwlfv vxfk dv vl}h1 Wklv zrxog w pruh dffxudwho| wkh suhvhqw vlwxdwlrq zkhuh odujh frpphufldo edqnv w|slfdoo| xvh wkh sulydwh v|vwhp iru vpdoo wr phglxp vl}h wudqvdfwlrqv dqg wkh sxeolf v|vwhp iru odujh wudqvdfwlrqv iru zklfk lpphgldwh qdolw| lv fuxfldo1 Lw lv sodqqhg wr dgguhvv wklv h{whqvlrq lq d vhsdudwh sdshu1
DSSHQGL[= SURRIV
Surri ri Sursrvlwlrq 4= Zh ghfrpsrvh wkh Fhqwudo Edqn*v sureohp lqwr wzr sduwv= uvw/iru {hg txdqwlwlhv/lw fkrrvhv wkh rswlpdo &/dqg lq d vhfrqg vwhs/lw fkrrvhv wkh
txdqwlwlhv ^&1
Lw lv hdv| wr vhh wkdw EU-M lv qrw elqglqj/vlqfh EUM dqg EU-u lpso| M u1
Ixuwkhupruh/wkh lqfhqwlyh0frpsdwlelolw| frqvwudlqwv fdq eh vlpsolhg wr EwM wu^u M u EwM wu^M
Wkh euhdn0hyhq frqvwudlqw fdq eh uh0vwdwhg &s&Er& & @1 Iurp khuh/lw lv
lpphgldwh wkdw pd{lpl}lqj vxusoxv lv htxlydohqw wr plqlpl}lqj wkh vxp ri lqglylgxdo xwlolwlhv 4? &'ucM s&& vxfk wkdw EwM wu^u M u EwM wu^M u f
Lw lv hdv| wr vhh wkdw/dv xvxdo/wkh orzhu w|sh*v sduwlflsdwlrq frqvwudlqw qhhgv wr eh elqglqj/ u ' f/dv zhoo dv wkh kljkhu w|sh*v lqfhqwlyh frpsdwlelolw| frqvwudlqw/M '
EwM wu^u 1 Xvlqj wkhvh ydoxhv ri &/zh fdq lq wkh vhfrqg vwhs uh0vwdwh wkh sureohp ri
wkh fhqwudo edqn ri qglqj wkh rswlpdo txdqwlwlhv ^u dqg ^M wkdw pd{lpl}h vxusoxv xqghu
wkh euhdn0hyhq frqvwudlqw/xvlqj wkh Odjudqjldq u ' &'ucM s&r&n b &'ucM s&r& @ &'ucM s&& ' E n b &'ucM
s&iEw&c ^& S^&j b i@ n sMEwM wu^uj
Pd{lpl}lqj z1u1w1 ^M dqg ^u/zh qg
^EwMc ^M ' S
dqg E n bsu^Ewuc ^u ' S n bEwM wu/ru
^Ewuc ^u ' S n n bb ssM
Wrjhwkhu zlwk htxdwlrq +6,/wklv hvwdeolvkhv Sursrvlwlrq 41
Surri ri Sursrvlwlrq 5= Wkh lqgluhfw xwlolw| ixqfwlrq ri wkh edqnv lv ghqhg lq +5,/ dqg +6, krogv1 D vlpsoh uhyhdohg suhihuhqfh dujxphqw/wrjhwkhu zlwk wkh vlqjoh furvvlqj surshuw| wkdw w^ : f/lpsolhv wkdw ^E pxvw eh hyhu|zkhuh qrq0ghfuhdvlqj1 D fodvvlfdo
uhvxow +iru d surri/vhh iru lqvwdqfh Ixghqehuj dqg Wluroh, vkrzv wkdw frqyhuvho| dq| qrq0ghfuhdvlqj ixqfwlrq ^E fdq eh lpsohphqwhg e| d wdul vdwlvi|lqj +6,1 Wkh hqyhorsh sulqflsoh dssolhg wr frqglwlrq +5, wkhq lpsolhv wkdw iru doprvw hyhu| w=
Ew '
wEwc ^Ew +D14,
Dgrswlqj wkh gxdo dssurdfk ghyhorshg e| Pluuohhv/zh xvh E dqg ^E dv srolf| yduldeohv +lqvwhdg ri A ,1 A zloo odwhu eh ghulyhg lpsolflwo| e| wkh irupxod=
A d^Ewo ' Ewc ^Ew Ew Zh wkhuhiruh kdyh wr qg ^E dqg E wkdw vroyh
4@ 7w
wf
iEwc ^Ew S^Ewj_8Ew Ew '
wEwc ^Ew w 5owc 7wd +D15,
7w
w iEwc ^Ew S^Ew Ewj_8 Ew @ +D16,
Ewf ' f +D17,
Wkh vroxwlrq wr wkh deryh sureohp fdq eh rewdlqhg e| pd{lpl}lqj lwv Odjudqjldq= u ' 7w
wf
dE n biEwc ^Ew S^Ewj bEwo sEw_wc
xqghu +D14, dqg +D16,1 Wkh whup lq fdq eh holplqdwhg e| dq lqwhjudwlrq e| sduwv=
7w wf EwsEw_w ' 7w wf ^EwE 8 Ew_w zklfk jlyhv u ' 7w wf
dE n biEwc ^Ew S^EwjsEw b^EwE 8 Ewo _wc zklfk lv pd{lpl}hg zkhq
Wkh rswlpdo pdujlqdo ihh AE^ lv wkxv ghwhuplqhg mrlqwo| zlwk wkh rswlpdo yroxph
^Ew e| +D7, dqg wkh frqglwlrq
AE^Ew '
^Ewc ^Ew
Vlqfh 38
s ghfuhdvhv lq w +vlqfh s lv orj0frqfdyh,/wrwdo glhuhqwldwlrq ri wkh uvw
htxdwlrq jlyhv
w^n ^^^Ew fc
zklfk lpsolhv ^Ew : f +dv zdv wr eh fkhfnhg, vlqfh
w^ : f dqg ^^ f1 Vlploduo|/e|
glhuhqwldwlqj wkh vhfrqg htxdwlrq zh vhh wkdw A lv ghfuhdvlqj1
Wkh sduwlflsdwlrq wkuhvkrog lv ghwhuplqhg e| pd{lpl}lqj u zlwk uhvshfw wr wf1 Zh
rewdlq=
E n biEwfc ^Ewf S^EwfjsEwf ' b^EwfE 8 Ewf
Wkxv Ewfc ^Ewf ^Ewf ' S n b n b 8 Ewf sEwf ' ^Ewfc ^Ewf
Jlyhq wkh vwulfw frqfdylw| ri lq ^ +dqg wkh idfw wkdw Ewfc f ' f, wklv lv rqo| srvvleoh
zkhq ^Ewf ' f1 Wklv lpsolhv lq wxuq wkdw wkh rswlpdo {hg ihh lv }hur/vlqfh lw lv ghqhg
dv
A ' *4
^<fnA E^ ' *4w<wfAE^Ew
Exw A E^Ew ' Ewc ^Ew Ew dqg erwk whupv whqg wr }hur zkhq w $ wf1
Surri ri Sursrvlwlrq 6= Dv ehiruh/zh glylgh wkh sureohp lqwr wzr vwhsv/dqg dv d uvw vwhs/qg wkh rswlpdo & iru jlyhq txdqwlwlhv ^u dqg ^1 Djdlq/pd{lpl}dwlrq ri vxusoxv
uhtxluhv plqlpl}dwlrq ri & xqghu wkh frqvwudlqwv
u f
r s@ M
Ew wu ^u u Ew wu ^
Xqghu dvvxpswlrq +4:,/lw lv hdv| wr vhh wkdw wkh plqlpdo & vdwlvi|=
' r s@
u ' Ew wu ^
Dvvxpswlrq +4:, lpsolhv wkdw lq rughu wr lqgxfh wkh plggoh w|shv qrw wr fkdqjh wr wkh sulydwh v|vwhp/ qhhgv wr eh vr kljk wkdw u ' f lv qr orqjhu dwwdlqdeoh ehfdxvh wklv
zrxog ylrodwh wkh orzhu w|shv lqfhqwlyh frqvwudlqw qrw wr sdvv r dv d plggoh w|sh1 Jlyhq wkh rswlpdo ydoxhv ri &/wkh vhfrqg vwhs ri wkh pd{lpl}dwlrq sureohp lv wr qg
wkh rswlpdo txdqwlwlhv ^u dqg ^1 Wkh exgjhw edodqfh uhvwulfwlrq fdq eh uhzulwwhq dv=
surun sr @ n suun s
Ghqrwlqj e| b wkh pxowlsolhu dvvrfldwhg zlwk wkh exgjhw frqvwudlqw ri wkh sxeolf v|vwhp/wkh Odjudqjldq lv u ' &'uc s&r&n b &'uc s&r& @ suu sMM
' E n b s&r& b @ n Esun sMEr s@
M S^
Khuh/zh kdyh ohiw rxw wkh vxusoxv ri wkh wM0w|shv/dv lw lv frqvwdqw iurp srlqw ri ylhz
ri wkh sxeolf v|vwhp1 Pd{lpl}dwlrq zlwk uhvshfw wr ^u dqg ^ |lhogv
^Ewuc ^u ' S
^Ewc ^ ' S n bb ssu
MEw wu
Wrjhwkhu zlwk wkh edqn*v rswlpdolw| frqglwlrq AE^
& ' ^Ew&c ^&/zh fdq hvwdeolvk Sursr0
vlwlrq 614:
Surri ri Sursrvlwlrq 8= Dv ehiruh/wkh uvw vwhs ri wkh pd{lpl}dwlrq sureohp frq0 vlvwv lq plqlpl}lqj h{shfwhg uhqwv vxemhfw wr wkh lqfhqwlyh frpsdwlelolw|0 dqg lqglylgxdo udwlrqdolw| frqvwudlqwv/l1h1
4@
c&
s &&
4:Wkh Odjudqjh pxowlsolhu fdq eh ghwhuplqhg wrjhwkhu zlwk tP e| xvlqj wkh vhfrqg IRF dqg wkh
exgjhw frqvwudlqw1 Khuh/lw lv xvhixo wr zrun zlwk wkh yluwxdo w|sh P P .
vxfk wkdw u f Ek M u EwM wu^M Ek2 EwM wu^u M u Ek M 2M Eke duh vdwlvhg iru ' c 2/dqg k ghqrwh wkh Odjudqjh pxowlsolhuv dvvrfldwhg zlwk wkh
frqvwudlqwv1 Zh irfxv rq wkh fdvh zkhuh wkh odvw frqvwudlqw lv elqglqj/vr wkdw 2
M ' M1
Ixuwkhupruh/wkhuh duh wzr srvvlelolwlhv/ghshqglqj rq zkhwkhu
M EwM wu^2M +D19,
lv vdwlvhg1 Vxssrvh wkdw +D19, krogv1 Wkh plqlpdo ydoxhv iru
&/ ' c 2/ & ' uc M/wkdw
vdwlvi| doo vhyhq frqvwudlqwv duh wkhq
u' f 2u' EwM wu E^u ^M2
M ' EwM wu^u 2M ' EwM wu^u
Dv ehiruh/wkhvh ydoxhv duh xvhg lq wkh vhfrqg vwhs ri qglqj wkh rswlpdo txdqwlwlhv ^
&1 Wkh Odjudqjldq ri wkh sureohp lv
m ' 'c2 &'ucM s &r&n 'c2 b &'ucM s &r& &'ucM s && ' 'c2 E n b &'ucM s &r& bsMEwM wu^u b2 su2 n sM2 EwM wu^u n b2^2M
Wkh uvw rughu frqglwlrqv |lhog
^Ewuc ^u ' Sn bs Mn b2Esu2 n sM2 E n bsu EwM wu ^EwMc ^M ' S ^Ewuc ^u2 ' S2 ^EwMc ^M2 ' S2 n bb2 2 s2 u s2 MEwM wu
UHIHUHQFHV
Dqjholql/S1 +4<<7,/Derxw wkh Ohyho ri Gd|oljkw Fuhglw/Vshhg ri Vhwwohphqw dqg Uhvhuyhv lq Hohfwurqlf Sd|phqw V|vwhpv/Whpl gl glvfxvvlrqh qf 55</
Edqfd g*Lwdold1
Dqjholql/S1 dqg F1 Jldqqlql +4<<6,/Rq wkh Hfrqrplfv ri Lqwhuedqn Sd|phqw V|vwhpv/Whpl gl glvfxvvlrqh qf 4<6/Edqfd g*Lwdold1
Edjqrol/P1 dqg W1 Ehujvwurp +4<;<,/Orj0frqfdyh Suredelolw| dqg lwv Ds0 solfdwlrqv/FUHVW zrunlqj sdshu &;<056/Xqlyhuvlw| ri Plfkljdq1 Edqn iru Lqwhuqdwlrqdo Vhwwohphqwv +4<<3,/Uhsruw ri wkh Frpplwwhh rq Lqwhu0
edqn Qhwwlqj Vfkhphv ri wkh Fhqwudo Edqnv ri wkh Jurxs ri Whq frxqwulhv +Odpidoxvv| Uhsruw,1
Ehujhu/D1/G1 Kdqfrfn dqg M1 Pdutxdugw +4<<9,/D Iudphzrun iru Dqdo|}lqj H!flhqf|/Ulvnv/Frvwv dqg Lqqrydwlrqv lq wkh Sd|phqwv V|vwhp/Mrxuqdo
ri Prqh|/ Fuhglw dqg Edqnlqj/5;+7,= 9<90:651
Erulr/F1H1Y1/dqg S1 Ydq ghu Ehujk +4<<6,/Wkh Qdwxuh dqg Pdqdjhphqw ri Sd|phqw V|vwhp Ulvnv= Dq Lqwhuqdwlrqdo Shuvshfwlyh/ELV Hfrqrplf Sdshuv 691
Eùv/G1 +4<<7,/Sulflqj dqg Sulfh Uhjxodwlrq/Dgydqfhg Wh{werrnv lq Hfr0 qrplfv Yro1 67/Qruwk0Kroodqg1
Iuhl{dv/[1 dqg E1 Sduljl +4<<;,= Frqwdjlrq dqg H!flhqf| lq Jurvv dqg Qhw Lqwhuedqn Sd|phqw V|vwhpv/ Mrxuqdo ri Ilqdqfldo Lqwhuphgldwlrq/ 43= 60641
Ixuqh/F1K1 dqg M1 Vwhkp +4<<;,/Dqdo|}lqj Dowhuqdwlyh Lqwudgd| Fuhglw Srolflhv lq Uhdo0Wlph Jurvv Vhwwohphqw V|vwhpv/ Mrxuqdo ri Prqh|/ Fuhglw
dqg Edqnlqj/ 63+7,= ;650;7;1
Kdqfrfn/G1/G1E1 Kxpskuh| dqg M1D1 Zlofr{ +4<<<,/Frvw Uhgxfwlrqv lq Hohfwurqlf Sd|phqwv= Wkh Urohv ri Frqvrolgdwlrq/Hfrqrplhv ri Vfdoh dqg Whfkqlfdo Fkdqjh/ Mrxuqdo ri Edqnlqj dqg Ilqdqfh/ 56= 6<407541
Krowkdxvhq/F1 dqg W1 Uûqgh +5335,= Uhjxodwlrq ri Lqwhuqdwlrqdo Odujh0 Ydoxh Sd|phqw V|vwhpv/iruwkfrplqj lq Uhylhz ri Ilqdqfldo Vwxglhv/ 48+8,1
Ndkq/F1 dqg Z1 Urehugv +4<<;,= Sd|phqw V|vwhp Vhwwohphqw dqg Edqn Lqfhqwlyhv/ Uhylhz ri Ilqdqfldo Vwxglhv/44+7,= ;78;:31
Nred|dndpd/V1 +4<<:,/Wkh Frpsdudwlyh Dqdo|vlv ri Vhwwohphqw V|vwhpv/ FHSU Glvfxvvlrq Sdshu qf 499:1
Odrqw/M1M1 dqg M1 Wluroh/+5333,/Frpshwlwlrq lq Whohfrppxqlfdwlrqv/PLW Suhvv/Fdpeulgjh1
PfDqguhzv/M1 +4<<;,/4<<< Ihgzluh Wudqvihu Sulflqj Sursrvdo/plphr Ihg0 hudo Uhvhuyh Edqn ri Qhz \run1
Urfkhw/M1F1 dqg S1 Fkrqì/+4<<:,/Lurqlqj/Vzhhslqj dqg Pxowlglphqvlrqdo Vfuhhqlqj/ Hfrqrphwulfd/99+7,= :;60;591
Urfkhw/M1F1 dqg M1 Wluroh +4<<9,/Frqwuroolqj Ulvn lq Odujh Ydoxh Sd|phqw V|vwhpv/ Mrxuqdo ri Prqh|/ Fuhglw dqg Edqnlqj/ 5;= ;650;941
Vxpphuv/E1 +4<<7,/Wkh Sd|phqw V|vwhp= Ghvljq/ Pdqdjhphqw dqg Vxshu0
ylvlrq/Zdvklqjwrq G1F1/Lqwhuqdwlrqdo Prqhwdu| Ixqg1
Ydq Krrvh/G1G1 +5333,/Fhqwudo Edqn Srolf|pdnlqj lq Frpshwlqj Sd|phqw V|vwhpv/ Dwodqwlf Hfrqrplf Mrxuqdo/ 5;+5,= 44:046<1
(XURSHDQ&HQWUDO%DQNZRUNLQJSDSHUVHULHV )RUDFRPSOHWHOLVWRI:RUNLQJ3DSHUVSXEOLVKHGE\WKH(&%SOHDVHYLVLWWKH(&%·VZHEVLWH KWWSZZZHFELQW ´)LQDQFLDOIULFWLRQVDQGWKHPRQHWDU\WUDQVPLVVLRQPHFKDQLVPWKHRU\HYLGHQFHDQGSROLF\ LPSOLFDWLRQVµE\&%HDQ-/DUVHQDQG.1LNRORY-DQXDU\ ´0RQHWDU\WUDQVPLVVLRQLQWKHHXURDUHDZKHUHGRZHVWDQG"µE\,$QJHORQL$.DVK\DS %0RMRQ'7HUOL]]HVH-DQXDU\ ´0RQHWDU\SROLF\UXOHVPDFURHFRQRPLFVWDELOLW\DQGLQIODWLRQDYLHZIURPWKHWUHQFKHVµ E\$2USKDQLGHV'HFHPEHU ´5HQWLQGLFHVIRUKRXVLQJLQ:HVW*HUPDQ\WRµE\-+RIIPDQQDQG&.XU] -DQXDU\ ´+HGRQLFKRXVHSULFHVZLWKRXWFKDUDFWHULVWLFVWKHFDVHRIQHZPXOWLXQLWKRXVLQJµE\ 2%RYHUDQG39HOLOOD-DQXDU\ ´'XUDEOHJRRGVSULFHLQGH[HVDQGTXDOLW\FKDQJHDQDSSOLFDWLRQWRDXWRPRELOHSULFHVLQ ,WDO\µE\*07RPDW-DQXDU\ ´0RQHWDU\SROLF\DQGWKHVWRFNPDUNHWLQWKHHXURDUHDµE\1&DVVRODDQG&0RUDQD -DQXDU\ ´/HDUQLQJVWDELOLW\LQHFRQRPLFVZLWKKHWHURJHQRXVDJHQWVµE\6+RQNDSRKMDDQG.0LWUD -DQXDU\ ´1DWXUDOUDWHGRXEWVµE\$%H\HUDQG5($)DUPHU)HEUXDU\ ´1HZWHFKQRORJLHVDQGSURGXFWLYLW\JURZWKLQWKHHXURDUHDµE\)9LMVHODDUDQG5$OEHUV )HEUXDU\ ´$QDO\VLQJDQGFRPELQLQJPXOWLSOHFUHGLWDVVHVVPHQWVRIILQDQFLDOLQVWLWXWLRQVµE\(7DEDNLV DQG$9LQFL)HEUXDU\ ´0RQHWDU\SROLF\H[SHFWDWLRQVDQGFRPPLWPHQWµE\*:(YDQVDQG6+RQNDSRKMD )HEUXDU\ ´'XUDWLRQYROXPHDQGYRODWLOLW\LPSDFWRIWUDGHVµE\60DQJDQHOOL)HEUXDU\ ´2SWLPDOFRQWUDFWVLQDG\QDPLFFRVWO\VWDWHYHULILFDWLRQPRGHOµE\&0RQQHWDQG (4XLQWLQ)HEUXDU\ ´3HUIRUPDQFHRIPRQHWDU\SROLF\ZLWKLQWHUQDOFHQWUDOEDQNIRUHFDVWLQJµE\6+RQNDSRKMD DQG.0LWUD)HEUXDU\ ´2SHQQHVVLPSHUIHFWH[FKDQJHUDWHSDVVWKURXJKDQGPRQHWDU\SROLF\µE\)6PHWVDQG 5:RXWHUV)HEUXDU\
´1RQVWDQGDUGFHQWUDOEDQNORVVIXQFWLRQVVNHZHGULVNVDQGFHUWDLQW\HTXLYDOHQFHµE\ $DO1RZDLKLDQG/6WUDFFD0DUFK ´+DUPRQL]HGLQGH[HVRIFRQVXPHUSULFHVWKHLUFRQFHSWXDOIRXQGDWLRQVµE\('LHZHUW 0DUFK ´0HDVXUHPHQWELDVLQWKH+,&3ZKDWGRZHNQRZDQGZKDWGRZHQHHGWRNQRZ"µE\ 0$:\QQHDQG'5RGUtJXH]3DOHQ]XHOD0DUFK ´,QIODWLRQG\QDPLFVDQGGXDOLQIODWLRQLQDFFHVVLRQFRXQWULHVD´QHZ.H\QHVLDQµ SHUVSHFWLYHµE\2$UUDWLEHO'5RGUtJXH]3DOHQ]XHODDQG&7KLPDQQ0DUFK ´&DQFRQILGHQFHLQGLFDWRUVEHXVHIXOWRSUHGLFWVKRUWWHUPUHDO*'3JURZWK"µE\ $0RXURXJDQHDQG05RPD0DUFK ´7KHFRVWRISULYDWHWUDQVSRUWDWLRQLQWKH1HWKHUODQGVµE\%%RGHDQG -9DQ'DOHQ0DUFK ´7KHRSWLPDOPL[RIWD[HVRQPRQH\FRQVXPSWLRQDQGLQFRPHµE\)'H)LRUHDQG 37HOHV$SULO ´5HWDLOEDQNLQWHUHVWUDWHSDVVWKURXJKWKHQHZHYLGHQFHDWWKHHXURDUHDOHYHOµE\ *GH%RQGW$SULO ´(TXLOLEULXPELGGLQJLQWKHHXURV\VWHP·VRSHQPDUNHWRSHUDWLRQVµE\8%LQGVHLO$SULO ´1HZµYLHZVRQWKHRSWLPXPFXUUHQF\DUHDWKHRU\ZKDWLV(08WHOOLQJXV"µE\ )30RQJHOOL$SULO ´2QFXUUHQF\FULVHVDQGFRQWDJLRQµE\0)UDW]VFKHU$SULO ´3ULFHVHWWLQJDQGWKHVWHDG\VWDWHHIIHFWVRILQIODWLRQµE\0&DVDUHV0D\ ´$VVHWSULFHVDQGILVFDOEDODQFHVµE\)(VFKHQEDFKDQG/6FKXNQHFKW0D\ ´0RGHOOLQJWKHGDLO\EDQNQRWHVLQFLUFXODWLRQLQWKHFRQWH[WRIWKHOLTXLGLW\PDQDJHPHQWRI WKH(XURSHDQ&HQWUDO%DQNµE\$&DEUHUR*&DPED0HQGH]$+LUVFKDQG)1LHWR 0D\ ´$QRQSDUDPHWULFPHWKRGIRUYDOXLQJQHZJRRGVµE\,&UDZIRUG0D\ ´$IDLOXUHLQWKHPHDVXUHPHQWRILQIODWLRQUHVXOWVIURPDKHGRQLFDQGPDWFKHGH[SHULPHQW XVLQJVFDQQHUGDWDµE\06LOYHUDQG6+HUDYL0D\ ´7RZDUGVDQHZHDUO\ZDUQLQJV\VWHPRIILQDQFLDOFULVHVµE\0)UDW]VFKHUDQG0%XVVLHUH 0D\ ´&RPSHWLWLRQDQGVWDELOLW\²ZKDW·VVSHFLDODERXWEDQNLQJ"µE\(&DUOHWWLDQG3+DUWPDQQ 0D\
´7LPHWREXLOGDSSURDFKLQDVWLFN\SULFHVWULFN\ZDJHRSWLPL]LQJPRQHWDU\PRGHOE\ 0&DVDUHV0D\ ´7KHIXQFWLRQDOIRUPRI\LHOGFXUYHVµE\9%URXVVHDX0D\ ´7KH6SDQLVKEORFNRIWKH(6&%PXOWLFRXQWU\PRGHOµE\$(VWUDGDDQG$:LOOPDQ0D\ ´(TXLW\DQGERQGPDUNHWVLJQDOVDVOHDGLQJLQGLFDWRUVRIEDQNIUDJLOLW\µE\5*URSS -9HVDODDQG*9XOSHV-XQH ´*LQIODWLRQIRUHFDVWVµE\)&DQRYD-XQH ´6KRUWWHUPPRQLWRULQJRIILVFDOSROLF\GLVFLSOLQHµE\*&DPED0HQGH]DQG$/DPR-XQH ´(XURDUHDSURGXFWLRQIXQFWLRQDQGSRWHQWLDORXWSXWDVXSSO\VLGHV\VWHPDSSURDFKµE\ $:LOOPDQ-XQH ´7KHHXUREORFWKHGROODUEORFDQGWKH\HQEORFKRZPXFKPRQHWDU\SROLF\LQGHSHQGHQFH FDQH[FKDQJHUDWHIOH[LELOLW\EX\LQDQLQWHUGHSHQGHQWZRUOG"µE\0)UDW]VFKHU-XQH ´<RXWKXQHPSOR\PHQWLQWKH2(&'GHPRJUDSKLFVKLIWVODERXUPDUNHWLQVWLWXWLRQVDQG PDFURHFRQRPLFVKRFNVµE\-)-LPHQRDQG'5RGULJXH]3DOHQ]XHOD-XQH ´,GHQWLI\LQJHQGRJHQRXVILVFDOSROLF\UXOHVIRUPDFURHFRQRPLFPRGHOVµE\--3HUH] DQG3+LHEHUW-XO\ ´%LGGLQJDQGSHUIRUPDQFHLQUHSRDXFWLRQVHYLGHQFHIURP(&%RSHQPDUNHWRSHUDWLRQVµ E\.*1\ERUJ8%LQGVHLODQG,$6WUHEXODHY-XO\ ´4XDQWLI\LQJ(PERGLHG7HFKQRORJLFDO&KDQJHµE\36DNHOODULVDQG'-:LOVRQ-XO\ ´2SWLPDOSXEOLFPRQH\µE\&0RQQHW-XO\ ´0RGHOXQFHUWDLQW\DQGWKHHTXLOLEULXPYDOXHRIWKHUHDOHIIHFWLYHHXURH[FKDQJHUDWHµE\ &'HWNHQ$'LHSSH-+HQU\&0DULQDQG)6PHWV-XO\ ´7KHRSWLPDODOORFDWLRQRIULVNVXQGHUSURVSHFWWKHRU\µE\/6WUDFFD-XO\ ´3XEOLFGHEWDV\PPHWULHVWKHHIIHFWRQWD[HVDQGVSHQGLQJLQWKH(XURSHDQ8QLRQµE\ 6.URJVWUXS$XJXVW ´7KHUDWLRQDOLW\RIFRQVXPHUV·LQIODWLRQH[SHFWDWLRQVVXUYH\EDVHGHYLGHQFHIRUWKHHXUR DUHDµE\0)RUVHOOVDQG*.HQQ\$XJXVW ´(XURDUHDFRUSRUDWHGHEWVHFXULWLHVPDUNHWILUVWHPSLULFDOHYLGHQFHµE\*GH%RQGW $XJXVW
´7KHLQGXVWU\HIIHFWVRIPRQHWDU\SROLF\LQWKHHXURDUHDµE\*3HHUVPDQDQG)6PHWV $XJXVW ´0RQHWDU\DQGILVFDOSROLF\LQWHUDFWLRQVLQDPLFURIRXQGHGPRGHORIDPRQHWDU\XQLRQµE\ 50:-%HHWVPDDQG+-HQVHQ$XJXVW ´,GHQWLI\LQJWKHHIIHFWVRIPRQHWDU\SROLF\VKRFNVRQH[FKDQJHUDWHVXVLQJKLJKIUHTXHQF\ GDWDE\-)DXVW-+5RJHUV(6ZDQVRQDQG-+:ULJKW$XJXVW ´(VWLPDWLQJWKHHIIHFWVRIILVFDOSROLF\LQ2(&'FRXQWULHVµE\53HURWWL$XJXVW ´0RGHOLQJPRGHOXQFHUWDLQW\µE\$2QDWVNLDQG1:LOOLDPV$XJXVW ´:KDWPHDVXUHRILQIODWLRQVKRXOGDFHQWUDOEDQNWDUJHW"µE\*0DQNLZDQG55HLV $XJXVW ´$QHVWLPDWHGVWRFKDVWLFG\QDPLFJHQHUDOHTXLOLEULXPPRGHORIWKHHXURDUHDµE\)6PHWV DQG5:RXWHUV$XJXVW ´&RQVWUXFWLQJTXDOLW\DGMXVWHGSULFHLQGLFHVDFRPSDULVRQRIKHGRQLFDQGGLVFUHWHFKRLFH PRGHOVµE\1-RQNHU6HSWHPEHU ´2SHQQHVVDQGHTXLOLEULXPGHWHUPLQDF\XQGHULQWHUHVWUDWHUXOHVµE\)GH)LRUHDQG =/LX6HSWHPEHU ´,QWHUQDWLRQDOPRQHWDU\SROLF\FRRUGLQDWLRQDQGILQDQFLDOPDUNHWLQWHJUDWLRQµE\ $6XWKHUODQG6HSWHPEHU ´0RQHWDU\SROLF\DQGWKHILQDQFLDODFFHOHUDWRULQDPRQHWDU\XQLRQµE\6*LOFKULVW -2+DLUDXOWDQG+.HPSI6HSWHPEHU ´0DFURHFRQRPLFVRILQWHUQDWLRQDOSULFHGLVFULPLQDWLRQµE\*&RUVHWWLDQG/'HGROD 6HSWHPEHU ´$WKHRU\RIWKHFXUUHQF\GHQRPLQDWLRQRILQWHUQDWLRQDOWUDGHµE\3%DFFKHWWDDQG (YDQ:LQFRRS6HSWHPEHU ´,QIODWLRQSHUVLVWHQFHDQGRSWLPDOPRQHWDU\SROLF\LQWKHHXURDUHDµE\3%HQLJQRDQG -'/ySH]6DOLGR6HSWHPEHU ´2SWLPDOPRQHWDU\SROLF\ZLWKGXUDEOHDQGQRQGXUDEOHJRRGVµE\&-(UFHJDQG $7/HYLQ6HSWHPEHU ´5HJLRQDOLQIODWLRQLQDFXUUHQF\XQLRQILVFDOSROLF\YVIXQGDPHQWDOVµE\0'XDUWHDQG $/:ROPDQ6HSWHPEHU ´,QIODWLRQG\QDPLFVDQGLQWHUQDWLRQDOOLQNDJHVDPRGHORIWKH8QLWHG6WDWHVWKHHXURDUHD DQG-DSDQµE\*&RHQHQDQG9:LHODQG6HSWHPEHU ´7KHLQIRUPDWLRQFRQWHQWRIUHDOWLPHRXWSXWJDSHVWLPDWHVDQDSSOLFDWLRQWRWKHHXUR DUHDµE\*5QVWOHU6HSWHPEHU
´0RQHWDU\SROLF\LQDZRUOGZLWKGLIIHUHQWILQDQFLDOV\VWHPVµE\()DLD2FWREHU ´(IILFLHQWSULFLQJRIODUJHYDOXHLQWHUEDQNSD\PHQWV\VWHPVµE\&+ROWKDXVHQDQG