BANK OF FINLAND DISCUSSION PAPERS

Transkriptio

1 BANK OF FINLAND DISCUSSION PAPERS Tuomas Välimäki Research Department Variable rate liquidity tenders Suomen Pankin keskustelualoitteita Finlands Banks diskussionsunderlag

2 Suomen Pankki Bank of Finland P.O.Box 160 FIN HELSINKI Finland

3 BANK OF FINLAND DISCUSSION PAPERS Tuomas Välimäki Research Department Variable rate liquidity tenders The views expressed are those of the author and do not necessarily reflect the views of the Bank of Finland. I am grateful to Jouko Vilmunen for encouraging and helpful comments. Also the comments from Juha Tarkka, Tuomas Takalo, Martin Ellison and the participants of the Bank of Finland workshop on modelling of monetary policy are gratefully acknowledged. Suomen Pankin keskustelualoitteita Finlands Banks diskussionsunderlag

4 ISBN ISSN (print) ISBN X ISSN (online) Suomen Pankin monistuskeskus Helsinki 2002

5 Variable rate liquidity tenders Bank of Finland Discussion Papers 24/2002 Tuomas Välimäki Research Department Abstract This paper constructs an equilibrium model for the short-term money market, when the central bank provides liquidity via variable rate tenders. The relation between market rate of interest and liquidity is derived from a single bank s profit maximisation problem in the interbank market, and the CB determines its liquidity provision by minimising a quadratic loss function that contains both deviations of expected market rate from CB target rate and differences between liquidity supply and target liquidity. We model equilibrium bid behaviour in the tenders and explain the underbidding phenomenon resulting from the minimum bid rate. We also show that, when maturities of consecutive operations overlap, the expected market interest rate will rise above the CB s target whenever a target rate change (hike or cut) is expected to occur in the same reserve maintenance period. Finally, we review the data from the ECB variable rate tenders and find that the ECB has been fairly liquidity oriented in its allotment decisions. Key words: money market tenders, liquidity policy, bidding, central bank operational framework 3

6 Vaihtuvakorkoiset likviditeettihuutokaupat Suomen Pankin keskustelualoitteita 24/2002 Tuomas Välimäki Tutkimusosasto Tiivistelmä Tutkimuksessa mallinnetaan lyhyen rahan markkinoiden tasapaino, kun keskuspankki ohjaa likviditeettiä vaihtuvakorkoisilla huutokaupoilla. Markkinakoron ja likviditeetin välinen suhde johdetaan yksittäisen pankin voitonmaksimointiongelmasta pankkienvälisillä rahamarkkinoilla. Keskuspankki mitoittaa tavoittelemansa likviditeetinjaon minimoimalla tappiofunktiota, joka sisältää sekä odotetun rahamarkkina- ja tavoitekoron välisen kvadraattisen poikkeaman että likviditeetin kvadraattisen poikkeaman keskuspankin tavoitemäärästä. Tutkimuksessa mallinnetaan lisäksi huutokauppojen tarjousmäärä tasapainossa sekä selitetään tavoiteltua vähäisemmän tarjousmäärän ongelma (nk. underbidding-ilmiö) minimitarjouskoron avulla. Lisäksi markkinakoron osoitetaan nousevan tavoitekoron yläpuolelle, jos peräkkäisten operaatioiden maturiteetit menevät limittäin ja keskuspankin odotetaan muuttavan tavoitekorkoaan jäljellä olevan vähimmäisvarantojen keskiarvoistuperiodin kuluessa huolimatta siitä, odotetaanko koron nostoa vai laskua. Lopuksi tarkastellaan EKP:n vaihtuvakorkoisia huutokauppoja. Niiden pohjalta EKP näyttäisi likviditeetinjakopäätöksissään painottaneen nimenomaan likviditeetin poikkeamia tavoitetasolta. Asiasanat: rahamarkkinahuutokaupat, likviditeettipolitiikka, huutokauppatarjoukset, keskuspankin toimintakehikko 4

7 Contents Abstract Introduction Brief outline over the operational framework of the ECB Market rate as a function of liquidity Final day of the MP (no averaging) First day of the MP (averaging) Central bank behaviour: the supply of liquidity Final day of the MP (no averaging) First day of the MP (averaging) Static interest rate expectations Change in central bank rates expected Bidding in tenders Multiple rate auctions Minimum bid rate Underbidding Single rate auctions Experience with ECB variable rate tenders Liquidity provision of the ECB Underbidding episodes Bidding in ECB main refinancing operations Summary and conclusion...39 References...42 Appendix A Heterogeneous banks

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15 wkh dprxqw ri uhvhuyhv khog gxulqj wkh uvw gd ri wkh pdlqwhqdqfh shulrg +o_k 2 '2-5 /zkhuh5 ghqrwhv, > rs /zlwkrs ghqrwlqj wkh srvvleoh xvh ri wkh vwdqglqj idflolwlhv dw hqg ri shulrg 4,1 Wkxv/ zh fdq zulwh htxdwlrq +8, dv= o 2 ' o E2-5, 2 no _ 2 E 8 E2-5, 2 c +9, Ixuwkhupruh/ wkh h{shfwhg ydoxh ri wkh pdunhw udwh ri lqwhuhvw rq wkh vhfrqg gd lv jlyhq e = H do 2 o'o 6 2 CEo_K 2, 2 no _ 2E CEo_K 2, 2 c +:, zkhuh wkh h{shfwdwlrqv duh wdnhq ryhu wkh glvwulexwlrq s > /dqgc E lv wkh fgi ri wkh vxp ri wkh wzr oltxlglw vkrfnv > 2 dqg Wkh surri iru wklv fdq eh irxqg lq Yçolpçnl +5334,1 Htxdwlrq +:, vd v wkdw wkh h{shfwhg pdunhw udwh zlwk d jlyhq doorwphqw htxdov wkh suredelolw zhljkwhg dyhudjh ri wkh vwdqglqj idflolw udwhv/ zkhuh wkh suredelolw zhljkwv wdnh lqwr dffrxqw erwk ri wkh vkrfnv dqg wkh dprxqw doorwwhg lq wkh whqghu1 515 Iluvw gd ri wkh PS +dyhudjlqj, Rq wkh uvw gd ri wkh wzr gd uhvhuyhv pdlqwhqdqfh shulrg wkh dprxqw ri uhvhuyhv +sulru wr wkh xvh ri wkh vwdqglqj idflolwlhv, edqn krogvlvglylghg ehwzhhq wkh uhvhuyh edodqfhv dqg xvh ri wkh vwdqglqj idflolwlhv dv iroorzv= iru, c f wkh edqn pxvw dftxluh, c xqlwv ri oltxlglw iurp wkh pdujlqdo ohqglqj idflolw > li, c : 2- wkhedqnzlookdyh2- dv uhvhuyh edodqfhv zkloh, c 2- xqlwv pxvw eh sodfhg lqwr wkh ghsrvlw idflolw > li f, c 2- doo wkh oltxlglw zloo eh khog dv uhvhuyh ghsrvlwv1 Wkh surw pd{lpl}dwlrq sureohp ri wkh edqn wdnhv wkh iroorzlqj irup= 4@ K c HE ' o ] 3, c 3K c 3" 5 9 nh do 2 o 7 6 E, c n K c n 0 se0 _0 8 "] 6 : E, c n K c n 0 se0 _0 8 3, c 3K c 5 n o _ H do 2 o 9 7 "] 6 : E, c n K c 2- c n 0 se0 _ c 3, c 3K c o K c c +;, iurp zklfk zh jhw wkh IRF iru wkh surw pd{lpl}lqj sureohp ri lqwhuedqn eruurzlqj= o 6 8 E, c K c nh do 2 od8e2- c, c K c 8 E, c K c o n o _ d 8 E2-c, c K c o o K c 'fc +<, 46

16 Iurp htxdwlrq +<, zh fdq ghulyh +diwhu djjuhjdwlrq, wkh pdunhw udwh ri lqwhuhvw dv d ixqfwlrq ri oltxlglw = o ' H do 2 o i8 E2-, 8 E, j no 6 8 E, no _ d 8 E2-, o +43, Wkh pdunhw udwh ri lqwhuhvw dw wkh uvw gd ri wkh pdlqwhqdqfh shulrg zloo eh d suredelolw zhljkwhg dyhudjh ri wkh udwhv ri wkh vwdqglqj idflolwlhv dqg wkh pdunhw udwh ri lqwhuhvw h{shfwhg wr suhydlo dw wkh iroorzlqj gd ri wkh pdlqwhqdqfh shulrg1 Qrz/ olnh lq wkh fdvh ri wkh vhfrqg gd / wkh h{shfwhg ydoxh iru wkh pdunhw udwh dw wkh uvw gd ri wkh uhvhuyhv pdlqwhqdqfh shulrg lv jlyhq e = H do o'h do 2 o ice2-, CE, jno 6 CE, no _ d CE2-, o c +44, Qh{w zh zloo wxuq wr wkh dqdo vlv ri wkh fhqwudo edqn ehkdylrxu lq wkh whqghuv1 6 Fhqwudo edqn ehkdylrxu= wkh vxsso ri oltxlglw Lq lwv oltxlglw doorwphqw ghflvlrq/ wkh prgho fhqwudo edqn dlpv dw pdlqwdlqlqj wkh h{shfwhg ydoxh ri wkh pdunhw udwh ri lqwhuhvw dv forvh dv srvvleoh wr d wdujhw wkdw lv ghulyhg iurp wkh xowlpdwh jrdo ri wkh fhqwudo edqn +hj pdlqwdlqlqj sulfh vwdelolw,1 Krzhyhu/ wkh fhqwudo edqn pljkw dovr olnh wr vwdelol}h wkh uhvhuyh kroglqjv zlwklq d uhvhuyh pdlqwhqdqfh shulrg1 Iru h{dpsoh/ lq HFE +5333, lw lv vwdwhg wkdw lq wkh qdo doorwphqw ghflvlrq wkh frqvlghudwlrqv ri wkh HFE uhodwh wr wkh vprrwkqhvv ri wkh uhvhuyh ixooophqw sdwk dqg wkh ohyho ri wkh lqwhuhvw udwhv1 Khqfh/ khuh wkh prgho fhqwudo edqn plqlpl}hv d orvv ixqfwlrq wkdw frqvlvwv ri wzr sduwv= wkh h{shfwhg glhuhqfh ehwzhhq wkh pdunhw udwh dqg wkh wdujhw udwh dqg wkh ghyldwlrqv ri h{shfwhg oltxlglw iurp wkh vwhdg sdwk ri uhvhuyh kroglqj1 Wkh suhflvh ixqfwlrqdo irup ri wkh fhqwudo edqn*v orvv ixqfwlrq lv xvxdoo qrw h{solflwo dqqrxqfhg1 Khuh/ wkh fhqwudo edqn lv dvvxphg wr plqlpl}h d txdgudwlf orvv ixqfwlrq/ wkdw frqvlvwv ri wkh zhljkwhg vxp ri vtxduhg shufhqwdjh ghyldwlrqv ri wkh h{shfwhg pdunhw udwh ri lqwhuhvw dqg h{shfwhg oltxlglw iurp wkhlu wdujhw ydoxhv1 Wkh orvv ixqfwlrq wdnhv wkh iroorzlqj irup= u ' 2 H 2 E b do o o n 2 H o 2 b d6 n # o 6 c +45, 6 r o ' o E6 n # zkhuh 6 lv wkh fhqwudo edqn*v hvwlpdwh ri wkh oltxlglw dw wkh ryhuqljkw pdu0 nhw zlwk d jlyhq vxsso ri oltxlglw +lh 6 ' - 3 n ^ / zkhuh@ lv wkh fhqwudo edqn*v hvwlpdwh ryhu wkh dxwrqrprxv oltxlglw idfwruv,/ # lv d }hur phdq oltxlglw vkrfn +lh wkh hvwlpdwlrq huuru lq wkh dxwrqrprxv oltxlg0 lw idfwruv,/ b phdvxuhv wkh uhodwlyh zhljkw ri wkh suhihuhqfhv ryhu wkh wzr remhfwlyhv/ dqg qdoo wkh plqlpl}dwlrq lv vxemhfwhg wr wkh lqyhuvh ghpdqg 47

17 ixqfwlrq o ' o E6 n # wkdw jlyhv wkh pdunhw udwh ri lqwhuhvw dv d ixqfwlrq ri wkh prqh pdunhw oltxlglw 1 Zh fdq vxevwlwxwh wkh uhvwulfwlrq gluhfwo lqwr wkh orvv ixqfwlrq1 Khqfh/ wkh rswlpl}dwlrq sureohp fdq eh zulwwhq dv= 4? u ' 6 2 E b H do E6 n # o o o 2 n 2 b c +46, iru zklfk wkh uvw rughu frqglwlrq lv= b ih do 2 E6 W n # o o o j YH do E6 W n # o n b E6 W Y 'f +47, Wkh IRF lpsolflwo ghwhuplqhv wkh rswlpdo oltxlglw vxsso / lh wkh dprxqw ri prqh pdunhw oltxlglw wkh fhqwudo edqn sodqv wr vxsso lq wkh whqghu rshud0 wlrq ^W ' 6W - 1 Iurp htxdwlrq +47, zh vhh/ wkdw wkh h{shfwhg lqwhuhvw udwh zloo eh deryh +ehorz, wkh wdujhw udwh/ li wkh rswlpdo oltxlglw lv deryh lwv wdujhw1 ; Frqvhtxhqwo /liwkhh{shfwhgpdunhwudwhrilqwhuhvwzlwk wkh wdujhw oltxlglw lv deryh wkh wdujhw udwh +lh Hdo E6o : o,/ erwk wkh rswlpdo oltxlglw dqg wkh h{shfwhg lqwhuhvw udwh zloo eh deryh wkhlu wdujhw ydoxhv +lh 6 W : 6/ dqghdo E6 W o : o,1 Vlploduo / li Hdo E6o o +Hdo E6o ' o, zh*oo kdyh 6 W 6 dqg Hdo E6 W o o + 6 W ' 6 dqg Hdo E6 W o ' o,1 Wr looxvwudwh wkh hhfw d fkdqjh lq wkh ghpdqg iru oltxlglw kdv rq wkh htxloleulxp oltxlglw dqg pdunhw udwh ri lqwhuhvw/ jxuh 4 vkrzv wkuhh glhuhqw ghpdqg fxuyhv iru prqh pdunhw oltxlglw +wkh wklfn fxuyhv,/ dqg dq lqglhu0 hqfh fxuyhv edvhg rq wkh fhqwudo edqn*v plqlpl}dwlrq sureohp +wkh wklq fxuyh,1 Wkh +lqyhuvh, ghpdqg fxuyhv duh ghulyhg e htxdwlrq +43, zlwk glhuhqw ydoxhv iru wkh h{shfwhg ixwxuh lqwhuhvw udwh1 Wkh kljkhu lv wkh h{shfwhg lqwhuhvw udwh iru wkh vhfrqg shulrg/ wkh odujhu lv wkh ghpdqg zlwk d jlyhq pdunhw udwh iru wkh uvw shulrg1 Qrz/ rqo li wkh edqnv* ghpdqg iru oltxlglw sdvvhv wkurxjk +6c o,/ zloo wkh h{shfwhg lqwhuhvw udwh dqg wkh h{shfwhg oltxlglw eh dw wkhlu wdujhw ohyhov1 Dovr/ li wkh lqyhuvh ghpdqg fxuyh dw 6 lv deryh +ehorz, o/ erwk htxloleulxp oltxlglw dqg wkh h{shfwhg pdunhw udwh zloo eh kljkhu +orzhu, wkdq wkh wdujhw ydoxhv duh1 Ohw*v dvvxph wkdw wkh fhqwudo edqn fkrrvhv lwv oltxlglw wdujhw +6,vxfk wkdw/ uvw ri doo/ lw dlpv dw vxsso lqj wkh pdunhw zlwk wkh uhtxluhg uhvhuyhv/ dqg vhfrqgo / lw zdqwv wr krog wkh pdunhw oltxlglw dv vwdeoh dv srvvleoh wkurxjkrxw wkh uhvw ri wkh pdlqwhqdqfh shulrg1 Khqfh/ wkh oltxlglw wdujhw zloo dozd v htxdo o_k / zklfk dw wkh uvw gd ri d wzr shulrg pdlqwhqdqfh shulrg lv vlpso wkh uhtxluhg uhvhuyhv +6 ' -,/ dqg iru wkh vhfrqg gd lw*v wkh vxp ri wkh gdlo uhvhuyh uhtxluhphqwv plqxv wkh uhvhuyhv khog gxulqj wkh uvw gd +6 2 '2-, 0 rs,1 Ixuwkhupruh/ zh dvvxph wkdw wkh wdujhw udwh o lv fkrvhq e wkh ; Wklv uhvxowv iurp wkh iroorzlqj= 5 vljq u 5 ih ^u +o Æ.,` uj CH ^u +oæ.,` Co ~} A3, vljq ^H ^u +o Æ.,` o Æ o ~}? : vljq 9 7 o Æ o 5 o : 8 ~}?3 48

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21 iru zklfk wkh IRF lv= b Eo ih 2 do 2 oneo 6 H do W o 2 CE6W n o _ H do 2 o d CE2-6 W o o o _ H do 2 o }E2-6 W Eo6 H do 2 o }E6 W +4;, n b - 2 E6W - 'f Htxdwlrq +4;, lpsolflwo ghqhv wkh rswlpdo oltxlglw vxsso iru wkh uvw gd ri wkh uhvhuyhv pdlqwhqdqfh shulrg dv d ixqfwlrq ri fxuuhqw dqg h{shfwhg ix0 wxuh fhqwudo edqn udwhv/ wkh fhqwudo edqn suhihuhqfh zhljkwlqj sdudphwhu/ wkh oltxlglw vkrfn glvwulexwlrqv dqg wkh uhvhuyh uhtxluhphqw1 Ohw*v qh{w vwxg wkh rswlpdo oltxlglw vxsso lq wzr sduwv1 Iluvw/ zh dvvxph wkh lqwhuhvw udwh h{shfwdwlrqv wr eh vwdwlf/ dqg diwhu wkdw zh dqdo }h wkh hhfw ri d fkdqjh lq wkh lqwhuhvw udwh h{shfwdwlrqv Vwdwlf lqwhuhvw udwh h{shfwdwlrqv Zkhq wkh lqwhuhvw udwh fruulgru lv qrw xvhg dv dq lqghshqghqw vljqdoolqj ghylfh/ wkh h{shfwhg pdunhw udwh iru wkh qdo gd ri wkh pdlqwhqdqfh shulrg htxdov wkh wdujhw udwh h{shfwhg wr suhydlo gxulqj wkdw gd +lh H do 2 o'h do 2 o,1 Zlwk vwdwlf h{shfwdwlrqv ryhu wkh fhqwudo edqn wdujhw udwh +H do 2 o'o o, zhpd zulwh wkh IRF ri htxdwlrq +4;, dv= b Eo 6 Eo 2 o _ o }E2-6 W Eo 6 o CE6 W n o _ o d CE2-6 W o o }E6 W ' b - 2 E- 6W +4<, Li wkh vkrfn glvwulexwlrq lv v pphwulf/ wkh h{shfwhg pdunhw udwh ri lqwhuhvw dw wkh qdo gd htxdov wkh plg0srlqw ri wkh lqwhuhvw udwh fruulgru h{shfwhg iru wkdw gd / zklfk xqghu vwdwlf h{shfwdwlrqv lv wkh plg0srlqw ri wrgd *v fruulgru ' o 6_ +lh H do2o'h W do 2 o'h o 6_ 2 htxdwlrq +4<, fdq eh ixuwkhu uhgxfhg lqwr= o 6_,1 Khqfh/ iru v pphwulf vkrfnv b o _ Eo 6_ 2 o 6_ 2 i CE6 CE2-6 j d}e2-6 n}e6 o +53, ' b - E- 2 6W Wkh -M7 lv ghfuhdvlqj lq 6 W / dqg lv srvlwlyh iru 6 W -/ }hur iru 6 W ' - dqg qhjdwlyh iru 6 W :-1 Wkh vljq iru wkh um7 lv jlyhq e = ;? / li6 W - vljq ice6 2- CE6 j ' fc li 6 W = nc li 6 W :- 4<

22 Wkh IRF lv ixooohg li dqg rqo li 6 W ' -1 Wkxv/ zh pd frqfoxgh wkdw xqghu vwdwlf lqwhuhvw udwh h{shfwdwlrqv/ wkh fhqwudo edqn zloo surylgh wkh pdunhwv zlwk oltxlglw wkdw htxdov wkh wdujhw oltxlglw / dqg wkh h{shfwhg pdunhw udwh ri lqwhuhvw zloo eh dw wkh ohyho wdujhwhg e wkh fhqwudo edqn uhjdugohvv ri wkh suhihuhqfhv zhljkwlqj sdudphwhu li wkh vkrfn glvwulexwlrq lv v pphwulf1 44 Iru dv pphwulf vkrfn glvwulexwlrqv/ wkh vljq ri wkh OKV ri htxdwlrq +4<, lv= ;? vljq um7 +4<, ' = n/ li Eo 6 o CE6W o o _ d CE2-6 W o f/ li Eo 6 o CE6 W ' o o _ d CE2-6 W o / li Eo 6 o CE6 W : o o _ d CE2-6 W o Wkdw lv wkh vljq ri wkh um7 ghshqgv rq wkh vl}h ri wkh suredelolw zhljkwhg h{shfwhg frvw ri pdujlqdo ohqglqj yhuvxv wkh suredelolw zhljkwhg h{shfwhg frvw ri kdylqj wr xvh wkh ghsrvlw idflolw 1 Qrz/ wkh fhqwudo edqn zloo surylgh oltxlglw h{dfwo dffruglqj wr wkh wdujhw +lh 6 W ' -, rqo lid CE-o ' CE-1 Zlwk dv pphwulf vkrfn glvwulexwlrq wklv lv qrw +qhfhvvdulo, wkh fdvh/ khqfh/ wkh oltxlglw surylvlrq lv jrlqj wr ghshqg rq wkh dv pphwu ri wkh glvwulexwlrq dqg wkh vl}h ri wkh uhvhuyh uhtxluhphqw1 Hj li wkh suredelolw ri jrlqj ryhugudzq zlwk 6 ' - lv odujhu +vpdoohu, wkdq wkh suredelolw ri kdylqj uhvhuyhv lq h{fhvv ri wkh uhvhuyh uhtxluhphqw +CE-* d CE-o : +CE-* d CE-o,,/ wkh h{shfwhg lqwhuhvw udwh zlwk vxfk d oltxlglw srolf zrxog eh deryh +ehorz, wkh wdujhw udwh/ dqg frqvhtxhqwo / wkh rswlpdo oltxlglw surylvlrq zrxog eh 6 W :-+6W -,1 Lq wklv fdvh/ wkh oltxlglw vxsso zrxog ghshqg dovr rq wkh suhihuhqfh zhljkwlqj ri wkh fhqwudo edqn1 Wkh kljkhu wkh b / wkh pruh wkh lqwhuhvw udwh zrxog glhu iurp lwv wdujhw dqg wkh forvhu wkh htxloleulxp oltxlglw zrxog eh wr wkh uhvhuyh uhtxluhphqw Fkdqjh lq fhqwudo edqn udwhv h{shfwhg Wkh ghulydwlrq ri wkh rswlpdo oltxlglw vxsso ehfrphv d elw pruh frpsolfdwhg zkhq wkh edqnv h{shfw wkh fhqwudo edqn wr fkdqjh lwv wdujhw udwh zlwklq wkh uhvhuyhv pdlqwhqdqfh shulrg/ dv lq vxfk d fdvh wkh h{shfwhg fkdqjh lq wkh udwh dhfwv wkh ghpdqg iru oltxlglw ehiruh wkh fkdqjh dfwxdoo rffxuv1 Qrz/ e hqyhorsh wkhruhp zh nqrz wkdw wkh fkdqjh lq rswlpdo oltxlglw vxsso zkhq wkh h{shfwhg ixwxuh lqwhuhvw fkdqjhv lv jlyhq e = _6 EH do 2 o _H do 2 o ' Y2 u *Y6 YH do 2 o Y 2 u *Y6 2 Dv wkh fhqwudo edqn plqlpl}hv u / zh nqrz wkdw wkh ghqrplqdwru rq wkh uljkw kdqg vlgh lv srvlwlyh gxh wr wkh vhfrqg rughu frqglwlrq iru plqlpl}dwlrq1 Wkxv/ 44 H ^u rq 4 u plg. u p 4 u plg J+p Æ 4,. u g 4 u plg ^4 J+5U p Æ u plg. u p 4 u plg J+U,. u g 4 u plg plg +54, 53

23 zh kdyh= vljq _6 EH do 2 o _H do 2 o ' vljq Y 2 u Y6 YH do 2 o Wkdw lv/ wkh vljq ri wkh ghulydwlyh ri wkh rswlpdo oltxlglw z1u1w1 wkh h{shfwhg ixwxuh lqwhuhvw udwh lv plqxv ri wkh vljq ri wkh vhfrqg furvv0sduwldo ri wkh orvv ixqfwlrq z1u1w1 6 dqg H do 2 o1 Iru wkh uvw gd *v plqlpl}dwlrq sureohp zh kdyh= Y 2 u Y6 YH do 2 o ' b Eo idce2-6 CE6 2 o +55, o _ H do 2 o }E2-6 Eo 6 H do 2 o }E6 n H do 2 o o neo 6 H do 2 o CE6 n o _ H do 2 o d CE2-6 oj d}e6 }E2-6 oj Lqvhuwlqj wkh IRF lqwr htxdwlrq +55,/ zh fdq ghulyh wkh vljq ri wkh fhqwudo edqn*v rswlpdo oltxlglw uhvsrqvh wr dq lqfuhdvh lq wkh h{shfwdwlrqv ryhu wkh ixwxuh lqwhuhvw udwh iurp= vljq b Eo dce2-6 CE6 2 o +56, o _ H do 2 o }E2-6 Eo 6 H do 2 o }E6 b - E- 2 6W d}e6 }E2-6 o o _ H do 2 o }E2-6 W Eo 6 H do 2 o }E6 W zklfk lv srvlwlyh +dw ohdvw zkhq wkh vkrfn glvwulexwlrq lv v pphwulf dqg vlqjoh shdnhg, dv orqj dv wkhuh lv dq zhljkw jlyhq wr wkh lqwhuhvw udwh frqvlghudwlrqv +lh b,1 45 Wkhuhiruh/ zh pd frqfoxgh wkdw li wkh fhqwudo edqn sd v dq dwwhqwlrq wr wkh prqh pdunhw lqwhuhvw udwhv/ wkh fhqwudo edqn zloo surylgh pruh oltxlglw wkh kljkhu wkh h{shfwhg ixwxuh lqwhuhvw udwh lv1 Qrz/ zh nqrz/ wkdw wkh h{shfwhg ydoxh ri wkh pdunhw udwh iru wrgd zloo eh deryh wkh wdujhw udwh zkhq dq lqwhuhvw udwh klnh lv h{shfwhg1 Krzhyhu/ wkh vlpxowdqhrxv hhfw ri erwk wkh h{shfwhg lqwhuhvw udwh klnh dqg wkh lq0 fuhdvlqj oltxlglw vxsso rq wkh h{shfwhg pdunhw udwh iru wrgd lv qrw qhf0 hvvdulo prqrwrqlf1 Wkdw lv/ zkhq 6 W : 6 / zh*oo kdyh H do o : o /krz0 hyhu/ li 6 W : e6 : 6 zh fdq qrw frqfoxgh wkdw H do o lv deryh eo /iru eo 'H do E e6 n # o : o 1 Wkh hhfw ri d fkdqjh lq wkh h{shfwhg ixwxuh udwh rq wkh h{shfwhg udwh iru wrgd lv jlyhq e = YH do o YH do 2 o ' ice2-6 CE6 j +57, H do 2 o o _ }E2-6 neo 6 H do 2 o }E6 Y6 YH do 2 o c 45 Wklv uhvxowv iurp wkh iroorzlqj= +4 4,+u 4, 5 ^J+5U p 4, J+p 4,` A 3> u g 4 H 4 ^u 5` j+5u p 4, +u p 4 H 4 ^u 5`, j+p 4,? 3/ dv orqj dv wkh h{shfwhg ixwxuh udwh lv zlwklq wkh lqwhuhvw udwh fruulgru> li zh lqlwldoo kdyh p Æ 4 AU/ +U p Æ 4,? 3/ dqgzlwk v pphwulf vlqjoh shdnhg vkrfnglvwulexwlrq ^j+p 4, j+5u p 4,`? 3/ zkloh zkhq lqlwldoo p Æ 4?U+p Æ U, zhkdyh+u p Æ 4, A 3 ++U p Æ 4,@3,dqg^j+p 4, j+5u p 4,` A 31 54

24 r m 1 E[r 2 ] - r 1. r d m=rdb rdb 1 Iljxuh 5= Wkh hhfw ri xqfhuwdlqw rq wkh ghpdqg iru oltxlglw 1 zkhuh wkh uvw whup rq wkh -M7 lv wkh suredelolw ri qrw kdy0 lqj wr uho rq wkh vwdqglqj idflolwlhv wrgd zlwk 6 xqlwv ri oltxlg0 lw / zkloh wkh vhfrqg whup jlyhv wkh hhfw ri wkh fkdqjh lq wkh sure0 delolw ri ehlqj irufhg wr xvh wkh vwdqglqj idflolwlhv rq wkh h{shfwhg frvw ri xvlqj wkhp1 Iurp deryh zh nqrz wkdw Y6 *YH do 2 o : f1 Wkxv/ wkh h{shfwhg lqwhuhvw udwh iru wrgd zloo lqfuhdvh gxh wr dq lq0 fuhdvh lq wkh h{shfwhg udwh iru wrpruurz/ li ice2-6 CE6 j : H do 2 o o _ }E2-6 neo 6 H do 2 o }E6 Y6 *YH do 2 o1 Wkh ixqf0 wlrqdo irup ri +57, lv whglrxv/ khqfh/ zh duh vdwlvhg zlwk wkh idfw wkdw wkh kljkhu wkh suhihuhqfhv zhljkwlqj sdudphwhu lv +lh wkh pruh zhljkw lv jlyhq wr wkh oltxlglw frqvlghudwlrqv, wkh pruh olnho lw lv wkdw dq lqfuhdvh lq wkh h{0 shfwhg ixwxuh udwh zloo ohdg wr d srvlwlyh fkdqjh lq wkh h{shfwhg pdunhw udwh iru wrgd 1 Wklv frphv iurp wkh idfw wkdw Y 2 6 *YH do 2 o Yb f1 Ohw xv qh{w h{dplqh judsklfdoo d ihz h{dpsohv wr jhw vrph lqwxlwlrq krz wkh hhfw ri h{shfwdwlrqv ri ixwxuh udwhv rq wkh h{shfwhg udwh iru wrgd ghshqgv rq wkh glvwulexwlrq ri vkrfnv +khqfh wkh lqwhuhvw udwh hodvwlflw ri wkh ghpdqg iru oltxlglw, dqg rq wkh vl}h ri wkh h{shfwhg fkdqjh1 Iljxuh 5 vkrzv d vhw ri lqyhuvh ghpdqg ixqfwlrqv iru oltxlglw dw glhu0 hqw ohyhov ri xqfhuwdlqw derxw wkh ghyhorsphqw ri oltxlglw 1 Doo wkh ghpdqg ixqfwlrqv duh fdofxodwhg zlwk qrupdoo glvwulexwhg }hur phdq vkrfnv/ uhvhuyh uhtxluhphqw +lh wkh wdujhw oltxlglw, dw 5333/ vwdqgdug ghyldwlrqv ri +583> 833> 4333,/ dqg xqghu lqwhuhvw udwh klnh h{shfwdwlrqv ri 58 edvlv srlqwv 46 1 Wkh fxuydwxuh ri wkh lqyhuvh ghpdqg ixqfwlrqv lqfuhdvh dv wkh vkrfn glvwulexwlrqv jhw zlghu1 Qrz/ wkh pruh wkhuh lv oltxlglw xqfhuwdlqw / wkh pruh olnho wkh fhqwudo edqn*v uhdfwlrq wr kljkhu lqwhuhvw udwh h{shfwdwlrqv lv wr ohw erwk wkh 46 Zh xvhg wkh iroorzlqj udwh dvvxpswlrqv zkloh gudzlqj wkh jxuh> wdujhw udwh dw 6(/ ghsrvlw udwh dw 5(/ pdujlqdo ohqglqj udwh dw 7( dqg wkh h{shfwhg udwh iru wkh vhfrqg shulrg 6/58(1 55

25 4,00 % 3,75 % 3,50 % 3,25 % U - 3,00 % UGE 2UGE Iljxuh 6= Wkh hhfw ri lqwhuhvw udwh klnh h{shfwdwlrqv rq wkh htxloleulxp olt0 xlglw vxsso / zlwk kljk oltxlglw xqfhuwdlqw 1 lqwhuhvw udwh dqg wkh oltxlglw wr glhu iurp wkh wdujhw1 Iljxuh 6 looxvwudwhv wklv hhfw zkhq wkh vwdqgdug ghyldwlrqv ri wkh oltxlglw vkrfnv lv kdoi ri wkh uhvhuyh uhtxluhphqw1 Wkh htxloleulxp ohyhov iru wkh lqwhuhvw udwh dqg oltxlglw qdwx0 udoo ghshqg fuxfldoo rq wkh fhqwudo edqn*v suhihuhqfhv zhljkwlqj sdudphwhu1 Krzhyhu/ lw*v txlwh reylrxv wkdw zkhq wkh lqyhuvh ghpdqg ixqfwlrq lv qhduo olqhdu/ wkh erwk lqfuhdvh zlwk wkh h{shfwdwlrqv1 Wkh ehwwhu wkh hyroxwlrq ri wkh prqh pdunhw oltxlglw fdq eh hvwlpdwhg/ wkh odujhu zloo wkh lqwhuhvw udwh hodvwlflw ri wkh ghpdqg iru oltxlglw eh zlwk oltxlglw lwvhoi forvh wr wkh wdu0 jhw ohyho1 Wkxv/ zlwk orz oltxlglw xqfhuwdlqw / lw*v olnho wkdw wkh htxloleulxp lqwhuhvw udwh0oltxlglw srlqw zloo olh forvh wr hlwkhu ri wkh wdujhwv/ lh wkh fhqwudo edqn zloo ohw wkh h{shfwdwlrqv wr eh vkrzq prvwo hlwkhu lq wkh oltxlglw ru lq wkh pdunhw udwh1 Wklv lv looxvwudwhg zlwk jxuh 7/ zkhuh wkh vwdqgdug ghyldwlrq ri wkh oltxlglw vkrfn lv 43( ri wkh uhvhuyh uhtxluhphqw1 Ixuwkhupruh/ zlwk uhdvrqdeo orz oltxlglw xqfhuwdlqw lw*v srvvleoh wkdw wkh rswlpdo uhdfwlrq ri d fhqwudo edqn plqlpl}lqj wkh txdgudwlf glhuhqfhv lv wr mxpsiurp wljkw frqwuro ri oltxlglw lqwr wljkw frqwuro ri lqwhuhvw udwhv dv wkh lqwhuhvw udwh klnh h{shf0 wdwlrqv uhdfk kljk hqrxjk ohyho1 Wklv fdvh lv looxvwudwhg lq jxuh 81 Qh{w zh wxuq wr dqdo }lqj wkh elg ehkdylrxu ri wkh edqnv lq wkh whqghuv1 7 Elgglqj lq whqghuv Wkhuh duh? krprjhqrxv edqnv holjleoh iru sduwlflsdwlqj wkh whqghuv1 Hdfk ri wkh edqnv fdq sodfh xs wr 43 elgv lq hyhu whqghu1 D elg frqvlvwv ri d txdqwlw 0 lqwhuhvw udwh sdlu/ lq zklfk wkh vshflhg lqwhuhvw udwh lv wkh rqh dw zklfk wkh elgghu zdqwv wr hqwhu lqwr wudqvdfwlrq/ dqg wkh txdqwlw lv wkh dprxqw lw zdqwv wr wudqvdfw zlwk dw wkh jlyhq udwh1 Ohw*v duudqjh wkh elgv ri edqn 56

26 4,00 % 3,75 % 3,50 % 3,25 % 3,00 % UGE 2UGE - Iljxuh 7= Wkh hhfw ri lqwhuhvw udwh klnh h{shfwdwlrqv rq wkh htxloleulxp olt0 xlglw vxsso / zlwk orz oltxlglw xqfhuwdlqw 1 4,00 % 3,75 % 3,50 % 3,25 % 3,00 % UGE UGE Iljxuh 8= 57

27 lq ghvfhqglqj rughu/ vxfk wkdw wkh elg dprxqw zlwk wkh kljkhvw elg udwh o A c lv ghqrwhg e K / zlwk wkh vhfrqg kljkhvw udwh co A c oa c2 e K /dqgvrrq+lh A co c2 o A c :o A c2 : : oc f,1 A Wkh prqrsro vxssolhu ri wkh oltxlglw +wkh fhqwudo edqn, dlpv dw vxsso lqj 6 W +ghqhg lq suhylrxv fkdswhu, xqlwv ri oltxlglw wr wkh pdunhw/ uhjdugohvv ri wkh vkdsh ri wkh ghpdqg vfkhgxoh jlyhq e wkh edqnv> lh xqolnh lq prvw dxfwlrqv khuh wkh vhoohu lv qrw wu lqj wr pd{lpl}h lwv lqfrph iurp wkh whqghu1 Krzhyhu/ zh dvvxph wkdw li frooxvlrq +ru frooxvlrq olnh ehkdylrxu, ehwzhhq wkh elgghuv zhuh ghwhfwhg e wkh fhqwudo edqn/ lw zrxog uhgxfh wkh vxsso ehorz 6 W / zklfk lv frvwo hqrxjk iru wkh edqnv wr ghwhu dq frooxvlyh ehkdylrxu1 Wkh h{ srvw ydoxh iru d xqlw ri oltxlglw lv wkh vhfrqgdu pdunhw sulfh iru lw/ dqg lv frpprq wr doo edqnv1 Dv vkrzq deryh/ wklv sulfh lv d ghfuhdvlqj ixqfwlrq ri wkh oltxlglw / dqg lw dozd v olhv zlwklq wkh lqwhuhvw udwh fruulgru vhw e wkh udwhv ri wkh vwdqglqj idflolwlhv1 Wkhuhiruh/ zlwkrxw d uhvhuyh sulfh 47 / wkhuh zloo dozd v eh hqrxjk elgv iru wkh fhqwudo edqn wr eh deoh wr surylgh oltxlglw dffruglqj wr 6 W 1 48 Wkhuhdol}lqjpdunhwudwhrilqwhuhvwlvdudqgrp yduldeoh/ gxh wr wkh oltxlglw vkrfn #1 Krzhyhu/ wkh h{shfwhg pdunhw udwh ri lqwhuhvw lv frpprq wr doo edqnv/ dv zh dvvxph wkdw hlwkhu wkhuh lv dq h{solflwo dqqrxqfhg fhqwudo edqn wdujhw iru wkh pdunhw udwh +lq zklfk fdvh Hdoo 'o wdujhw, ru wkh edqnv uhfhlyh d frpprq vljqdo rq wkh iruwkfrplqj pdunhw udwh +lq fdvh ri wkh hxurduhd hj wkh txrwdwlrqv rq wkh wzr zhhn HRQLD0vzdsudwh frxog vhuyh dv vxfk d vljqdo,1 Khqfh/ H do E6 W n #o 'Hdo E6 W n #o iru doo edqnv/ dv orqj dv d uhvhuyh sulfh lv qrw xvhg ru li lw lv lqhhfwlyh1 Zh uhwxuq odwhu wr wkh fdvh zkhuh zh kdyh elqglqj uhvhuyh sulfh iru wkh elgv1 Wkh dqdo vlv ri wkh elg ehkdylrxu lv glylghg lqwr wzr sduwv1 Zh ehjlq zlwk wkh pxowlsoh udwh surfhgxuh +Dphulfdq ru glvfulplqdwru dxfwlrq,/ lq zklfk wkh doorwphqw udwh iru dffhswhg elgv lv wkh elg udwh +lh wkh udwh vshflhg lq wkh jlyhq elg,1 Diwhu wkdw zh pryh wr vlqjoh udwh surfhgxuh +Gxwfk ru xqlirup sulfh dxfwlrq,/ zkhuh wkh pdujlqdo udwh 49 ri wkh doorwphqw lv dssolhg wr doo dffhswhg elgv1 Wkh HFE kdv xvhg pxowlsoh udwh dxfwlrqv lq doo pdlq uhqdqflqj rshudwlrqv frqgxfwhg lq wkh irup ri yduldeoh udwh whqghuv dqg dovr lq prvw ri wkh orqjhu whup uhqdqflqj rshudwlrqv1 Gxwfk dxfwlrq kdv ehhq dssolhg vr idu rqo lq wkh uvw wzr orqjhu whuq uhqdqflqj rshudwlrqv1 714 Pxowlsoh udwh dxfwlrqv Wkh surw iru edqn iurp sduwlflsdwlqj d yduldeoh udwh whqghu/ lq zklfk wkh pxowlsoh udwh surfhgxuh lv dssolhg/ lv vlpso wkh doorwphqw yroxph zhljkwhg vxp ri wkh glhuhqfhv ehwzhhq wkh h{shfwhg pdunhw udwh dqg wkh elg udwh1 Lw 47 Wkh uhvhuyh sulfh lv wkh orzhvw sulfh dw zklfk wkh frxqwhusduwlhv duh doorzhg wr vxeplw elgv lq dxfwlrqv1 48 Wklv iroorzv iurp wkh idfw wkdw d edqn fdq pdnh srvlwlyh surw e eruurzlqj oltxlglw iurp wkh dxfwlrq dqg ohqglqj lw edfn wr wkh fhqwudo edqn/ li wkh sulfh ri oltxlglw dw wkh whqghu lv ehorz wkh ghsrvlw udwh1 49 Wkh pdujlqdo udwh ri doorwphqw lv d whup xvhg e wkh HFE iru wkh orzhvw udwh dw zklfk elgv duh dffhswhg1 Lq dxfwlrq olwhudwxuh wklv nlqg ri udwh lv xvxdoo uhihuhg wr dv wkh vwrs0rxw sulfh1 58

28 lv jlyhq e = r ^co A c ' ' f[ ' ; A? A= ^co A c 6 W 3 o A 3 K o A c H do E6 W n #o o A c K co A /li c o A c K co A /li c o A 3 6 W f/ li o A 3 6W 6 W o A c c +58, zkhuh K o A lv wkh edqnlqj vhfwru zlgh djjuhjdwh elg dw o A c c/ o A ghqrwhv wkh c fxpxodwlyhelgdprxqwridooedqnvdwlqwhuhvwudwhhtxdowrruderyhoc A /dqg ghqrwhv wkh fxpxodwlyh elg dprxqw dw doo udwhv kljkhu wkdq o A oa 3 c 1 Wkh kljkhvw udwh dw zklfk o A h{fhhgv wkh dprxqw wkh fhqwudo edqn lv zloolqj wr c surylgh wr wkh pdunhw lv fdoohg wkh pdujlqdo udwh ri wkh doorwphqw +lh o pdujlqdo o A wkdw vdwlvhv o A 6 W 3 o A, 4: 1 Wkh qhw surw iurp elg K co A lv wkh c glhuhqfh ehwzhhq wkh elg udwh dqg wkh iruwkfrplqj pdunhw udwh ri lqwhuhvw wlphv wkh dprxqw ri oltxlglw dfwxdoo surylghg wr wkh edqn zlwk wkh jlyhq udwh1 Qrz/ wkh edqn zloo qrw eh doorwwhg dq oltxlglw iru d elgv dw udwhv ehorz wkh pdujlqdo udwh/ zkhuhdv wkh elgv dw udwhv deryh wkh pdujlqdo udwh duh dffhswhg lq ixoo +lh lq wklv fdvh wkh doorwwhg dprxqw zloo htxdo wkh elg dprxqw,1 Ixuwkhupruh/ iru elgv dw wkh pdujlqdo udwh/ wkh fhqwudo edqn zloo xvh sur udwd udwlrqlqj lq wkh doorwphqw surfhgxuh1 Wklv phdqv wkdw wkh elgv dw wkh pdujlqdo udwh duh dffhswhg rqo sduwldoo / vxfk wkdw wkh vkduh ri wkh wrwdo doorwphqw iru hdfk elg dw wkh pdujlqdo udwh htxdov lwv iudfwlrq ri wkh wrwdo elgv dw wkh udwh1 Lw*v hdv wr vhh wkdw rswlpdo elg lv }hur dw doo udwhv h{fhhglqj wkh h{shfwhg pdunhw udwh ri lqwhuhvw +lh K W 'fzkhq o A :Hdo co A c E6W o,/ dv rwkhuzlvh wkh elg c zrxog lhog qhjdwlyh h{shfwhg surwv1 Dovr/ elgv dw udwhv ehorz wkh pdujlqdo udwh lhog }hur surw/ dv wkhuh zloo qrw eh dq uhvlgxdo vxsso iru oltxlglw ohiw dw wkhvh udwhv1 Khqfh/ srvlwlyh h{shfwhg surw fdq eh pdgh rqo zlwk elgv dw udwhv ehwzhhq wkh pdujlqdo udwh dqg wkh h{shfwhg pdunhw udwh ri lqwhuhvw1 Ohw*v vxssrvh iru d prphqw wkdw wkh pdujlqdo udwh ri wkh doorwphqw lv orzhu wkdq wkh h{shfwhg pdunhw udwh ri lqwhuhvw +lh o pdujlqdo Hdo E6 W n #o,1 Qrz/ frqvlghu edqn sodflqj d elg iru wkh hqwluh txdqwlw ri wkh doorwphqw dw d udwh lqqlwhvlpdoo deryh wkh pdujlqdo udwh +K co pdujlqdo nm ' 6 W /zkhuh o pdujlqdo n 5 Hdo E6 W n #o,1 Qrz/ wkh doorwphqw iru edqn zlwk wklv elg pxvw eh dw ohdvw dv odujh dv lw zrxog eh zlwk d elg dw wkh pdujlqdo udwh1 Wkxv/ wkh edqn zrxog eh pdnlqj srvlwlyh surw zlwk wklv nlqg ri ehkdylrxu1 Krzhyhu/ wklv lqfhqwlyh dssolhv iru doo edqnv/ wkhuhiruh/ wkh rswlpdo srolf iru dqrwkhu edqn zrxog eh wr sodfh d elg odujh hqrxjk wr vdwlvi wkh zkroh vxsso dw d udwh wkdw lv lqqlwhvlpdoo kljkhu wkdq wkdw ri edqn *v/ dqg vr iruwk xqwlo wkh pdujlqdo udwh uhdfkhv wkh h{shfwhg pdunhw udwh ri lqwhuhvw1 Dv d frqvhtxhqfh/ dw wkh htxloleulxp doo edqnv sodfh odujh hqrxjk elgv iru wkh fhqwudo edqn wr eh deoh wr surylgh oltxlglw dffruglqj wr lwv wdujhw +6 W, dw wkh sulfh htxdoolqj wkh h{shfwhg pdunhw udwh/ lh HdoE6 W n#o 6 W dqg oc A 'Hdo E6 W n #o iru 4: Qrwh wkdw zh kdyh rplwwhg wkh edqn lqgh{ l iurp vxevfulswv ri wkh udwhv wkdw dsso iru doo edqnv1 59