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                                             8
Ranking Informational Content of Incoming Trade


                    Choice of Action


 Change Bid/Ask                    Trade on Interdealer Market
(Exogenous Trade)                      (Endogenous Trade)


                                      Choice of Counterpart


                                       Trade with Well Informed Dealer
                                       (Smart Market Timer, Contrarian)

                                          Trade with Informed Dealer
                                        (Market Timer, Quasi-Contrarian)

                                        Trade with Uninformed Dealer
                                                 (Averages)



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                                              47
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                                                      58
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                                                 59
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Hdvoh|/ Gdylg dqg Pdxuhhq R*Kdud/ _Wlph dqg wkh Surfhvv ri Vhfxulw| Sulfh Dgmxvwphqw/%
     Mrxuqdo ri Ilqdqfh/ 45/ 7: +5,/ 8:9~9381
Ilvkpdq/ Plfkdho M1 dqg Iudqflv D1 Orqjvwd/ _Gxdo Wudglqj lq Ixwxuhv Pdunhwv/% Mrxuqdo
    ri Ilqdqfh/ 45/ 7: +5,/ 976~9:41
Iohplqj/ Plfkdho M1 dqg Hol P1 Uhprorqd/ _Sulfh Irupdwlrq dqg Oltxlglw| lq wkh X1V1
    Wuhdvxu| Pdunhw= Wkh Uhvsrqvh wr Sxeolf Lqirupdwlrq/% Wkh Mrxuqdo ri Ilqdqfh/
    Qryhpehu 4/ 87 +8,/ 434~4481
Irxfdxow/ W1/ D1 Urhoo/ dqg S1 Vdqgdv/ _Lpshuizfw Pdunhw Prqlwrulqj dqg VRHV Wudglqj/%
    Whfkqlfdo Uhsruw 41 KHF Zrunlqj Sdshu1
Jduedgh/ Nhqqhwk G1/ Md| O1 Srpuhq}h/ dqg Zlooldp O1 Vloehu/ _Rq wkh Lqirupdwlrq
    Frqwhqw ri Sulfhv/% Dphulfdq Hfrqrplf Uhylhz/ 4:/ 9 +4,/ 83~81




                                          6:
Jorvwhq/ Odzuhqfh U1 dqg Sdxo U1 Plojurp/ _Elg/ Dvn/ dqg Wudqvdfwlrq Sulfhv lq d Vshfldo0
    lvw Pdunhw zlwk Khwhurjhqhrxvo| Lqiruphg Wudghuv/% Mrxuqdo ri Ilqdqfldo Hfrqrplfv/
    4;8/ 47 +4,/ :4~4331
Kdqvfk/ Rolyhu/ Qdud|dq 1 Qdln/ dqg V1 Ylvzdqdwkdq/ _Gr Lqyhqwrulhv Pdwwhu lq Ghdo0
    huvkls PdunhwvB Hylghqfh iurp wkh Orqgrq Vwrfn H{fkdqjh/% Mrxuqdo ri Ilqdqfh/
    4;/ 86 +8,/ 4956~49891
Kr/ Wkrpdv dqg Kdqv U1 Vwroo/ _Rswlpdo Ghdohu Sulflqj xqghu Wudqvdfwlrqv dqg Uhwxuq
    Xqfhuwdlqw|/% Mrxuqdo ri Ilqdqfldo Hfrqrplfv/ 4;4/  +4,/ 7:~:61
Lwr/ Wdndwrvkl/ Ulfkdug N1 O|rqv/ dqg Plfkdho W1 Phoylq/ _Lv Wkhuh Sulydwh Lqirupdwlrq
     lq wkh I[ PdunhwB Wkh Wrn|r H{shulphqw/% Mrxuqdo ri Ilqdqfh/ 4;/ 86 +6,/ 4444~
     44631
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     Uhylhz ri Hfrqrplf Vwxglhv/ 4/ 99 +6,/ 7:8~83:1
N|oh/ Doehuw V1/ _Frqwlqxrxv Dxfwlrqv dqg Lqvlghu Wudglqj/% Hfrqrphwulfd/ 4;8/ 86 +9,/
    4648~46681
    / _Lqiruphg Vshfxodwlrq zlwk Lpshuihfw Frpshwlwlrq/% Uhylhz ri Hfrqrplf Vwxglhv/
    4;/ 89 +6,/ 64:~6881
Ohdfk/ M1 Fkulv dqg Dqdqwk Q1 Pdgkdydq/ _Lqwhuwhpsrudo Sulfh Glvfryhu| e| Pdunhw
    Pdnhuv= Dfwlyh yhuvxv Sdvvlyh Ohduqlqj/% Mrxuqdo ri Ilqdqfldo Lqwhuphgldwlrq/ 45/
    5 +5,/ 53:~5681
     dqg      / _Sulfh H{shulphqwdwlrq dqg Vhfxulw| Pdunhw Vwuxfwxuh/% Uhylhz ri Il0
    qdqfldo Vwxglhv/ 46/ 9 +5,/ 6:8~7371
Olswvhu/ Urehuw dqg Doehuw Vklu|dhy/ Vwdwlvwlfv ri Udqgrp Surfhvvhv L= Jhqhudo Wkhru|/
     Qhz run= Vsulqjhu0Yhuodj/ 4::1
O|rqv/ Ulfkdug N1/ _Whvwv ri Plfurvwuxfwxudo K|srwkhvhv lq wkh Iruhljq H{fkdqjh Pdu0
    nhw/% Mrxuqdo ri Ilqdqfldo Hfrqrplfv/ 48/ 6 +506,/ 654~6841
    / _D Vlpxowdqhrxv Wudgh Prgho ri wkh Iruhljq H{fkdqjh Krw Srwdwr/% Mrxuqdo ri
    Lqwhuqdwlrqdo Hfrqrplfv/ 4:/ 75 +607,/ 5:8~5;1
Pdgkdydq/ Dqdqwk dqg Vh|prxu Vplgw/ _D Ed|hvldq Prgho ri Lqwudgd| Vshfldolvw Sulf0
   lqj/% Mrxuqdo ri Ilqdqfldo Hfrqrplfv/ 44/ 63 +4,/ ~4671
    / Pdwwkhz Ulfkdugvrq/ dqg Pdun Urrpdqv/ _Zk| Gr Vhfxulw| Sulfhv FkdqjhB D
    Wudqvdfwlrq0Ohyho Dqdo|vlv ri QVH Vwrfnv/% Uhylhz ri Ilqdqfldo Vwxglhv/ 4:/ 43
    +7,/ 4368~43971
Prvfdulql/ Jxvhssh dqg O1 Vplwk/ _Zdog Uhylvlwhg= Wkh Rswlpdo Ohyho ri H{shulphqwd0
    wlrq2/% 53331
Sdjdq/ Dguldq/ _Hfrqrphwulf Lvvxhv lq wkh Dqdo|vlv ri Uhjuhvvlrqv zlwk Jhqhudwhg Uh0
    juhvvruv/% Lqwhuqdwlrqdo Hfrqrplf Uhylhz/ 4;7/ 58 +5,/ 554~5791
Urhoo/ Dlovd/ _Gxdo0Fdsdflw| Wudglqj dqg wkh Txdolw| ri wkh Pdunhw/% Mrxuqdo ri Ilqdqfldo
    Lqwhuphgldwlrq/ 43/ 4 +4,/ 438~4571


                                           6;

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Dealership market

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  • 7. Ranking Informational Content of Incoming Trade Choice of Action Change Bid/Ask Trade on Interdealer Market (Exogenous Trade) (Endogenous Trade) Choice of Counterpart Trade with Well Informed Dealer (Smart Market Timer, Contrarian) Trade with Informed Dealer (Market Timer, Quasi-Contrarian) Trade with Uninformed Dealer (Averages) Iljxuh 4= Wkh ghflvlrq surfhvv ri pdunhw pdnhu1 9
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  • 10. lv wkh surw jhqhudwhg e| fkdqjlqj wkh elg dqg dvn txrwhv1 Wkh sduw ri pdunhw pdnhu*v surw wkdw lv gxh wr wkh h{sorlwdwlrq ri ehwwhu lqirupdwlrq fdq eh uhsuhvhqwhg dv wkh glhuhqfh ehwzhhq wkh ydoxh ri wkh dvvhw dqg lwv sulfh pxowlsolhg e| wkh txdqwlw| wudghg +t,1 Wkdw lv=  @ t ec•t +y s, @ t ec•t vW zkhuh y lv wkh wuxh ydoxh ri wkh dvvhw dqg s lv wkh sulfh dw zklfk wkh wudgh lv h{hfxwhg +N|oh 4;8/ Urhoo 43,1 Wkh frvw ri nhhslqj wkh elg dqg dvn txrwhv xqdowhuhg fdq eh uhsuhvhqwhg dv= 2 @ te7t / zkhuh lv wkh frvw ri ehlqj klw dw wkh plvdoljqhg txrwhv1 Lw lv sursruwlrqdo wr wkh glhuhqfh ehwzhhq srvwhg sulfh dqg h{shfwhg ydoxh1 Wklv frvw fdq eh wkrxjkw ri dv wkh suredelolw| ri ehlqj klw e| dqrwkhu ghdohu dw wkh plvdoljqhg txrwhv zhljkwhg e| lwv frvw1 Wkh pdunhw pdnhu fdq uhgxfh wkh frvw e| fkdqjlqj wkh srvwhg elg dqg dvn sulfhv1 Wklv zrxog jhqhudwh h{rjhqrxv wudgh/ exw dw d sulfh douhdg| lq olqh zlwk wkh h{shfwhg ydoxh1
  • 11. @ t e7t ED/ zkhuh ED lv wkh jdlq wkdw wkh pdunhw pdnhu pdnhv e| fkdqjlqj wkh elg0dvn/ vwdqgdugl}hg shu xqlw ri lqfrplqj wudgh1 ED lv htxdo wr wkh vxp ri wzr jdlqv= wkh rqh gxh wr wkh elg0dvn vsuhdg +, dqg wkh dyrlgdqfh ri wkh orvv wkdw zrxog kdyh rffxuuhg li wkh pdunhw pdnhu kdg ehhq klw dw wkh plvdoljqhg txrwhv +,1 Wkh lqwxlwlrq lv :
  • 12. wkdw h{rjhqrxv wudgh lv d vruw ri vwrs0orvv vwudwhj| wkdw surylghv wkh pdunhw pdnhu zlwk d %qrupdo% surw htxdo wr wkh elg0dvn vsuhdg1 Li zh uhghqh surwv diwhu qhwwlqj rxw wkh frvw ri qrw fkdqjlqj wkh elg dqg dvn txrwhv uhsuhvhqwhg e| 2/ zh kdyh= @ t ec•t vW . t e7t Jlyhq wkdw wkh pdunhw pdnhu fdq fkrrvh wr wudgh hlwkhu zlwk pruh lqiruphg pdunhw pdnhuv +t , ru zlwk ohvv lqiruphg rqhv +t Ä ,/ wkh txdqwlw| wudghg hqgrjhqrxvo| fdq eh h{suhvvhg dv= t ec•t @ +t . t Ä ,= Wkh glhuhqfh ehwzhhq pdunhw sulfh dqg dvvhw ydoxh lv dhfwhg e| wkh sulfh lpsdfw ri pdunhw pdnhu*v wudglqj1 Lq sduwlfxodu/ vW lv d qhjdwlyh ixqfwlrq ri wkh sulfh lpsdfw= wkh pruh wkh pdunhw pdnhu wudghv/ wkh pruh kh uhyhdov lqirupdwlrq derxw wkh wuxh ydoxh ri wkh dvvhw dqg uhgxfhv wkh vsuhdg ehwzhhq wkh sulfh ri wkh dvvhw dqg lwv ydoxh1 Zh dvvxph wkdw vxfk d glhuhqfh iroorzv d vwrfkdvwlf surfhvv= Ä Ä gvW @ +4 e7t t e7t t t ,gw . g} +5, 2 2 zkhuh uhsuhvhqwv wkh glhuhqfh ehwzhhq wkh ydoxh ri wkh dvvhw dqg lwv pdunhw sulfh li wkh pdunhw pdnhu glg qrw wudgh/ wkdw lv wkh srwhqwldo surwv ri wkh pdunhw pdnhu1 Wkh ehkdylru ri lv ghvfulehg e| d Srlvvrq surfhvv wkdw fdq wdnh xs wzr ydoxhv= kljk +w , dqg orz +u ,1 Wkh suredelolw| wudqvlwlrq pdwul{ ehwzhhq wlph w dqg wlph w . gw lv= w u w 4 gw gw +6, u gw 4 gw Dovr/ e7t dqg Ä uhsuhvhqw wkh lpsdfw rq sulfh ri h{rjhqrxv wudgh/ lqiruphg hqgrjh0 qrxv wudgh dqg xqlqiruphg hqgrjhqrxv wudgh uhvshfwlyho|1 Wkh pdunhw pdnhu lv ixoo|  W?_ii_ | i } ih | i tThi@_c | i *itt | i _i@*iht t **?} |L hi_ Ui | | hL } | ih L? |h@_?} @?_c | ihiuLhic hi_ Ui i Tih4i?|@|L? W| t Lh| ?L|?} | @| | t ui@| hi hit *|t uhL4 | i u@U| | @| | i ULt| Lu i Tih4i?|?} t ThLTLh|L?@* |L | i tThi@_ EE 3 b ^ 3 bÄ ^ Ä A i @*|ih?@|i tTiU€U@|L? E 3 b ^ 3 bÄ ^ Ä L *_ ThL_ Ui | i t@4i hit *|tc i UiT| uLh | i u@U| | @| | i i TiU|i_ @* i Lu | i @tti| L *_ ?L| @giU| | i _iUtL? |L |h@_i | ?uLh4i_ 4@h!i| 4@!ih `i | ?! | @| | t tTiU€U@|L? Mi||ih U@T| hit | i u@U| | @| | i } ih | i T@)Lg tc | i }hi@|ih | i 4T@|i?Ui Lu | i _i@*ih t L *_ Mic @?_ | i i@!ih t _ithi |L i Tih4i?| ;
  • 13. dzduh wkdw h{rjhqrxv wudgh kdv d vwurqjhu lpsdfw rq sulfhv wkdq grhv hqgrjhqrxv wudgh1 Kh dovr nqrzv wkdw sodflqj dq rughu zlwk d pruh lqiruphg pdunhw pdnhu kdv d vwurqjhu lpsdfw rq sulfhv wkdq sodflqj dq rughu zlwk d ohvv lqiruphg rqh1 Wkh uhdvrq lv wkdw lq0 iruphg wudghuv douhdg| kdyh dq lqirupdwlrq vhw zklfk doorzv wkhp wr h{sorlw wkh dgglwlrqdo lqirupdwlrq1 Wkhuhiruh/ e7t A A Ä = Jlyhq wkdw fkdqjlqj wkh elg dqg dvn txrwhv uhyhdov prvw ri wkh lqirupdwlrq/ zh dvvxph/ wkdw e7t @ 4= Zh dovr dvvxph/ zlwk qr orvv ri jhqhudolw|/ wkdw Ä @ 31 Wkh sulfh lpsdfw ri hqgrjhqrxv wudgh ghshqgv rq wkh pdunhw yrodwlolw|1 Wkh kljkhu yrodwlolw| lv/ wkh pruh wkh pdunhw pdnhu zloo eh deoh wr fdprxdjh klv wudgh1 Rq wkh frqwudu|/ h{rjhqrxv wudgh uhyhdov lqirupdwlrq wr wkh uhvw ri wkh pdunhw uhjdugohvv ri pdunhw yrodwlolw|1 Rq wkh edvlv ri wkhvh dvvxpswlrqv/ zh fdq zulwh wkh odz ri prwlrq ri surwv dv= g @ +4 t e7t t ,+t . t Ä ,gw . te7t gw . +t . t Ä ,g}= +7, 2 Lw lv lpsruwdqw wr qrwh wkdw lq zkdw iroorzv zh gr qrw pdnh dq| dwwhpsw wr vroyh iru htxloleulxp v1 Lqvwhdg/ zh irfxv rq ghulylqj whvwdeoh suhglfwlrqv derxw wkh ehkdylru ri wkh lqglylgxdo pdunhw pdnhu xqghu wkh dvvxpswlrq ri khwhurjhqhlw| ri pdunhw pdnhuv* uhdfwlrq wr klv wudgh1 Dovr/ zh zloo vkrz wkdw glhuhqfhv lq ulvn dyhuvlrq duh hqrxjk wr lqgxfh vrph pdunhw pdnhuv wr h{shulphqw dqg rwkhuv wr klgh1 Wklv lpsolhv wkdw dw htxloleulxp wkh lqirupd0 wlrqdo frqwhqw ri wkh lqfrplqj rughuv lv dozd|v srvlwlyh1 Wkh phuh idfw wkdw vrph djhqwv zloolqjo| uhohdvh sduw ri wkhlu lqirupdwlrq wkurxjk h{shulphqwdwlrq mxvwlhv wkh idfw wkdw dw htxloleulxp pdunhw pdnhuv duh deoh wr udqn hdfk rwkhuv lq whupv ri wkh lqirupdwlrqdo frqwhqw ri wkhlu wudghv1 2 A i @h!i| @!iht wi@h??} Xs wr qrz zh kdyh dvvxphg wkdw wkh pdunhw pdnhu nqrzv wkh wuxh ydoxh ri 1 Lq wklv fdvh/ wkh ghflvlrq vlpso| lqyroyhv d wudgh0r ehwzhhq h{sorlwlqj wkh lqirupdwlrq derxw wkh h{shfwhg ydoxh ri wkh dvvhw dqg lqfxuulqj d frvw gxh wr wkh lpsdfw ri wudglqj rq pdunhw sulfh1 Krzhyhu/ li wkh pdunhw pdnhu lv qrw ixoo| lqiruphg/ wkh ghflvlrq sureohp fkdqjhv gudvwlfdoo|1 Lqghhg/ wkh pdunhw pdnhu fdq qrz ohduq e| revhuylqj wkh uhdfwlrq ri rwkhu pdunhw pdnhuv wr klv rughuv1 Wklv phdqv wkdw wudglqj surylghv klp zlwk d zd| ri
  • 14. h{shulphqwlqj dqg xsgdwlqj klv eholhiv rq wkh txdolw| ri wkh lqirupdwlrq frqwdlqhg lq wkh rughu uhfhlyhg1 Lq sduwlfxodu/ zh dvvxph wkdw hdfk xqlw ri wkh lqfrplqj wudgh wkh pdunhw pdnhu uhfhlyhv frqwdlqv d vljqdo +, derxw wkh xqghuo|lqj ydoxh ri wkh dvvhw1 Vxfk d vljqdo lv dq xqeldvhg suhglfwru dqg iroorzv wkh surfhvv= I g @ gw . t g} +8, n” j2 zkhuh g} lv wkh qrlvh ri wkh vljqdo dqg I lv lwv glxvlrq frhflhqw1 Wkh pdunhw pdnhu fdq uhgxfh wkh qrlvh e| h{shulphqwlqj1 Wkdw lv/ kh fdq dvvhvv wkh txdolw| ri wkh vljqdo e| wudglqj zlwk rwkhu/ srwhqwldoo| pruh lqiruphg/ pdunhw pdnhuv1 Wkhuhiruh/ wkh lqirupdwlyhqhvv ri wkh vljqdo lv srvlwlyho| uhodwhg wr wkh %lqiruphg wudglqj% ri wkh pdunhw pdnhu +t ,1 Klv fdsdflw| wr ohduq e| sodflqj rughuv zlwk rwkhu pdunhw pdnhuv ghshqgv dovr rq wkh ryhudoo pdunhw yrodwlolw| +,1 Wkh kljkhu wkh pdunhw yrodwlolw|/ wkh ohvv lqirupdwlyh lv wkh uhdfwlrq ri wkh pdunhw pdnhu kh wudghv zlwk1 Zh fdq wkhuhiruh ghqh wkh odz ri prwlrq ri pdunhw pdnhuv* eholhiv rq 1 Sursrvlwlrq 4 Wkh hyroxwlrq ri wkh srvwhulru suredelolw| ri wkh uhjlph w lv= g bw @ b gw . g +9, w zkhuh bw +4 bw ,+w u , b @ +4 5 bw , @+ , dqg w 2 I gv g @ bw w . +4 bw ,u gw +surri lq Dsshqgl{ D,= v uhsuhvhqwv wkh rz ydoxh ri lqirupdwlrq1 Lw fdq eh uhzulwwhq dv @ … Ebwt bu ru / li … 3 zh wdnh wkh orjdulwkp/ oq+ , @ oq+w u , +oq+Lt , oq+L ,, @ oq+w u , . +:, zkhuh fdq eh orrvho| ghqhg dv wkh glhuhqwldo lq lqirupdwlrq ehwzhhq lqfrplqj dqg rxwjrlqj wudgh1 Lw uhsuhvhqwv wkh lqfuhdvh lq lqirupdwlyhqhvv gxh wr wudglqj zlwk lqiruphg pdunhw pdnhuv1 Wkh pdunhw pdnhu/ diwhu kdylqj uhfhlyhg dq rughu kdv eholhiv zkrvh df0 fxudf| ghshqgv rq wkh qrlvh ri wkh vljqdo +2 ,1 E| sodflqj rughuv zlwk lqiruphg pdunhw I 43
  • 15. pdnhuv +t , wkh ghdohu lpsuryhv wkh dffxudf| ri klv eholhiv1 Wkh juhdwhu dffxudf| lv uhsuh0 vhqwhg e| d wljkwhu glvwulexwlrq ri wkh srvwhulru +vpdoohu bw +4 bw ,,1 Zh fdq wklqn ri wklv dv li wkh pdunhw pdnhu zhuh xvlqj wkh uhdfwlrq ri wkh lqiruphg pdunhw pdnhuv wr klv rughuv dv d uholdelolw| fkhfn iru wkh lqirupdwlrq kh kdv uhfhlyhg zlwk wkh lqfrplqj wudgh1 22 A i @h!i| @!iht T|4@* Ah@_?} 5|h@|i}) Wkh pdunhw pdnhu vroyhv wkh iroorzlqj sureohp= ] Pd{” ™”Ä ™”e7t H ^ h3$r X+ ,gv` +;, r f v=w= = t . t Ä . t e7t @ 4 +, Xvlqj wkh idfw wkdw 4 A A 3 ohw*v ghqh { @ 4 wkdw lv wkh glhuhqfh lq lpsdfw wkdw wudglqj hqgrjhqrxvo| zlwk lqiruphg pdunhw pdnhuv surgxfhv dv rssrvhg wr fkdqjlqj wkh elg dqg dvn txrwhv1 Wkh ydoxh ixqfwlrq ri wkh pdunhw pdnhu fdq wkhq eh h{suhvvhg dv= +4 {, 4 4 4 . t M @ M% +4 t e7t t ,+t .t Ä , .t e7t M% . M%% +t . tÄ ,2 2 . M + 2 , .M| e 2 5 5 +43, zkhuh M% A 3/ M%% ? 3 dqg M| ? 3= M lv wkh vhfrqg ghulydwlyh ri wkh ydoxh ixqfwlrq zlwk uhvshfw wr lqirupdwlrq dqg lv dozd|v srvlwlyh1 Zh vhh lpphgldwho| wkdw wkh pdunhw pdnhu ” idfhv wzr wudgh0rv1 Wkh uvw rqh lv ehwzhhq wkh jdlq iurp h{shulphqwdwlrq +  M + n2 , , 2 j dqg wkh frvw lqfxuuhg wr h{shulphqw1 Wklv frvw frqvlvwv ri wkh ri orzhu h{shfwhg uhwxuq gxh wr wkh lpsdfw ri pdunhw pdnhu*v rzq wudglqj rq sulfhv + M% Ej27 t +t . t Ä ,,1 Wkh 3 e frvw lqfuhdvhv zlwk wkh h{shfwhg uhwxuqv +, dqg zlwk wkh lpsdfw ri wudglqj hqgrjhqrxvo| e zlwk lqiruphg pdunhw pdnhuv + {, dqg ghfuhdvhv zlwk pdunhw yrodwlolw| +2 ,1 Wkh kljkhu wkh h{shfwhg uhwxuq dqg wkh vwurqjhu lv wkh sulfh lpsdfw/ wkh pruh frvwo| lw ehfrphv wr iruhjr sduw ri lw e| uhyhdolqj lqirupdwlrq wkurxjk h{shulphqwdwlrq1 Rq wkh rwkhu kdqg/ wkh kljkhu wkh yrodwlolw|/ wkh orzhu wkh sulfh lpsdfw dqg wkhuhiruh wkh orzhu wkh frvw ri h{shulphqwlqj1 Wkh vhfrqg wudgh0r lv wkh rqh ehwzhhq wkh ehqhwv ri jrlqj h{rjhqrxv +t e7t , dqg wkh frvw ri grlqj vr + M% t e7t +t . tÄ ,,1 Wklv frvw lv djdlq h{suhvvhg lq whupv ri iruhjrqh e surwv dqg/ dv ehiruh/ lv d gluhfw ixqfwlrq ri pdunhw h{shfwhg uhwxuqv +,1 Vroylqj wkh e 44
  • 16. rswlpl}dwlrq sureohp ghqhg lq htxdwlrqv ; dqg zh fdq ghqh wkh rswlpdo dprxqw ri h{shulphqwdwlrq1 Sursrvlwlrq 5 Wkh rswlpdo dprxqw ri wudgh zlwk wkh lqiruphg pdunhw pdnhuv lv= 5 ^+{ e 4,u . M ` u M t @ = 52 u+{ 4,2 e
  • 17. ,4ThU@* +it|hU|L?t Wkh prgho frqwdlqv whvwdeoh uhvwulfwlrqv1 Zh xvh wkhvh wr ghwhuplqh zkhwkhu pdunhw pdnhuv ohduq iurp wkh rughuv wkh| uhfhlyh dqg li wkh| uhdfw vhohfwlyho| dqg vwudwhjlfdoo| wr wkh rqhv fkdudfwhul}hg e| kljkhu lqirupdwlrqdo frqwhqw1 Lq sduwlfxodu/ zh zdqw wr whvw zkhwkhu h{shulphqwdwlrq lv rqh ri wkh vwudwhjlhv pdunhw pdnhuv sod|1 K|srwkhvlv 4= Pdunhw pdnhuv uhvruw wr hqgrjhqrxv wudgh pruh iuhtxhqwo| lq fdvh zkhuh wkh| uhfhlyh sulylohjhg lqirupdwlrq1 Li wkh ghflvlrq ri wkh pdunhw pdnhu wr sodfh rughuv gluhfwo| zlwk rwkhu pdunhw pdnhuv lv pdlqo| lqirupdwlrq0gulyhq/ zh vkrxog revhuyh pdunhw pdnhuv uhvruwlqj wr hqgrjhqrxv wudgh pruh iuhtxhqwo| lq fdvhv zkhuh wkh| uhfhlyh sulylohjhg lqirupdwlrq1 Iurp Htxdwlrq +:, lw iroorzv wkdw= M M L +w u , t ec•t @ t . t Ä @ @ @ i +L ,= +44, 5u+4 e {, 5u+4 e {, Lt Wklv lpsolhv d srvlwlyh uhodwlrqvkls ehwzhhq wkh ghflvlrq ri jrlqj hqgrjhqrxv dqg wkh lq0 irupdwlyhqhvv ri wkh lqfrplqj wudgh +L ,1 Wkh rssrvlwh lv wuxh iru h{rjhqrxv wudgh zklfk lv= 5+4 {,u M e t e7t @ @ i + L ,= +45, 5u+4 {, e Wkdw lv/ lqirupdwlrq0gulyhq wudghv vkrxog kdyh kljkhu srzhu wr h{sodlq hqgrjhqrxv wudghv wkdq wr h{sodlq h{rjhqrxv rqhv1 Lqghhg/ li wkh pdunhw pdnhu rqo| zdqwv wr uhedodqfh klv lqyhqwru|/ kh fdq vlpso| fkdqjh wkh elg dqg dvn txrwhv1 Hqgrjhqrxv wudgh/ krzhyhu/ dovr suhvhqwv wkh pdunhw pdnhu zlwk wkh rssruwxqlw| wr h{sorlw klv lqirupdwlrq1 Wklv lpsolhv wkdw lqyhqwru|0uhedodqflqj vkrxog eh pdlqo| uhodwhg wr h{rjhqrxv wudglqj/ zkloh 45
  • 18. lqirupdwlrq0h{sorlwdwlrq vkrxog eh pruh fruuhodwhg wr hqgrjhqrxv wudglqj1 Wkhuhiruh/ wkh ghflvlrq wr wudgh hqgrjhqrxvo| vkrxog eh vwurqjhvw lq wkh fdvh zkhuh wkh lqfrplqj wudgh lv yhu| lqirupdwlyh/ dqg zhdnhvw lq wkh fdvh zkhuh wkh lqfrplqj wudgh lv xqlqirupdwlyh1 K|srwkhvlv 5= Pdunhw pdnhuv* vwudwhjlf ehkdylru rq wkh vhfrqgdu| pdunhw vkrxog fkdqjh dw wkh wlph ri wkh dxfwlrq1 Wkh vwudwhjlf ehkdylru ri wkh pdunhw pdnhu vkrxog fkdqjh zkhq vrph lqirupdwlrqdo hyhqw prglhv wkh glhuhqfh lq frvw ehwzhhq wudglqj hqgrjhqrxvo| dqg wudglqj h{rjhqrxvo| +{ ,1 Wkh lqfhqwlyh wr wudgh h{rjhqrxvo| lv d ixqfwlrq ri {= Ct e7t M @ ? 31 +46, C{ 5u+{ 4,2 e Wkdw lv/ h{rjhqrxv wudgh gursv zkhq wkh glhuhqfh ehwzhhq wkh frvw ri jrlqj h{rjhqrxv dqg wkh frvw ri jrlqj hqgrjhqrxv +{ , lqfuhdvhv1 Lq wkh fdvh ri wkh Wuhdvxu| erqgv pdunhw/ wkh Wuhdvxu| dxfwlrq lv wkh hyhqw zkhq jrlqj h{rjhqrxv lv vxevwdqwldoo| pruh frvwo| wkdq jrlqj hqgrjhqrxv1 Lqghhg/ wkh dxfwlrq surylghv vrph ghdohuv zlwk dq lqirupdwlrq dgydqwdjh dv wkh pdunhw pdnhuv zkr lqwhuphgldwh wkh eljjhvw vkduh ri erqgv ehlqj dxfwlrqhg r kdyh dgglwlrqdo lqirupdwlrq derxw wkh ryhudoo pdunhw ghpdqg vfkhgxoh dqg oltxlglw| vkrfnv1 Dw wkh vdph wlph/ wkh dxfwlrq dovr surylghv wkh lqiruphg ghdohuv zlwk d zd| ri h{sorlwlqj wklv lqirupdwlrq zlwkrxw uhyhdolqj lw1 Wkhuhiruh/ fkdqjlqj wkh elg dqg dvn txrwhv ehiruh wkh dxfwlrq ehfrphv pruh h{shqvlyh dv lw uhyhdov lqirupdwlrq wkdw frxog eh xvhg surwdeo| erwk lq wkh vhfrqgdu| pdunhw dqg dw wkh dxfwlrq1 Wklv lpsolhv wkdw lq jhqhudo zh h{shfw d uhgxfwlrq ri h{rjhqrxv wudgh dqg dq lqfuhdvh ri hqgrjhqrxv wudgh wkh gd| ehiruh wkh dxfwlrq1 Dovr/ wkh uhdfwlrq vkrxog glhu dffruglqj wr wkh delolw| ri wkh pdunhw pdnhuv dw wkh dxfwlrq1 Wkh %pruh fdsdeoh% pdunhw pdnhuv 0l1h1 wkh rqhv zkr kdyh ehwwhu lqirupdwlrq dw wkh dxfwlrq 0 fdq drug uhgxflqj erwk h{rjhqrxv dqg hqgrjhqrxv wudgh/ dv wkh| fdq phhw wkh ghpdqg dw wkh dxfwlrq wkh| lqwhuphgldwh1 Krzhyhu/ ohvv fdsdeoh pdunhw pdnhuv/ ehlqj pruh xqfhuwdlq derxw wkh uhvxowv ri wkh dxfwlrq/ kdyh wr wudgh lq wkh vhfrqgdu| pdunhw lq rughu wr phhw wkh ghpdqg ri erqgv wkh| lqwhuphgldwh12 Wkhuhiruh/ zh h{shfw wkdw lq 2 `i _i@* | | i U@ti ihi | i ML?_t L? @ U|L? @hi UL4T*i|i*) _i?|U@* @?_ u ?}M*i |L | i L?it @*hi@_) |h@_i_ ? | i tiUL?_@h) 4@h!i| A t t ?_ii_ | i U@ti uLh | i W|@*@? 4@h!i| @t i T*@?i_ ? 5iU|L? e 46
  • 19. wkh shulrg ehiruh wkh dxfwlrq wkh pruh lqiruphg pdunhw pdnhuv gudvwlfdoo| uhgxfh dq| lqirupdwlrq0uhodwhg wudglqj dfwlylw|/ zkloh wkh ohvv lqiruphg rqhv fkdqqho prvw ri wkhlu dfwlylw| wkurxjk ohvv lqirupdwlrq0uhyhdolqj hqgrjhqrxv wudgh1 K|srwkhvlv 6= Pdunhw pdnhuv vwudwhjlfdoo| vhohfw wkh rwkhu pdunhw pdnhuv wr dssurdfk lq rughu wr hlwkhu lqfuhdvh wkhlu lqirupdwlrq +%h{shulphqwdwlrq%, ru klgh lw +%klglqj%,1 Li rughu rzv duh lqirupdwlyh dqg pdunhw pdnhuv uhdfw vwudwhjlfdoo| wr wkhp/ wkh ghflvlrq wr jr hqgrjhqrxv hqwdlov wkh vhohfwlyh fkrlfh ri wkh frxqwhusduwv zlwk zkrp wr wudgh1 D pdunhw pdnhu uhdfwlqj wr wkh lqirupdwlrq frqwdlqhg lq dq lqfrplqj rughu kdv wr ghflgh krz wr xvh vxfk lqirupdwlrq1 Li kh lv frqghqw derxw lwv txdolw|/ kh fdq wu| wr %klgh% klv lqirupdwlrq dqg h{sorlw lw e| wudglqj zlwk d ghdohu ohvv lqiruphg wkdq wkh rqh zkr kdv klw klp1 Dowhuqdwlyho|/ wkh pdunhw pdnhu pd| zdqw wr lqfuhdvh klv lqirupdwlyhqhvv dqg _h{shulphqw%/ e| sodflqj rughuv zlwk pruh lqiruphg pdunhw pdnhuv1 Zh fdq wkhuhiruh ghqh wzr w|shv ri vwudwhjlhv= klglqj dqg h{shulphqwlqj1 Wkh qhw ehqhw ri sodflqj rughuv zlwk lqiruphg pdunhw pdnhuv lv d srvlwlyh ixqfwlrq ri wkh rz ydoxh iurp h{shulphqwdwlrq + ,1 Xvlqj wkh ghqlwlrq ri +htxdwlrq :, zh fdq uhodwh wkh ghflvlrq wr sodfh dq rughu zlwk lqiruphg pdunhw pdnhuv wr wkh glhuhqwldo ehwzhhq wkh ghjuhh ri lqirupdwlyhqhvv ri wkh ghdohu zkr lv sodflqj wkh rughu dqg wkdw ri wkh rwkhu pdunhw pdnhu zkrp wkh %klw% pdunhw pdnhu lv dssurdfklqj1 Lq sduwlfxodu/ zh kdyh wkdw= Ct M +5 u, e @ 2 = +47, C 5 u+{ 4,2 e Wklv lpsolhv wkdw= Ct Ct A 3 li u lv kljk dqg ? 3 li u lv orz1 +48, C C Wkdw lv/ ghshqglqj rq wkh ghjuhh ri ulvn dyhuvlrq +u,/ pdunhw pdnhuv fdq eh glylghg lqwr wzr jurxsv zklfk zh zrxog fdoo %vqhdnlhv% dqg %vnhswlfv%1 Vnhswlfv sodfh wkhlu wudgh zlwk frxqwhusduwv zkr duh pruh lqiruphg wkdq wkh rqhv zkrp wkh| duh uhfhlylqj wkhlu rughuv iurp1 Vqhdnlhv sodfh wkhlu rughuv zlwk frxqwhusduwv zkr duh ohvv lqiruphg wkdq wkh rqhv zkrp wkh| duh uhfhlylqj wkhlu rughuv iurp1 Wkh lqwxlwlrq lv wkdw wkh iruphu wu| wr ohduq 47
  • 20. e| klwwlqj pruh lqiruphg pdunhw pdnhuv/ zkloh wkh odwwhu rqo| dssurdfk wkh ohvv lqiruphg rqhv lq rughu wr klgh wkhlu lqirupdwlrq1 Wkh vnhswlfv duh pruh ulvn dyhuvh dqg/ wkhuhiruh/ dwwhpsw wr ohduq1 Wkh vqhdnlhv duh rqo| frqfhuqhg zlwk surwv dqg wkhuhiruh dwwhpsw wr klgh wkhlu lqirupdwlrq wr h{sorlw lw ehwwhu1 Hpslulfdoo| wklv lpsolhv wkdw/ lq wkh fdvh ri klglqj/ zh h{shfw d qhjdwlyh uhodwlrqvkls ehwzhhq wkh ghjuhh ri lqirupdwlyhqhvv ri wkh ghdohu zkr sodfhv wkh ruljlqdwlqj wudgh dqg wkh ghjuhh ri lqirupdwlyhqhvv ri wkh pdunhw pdnhuv zlwk zkrp wkh klw pdunhw pdnhu sodfhv dq rughu1 Lq wkh fdvh ri h{shulphqwlqj/ rq wkh frqwudu|/ d srvlwlyh uhodwlrqvkls lv suhglfwhg1 K|srwkhvlv 7= Pdunhw pdnhuv* uhdfwlrq wr pdunhw yrodwlolw| ghshqgv rq wkh vwudwhj| wkh| sod|1 Yrodwlolw| lqfuhdvhv vqhdnlhv* lqiruphg hqgrjhqrxv wudgh dqg uhgxfhv vnhswlfv*v rqh1 Lq whupv ri wkh uhodwlrqvkls zlwk wkh pdunhw yrodwlolw| wkh wzr fodvvhv ri pdunhw pdnhuv glvsod| rssrvlwh ehkdylru1 Lq sduwlfxodu/ Ct +M e . u+{ 4,, M u @ = +49, C 2 2 u+{ 4,2 e Wklv lpsolhv wkdw= Ct Ct ? 3 li u lv kljk dqg A 3 li u lv orz1 +4:, C2 C2 wkdw lv/ kljkhu xqfhuwdlqw| lq wkh pdunhw kdv d qhjdwlyh lpsdfw rq h{shulphqwdwlrq iru wkh vnhswlfv dqg d srvlwlyh rqh iru wkh vqhdnlhv1 Wkh uhdvrq fdq eh irxqg lq wkh dyhuvlrq wr ulvn= wkh kljkhu wkh yrodwlolw|/ wkh kljkhu wkh ulvn/ wkh ohvv wkh vnhswlfv h{shulphqw/ dqg wkhuhiruh wkh ohvv wkh| uhvruw wr hqgrjhqrxv wudgh1 Wkh rssrvlwh lv wuxh iru wkh vqhdnlhv zkr/ ehlqj ohvv ulvn dyhuvh/ xvh wkh rssruwxqlw| surylghg e| kljkhu yrodwlolw| wr klgh wkhlu wudgh ehwwhu1 Wklv doorzv wkhp wr lqfuhdvh wkhlu hqgrjhqrxv wudgh1 e A i @h!i| @?_ | i #@|@ti| Lq Lwdo|/ wkhuh duh wkuhh pdlq w|shv ri wudghg erqgv= Wuhdvxu| Qrwhv/ Wuhdvxu| Erqgv dqg qdqfldoo| lqgh{hg erqgv1 Wuhdvxu| Erqgv +Exrql gho whvrur Srolhqqdol/ ru EWS, duh phglxp0 dqg orqj0whup frxsrq erqgv1 Ilqdqfldoo| lqgh{hg erqgv +Fhuwlfdwl gl Fuhglwr 48
  • 21. gho whvrur ru FFW, duh phglxp0orqj whup frxsrq erqgv zlwk wkh ydoxh ri wkh frxsrq lq0 gh{hg wr vkruw0whup Wuhdvxu| Eloov1 Wuhdvxu| Qrwhv +Fhuwlfdwl gho Whvrur d ]hur Frxsrq/ ru FW], duh 50|hdu }hur0frxsrq erqgv1 Erqgv duh prvwo|
  • 22. wudghg rq dq lqwhu0ghdohu edvhg Wuhdvxu| Erqg Pdunhw +Phufdwr Whohpdwlfr ghl wlwrol gl Vwdwr/ PWV,1 Wkh PWV pdunhw lv d vfuhhq0edvhg v|vwhp/ rshudwlqj ehwzhhq 133 d1p1 dqg 8133 s1p1 Wkhuh duh wkuhh w|shv ri ghdohuv wudglqj rq wkh PWV= ruglqdu| ghdohuv +dssur{lpdwho| 693,/ ruglqdu| pdunhw pdnhuv +73, dqg _sulpdu| ghdohuv% ru _vshfldolvwv%+49,1 Rqo| edqnv/ lqyhvwphqw upv dqg lqvxudqfh frpsdqlhv duh doorzhg wr dfw dv ghdohuv1 Ruglqdu| ghdohuv pd| rqo| sodfh rughuv zlwk pdunhw pdnhuv dqg fdqqrw srvw elg dqg dvn sulfhv1 Pdunhw pdnhuv frpplw wkhpvhoyhv wr frqwlqxrxvo| srvwlqj elg dqg dvn sulfhv1 Wkh| pd| sodfh rughuv zlwk rwkhu pdunhw pdnhuv1e Vshfldolvwv duh pdunhw pdnhuv zkr pxvw wudgh d plql0 pxp shufhqwdjh ri hdfk w|sh ri erqg rq wkh vhfrqgdu| pdunhw dqg sxufkdvh d plqlpxp shufhqwdjh ri wkh erqgv ehlqj dxfwlrqhg r dw hdfk dxfwlrq1 Lq h{fkdqjh iru rshudwlqj zlwklq pruh elqglqj wudglqj uhtxluhphqwv/ wkh| hqmr| uh0qdqflqj ehqhwv/ ehlqj hqwlwohg wr eruurz dw d sduwlfxodu frqyhqlhqw udwh dw wkh glvfrxqw zlqgrz ri wkh Edqn ri Lwdo|1 Hdfk vlqjoh wudghu +ruglqdu| ghdohu/ ruglqdu| pdunhw pdnhu dqg sulpdu| ghdohu, kdv dffhvv wr d vfuhhq zkhuh kh fdq revhuyh wkh elg dqg dvn sulfhv wkh ghdohuv +erwk vshfldolvwv dqg ruglqdu| pdunhw pdnhuv, srvw dqg wkh pd{lpxp qxpehu ri erqgv wkh| frpplw wkhp0 vhoyhv wr wudgh +ghswk,1 Pdunhw pdnhuv duh qrw dqrq|prxv h{ dqwh1 Wkdw lv/ wkh qdph ri wkh pdunhw pdnhu dsshduv rq wkh vfuhhq qh{w wr wkh elg dqg dvn sulfhv kh lv srvwlqj1 Zkloh hdfk ghdohu nqrzv wkh lghqwlw| rqo| ri wkh frxqwhusduw zlwk zkrp kh lv wudglqj/ qr pdunhw sduwlflsdqw +ruglqdu| ghdohu/ ruglqdu| pdunhw pdnhu ru vshfldolvw, nqrzv wkh lghqwlwlhv ri rwkhu pdunhw sduwlflsdqwv lqyroyhg lq d wudqvdfwlrq lq zklfk kh lv qrw gluhfwo| lqyroyhg1 Wklv pdnhv PWV yhu| vlplodu wr QDVGDT1 Wkh wudqvdfwlrq wdnhv sodfh rqo| dw wkh srvwhg sulfh1 Zkhq lw lv h{hfxwhg/ wkh qdph ri wkh ghdohu _klw% eolqnv/ vljqdoolqj wr wkh pdunhw wkdw kh lv wudglqj dqg olvwlqj wkh sulfh
  • 23. L?_t @hi @*Lt |h@_i_ L? | i *@? 5|LU! , U @?}i OLiihc | i Lih i*4?} 4@Lh|) Lu |h@_i ? Ahi@t h) L?_t |@!it T*@Ui L? | i A5 A i ? 4Mih Lu ML?_t |h@_i_ L? | i 5|LU! , U @?}i t *4|i_ @?_ ThUit hiiU| | i L?it _i|ih4?i_ ? | i A5 e A i) | _h@ |i4TLh@h*) uhL4 | i 4@h!i| u | i) hiUii @? Lh_ih i^ @* |L | i 4@ 4 4 ? 4Mih Lu ML?_t | i) @hi UL44|i_ |L |h@_i 49
  • 24. dw zklfk wkh wudgh wdnhv sodfh1 Wkh yroxph ri wkh wudqvdfwlrq lv qhyhu uhyhdohg/ h{fhsw lq wkh uduh fdvh zkhq d ghdohu uhfhlyhv dq rughu htxdo wr wkh pd{lpxp qxpehu ri erqgv kh kdv frpplwwhg klpvhoi wr wudgh1 Lq wkdw fdvh/ kh dxwrpdwlfdoo| zlwkgudzv iurp wkh pdunhw iru d shulrg qrw orqjhu wkdq 93 vhfrqgv1 D Wklv zlwkgudzdo lv wkh rqo| vljqdo wkh pdunhw uhfhlyhv derxw wkh vl}h ri wkh wudqvdfwlrq1 Dqdorjrxvo| wr wkh I[ pdunhw +O|rqv 48,/ wkh vorz glxvlrq ri lqirupdwlrq yld lqwhughdohu wudgh lv idflolwdwhg e| wkh devhqfh ri wudgh uhsruwlqj +hyhq h{ srvw,1 Rqo| djjuhjdwh jxuhv iru wkh zkroh pdunhw duh dydlodeoh dw wkh hqg ri wkh gd|1 Wkh vfuhhq0 edvhg v|vwhp lv wudqvsduhqw wr wkh jhqhudo sxeolf/ dqg wkh ehvw elg dqg dvn sulfhv duh uhsruwhg rq d vshflf sdjh e| Uhxwhuv1 S Wkh sulpdu| Wuhdvxu| erqg pdunhw lv edvhg rq xqlirup w|sh dxfwlrqv1 Wkh vfkhgxoh ri wkh dxfwlrqv lv frppxqlfdwhg e| wkh Wuhdvxu| dw wkh ehjlqqlqj ri wkh |hdu/ zkloh wkh qxpehu ri erqgv wkdw wr eh dxfwlrqhg r lv dqqrxqfhg rqh zhhn ehiruh1 Wkh rfldo vxeplvvlrq ri wkh ghpdqgv dw wkh dxfwlrq wdnhv sodfh wkurxjk d frpsxwhul}hg vfuhhq0 edvhg v|vwhp1 Hdfk sduwlflsdqw lq wkh dxfwlrq lv lqiruphg ri wkh dprxqw kh kdv ehhq doorwwhg/ zkloh wkh pdunhw dv zkroh lv lqiruphg ri wkh wrwdo qxpehu dvvljqhg/ wkh dxfwlrq sulfh dqg wkh fryhu udwlr/ wkdw lv/ wkh udwlr ehwzhhq wkh qxpehu ri erqgv ghpdqghg dqg wkh qxpehu doorwwhg1 Wr lqfuhdvh wkh ghswk ri wkh pdunhw/ wkh Wuhdvxu| lvvxhv wkh vdph erqgv uhshdwhgo| +_uhrshqv wkh dxfwlrq%,1 Wkh gdwdvhw frqwdlqv doo wkh wudqvdfwlrqv iurp 5 Vhswhpehu 47 wr 5; Iheuxdu| 49 iru doo wkh olvwhg erqgv +wrwdo ri 6:,1 Lq doo/ wkh| wrwdo 4/66/76: wudqvdfwlrqv1 Iru hdfk wudqvdfwlrq/ zh kdyh gdwd vkrzlqj wkh wlph dw zklfk wkh wudqvdfwlrq lv h{hfxwhg/ wkh vl}h ri wkh wudqvdfwlrq/ wkh sulfh dqg wkh qdph ri wkh frxqwhusduwv dqg wkh lghqwlfdwlrq ri wkh ghdohu zkr ruljlqdwhg wkh wudqvdfwlrq1 Ghvfulswlyh vwdwlvwlfv ri wkh gdwd duh uhsruwhg lq Wdeoh 41 D W| U@? Mi it|4@|i_ | @| L? @ih@}i | t LUU hhi_ *itt | @? Dff |4it ? L h t@4T*i S ** | i |h@?t@U|L?t @hi ti||*i_ | hL } @ t)t|i4 L?i_ @?_ LTih@|i_ M) @ UL4T@?) | @| @U|t @t @ t Mt_@h) Lu | i i?|h@* @?! E5W A i |h@?t@U|L?t @hi @*tL UL?|? L t*) 4L?|Lhi_ M) | i i?|h@* @?! |ti*uc U @t |L U iU! u | i _i@*iht 4ii| | i hi^ hi4i?|t ? |ih4t Lu | i UL?|? L t TLt|?} Lu M_@t! ThUitc | i 4?4 4 ? 4Mih Lu |h@?t@U|L?t i iU |i_ Tih U@|i}Lh) Lu ML?_ @?_ | i t3i Lu | i M_ @?_ @t! tThi@_ Bi? | @| | i i?|h@* @?! @*tL @U|t @t @ U*i@h?} L ti @?_ ThL_ih Lu *^ _|) |L | i L*i ?|ihM@?! T@)4i?|t ti||*i4i?| t)t|i4c | i Uhi_|Lh| ?itt Lu | i _i@*iht t 4T*U|*) } @h@?|ii_ M) | i i?|h@* @?! |ti*u 4:
  • 25. Wr irfxv rq wkh uhdfwlrq ri wkh pdunhw pdnhu/ zh frqvlghu wkh wudqvdfwlrqv iroorzlqj wkh ruljlqdwlqj rqh1 Lq sduwlfxodu/ iru hdfk wudqvdfwlrq/ zh frqvlghu doo wkh wudqvdfwlrqv ri wkh vdph pdunhw pdnhu lq wkh iroorzlqj 43 plqxwhv1 Wkhvh frpsulvh erwk wkh dgglwlrqdo rughuv sodfhg zlwk wkh pdunhw pdnhu +h{rjhqrxv wudgh, dqg wkh rughuv wkdw kh sodfhv zlwk wkh rwkhu pdunhw pdnhuv +hqgrjhqrxv wudgh,1 Zh ghqh dv hqgrjhqrxv wudgh wkh dprxqw ri wudgh rq wkh n0wk erqg wkdw lv hqgrjhqrxvo| ruljlqdwhg e| wkh m0wk pdunhw pdnhu/ zkhq kh sodfhv dq rughu zlwk rwkhu pdunhw pdnhuv1 H{rjhqrxv wudgh/ rq wkh frqwudu|/ uhsuhvhqwv wkh dprxqw ri wudgh rq wkh n0wk erqg wkdw lv qrw gluhfwo| ruljlqdwhg e| m0wk pdunhw pdnhu1 Lw frxog frph wr klp hlwkhu iru pdunhw h{rjhqrxv uhdvrqv ru ehfdxvh lw lv lqgxfhg e| d fkdqjh lq wkh elg dqg dvn txrwhv kh srvwv1 Wkh vdpsoh kdv ehhq glylghg lqwr _gd|v ehiruh wkh dxfwlrq% dqg _doo rwkhu gd|v%1 Wkh hvwlpdwhv iru _gd|v ehiruh wkh dxfwlrq% . duh pdgh rqo| iru wkh erqgv wkdw duh dxfwlrqhg wkh qh{w gd|1 Doo wkh hvwlpdwlrqv duh fduulhg rxw xvlqj Kdqvhq*v Jhqhudol}hg Phwkrg ri Prphqwv/ zlwk fruuhfwlrq rq wkh yduldqfh0fryduldqfh pdwul{ wr frqwuro iru erwk khwhurvfhgdvwlflw| dqg dxwrfruuhodwlrq1 Lq rughu wr ghdo zlwk wkh jhqhudwhg uhjuhvvruv lq rxu hvwlpdwlrqv/ zh dgrsw wkh Sdjdq*v +4;7, dssurdfk edvhg rq lqvwuxphqwdo yduldeoh hvwlpdwlrq1 D OG ,?_L}i?L t Ah@_i @?_ W?uLh4@|L? D _i€?|L? Lu | i W?uLh4@|i?itt Lu Ah@_i Wkh lqirupdwlrqdo frqwhqw ri wkh lqfrplqj wudgh fdq eh lqihuuhg e| orrnlqj dw wkh ghdohu zkr kdv ruljlqdwhg wkh wudgh1 Dv Fr{ dqg Uxelqvwhlq +4;8/ s1 ;4, srlqwhg rxw= % iurp shukdsv elwwhu h{shulhqfh pdunhw pdnhuv ohduq wr lghqwli| olnho| lqupdwlrq wudghuv1% Wkdw lv/ hdfk pdunhw pdnhu ohduqv derxw wkh ghjuhh ri wkh lqirupdwlyhqhvv ri wkh rwkhu pdunhw pdnhuv kh lv wudglqj zlwk e| vlpso| orrnlqj dw wkh ehkdylru ri sulfhv lq wkh shulrg iroorzlqj wkh wudqvdfwlrq kh hhfwhg zlwk wkhp1 Lq sduwlfxodu/ d ghdohu zkr frqvlvwhqwo| ex|v ehiruh sulfhv ulvh dqg vhoov ehiruh wkh| gurs lv fodvvlhg dv _lqiruphg%1 Wudglqj doorzv wkh pdunhw pdnhu wr xsgdwh frqwlqxrxvo| klv sulruv rq wkh ghjuhh ri lqirupdwlyhqhvv ri . A i _@)t MiuLhi | i @ U|L? @hi _i€?i_ @t | i TihL_ ULih?} | i L*i |h@_?} _@) MiuLhi | i @ U|L? @?_ | i 4Lh??} Lu | i @ U|L? MiuLhi | i _i@_*?i |L t M4| | i M_t 4;
  • 26. wkh rwkhu pdunhw pdnhuv dqg wkhuhiruh rq wkh lqirupdwlrqdo frqwhqw ri wkh lqfrplqj wudgh/ ghqhg lq whupv ri wkh ghdohu ruljlqdwlqj lw1 Wkh sulruv rq rwkhu ghdohuv ehfrph wkh edvlv ri pdunhw pdnhuv* dvvhvvphqw ri wkh txdolw| ri lqirupdwlrq frqwdlqhg lq wkh wudgh wkh| uhfhlyh1 Zh zloo uhihu lqwhufkdqjhdeo| wr wkh lqirupdwlrqdo frqwhqw ri wudgh dqg wr wkh ghjuhh ri lqirupdwlyhqhvv ri wkh ghdohu ruljlqdwlqj lw1 Zh orrn dw wkh fkdqjhv lq sulfhv ri wkh vdph erqg lq wkh 8 plqxwhv wkdw iroorz hdfk wudqvdfwlrq dqg/ iru hdfk pdunhw pdnhu m/ zh uxq wkh dx{loldu| uhjuhvvlrq= S8™| @ W8™| . %8™| +4;, lq d sdluzlvh uhodwlrq yhuvxv doo wkh rwkhu l ghdohuv iru hdfk lqglylgxdo erqg n1 Zh ghqh W8™| dv wkh wrwdo qxpehu ri vljqhg wudghv uhfhlyhg e| wkh m0wk pdunhw pdnhu iurp wkh l0wk ghdohu iru wkh n0wk erqg dw wlph w1 S8™| @ +S8™|nD S8™| , lv wkh fkdqjh lq wkh sulfh ri wkh n0wk erqg lq wkh 8 plqxwhv iroorzlqj wkh wudqvdfwlrq1 Iroorzlqj Pdgkdydq/ Ulfkdugvrq dqg Urrpdqv +4:,/ zh xvh wkh dfwxdo wudqvdfwlrq sulfhv1 Wkh surfhgxuh zh iroorz wr lghqwli| wudghv zlwk srvvleoh lqirupdwlrqdo frqwhqw lv uhplqlvfhqw ri wkh vwdwlvwlfdo surfhgxuh wkdw vshfldolvwv xvh wr lghqwli| wkh lqirupdwlrq0gulyhq wudgh ruljlqdwhg e| wkh eurnhuv dw wkh QVH +Ehqyhqlvwh/ Pdufxv dqg Zlokhop 45,1 Wkh frhflhqw uhsuhvhqwv wkh ghjuhh ri lqirupdwlyhqhvv ri wkh vshflf l0wk ghdohu zkr lv sodflqj wkh rughu/ dv shufhlyhg e| wkh m0wk pdunhw pdnhu1H D vljqlfdqw ydoxh ri lpsolhv wkdw wkh ghdohu lv lqiruphg1 Wkh juhdwhu wkh ydoxh ri wkh frhflhqw/ wkh kljkhu wkh ghjuhh ri lqirupdwlyhqhvv ri wkh ghdohu lv/ dqg wkh juhdwhu wkh lqirupdwlrqdo frqwhqw ri wkh rughu uhfhlyhg1 b Lq Wdeoh 5/ zh uhsruw wkh uhvxowv ri wkh hvwlpdwlrq ri Htxdwlrq +4;,1 Wkh| vkrz hylghqfh ri dq lqirupdwlrqdo frqwhqw ri wudghv1 Lq sduwlfxodu/ li @ 3=334 iru d orw ri vwdqgdug vl}h ri 8 eloolrq oluh/ wkh h{shfwhg sulfh lpsdfw lv ri wkh rughu ri 318 es1 Wkh dyhudjh sulfh lpsdfw ri d wudgh lqwhuphgldwhg e| d vshfldolvw lv derxw 3198 es/ zkloh wkh sulfh lpsdfw ri d wudgh lqwhuphgldwhg e| dq ruglqdu| pdunhw pdnhu lv derxw 31:8 es1 Wkh ghdohuv zkr duh shufhlyhg dv ehlqj pruh lqiruphg/ erwk lq whupv ri ydoxh ri wkh H AL U iU! | i hLM t|?itt Lu | i hit *|tc i i Tih4i?| | _gihi?| R*i@h??} ?_Lt 6Lh _i|@*tc tii TTi?_ b AL @L_ ThLM*i4t _ i |L | ? |h@_?}c i UL?t_ih L?*) | i @* it Lu | @| @hi t}?€U@?| @| | i DI *ii*c @?_ uLh | i hi}hittL? | @| *i@t| D |h@_it 4
  • 27. frhflhqw + , dqg lwv vljqlfdqfh +w0vwdwlvwlfv,/ duh wkh vshfldolvwv1 Wklv wv zlwk rxu lqwxlwlrq1 Jlyhq wkdw wkh vshfldolvwv duh wkh eljjhvw wudghuv/ wkh| duh pruh olnho| wr eh lqiruphg1 Iru wkh vdph uhdvrq/ wkh ghjuhh ri lqirupdwlyhqhvv lv orzhu iru ruglqdu| pdunhw pdnhuv dqg wkh orzhvw iru ruglqdu| ghdohuv1 Lw lv lpsruwdqw wr qrwh wkdw d vwdwlvwlfdoo| vljqlfdqw fdswxuhv wkh whpsrudu| lq0 irupdwlrqdo dgydqwdjh ri wkh ghdohu l ryhu ghdohu m dw d jlyhq wlph1 Rq dyhudjh/ wkh suredelolw| ri jlyhq wr uhpdlq vljqlfdqw dw 8( ohyho diwhu wkuhh gd|v lv rqo| 3179 dqg jrhv grzq wr 314:: lq 43 gd|v1 Wkxv/ vshflfdwlrq +4;, lv fdswxulqj rqo| wkh whpsrudu| lqirupdwlrqdo dgydqwdjh wkdw lv uhodwhg wr %vhpl0ixqgdphqwdo lqirupdwlrq% olnh rughu rzv ru oltxlglw| vkrfnv +Iohplqj dqg Uhprorqd 4,1 D2 6ht| Ait| Lu 5|h@|i}U i @Lh Zh fdq qrz whvw krz wklv lqirupdwlrqdo frqwhqw lv uhodwhg wr pdunhw pdnhuv* ehkdylru1 Zh frqvlghu d olqhdu vshflfdwlrq zkhuh hqgrjhqrxv dv zhoo dv h{rjhqrxv wudgh duh gluhfwo| uhodwhg wr wkh lqirupdwlrqdo frqwhqw ri wkh lqfrplqj wudgh1 Wkh jhqhudo whvw lv= v8™| @ . T8™| . L™| . 2 . g . %8™| 8™| +4, zkhuh v8™| lv wkh udwlr ehwzhhq hqgrjhqrxv wudgh dqg wrwdo wudgh ri wkh m0wk pdunhw pdnhu iru wkh n0wk erqg lq wkh 43 plqxwhv iroorzlqj wkh ruljlqdwlqj wudgh +wlph w,1 Lw uhsuhvhqwv wkh %vkduh% ri hqgrjhqrxv wudgh ryhu wrwdo wudgh1 T8™| lv wkh vl}h ri wkh rughu zklfk wkh m0wk pdunhw pdnhu uhfhlyhv e| l0wk ghdohu +wkh %ruljlqdwlqj ghdohu%, iru wkh n0wk erqg dw wlph w1f L™| uhsuhvhqwv d phdvxuh ri wkh ghjuhh ri lqirupdwlyhqhvv ri wkh l0wk ghdohu dv shufhlyhg e| wkh m0wk pdunhw pdnhu1 Dv dowhuqdwlyh phdvxuhv ri wkh ghjuhh ri lqirupdwlyhqhvv ri wkh pdunhw pdnhu zh frq0 vlghu= wkh ydoxh ri wkh frhflhqw +dv hvwlpdwhg lq Htxdwlrq 4;,/ lwv vwdwlvwlfdo vljqli0 lfdqfh +s0ydoxh, dqg wkh surgxfw ehwzhhq wkh wzr + wlphv s0ydoxh,1 Wkh uvw sur{| uhsuhvhqwv wkh ghjuhh ri lqirupdwlyhqhvv ri wkh vshflf l0wk pdunhw pdnhu zkr lv sodflqj wkh rughu/ dv shufhlyhg e| wkh m0wk ghdohu/ wkh vhfrqg uhsuhvhqwv wkh ghjuhh ri dffxudf| ri wkh vljqdo dqg wkh wklug sur{lhv iru wkh %h{shfwhg% ghjuhh ri lqirupdwlyhqhvv ri wkh ghdohu1 2 lv d sur{| ri pdunhw xqfhuwdlqw| dw wkh wlph zkhq wkh pdunhw pdnhu uhfhlyhv wkh 8™| f L| |h@_i @?_ Lh_iht @hi i Thitti_ ? @MtL* |i @* i 53
  • 28. lqfrplqj rughuv1 Lw lv ghqhg dv wkh yduldqfh rq wkh n0wk erqg lq wkh 43 plqxwhv ehiruh wkh ruljlqdwlqj wudqvdfwlrq/ zkloh g lv d gxpp| wkdw frqwurov iru pdunhw pdnhu*v lglrv|q0 fudwlf fkdudfwhulvwlfv1 Vdpsolqj lv edvhg rq wudqvdfwlrq wlph1 Wkh dqdo|vlv lv fduulhg rxw glvdjjuhjdwhg dw wkh ohyho ri lqglylgxdo pdunhw pdnhuv1 Wkh uhvwulfwlrqv lpsrvhg e| Htxdwlrqv +44, dqg +45, srvwxodwh wkdw A 3= Wkdw lv/ wkh lqfhqwlyh wr wudgh hqgrjhqrxvo| lqfuhdvhv zlwk wkh ghjuhh ri lqirupdwlyhqhvv ri wkh ghdohu zkr sodfhv wkh rughu1 Ru/ wkh kljkhu wkh lqirupdwlyhqhvv +L™| , ri wkh wudghu sodflqj wkh rughu/ wkh pruh wkh pdunhw pdnhu vkrxog uhdfw wr klv rughu e| jrlqj hqgrjhqrxv1 Wdeoh 6/ Sdqhov D dqg E uhsruw wkh uhvxowv erwk dw wkh djjuhjdwh pdunhw ohyho dqg jurxshg e| w|sh ri ghdohu dffruglqj wr wkh lqvwlwxwlrqdo fodvvlfdwlrq1 Wkh| vxssruw wkh k|srwkhvlv ri fruuhodwlrq ehwzhhq lqirupdwlrqdo frqwhqw ri wudgh dqg wkh fkrlfh ri jrlqj hqgrjhqrxv1 Wkh idfw wkdw ruglqdu| pdunhw pdnhuv dqg vshfldolvwv dozd|v suhihu hqgrjhqrxv wudgh wr h{rjhqrxv wudgh lv vkrzq e| wkh srvlwlyh ydoxh ri wkh frhflhqwv +, dqg e| wkh kljk vljqlfdqfh ri wkhlu w0vwdwlvwlfv1 Dvvxplqj wkh vdph sulfh lpsdfw ri wkh lqfrplqj wudqvdfwlrqv/ wkh vkduh ri hqgrjhqrxv wudgh lqfuhdvhv e| 6( iru d 4( lpsuryhphqw lq wkh txdolw| ri wkh vljqdo +dv phdvxuhg e| s0ydoxh,1 Wkh lpsdfw lv vrphzkdw odujhu iru vshfldolvwv +616(, dqg orzhu iru ruglqdu| pdunhw pdnhuv +518(,1 S O2G 5|h@|i}U i @Lh ? | i hL 4|) Lu | i U|L? Lq wkh sur{lplw| ri wkh dxfwlrq/ wkh h{sodqdwru| srzhu ri wkh whvwv frqvlghuhg lq wkh suhylrxv vhfwlrq vkrxog fkdqjh1 Lq sduwlfxodu/ wkh uhvwulfwlrq lpsrvhg e| Htxdwlrq 46, wrjhwkhu zlwk wkh dvvxpswlrq ri glhuhqw delolw| ri wkh pdunhw pdnhuv dw wkh dxfwlrq uhtxluhv qrw wr eh vljqlfdqw iru wkh %pruh fdsdeoh% pdunhw pdnhuv1 Iru wkh ohvv fdsdeoh rqhv/ lqvwhdg/ •dC uestoe dă|tc A ctc3dă|tc •dCr 1 Zh dvvxph wkdw wkh vshfldolvwv duh wkh pdunhw pdnhuv pruh fdsdeoh dw wkh dxfwlrq1 Lqghhg/ wkhlu vl}h/ wkhlu vxshulru lqirupdwlrq rewdlqhg wkurxjk wkhlu delolw| wr lqwhuphgldwh d eljjhu vkduh ri ghpdqg dw wkh dxfwlrq dqg sduwlfxodu lqvwlwxwlrqdo duudqjhphqwv zlwk wkh Fhqwudo Edqn frqihu wkhp d pruh srzhuixo srvlwlrq dw wkh dxfwlrq1 Wkh uhvxowv/ uhsruwhg lq Wdeoh 6/ Sdqho E/ frqup rxu k|srwkhvlv= wkh vshfldolvwv uhgxfh wkhlu lqirupdwlrq0gulyhq wudghv1 Wkh ruglqdu| pdunhw pdnhuv/ lqvwhdg/ lqfuhdvh hqgrjhqrxv wudglqj1 Iru h{dpsoh/ lq wkh fdvh wkh frhflhqw rq wkh lqirupdwlyhqhvv ri 54
  • 29. lqfrplqj ghdohu lv phdvxuhg e| xvlqj wkh s0ydoxh +L‚3dD ,/ jrhv iurp 518 wr 71:8/ zlwk d vwurqj lqfuhdvh lq vljqlfdqfh +wkh w0vwdwlvwlfv mxpsv iurp 5166 wr 617;,1 Lw lv lqwhuhvwlqj wr qrwh wkdw wkh lqfuhdvh lq hqgrjhqrxv wudgh lv prvwo| pdgh ri wudglqj sodfhg zlwk ohvv lqiruphg ghdohuv1 Lqghhg/ Wdeoh 7 vkrzv wkdw wkh gd|v ehiruh wkh dxfwlrq wkh ruglqdu| pdunhw pdnhuv uhgluhfw wkhlu wudgh wrzdugv ohvv lqiruphg pdunhw pdnhuv1 Wklv lqglfdwhv wkdw wkh| fkrrvh wr wudgh hqgrjhqrxvo| lq rughu wr klgh dqg qrw wr h{shulphqw1 Zh zloo h{sdqg xsrq wklv srlqw ehorz1 . O
  • 30. G @h!i| @!iht 5|h@|i}itG O_?} t , Tih4i? |@|L? Whvwlqj wkh uhvwulfwlrq lpsrvhg e| Htxdwlrq +48, uhtxluhv xv wr lghqwli| wkh glhuhqw vwudwhjlhv lq whupv ri wkh uhdfwlrq wr wkh lqirupdwlrqdo frqwhqw ri wkh lqfrplqj wudgh1 Zh wkhuhiruh irfxv gluhfwo| rq krz wkh shufhlyhg ghjuhh ri lqirupdwlyhqhvv ri wkh lqfrplqj wudgh dhfwv wkh zd| wkh pdunhw pdnhu fkrrvhv wkh frxqwhusduw zkrp wr sodfh klv rughu zlwk1 . Ait|?} | i , t|i?Ui Lu #gihi?|@* i @Lh Dv d suholplqdu| vwhs/ zh whvw zkhwkhu wkhuh lv d sdwwhuq lq wkh zd| pdunhw pdnhuv uhdfw wr lqiruphg wudgh1 Lq sduwlfxodu/ zh zdqw wr vhh zkhwkhu wkhuh lv d uhodwlrqvkls ehwzhhq wkh lqirupdwlyhqhvv ri wkh ghdohu sodflqj wkh ruljlqdwlqj rughu dqg wkh lqirupdwlyhqhvv ri wkh pdunhw pdnhuv zkrp wkh %klw% pdunhw pdnhu lv dssurdfklqj1 Wkhuhiruh/ zh hvwlpdwh= v @ . T8™| . L™| . 2 . g . %8™| 8™| 8™| +53, zkhuh v lv wkh udwlr ehwzhhq hqgrjhqrxv lqiruphg wudgh dqg wrwdo hqgrjhqrxv wudgh ri 8™| wkh m0wk pdunhw pdnhu iru wkh n0wk erqg lq wkh 43 plqxwhv iroorzlqj wkh ruljlqdwlqj wudgh +wlph w,1 T8™| / L™| 2 dqg g duh ghqhg dv lq Htxdwlrq +4,1 Wrwdo lqiruphg wudgh 8™| lv vsolw lq wkuhh jurxsv/ ghshqglqj rq wkh ghjuhh ri lqirupdwlyhqhvv ri wkh pdunhw pdnhuv zkrp wkh klw pdunhw pdnhu dssurdfkhv diwhu kdylqj uhfhlyhg wkh rughu1 Zh xvh wkh s0 ydoxh ri wkh frhflhqw dv ghqhg lq Htxdwlrq +4;, dv d phdvxuh ri pdunhw pdnhuv* 55
  • 31. lqirupdwlyhqhvv1 Li wkhuh duh udwlrqdo vwudwhjlhv zklfk fdq eh wudfhg iurp wkh gdwd/ wkh v iru wkh glhuhqw jurxsv vkrxog eh glhuhqw1 Wkh uhvxowv/ uhsruwhg lq Wdeoh 7/ Sdqhov D dqg E/ vkrz wkdw wkhuh lv d vljqlfdqw fkdqjh lq wkh uhodwlrqvkls ehwzhhq wkh lqirupdwlyhqhvv ri wkh lqfrplqj wudgh dqg wkdw ri wkh rxwjrlqj rqh1 Lq sduwlfxodu/ d yhu| lqirupdwlyh vljqdo lqgxfhv wkh pdunhw pdnhu zkr uhfhlyhv lw wr dssurdfk hlwkhu d yhu| lqiruphg pdunhw pdnhu ru d frpsohwho| xqlqiruphg rqh1 Lqghhg/ wkh ydoxh ri lv vwurqjhu iru wkh uvw dqg wklug fodvv1 Wklv srodul}hg uhdfwlrq dw wkh djjuhjdwh ohyho vxjjhvwv wkh h{lvwhqfh ri wzr pdlq vwudwh0 jlhv1 Pdunhw pdnhuv fdq hlwkhu klgh wkhlu lqirupdwlrq e| wudglqj zlwk ohvv lqiruphg pdunhw pdnhuv/ ru dvvhvv wkh txdolw| ri wkhlu lqirupdwlrq e| dssurdfklqj pruh lqiruphg pdunhw pdnhuv1 Wkh iruphu zrxog hqwdlo d qhjdwlyh / zkloh wkh odwwhu d srvlwlyh rqh1 Dw djjuhjdwh ohyho wklv zrxog vkrz xs dv d el0prgdo glvwulexwlrq zlwk wkh ydoxhv ri v sduwlfxoduo| kljk iru wkh yhu| lqiruphg dqg yhu| xqlqiruphg frxqwhusduwv1 Lw lv dovr zruwk qrwlqj krz wkhvh uhvxowv fkdqjh lq wkh sur{lplw| ri wkh dxfwlrq1 Wkh ydoxh ri gursv iru wkh fodvv ri yhu| lqiruphg frxqwhusduwv dqg lqfuhdvhv iru wkh fodvv ri wkh ohdvw lqiruphg rqhv1 Wklv lv lq olqh zlwk wkh suhylrxv qglqjv dqg vxjjhvwv wkdw dv wkh dxfwlrq gudzv qhduhu/ klglqj ehkdylru suhydlov ryhu h{shulphqwdwlrq1 Lq djjuhjdwh/ pdunhw pdnhuv v|vwhpdwlfdoo| uhdfw wr wkh lqirupdwlrq frqwdlqhg lq wkh rughuv wkh| uhfhlyh e| dwwhpswlqj wr klgh lw1 Krzhyhu/ wklv vshflfdwlrq grhv qrw dqvzhu wkh txhvwlrq ri zkhwkhu wkh vdph pdunhw pdnhu vlpxowdqhrxvo| sod|v erwk vwudwhjlhv/ klglqj dqg h{shulphqwlqj1 Lqghhg/ rqo| wkh dqdo|vlv dw wkh ghdohu*v ohyho fdq dgguhvv wklv lvvxh1 .2 W_i?|€U@|L? Lu *|ih?@|i Ah@_?} 5|h@|i}it Rqfh zh kdyh dvfhuwdlqhg wkh h{lvwhqfh ri d uhodwlrqvkls ehwzhhq pdunhw pdnhuv* ehkdylru dqg lqirupdwlyhqhvv ri lqfrplqj wudgh/ zh fdq surfhhg wr lghqwli| wkh glhuhqw vwudwhjlhv1 Wr gr wklv/ zh xvh dq hfrqrphwulf dssurdfk wkdw h{solflwo| prghov pdunhw pdnhuv* ghflvlrq surfhvv1 Wkh vwduwlqj srlqw lv wkh hvwlpdwlrq ri Htxdwlrq +48,/ wkdw lv wkh uhdfwlrq ixqfwlrq ri wkh pdunhw pdnhu1 Wkh idfw wkdw wkh fkrlfh ri wkh pdunhw pdnhu lv d qrq0wulyldo ixqfwlrq ri wkh rwkhu pdunhw pdnhuv* fkrlfhv dqg fkdudfwhulvwlfv pdnhv wkh sureohp yhu| lqyroyhg1 Jlyhq wkdw hdfk vlqjoh pdunhw pdnhu ghflghv klv uhdfwlrq ixqfwlrq rq wkh edvlv ri rwkhu 56
  • 32. pdunhw pdnhuv* shufhswlrq ri klv ghjuhh ri lqirupdwlyhqhvv/ zh vkrxog frqwuro iru wkh uhdfwlrq ri doo wkh rwkhu pdunhw pdnhuv/ hvwlpdwlqj wkh furvv hodvwlflwlhv ri wkh uhdfwlrq ixqfwlrqv iru doo wkh sdluv ri pdunhw pdnhuv lq wkh pdunhw1 Fohduo|/ wklv lv frpsxwdwlrqdoo| fxpehuvrph dqg/ hyhq zlwk wkh ulfkqhvv ri d kljk iuhtxhqf| gdwdvhw/ xqihdvleoh1 Zh wkhuhiruh xvh dq dssurdfk lq zklfk zh uvw ghqh wkh srvvleoh dowhuqdwlyh fkrlfhv e| jurxslqj wkh pdunhw pdnhuv lq fodvvhv dffruglqj wr krprjhqrxv fkdudfwhulvwlfv1 Wkhq/ zh vroyh wkh hqgrjhqhlw| sureohp e| surmhfwlqj wkh fkrlfh vsdfh +wkdw kdv d glphqvlrq htxdo wr wkh qxpehu ri h{lvwlqj jurxsv, rqwr wkh vsdfh ri wkh fkrlfh fkdudfwhulvwlfv +wkdw kdv wkh glphqvlrq htxdo wr wkh pxfk vpdoohu vhw ri fkdudfwhulvwlfv lq hdfk jurxs, +Ehuu|/ Ohylqvrkq dqg Sdnhv 48,1 Wkh fkrlfh vsdfh lv ghqhg rq wkh edvlv ri wkh wuhh ri dowhuqdwlyhv +Iljxuh 4,1 Wkh pdunhw pdnhu fdq hlwkhu rshudwh rqo| e| fkdqjlqj wkh elg dqg dvn txrwhv dqg2ru zlwkgudz iurp wkh pdunhw/ ru gluhfwo| sodfh rughuv zlwk rwkhu pdunhw pdnhuv1 Li wkh pdunhw pdnhu ghflghv wr sodfh rughuv gluhfwo| zlwk rwkhu pdunhw pdnhuv/ kh kdv dovr wr fkrrvh zklfk rwkhu pdunhw pdnhu kh zdqwv wr dssurdfk1 Hdfk pdunhw pdnhu fdq fkrrvh wr sodfh wkh rughu zlwk yh glhuhqw w|shv ri pdunhw pdnhuv= _vpduw pdunhw0wlphuv%/ _pdunhw wlphuv%/ _dyhudjhv%/ _txdvl0frqwuduldqv% dqg _frqwuduldqv%1 Wkh vpduw pdunhw wlphuv duh wkh ghdohuv zkrp wkh pdunhw pdnhu lv frqghqw +zlwk frqghqfh lq h{fhvv ri 3(, duh deoh wr vxffhvvixoo| wlph wkh pdunhw/ l1h1/ wkh| ex| ehiruh dq lqfuhdvh lq sulfhv dqg vhoo ehiruh d uhgxfwlrq lq sulfhv1 Wkh pdunhw wlphuv duh wkh rqhv wkh pdunhw pdnhu eholhyhv wr eh deoh wr vxffhvvixoo| wlph wkh pdunhw zlwk frqghqfh ehwzhhq 83 dqg 3(1 Wkh dyhudjhv duh wkh rqhv zkrp wkh pdunhw pdnhu kdv orz nqrzohgjh derxw +frqghqfh ohyho orzhu wkdq 83(,1 Wkh frqwuduldqv duh wkh pdunhw pdnhuv zkrp wkh pdunhw pdnhuv lv yhu| frqghqw +3( frqghqfh ohyho, iroorz frqwuduldq vwudwhjlhv +vhoo ehiruh lqfuhdvh lq sulfhv dqg ex| ehiruh d uhgxfwlrq lq sulfhv,1 Ilqdoo| wkh txdvl0frqwuduldqv duh wkh pdunhw pdnhuv zkrp wkh pdunhw pdnhu eholhyhv wr  W| t Lh| ?L|?} | @| i @i tiT@h@|i_ | i 4@h!i| 4@!iht ?|L D }hL Tt L? | i M@tt Lu | i E 3 R @* i Lu | i ULiUi?| c *i i @i ti_ | i ThL_ U| Lu E 3 R @?_ |L _i?|u) | i 4@h!i| 4@!iht ? |ih4t Lu _i}hii Lu ?uLh4@|i?itt A i hi@tL? uLh | t t | @| | i _i}hii Lu ?uLh4@|i?itt t TL|i?|@**) ?ML ?_i_c *i | i @* i Lu  3 R t ML ?_i_ M)  @?_ fc @**L?} t |L tiT@h@|i | i 4@h!i| 4@!iht ?|L D }hL Tt A i _i}hii Lu ?uLh4@|i?itt |@!it ?|L @UUL ?| ?L| L?*) | i UL?€_i?Ui ? | i _i}hii Lu ?uLh4@|i?itt E 3 Rc M | @*tL | i 4T@U| L? | i 4@h!i| E Lu t U @ 4@h!i| 4@!ih A ihiuLhic | U@T| hit | i R*!i*) 4T@U| L? ThUit | @| |h@_?} | @ T@h|U *@h 4@h!i| 4@!ih ?L*it 57
  • 33. iroorz frqwuduldq vwudwhjlhv zlwk d frqghqfh ehwzhhq 83( dqg 3(1 Wkh frqwuduldqv dqg wkh txdvl0frqwuduldqv fdq eh frqvlghuhg dv lqwhuphgldulhv zkr kdyh rxwvlgh frqvwudlqwv lqgxflqj wkhp wr wlph wkh pdunhw lq wkh zurqj gluhfwlrq1 Rqh uhdvrq frxog eh wkdw wkh| lqwhuphgldwh oltxlglw| ghpdqg ru wkdw wkh| kdyh errnv zlwk dffxpxodwhg olplw0rughuv12 Frqwuduldq dqg pdunhw wlphuv fdq eh frqvlghuhg dv lqiruphg pdunhw pdnhuv zkr kdyh glhuhqw lqirupdwlrq1 Wklv lpsolhv wkdw wkh ghflvlrq ri d pdunhw pdnhu klw e| d pdunhw wlphu wr dssurdfk d frqwuduldq dv zhoo dv wkh ghflvlrq ri d pdunhw pdnhu klw e| d frqwuduldq wr klw d pdunhw wlphu fdq eh lqwhusuhwhg dv klglqj1 Wkh uhdvrq ehlqj wkdw wkh klw pdunhw pdnhu lv dssurdfklqj d pdunhw pdnhu zkr kdv lqirupdwlrq wkdw lv glhuhqw iurp wkdw khog e| wkh ghdohu zkr kdv sodfhg wkh ruljlqdwlqj wudgh1 Wkhuhiruh/ kh h{shfwv klp qrw wr eh deoh wr pdnh xvh ri wkh dgglwlrqdo lqirupdwlrq kh lv surylglqj zlwk klv wudgh1 Hyhu| vlqjoh wudqvdfwlrq lv d fkrlfh/ dqg wkh iuhtxhqf| ri wkh fkrlfh lv jlyhq e| wkh qxpehu ri wudqvdfwlrqv gxulqj wkh vshflhg wlph lqwhuydo1 Hdfk dowhuqdwlyh lv vlpxowdqh0 rxvo| frpshwlqj zlwk wkh rwkhu dowhuqdwlyhv dw wkh vdph ohyho ri wkh wuhh +h1j1/ dssurdfklqj d pdunhw pdnhu zkr lv zhoo lqiruphg yv1 dssurdfklqj d pdunhw pdnhu zkr lv qrw lqiruphg, dv zhoo dv zlwk doo wkh rwkhu dowhuqdwlyhv +l1h1/ qrw sodflqj dq| rughu gluhfwo| zlwk rwkhu pdunhw pdnhuv/ exw rqo| fkdqjlqj wkh elg dqg dvn txrwhv,1 Wkh pdunhw pdnhu vhohfwv wkh dowhuqdwlyh wkdw jxdudqwhhv klp d sd|r kljkhu wkdq wkdw surgxfhg e| wkh rwkhu dowhuqdwlyhv1 Lw fdq eh vkrzq +Ehuu| 47/ Ehuu| hw do1 48, wkdw wkh uhgxfhg irup fdq eh h{suhvvhg dv= oq+v™| , oq+v f™| , @ f . # oq+v™|ƒec•t , . F„ HY™| . j' 2 . . ™| = 8™| +54, +vhh Dsshqgl{ E iru d ghwdlohg ghulydwlrq,1 Wklv vshflfdwlrq uhodwhv wkh fkrlfh ri wkh m0wk pdunhw pdnhu wr wkh ghjuhh ri lqirupdwlyhqhvv ri wkh l0wk pdunhw pdnhu kh fkrrvhv wr ghdo zlwk +HY™| , dqg wr vrph fkdudfwhulvwlfv revhuydeoh e| wkh pdunhw pdnhu/ exw qrw shufhlyhg e| wkh hfrqrphwulfldq + ,1 Htxdwlrq +54, lv hvwlpdwhg erqg e| erqg/ exw/ iru vlpsolflw|/ zh gurs wkh vxevfulsw %n%1 v™| l @ 4 === 8 lv wkh suredelolw| wkdw wkh m0wk pdunhw pdnhu zrxog vhohfw wkh l0 2 tt 4i | @| | i _i@*ih @t @ ti| Lu Lh_iht |L ti** i? | i 4@h!i| hi@U it @ Uih|@? *ii* Oi t L *_ i iU |i | i Lh_ihtc ii? u i Mi*iit | @| | i 4@h!i| t @tt 4i_ |L }L T A t L *_ }i | i @TTi@h@?Ui | @| | i _i@*ih t |4?} | i 4@h!i| ? | i hL?} _hiU|L? 58
  • 34. wk hqgrjhqrxv dowhuqdwlyh1 Lw lv ghqhg dv wkh udwlr ehwzhhq wkh rughuv wkdw wkh m0wk pdunhw pdnhu sodfhv zlwk wkh pdunhw pdnhuv ehorqjlqj wr wkh l0wk jurxs lq wkh 43 plqxwhv iroorzlqj wkh ruljlqdwlqj wudgh/ dqg wkh wrwdo dprxqw ri wudghv +erwk hqgrjhqrxv dqg h{rjhqrxv, wkdw kh ghdov zlwk lq wkh vdph lqwhuydo1 v f™| lv wkh suredelolw| wkdw wkh m0wk pdunhw pdnhu zrxog vhohfw wr jr h{rjhqrxv= Lw lv ghqhg dv wkh udwlr ehwzhhq wkh rughuv wkdw wkh m0wk pdunhw pdnhu uhfhlyhv iurp rwkhu pdunhw pdnhuv lq wkh 43 plqxwhv iroorzlqj wkh ruljlqdwlqj rughu/ dqg wkh wrwdo qxpehu ri wudghv +erwk hqgrjhqrxv dqg h{rjhqrxv, wkdw kh ghdov zlwk gxulqj wkh vdph lqwhuydo1 SD Ilqdoo|/ v™|ƒec•t @ v™| @ ' v™| lv wkh suredelolw| wkdw wkh m0wk pdunhw pdnhu zrxog vhohfw wkh l0wk hqgrjhqrxv dowhuqdwlyh/ frqglwlrqdo rq kdylqj ghflghg wr jr hqgrjhqrxv1 Wkdw lv/ lw lv wkh udwlr ehwzhhq wkh rughuv wkh m0wk pdunhw pdnhu sodfhv zlwk rwkhu pdunhw pdnhuv ehorqjlqj wr wkh l0wk fkrlfh jurxs lq wkh 43 plqxwhv iroorzlqj wkh ruljlqdwlqj rughu/ dqg wkh wrwdo qxpehu ri rughuv wkdw/ gxulqj wkh vdph lqwhuydo/ wkh m0wk pdunhw pdnhu sodfhv hqgrjhqrxvo|1 Wkh vwrfkdvwlf whup frqwurov iru wkh glvwulexwlrq ri pdunhw pdnhuv* suhihuhqfhv dqg sod|v wkh uroh ri _phdq ri wkh ydoxdwlrqv wkdw hdfk pdunhw pdnhu kdv ri wkh rwkhu pdunhw pdnhuv1% Wklv lqfoxghv wklqjv vxfk dv _foxe uhodwlrqvkls% dprqj sduwlfxodu jurxsv/ suhihuhqwldo wuhdwphqwv/ dqg vr rq1 Wkh frhflhqw # uhsuhvhqwv wkh ghjuhh ri khwhurjhqhlw| dfurvv dowhuqdwlyh fkrlfhv zlwklq wkh jurxs1 Lw udqjhv iurp }hur wr rqh1 Zkhq lw lv htxdo wr }hur/ wkh fkrlfhv zlwklq wkh vshflf jurxs duh shufhlyhg dv glhuhqw iurp rqh dqrwkhu1 Zkhq lw lv htxdo wr rqh/ wkh fkrlfhv duh shufhlyhg dv forvh vxevwlwxwhv iru rqh dqrwkhu +vhh Dsshqgl{ E iru d ghwdlohg ghulydwlrq,1 HY™| ghqhv wkh fkdudfwhulvwlfv ri wkh frxqwhusduwv wkh pdunhw pdnhu lv wudglqj zlwk1 Lq sduwlfxodu/ lw fdswxuhv wkh glhuhqfh lq wkh ghjuhh ri lqirupdwlyhqhvv ehwzhhq wkh pdunhw pdnhu sodflqj wkh ruljlqdwlqj rughu dqg wkh pdunhw pdnhu zkrp wkh %klw% pdunhw pdnhu dssurdfkhv1 Wr ghqh wklv/ zh uvw fdofxodwh wkh surgxfw ri wkh ydoxh ri dqg +4 s,/ zkhuh s lv wkh suredelolw| ydoxh ri wkh frhflhqw dv ghqhg lq Htxdwlrq +4;,1 Wkhq zh fdofxodwh wkh glhuhqfh ehwzhhq wkh dyhudjh ri wkh h{shfwhg ydoxh ri wkh ghjuhh ri lqirupdwlyhqhvv ri wkh pdunhw pdnhuv ri hdfk jurxs/ dqg wkh h{shfwhg lqirupdwlyhqhvv ri wkh ghdohu zkr lv sodflqj wkh ruljlqdwlqj rughu1 59
  • 35. Wkh prgho +54, lv hvwlpdwhg iru hdfk pdunhw pdnhu vhsdudwho| rq wkh edvlv ri wudqvdf0 wlrq wlph1 Wkhq/ wkh pdunhw pdnhuv duh fodvvlhg lqwr wkuhh jurxsv edvhg rq wkh qdwxuh ri wkhlu uhvsrqvh wr lqiruphg wudgh +frhflhqw F„ ,1 D furvv0ydolgdwlrq whfkqltxh lv xvhg wr lghqwli| wkh fodvvhv ri pdunhw pdnhuv/ wr jurxs wkhp dqg wr whvw wkh vwdelolw| ri vxfk d jurxslqj1 
  • 36. Ixuwkhupruh/ lq rughu wr dvvhvv wkh vwdelolw| ri wkh uhvxowv wr d fkdqjh lq wkh pdunhw yrodwlolw|/ zh hvwlpdwh Htxdwlrq +54, lq wzr glhuhqw yrodwlolw| uhjlphv +kljk dqg orz yrodwlolw|,1 %Kljk yrodwlolw|% shulrgv duh wkh gd|v zkhq wkh gdlo| yrodwlolw| h{fhhgv wkh yrodwlolw| ryhu wkh suhylrxv 43 wudglqj gd|v1 Wkh uhvxowv/ uhsruwhg lq Wdeoh 8/ Sdqho F/ djuhh zlwk wkh rwkhu rqhv +Wdeoh 8/ sdqhov D dqg E,1 Wkh uhvxowv vwurqjo| vxssruw rxu k|srwkhvhv1 Lq Wdeoh 8/ Sdqho D/ zh uhsruw wkh uhvxowv ri wkh vshflfdwlrq edvhg rq wudqvdfwlrq wlph/ hvwlpdwhg e| jurxslqj wkh pdunhw pdnhuv dffruglqj wr wkh lqvwlwxwlrqdo fodvvlfdwlrq dv zhoo dv wr wkh wudglqj0edvhg rqh1 Wkhuh duh glhuhqw sdwwhuqv ri ehkdylru dprqj wkh fodvvhv ri pdunhw pdnhuv1 Lq jhqhudo/ vqhdnlhv wu| wr klgh wkhlu lqirupdwlrq1 Lq rughu wr gr wklv/ wkh| gluhfw wkhlu wudgh wrzdugv pdunhw pdnhuv ohvv lqiruphg wkdq wkh rqhv zkr kdyh klw wkhp1 Wkhuhiruh/ li wkh| duh klw e| pdunhw wlphuv/ wkh| sodfh rughuv zlwk ohvv vpduw pdunhw wlphuv/ dyhudjhv dqg frqwuduldqv1 Hpslulfdoo|/ wklv fruuhvsrqgv wr srvlwlyh dqg vwurqjo| vljqlfdqw F„ @ 3=43= Dovr/ li wkh| duh klw e| frqwuduldqv wkh| sodfh rughuv zlwk ohvv frqwuduldqv/ dyhudjhv dqg pdunhw wlphuv +hvwlpdwh ri F„ @ 45;=77 lv vwurqjo| vljqlfdqw/ w0vwdwlvwlfv lv 0;1:9,1 Wkdw lv/ wkh| dozd|v %jr iru wkh fhqwuh%/ wrzdugv wkh ohvv lqiruphg +fodvvhv LL/ LLL dqg LY,1 Wkh vnhswlfv ehkdyh lq wkh rssrvlwh idvklrq/ sodflqj rughuv zlwk pdunhw pdnhuv pruh lqiruphg wkdq wkh rqhv wkh| uhfhlyh rughuv iurp1 Wkdw lv/ li wkh| duh klw e| pdunhw wlphuv/ wkh| dssurdfk vpduwhu pdunhw wlphuv1 Hvwlpdwhv lq Wdeoh 8/ Sdqho D/ vkrz wkdw lq wkdw fdvh F„ @ 9=49 zlwk w0vwdwlvwlfv 071951 Dowhuqdwlyho|/ li vnhswlfv duh klw e| frqwuduldqv/ wkh| dssurdfk hyhq %pruh frqwudu|% frqwuduldqv + F„ @ ;:=35,1 Xqolnh wkh vqhdnlhv/ wkh| dozd|v jr iru wkh _zlqjv%/ wrzdug wkh h{wuhph fodvvhv +L dqg Y,1 
  • 37. W? T@h|U *@hc i tT*| | i t@4T*i ?|L L__ @?_ ii? _@)t A i? i it|4@|i ,^ @|L? E2 ? | i L__ _@)tc i ti | i @* it Lu | i it|4@|i_ ULiUi?|t q F„ |L _i?|u) | i U*@ttit | i 4@h!i| 4@!iht Mi*L?} |L @?_ | i? }hL T | i 4@h!i| 4@!iht @UULh_?} |L t U @ U*@tt€U@|L? A i?c i ti | i t@4T*i TihL_ M@ti_ L? ii? _@)t |L it|4@|i | i @* i Lu | i @}}hi}@|i_ ULiUi?|t W? A@M*i Dc @?i*t c @?_ i hiTLh| | i hit *|t it|4@|i_ L? L*i TihL_ *tLc @t @ ti?t||) @?@*)tt i h ? | i t@4i i Tih4i?| t?} | i ii? _@)t |L _i?|u) | i _i@*iht A i hit *|t @}hii | | i L?it hiTLh|i_ 5:
  • 38. Wkh vohhslhv ehkdyh ohvv vwudwhjlfdoo|1 Wkh| dfw rqo| zkhq wkh| duh vxuh derxw wkh lqirupdwlrqdo frqwhqw ri wkh wudgh wkh| uhfhlyh/ dqg gr qrw h{shulphqw1 Wkhuhiruh/ wkh| gr qrw jr hqgrjhqrxv dw doo zkhq wkh| duh klw e| frqwuduldqv ru dyhudjhv/ dowkrxjk wkh| klgh zkhq klw e| pdunhw wlphuv1 Lq Wdeoh 9 zh uhsruw vrph ghvfulswlyh vwdwlvwlfv derxw wkh wkuhh w|shv ri ghdohuv1 Lw dsshduv wkdw hyhq li vnhswlfv dqg vqhdnlhv uhsuhvhqw d plqrulw| ri wkh pdunhw pdnhuv +uhvshfwlyho| ( dqg 4;( ri doo wkh pdunhw pdnhuv,/ wkh| vwloo duh d vljqlfdqw iudfwlrq ri wkh ryhudoo lqiruphg hqgrjhqrxv wudglqj +uhvshfwlyho| 67( dqg 57(,1 Dovr/ li zh udqn doo wkh pdunhw pdnhuv rq wkh edvlv ri wkhlu dyhudjh gdlo| wudglqj yroxph/ irxu rxw ri wkh uvw yh pdunhw pdnhuv duh dozd|v hlwkhu vqhdnlhv ru vnhswlfv1 Li zh slhufh wkh yhlo dqg dwwhpsw wr frqvlghu wkh frusrudwh fkdudfwhulvwlfv ri wkh pdunhw pdnhuv/ zh qg wkdw wkh vqhdnlhv duh prvwo| iruhljq edqnv dqg vrph kljko| vshfldol}hg lqyhvwphqw frpsdqlhv1 Wkh idfw wkdw iruhljq edqnv lqwhuphgldwh wkh lqyhvwphqw lq wkh Lwdoldq pdunhw ri wkh odujh lqwhuqdwlrqdo lqvwlwxwlrqdo lqyhvwruv/ zrxog vxjjhvw wkdw wkh| kdyh d ehwwhu lqirupdwlrq vhw edvhg rq wkh nqrzohgjh ri wkh rzv1 Wklv zrxog vxjjhvw kljkhu lqirupdwlrqdo dgydqwdjh dqg vwurqjhu lqfhqwlyh wr klgh1 Wkh vnhswlfv/ lqvwhdg/ duh phglxp0vl}hg kljko| hflhqw edqnv1 Wkh uhodwlyho| vpdoo vl}h zrxog mxvwli| kljk ulvn dyhuvlrq ru/ lq dq| fdvh/ kljkhu fdxwlrxvqhvv1e Lw lv lqwhuhvwlqj wr qrwh wkdw zkhq pdunhw pdnhuv duh fodvvlhg dffruglqj wr wkh lqvwl0 wxwlrqdo fodvvlfdwlrq/ erwk vshfldolvwv dqg ruglqdu| pdunhw pdnhuv jhqhudoo| ehkdyh olnh vqhdnlhv +Wdeoh 8/ Sdqho E,1 Wklv uhhfwv d jhqhudo whqghqf| wr wu| wr klgh lqirupdwlrq1 Wkh dqdo|vlv ri wkh ghjuhh ri khwhurjhqhlw| dfurvv dowhuqdwlyh fkrlfhv wkdw frphv rxw ri wkhvh uhvxowv vkrzv wkdw/ lq jhqhudo/ wkh yh dowhuqdwlyh fkrlfhv duh shufhlyhg wr eh txlwh glhuhqw1 Wkh ghjuhh ri khwhurjhqhlw| lv udwkhu kljk/ zlwk # forvh wr wkh plggoh ri wkh udqjh +durxqg 318,1 Lw lv hyhq kljkhu iru vnhswlfv zkr kdyh wr dssurdfk pruh lqiruphg wudghuv udwkhu wkdq ohvv lqiruphg rqhv1 H OeG @h!i| @!iht 5|h@|i}it @?_ @h!i| VL*@|*|) Lq rughu wr whvw zkhwkhu glhuhqw vwudwhjlhv lpso| glhuhqw uhdfwlrqv wr pdunhw yrodwlolw|/ zh whvw wkh uhvwulfwlrqv lpsrvhg e| Htxdwlrq +4:,1 E| xvlqj wkh vshflfdwlrq 54,/ wkh e N?uLh| ?@|i*) ?L u h| ih ?it|}@|L? ? }hi@|ih _i|@* t @**Li_ M) UL?€_i?|@*) hi^ hi4i?|t 5;
  • 39. whvwdeoh lpsolfdwlrqv duh= r8e‚|ƒr ? 3 dqg rced8er A 3= j' j' Wkdw lv/ wkh fruuhodwlrq ehwzhhq pdunhw yrodwlolw| dqg lqiruphg hqgrjhqrxv wudgh lv qhj0 dwlyh iru wkh vnhswlfv dqg srvlwlyh iru wkh vqhdnlhv1 Wkh uhvxowv/ uhsruwhg lq Wdeoh 8/ Sdqhov D dqg E/ vkrz wkdw wklv lv lqghhg wkh fdvh dqg wkdw dq lqfuhdvh lq pdunhw yrodwlolw| lqgxfhv wkh vnhswlfv wr uhgxfh wkhlu wudglqj zlwk pruh lqiruphg pdunhw pdnhuv dqg wkh vqhdnlhv wr lqfuhdvh wkhlu wudglqj zlwk pruh lqiruphg pdunhw pdnhuv1 Doo frhflhqwv iru vqhdnlhv +vnhswlfv, duh srvlwlyh +qhjdwlyh, zlwk irxu rxw ri yh vljqlfdqw dw d 8( ohyho1 Dq dowhuqdwlyh vshflfdwlrq lv uhsruwhg lq Wdeoh 8/ Sdqho F zkhuh zh vhsdudwh wkh vdpsoh lq shulrgv ri kljk dqg orz yrodwlolw|1 Wkh whvwdeoh lpsolfdwlrqv ri K7 fdq qrz eh zulwwhq dv= m Å}Å m ? m Dt% m iru vnhswlfv dqg m Å}Å m A m Dt% m iru vqhdnlhv/ F„ F„ F„ F„ zkhuh wkh lqgh{hv kljk dqg orz uhihu wr wkh wzr vwdwhv ri kljk dqg orz yrodwlolw|1 Wkh uhvxowv vkrz wkdw lq jhqhudo wkrvh frqglwlrqv duh vdwlvhg iru uhohydqw jurxsv +L/ LL/ LY dqg Y,1 b L?U* tL?t Zh kdyh dqdo|}hg pdunhw pdnhuv* ghflvlrq wr vwudwhjlfdoo| h{shulphqw1 Zh prghoohg vxfk d ghflvlrq dv wkh uhvxow ri d frpsoh{ vwudwhj| lqyroylqj wkh gluhfw sodfhphqw ri rughuv zlwk rwkhu pdunhw pdnhuv lq wkh vhfrqgdu| pdunhw1 E| xvlqj d xqltxh gdwdvhw wkdw wudfhv pdunhw pdnhuv* ehkdylru rq wkh Lwdoldq Wuhdvxu| erqg pdunhw/ zh kdyh vkrzq wkdw pdunhw pdnhuv dfwlyho| ohduq iurp wkh pdunhw pdnhuv wkh| duh wudglqj zlwk1 Wkh| xvh wklv nqrzohgjh wr uhdfw vwudwhjlfdoo| wr wkh lqirupdwlrq frqwhqw ri wkh rughuv wkh| uhfhlyh/ sod|lqj vwudwhjlhv wkdw ghshqg rq wkh txdolw| ri wklv lqirupdwlrq1 Lq sduwlfxodu/ zh kdyh lghqwlhg wzr pdlq w|shv ri vwudwhjlf uhdfwlrq wr wkh lqirupdwlrqdo frqwhqw ri wudgh= _klglqj% dqg _h{shulphqwlqj% dqg vkrzq xqghu zklfk frqglwlrqv h{shulphqwdwlrq lv wkh suhihuuhg rqh1 5
  • 40. Wkhvh uhvxowv rshq xs d qhz dqg lqwhuhvwlqj dyhqxh ri uhvhdufk1 Lq sduwlfxodu/ li pdunhw pdnhuv uhdfw glhuhqwo| wr wkh lqirupdwlrq wkh| uhfhlyh/ wkhlu lpsdfw rq pdunhw sulfhv dovr glhuv1 Iurp wklv shuvshfwlyh/ lw pd| eh srvvleoh wr xvh pdunhw pdnhuv* uhdfwlrqv wr lqirupdwlrq wr h{sodlq rwkhuzlvh sx}}olqj hylghqfh rq dvvhw sulfhv/ yroxph dqg yrodwlolw|1 Pdunhw hflhqf| dqg sulfh uhdfwlrq wr wudgh fdq eh ehwwhu dqdo|}hg dqg h{sodlqhg lq wkh frqwh{w ri pdunhw pdnhuv* vwudwhjlf lqwhudfwlrq1 63
  • 41. Pdunhw Pdnhu*v Sureohp Surri ri Sursrvlwlrq 4 Pdunhw pdnhuv revhuyh d vljqdo +, dqg wu| wr lqihu wkh ydoxh ri 1 Ohw xv dvvxph wkdw + , lv d wzr0glphqvlrqdo sduwldoo| revhuydeoh udqgrp surfhvv zkhuh lv wkh revhuydeoh frpsrqhqw/ lv wkh xqrevhuydeoh frpsrqhqw dqg H lv wkh vhw ri srvvleoh ydoxhv wkdw wkh xqrevhuydeoh frpsrqhqw +, fdq wdnh1 Lq sduwlfxodu/ dvvxph wkdw wkh xqrevhuydeoh frpsrqhqw iroorzv= g | @ D| + | ,gw . E| +,gZ| zkhuh Z| lv d Zlhqhu surfhvv1 Iurp Olswvhu dqg Vklu|dhy +4::/ sdjh 666, zh nqrz wkdw wkh srvwhulru suredelolw| ri wkh vwdwh 5 H lv= ] | ] | DÄ + , DÄ +, q +w, @ sq +w, . ? q +x,gx . q +x, gZ Ä +55, f f EÄ +, S S zkhuh= ? q +x, @ M, q +x, +x,/ DÄ +, @ M, DÄ + , +x, dqg Z @ +Z | @| , U| lv d Zlhqhu surfhvv zlwk= Z | @ f •IÄ 3ÈIÄEI = Khuh @| lv wkh lqirupdwlrq vhw dydlodeoh Ä E dw wlph w= Lq rxu fdvh/ wkh xqrevhuydeoh frpsrqhqw +, fdq wdnh ydoxhv d dqg e +wkdw lv H @ ^w u `,1 Wkh revhuydeoh frpsrqhqw lv 1 Dsso|lqj Htxdwlrq +55,/ zh kdyh= g bw @ +4 5 bw ,gw . bw +4 bw ,+w u , gv bw w . +4 bw ,u gw 2 I v Li zh ghqh b @ +4 5 bw ,/ g @ •r bw w . +4 bw ,u gw dqg @ w r  E3bw Ebw 3bu + bw j2 , zh kdyh= I g bw @ b gw . g= w Hfrqrphwulf Vshflfdwlrq Lq wklv Dsshqgl{/ zh rxwolqh wkh ghulydwlrq ri d glvfuhwh fkrlfh prgho edvhg rq Ehuu| +47, dqg Ehuu| hw do1 +48,1 Ohw* v ghqh wkh sd|r ri wkh l0wk fkrlfh iru wkh m0wk pdunhw pdnhu dv= x @ { . . % +56, zkhuh wkh vxevfulsw m iru wkh pdunhw pdnhu lv rplwwhg iru vlpsolflw|1 Htxdwlrq +56, lpsolhv wkdw wkh sd|r ri hdfk lqglylgxdo pdunhw pdnhu lv d ixqfwlrq ri wkh fkdudfwhulvwlfv ri wkh rwkhu pdunhw pdnhuv kh ghdov zlwk +{ , dqg vrph fkdudfwhulvwlfv revhuydeoh e| wkh pdunhw pdnhu/ exw qrw shufhlyhg e| wkh hfrqrphwulfldq +,1 D qrlvh whup % lv jlyhq e| wkh glvwulexwlrq ri pdunhw pdnhuv* suhihuhqfhv +ulvn dyhuvlrq/ hwf1, durxqg d phdq ydoxh 64
  • 42. uhsuhvhqwhg e| = Wkh m0wk pdunhw pdnhu vhohfwv wkh dfwlrq wkdw jxdudqwhhv d sd|r kljkhu wkdq wkdw ri wkh rwkhu dowhuqdwlyhv/ wkdw lv x+{ % • , A x+{8 8 % • , iru hdfk n @ 4 === l 4 l . 4 === N zkhuh • lv wkh vhw ri fkrlfhv1 Wkh suredelolw| ri fkrrvlqj wkh l0wk dowhuqdwlyh ryhu wkh rwkhuv fdq eh uhsuhvhqwhg e|= ] v ++{ , { , @ i+% { H ,g%8 +57, È Ef zkhuh v lv wkh suredelolw| wkdw wkh l0wk dowhuqdwlyh lv fkrvhq lq wkh pdunhw dqg lv wkh phdq sd|r dvvrfldwhg zlwk fkrlfh ri wkh l0wk dowhuqdwlyh1 Lw lv fdofxodwhg e| lqwhjudwlrq ryhu wkh duhd DEf / wkdw lv dfurvv doo wkh srvvleoh fkrlfhv1 Zh dvvxph wkdw wkh pdunhw pdnhu kdv uvw wr ghflgh zkhwkhu wr jr h{rjhqrxv ru hqgrjhqrxv dqg/ lq wkh odwwhu fdvh/ zklfk rwkhu pdunhw pdnhu wr dssurdfk1 Wkh vhw ri hqgrjhqrxv fkrlfhv lv n @ 4 === l === N 5 hqgr= Zh dovr dvvxph wkdw wkh suhihuhqfhv ri wkh pdunhw pdnhuv % eh l1l1g1 zlwk _h{wuhph ydoxh% glvwulexwlrq ixqfwlrq1 Zh fdq wkhuhiruh uhsuhvhqw wkh suredelolw| ri hdfk fkrlfh dv d ixqfwlrq ri wkh dyhudjh ydoxh ri lwv fkdudfwhulvwlfv + @ { . ,= Wkh suredelolw| ri vhohfwlqj wkh l0wk dowhuqdwlyh lv= f h{s+ , h{s+ 3Æ , v +, @ SÇ @ vƒec•t +,vec•t +, zkhuh vƒec•t +, @ S f +58, 8'f h{s+ 8 , Mec•t h{s+ 3Æ , uhsuhvhqwv wkh suredelolw| ri fkrrvlqj wkh l0wk dowhuqdwlyh rqfh wkh ghflvlrq ri jrlqj hq0 grjhqrxv kdv ehhq wdnhq/ dqg S f + Mec•t h{s+ 3Æ ,,E3Æ vec•t +, @ S f +59, + Mec•t h{s+ 3Æ ,,E3Æ . h{s+ e7t , uhsuhvhqwv wkh suredelolw| ri jrlqj hqgrjhqrxv uhodwlyh wr wkh suredelolw| ri jrlqj h{rjh0 qrxv1 Wkh frhflhqw # uhsuhvhqwv wkh ghjuhh ri khwhurjhqhlw| dfurvv dowhuqdwlyh fkrlfhv zlwklq wkh jurxs1 Lw udqjhv iurp }hur +zkhq wkh fkrlfhv zlwklq wkh vshflf jurxs duh shufhlyhg dv glhuhqw, wr rqh +zkhq wkh fkrlfhv duh shufhlyhg dv forvh vxevwlwxwhv,1 Jlyhq wkh h{lvwhqfh ri d xqltxh pdsslqj iurp wkh phdq sd|r wr wkh suredelolw| ri fkrrvlqj rqh dowhuqdwlyh +htxdwlrq 57,/ zh fdq lqyhuw wklv uhodwlrqvkls vr dv wr h{suhvv wkh suredelolw| ri fkrrvlqj rq dowhuqdwlyh dv d ixqfwlrq ri wkh phdq sd|r1 E| htxdol}lqj wkh suredelolw| ghulyhg iurp htxdwlrq 57 wr wkh dfwxdo fkrlfhv gluhfwo| revhuyhg rq wkh pdunhw +v™| , zh fdq ghulyh wkh uhdfwlrq ixqfwlrqv ri wkh pdunhw pdnhuv1 Lq sduwlfxodu/ iru wkh e m0wk pdunhw pdnhu vhohfwlqj wkh l0wk dowhuqdwlyh= oq+v™| , oq+v f™| , @ # oq+v™|ƒec•t , . {™| . . ™| = +5:, Urexvwqhvv Fkhfnv Wklv Dsshqgl{ ghvfulehv wkh qxphurxv urexvwqhvv fkhfnv shuiruphg zkloh whvwlqj wkh k|srwkhvhv ri wkh sdshu1 Wkhvh uhvxowv duh dydlodeoh xsrq uhtxhvw iurp wkh dxwkruv1 65
  • 43.  K4= Lqirupdwlrqdo frqwhqw ri wudghv Lq dgglwlrq wr xvlqj wkh rfldo dqg wkh wudgh0edvhg fodvvlfdwlrq ri pdunhw pdnhuv/ zh dovr frqvlghu dq dowhuqdwlyh fulwhulrq/ vhsdudwlqj pdunhw pdnhuv dffruglqj wr wkhlu yroxph ri wudglqj lq wkh vhfrqgdu| pdunhw1 Iru hdfk prqwk/ zh fdofxodwh wkh wudglqj yroxph ri hdfk vlqjoh pdunhw pdnhu lq wkh pdunhw dqg wkhq zh jurxs wkh pdunhw pdnhuv lqwr txduwlohv rq wkh edvlv ri wkhlu wrwdo yroxph1 Wkh vshfldolvwv dozd|v frlqflgh zlwk wkh eljjhvw pdunhw pdnhuv/ idoolqj lqwr wkh uvw txduwloh/ zkloh wkh ruglqdu| pdunhw pdnhuv idoo prvwo| lqwr wkh vhfrqg/ dqg sduwo| lqwr wkh wklug txduwloh1 Ruglqdu| pdunhw pdnhuv ehorqj sduwo| wr wkh wklug dqg prvwo| wr wkh irxuwk txduwloh1 Dowhuqdwlyho|/ zh dovr jurxs ghdohuv vhsdudwlqj wkhp dffruglqj wr yroxph ri wudgh rq wkh vhfrqgdu| pdunhw dqg doorfdwlqj wkhp wr txduwlohv zlwk htxdo qxpehu ri ghdohuv lq hdfk1 Wklv uhvxowv lq kdylqj pruh wkdq kdoi ri wkh wrwdo yroxph wudghg frqfhqwudwhg lq wkh uvw txduwloh1 Zh dovr h{shulphqw zlwk h{whqglqj wkh uhdfwlrq shulrg wr 63 plqxwhv1 Wkdw lv/ zh frqvlghu doo wkh wudghv +hlwkhu h{rjhqrxv ru hqgrjhqrxv, hqdfwhg e| wkh pdunhw pdnhu lq wkh qh{w 63 plqxwhv1 Wkh udwlrqdoh lq grlqj wklv lv wkdw wkh suredelolw| ri uhfhlylqj wzr frqvhfxwlyh rughuv zlwk wkh vdph vljq fdq eh gxh wr pdunhw pdnhuv* lqgxfhg wudgh +h{rjhqrxv wudglqj,/ dv zhoo dv wr pdunhw pdnhuv* lqdelolw| wr pryh wkh elg0dvn vsuhdg lq wlph wr dyrlg ehlqj _slfnhg r% e| rwkhu lqiruphg djhqwv +Irxfdxow/ Urhoo dqg Vdqgdv 4, H{whqglqj wkh zlqgrz doorzv xv wr glvfulplqdwh djdlqvw vxfk k|srwkhvlv1 Lq wkh fdvh zkhuh wkh pdunhw pdnhu lv slfnhg r/ wkh vljq ri wkh uhodwlrqvkls vkrxog eh qhjdwlyh dqg vkrxog qrw uhpdlq vljqlfdqw zkhq wkh uhdfwlrq zlqgrz lv h{whqghg iurp 8 wr 63 plqxwhv1 Wkh uhvxowv vkrz wkdw h{rjhqrxv wudglqj lv gxh wr wkh ghflvlrq wr fkdqjh wkh elg dqg dvn sulfhv srvwhg e| wkh pdunhw pdnhu dqg qrw wr slfn0r1 Ixuwkhupruh/ wkh idfw wkdw wkh uhodwlrqvkls lv vwdeoh zkhq zh h{whqg wkh uhdfwlrq zlqgrz iurp 8 wr 63 plqxwhv vxjjhvwv wkdw wkh uhdfwlrq lv yhu| xqolnho| wr eh gxh wr odfn ri wlph iru wkh pdunhw pdnhu wr fkdqjh klv elg dqg dvn1 2 K5= Suholplqdu| whvwlqj ri lqirupdwlyhqhvv ri wudghv F1514 Frqwuroolqj iru wkh uroh sod|hg e| lqiruphg wudgh Zh lqyhvwljdwh wkh uhodwlrqvkls ehwzhhq %lqiruphg lqfrplqj wudgh% dqg rxwjrlqj wudgh/ e| frqvlghulqj d olqhdu vshflfdwlrq zkhuh hqgrjhqrxv dqg h{rjhqrxv wudgh duh gluhfwo| uhodwhg wr wkh lqirupdwlrqdo frqwhqw ri wudgh= …cs TD 8™| @ . W8™| . %8™| = +5;, …cs W8™| @ W8™| uhsuhvhqwv wkh _lqirupdwlyh rughu% lq wkh n0wk erqg uhfhlyhg e| wkh m0wk pdunhw pdnhu iurp wkh l0wk ghdohu dw wlph w1 Lw sur{lhv iru wkh lqirupdwlrq frqwdlqhg lq wkh wudghv dqg lv frqvwuxfwhg dv wkh surgxfw ri wkh wudgh wkdw wkh m0wk pdunhw pdnhu kdv uhfhlyhg lq wkh vshflhg wlph lqwhuydo e| wkh l0wk ghdohu dqg klv sulru rq klv wkh ghjuhh ri lqirupdwlyhqhvv1 TD ec•t e7t 8™| @ T8™| T8™| uhsuhvhqwv wkh hqgrjhqrxv ru h{rjhqrxv wudgh ri wkh m0wk pdunhw pdnhu lq wkh 43 plqxwhv iroorzlqj wkh ruljlqdwlqj wudgh1 Wklv vshfl0 fdwlrq vkrxog fdswxuh wkh sduw ri pdunhw pdnhuv* uhdfwlrq lq dgglwlrq wr wkdw rwkhuzlvh ghwhuplqhg e| lqyhqwru| uhedodqflqj1 Vdpsolqj lv edvhg rq wudqvdfwlrq wlph1 Wkh dqdo|vlv lv fduulhg rxw glvdjjuhjdwhg dw wkh ohyho ri lqglylgxdo pdunhw pdnhuv1 Wkh sdluzlvh uhdfwlrqv iurp hdfk fodvv ri pdunhw pdnhu yhuvxv wkh rwkhu pdunhw pdnhuv duh vhsdudwho| frqvlghuhg dqg duh fodvvlhg rq wkh edvlv ri wkh w|sh ri ghdohu zkr kdv sodfhg wkh ruljlqdwlqj wudgh1 Wr dvvhvv wkh urexvwqhvv 66
  • 44. ri wkh uhvxowv wr wkh fkdqjh ri wkh xqghuo|lqj glvwulexwlrq ri wkh prgho/ zh dovr whvw wkhp e| uxqqlqj d errwvwudsslqj surfhgxuh edvhg rq 43/333 uhvdpsolqjv1 Wkh uhvxowv/ frqvlvwhqw zlwk wkh rqhv uhsruwhg lq wkh wh{w/ vkrz wkdw lq jhqhudo wkh lqirupdwlrq0gulyhq wudghv kdyh kljkhu srzhu wr h{sodlq hqgrjhqrxv wudgh wkdq wr h{sodlq h{rjhqrxv wudgh1 Lqghhg/ wkh devroxwh ydoxh ri wkh frhflhqwv +, dqg wkh kljk vljql0 fdqfh ri wkhlu w0vwdwlvwlf vkrz wkdw ruglqdu| pdunhw pdnhuv dqg vshfldolvwv dozd|v uhdfw wr lqiruphg wudgh e| jrlqj hqgrjhqrxv1 Wklv krogv erwk lq wkh fdvh ri wkh lqvwlwxwlrqdo fodvvlfdwlrq dqg q wkh fdvh ri wkh wudglqj0edvhg rqh1 F1515 Frqwuroolqj iru glhuhqw ghqlwlrqv ri yduldeohv Zh h{shulphqw zlwk glhuhqw ohduqlqj zlqgrzv1 Lq sduwlfxodu/ zh h{whqg wkh ohduqlqj shulrg wr wkh 58 suhylrxv gd|v1 Wkh uhvxowv djuhh txdolwdwlyho| zlwk wkrvh irxqg xvlqj wkh 43 gd| ohduqlqj lqwhuydo= rqo| wkh ghjuhh ri vljqlfdqfh gursv/ jlyhq wkh dgglwlrqdo qrlvh lqgxfhg e| wkh ohqjwkhqlqj ri wkh vdpsoh shulrg1 Dovr/ zh uhghqh wkh ohduqlqj lqwhuydo durxqg dxfwlrq gd|v1 Lq sduwlfxodu/ dxfwlrq gd|0ohduqlqj lv ghqhg rq wkh suhylrxv 43 dxfwlrq gd|v/ zkloh qrq0dxfwlrq gd|0ohduqlqj lv ghqhg lq wkh suhylrxv 43 qrq0dxfwlrq gd|v1 Wkh lqwxlwlrq lv wkdw/ li lq dxfwlrq gd|v pdunhw pdnhuv ehkdyh glhuhqwo|/ zh h{shfw ohduqlqj qrw wr eh wkh vdph lq wkh wzr uhjlphv dqg wkh sulru rq wkh ghjuhh ri lqirupdwlyhqhvv ri vshflf pdunhw pdnhuv wr glyhujh1 Wkh uhvxowv djuhh zlwk wkrvh edvhg rq d vlqjoh ohduqlqj pdwul{ iru wkh zkroh shulrg1 F1516 Frqwuroolqj iru sulfh prphqwxp Zh zdqw wr frqwuro iru wkh srvvlelolw| ri d vruw ri _prphqwxp% rq sulfhv1 Wkdw lv/ wkh srvvlelolw| wkdw wudgh lv pruh ghwhuplqhg dv d uhdfwlrq wr fkdqjhv lq sulfhv wkdq dq dx0 wrqrprxv ghflvlrq ri wkh pdunhw pdnhu1 Zh wkhuhiruh hvwlpdwh wkh iroorzlqj vshflfdwlrq= S8™| @ W8™| . S8™|3D . %8™| +5, zkhuh S8™|3D uhsuhvhqwv wkh fkdqjh ri sulfhv lq wkh sdvw 8 plqxwhv ri wkh n0wk erqg1 Wkh uhvxowv ri wkh hvwlpdwh vhhp wr lqglfdwh wkdw wkh wudgh ri ruglqdu| pdunhw pdnhuv lv vrphzkdw gulyhq e| prphqwxp frqvlghudwlrqv/ exw lq doo wkh rwkhu dvshfwv/ wkh uhvxowv djuhh zlwk wkh rqhv uhsruwhg lq wkh wh{w1 F1517 Frqwuroolqj iru lqyhqwru| uhedodqflqj Lq rughu wr frqwuro iru lqyhqwru| hhfwv/ zh frqvlghu wzr dowhuqdwlyh vshflfdwlrqv1 Wkh uvw frqvlvwv ri whvwlqj h{solflwo| wkh lqirupdwlrqdo frqwhqw ri hdfk wudgh/ diwhu kdylqj holplqdwhg wkh uhvlgxdo hhfwv gxh wr lqyhqwru| uhedodqflqj1 Wr gr wklv/ zh uvw ghwhuplqh wkh frpsrqhqw ri wkh wudgh uhdfwlrq ri wkh pdunhw pdnhuv ruwkrjrqdo wr wrwdo wudghv +%8™| ,/ dqg wkhq zh vhh krz pxfk ri lw lv h{sodlqhg e| rxu phdvxuh ri lqiruphg wudgh1 Lq sduwlfxodu/ zh hvwlpdwh= TD8™| @ . W8™| . %8™| zkhuh wkh yduldeoh %8™| lv ruwkrjrqdo wr wrwdo wudghv1 Wklv lv wkhq uhjuhvvhg rq lqirupd0 wlrqdo wudgh dffruglqj wr= …cs %8™| @ . W8™| . 8™| +63, 67
  • 45. …cs Lw lv zruwk qrwlqj wkdw wkh dgglwlrqdo h{sodqdwru| srzhu ri W8™| lv gxh wr wkh ohduqlqj e t| pdwul{ wkdw pxowlsolhv wkh sduw ri wrwdo wudghv +W8™| , wkdw duh lghqwlhg dv _lqiruphg%1D D vhfrqg vshflfdwlrq gluhfwo| vhsdudwhv wkh lqirupdwlrqdo hhfw iurp wkh sxuh lqyhq0 wru| rqh= …cs TD 8™| @ . W8™| . Lqy8™| . %8™| +64, zkhuh Lqy8™| lv wkh l0wk pdunhw pdnhu*v lqyhqwru| srvlwlrq dw wlph w rq wkh n wk erqg1 Lq sduwlfxodu/ iru hdfk pdunhw pdnhu/ zh frqvwuxfw lqyhqwru| +Lqy8™| , dv d wlph vhulhv edvhg rq pdunhw pdnhuv* sxufkdvhv dqg vdohv ryhu wlph1 Zh xvh wkh ghqlwlrq ri lqyhqwru| ri Kdqvfk hw do1 +4;,/ fdofxodwlqj wkh vwdqgdugl}hg lqyhqwru| Lqy8™| H…c8™| Lqy8™| @ …c8™| zkhuh iru hdfk erqg n/ H…c8™| dqg …c8™| duh/ uhvshfwlyho|/ wkh phdq dqg wkh vwdqgdug ghyldwlrq ri lqyhqwru| ryhu wkh vdpsoh1 Li pdunhw pdnhuv uhdfw wr wkh lqirupdwlrq frq0 wdlqhg lq wkh rughuv uhfhlyhg/ dqg li wkh lqiruphg wudgh kdv h{sodqdwru| srzhu dgglwlrqdo wr wkdw ri wkh lqyhqwru|/ wkhuh vkrxog eh d srvlwlyh fruuhodwlrq ehwzhhq lqirupdwlrq dqg pdunhw pdnhuv* wudglqj uhdfwlrqv1 D srvlwlyh vljq ri lpsolhv wkdw pdunhw pdnhuv uhdfw wr lqiruphg wudgh/ zkloh d srvlwlyh lv d vljq ri lqyhqwru|0gulyhq ehkdylru1 Wkh uhvxowv djuhh zlwk wkh rqhv uhsruwhg lq wkh wh{w1 F1518 Frqwuroolqj iru luuhjxodu vsdflqj ri revhuydwlrqv Wkh xvh ri wudqvdfwlrq wlph kdv wkh ehqhw ri fdswxulqj wkh ydu|lqj ghjuhhv ri vljqlfdqfh wkdw kljk dqg orz yroxph shulrgv kdyh1 Krzhyhu/ wkh gudzedfn ri wklv dssurdfk lv wkdw lw plvvhv wkh hhfw gxh wr wkh odsvh ri wlph zkhq qr wudqvdfwlrqv rffxu +Hdvoh| dqg R*Kdud 45/ Gldprqg dqg Yhuuhffkld 4;:,1 Wr dgguhvv wklv lvvxh/ zh uh0hvwlpdwh vrph vshflfdwlrqv xvlqj d JDUFK vwuxfwxuh zkhuh huuruv duh prghoohg lq wkh iroorzlqj zd|= 3{| %8™| @ %8™|3 hE . 8™| = zkhuh wkh wlph ehwzhhq wzr frqvhfxwlyh wudqvdfwlrqv + w, lv h{solflwo| dffrxqwhg iru dv lw lqwhudfwv zlwk wkh dxwruhjuhvvlyh vwuxfwxuh ri wkh yduldqfh1 Dovr/ dqg duh frqvwdqwv wr eh hvwlpdwhg wrjhwkhu zlwk wkh rwkhu sdudphwhuv1 Wkh uhvxowv djuhh zlwk wkh rqhv uhsruwhg lq wkh wh{w1
  • 46. K6= Pdunhw pdnhuv* vwudwhjlf uhdfwlrqv wr lqirupdwlrq= klglqj yv1 h{0 shulphqwdwlrq Rqh srvvleoh sureohp lq wkh hvwlpdwlrq ri wkh orjlw prgho lv wkh txdqwlfdwlrq ri wkh rxwvlgh dowhuqdwlyh +vf , jlyhq wkdw wklv vkrxog dffrxqw iru vlwxdwlrqv zkhuh wkhuh lv sxuh h{rjhqrxv wudgh/ dqg zkhuh wkh pdunhw pdnhu zlwkgudzv iurp wkh pdunhw1 Wr frsh zlwk wklv/ zh ghqh wzr dowhuqdwlyh vshflfdwlrqv= lq wkh uvw rqh/ zh frqvlghu rqo| wkh fdvhv zkhuh wkhuh lv dw ohdvw rqh hqgrjhqrxv wudqvdfwlrq lq wkh 43 plqxwhv iroorzlqj wkh D Wkhvh duh wkh wudghv iru zklfk wkh ohduqlqj pdwul{ lv ghqhg1 Wkdw lv/ wkh wudqvdfwlrq kdv ehhq ruljlqdwhg e| d ghdohu zlwk d ydoxh ri vwdwlvwlfdoo| vljqlfdqw dw wkh 8( ohyho1 68
  • 47. ruljlqdwlqj wudgh1S Lq wkh vhfrqg vshflfdwlrq/ zh frqvlghu doo wkh fdvhv/ dvvljqlqj d zhljkw ri 433( wr wkh fkrlfh wr jr h{rjhqrxv li qr wudqvdfwlrq wdnhv sodfh lq wkh 43 plqxwhv iroorzlqj wkh ruljlqdwlqj wudqvdfwlrq1 Khuh/ wkh revhuydwlrqv duh vwloo ghqhg lq whupv ri wkh wudqvdfwlrq wlphv wkdw lv/ doo wkh wudqvdfwlrqv wkh pdunhw pdnhu lv lqyroyhg lq gxulqj wkh 43 plqxwhv iroorzlqj wkh lqfrplqj rqh1 Exw/ xqolnh wkh suhylrxv fdvh/ wkh| duh oxpshg wrjhwkhu hyhu| 43 plqxwhv rq wkh edvlv ri fdohqgdu wlph1 Wklv doorzv xv wr fdswxuh wkh ghflvlrq wr zlwkgudz iurp wkh pdunhw1 Lq wklv fdvh zh xvh forfn wlph1 Wkh uhvxowv djuhh zlwk wkh rqhv uhsruwhg lq wkh wh{w1 S Zh dovr orrnhg dw wkh fdvh zkhuh wkh owhu zdv wr frqvlghu rqo| wkh revhuydwlrqv uhodwlyh wr vlwxdwlrqv zkhuh wkhuh zhuh dw ohdvw wkuhh wudqvdfwlrqv gxulqj wkh 43 plqxwhv iroorzlqj wkh ruljlqdwlqj lqfrplqj rughu1 Jlyhq wkdw wkh uhvxowv djuhh zlwk wkrvh edvhg rq d rqh wudqvdfwlrq owhu/ zh gr qrw uhsruw wkhp1 Wkh| duh dydlodeoh xsrq uhtxhvw iurp wkh dxwkruv1 69
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