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HIER
Harvard Institute of Economic Research
                 Discussion Paper Number 1897



 Asset Pricing at the Millennium
                                   By

                   John Y. Campbell
                              May 2000


               Harvard University
             Cambridge, Massachusetts
           This paper can be downloaded without charge from the
            Social Science Research Network electronic library at:
             http://papers.ssrn.com/paper.taf?abstract_id=236584
                                      or
      http://post.economics.harvard.edu/hier/2000papers/2000list.html
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                                   John Y. Campbell



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                                          57
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                                            58
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ydu| wkhlu oderu vxsso| hqgrjhqrxvo|1 Wkh| qg wkdw wklv lqfuhdvhv wkh zloolqjqhvv wr
wdnh ulvnv ehfdxvh lqyhvwruv fdq devrue qdqfldo orvvhv erwk e| fxwwlqj frqvxpswlrq
dqg e| dgmxvwlqj oderu vxsso|1

                                          66
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                                           67
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                                          68
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   Hsvwhlq0]lq xwlolw| fdq eh khosixo lq uhvroylqj wkh ulvniuhh udwh sx}}oh1 Lw/ olnh wkh

                                          69
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium
Asset Pricing at the millennium

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Asset Pricing at the millennium

  • 1. HIER Harvard Institute of Economic Research Discussion Paper Number 1897 Asset Pricing at the Millennium By John Y. Campbell May 2000 Harvard University Cambridge, Massachusetts This paper can be downloaded without charge from the Social Science Research Network electronic library at: http://papers.ssrn.com/paper.taf?abstract_id=236584 or http://post.economics.harvard.edu/hier/2000papers/2000list.html
  • 2. Dvvhw Sulflqj dw wkh Ploohqqlxp 4 John Y. Campbell Iluvw gudiw= Mdqxdu| 5333 Wklv yhuvlrq= Iheuxdu| 5333 Iruwkfrplqj/ Mrxuqdo ri Ilqdqfh/ Dxjxvw 5333 4 Ghsduwphqw ri Hfrqrplfv/ Olwwdxhu Fhqwhu 546/ Kduydug Xqlyhuvlw|/ Fdpeulgjh PD 3546;/ XVD/ dqg QEHU1 Hpdlo mrkqbfdpsehooCkduydug1hgx1 Wklv sdshu lv d vxuyh| ri dvvhw sulflqj suhvhqwhg dw wkh 5333 dqqxdo phhwlqj ri wkh Dphulfdq Ilqdqfh Dvvrfldwlrq/ Ervwrq/ PD1 L dp judwhixo iru wkh lqvljkwv dqg vwlpxodwlrq surylghg e| p| frdxwkruv/ vwxghqwv/ dqg froohdjxhv lq wkh QEHU Dvvhw Sulflqj Surjudp/ zlwkrxw zkrp L frxog qrw hyhq dwwhpsw vxfk d vxuyh|1 Iudqnolq Doohq/ Qlfn Eduehulv/ Jhhuw Ehndhuw/ Ohzlv Fkdq/ Mrkq Frfkudqh/ Gdylg Ihogpdq/ Zloo Jrhw}pdqq/ Pduwlq Ohwwdx/ V|gqh| Oxgyljvrq/ Juhj Pdqnlz/ Urehuw Vkloohu/ Dqguhl Vkohlihu/ Slhwur Yhurqhvl/ Oxlv Ylfhlud/ dqg Wxrpr Yxrowhhqdkr jdyh khosixo frpphqwv rq wkh uvw gudiw1 L dfnqrzohgjh wkh qdqfldo vxssruw ri wkh Qdwlrqdo Vflhqfh Irxqgdwlrq1
  • 3. Devwudfw Wklv sdshu vxuyh|v wkh hog ri dvvhw sulflqj1 Wkh hpskdvlv lv rq wkh lqwhusod| ehwzhhq wkhru| dqg hpslulfdo zrun/ dqg rq wkh wudghr ehwzhhq ulvn dqg uhwxuq1 Prghuq uhvhdufk vhhnv wr xqghuvwdqg wkh ehkdylru ri wkh vwrfkdvwlf glvfrxqw idfwru +VGI, wkdw sulfhv doo dvvhwv lq wkh hfrqrp|1 Wkh ehkdylru ri wkh whup vwuxfwxuh ri uhdo lqwhuhvw udwhv uhvwulfwv wkh frqglwlrqdo phdq ri wkh VGI/ zkloh sdwwhuqv ri ulvn suhpld uhvwulfw lwv frqglwlrqdo yrodwlolw| dqg idfwru vwuxfwxuh1 Vw|ol}hg idfwv derxw lqwhuhvw udwhv/ djjuhjdwh vwrfn sulfhv/ dqg furvv0vhfwlrqdo sdwwhuqv lq vwrfn uhwxuqv kdyh vwlpxodwhg qhz uhvhdufk rq rswlpdo sruwirolr fkrlfh/ lqwhuwhpsrudo htxloleulxp prghov/ dqg ehkdylrudo qdqfh1 MHO fodvvlfdwlrq= J451
  • 4. Wklv sdshu vxuyh|v wkh hog ri dvvhw sulflqj1 Wkh hpskdvlv lv rq wkh lqwhusod| eh0 wzhhq wkhru| dqg hpslulfdo zrun1 Wkhrulvwv ghyhors prghov zlwk whvwdeoh suhglfwlrqv hpslulfdo uhvhdufkhuv grfxphqw sx}}ohvvw|ol}hg idfwv wkdw idlo wr w hvwdeolvkhg wkhrulhvdqg wklv vwlpxodwhv wkh ghyhorsphqw ri qhz wkhrulhv1 Vxfk d surfhvv lv sduw ri wkh qrupdo ghyhorsphqw ri dq| vflhqfh1 Dvvhw sulflqj/ olnh wkh uhvw ri hfrqrplfv/ idfhv wkh vshfldo fkdoohqjh wkdw gdwd duh jhqhudwhg qdwxudoo| udwkhu wkdq h{shulphqwdoo|/ dqg vr uhvhdufkhuv fdqqrw frqwuro wkh txdqwlw| ri gdwd ru wkh udqgrp vkrfnv wkdw dhfw wkh gdwd1 D sduwlfxoduo| lqwhuhvwlqj fkdudfwhulvwlf ri wkh dvvhw sulflqj hog lv wkdw wkhvh udqgrp vkrfnv duh dovr wkh vxemhfw pdwwhu ri wkh wkhru|1 Dv Fdpsehoo/ Or/ dqg PdfNlqod| +4:/ Fkdswhu 4/ s16, sxw lw= Zkdw glvwlqjxlvkhv qdqfldo hfrqrplfv lv wkh fhqwudo uroh wkdw xqfhu0 wdlqw| sod|v lq erwk qdqfldo wkhru| dqg lwv hpslulfdo lpsohphqwdwlrq1 Wkh vwduwlqj srlqw iru hyhu| qdqfldo prgho lv wkh xqfhuwdlqw| idflqj lq0 yhvwruv/ dqg wkh vxevwdqfh ri hyhu| qdqfldo prgho lqyroyhv wkh lpsdfw ri xqfhuwdlqw| rq wkh ehkdylru ri lqyhvwruv dqg/ xowlpdwho|/ rq pdunhw sulfhv1111 Wkh udqgrp xfwxdwlrqv wkdw uhtxluh wkh xvh ri vwdwlvwlfdo wkh0 ru| wr hvwlpdwh dqg whvw qdqfldo prghov duh lqwlpdwho| uhodwhg wr wkh xqfhuwdlqw| rq zklfk wkrvh prghov duh edvhg1 Iru urxjko| wkh odvw wzhqw| |hduv/ wkhruhwlfdo dqg hpslulfdo ghyhorsphqwv lq dvvhw sulflqj kdyh wdnhq sodfh zlwklq d zhoo hvwdeolvkhg sdudgljp1 Wklv sdudgljp hp0 skdvl}hv wkh vwuxfwxuh sodfhg rq qdqfldo dvvhw uhwxuqv e| wkh dvvxpswlrq wkdw dvvhw pdunhwv gr qrw shuplw wkh suhvhqfh ri duelwudjh rssruwxqlwlhvorrvho|/ rssruwxqlwlhv wr pdnh ulvnohvv surwv rq dq duelwudulo| odujh vfdoh1 Lq wkh devhqfh ri duelwudjh rs0 sruwxqlwlhv/ wkhuh h{lvwv d vwrfkdvwlf glvfrxqw idfwru wkdw uhodwhv sd|rv wr pdunhw sulfhv iru doo dvvhwv lq wkh hfrqrp|1 Wklv fdq eh xqghuvwrrg dv dq dssolfdwlrq ri wkh Duurz0Gheuhx prgho ri jhqhudo htxloleulxp wr qdqfldo pdunhwv1 D vwdwh sulfh h{lvwv iru hdfk vwdwh ri qdwxuh dw hdfk gdwh/ dqg wkh pdunhw sulfh ri dq| qdqfldo dvvhw lv mxvw wkh vxp ri lwv srvvleoh ixwxuh sd|rv/ zhljkwhg e| wkh dssursuldwh vwdwh sulfhv1 Ixuwkhu dvvxpswlrqv derxw wkh vwuxfwxuh ri wkh hfrqrp| surgxfh ixuwkhu uhvxowv1 Iru h{dpsoh/ li pdunhwv duh frpsohwh wkhq wkh vwrfkdvwlf glvfrxqw idfwru lv xqltxh1 Li wkh vwrfkdvwlf glvfrxqw idfwru lv olqhduo| uhodwhg wr d vhw ri frpprq vkrfnv/ wkhq dvvhw uhwxuqv fdq eh ghvfulehg e| d olqhdu idfwru prgho1 Li wkh hfrqrp| kdv d uhsuhvhqwdwlyh djhqw zlwk d zhoo0ghqhg xwlolw| ixqfwlrq/ wkhq wkh vwrfkdvwlf glvfrxqw idfwru lv uhodwhg wr wkh pdujlqdo xwlolw| ri djjuhjdwh frqvxpswlrq1 Hyhq 4
  • 5. uhfhqw ghyhorsphqwv lq ehkdylrudo qdqfh/ zklfk hpskdvl}h qrqvwdqgdug suhihuhqfhv ru luudwlrqdo h{shfwdwlrqv/ fdq eh xqghuvwrrg zlwklq wklv sdudgljp1 Iurp d wkhruhwlfdo shuvshfwlyh/ wkh vwdelolw| ri wkh sdudgljp pd| vhhp wr lqglfdwh vwdjqdwlrq ri wkh hog1 Lqghhg Gx!h +45/ Suhidfh/ ss1 {lll0{ly, glvsdudjhv uhfhqw surjuhvv e| frqwudvwlqj lw zlwk hduolhu wkhruhwlfdo dfklhyhphqwv= Wr vrphrqh zkr fdph rxw ri judgxdwh vfkrro lq wkh plg0hljkwlhv/ wkh ghfdgh vsdqqlqj urxjko| 49: vhhpv olnh d jroghq djh ri g|qdplf dvvhw sulflqj wkhru|1111 Wkh ghfdgh ru vr vlqfh 4: kdv/ zlwk uhodwlyho| ihz h{fhswlrqv/ ehhq d prsslqj0xs rshudwlrq1 Zlwkrxw ghq|lqj wkh h{wudruglqdu| dffrpsolvkphqwv ri wkh hduolhu shulrg/ L krsh wr vkrz lq wklv sdshu wkdw wkh shulrg 4: wr 4 kdv dovr ehhq d kljko| surgxfwlyh rqh1 Suhflvho| ehfdxvh wkh frqglwlrqv iru wkh h{lvwhqfh ri d vwrfkdvwlf glvfrxqw idfwru duh vr jhqhudo/ wkh| sodfh doprvw qr uhvwulfwlrqv rq qdqfldo gdwd1 Wkh fkdoohqjh qrz lv wr xqghuvwdqg wkh hfrqrplf irufhv wkdw ghwhuplqh wkh vwrfkdvwlf glvfrxqw idfwru/ ru sxw dqrwkhu zd|/ wkh uhzdugv wkdw lqyhvwruv ghpdqg iru ehdulqj sduwlfxodu ulvnv1 Zh nqrz d juhdw ghdo pruh derxw wklv vxemhfw wrgd| wkdq zh glg wzhqw| |hduv djr1 hw rxu xqghuvwdqglqj lv idu iurp shuihfw dqg pdq| h{flwlqj uhvhdufk rssruwxqlwlhv uhpdlq1 Dq| dwwhpsw wr vxuyh| vxfk d odujh dqg dfwlyh hog pxvw qhfhvvdulo| eh olplwhg lq pdq| uhvshfwv1 Wklv sdshu frqfhqwudwhv rq wkh wudghr ehwzhhq ulvn dqg uhwxuq1 Prvw ri wkh olwhudwxuh rq wklv vxemhfw pdnhv wkh vlpsoli|lqj dvvxpswlrq wkdw lqyhvwruv kdyh krprjhqhrxv lqirupdwlrq1 L wkhuhiruh qhjohfw wkh wkhru| ri dv|pphwulf lqiru0 pdwlrq dqg lwv dssolfdwlrqv wr frusrudwh qdqfh/ pdunhw plfurvwuxfwxuh/ dqg qdqfldo lqwhuphgldwlrq1 L frqfhqwudwh rq wkh X1V1 qdqfldo pdunhwv dqg gr qrw glvfxvv lq0 whuqdwlrqdo qdqfh1 L phqwlrq lvvxhv lq qdqfldo hfrqrphwulfv rqo| lq wkh frqwh{w ri dssolfdwlrqv wr ulvn0uhwxuq prghov/ dqg L gr qrw uhylhz wkh hfrqrphwulf olwhudwxuh rq fkdqjlqj yrodwlolw| dqg qrq0qrupdolw| ri dvvhw uhwxuqv1 L gr qrw gudz lpsolfd0 wlrqv ri wkh dvvhw sulflqj olwhudwxuh iru dvvhw pdqdjhphqw/ shuirupdqfh hydoxdwlrq/ ru fdslwdo exgjhwlqj1 L ohdyh prvw frqwlqxrxv0wlph uhvhdufk/ dqg lwv dssolfdwlrqv wr ghulydwlyh vhfxulwlhv dqg frusrudwh erqgv/ wr wkh frpsohphqwdu| vxuyh| ri Vxqgduh0 vdq +5333,1 L gudz khdylo| rq hduolhu h{srvlwlrq lq Fdpsehoo/ Or/ dqg PdfNlqod| +4:, dqg Fdpsehoo +4,1 Wkh odwwhu sdshu uhsruwv frpsdudwlyh hpslulfdo uhvxowv rq djjuhjdwh vwrfn dqg erqg uhwxuqv lq rwkhu ghyhorshg qdqfldo pdunhwv1 5
  • 6. L1 Dvvhw Uhwxuqv dqg wkh Vwrfkdvwlf Glvfrxqw Idfwru Wkh edvlf htxdwlrq ri dvvhw sulflqj fdq eh zulwwhq dv iroorzv= | ' ,| d|n fc|n oc +4, zkhuh | lv wkh sulfh ri dq dvvhw dw wlph | +wrgd|,/ ,| lv wkh frqglwlrqdo h{shf0 wdwlrqv rshudwru frqglwlrqlqj rq wrgd|*v lqirupdwlrq/ fc|n lv wkh udqgrp sd|r rq dvvhw dw wlph | n  +wrpruurz,/ dqg |n lv wkh vwrfkdvwlf glvfrxqw idfwru ru VGI1 Wkh VGI lv d udqgrp yduldeoh zkrvh uhdol}dwlrqv duh dozd|v srvlwlyh1 Lw jhqhudo0 l}hv wkh idploldu qrwlrq ri d glvfrxqw idfwru wr d zruog ri xqfhuwdlqw| li wkhuh lv qr xqfhuwdlqw|/ ru li lqyhvwruv duh ulvn0qhxwudo/ wkh VGI lv mxvw d frqvwdqw wkdw frqyhuwv h{shfwhg sd|rv wrpruurz lqwr ydoxh wrgd|1 Htxdwlrq +4, fdq eh xqghuvwrrg lq wzr zd|v1 Iluvw/ lq d glvfuhwh0vwdwh vhwwlqj/ wkh dvvhw sulfh fdq eh zulwwhq dv d vwdwh0sulfh0zhljkwhg dyhudjh ri wkh sd|rv lq hdfk vwdwh ri qdwxuh1 Htxlydohqwo|/ lw fdq eh zulwwhq dv d suredelolw|0zhljkwhg dyhudjh ri wkh sd|rv/ pxowlsolhg e| wkh udwlr ri vwdwh sulfh wr suredelolw| iru hdfk vwdwh1 Wkh frqglwlrqdo h{shfwdwlrq lq +4, lv mxvw wkdw suredelolw|0zhljkwhg dyhudjh1 Wkh devhqfh ri duelwudjh rssruwxqlwlhv hqvxuhv wkdw d vhw ri srvlwlyh vwdwh sulfhv h{lvwv/ dqg khqfh wkdw d srvlwlyh VGI h{lvwv1 Li pdunhwv duh frpsohwh/ wkhq vwdwh sulfhv dqg wkh VGI duh xqltxh1 Vhfrqg/ frqvlghu wkh rswlpl}dwlrq sureohp ri dq djhqw zlwk wlph0vhsdudeoh xwlolw| ixqfwlrq LE| n BLEc|n 1 Li wkh djhqw lv deoh wr iuhho| wudgh dvvhw / wkhq wkh uvw0rughu frqglwlrq lv L E| | ' B,| dL Ec|n fc|n oc +5, zklfk htxdwhv wkh pdujlqdo frvw ri dq h{wud xqlw ri dvvhw / sxufkdvhg wrgd|/ wr wkh h{shfwhg pdujlqdo ehqhw ri wkh h{wud sd|r uhfhlyhg wrpruurz1 Htxdwlrq +5, lv frqvlvwhqw zlwk htxdwlrq +4, iru |n ' BL Ec|n *L E| / wkh glvfrxqwhg udwlr ri pdujlqdo xwlolw| wrpruurz wr pdujlqdo xwlolw| wrgd|1 Wklv pdujlqdo xwlolw| udwlr/ iru lqyhvwruv zkr duh deoh wr wudgh iuhho| lq d vhw ri dvvhwv/ fdq dozd|v eh xvhg dv wkh VGI iru wkdw vhw ri dvvhwv1 Htxdwlrq +4, doorzv iru wkh h{lvwhqfh ri dvvhwvru lqyhvwphqw vwudwhjlhvzlwk }hur frvw wrgd|1 Li | lv qrq}hur/ krzhyhu/ rqh fdq glylgh wkurxjk e| | +zklfk 6
  • 7. lv nqrzq dw wlph |/ dqg wkxv fdq eh sdvvhg wkurxjk wkh frqglwlrqdo h{shfwdwlrqv rshudwru, wr rewdlq  ' ,| d|n E n -c|n oc +6, zkhuh E n -c|n fc|n *| 1 Wklv irup lv pruh frpprqo| xvhg lq hpslulfdo zrun1 Wkh ruljlqv ri wklv uhsuhvhqwdwlrq iru dvvhw sulfhv olh lq wkh Duurz0Gheuhx prgho ri jhqhudo htxloleulxp/ dqg lq wkh dssolfdwlrq ri wkdw prgho wr rswlrq sulflqj e| Fr{ dqg Urvv +4:9, dqg Urvv +4:;,/ dorqj zlwk wkh Duelwudjh Sulflqj Wkhru| ri Urvv +4:9,1 D ghqlwlyh wkhruhwlfdo wuhdwphqw lq frqwlqxrxv wlph zdv surylghg e| Kduulvrq dqg Nuhsv +4:,/ dqg wkh glvfuhwh0wlph uhsuhvhqwdwlrq zdv uvw suhvhqwhg dqg dssolhg hpslulfdoo| e| Jurvvpdq dqg Vkloohu +4;4,1 Kdqvhq dqg Ulfkdug +4;:, ghyhorshg wkh glvfuhwh0wlph dssurdfk ixuwkhu/ hpskdvl}lqj wkh glvwlqfwlrq ehwzhhq frqglwlrqdo dqg xqfrqglwlrqdo h{shfwdwlrqv1 Wh{werrn wuhdwphqwv duh jlyhq e| Lqjhuvroo +4;:, dqg Gx!h +45,1 Frfkudqh +4, uhvwdwhv wkh zkroh ri dvvhw sulflqj wkhru| zlwklq wklv iudphzrun1 Krz duh wkhvh htxdwlrqv xvhg lq hpslulfdo zrunB D uvw srvvlelolw| lv wr lpsrvh plqlpdo wkhruhwlfdo vwuxfwxuh/ xvlqj gdwd rq dvvhw uhwxuqv dorqh dqg gudzlqj lpsol0 fdwlrqv iru wkh vwrfkdvwlf glvfrxqw idfwru1 Zrun lq wklv vw|oh/ lqfoxglqj uhvhdufk wkdw vlpso| grfxphqwv vw|ol}hg idfwv derxw phdqv/ yduldqfhv/ dqg suhglfwdelolw| ri dvvhw uhwxuqv/ lv uhylhzhg odwhu lq wklv vhfwlrq1 D vhfrqg srvvlelolw| lv wr exlog d wlph0vhulhv prgho ri wkh VGI wkdw wv gdwd rq erwk dvvhw sd|rv dqg sulfhv zrun dorqj wkhvh olqhv/ lqfoxglqj uhvhdufk rq wkh whup vwuxfwxuh ri lqwhuhvw udwhv/ lv uhylhzhg lq vhf0 wlrq LL1 D wklug dssurdfk lv plfurhfrqrplf1 Rqh fdq xvh htxdwlrq +5,/ dorqj zlwk dvvxphg suhihuhqfhv iru dq lqyhvwru/ wkh lqyhvwru*v lqwhuwhpsrudo exgjhw frqvwudlqw/ dqg d surfhvv iru dvvhw uhwxuqv ru htxlydohqwo| iru wkh VGI/ wr qg wkh lqyhvwru*v rswlpdo frqvxpswlrq dqg sruwirolr uxohv1 Wklv yhu| dfwlyh duhd ri uhfhqw uhvhdufk lv uhylhzhg lq vhfwlrq LLL1 Irxuwk/ rqh fdq dvvxph wkdw htxdwlrq +5, dssolhv wr d uhsuh0 vhqwdwlyh lqyhvwru zkr frqvxphv djjuhjdwh frqvxpswlrq lq wklv fdvh | lv uhsodfhg e| djjuhjdwh frqvxpswlrq | / dqg +5, uhvwulfwv dvvhw sulfhv lq uhodwlrq wr frqvxps0 wlrq gdwd1 Zrun dorqj wkhvh olqhv lv glvfxvvhg lq vhfwlrq LY1 Ilqdoo|/ rqh fdq wu| wr h{sodlq htxloleulxp dvvhw sulfhv dv dulvlqj iurp wkh lqwhudfwlrqv ri khwhurjhqhrxv djhqwv1 Vhfwlrq Y glvfxvvhv prghov zlwk udwlrqdo djhqwv zkr duh khwhurjhqhrxv lq wkhlu lqirupdwlrq/ lqfrph/ suhihuhqfhv/ ru frqvwudlqwv1 Vhfwlrq YL glvfxvvhv uhfhqw uh0 vhdufk rq ehkdylrudo qdqfh/ lq zklfk vrph djhqwv duh dvvxphg wr kdyh qrqvwdqgdug suhihuhqfhv ru luudwlrqdo h{shfwdwlrqv/ zkloh rwkhu djhqwv kdyh vwdqgdug suhihuhqfhv dqg udwlrqdo h{shfwdwlrqv1 Vhfwlrq YLL frqfoxghv1 7
  • 8. D1 Phdq dqg Yduldqfh ri wkh VGI D141 Wkh Uhdo Lqwhuhvw Udwh Dvvhw uhwxuq gdwd uhvwulfw wkh prphqwv ri wkh VGI1 Wkh rqh0shulrg uhdo lqwhuhvw udwh lv forvho| uhodwhg wr wkh frqglwlrqdo phdq ri wkh VGI/ frqglwlrqlqj rq lqirupdwlrq dydlodeoh dw wkh vwduw ri wkh shulrg1 Li wkhuh lv d vkruw0whup ulvnohvv uhdo dvvhw s zlwk d sd|r ri rqh wrpruurz/ wkhq htxdwlrq +4, lpsolhv wkdw  ,| |n ' s | ' +7,  n -sc|n Wkh h{shfwhg vwrfkdvwlf glvfrxqw idfwru lv mxvw wkh uhdo sulfh ri wkh vkruw0whup ulvnohvv uhdo dvvhw/ ru htxlydohqwo|/ wkh uhflsurfdo ri lwv jurvv |lhog1 Ri frxuvh/ wkhuh lv qr wuxo| ulvnohvv rqh0shulrg uhdo dvvhw lq wkh hfrqrp|1 Vkruw0 whup Wuhdvxu| eloov duh ulvnohvv lq qrplqdo whupv udwkhu wkdq uhdo whupv/ dqg hyhq lq dwlrq0lqgh{hg erqgv kdyh dq lqgh{dwlrq odj wkdw ghsulyhv wkhp ri surwhfwlrq djdlqvw vkruw0whup lq dwlrq vkrfnv1 Lq sudfwlfh/ krzhyhu/ vkruw0whup lq dwlrq ulvn lv vx!flhqwo| prghvw lq wkh X1V1 dqg rwkhu ghyhorshg hfrqrplhv wkdw qrplqdo Wuhdvxu| eloo uhwxuqv duh d jrrg sur{| iru d ulvnohvv rqh0shulrg uhdo dvvhw1 Wklv phdqv wkdw wkh frqglwlrqdo h{shfwdwlrq ri wkh VGI lv slqqhg grzq e| wkh h{shfwhg uhdo uhwxuq rq Wuhdvxu| eloov1 Wklv uhwxuq lv idluo| orz rq dyhudjh +Fdpsehoo +4, uhsruwv d phdq orj uhwxuq ri 31; shufhqw shu |hdu lq txduwhuo| X1V1 gdwd ryhu wkh shulrg 47:15 wr 4917,1 Lw lv dovr idluo| vwdeoh +wkh vwdqgdug ghyldwlrq lv 41:9 shufhqw lq wkh vdph gdwd vhw/ dqg shukdsv kdoi ri wklv lv gxh wr h{ srvw lq dwlrq vkrfnv,1 Lq idfw/ Idpd +4:8, dujxhg wkdw lq wkh 483v dqg 493v wkh uhdo lqwhuhvw udwh zdv dfwxdoo| frqvwdqw1 Vlqfh wkh hduo| 4:3v/ krzhyhu/ wkhuh kdyh ehhq vrph orzhu0iuhtxhqf| yduldwlrqv lq wkh uhdo lqwhuhvw udwh lw zdv yhu| orz ru hyhq qhjdwlyh gxulqj wkh odwh 4:3v/ pxfk kljkhu lq wkh hduo| 4;3v/ dqg guliwhg orzhu gxulqj wkh odwh 4;3v1 D uhdvrqdeoh prgho ri wkh VGI pxvw wkhuhiruh kdyh d frqglwlrqdo h{shfwdwlrq wkdw lv voljkwo| ohvv wkdq rqh/ wkdw grhv qrw pryh gudpdwlfdoo| lq wkh vkruw uxq/ exw kdv vrph orqjhu0whup yduldwlrq1 Vxfk ehkdylru fdq eh fdswxuhg xvlqj shuvlvwhqw olqhdu wlph0vhulhv prghov +vwdqgdug lq wkh olwhudwxuh rq wkh whup vwuxfwxuh ri lqwhuhvw udwhv/ glvfxvvhg lq Vhfwlrq LL1E15, ru uhjlph0vzlwfklqj prghov +Jud| +49,/ Jdufld dqg Shuurq +49,,1 Wkhuh lv dovr d juhdw ghdo ri uhvhdufk rq wkh wlph0vhulhv surshuwlhv ri wkh qrplqdo lqwhuhvw udwh1 Rqh fdq ghqh d qrplqdo vwrfkdvwlf glvfrxqw idfwru dv wkh uhdo VGI 8
  • 9. wlphv wkh sulfh ohyho wrgd|/ glylghg e| wkh sulfh ohyho wrpruurz1 Wkh h{shfwdwlrq ri wkh qrplqdo VGI lv wkh sulfh ri d vkruw0whup ulvniuhh qrplqdo dvvhw1 Wklv zrun lv ohvv uhohydqw iru wkh htxloleulxp lvvxhv glvfxvvhg lq wklv sdshu/ krzhyhu/ dv wkh qrplqdo VGI fdqqrw eh uhodwhg wr rswlpdo frqvxpswlrq lq wkh vdph zd| dv wkh uhdo VGI1 Pxfk ri wklv olwhudwxuh lv vxuyh|hg e| Fdpsehoo/ Or/ dqg PdfNlqod| +4:/ Fkdswhu 44, dqg Vxqgduhvdq +5333,1 D151 Ulvn Suhpld Ulvn suhpld uhvwulfw wkh yrodwlolw| ri wkh VGI1 Frpsdulqj htxdwlrq +6, iru d ulvn| dvvhw dqg iru wkh ulvnohvv dvvhw/ zh kdyh f ' ,| d|n E-c|n -sc|n o ' ,| |n ,| E-c|n -sc|n nJ | E|nc -c|n -sc|n 1 Uhduudqjlqj/ wkh h{shfwhg h{fhvv uhwxuq rq dq| dvvhw vdwlvhv L| E|nc -c|n -sc|n ,| E-c|n -sc|n ' +8, ,| |n Wkh h{shfwhg h{fhvv uhwxuq lv ghwhuplqhg e| ulvn/ dv phdvxuhg e| wkh qhjdwlyh ri fryduldqfh zlwk wkh VGI/ glylghg e| wkh h{shfwhg VGI ru htxlydohqwo| wkh sulfh ri d ulvnohvv dvvhw1 Dq dvvhw zkrvh fryduldqfh zlwk wkh VGI lv odujh dqg qhjdwlyh whqgv wr kdyh orz uhwxuqv zkhq wkh VGI lv kljk/ wkdw lv zkhq pdujlqdo xwlolw| lv kljk1 Lq htxloleulxp vxfk dq dvvhw pxvw kdyh d kljk h{fhvv uhwxuq wr frpshqvdwh iru lwv whqghqf| wr gr srruo| lq vwdwhv ri wkh zruog zkhuh zhdowk lv sduwlfxoduo| ydoxdeoh wr lqyhvwruv1 Vlqfh wkh fruuhodwlrq ehwzhhq wkh VGI dqg wkh h{fhvv uhwxuq pxvw eh juhdwhu wkdq plqxv rqh/ wkh qhjdwlyh fryduldqfh lq +8, pxvw eh ohvv wkdq wkh surgxfw ri wkh vwdqgdug ghyldwlrqv ri wkh h{fhvv uhwxuq dqg wkh VGI1 Uhduudqjlqj/ zh kdyh j| E|n ,| E-c|n -sc|n +9, ,| |n j| E-c|n -sc|n Lq zrugv/ wkh Vkdush udwlr iru dvvhw wkh dvvhw*v ulvn suhplxp glylghg e| lwv vwdqgdug ghyldwlrqsxwv d orzhu erxqg rq wkh yrodwlolw| ri wkh vwrfkdvwlf glvfrxqw idfwru1 Wkh wljkwhvw orzhu erxqg lv dfklhyhg e| qglqj wkh ulvn| dvvhw/ ru sruwirolr ri dvvhwv/ zlwk wkh kljkhvw Vkdush udwlr1 Wklv erxqg zdv uvw vwdwhg e| Vkloohu +4;5, Kdqvhq dqg Mdjdqqdwkdq +44, kdyh h{whqghg lw wr d vhwwlqj zlwk pdq| ulvn| dvvhwv exw qr ulvnohvv dvvhw/ vkrzlqj krz wr frqvwuxfw d iurqwlhu uhodwlqj wkh orzhu erxqg rq 9
  • 10. wkh yrodwlolw| ri wkh VGI wr wkh phdq ri wkh VGI1 Wklv iurqwlhu frqwdlqv wkh vdph lqirupdwlrq dv wkh idploldu phdq0yduldqfh h!flhqw iurqwlhu uhodwlqj wkh orzhu erxqg rq wkh yduldqfh ri d sruwirolr uhwxuq wr wkh phdq sruwirolr uhwxuq1 Wkh orzhu erxqg lv dfklhyhg e| dq VGI wkdw lv d olqhdu frpelqdwlrq ri d k|srwkhwlfdo ulvnohvv dvvhw dqg wkh ulvn| dvvhwv xqghu frqvlghudwlrq1 Kdqvhq dqg Mdjdqqdwkdq dovr ghulyh d wljkwhu erxqg e| xvlqj wkh uhvwulfwlrq wkdw wkh VGI pxvw dozd|v eh srvlwlyh1 Frfkudqh dqg Kdqvhq +45, suhvhqw ixuwkhu hpslulfdo uhvxowv/ dqg Kdqvhq dqg Mdjdqqdwkdq +4:, h{whqg wkh phwkrgrorj| wr frqvlghu wkh sulflqj huuruv wkdw fdq eh pdgh e| d idovh hfrqrplf prgho iru wkh VGI1 Wkh| vkrz wkdw wkh odujhvw srvvleoh sulflqj huuruv duh erxqghg e| wkh vwdqgdug ghyldwlrq ri wkh glhuhqfh ehwzhhq wkh idovh VGI dqg wkh wuxh VGI/ lq d pdqqhu dqdorjrxv wr +9,1 Dv zulwwhq/ doo wkh txdqwlwlhv lq +9, duh frqglwlrqdo rq lqirupdwlrq dw wlph |/ wkdw lv/ wkh| kdyh wlph vxevfulswv1 Iruwxqdwho| lw lv vlpsoh wr ghulyh dq xqfrqglwlrqdo yhuvlrq e| uhwxuqlqj wr htxdwlrq +6, dqg wdnlqj xqfrqglwlrqdo h{shfwdwlrqv wkh irup ri +9, lv xqfkdqjhg1 Wkh rqo| vxewohw| lv wkdw wkh xqfrqglwlrqdo phdq VGI lv wkh xqfrqglwlrqdo phdq sulfh ri d ulvnohvv dvvhw/ zklfk lv qrw wkh vdph dv wkh uhflsurfdo ri wkh xqfrqglwlrqdo phdq ulvnohvv uhdo lqwhuhvw udwh1 D161 Wkh Htxlw| Suhplxp Sx}}oh Lw lv qrw kdug wr qg dvvhwv wkdw lpso| vxusulvlqjo| odujh qxpehuv iru wkh yrodwlolw| ri wkh VGI1 Wkh djjuhjdwh X1V1 vwrfn pdunhw lv wkh ehvw0nqrzq h{dpsoh1 Lq srvwzdu txduwhuo| X1V1 gdwd vxppdul}hg e| Fdpsehoo +4, wkh dqqxdol}hg Vkdush udwlr iru d ydoxh0zhljkwhg vwrfn lqgh{ lv derxw rqh0kdoi/ lpso|lqj d plqlpxp dqqxdol}hg vwdqgdug ghyldwlrq ri 83 shufhqw iru wkh VGI1 Wklv lv d odujh ydoxh iru d udqgrp yduldeoh zkrvh phdq pxvw eh forvh wr rqh dqg zkrvh orzhu erxqg lv }hur1 Dv zh vkdoo vhh odwhu lq wkh sdshu/ lw lv dovr yhu| odujh uhodwlyh wr wkh suhglfwlrqv ri vlpsoh htxloleulxp prghov1 Wkh dqqxdol}hg vwdqgdug ghyldwlrq ri djjuhjdwh frqvxpswlrq jurzwk lq srvwzdu X1V1 gdwd lv derxw rqh shufhqw1 D uhsuhvhqwdwlyh0djhqw prgho zlwk srzhu xwlolw| pxvw wkhuhiruh kdyh d yhu| odujh frh!flhqw ri uhodwlyh ulvn dyhuvlrq/ rq wkh rughu ri 83/ wr pdwfk wkh vwdqgdug ghyldwlrq ri wkh VGI1 Phkud dqg Suhvfrww +4;8, uvw guhz wkh dwwhqwlrq ri wkh surihvvlrq wr wklv skhqrphqrq dqg qdphg lw wkh htxlw| suhplxp sx}}oh1 Ri frxuvh/ wkhuh lv frqvlghudeoh xqfhuwdlqw| derxw wkh prphqwv wkdw hqwhu htxdwlrq +9,1 Fhffkhwwl/ Odp/ dqg Pdun +47, dqg Kdqvhq/ Khdwrq/ dqg Oxwwphu +48, gh0 :
  • 11. yhors vwdwlvwlfdo phwkrgv/ edvhg rq Kdqvhq*v +4;5, Jhqhudol}hg Phwkrg ri Prphqwv +JPP,/ wr hvwlpdwh d frqghqfh lqwhuydo iru wkh yrodwlolw| ri wkh VGI1 Phdq dvvhw uhwxuqv duh sduwlfxoduo| kdug wr hvwlpdwh ehfdxvh/ dv Phuwrq +4;3, srlqwhg rxw/ wkh suhflvlrq ri wkh hvwlpdwh ghshqgv rq wkh wrwdo ohqjwk ri fdohqgdu wlph udwkhu wkdq wkh qxpehu ri revhuydwlrqv shu vh1 Iruwxqdwho| X1V1 vwrfn pdunhw gdwd duh dydlodeoh iru d shulrg ri doprvw wzr fhqwxulhv +Vfkzhuw +43, suhvhqwv gdwd vwduwlqj lq 4;35, wklv orqj vsdq ri gdwd phdqv wkdw hyhq d orzhu frqghqfh erxqg rq wkh yrodwlolw| ri wkh VGI lv txlwh odujh1 Vrph dxwkruv kdyh dujxhg wkdw wkhvh uhvxowv duh plvohdglqj1 Li dfdghplf vwxglhv irfxv rq orqj0whup X1V1 gdwd suhflvho| ehfdxvh wkh hfrqrp| dqg wkh vwrfn pdunhw kdyh shuiruphg vr zhoo/ wkhq wkhuh lv dq xszdug vhohfwlrq eldv lq phdvxuhg dyhudjh X1V1 uhwxuqv +Eurzq/ Jrhw}pdqq/ dqg Urvv +48,,1 Prvw rwkhu ghyhorshg vwrfn pdunhwv kdyh rhuhg frpsdudeoh uhwxuqv wr wkh X1V1 lq wkh srvwzdu shulrg +Fdpsehoo +4,,/ exw Mrulrq dqg Jrhw}pdqq +4, vkrz wkdw sulfh uhwxuqv lq pdq| ri wkhvh rwkhu pdunhwv zhuh orz lq wkh hduo| 53wk Fhqwxu| wklv pd| lqglfdwh wkh lpsruwdqfh ri vhohfwlrq eldv/ dowkrxjk lw lv srvvleoh wkdw orzhu uhwxuqv zhuh frpshqvdwhg e| kljkhu glylghqg |lhogv lq wkdw shulrg1 Ulhw} +4;;, kdv dujxhg wkdw wkh X1V1 gdwd duh plvohdglqj iru d glhuhqw uhdvrq1 Lqyhvwruv pd| kdyh udwlrqdoo| dqwlflsdwhg wkh srvvlelolw| ri d fdwdvwursklf hyhqw wkdw kdv qrw |hw rffxuuhg1 Wklv shvr sureohp lpsolhv wkdw vdpsoh yrodwlolw| xqghuvwdwhv wkh wuxh ulvn ri htxlw| lqyhvwphqw1 Rqh gl!fxow| zlwk wklv dujxphqw lv wkdw lw uhtxluhv qrw rqo| d srwhqwldo fdwdvwurskh/ exw rqh zklfk dhfwv vwrfn pdunhw lqyhvwruv pruh vhulrxvo| wkdq lqyhvwruv lq vkruw0whup ghew lqvwuxphqwv1 Pdq| frxqwulhv wkdw kdyh h{shulhqfhg srolwlfdo xskhdydo ru ghihdw lq zdu kdyh vhhq yhu| orz uhwxuqv rq vkruw0 whup jryhuqphqw ghew dv zhoo dv rq htxlwlhv1 D shvr sureohp wkdw dhfwv erwk dvvhw uhwxuqv htxdoo| zloo qrw qhfhvvdulo| dhfw wkh hvwlpdwhg yrodwlolw| ri wkh VGI1 Wkh pdmru h{dpsoh ri d glvdvwhu iru vwrfnkroghuv wkdw glg qrw qhjdwlyho| dhfw erqgkroghuv lv wkh Juhdw Ghsuhvvlrq ri wkh 463v/ exw ri frxuvh wklv hyhqw lv douhdg| lqfoxghg lq orqj0whup X1V1 gdwd1 D171 Suhglfwdelolw| ri Djjuhjdwh Vwrfn Uhwxuqv Ixuwkhu lqwhuhvwlqj uhvxowv duh dydlodeoh li rqh xvhv frqglwlrqlqj lqirupdwlrq1 Wkhuh lv dq hqruprxv olwhudwxuh grfxphqwlqj wkh suhglfwdelolw| ri djjuhjdwh vwrfn uhwxuqv iurp sdvw lqirupdwlrq lqfoxglqj odjjhg uhwxuqv +Idpd dqg Iuhqfk +4;;d,/ Srwhued ;
  • 12. dqg Vxpphuv +4;;,,/ wkh glylghqg0sulfh udwlr +Fdpsehoo dqg Vkloohu +4;;d,/ Idpd dqg Iuhqfk +4;;e,/ Krgulfn +45,,/ wkh hduqlqjv0sulfh udwlr +Fdpsehoo dqg Vkloohu +4;;e,,/ wkh errn0wr0pdunhw udwlr +Ohzhoohq +4,,/ wkh glylghqg sd|rxw udwlr +Od0 prqw +4;,,/ wkh vkduh ri htxlw| lq qhz qdqfh +Qhovrq +48,/ Ednhu dqg Zxujohu +5333,,/ |lhog vsuhdgv ehwzhhq orqj0whup dqg vkruw0whup lqwhuhvw udwhv dqg ehwzhhq orz0 dqg kljk0txdolw| erqg |lhogv +Fdpsehoo +4;:,/ Idpd dqg Iuhqfk +4;,/ Nhlp dqg Vwdpedxjk +4;9,,/ uhfhqw fkdqjhv lq vkruw0whup lqwhuhvw udwhv +Fdpsehoo +4;:,/ Krgulfn +45,,/ dqg wkh ohyho ri frqvxpswlrq uhodwlyh wr lqfrph dqg zhdowk +Ohwwdx dqg Oxgyljvrq +4d,,1 Pdq| ri wkhvh yduldeohv duh uhodwhg wr wkh vwdjh ri wkh exvl0 qhvv f|foh dqg suhglfw frxqwhuf|folfdo yduldwlrq lq vwrfn uhwxuqv +Idpd dqg Iuhqfk +4;,/ Ohwwdx dqg Oxgyljvrq +4d,,1 D qxpehu ri hfrqrphwulf slwidoov duh uhohydqw iru hydoxdwlqj wkhvh hhfwv1 Iluvw/ uhwxuq suhglfwdelolw| dsshduv pruh vwulnlqj dw orqj krul}rqv wkdq dw vkruw krul}rqv wkh h{sodqdwru| srzhu ri d uhjuhvvlrq ri vwrfn uhwxuqv rq wkh orj glylghqg0sulfh udwlr/ iru h{dpsoh/ lqfuhdvhv iurp durxqg wzr shufhqw dw d prqwko| iuhtxhqf| wr 4; shufhqw dw dq dqqxdo iuhtxhqf| dqg 67 shufhqw dw d wzr0|hdu iuhtxhqf| lq srvwzdu txduwhuo| X1V1 gdwd +Fdpsehoo +4,,1 Wkh gl!fxow| lv wkdw wkh qxpehu ri qrq0ryhuodsslqj revhuydwlrqv ghfuhdvhv zlwk wkh iruhfdvw krul}rq/ dqg lw lv hvvhqwldo wr dgmxvw vwdwlvwl0 fdo lqihuhqfh iru wklv1 Vwdqgdug dgmxvwphqwv zrun srruo| zkhq wkh vl}h ri wkh ryhuods lv odujh uhodwlyh wr wkh vdpsoh vl}h Ulfkdugvrq dqg Vwrfn +4;, vxjjhvw dq dowhuqd0 wlyh dssurdfk wr kdqgoh wklv fdvh1 Vhfrqg/ pdq| ri wkh yduldeohv wkdw dsshdu wr suhglfw uhwxuqv duh kljko| shuvlvwhqw dqg wkhlu lqqrydwlrqv duh fruuhodwhg zlwk uhwxuq lqqrydwlrqv1 Hyhq zkhq uhwxuqv duh phdvxuhg dw vkruw krul}rqv/ wklv fdq ohdg wr vpdoo0vdpsoh eldvhv lq vwdqgdug whvw vwdwlvwlfv1 Qhovrq dqg Nlp +46, dqg rwkhuv xvh Prqwh Fduor phwkrgv wr dgmxvw iru wklv sureohp1 Ghvslwh wkhvh gl!fxowlhv/ wkh hylghqfh iru suhglfwdelolw| vxuylyhv dw uhdvrqdeoh li qrw ryhuzkhoplqj ohyhov ri vwdwlvwlfdo vljqlfdqfh1 Prvw qdqfldo hfrqrplvwv ds0 shdu wr kdyh dffhswhg wkdw djjuhjdwh uhwxuqv gr frqwdlq dq lpsruwdqw suhglfwdeoh frpsrqhqw1 Hyhq wkh uhfhqw lqfuhdvh lq X1V1 vwrfn sulfhv/ zklfk kdv zhdnhqhg wkh sxuho| vwdwlvwlfdo hylghqfh iru phdq0uhyhuvlrq dqg frxqwhuf|folfdo suhglfwdelolw|/ kdv qrw eurnhq wklv frqvhqvxv ehfdxvh lw lv gl!fxow wr udwlrqdol}h wkh uxqxs lq sulfhv zlwk uhdvrqdeoh glylghqg ru hduqlqjv iruhfdvwv dqg frqvwdqw glvfrxqw udwhv +Khdwrq dqg Oxfdv +4,,1 Frqglwlrqlqj lqirupdwlrq fdq eh xvhg wr ohduq derxw wkh VGI lq wzr glhuhqw zd|v1 Iluvw/ rqh fdq fuhdwh d pdqdjhg sruwirolr wkdw lqfuhdvhv wkh sruwirolr zhljkw
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  • 16. wkhq wkh qhjdwlyh ri wkh fryduldqfh ri dq| h{fhvv uhwxuq zlwk wkh VGI fdq eh zulwwhq dv [g [g [ g 2 j| L| E|nc -c|n -sc|n ' K| j| ' EK| j| ' b| q | +;, ' ' j2 | ' Khuh j| lv wkh frqglwlrqdo fryduldqfh ri dvvhw uhwxuq zlwk wkh *wk idfwru/ j2 lv wkh | frqglwlrqdo yduldqfh ri wkh *wk idfwru/ b| K| j2 lv wkh sulfh ri ulvn ri wkh *wk | idfwru/ dqg q | j| *j 2 lv wkh ehwd ru uhjuhvvlrq frh!flhqw ri dvvhw uhwxuq rq | wkdw idfwru1 Wklv htxdwlrq/ wrjhwkhu zlwk +8,/ lpsolhv wkdw wkh ulvn suhplxp rq dq| dvvhw fdq eh zulwwhq dv d vxp ri wkh dvvhw*v ehwdv zlwk frpprq idfwruv wlphv wkh ulvn sulfhv ri wkrvh idfwruv1 Wklv zd| ri ghulylqj d pxowlidfwru prgho lv frqvlvwhqw zlwk wkh hduolhu lqvljkwv1 Lq d vlqjoh0shulrg prgho zlwk txdgudwlf xwlolw|/ iru h{dpsoh/ frqvxpswlrq htxdov zhdowk dqg wkh pdujlqdo xwlolw| ri frqvxpswlrq lv olqhdu1 Lq wklv fdvh wkh VGI pxvw eh olqhdu lq ixwxuh zhdowk/ ru htxlydohqwo| olqhdu lq wkh pdunhw sruwirolr uhwxuq1 Lq d vlqjoh0shulrg prgho zlwk g frpprq vkrfnv dqg frpsohwho| glyhuvldeoh lglrv|qfudwlf ulvn/ wkh VGI fdq ghshqg rqo| rq wkh frpprq vkrfnv1 Lw lv lpsruwdqw wr qrwh wkh frqglwlrqlqj lqirupdwlrq lq htxdwlrq +;,1 Erwk wkh eh0 wdv dqg wkh sulfhv ri ulvn duh frqglwlrqdo rq lqirupdwlrq dw wlph |1 Xqiruwxqdwho|/ wklv frqglwlrqdo pxowlidfwru prgho grhv qrw jhqhudoo| lpso| dq xqfrqglwlrqdo pxowlidfwru prgho ri wkh vdph irup1 Wkh uhohydqw fryduldqfh iru dq xqfrqglwlrqdo prgho lv wkh xq0 S frqglwlrqdo fryduldqfh LE|nc -c|n -sc|n ' LE@| g K| sc|nc -c|n ' -sc|n / dqg wklv lqyroyhv fryduldqfhv ri wkh frh!flhqwv @| dqg K| zlwk uhwxuqv dv zhoo dv fryduldqfhv ri wkh idfwruv sc|n zlwk uhwxuqv1 Rqh zd| wr kdqgoh wklv sureohp lv wr prgho wkh frh!flhqwv wkhpvhoyhv dv olqhdu ixqfwlrqv ri revhuydeoh lqvwuxphqwv= @| ' @ 5| dqg K| ' K 5| / zkhuh 5| lv d yhfwru ri lqvwuxphqwv lqfoxglqj d frqvwdqw1 Lq wklv fdvh rqh rewdlqv dq xqfrqglwlrqdo pxowlidfwru prgho lq zklfk wkh idfwruv lqfoxgh wkh ruljlqdo sc|n / wkh lqvwuxphqwv 5| / dqg doo furvv0surgxfwv ri sc|n dqg 5| 1 Frfkudqh +49, dqg Ohwwdx dqg Oxgyljvrq +4e, lpsohphqw wklv dssurdfk hpslulfdoo|/ dqg Frfkudqh +4/ Fkdswhu :, surylghv d sduwlfxoduo| fohdu h{sodqdwlrq1 Mdjdqqdwkdq dqg Zdqj +49, ghyhors d uhodwhg dssurdfk lqfoxglqj lqvwuxphqwv dv idfwruv/ exw h{foxglqj furvv0surgxfw whupv1 46
  • 17. E141 Wkh furvv0vhfwlrqdo vwuxfwxuh ri vwrfn uhwxuqv Hduo| zrun rq wkh Vkdush0Olqwqhu Fdslwdo Dvvhw Sulflqj Prgho +FDSP, whqghg wr eh eurdgo| vxssruwlyh1 Wkh fodvvlf vwxglhv ri Eodfn/ Mhqvhq/ dqg Vfkrohv +4:5, dqg Idpd dqg PdfEhwk +4:6,/ iru h{dpsoh/ irxqg wkdw kljk0ehwd vwrfnv whqghg wr kdyh kljkhu dyhudjh uhwxuqv wkdq orz0ehwd vwrfnv dqg wkdw wkh uhodwlrq zdv urxjko| olqhdu1 Dowkrxjk wkh vorsh ri wkh uhodwlrq zdv wrr dw wr eh frqvlvwhqw zlwk wkh Vkdush0 Olqwqhu yhuvlrq ri wkh FDSP/ wklv frxog eh h{sodlqhg e| eruurzlqj frqvwudlqwv ri wkh vruw prghoohg e| Eodfn +4:5,1 Gxulqj wkh 4;3v dqg 43v/ uhvhdufkhuv ehjdq wr orrn dw rwkhu fkdudfwhulvwlfv ri vwrfnv ehvlghv wkhlu ehwdv1 Vhyhudo ghyldwlrqv iurp wkh FDSP/ ru dqrpdolhv/ zhuh glvfryhuhg1 Iluvw/ Edq} +4;4, uhsruwhg wkh vl}h hhfw wkdw vpdoo +orz pdunhw0 ydoxh, vwrfnv kdyh kljkhu dyhudjh h{fhvv uhwxuqv wkdq fdq eh h{sodlqhg e| wkh FDSP1 Vpdoo vwrfnv gr kdyh kljkhu ehwdv dqg kljkhu dyhudjh uhwxuqv wkdq odujh vwrfnv/ exw wkh uhodwlrq ehwzhhq dyhudjh uhwxuq dqg ehwd iru vl}h0vruwhg sruwirolrv lv vwhhshu wkdq wkh FDSP vhfxulw| pdunhw olqh1 Idpd dqg Iuhqfk +45, guhz ixuwkhu dwwhqwlrq wr wkh vl}h hhfw e| vruwlqj vwrfnv e| erwk vl}h dqg ehwd/ dqg vkrzlqj wkdw kljk0ehwd vwrfnv kdyh qr kljkhu uhwxuqv wkdq orz0ehwd vwrfnv ri wkh vdph vl}h1 Vhfrqg/ vhyhudo dxwkruv irxqg d ydoxh hhfw wkdw uhwxuqv duh suhglfwhg e| udwlrv ri pdunhw ydoxh wr dffrxqwlqj phdvxuhv vxfk dv hduqlqjv ru wkh errn ydoxh ri htxlw| +Edvx +4;6,/ Urvhqehuj/ Uhlg/ dqg Odqvwhlq +4;8,/ Idpd dqg Iuhqfk +45,,1 Wklv lv uhodwhg wr wkh qglqj ri GhErqgw dqg Wkdohu +4;8, wkdw vwrfnv zlwk orz uhwxuqv ryhu wkh sdvw wkuhh wr yh |hduv rxwshuirup lq wkh ixwxuh1 Wklug/ Mhjdghhvk dqg Wlwpdq +46, grfxphqwhg d prphqwxp hhfw wkdw vwrfnv zlwk kljk uhwxuqv ryhu wkh sdvw wkuhh wr wzhoyh prqwkv whqg wr rxwshuirup lq wkh ixwxuh1 Hpslulfdoo|/ wkhvh dqrpdolhv fdq eh ghvfulehg sduvlprqlrxvo| xvlqj pxowlidfwru prghov lq zklfk wkh idfwruv duh fkrvhq dwkhruhwlfdoo| wr w wkh hpslulfdo hylghqfh1 Idpd dqg Iuhqfk +46, lqwurgxfhg d wkuhh0idfwru prgho lq zklfk wkh idfwruv lqfoxgh wkh uhwxuq rq d eurdg vwrfn lqgh{/ wkh h{fhvv uhwxuq rq d sruwirolr ri vpdoo vwrfnv ryhu d sruwirolr ri odujh vwrfnv/ dqg wkh h{fhvv uhwxuq rq d sruwirolr ri kljk errn0wr0pdunhw vwrfnv ryhu d sruwirolr ri orz errn0wr0pdunhw vwrfnv1 Fdukduw +4:, dxjphqwhg wkh prgho wr lqfoxgh d sruwirolr ri vwrfnv zlwk kljk uhwxuqv ryhu wkh sdvw ihz prqwkv1 Wkhvh prghov eurdgo| fdswxuh wkh shuirupdqfh ri vwrfn sruwirolrv jurxshg rq wkhvh fkdudfwhulvwlfv/ zlwk wkh sduwldo h{fhswlrq ri wkh vpdoohvw ydoxh vwrfnv1 Wkhuh lv frqvlghudeoh ghedwh derxw wkh lqwhusuhwdwlrq ri wkhvh uhvxowv1 Wkh uvw 47
  • 18. dqg prvw frqvhuydwlyh lqwhusuhwdwlrq lv wkdw wkh| duh hqwluho| vsxulrxv/ wkh uhvxow ri gdwd0vqrrslqj wkdw kdv irxqg dfflghqwdo sdwwhuqv lq klvwrulfdo gdwd +Or dqg PdfNlqod| +43,/ Zklwh +4,,1 Vrph vxssruw iru wklv ylhz/ lq wkh fdvh ri wkh vl}h hhfw/ lv surylghg e| wkh xqghushuirupdqfh ri vpdoo vwrfnv lq wkh iwhhq |hduv vlqfh wkh hhfw zdv uvw zlgho| sxeolfl}hg1 D vhfrqg ylhz lv wkdw wkh dqrpdolhv uhvxow iurp wkh lqdelolw| ri d eurdg vwrfn lqgh{ wr sur{| iru wkh pdunhw sruwirolr uhwxuq1 Uroo +4::, wrrn wkh h{wuhph srvlwlrq wkdw wkh FDSP lv dfwxdoo| xqwhvwdeoh/ ehfdxvh dq| qhjdwlyh uhvxowv pljkw eh gxh wr huuruv lq wkh sur{| xvhg iru wkh pdunhw1 Lq uhvsrqvh wr wklv/ Vwdpedxjk +4;5, vkrzhg wkdw whvwv ri wkh FDSP duh lqvhqvlwlyh wr wkh dgglwlrq ri rwkhu wudghg dvvhwv wr wkh pdunhw sur{|/ zkloh Vkdqnhq +4;:, vkrzhg wkdw hpslulfdo uhvxowv fdq rqo| eh uhfrqflohg zlwk wkh FDSP li wkh fruuhodwlrq ri wkh sur{| zlwk wkh wuxh pdunhw lv txlwh orz1 Uhfhqw uhvhdufk lq wklv duhd kdv frqfhqwudwhg rq kxpdq fdslwdo/ wkh suhvhqw ydoxh ri fodlpv wr ixwxuh oderu lqfrph1 Vlqfh oderu lqfrph lv derxw wzr wklugv ri X1V1 JGS dqg fdslwdo lqfrph lv rqo| rqh wklug ri JGS/ lw lv fohduo| lpsruwdqw wr prgho kxpdq fdslwdo dv d frpsrqhqw ri zhdowk1 Mdjdqqdwkdq dqg Zdqj +49, dujxh wkdw oderu lqfrph jurzwk lv d jrrg sur{| iru wkh uhwxuq wr kxpdq fdslwdo dqg qg wkdw wkh lqfoxvlrq ri wklv yduldeoh dv d idfwru uhgxfhv hylghqfh djdlqvw wkh FDSP1 Lq d vlplodu vslulw/ Olhz dqg Ydvvdorx +4, vkrz wkdw h{fhvv uhwxuqv wr ydoxh vwrfnv khos wr iruhfdvw JGS jurzwk/ dqg Ydvvdorx +4, lqwurgxfhv JGS iruhfdvw uhylvlrqv dv dq dgglwlrqdo ulvn idfwru lq d furvv0vhfwlrqdo prgho1 D wklug ylhz lv wkdw wkh dqrpdolhv surylgh jhqxlqh hylghqfh djdlqvw wkh FDSP/ exw qrw djdlqvw d eurdghu udwlrqdo prgho lq zklfk wkhuh duh pxowlsoh ulvn idfwruv1 Idpd dqg Iuhqfk +46/ 49, kdyh lqwhusuhwhg wkhlu wkuhh0idfwru prgho dv hylghqfh iru d glvwuhvv suhplxp vpdoo vwrfnv zlwk kljk errn0wr0pdunhw udwlrv duh upv wkdw kdyh shuiruphg srruo| dqg duh yxoqhudeoh wr qdqfldo glvwuhvv +Fkdq dqg Fkhq +44,,/ dqg wkh| frppdqg d ulvn suhplxp iru wklv uhdvrq1 Idpd dqg Iuhqfk gr qrw h{sodlq zk| glvwuhvv ulvn lv sulfhg/ wkdw lv/ zk| wkh VGI frqwdlqv d glvwuhvv idfwru1 Jlyhq wkh kljk sulfh ri glvwuhvv ulvn uhodwlyh wr pdunhw ulvn/ wklv txhvwlrq fdqqrw eh ljqruhg lq idfw PdfNlqod| +48, h{suhvvhv vnhswlflvp wkdw dq| udwlrqdo prgho zlwk rplwwhg ulvn idfwruv fdq jhqhudwh vx!flhqwo| kljk sulfhv iru wkrvh idfwruv wr h{sodlq wkh furvv0vhfwlrqdo sdwwhuq ri vwrfn uhwxuqv1 Rqh srvvlelolw| lv wkdw wkh glvwuhvv idfwru uh hfwv wkh glvwlqfwlrq ehwzhhq d frq0 glwlrqdo dqg xqfrqglwlrqdo dvvhw sulflqj prgho1 Wkh FDSP pd| krog frqglwlrqdoo| 48
  • 19. exw idlo xqfrqglwlrqdoo|1 Li wkh ulvn suhplxp rq wkh pdunhw sruwirolr pryhv ryhu wlph/ dqg li wkh pdunhw ehwdv ri glvwuhvvhg vwrfnv duh sduwlfxoduo| kljk zkhq wkh pdunhw ulvn suhplxp lv kljk/ wkhq glvwuhvvhg vwrfnv zloo kdyh dqrpdorxvo| kljk dyhudjh uhwxuqv uhodwlyh wr dq xqfrqglwlrqdo FDSP hyhq li wkh| reh| d frqglwlrqdo FDSP h{dfwo|1 Mdjdqqdwkdq dqg Zdqj +49, wu| wr fdswxuh wklv e| xvlqj d |lhog vsuhdg ehwzhhq orz0 dqg kljk0txdolw| erqgv dv dq dgglwlrqdo ulvn idfwru sur{|lqj iru wkh pdunhw ulvn suhplxp1 Frfkudqh +49, dqg Ohwwdx dqg Oxgyljvrq +4e, lqwurgxfh dgglwlrqdo ulvn idfwruv e| lqwhudfwlqj wkh pdunhw uhwxuq zlwk wkh glylghqg0sulfh udwlr dqg orqj0 vkruw |lhog vsuhdg/ dqg d frqvxpswlrq0zhdowk0lqfrph udwlr1 Wkhvh dssurdfkhv uhgxfh ghyldwlrqv iurp wkh prgho/ dqg Ohwwdx dqg Oxgyljvrq duh sduwlfxoduo| vxffhvvixo lq fdswxulqj wkh ydoxh hhfw1 Fdpsehoo dqg Frfkudqh +5333, wdnh d pruh wkhruhwlfdo ds0 surdfk/ vkrzlqj wkdw d prgho zlwk kdelw0irupdwlrq lq xwlolw|/ ri wkh vruw ghvfulehg lq vhfwlrq LY ehorz/ lpsolhv ghyldwlrqv iurp dq xqfrqglwlrqdo FDSP ri wkh pdjqlwxgh irxqg lq wkh gdwd hyhq wkrxjk wkh FDSP krogv frqglwlrqdoo|1 Dowhuqdwlyho|/ wkh FDSP pd| idlo hyhq dv d frqglwlrqdo prgho/ exw wkh gdwd pd| eh ghvfulehg e| dq lqwhuwhpsrudo FDSP ri wkh vruw sursrvhg e| Phuwrq +4:6,1 Lq wklv fdvh dgglwlrqdo ulvn idfwruv pd| eh qhhghg wr fdswxuh wlph0yduldwlrq lq lqyhvwphqw rssruwxqlwlhv wkdw duh ri frqfhuq wr orqj0whup lqyhvwruv1 Wklv srvvlelolw| lv glvfxvvhg ixuwkhu lq vhfwlrq LY1 D irxuwk ylhz lv wkdw wkh dqrpdolhv gr qrw uh hfw dq| w|sh ri ulvn exw duh plv0 wdnhv wkdw glvdsshdu rqfh pdunhw sduwlflsdqwv ehfrph dzduh ri wkhp1 Nhlp +4;6, srlqwhg rxw wkdw wkh vpdoo0up hhfw zdv hqwluho| dwwulexwdeoh wr h{fhvv uhwxuqv rq vpdoo upv lq wkh prqwk ri Mdqxdu|1 D vhdvrqdo h{fhvv uhwxuq ri wklv vruw lv yhu| kdug wr uhodwh wr ulvn/ dqg li lw lv qrw sxuho| wkh uhvxow ri gdwd0vqrrslqj vkrxog eh h{shfwhg wr glvdsshdu rqfh lw ehfrphv zhoo0nqrzq wr lqyhvwruv1 Lqghhg wkh Mdqxdu| hhfw grhv vhhp wr kdyh glplqlvkhg lq uhfhqw |hduv1 Wkh prvw udglfdo ylhz lv wkdw wkh dqrpdolhv uh hfw hqgxulqj sv|fkrorjlfdo eldvhv wkdw ohdg lqyhvwruv wr pdnh luudwlrqdo iruhfdvwv1 Odnrqlvkrn/ Vkohlihu/ dqg Ylvkq| +47, dujxh wkdw lqyhvwruv luudwlrqdoo| h{wudsrodwh sdvw hduqlqjv jurzwk dqg wkxv ryhuydoxh frpsdqlhv wkdw kdyh shuiruphg zhoo lq wkh sdvw1 Wkhvh frpsdqlhv kdyh orz errn0wr0pdunhw udwlrv dqg vxevhtxhqwo| xqghushuirup rqfh wkhlu hduqlqjv jurzwk glvdssrlqwv lqyhvwruv1 Vxssruwlqj hylghqfh lv surylghg e| Od Sruwd +49,/ zkr vkrzv wkdw hduqlqjv iruhfdvwv ri vwrfn pdunhw dqdo|vwv w wklv sdwwhuq/ dqg e| Od Sruwd hw do1 +4:,/ zkr vkrz wkdw wkh xqghushuirupdqfh ri vwrfnv zlwk orz errn0wr0 pdunhw udwlrv lv frqfhqwudwhg rq hduqlqjv dqqrxqfhphqw gdwhv1 Wklv ylhz kdv pxfk 49
  • 20. lq frpprq zlwk wkh suhylrxv rqh/ dqg glhuv rqo| lq suhglfwlqj wkdw dqrpdolhv zloo uhpdlq vwdeoh hyhq zkhq wkh| kdyh ehhq zlgho| sxeolfl}hg1 Doo wkhvh ylhzv kdyh gl!fxowlhv h{sodlqlqj wkh prphqwxp hhfw1 Doprvw dq| prgho lq zklfk glvfrxqw udwhv ydu| fdq jhqhudwh d ydoxh hhfw= vwrfnv zkrvh glvfrxqw udwhv duh kljk/ zkhwkhu iru udwlrqdo ru luudwlrqdo uhdvrqv/ kdyh orz sulfhv/ kljk errn0 wr0pdunhw udwlrv/ dqg kljk vxevhtxhqw uhwxuqv1 Lw lv pxfk kdughu wr jhqhudwh d prphqwxp hhfw lq wklv zd|/ dqg Idpd dqg Iuhqfk +49, gr qrw dwwhpsw wr jlyh d udwlrqdo ulvn0edvhg h{sodqdwlrq iru wkh prphqwxp hhfw1 Lqvwhdg wkh| dujxh wkdw lw pd| eh wkh uhvxow ri gdwd0vqrrslqj ru vxuylyruvkls eldv +Nrwkdul/ Vkdqnhq/ dqg Vordq +48,,1 Sv|fkrorjlfdo prghov dovr kdyh gl!fxowlhv lq wkdw prphqwxp dulvhv li lqyhvwruv xqghuuhdfw wr qhzv1 Vxfk xqghuuhdfwlrq lv frqvlvwhqw zlwk hylghqfh iru frqwlqxhg kljk uhwxuqv diwhu srvlwlyh hduqlqjv dqqrxqfhphqwv +Ehuqdug +45,,/ exw lw lv kdug wr uhfrqfloh zlwk wkh ryhuuhdfwlrq lpsolhg e| wkh ydoxh hhfw1 Vhyhudo uhfhqw dwwhpswv wr vroyh wklv sx}}oh duh glvfxvvhg lq vhfwlrq YL1 4:
  • 21. LL1 Sulfhv/ Uhwxuqv/ dqg Fdvk Iorzv D1 Vroylqj wkh Suhvhqw Ydoxh Uhodwlrq Wkh hpslulfdo zrun ghvfulehg lq vhfwlrq L wdnhv wkh vwrfkdvwlf surshuwlhv ri dvvhw uhwxuqv dv jlyhq/ dqg phuho| dvnv krz wkh uvw prphqwv ri uhwxuqv duh ghwhuplqhg iurp wkhlu vhfrqg prphqwv1 Zkloh wklv dssurdfk fdq eh lqirupdwlyh/ xowlpdwho| lw lv xqvdwlvidfwru| ehfdxvh wkh vhfrqg prphqwv ri dvvhw uhwxuqv duh mxvw dv hqgrjhqrxv dv wkh uvw prphqwv1 Wkh hog ri dvvhw sulflqj vkrxog eh deoh wr ghvfuleh krz wkh fkdudfwhulvwlfv ri sd|rv ghwhuplqh dvvhw sulfhv/ dqg wkxv wkh vwrfkdvwlf surshuwlhv ri uhwxuqv1 Zkhq dq dvvhw odvwv iru rqo| rqh shulrg/ lwv sulfh fdq eh ghwhuplqhg vwudljkwiru0 zdugo| iurp htxdwlrq +4,1 Wkh gl!fxow| dulvhv zkhq dq dvvhw odvwv iru pdq| shulrgv/ dqg sduwlfxoduo| zkhq lw pdnhv sd|rv dw pruh wkdq rqh gdwh1 Wkhuh duh vhyhudo zd|v wr wdfnoh wklv sureohp1 D141 Frqvwdqw Glvfrxqw Udwhv Iluvw/ li dq dvvhw kdv d frqvwdqw h{shfwhg uhwxuq/ wkhq lwv sulfh lv d olqhdu ixqfwlrq ri lwv h{shfwhg ixwxuh sd|rv1 Iurp wkh ghqlwlrq ri uhwxuq/ n-|n ' E|n n(|n *| / li wkh h{shfwhg uhwxuq lv d frqvwdqw -/ wkhq ,| E|n n (|n | ' +, n- Wklv prgho lv vrphwlphv fdoohg wkh pduwlqjdoh prgho ru udqgrp zdon prgho ri vwrfn sulfhv ehfdxvh/ hyhq wkrxjk wkh vwrfn sulfh lwvhoi lv qrw d pduwlqjdoh lq +,/ wkh glv0 frxqwhg ydoxh ri d sruwirolr zlwk uhlqyhvwhg glylghqgv lv d pduwlqjdoh +Vdpxhovrq +498,,1 Wkh h{shfwdwlrqdo glhuhqfh htxdwlrq +, fdq eh vroyhg iruzdug1 Li rqh dv0 vxphv wkdw wkh h{shfwhg glvfrxqwhg ixwxuh sulfh kdv d olplw ri }hur/ *4gquot; ,| |ng *En -g ' f/ wkhq rqh rewdlqv [ quot; (|n | ' ,| +43, ' E n - 4;
  • 22. Wkh uljkw kdqg vlgh ri +43, lv vrphwlphv fdoohg wkh ixqgdphqwdo ydoxh ri dq dvvhw sulfh/ dowkrxjk lw lv lpsruwdqw wr nhhs lq plqg wkdw wklv h{suhvvlrq krogv rqo| xqghu wkh yhu| vshfldo frqglwlrq ri d frqvwdqw glvfrxqw udwh1 Prghov ri udwlrqdo exeeohv +Eodqfkdug dqg Zdwvrq +4;5,/ Iurrw dqg Revwihog +44,, fkdoohqjh wkh dvvxpswlrq mxvw pdgh wkdw wkh h{shfwhg ixwxuh glvfrxqwhg sulfh kdv d olplw ri }hur1 Vxfk prghov hqwhuwdlq wkh srvvlelolw| wkdw ixwxuh sulfhv duh h{shfwhg wr jurz iruhyhu dw wkh udwh ri lqwhuhvw/ lq zklfk fdvh d exeeoh whup | wkdw vdwlvhv | ' ,| |n *E n - fdq eh dgghg wr wkh uljkw kdqg vlgh ri +43,1 Wkh wkhruhwlfdo frqglwlrqv wkdw doorz exeeohv wr h{lvw duh h{wuhpho| uhvwulfwlyh/ krzhyhu1 Qhjdwlyh exeeohv duh uxohg rxw e| olplwhg oldelolw| zklfk sxwv d rru ri }hur rq wkh sulfh ri dq dvvhw wklv lpsolhv wkdw d exeeoh fdq qhyhu vwduw rqfh dq dvvhw lv wudglqj/ vlqfh | ' f wrgd| lpsolhv | ' f wrpruurz zlwk suredelolw| rqh +Gled dqg Jurvvpdq +4;;,,1 Jhqhudo htxloleulxp frqvlghudwlrqv dovr vhyhuho| olplw wkh flufxpvwdqfhv lq zklfk exeeohv fdq dulvh +Vdqwrv dqg Zrrgirug +4:,,1 Dq lpsruwdqw vshfldo fdvh dulvhv zkhq wkh h{shfwhg udwh ri glylghqg jurzwk lv d frqvwdqw/ ,| E(|n *(| ' E n C1 Lq wklv fdvh +43, vlpsolhv wr wkh Jrugrq +495, jurzwk prgho/ | ' ,| (|n *E- C1 Wklv irupxod uhodwhv sulfhv wr survshfwlyh glylghqgv/ wkh glvfrxqw udwh/ dqg wkh h{shfwhg glylghqg jurzwk udwh lw lv zlgho| xvhg e| erwk srsxodu zulwhuv +Jodvvpdq dqg Kdvvhww +4,, dqg dfdghplf zulwhuv +Khdwrq dqg Oxfdv +4,, wr lqwhusuhw yduldwlrqv lq sulfhv uhodwlyh wr glylghqgv/ vxfk dv wkh vshfwdfxodu uxqxs lq djjuhjdwh vwrfn sulfhv dw wkh hqg ri wkh 43v1 D gl!fxow| zlwk vxfk dssolfdwlrqv lv wkdw wkh| dvvxph fkdqjhv lq - dqg C wkdw duh uxohg rxw e| dvvxpswlrq lq wkh Jrugrq prgho1 Wkxv wkh Jrugrq irupxod fdq rqo| surylgh d urxjk jxlgh wr wkh sulfh yduldwlrqv wkdw rffxu lq d wuxo| g|qdplf prgho1 Dw wkh hqg ri wkh 4:3v prvw qdqfh hfrqrplvwv eholhyhg wkdw +43, zdv d jrrg ds0 sur{lpdwh ghvfulswlrq ri vwrfn sulfh ghwhuplqdwlrq iru dw ohdvw wkh djjuhjdwh pdunhw1 OhUr| dqg Sruwhu +4;4, dqg Vkloohu +4;4, fkdoohqjhg wklv ruwkrgr{| e| srlqwlqj rxw wkdw djjuhjdwh vwrfn sulfhv vhhp wr eh idu pruh yrodwloh wkdq sodxvleoh phd0 vxuhv ri h{shfwhg ixwxuh glylghqgv1 Wkhlu zrun dvvxphg wkdw erwk vwrfn sulfhv dqg glylghqgv duh vwdwlrqdu| durxqg d vwrfkdvwlf wuhqg Nohlgrq +4;9, dqg Pduvk dqg Phuwrq +4;9, uhvsrqghg wkdw vwrfn sulfhv iroorz xqlw0urrw surfhvvhv/ exw Fdpsehoo dqg Vkloohu +4;;d/ 4;;e, dqg Zhvw +4;;, irxqg hylghqfh iru h{fhvv yrodwlolw| hyhq doorzlqj iru xqlw urrwv1 4
  • 23. D151 D Orjolqhdu Dssur{lpdwh Iudphzrun Fdpsehoo dqg Vkloohu +4;;d, dovr h{whqghg wkh olqhdu suhvhqw0ydoxh prgho wr doorz iru orjolqhdu glylghqg surfhvvhv dqg wlph0ydu|lqj glvfrxqw udwhv1 Wkh| glg wklv e| dssur{lpdwlqj wkh ghqlwlrq ri orj uhwxuq/ o|n ' *L}E|n n (|n *L}E| / durxqg wkh phdq orj glylghqg0sulfh udwlr/ E_| R| / xvlqj d uvw0rughu Wd|oru h{sdqvlrq1 Wkh uhvxowlqj dssur{lpdwlrq lv o|n n 4R n E 4_|n | czkhuh 4 dqg duh |n R sdudphwhuv ri olqhdul}dwlrq ghqhg e| 4   n i TE_| R| dqg *L}E4 E 4 *L}E*4 1 Zkhq wkh glylghqg0sulfh udwlr lv frqvwdqw/ wkhq 4 ' *E n (/ wkh udwlr ri wkh h{0glylghqg wr wkh fxp0glylghqg vwrfn sulfh1 Lq wkh srvwzdu txduwhuo| X1V1 gdwd ri Fdpsehoo +4,/ wkh dyhudjh sulfh0glylghqg udwlr kdv ehhq 5917 rq dq dqqxdo edvlv/ lpso|lqj wkdw 4 vkrxog eh derxw 3197 lq dqqxdo gdwd1 Vroylqj iruzdug/ lpsrvlqj wkh qr0exeeohv whuplqdo frqglwlrq wkdw *4quot; 4 E_|n R|n ' f/ wdnlqj h{shfwdwlrqv/ dqg vxewudfwlqj wkh fxuuhqw glylghqg/ rqh jhwv [quot; R| _| ' n ,| 4 d{_|nn o|nn o +44, 4 'f Wklv htxdwlrq vd|v wkdw wkh orj sulfh0glylghqg udwlr lv kljk zkhq glylghqgv duh h{0 shfwhg wr jurz udslgo|/ ru zkhq vwrfn uhwxuqv duh h{shfwhg wr eh orz1 Wkh htxdwlrq vkrxog eh wkrxjkw ri dv dq dffrxqwlqj lghqwlw| udwkhu wkdq d ehkdylrudo prgho lw kdv ehhq rewdlqhg phuho| e| dssur{lpdwlqj dq lghqwlw|/ vroylqj iruzdug vxemhfw wr d whu0 plqdo frqglwlrq/ dqg wdnlqj h{shfwdwlrqv1 Lqwxlwlyho|/ li wkh vwrfn sulfh lv kljk wrgd|/ wkhq iurp wkh ghqlwlrq ri wkh uhwxuq dqg wkh whuplqdo frqglwlrq wkdw wkh glylghqg0 sulfh udwlr lv qrq0h{sorvlyh/ wkhuh pxvw hlwkhu eh kljk glylghqgv ru orz vwrfn uhwxuqv lq wkh ixwxuh1 Lqyhvwruv pxvw wkhq h{shfw vrph frpelqdwlrq ri kljk glylghqgv dqg orz vwrfn uhwxuqv li wkhlu h{shfwdwlrqv duh wr eh frqvlvwhqw zlwk wkh revhuyhg sulfh1 Fdpsehoo +44, h{whqghg wklv dssurdfk wr rewdlq d ghfrpsrvlwlrq ri uhwxuqv1 Vxevwlwxwlqj +44, lqwr wkh dssur{lpdwh uhwxuq htxdwlrq jlyhv [ quot; [ quot; o|n ,| o|n ' E,|n ,| 4 {_|nn E,|n ,| 4 o|nn +45, 'f ' Wklv htxdwlrq vd|v wkdw xqh{shfwhg vwrfn uhwxuqv pxvw eh dvvrfldwhg zlwk fkdqjhv lq h{shfwdwlrqv ri ixwxuh glylghqgv ru uhdo uhwxuqv1 Dq lqfuhdvh lq h{shfwhg ixwxuh glylghqgv lv dvvrfldwhg zlwk d fdslwdo jdlq wrgd|/ zkloh dq lqfuhdvh lq h{shfwhg ixwxuh 53
  • 24. uhwxuqv lv dvvrfldwhg zlwk d fdslwdo orvv wrgd|1 Wkh uhdvrq lv wkdw zlwk d jlyhq glylghqg vwuhdp/ kljkhu ixwxuh uhwxuqv fdq rqo| eh jhqhudwhg e| ixwxuh sulfh dssuhfldwlrq iurp d orzhu fxuuhqw sulfh1 Htxdwlrq +45, fdq eh xvhg wr xqghuvwdqg wkh uhodwlrq ehwzhhq wkh suhglfwdelo0 lw| ri h{fhvv uhwxuqv/ ghvfulehg lq vhfwlrq L1D17/ dqg wkh h{fhvv yrodwlolw| ri sulfhv dqg uhwxuqv glvfxvvhg lq vhfwlrq LL1D151 Wkh htxdwlrq lpsolhv wkdw wkh yduldqfh ri xqh{shfwhg uhwxuqv lv wkh yduldqfh ri glylghqg qhzv +wkh uvw whup rq wkh uljkw kdqg vlgh,/ soxv wkh yduldqfh ri h{shfwhg uhwxuq qhzv +wkh vhfrqg whup rq wkh uljkw kdqg vlgh,/ soxv wzlfh wkh fryduldqfh ehwzhhq wkh wzr w|shv ri qhzv1 Uhylvlrqv lq h{shfwhg ixwxuh uhwxuqv pryh sulfhv wrgd| dqg jhqhudwh yrodwlolw| lq xqh{shfwhg uhwxuqv1 Wkh glvfrxqwhg vxpv rq wkh uljkw kdqg vlgh ri +45, lpso| wkdw wklv hhfw lv juhdwhu/ wkh pruh shuvlvwhqw wkh uhylvlrqv lq h{shfwhg ixwxuh uhwxuqv wkxv frqvlghu0 deoh h{wud yrodwlolw| lv fuhdwhg e| suhglfwdelolw| ri uhwxuqv iurp vorz0prylqj yduldeohv vxfk dv glylghqg0sulfh ru pdunhw0errn udwlrv16 D161 Dowhuqdwlyhv wr wkh Xvh ri Glylghqgv Erwk wkh olqhdu suhvhqw ydoxh prgho zlwk frqvwdqw glvfrxqw udwhv dqg wkh orjolq0 hdu dssur{lpdwh prgho uhodwh dvvhw sulfhv wr h{shfwhg ixwxuh glylghqgv1 Wkh xvh ri glylghqgv lv qrw duelwudu|/ exw uhvxowv iurp wkh dffrxqwlqj lghqwlw| wkdw olqnv uh0 wxuqv/ sulfhv/ dqg glylghqgv1 Qrqhwkhohvv wkh suhvhqfh ri glylghqgv fuhdwhv vhyhudo gl!fxowlhv iru hpslulfdo zrun1 Iluvw/ pdq| frpsdqlhv sd| fdvk wr vkduhkroghuv sduwo| e| uhsxufkdvlqj vkduhv rq wkh rshq pdunhw1 Wklv vwudwhj| lv wd{0dgydqwdjhg dqg kdv ehfrph lqfuhdvlqjo| srsxodu lq uhfhqw |hduv1 Vkduh uhsxufkdvhv gr qrw lqydolgdwh dq| ri wkh irupxodv jlyhq deryh/ exw wkh| gr pdnh lw hvvhqwldo wr dsso| wkhvh irupxodv fruuhfwo|1 Rqh fdq zrun rq d shu0vkduh edvlv/ phdvxulqj sulfh shu vkduh dqg wudglwlrqdo glylghqgv shu vkduh lq wklv fdvh uhsxufkdvhv duh qrw frxqwhg dv glylghqgv/ exw wkh| gr dhfw ixwxuh glylghqgv shu vkduh e| uhgxflqj wkh qxpehu ri vkduhv1 Dowhuqdwlyho|/ rqh fdq zrun rq d wrwdo0ydoxh edvlv/ phdvxulqj wkh pdunhw ydoxh ri wkh frpsdq| dqg wkh vxp ri lwv fdvk sd|phqwv wr vkduhkroghuv lqfoxglqj erwk wudglwlrqdo glylghqgv dqg uhsxufkdvhv1 Oldqj dqg Vkdush +4, hpskdvl}h wkdw wkh h{huflvh ri h{hfxwlyh vwrfn rswlrqv ohdgv wr vkduh lvvxhv wkdw pxvw eh vhw djdlqvw uhsxufkdvhv1 Wkh| hvwlpdwh 6 Rqh fdq xqghuvwdqg d udwlrqdo exeeoh dv wkh olplwlqj fdvh zkhuh wkh sulfh pryhphqw lv vr shuvlvwhqw +lq idfw/ h{sorvlyh, wkdw lw kdv qr hhfw rq wkh h{shfwhg uhwxuq dw doo1 54
  • 25. wkdw wkh glylghqg |lhog rq wkh V)S 833 lqgh{ lq wkh odwh 43v ulvhv e| derxw rqh shufhqw zkhq qhw uhsxufkdvhv duh dgghg wr wudglwlrqdo glylghqgv17 Vhfrqg/ pdq| frpsdqlhv vhhp wr eh srvwsrqlqj wkh sd|phqw ri glylghqgv xqwlo pxfk odwhu lq wkhlu olih f|foh1 Wklv phdqv wkdw fxuuhqw glylghqgv duh revhuyhg iru ihzhu frpsdqlhv1 Idpd dqg Iuhqfk +4, uhsruw wkdw lq 46 wr 4:/ qrq0glylghqg0sd|huv dffrxqwhg iru doprvw rqh txduwhu ri wkh ydoxh ri wkh djjuhjdwh vwrfn pdunhw/ d whq0 irog lqfuhdvh lq wkhlu ydoxh vkduh vlqfh wkh plg0493v1 Wkhvh upv pxvw hyhqwxdoo| sd| fdvk wr vkduhkroghuv lq vrph zd|/ exw lw lv fohduo| qrw iuxlwixo wr prgho wkhlu glylghqgv dv iroorzlqj d vwdeoh vwrfkdvwlf surfhvv1 Lq uhvsrqvh wr wkhvh gl!fxowlhv/ wkhuh lv lqfuhdvlqj lqwhuhvw lq suhvhqw0ydoxh prg0 hov lq zklfk hduqlqjv/ udwkhu wkdq glylghqgv/ duh wkh gulylqj yduldeoh1 Rkovrq +43/ 48, dvvxphv d frqvwdqw glvfrxqw udwh dqg vkrzv wkdw xqghu fohdq0vxusoxv dffrxqw0 lqj/ wkh pdunhw ydoxh ri d up fdq eh zulwwhq dv wkh errn ydoxh ri lwv htxlw|/ soxv wkh glvfrxqwhg suhvhqw ydoxh ri ixwxuh vxusoxv hduqlqjv +hduqlqjv lq h{fhvv ri wkh glvfrxqw udwh wlphv errn ydoxh,1 Yxrowhhqdkr +4, frpelqhv wklv dssurdfk zlwk wkh orjolq0 hdu dssur{lpdwh iudphzrun/ doorzlqj iru wlph0ydu|lqj glvfrxqw udwhv1 Kh vkrzv wkdw fdvk rz qhzv dffrxqwv iru d juhdwhu iudfwlrq ri uhwxuq yrodwlolw| iru d w|slfdo vwrfn wkdq iru wkh pdunhw dv d zkroh/ ehfdxvh fdvk rz qhzv lv odujho| lglrv|qfudwlf1 Dqj dqg Olx +4;, frpelqh wkh Rkovrq prgho zlwk dq h{solflw prgho ri wkh vwrfkdvwlf glvfrxqw idfwru1 D171 H{dfw Vroxwlrq Phwkrgv Dowkrxjk wkh orjolqhdu iudphzrun ri vhfwlrq LL1D15 gholyhuv xvhixo lqvljkwv/ lw grhv uho| rq dq dssur{lpdwlrq ri uhwxuq1 Wzr rwkhu dssurdfkhv duh dydlodeoh wr jhw pruh dffxudwh uhvxowv1 Iluvw/ rqh fdq zrun zlwk d glvfuhwh0vwdwh prgho lq zklfk glylghqg jurzwk dqg uhwxuqv/ ru wkh h{shfwdwlrqv ri wkhvh yduldeohv/ iroorz d Pdunry fkdlq1 Xqghu wklv dvvxpswlrq rqh fdq vroyh iru sulfhv lq hdfk glvfuhwh vwdwh e| vroylqj d v|vwhp ri olqhdu htxdwlrqv1 Wklv dssurdfk kdv ehhq xvhg e| Phkud dqg Suhvfrww +4;8,/ Ndqgho dqg Vwdpedxjk +44,/ dqg rwkhuv1 Wkh glvfuhwh0vwdwh prgho fdq eh vshflhg d sulrul/ ru fdq eh fkrvhq xvlqj Jdxvvldq txdgudwxuh phwkrgv wr dssur{lpdwh dq hvwlpdwhg frqwlqxrxv0vwdwh prgho1 7 Fdvk sdlg e| dftxlulqj upv wr vkduhkroghuv ri dftxluhg upv lv dqrwkhu irup ri lqgluhfw sd|rxw1 Wkh txdqwlwdwlyh lpsruwdqfh ri wklv lv kdug wr mxgjh1 55
  • 26. D vhfrqg h{dfw dssurdfk wuhdwv dq dvvhw sd|lqj glylghqgv dw pdq| ixwxuh gdwhv dv wkh vxp ri pdq| dvvhwv/ hdfk ri zklfk sd|v d glylghqg dw d vlqjoh ixwxuh gdwh1 Wkhvh vlqjoh0sd|phqw ru }hur0frxsrq dvvhwv duh riwhq hdvlhu wr prgho1 Wklv dssurdfk lv prvw qdwxudo/ dqg kdv ehhq ghyhorshg ixuwkhvw/ lq wkh olwhudwxuh rq {hg0lqfrph vhfxulwlhv zklfk L qrz ghvfuleh1 E1 D!qh0lhog Prghov E141 Wkhruhwlfdo Vwuxfwxuh Frqvlghu d uhdo }hur0frxsrq erqg wkdw pdnhv d vlqjoh sd|phqw ri rqh xqlw ri frqvxpswlrq dw wlph | n ?1 Wkh erqg sulfh dw wlph |/ ?| / pxvw vdwlvi| wkh jhqhudo VGI uhodwlrq +4,/ zklfk lq wklv vshfldo fdvh ehfrphv ?| ' ,| d|n ?3c|n o +46, Wklv htxdwlrq fdq eh vroyhg iruzdug wr rewdlq ?| ' ,| d|n |n2 |n? o +47, Mxvw dv wkh sulfh ri d vlqjoh0shulrg uhdo erqg lv wkh h{shfwdwlrq ri wkh vlqjoh0shulrg VGI lq +7,/ vr wkh sulfh ri dq ?0shulrg uhdo erqg lv wkh h{shfwdwlrq ri wkh ?0shulrg VGI +wkh surgxfw ri ? vxffhvvlyh vlqjoh0shulrg VGI*v,1 Wklv lv qdwxudo vlqfh dq ?0shulrg uhdo erqg lv wkh ulvnohvv uhdo dvvhw iru dq lqyhvwru zlwk d krul}rq ri ? shulrgv +Prgljoldql dqg Vxwfk 499,1 Htxdwlrq +47, pdnhv lw fohdu wkdw d prgho ri erqg sulfhv lv htxlydohqw wr d wlph0vhulhv prgho ri wkh VGI1 Wkh |lhog rq dq ?0shulrg erqg/ t?| / lv ghqhg wr eh wkh glvfrxqw udwh wkdw htxdwhv wkh erqg*v sulfh wr wkh suhvhqw ydoxh ri lwv ixwxuh sd|phqw= ?| ' *E n t?| ? 1 Wdnlqj orjv/ +?| ' E*?R?| / vr wkh orj erqg |lhog lv mxvw d olqhdu wudqvirupdwlrq ri wkh orj erqg sulfh1 D!qh0|lhog prghov kdyh wkh surshuw| wkdw doo orj erqg |lhogv duh olqhdu +d!qh, lq d vhw ri vwdwh yduldeohv ghvfulelqj wkh pryhphqwv ri wkh VGI1 Wklv surshuw| krogv rqo| xqghu uhvwulfwlyh frqglwlrqv rq wkh VGI1 Fodvvlf sdshuv e| Ydvlfhn +4::, dqg Fr{/ Lqjhuvroo/ dqg Urvv +4;8, suhvhqwhg vlpsoh h{dpsohv uhfhqw zrun kdv vrxjkw wr fkdudfwhul}h pruh jhqhudoo| wkh frqglwlrqv rq wkh VGI uhtxluhg iru dq d!qh0|lhog vwuxfwxuh1 Prvw ri wklv zrun lv vhw lq frqwlqxrxv wlph dqg lv vxuyh|hg e| Vxqgduhvdq +5333,1 Lq wkh glvfuhwh0wlph iudphzrun xvhg khuh/ li zh ghqh d 56
  • 27. yhfwru 5| frqwdlqlqj wkh orj VGI 6| dqg doo vwdwh yduldeohv uhohydqw iru suhglfwlqj lwv ixwxuh ydoxhv 6|n / wkhq dq d!qh0|lhog prgho uhtxluhv wkdw erwk wkh frqglwlrqdo phdq dqg wkh frqglwlrqdo yduldqfh0fryduldqfh pdwul{ ri 5|n vkrxog eh olqhdu lq 5| 1 Wkh prgho dovr uhtxluhv vrph uhvwulfwlrqv rq wkh frqglwlrqdo glvwulexwlrq ri 5|n d qrupdo glvwulexwlrq lv vx!flhqw exw qrw qhfhvvdu| +Edfnxv/ Iruhvl/ dqg Whophu +4;,,1 Wkh vlpsohvw h{dpsoh lv d xqlyduldwh krprvnhgdvwlf qrupdo DU+4, surfhvv iru 6|n / zklfk jlyhv d glvfuhwh0wlph yhuvlrq ri wkh Ydvlfhn +4::, prgho ri wkh whup vwuxfwxuh1 D qrupdo DU+4, surfhvv iru 6|n zlwk d yduldqfh sursruwlrqdo wr wkh ohyho ri 6|n jlyhv d glvfuhwh0wlph yhuvlrq ri wkh Fr{/ Lqjhuvroo/ dqg Urvv +4;8, prgho1 Lq frqwlqxrxv wlph wkh d!qh0|lhog uhvwulfwlrqv duh vlplodu1 Lw lv srvvleoh wr doorz iru mxpsv lq wkh vwdwh yhfwru surylghg wkdw wkh mxps lqwhqvlw| lv lwvhoi olqhdu lq wkh vwdwh yduldeohv1 Gdl dqg Vlqjohwrq +5333, suhvhqw d fduhixo dqdo|vlv ri wkh vxevwdqwlyh uhvwulfwlrqv lpsrvhg e| wkh d!qh0|lhog vwuxfwxuh1 Wkhuh duh wzr edvlf lvvxhv1 Iluvw/ wkh d!qh0 |lhog prgho olplwv wkh zd| lq zklfk yrodwlolw| +gulyhq hlwkhu e| d glxvlrq whup ru e| mxps lqwhqvlw| lq frqwlqxrxv wlph, fdq ydu| zlwk vwdwh yduldeohv1 Yduldqfhv fdq eh frqvwdqw ru/ pruh jhqhudoo|/ olqhdu lq vwdwh yduldeohv/ exw fdqqrw ydu| qrqolqhduo|1 Vhfrqg/ wkh lpsolhg yduldqfh0fryduldqfh pdwul{ ri wkh vwdwh yhfwru pxvw eh srvlwlyh ghqlwh1 Wklv sodfhv ihz uhvwulfwlrqv rq wkh fruuhodwlrqv ri vwdwh yduldeohv zkhq yrodwlolw| lv frqvwdqw/ exw lv pxfk kdughu wr hqvxuh zkhq yrodwlolw| lv wlph0ydu|lqj1 Wkh d!qh0|lhog vwuxfwxuh pdnhv lw srvvleoh wr vroyh uhfxuvlyho| iru wkh xqnqrzq frh!flhqwv uhodwlqj orj erqg |lhogv wr vwdwh yduldeohv1 Vwduwlqj iurp wkh whuplqdo frqglwlrq wkdw wkh erqg sulfh dw pdwxulw| lv rqh +vr wkh orj erqg sulfh lv }hur,/ rqh fdq zrun rxw wkh whup vwuxfwxuh ri lqwhuhvw udwhv wr sulfh erqgv ri duelwudu| pdwxulw|1 Frxsrq erqgv fdq wkhq eh sulfhg/ li ghvluhg/ dv sdfndjhv ri }hur0frxsrq erqgv/ rqh iru hdfk gdwh dw zklfk d frxsrq sd|phqw lv pdgh1 Wkh d!qh0|lhog vwuxfwxuh fdq dovr eh h{whqghg wr vwxg| dvvhwv zlwk xqfhuwdlq ixwxuh sd|rv1 Wkhuh duh wkuhh zd|v wr gr wklv1 Iluvw/ rqh fdq dvvxph wkdw wkh h{shfwhg dvvhw uhwxuqv duh xqdhfwhg e| sd|r xqfhuwdlqw|/ zklfk zloo eh wkh fdvh li wkh sd|r xqfhuwdlqw| lv xqfruuhodwhg zlwk wkh VGI1 Jleerqv dqg Udpdvzdp| +46,/ iru h{dpsoh/ dvvxph wkdw lq dwlrq xqfhuwdlqw| lv xqfruuhodwhg zlwk wkh VGI/ vr lq dwlrq ulvn lv xqsulfhg/ dqg vwxg| wkh uhdo uhwxuqv rq qrplqdo erqgv1 Vhfrqg/ rqh fdq fkdqjh wkh qxphudluh wr xqlwv lq zklfk ixwxuh sd|rv duh nqrzq1 Qrplqdo Wuhdvxu| erqgv/ iru h{dpsoh/ kdyh xqfhuwdlq uhdo sd|rv exw fhuwdlq qrplqdo sd|rv1 Rqh fdq ghqh d qrplqdo VGI/ wkh uhdo VGI wlphv wkh udwlr ri wkh sulfh ohyho wrgd| wr wkh sulfh ohyho wrpruurz/ dqg wkhq xvh dq d!qh prgho ri wkh qrplqdo VGI1 Wkh 57
  • 28. dgydqwdjh ri wklv dssurdfk lv lwv vlpsolflw| wkh glvdgydqwdjh lv wkdw lw lv kdug wr uhodwh wkh qrplqdo VGI wr wkh uhdo ulvnv wkdw dhfw lqyhvwruv1 Wklug/ rqh fdq h{solflwo| prgho wkh wlph0vhulhv surfhvv iru wkh sd|rv lq uhodwlrq wr wkh VGI1 Li wkh vwdwh yhfwru lqfoxghv wkrvh yduldeohv wkdw ghwhuplqh wkh sd|rv/ dqg li wkh suhylrxv dvvxpswlrqv rq wkh vwdwh yhfwru frqwlqxh wr krog/ wkhq wkh orj dvvhw sulfh frqwlqxhv wr eh olqhdu lq wkh orj vwdwh yhfwru dqg wkh dgydqwdjhv ri wkh d!qh iudphzrun duh suhvhuyhg1 Fdpsehoo dqg Ylfhlud +5333, dsso| wklv dssurdfk wr qrplqdo erqgv Ednvkl dqg Fkhq +4:,/ Dqj dqg Olx +4;,/ dqg Ehndhuw dqg Juhqdglhu +4, dsso| lw wr vwrfnv1 E151 Hpslulfdo Dssolfdwlrqv wr X1V1 Wuhdvxu| Erqgv Vhfwlrq L1D18 uhsruwhg vhyhudo vw|ol}hg idfwv derxw X1V1 Wuhdvxu| erqg |lhogv1 Erwk wkh vkdsh ri wkh dyhudjh |lhog fxuyh dqg wkh wlph0yduldwlrq ri whup suhpld duh lqfrqvlvwhqw zlwk vlqjoh0idfwru d!qh0|lhog prghov ri wkh qrplqdo whup vwuxfwxuh1 Lq vlqjoh0idfwru prghov/ wkh frqyh{lw| ri wkh dyhudjh |lhog fxuyh lv uhodwhg wr wkh udwh dw zklfk vkrfnv wr wkh vkruw0whup lqwhuhvw udwh glh rxw exw wlph0vhulhv hylghqfh lpsolhv wkdw lqwhuhvw0udwh vkrfnv glh rxw pxfk pruh vorzo| wkdq zrxog eh lpsolhg e| wkh udslgo| ghfolqlqj vorsh ri wkh dyhudjh |lhog fxuyh +Jleerqv dqg Udpdvzdp| +46,,1 Dv iru whup suhpld/ wkh| duh frxqwhuidfwxdoo| frqvwdqw lq d vlqjoh0idfwru Ydvlfhn +4::, prgho zlwk frqvwdqw yrodwlolw|1 D vlqjoh0idfwru Fr{/ Lqjhuvroo/ dqg Urvv +4;8, prgho zlwk yrodwlolw| olqhdu lq wkh ohyho ri wkh vkruw0whup lqwhuhvw udwh fdq jhqhudwh wlph0yduldwlrq lq whup suhpld/ exw lq wklv prgho wkh |lhog vsuhdg lv lqyhuvho| uhodwhg wr yrodwlolw|1 Li whup suhpld duh srvlwlyh rq dyhudjh/ wkh| pryh srvlwlyho| zlwk yrodwlolw| vr wkh| pryh lqyhuvho| zlwk wkh |lhog vsuhdg/ frqwudu| wr wkh hpslulfdo hylghqfh +Edfnxv hw do1 +4;,,1 Wkhvh sureohpv kdyh ohg wr dq h{sorvlrq ri uhvhdufk rq pruh frpsoh{ prghov ri wkh qrplqdo whup vwuxfwxuh1 Wkhvh lqfoxgh pxowlidfwru d!qh prghov wkdw lqfoxgh erwk shuvlvwhqw vwdwh yduldeohv wr w wkh vorzo| ghfd|lqj dxwrfruuhodwlrqv ri lqwhuhvw udwhv/ dqg wudqvlwru| vwdwh yduldeohv wr w wkh udslgo| ghfolqlqj vorsh ri wkh dyhudjh |lhog fxuyh qrq0d!qh prghov wkdw doorz iru d qrqolqhdu hhfw ri wkh ohyho ri wkh lqwhuhvw udwh rq lwv yrodwlolw| dqg guliw dqg uhjlph0vzlwfklqj prghov wkdw doorz iru rffdvlrqdo glvfuhwh fkdqjhv lq lqwhuhvw0udwh ehkdylru1 Sudfwlwlrqhuv kdyh jrqh lq d vrphzkdw glhuhqw gluhfwlrq/ lqwurgxflqj wlph0ghshqghqw sdudphwhuv lqwr vlpsoh d!qh prghov/ exw wklv grhv qrw exlog wkh xqghuvwdqglqj ri wkh xqghuo|lqj hfrqrplf vwuxfwxuh wkdw lv wkh xowlpdwh jrdo ri dfdghplf uhvhdufk1 Prvw ri wklv zrun lv vhw lq frqwlqxrxv wlph dqg lv uhylhzhg e| Vxqgduhvdq +5333,1 58
  • 29. Vhyhudo lvvxhv uhpdlq xquhvroyhg e| wklv uhvhdufk1 Iluvw/ uhdo0lqwhuhvw0udwh ulvn dqg lq dwlrq ulvn duh frqfhswxdoo| glvwlqfw dqg pd| kdyh yhu| glhuhqw ulvn sulfhv1 Wklv glvwlqfwlrq lv eoxuuhg zkhq whup0vwuxfwxuh prghov duh w gluhfwo| wr qrplqdo lqwhuhvw udwhv1 Lw fdq eh dgguhvvhg hlwkhu e| orrnlqj dw lq dwlrq gdwd mrlqwo| zlwk qrplqdo lqwhuhvw udwhv +Jleerqv dqg Udpdvzdp| +46,/ Fdpsehoo dqg Ylfhlud +5333,,/ ru e| vwxg|lqj lq dwlrq0lqgh{hg erqgv/ zklfk kdyh ehhq dfwlyho| wudghg lq wkh XN iru 48 |hduv +Eurzq dqg Vfkdhihu +47,, dqg kdyh ehhq lvvxhg lq wkh X1V1 vlqfh 4:1 Wkhuh lv vrph hylghqfh wkdw erwk lq dwlrq ulvn dqg uhdo0lqwhuhvw0udwh ulvn duh sulfhg/ vr wkdw wkh uhdo whup vwuxfwxuh lv xszdug vorslqj exw dwwhu wkdq wkh qrplqdo whup vwuxfwxuh krzhyhu pruh zrun lv qhhghg rq wklv vxemhfw1 Vhfrqg/ lw lv lpsruwdqw wr uhfrqfloh wkh fkdudfwhul}dwlrq ri wkh VGI surylghg e| erqg0pdunhw gdwd zlwk wkh hylghqfh iurp vwrfn0pdunhw gdwd1 Whup0vwuxfwxuh prghov ri wkh VGI duh xowlpdwho| xqvdwlvidfwru| xqohvv wkh| fdq eh uhodwhg wr wkh ghhshu jhqhudo0htxloleulxp vwuxfwxuh ri wkh hfrqrp|1 Uhvhdufkhuv riwhq fdoleudwh htxloleulxp prghov wr w vwrfn pdunhw gdwd dorqh/ exw wklv lv d plvwdnh ehfdxvh erqgv fduu| htxdoo| xvhixo lqirupdwlrq derxw wkh VGI1 Wkh vkruw0whup uhdo lqwhuhvw udwh lv forvho| uhodwhg wr wkh frqglwlrqdo h{shfwhg VGI/ dqg wkxv wr wkh h{shfwhg jurzwk udwh ri pdujlqdo xwlolw| lq d uhsuhvhqwdwlyh0djhqw prgho zlwk srzhu xwlolw| ri frqvxpswlrq/ wklv olqnv wkh uhdo lqwhuhvw udwh wr h{shfwhg frqvxpswlrq jurzwk dv glvfxvvhg lq Vhfwlrq LY1D1 Wkh ulvn suhplxp rq erqgv lv dovr lqirupdwlyh lw lv vpdoo uhodwlyh wr wkh htxlw| suhplxp/ dqg wklv uhpdlqv wuxh hyhq li rqh glylghv e| wkh vwdqgdug ghyldwlrq ri uhwxuq wr fdofxodwh d Vkdush udwlr1 Wklv idfw lv frqvlvwhqw zlwk ulvn0edvhg prghov ri wkh htxlw| suhplxp lq zklfk wkh VGI lv pruh kljko| fruuhodwhg zlwk vwrfnv wkdq zlwk erqgv/ exw lw uxqv frxqwhu wr prghov wkdw h{sodlq wkh htxlw| suhplxp dv wkh uhvxow ri oltxlglw| vhuylfhv iurp vkruw0whup Wuhdvxu| ghew zklfk gulyh grzq wkh htxloleulxp vkruw0whup lqwhuhvw udwh +Edqvdo dqg Frohpdq +49,,1 Xqohvv orqj0whup Wuhdvxu| erqgv dovr surylgh oltxlglw| vhuylfhv/ wkh oltxlglw|0edvhg prgho vkrxog lpso| d odujh |lhog vsuhdg ri orqj0whup ryhu vkruw0whup Wuhdvxu| ghew1 Wklug/ wkh vkruw0whup qrplqdo lqwhuhvw udwh lv dq lpsruwdqw gulylqj yduldeoh lq dq| qrplqdo whup0vwuxfwxuh prgho1 Rqh fdqqrw ljqruh wkh idfw wkdw wkh vkruw udwh lv gluhfwo| frqwuroohg e| wkh prqhwdu| dxwkrulw|/ zklfk uhvsrqgv wr pdfurhfrqrplf frqglwlrqv e| fkdqjlqj wkh udwh lq glvfuhwh mxpsv1 Edogx}}l/ Ehuwrod/ dqg Iruhvl +4:, dqg Sld}}hvl +4, dgguhvv wklv lvvxh1 59
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  • 33. Hsvwhlq +45,/ dqg kdyh ehhq xvhg wr vwxg| orqj0whup sruwirolr fkrlfh e| Vfkurghu dqg Vnldgdv +4,1 Lw lv srvvleoh wr frqvwuxfw rwkhu prghov ri xwlolw| wkdw suhvhuyh wkh ghvludeoh vfdoh0 lqghshqghqfh ri srzhu xwlolw|1 Rqh vwudwhj| lv wr zulwh xwlolw| dv d srzhu ixqfwlrq ri vrph yduldeoh rwkhu wkdq frqvxpswlrq= iru h{dpsoh/ frqvxpswlrq uhodwlyh wr d kdelw ru vxevlvwhqfh ohyho wkdw fdswxuhv wkh sdvw klvwru| ri frqvxpswlrq1 Wklv dssurdfk lv glvfxvvhg lq Vhfwlrq LY1E1 Dqrwkhu vwudwhj| lv wr prgho d uhihuhqfh srlqw wkdw jurzv zlwk frqvxpswlrq ru zhdowk/ dqg wr ghqh xwlolw| uhodwlyh wr wklv uhihuhqfh srlqw lq d vfdoh0lqghshqghqw zd|1 Wklv dssurdfk lv glvfxvvhg lq Vhfwlrq YL1E141 Iru wkh uhvw ri wklv vhfwlrq/ krzhyhu/ L zloo iroorz wkh exon ri wkh plfurhfrqrplf sruwirolr fkrlfh olwhudwxuh dqg frqvlghu lqyhvwruv zkr kdyh srzhu ru Hsvwhlq0]lq xwlolw|1 E1 Wlph0Ydu|lqj Lqyhvwphqw Rssruwxqlwlhv E141 Yduldwlrq lq Uhdo Lqwhuhvw Udwhv Rqh ri wkh prvw reylrxv zd|v lq zklfk lqyhvwphqw rssruwxqlwlhv ydu| lv wkdw uhdo lqwhuhvw udwhv fkdqjh ryhu wlph1 Uhdo d!qh0|lhog prghov vxuyh|hg lq vhfwlrq LL1E fdswxuh wklv yduldwlrq dqg ghulyh lpsolfdwlrqv iru orqj0whup erqg |lhogv1 Li wkhuh zhuh qr yduldwlrq lq uhdo lqwhuhvw udwhv/ lq dwlrq0lqgh{hg erqgv zrxog kdyh frqvwdqw sulfhv dqg zrxog eh shuihfw vxevwlwxwhv iru fdvk wkxv dq| frkhuhqw prgho ri wkh ghpdqg iru orqj0whup uhdo erqgv pxvw eh dq lqwhuwhpsrudo udwkhu wkdq d vwdwlf prgho1 Qrplqdo lqwhuhvw udwhv duh dovr lq xhqfhg e| lq dwlrq vkrfnv/ exw khuh wrr dq lqwhuwhpsrudo prgho lv dssursuldwh wr fdswxuh wkh hhfwv ri fkdqjlqj uhdo lqwhuhvw udwhv1 Lqyhvwphqw dgylvhuv riwhq dujxh wkdw orqj0whup erqgv duh dssursuldwh iru frqvhuyd0 wlyh orqj0whup lqyhvwruv1 Lq idfw/ wkh uhfrpphqghg lqyhvwphqw doorfdwlrqv ri vhyhudo qdqfldo froxpqlvwv dqg pxwxdo0ixqg frpsdqlhv vxppdul}hg e| Fdqqhu/ Pdqnlz/ dqg Zhlo +4:, v|vwhpdwlfdoo| lqfuhdvh wkh udwlr ri erqgv wr vwrfnv iru pruh frqvhu0 ydwlyh lqyhvwruv1 Erqg uhwxuqv duh ulvn| lq wkh vkruw whup/ krzhyhu/ vr wklv dgylfh frqwudglfwv wkh pxwxdo0ixqg wkhruhp ri Wrelq +48;,/ dffruglqj wr zklfk doo lqyhvwruv vkrxog krog wkh vdph sruwirolr ri ulvn| dvvhwv/ wkh wdqjhqf| sruwirolr ri phdq0yduldqfh dqdo|vlv1 Frqvhuydwlyh lqyhvwruv vkrxog krog ohvv ri wklv sruwirolr dqg pruh ri d vkruw0 whup vdih dvvhw/ exw wkh uhodwlyh sursruwlrqv ri glhuhqw ulvn| dvvhwvlqfoxglqj vwrfnv dqg erqgvvkrxog eh wkh vdph iru frqvhuydwlyh lqyhvwruv dv iru djjuhvvlyh lqyhvwruv1 Fdqqhu/ Pdqnlz/ dqg Zhlo fdoo wklv frqwudglfwlrq wkh dvvhw doorfdwlrq sx}}oh1 63
  • 34. Wkh Wrelq pxwxdo0ixqg wkhruhp wdnhv d vkruw0whup shuvshfwlyh/ ghqlqj d vkruw0 whup vdih dvvhw dv ulvnohvv dqg orqj0whup erqgv dv ulvn|1 Vxfk d shuvshfwlyh lv lqdssursuldwh iru d orqj0whup lqyhvwru zkr fduhv derxw wkh glvwulexwlrq ri zhdowk dw d {hg gdwh lq wkh glvwdqw ixwxuh1 Vkruw0whup dvvhwv duh qrw vdih iru vxfk dq lqyhvwru/ ehfdxvh wkh| pxvw eh uroohg ryhu dw xqfhuwdlq ixwxuh lqwhuhvw udwhv1 Lqvwhdg/ d orqj0 whup }hur0frxsrq erqg wkdw pdwxuhv rq wkh whuplqdo gdwh lv wkh vdih dvvhw iru wklv lqyhvwru +Prgljoldql dqg Vxwfk +499,,1 Wklv lqvljkw kdv uhfhqwo| ehhq h{whqghg wr wkh pruh uhdolvwlf fdvh lq zklfk wkh lqyhvwru fduhv derxw wkh vwuhdp ri frqvxpswlrq wkdw fdq eh qdqfhg e| zhdowk/ udwkhu wkdq wkh glvwulexwlrq ri zhdowk dw dq| sduwlfxodu gdwh1 Euhqqdq dqg [ld +4;, frqvlghu d srzhu0xwlolw| lqyhvwru zlwk d qlwh krul}rq/ deoh wr ex| lq dwlrq0lqgh{hg erqgv dw lqwhuhvw udwhv ghwhuplqhg e| wkh Ydvlfhn +4::, prgho1 Wkh| vkrz wkdw dv ulvn dyhuvlrq lqfuhdvhv/ wkh lqyhvwru*v sruwirolr frqyhujhv wr dq lq dwlrq0lqgh{hg frxsrq erqg pdwxulqj dw wkh krul}rq1 Zdfkwhu +4;, suryhv d pruh jhqhudo yhuvlrq ri wklv uhvxow1 Fdpsehoo dqg Ylfhlud +5333, w d wzr0idfwru krprvnhgdvwlf prgho ri wkh VGI wr gdwd rq X1V1 qrplqdo lqwhuhvw udwhv/ vwrfn uhwxuqv/ dqg lq dwlrq1 Wkh| frqvlghu dq lqqlwho|0olyhg lqyhvwru zlwk Hsvwhlq0]lq xwlolw|/ ghulyh d sruwirolr vroxwlrq wkdw lv h{dfw zkhq '  dqg dssur{lpdwh rwkhuzlvh/ dqg vkrz wkdw wkh vkduh ri qrplqdo erqgv uhodwlyh wr vwrfnv lqfuhdvhv zlwk ulvn dyhuvlrq zkhq erqgv duh lq dwlrq0lqgh{hg/ ru zkhq lq dwlrq ulvn lv prghudwh dv lw kdv ehhq lq wkh X1V1 lq wkh odvw 48 |hduv1 Lq wklv zd| wkh| uhvroyh wkh dvvhw doorfdwlrq sx}}oh1 E151 Yduldwlrq lq Ulvn Suhpld Lw lv riwhq dujxhg wkdw vwrfnv duh uhodwlyho| vdihu iru orqj0whup lqyhvwruv +Vlhjho 4,1 Li dvvhw uhwxuqv duh LLG/ wklv fdqqrw eh wuxh ehfdxvh wkh phdqv dqg yduldqfhv ri doo dvvhw uhwxuqv lqfuhdvh lq sursruwlrq zlwk wkh lqyhvwphqw krul}rq1 Wkxv dq| fodlp ri wklv vruw pxvw eh edvhg rq suhglfwdelolw| ri vwrfn uhwxuqv1 Lq idfw/ wkh hpslulfdo hylghqfh vxppdul}hg lq L1D17 grhv lpso| wkdw wkh yduldqfh ri vwrfn uhwxuqv lqfuhdvhv pruh vorzo| wkdq sursruwlrqdoo| zlwk wkh lqyhvwphqw krul}rq1 Srwhued dqg Vxpphuv +4;;, suhvhqw gluhfw hylghqfh iru wklv hhfw edvhg rq wkh suhgrplqdqwo| qhjdwlyh xqlyduldwh dxwrfruuhodwlrqv ri vwrfn uhwxuqv/ dqg Fdpsehoo +44, uhsruwv lqgluhfw hylghqfh edvhg rq wkh suhglfwdelolw| ri vwrfn uhwxuqv iurp wkh glylghqg0sulfh udwlr dqg wkh qhjdwlyh fruuhodwlrq ehwzhhq lqqrydwlrqv wr wkh vwrfn uhwxuq dqg wkh 64
  • 35. glylghqg0sulfh udwlr1 Suhglfwdelolw| ri wklv vruw/ wkdw uhgxfhv orqj0whup ulvn uhodwlyh wr vkruw0whup ulvn/ lv riwhq fdoohg phdq uhyhuvlrq1 Li vwrfn uhwxuqv duh phdq0uhyhuwlqj/ wklv djdlq lpsolhv wkdw lqyhvwphqw rssruwx0 qlwlhv duh wlph0ydu|lqj1 Rqfh djdlq dq lqwhuwhpsrudo prgho lv qhhghg wr fdofxodwh rswlpdo lqyhvwphqw doorfdwlrqv1 Nlp dqg Rpehuj +49, vroyh wkh sruwirolr fkrlfh sureohp ri d orqj0olyhg lqyhvwru/ zlwk srzhu xwlolw| ghqhg ryhu zhdowk dw d glvwdqw ixwxuh gdwh/ zkr idfhv d frqvwdqw ulvnohvv lqwhuhvw udwh dqg d wlph0ydu|lqj htxlw| suhplxp wkdw iroorzv d krprvnhgdvwlf DU+4, surfhvv1 Wkh| vkrz wkdw zkhq wkh vwrfn uhwxuq lv qhjdwlyho| fruuhodwhg zlwk lqqrydwlrqv wr wkh htxlw| suhplxp/ wkhq wkh lqyhvwru lqfuhdvhv wkh dyhudjh doorfdwlrq wr vwrfnv li ulvn dyhuvlrq lv juhdwhu wkdq rqh1 Zdfkwhu +4, ghulyhv d vlplodu uhvxow iru dq lqyhvwru zkr kdv srzhu xwlolw| gh0 qhg ryhu frqvxpswlrq/ lq wkh vshfldo fdvh zkhuh wkh lqqrydwlrqv wr wkh vwrfn uhwxuq dqg wkh htxlw| suhplxp duh shuihfwo| fruuhodwhg1 Fdpsehoo dqg Ylfhlud +4, frq0 vlghu dq lqqlwho|0olyhg lqyhvwru zlwk Hsvwhlq0]lq xwlolw| ghqhg ryhu frqvxpswlrq1 Wkhlu vroxwlrq lv h{dfw zkhq ' / dqg dssur{lpdwh rwkhuzlvh1 Wkh| hvwlpdwh wkh sdudphwhuv ri wkh prgho iurp srvwzdu X1V1 gdwd/ dqg qg wkdw wkh hvwlpdwhg phdq uh0 yhuvlrq gudpdwlfdoo| lqfuhdvhv wkh dyhudjh rswlpdo htxlw| doorfdwlrq ri d frqvhuydwlyh orqj0whup lqyhvwru1 Lq doo wkhvh prghov wkh lqyhvwru rswlpdoo| wlphv wkh pdunhw/ dowhulqj wkh doorfdwlrq wr vwrfnv dv wkh htxlw| suhplxp fkdqjhv1 Wkxv wkh prghov gr qrw vxssruw wkh ex|0 dqg0krog srolf| uhfrpphqghg e| Vlhjho +4, iru orqj0whup lqyhvwruv19 Wklv dovr udlvhv wkh lvvxh ri frqvlvwhqf| zlwk jhqhudo htxloleulxp zlwk d frqvwdqw vxsso| ri vwrfnv qrw doo lqyhvwruv fdq ex| ru vhoo vwrfnv dw wkh vdph wlph/ vr wkhvh prghov fdqqrw eh xvhg wr ghvfuleh wkh ehkdylru ri d uhsuhvhqwdwlyh djhqw lq jhqhudo htxloleulxp1 Prghov zlwk wlph0ydu|lqj ulvn dyhuvlrq/ ri wkh vruw ghvfulehg lq Vhfwlrq LY1E/ vroyh wkh frpsohphqwdu| sureohp ri qglqj suhihuhqfhv wkdw pdnh d uhsuhvhqwdwlyh djhqw frqwhqw wr ex| dqg krog wkh pdunhw lq wkh idfh ri d wlph0ydu|lqj htxlw| suhplxp1 Euhqqdq/ Vfkzduw}/ dqg Odjqdgr +49,/ Fdpsehoo/ Fkdq/ dqg Ylfhlud +4,/ dqg O|qfk +4, frpelqh wlph0ydu|lqj uhdo lqwhuhvw udwhv zlwk wlph0ydu|lqj ulvn suhpld1 Wkh| hvwlpdwh pruh frpsoh{ hpslulfdo prghov lq zklfk erwk erqgv dqg vwrfnv fdq eh xvhg wr khgjh djdlqvw fkdqjhv lq lqyhvwphqw rssruwxqlwlhv1 Wkh hvwl0 pdwhg suhglfwdelolw| ri vwrfn uhwxuqv whqgv wr lpso| wkdw khgjlqj ghpdqg lv odujhvw 9 D ex|0dqg0krog srolf| pd| eh d frqvwudlqhg rswlpxp li lqyhvwruv duh xqdeoh wr ohyhudjh wkhlu htxlw| kroglqjv1 Lq wklv fdvh/ krzhyhu/ wkh frqvwudlqhg sureohp pxvw eh vroyhg iurp uvw sulqflsohv vlqfh wkh frqvwudlqw dhfwv wkh rswlpdo frqvxpswlrq srolf| dv zhoo dv wkh rswlpdo sruwirolr1 65
  • 36. iru vwrfnv1 Eudqgw +4, xvhv d qrqsdudphwulf dssurdfk/ dyrlglqj wkh vshflfdwlrq ri d sdudphwulf prgho/ dqg rewdlqv jhqhudoo| vlplodu uhvxowv1 Edogx}}l dqg O|qfk +4, vkrz krz wudqvdfwlrqv frvwv fdq dhfw rswlpdo orqj0whup sruwirolrv1 Doo wkhvh prghov dvvxph wkdw lqyhvwruv nqrz wkh sdudphwhuv ri wkh prgho iru dvvhw uhwxuqv1 Wklv lv fohduo| xquhdolvwlf jlyhq wkh vxevwdqwldo xqfhuwdlqw| dprqj qdqfldo hfrqrplvwv derxw wkhvh sdudphwhuv1 Edzd/ Eurzq/ dqg Nohlq +4:, surylghg dq hduo| wuhdwphqw ri sdudphwhu xqfhuwdlqw| lq d vkruw0krul}rq prgho zlwk LLG dvvhw uhwxuqv/ dqg Ndqgho dqg Vwdpedxjk +49, kdyh frqvlghuhg wkh hhfwv rq d vkruw0 krul}rq lqyhvwru ri xqfhuwdlqw| derxw uhwxuq suhglfwdelolw|1 Zlooldpv +4::,/ Grwkdq dqg Ihogpdq +4;9,/ dqg Jhqqrwwh +4;9, srlqwhg rxw wkdw lq d orqj0krul}rq vhwwlqj/ rswlpdo sruwirolrv duh dhfwhg e| wkh idfw wkdw lqyhvwruv fdq ohduq derxw sdudphwhuv ryhu wlph1 Euhqqdq +4;, dqg Eduehulv +4, h{soruh wklv lvvxh hpslulfdoo|1 Li dq lqyhvwru ohduqv derxw wkh phdq vwrfn uhwxuq e| revhuylqj uhdol}hg uhwxuqv/ wkhq d srvlwlyh vwrfn uhwxuq zloo ohdg wkh lqyhvwru wr uhylvh xszdugv klv hvwlpdwh ri wkh phdq vwrfn uhwxuq1 Wklv pdnhv vwrfn uhwxuqv srvlwlyho| fruuhodwhg zlwk h{shfwhg ixwxuh vwrfn uhwxuqv/ wkh rssrvlwh ri wkh phdq0uhyhuvlrq hhfw1 Khgjlqj ghpdqg lv fruuhvsrqglqjo| uhyhuvhg/ dqg wkh vwrfn ghpdqg ri frqvhuydwlyh orqj0whup lqyhvwruv lv uhgxfhg1 [ld +4, frqvlghuv wkh srvvlelolw| ri ohduqlqj derxw wkh ghjuhh ri phdq0 uhyhuvlrq lwvhoi1 Ixwxuh uhvhdufk zloo xqgrxewhgo| sxvk ixuwkhu lq wkh gluhfwlrq ri lqwhjudwlqj wkh hvwlpdwlrq dqg sruwirolr fkrlfh sureohpv Eudqgw +4, vkrzv rqh zd| wr gr wklv e| gluhfwo| hvwlpdwlqj dq rswlpdo sruwirolr uxoh udwkhu wkdq d surfhvv iru dvvhw uhwxuqv1 F1 Oderu Lqfrph dqg Sruwirolr Fkrlfh Oderu lqfrph fdq dovr kdyh lpsruwdqw hhfwv rq sruwirolr fkrlfh iru orqj0whup lqyhvwruv1 Dq lpsruwdqw sdshu rq wklv wrslf lv Erglh/ Phuwrq/ dqg Vdpxhovrq +khuh0 diwhu EPV 44,1 Wkhvh dxwkruv vkrz wkdw h{rjhqrxv/ ulvnohvv oderu lqfrph lv htxlydohqw wr dq lpsolflw kroglqj ri ulvnohvv dvvhwv1 Suhylrxv uhvxowv dsso| wr wrwdo dvvhw kroglqjv/ vr ulvnohvv oderu lqfrph wlowv h{solflw dvvhw kroglqjv wrzdugv ulvn| dv0 vhwv1 H{rjhqrxv oderu lqfrph wkdw lv shuihfwo| fruuhodwhg zlwk ulvn| dvvhwv/ rq wkh rwkhu kdqg/ lv htxlydohqw wr dq lpsolflw kroglqj ri ulvn| dvvhwv dqg wlowv wkh qdqfldo sruwirolr wrzdugv vdih dvvhwv1 EPV dovr frqvlghu wkh srvvlelolw| wkdw lqyhvwruv fdq ydu| wkhlu oderu vxsso| hqgrjhqrxvo|1 Wkh| qg wkdw wklv lqfuhdvhv wkh zloolqjqhvv wr wdnh ulvnv ehfdxvh lqyhvwruv fdq devrue qdqfldo orvvhv erwk e| fxwwlqj frqvxpswlrq dqg e| dgmxvwlqj oderu vxsso|1 66
  • 37. EPV gr qrw frqvlghu lglrv|qfudwlf ulvn lq oderu lqfrph wkdw fdqqrw eh khgjhg xvlqj qdqfldo dvvhwv1 Uhfhqw wkhruhwlfdo zrun vkrzv wkdw vxfk edfnjurxqg ulvn fdq kdyh lpsruwdqw hhfwv rq frqvxpswlrq dqg sruwirolr ghflvlrqv Jroolhu +5333, surylghv d wh{werrn wuhdwphqw1 Khuh wrr lw lv h{wuhpho| fkdoohqjlqj wr h{whqg wzr0shulrg uhvxowv wr d pruh uhdolvwlf pxowl0shulrg vhwwlqj1 Ylfhlud +4, vkrzv wkdw orjqrupdoo| glvwulexwhg oderu lqfrph ulvn/ xqfruuhodwhg zlwk qdqfldo dvvhw ulvn/ uhgxfhv wkh wlow wrzdugv ulvn| dvvhwv exw grhv qrw uhyhuvh lw1 Wklv w|sh ri ulvn dovr kdv d odujh hhfw lq vwlpxodwlqj zhdowk dffxpxodwlrq wkurxjk suhfdxwlrqdu| vdylqj dv hpskdvl}hg e| Fduuroo +4:,1 Ehuwdxw dqg Kdoldvvrv +4:,/ Khdwrq dqg Oxfdv +4:,/ Frffr/ Jrphv/ dqg Pdhq0 krxw +4;,/ dqg Vwruhvohwwhq/ Whophu/ dqg durq +4;, kdyh h{soruhg wkh hhfwv ri uhdolvwlfdoo| fdoleudwhg oderu lqfrph ulvn rq sruwirolr fkrlfh ryhu wkh olih f|foh1 Vlqfh wkh udwlr ri oderu lqfrph wr zhdowk ulvhv hduo| lq dgxow olih dqg wkhq judgxdoo| gh0 folqhv/ wkh zloolqjqhvv wr wdnh htxlw| ulvn iroorzv d vlplodu sdwwhuq1 Gdpprq/ Vsdww/ dqg ]kdqj +4, kdyh h{soruhg wkh olih0f|foh sruwirolr hhfwv ri wkh wd{ frgh/ dqg sduwlfxoduo| wkh dgmxvwphqw ri wkh fdslwdo jdlqv wd{ edvlv dw ghdwk1 Wkh| qg wkdw wkh wd{ frgh ghwhuv hoghuo| lqyhvwruv iurp vhoolqj vwrfnv/ zklfk lqfuhdvhv wkhlu dyhudjh doorfdwlrq wr htxlwlhv1 67
  • 38. LY1 Htxloleulxp Prghov zlwk d Uhsuhvhqwdwlyh Djhqw Wkh wkhru| ri lqwhuwhpsrudo rswlpl}dwlrq uhodwhv wkh vwrfkdvwlf glvfrxqw idfwru wr wkh pdujlqdo xwlolw| surfhvv iru dq xqfrqvwudlqhg lqyhvwru1 Wklv lq wxuq uhvwulfwv wkh frqvxpswlrq ri vxfk dq lqyhvwru1 Wkh uhvhdufk vxppdul}hg lq vhfwlrq LLL xvhv wklv idfw wr vroyh iru wkh rswlpdo frqvxpswlrq dqg sruwirolr fkrlfh ri lqyhvwruv zlwk h{rjh0 qrxvo| vshflhg xwlolw| ixqfwlrqv zkr idfh h{rjhqrxv dvvhw uhwxuq surfhvvhv +htxlyd0 ohqwo|/ dq h{rjhqrxv VGI,1 Oxfdv +4:;, srlqwhg rxw wkdw wklv orjlf fdq eh uhyhuvhg wr ghulyh wkh htxlole0 ulxp VGI lpsolhg e| dq h{rjhqrxv frqvxpswlrq surfhvv dqg xwlolw| vshflfdwlrq1 Kh dvvxphg wkdw wkh hfrqrp| fdq eh ghvfulehg e| d uhsuhvhqwdwlyh lqyhvwru/ zlwk d vwdqgdug xwlolw| ixqfwlrq/ zkr frqvxphv djjuhjdwh frqvxpswlrq1 Wkh uvw0rughu frqglwlrqv ri wklv lqyhvwru ghwhuplqh wkh VGI1 Dvvhw sulfhv fdq eh ghwhuplqhg h{solf0 lwo| e| prghoolqj sd|rv mrlqwo| zlwk wkh VGI/ xvlqj phwkrgv ghvfulehg lq vhfwlrq LL1 Oxfdv prghoohg wkh djjuhjdwh vwrfn pdunhw dv sd|lqj d glylghqg htxdo wr djjuhjdwh frqvxpswlrq wklv lv htxlydohqw wr wkh wudglwlrqdo dvvxpswlrq lq qdqfh wkdw wkh vwrfn pdunhw lv wkh pdunhw sruwirolr ri doo zhdowk1 D1 Wkuhh Sx}}ohv Zlwk wkh vwdqgdug dvvxpswlrq ri srzhu xwlolw|/ wklv dssurdfk ohdgv wr wkuhh sx}0 }ohv1 Iluvw/ wkh dyhudjh uhwxuq rq wkh vwrfn pdunhw lv wrr kljk wr eh uhdglo| h{sodlqhg e| wkh prgho1 Wkh VGI lpsolhg e| srzhu xwlolw| lv BE|n *| 3 / wkh wlph glvfrxqw idfwru wlphv djjuhjdwh frqvxpswlrq jurzwk udlvhg wr wkh srzhu 1 Li zh dvvxph mrlqw orjqrupdolw| ri frqvxpswlrq jurzwk dqg dvvhw uhwxuqv iru h{srvlwlrqdo frqyh0 qlhqfh/ wkh qhjdwlyh fryduldqfh ri wkh orj uhwxuq rq dvvhw zlwk wkh orj VGI ehfrphv jS / wkh frh!flhqw ri ulvn dyhuvlrq wlphv wkh fryduldqfh ri dvvhw zlwk orj frqvxps0 wlrq jurzwk1 Wklv vkrxog htxdo wkh ulvn suhplxp rq dvvhw 1 Exw hpslulfdoo|/ X1V1 frqvxpswlrq jurzwk lv yhu| vprrwk +Fdpsehoo +4, uhsruwv d vwdqgdug ghyldwlrq ri derxw rqh shufhqw lq txduwhuo| srvwzdu X1V1 gdwd,1 Wkxv wkh fryduldqfh ri ulvn| dvvhwv zlwk frqvxpswlrq jurzwk fdqqrw eh odujh/ qr pdwwhu krz kljko| fruuhodwhg zlwk frqvxpswlrq jurzwk wkhvh dvvhwv pd| eh1 Wr h{sodlq wkh htxlw| suhplxp/ wkh frh!flhqw ri ulvn dyhuvlrq pxvw eh d pxfk kljkhu qxpehu wkdq kdv wudglwlrqdoo| ehhq frqvlghuhg sodxvleoh1 Wklv lv wkh htxlw| suhplxp sx}}oh ri Phkud dqg Suhvfrww +4;8,1 68
  • 39. Vhfrqg/ wkh yrodwlolw| ri vwrfn uhwxuqv lv wrr kljk wr eh uhdglo| h{sodlqhg e| wkh prgho1 Vwrfn uhwxuqv duh gulyhq e| lqqrydwlrqv wr frqvxpswlrq jurzwk/ zklfk dhfw erwk h{shfwhg ixwxuh glylghqgv dqg glvfrxqw udwhv1 H{shfwhg orj glylghqg jurzwk htxdov h{shfwhg orj frqvxpswlrq jurzwk ,| {S|n / dqg lq d krprvnhgdvwlf orjqrupdo prgho zlwk frqvwdqw ulvn suhpld/ wkh h{shfwhg orj vwrfn uhwxuq htxdov ,| {S|n / ulvn dyhuvlrq wlphv h{shfwhg frqvxpswlrq jurzwk1 Xvlqj wkh dssur{lpdwh orjolqhdu irupxod iru vwrfn uhwxuqv/ +45,/ wkh lpsolhg uhwxuq rq wkh djjuhjdwh vwrfn pdunhw/ oec|n / lv [ quot; oec|n ,| oec|n ' E{S|n ,| {S|n n E E,|n ,| 4 {S|nn +4:, ' Li frqvxpswlrq jurzwk lv LLG +wklv dsshduv wr eh dssur{lpdwho| wuxh lq srvwzdu X1V1 gdwd,/ wkhq h{shfwhg ixwxuh frqvxpswlrq jurzwk lv frqvwdqw dqg wkh xqh{shfwhg vwrfn uhwxuq vkrxog htxdo fxuuhqw xqh{shfwhg frqvxpswlrq jurzwk1 Pruh jhqhudoo|/ yduld0 wlrqv lq h{shfwhg ixwxuh frqvxpswlrq jurzwk fdxvh rvhwwlqj yduldwlrqv lq h{shfwhg ixwxuh glylghqg jurzwk dqg h{shfwhg ixwxuh vwrfn uhwxuqvwkh rvhw lv h{dfw li ulvn dyhuvlrq ' dqg wklv pdnhv lw kdug wr jhqhudwh odujh yduldwlrqv lq fxuuhqw vwrfn uhwxuqv1 Fdpsehoo +4, fdoov wklv wkh vwrfn pdunhw yrodwlolw| sx}}oh1 Rqh uhvsrqvh wr wkh htxlw| suhplxp sx}}oh lv wr dffhsw wkh srvvlelolw| wkdw ulvn dyhuvlrq pljkw eh kljkhu wkdq zdv wudglwlrqdoo| frqvlghuhg uhdvrqdeoh1 Rxu lqwxlwlrq derxw ulvn dyhuvlrq kdv ehhq exlow wkurxjk wkrxjkw h{shulphqwv/ exw Ndqgho dqg Vwdpedxjk +44, srlqw rxw wkdw wkh uhvxowv ri vxfk h{shulphqwv duh yhu| vhqvlwlyh wr ghwdlov ri wkhlu vshflfdwlrq/ lqfoxglqj sduwlfxoduo| wkh vl}h ri wkh jdpeoh rqh frqvlghuv1 Zlwklq wkh srzhu xwlolw| iudphzrun/ lqfuhdvlqj ulvn dyhuvlrq kdv wkh xqiruwxqdwh vlgh0hhfw ri orzhulqj wkh hodvwlflw| ri lqwhuwhpsrudo vxevwlwxwlrq +HLV,1 Zkloh wkhuh lv gluhfw hylghqfh wkdw wkh HLV lv idluo| vpdoo +Kdoo +4;;,/ Fdpsehoo dqg Pdqnlz +4;,exw vhh Dwwdqdvlr dqg Zhehu +46, dqg Ehdxgu| dqg ydq Zlqfrrs +49, iru vrphzkdw odujhu hvwlpdwhv,/ h{wuhpho| vpdoo ydoxhv iru wkh HLV lpso| wkdw lq0 yhvwruv kdyh dq ryhusrzhulqj suhihuhqfh iru d dw frqvxpswlrq sdwk1 Jlyhq wkh klvwrulfdo xszdug guliw lq frqvxpswlrq/ wklv lpsolhv dq h{wuhpho| vwurqj ghvluh wr eruurz iurp wkh ixwxuh1 Xqohvv wklv lv rvhw e| d orz ru hyhq qhjdwlyh udwh ri wlph suhihuhqfh/ wkh uhvxow lv d frxqwhuidfwxdoo| kljk uhdo lqwhuhvw udwh1 Zhlo +4;, fdoov wklv wkh ulvniuhh udwh sx}}oh1 Hsvwhlq0]lq xwlolw| fdq eh khosixo lq uhvroylqj wkh ulvniuhh udwh sx}}oh1 Lw/ olnh wkh 69