HIER
Harvard Institute of Economic Research
                 Discussion Paper Number 1897



 Asset Pricing at the Millenn...
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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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Transcript of "Asset Pricing at the millennium"

  1. 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
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  9. 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
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  26. 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
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  35. 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. 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. 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. 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. 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

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