Using Quantum Behaved Particle Swarm Optimization for Portfolio

7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO1R0DUFK
8VLQJ4XDQWXP%HKDYHG3DUWLFOH6ZDUP
2SWLPL]DWLRQIRU3RUWIROLR6HOHFWLRQ3UREOHP
6DHHG)DU]L$OLUH]D5D\DWL6KDYD]LDQG$EEDV3DQGDUL
)DFXOW\RI&RPSXWHU(QJLQHHULQJ,VODPLF$]DG8QLYHUVLW\%UDQFKRI.HUPDQVKDK,UDQ
)DFXOW\RI0DQDJHPHQWDQG$FFRXQWLQJ$OODPH7DEDWDEDHL8QLYHUVLW\,UDQ
)DFXOW\RI0DQDJHPHQWDQG(FRQRPLF7DUELDW0RGDUHV8QLYHUVLW\,UDQ
$EVWUDFW2QHRIWKHSRSXODUPHWKRGVIRURSWLPL]LQJFRPELQDWLRQDOSUREOHPVVXFKDVSRUWIROLRVHOHFWLRQSUREOHPLVVZDUP
EDVHG PHWKRGV ,Q WKLV SDSHU ZH KDYH SURSRVHG DQ DSSURDFK EDVHG RQ 4XDQWXP%HKDYHG 3DUWLFOH 6ZDUP 2SWLPL]DWLRQ
4362IRUWKHSRUWIROLRVHOHFWLRQSUREOHP7KH3DUWLFOH6ZDUP2SWLPL]DWLRQ362LVDZHOONQRZQSRSXODWLRQEDVHGVZDUP
LQWHOOLJHQFHDOJRULWKP4362LVDOVRSURSRVHGE\FRPELQLQJWKHFODVVLFDO362SKLORVRSK\DQGTXDQWXPPHFKDQLFVWRLPSURYH
SHUIRUPDQFHRI362*HQHUDOO\LQYHVWRUVLQSRUWIROLRVHOHFWLRQVLPXOWDQHRXVO\FRQVLGHUVXFKFRQWUDGLFWRU\REMHFWLYHVDVWKH
UDWHRIUHWXUQULVNDQGOLTXLGLW\:HHPSOR\HG4362PRGHOWRVHOHFWWKHEHVWSRUWIROLRLQVXSUHPHWHKUDQVWRFNH[FKDQJH
FRPSDQLHV LQ RUGHU WR RSWLPL]H WKH REMHFWLYHV RI WKH UDWH RI UHWXUQ V\VWHPDWLF DQG QRQV\VWHPDWLF ULVNV UHWXUQ VNHZQHVV
OLTXLGLW\DQGVKDUSUDWLR)LQDOO\WKHREWDLQHGUHVXOWVZHUHFRPSDUHGZLWK0DUNRZLW]CVFODVVLFDQG*HQHWLF$OJRULWKPV*$
PRGHOV LQGLFDWHG WKDW DOWKRXJK UHWXUQ RI WKH SRUWIROLR RI 4362 PRGHO ZDV OHVV WKDW WKDW LQ 0DUNRZLW]¶V FODVVLF PRGHO WKH
4362KDGEDVLFDOO\VRPHDGYDQWDJHVLQGHFUHDVLQJULVNLQWKHVHQVHWKDWLWFRPSOHWHO\FRYHUVWKHUDWHRIUHWXUQDQGOHDGVWR
EHWWHUUHVXOWVDQGSURSRVHVPRUHYHUVDWLOLW\SRUWIROLRVLQFRPSDUHGZLWKWKHRWKHUPRGHOV7KHUHIRUHZHFRXOGFRQFOXGHWKDW
DVIDUDVVHOHFWLRQRIWKHEHVWSRUWIROLRLVFRQFHUQHG4362PRGHOFDQOHDGWREHWWHUUHVXOWVDQGPD\KHOSWKHLQYHVWRUVWRPDNH
WKHEHVWSRUWIROLRVHOHFWLRQ
.H\ZRUGV6ZDUPDOJRULWKPSRUWIROLRVHOHFWLRQ*$ULVNUHWXUQ
5HFHLYHG-DQXDU\DFFHSWHG$XJXVW
,QWURGXFWLRQ
0DUNRZLW]¶V ZRUN > @ LV FRQVLGHUHG DV WKH PRVW
LQIOXHQWLDO WKHRU\ IRU SRUWIROLR VHOHFWLRQ 6LQFH KH
SURSRVHG KLV GLVWLQJXLVKHG ZRUN XVLQJ TXDQWLWDWLYH
PHWKRGVVFKRODUVEHJDQWRUHVHDUFKSRUWIROLRVHOHFWLRQ
0DUNRZLW] DQDO\]HG SRUWIROLRV FRQWDLQLQJ ODUJH
QXPEHUV RI VHFXULWLHV +H FRQVLGHUHG UHWXUQV RI
LQGLYLGXDOVHFXULWLHVDVUDQGRPYDULDEOHV7KHSXUSRVH
RIKLVDQDO\VLVZDVWRILQGSRUWIROLRVWKDWEHVWPHHWWKH
REMHFWLYHV RI LQYHVWRUV 0DUNRZLW] SUHVHQWHG KLV
IDPRXV PHDQYDULDQFH PRGHO WKURXJK TXDQWLI\LQJ
SRUWIROLR UHWXUQ DV PHDQ DQG FDOFXODWLQJ YDULDQFH DV
ULVN )RU D JLYHQ VSHFLILF UHWXUQ OHYHO DQ RSWLPDO
SRUWIROLR FDQ EH REWDLQHG ZKHQ WKH YDULDQFH RI
SRUWIROLR LV PLQLPL]HG :KLOH IRU D JLYHQ ULVN OHYHO
ZKLFK WKH LQYHVWRU FDQ EHDU DQ RSWLPDO SRUWIROLR FDQ
EH REWDLQHG ZKHQ WKH H[SHFWHG UHWXUQ RI SRUWIROLR LV
PD[LPL]HG
6LQFHWKHLQWURGXFWLRQRI0DUNRZLW]¶VPRGHOPDQ\
HIIRUWV KDYH EHHQ PDGH WR LPSURYH PHDQYDULDQFH
PRGHOV 6KDUS >@ JUHDWO\ VLPSOLILHG WKH QXPEHU DQG
WKHW\SHRILQSXWGDWD%HVW>@0HUWRQ>@DQG9RURV
>@ FRQWULEXWHG JUHDWO\ WR WKH HIILFLHQW SRUWIROLR
IURQWLHU %DVHG RQ WKH FRUH RI 0DUNRZLW]¶V WKHRU\ RI
DSSO\LQJPHDQDQGYDULDQFHWRGHVFULEHUHWXUQDQGULVN
PHDQYDULDQFH PRGHOV ZHUH DOVR H[WHQGHG WR GLVFXVV
YDULRXV LVVXHV LQ SRUWIROLR PDQDJHPHQW +XDQJ DQG
/LW]HQEHUJHU>@UHVHDUFKHGSRUWIROLRVHOHFWLRQWKHRU\
ZKHQDULVNOHVVDVVHWDQGVKRUWVHOOLQJRIULVNOHVVDVVHW
DUH DOORZHG .RQQR DQG 6X]XNL >@ FRQVLGHUHG
VNHZQHVVLQSRUWIROLRPDQDJHPHQW
7KHVH UHVHDUFKHV JUHDWO\ GHYHORSHG 0DUNRZLW]¶V
PHDQYDULDQFHPRGHODQGPDGHJUHDWDFKLHYHPHQWVLQ
SRUWIROLRVHOHFWLRQWKHRU\7KHFRPPRQDVVXPSWLRQVLQ
WKHLU PRGHOV DUH WKDW LQYHVWRUV KDYH HQRXJK KLVWRULFDO
GDWDRIVHFXULWLHVDQGWKDWWKHVLWXDWLRQRIDVVHWPDUNHWV
LQIXWXUHFDQEHFRUUHFWO\UHIOHFWHGE\WKHDVVHWGDWDLQ
WKH SDVW +RZHYHU LW LV KDUG WR DOZD\V HQVXUH VXFK
DVVXPSWLRQV 6RPHWLPHV IRU H[DPSOH ZKHQ QHZ
VWRFNV DUH OLVWHG LQ WKH VWRFN PDUNHW WKHUH LV QR SDVW
SHUIRUPDQFHLQIRUPDWLRQIRUWKHLUVHFXULWLHVDQGIRUDQ
HYHUFKDQJLQJ UHDO DVVHW PDUNHW WKH VHFRQG
DVVXPSWLRQFDQKDUGO\EHHQVXUHGHLWKHU
$OWKRXJK WKHUH DUH GLIIHUHQW PHWKRGV WR VROYH
SRUWIROLR VHOHFWLRQ DQG RWKHU FRPELQDWRULDO
RSWLPL]DWLRQ SUREOHPV LQ ILQDQFLDO DQG RWKHU DSSOLHG
VFLHQFHVXVHRI*HQHWLF$OJRULWKP*$LVSURPLVLQJ
DSSURDFKWRVROYHFRPELQDWRULDORSWLPL]DWLRQSUREOHPV
>@
7KH*$LQWURGXFHGE\+ROODQGLQLVDZHOO
NQRZQHIILFLHQWQRQOLQHDUVHDUFKPHWKRGRORJ\LQODUJH
VSDFHV >@ *$ XVHV D SRSXODWLRQ ZKLFK LV VLPSO\ D
VHW RI FKURPRVRPHV WR VHDUFK WKH VROXWLRQ VSDFH
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO1R0DUFK
'XULQJ HDFK JHQHUDWLRQ WKUHH JHQHWLF RSHUDWRUV DUH
DSSOLHG WR WKH SRSXODWLRQ VHOHFWLRQ FURVVRYHU DQG
PXWDWLRQ6HOHFWLRQRSHUDWRUSLFNVFKURPRVRPHVLQWKH
SRSXODWLRQ EDVHG RQ WKHLU ILWQHVV (DFK SDLU RI
FKURPRVRPHVRUSDUHQWVXQGHUJRFURVVRYHUDWUDQGRP
E\ H[FKDQJLQJ WKHLU LQIRUPDWLRQ ZLWK HDFK RWKHU WR
JHQHUDWH QHZ FKURPRVRPH RU RIIVSULQJ 7KH HIILFLHQW
VHW VHOHFWLRQ ZLWKLQ D SRUWIROLR PD\ EH HIILFLHQWO\
VROYHG E\ XVLQJ *$ > @ 7KHVH *$ EDVHG
SRUWIROLRVHOHFWLRQDOJRULWKPVPHUHO\IRFXVRQVWDQGDUG
GHYLDWLRQDVDQDSSURSULDWHPHDVXUHIRUQRQV\VWHPDWLF
ULVN 7KLV LQGLFDWHV WKDW LQYHVWRUV ZHLJK WKH
SUREDELOLWLHV RI QHJDWLYH UHWXUQV HTXDOO\ DJDLQVW
SRVLWLYHUHWXUQV>@,QDGGLWLRQ*$KDVDOVREHHQXVHG
WR PHDVXUH SRUWIROLR YRODWLOLW\ LQ UHODWLRQ WR WKH VWRFN
PDUNHW >@ WR HYLGHQFH WKDW WKH WHFKQLFDO WUDGLQJ LV
HIILFLHQWLQWKH6DQWD)HDUWLILFLDOVWRFNPDUNHW>@DQG
WR H[SORUH WKH UHODWLRQVKLS EHWZHHQ WKH ZHDOWK
G\QDPLFVDQGULVNSUHIHUHQFHVLQDPXOWLDVVHWDUWLILFLDO
VWRFN PDUNHW >@ $V XVLQJ JHQHWLF DOJRULWKP LV
FRPPRQ DQG GLIIHUHQW DUWLFOHV ZHUH FRYHUHG WKLV
SUREOHP ZH MXVW VKRZ WKH UHVXOWV RI UXQQLQJ WKLV
PHWKRG LQ RUGHU WR IRFXV RQ SURSRVHG 4XDQWXP
%HKDYHG 3DUWLFOH 6ZDUP 2SWLPL]DWLRQ DOJRULWKP
4362
$QRWKHU SRSXODU PHWKRG IRU RSWLPL]LQJ FRPSOH[
SUREOHPV ZKLFK LV NLQG RI SRSXODWLRQEDVHG
DOJRULWKPVLVWRDSSO\VZDUPDOJRULWKPEHFDXVHLWFDQ
EHLPSOHPHQWHGUHODWLYHO\HDVLO\DQGLVDSSOLFDEOHWRD
YHU\ ZLGH UDQJH RI SUREOHPV 6ZDUP DOJRULWKP LV D
W\SH RI DUWLILFLDO DOJRULWKP EDVHG RQ WKH FROOHFWLYH
EHKDYLRXU RI GHFHQWUDOL]HG VHOIRUJDQL]HG V\VWHPV
2QH RI WKH IDPRXV VZDUP EDVHG DOJRULWKPV WKDW LV
LQWURGXFHG VR IDU LV 3DUWLFOH 6ZDUP 2SWLPL]DWLRQ
3627KH362EHORQJVWRWKHFODVVRIGLUHFWVHDUFK
PHWKRGV XVHG WR ILQG DQ RSWLPDO VROXWLRQ WR DQ
REMHFWLYH IXQFWLRQ DND ILWQHVV IXQFWLRQ LQ D VHDUFK
VSDFH ZKLFK LV ILUVW GHVFULEHG LQ E\ .HQQHG\
DQG (EHUKDUW >@ 362 LV QRW D JOREDO FRQYHUJHQFH
JXDUDQWHHG RSWLPL]DWLRQ DOJRULWKP DV YDQ GHQ %HUJK
KDV GHPRQVWUDWHG >@ 7KHUHIRUH 6XQ HW DO > @
SURSRVHG D JOREDO FRQYHUJHQFHJXDUDQWHHG VHDUFK
WHFKQLTXH4362ZKRVHSHUIRUPDQFHLVVXSHULRUWRWKH
362 >@ 7KH 4362 LV SURSRVHG E\ FRPELQLQJ WKH
FODVVLFDO 362 SKLORVRSK\ DQG TXDQWXP PHFKDQLFV WR
LPSURYHSHUIRUPDQFHRI362
,Q WKLV SDSHU ULVN HYDOXDWLRQV FRQFHQWUDWH RQ
HVWLPDWLQJ WKH GLVWULEXWLRQV RI ILQDQFLDO UHWXUQ VHULHV
7KH PDLQ REMHFWLYH LV WR RSWLPL]H WKH SRUWIROLR VHW
EDVHG RQ DSSURSULDWH WKUHVKROG VHOHFWLRQ 7KXV ZH
LQWURGXFHD4362 EDVHGSRUWIROLRYRODWLOLW\WRIRUHFDVW
D PRGHO LQ RUGHU WR VHOHFW WKH EHVW SRUWIROLR VHW DQG
G\QDPLFDOO\ WR HVWLPDWH D VXLWDEOH SHDN WKUHVKROG IRU
HDFK DVVHW LQ WKH SRUWIROLR VLPXOWDQHRXVO\ 7KH
SURSRVHG PHWKRG LV KLJKO\ HIILFLHQW DQG HIIHFWLYH LQ
SURYLGLQJQHDURSWLPDOVROXWLRQVZLWKLQDIHZPLQXWHV
7KH SDSHU LV RUJDQL]HG DV IROORZV ,Q VHFWLRQ 0DUNRZLW] PRGHOV IRU SRUWIROLR VHOHFWLRQ DUH EULHIO\
UHYLHZHGDQGDIWHUWKHLQWURGXFWLRQRIVRPHQHFHVVDU\
NQRZOHGJH DERXW 362 $ 43623RUWIROLR 6HOHFWLQJ
DOJRULWKP LV GHVLJQHG WR VROYH WKH SRUWIROLR VHOHFWLRQ
SUREOHP LQ VHFWLRQ WKDW LV FRYHUHG DOO DVSHFWV RI
UHVHDUFK PHWKRGRORJ\ ,Q VHFWLRQ UHVXOWV ZLOO WHVW
ZLWK GLIIHUHQW UDWLRV DQG LQ WKH HQG RI WKLV SDUW
QXPHULFDO UHVXOWV DUH SUHVHQWHG WR VKRZ WKH SRWHQWLDO
DSSOLFDWLRQV RI WKH GLIIHUHQW PRGHOV &RQFOXVLRQ
UHPDUNVDUHILQDOO\JLYHQLQVHFWLRQ
'HILQLWLRQDQG/LWHUDWXUH
3RUWIROLR6HOHFWLRQ
)LUVW OHW XV UHPHPEHU WKH ZHOONQRZQ 0DUNRZLW]¶V
PHDQYDULDQFH PRGHO > @ IRU SRUWIROLR VHOHFWLRQ
SUREOHP/HW1EHWKHQXPEHURIGLIIHUHQWDVVHWV—LEH
WKH PHDQ UHWXUQ RI DVVHW L ıLM EH WKH FRYDULDQFH
EHWZHHQWKHUHWXUQVRIDVVHWVLDQGMDQGILQDOO\Ȝ>
@ EH WKH ULVN DYHUVLRQ SDUDPHWHU 7KH GHFLVLRQ
YDULDEOHV [L UHSUHVHQW WKH SURSRUWLRQ RI FDSLWDO WR EH
LQYHVWHGLQWKHDVVHWLXVLQJWKLVQRWDWLRQWKHVWDQGDUG
0DUNRZLW]¶V PHDQYDULDQFH PRGHO IRU WKH SRUWIROLR
VHOHFWLRQSUREOHPZRXOGEH
1 1
1
PLQLPL]HO ª ¦ ¦ [ L V LM [ M º O ª ¦ P L [ L º »¼
«¬L M «¬ L »¼
1
VXEMHFW WR ¦ [ L
L d [ L d L 1 7KH FDVH ZLWK Ȝ UHSUHVHQWV PD[LPL]LQJ RI WKH
SRUWIROLRPHDQUHWXUQZLWKRXWFRQVLGHULQJWKHYDULDQFH
DQG WKH RSWLPDO VROXWLRQ ZLOO IRUP RQO\ E\ WKH DVVHW
ZLWK WKH JUHDWHVW PHDQ UHWXUQ 7KH FDVH ZLWK Ȝ UHSUHVHQWV PLQLPL]LQJ RI WKH WRWDO YDULDQFH DVVRFLDWHG
WR WKH SRUWIROLR UHJDUGOHVV RI WKH PHDQ UHWXUQ DQG WKH
RSWLPDOVROXWLRQZLOOW\SLFDOO\FRQVLVWRIVHYHUDODVVHWV
$Q\ YDOXH RI Ȝ LQVLGH WKH LQWHUYDO UHSUHVHQWV D
WUDGHRII EHWZHHQ WKH PHDQ UHWXUQ DQG WKH YDULDQFH
JHQHUDWLQJ D VROXWLRQ EHWZHHQ WKH WZR H[WUHPHV Ȝ DQG
0HDQUHWXUQ
9DULDQFHRIUHWXUQ
)LJXUH 6WDQGDUG HIILFLHQW IURQWLHU FRUUHVSRQGLQJ WR WKH VPDOOHVW
EHQFKPDUNSUREOHP
6LQFH HYHU\ VROXWLRQ VDWLVI\LQJ DOO WKH FRQVWUDLQWV
IHDVLEOHVROXWLRQFRUUHVSRQGVZLWKRQHRIWKHSRVVLEOH
SRUWIROLRV IURP QRZ RQ ZH ZLOO VSHDN ZLWKRXW
GLVWLQJXLVKLQJ EHWZHHQ WKH VROXWLRQV IRU WKH DERYH
8VLQJ4XDQWXP%HKDYHG3DUWLFOH6ZDUP2SWLPL]DWLRQIRU3RUWIROLR6HOHFWLRQ3UREOHP
SUREOHP DQG SRUWIROLRV 7KH SRUWIROLR VHOHFWLRQ
SUREOHPLVDQLQVWDQFHRIWKHIDPLO\RIPXOWLREMHFWLYH
RSWLPL]DWLRQSUREOHPV7KHUHIRUHILUVWZHKDYHWRILQG
RXW DGRSW D GHILQLWLRQ IRU WKH FRQFHSW RI RSWLPDO
VROXWLRQ +HUH ZH ZLOO XVH WKH 3DUHWR RSWLPDOLW\
GHILQLWLRQ>@
³$ IHDVLEOH VROXWLRQ RI WKH SRUWIROLR VHOHFWLRQ
SUREOHPZLOOEHDQRSWLPDOVROXWLRQRUQRQGRPLQDWHG
VROXWLRQ LI WKHUH LV QRW DQ\ RWKHU IHDVLEOH VROXWLRQ
LPSURYLQJ RQH REMHFWLYH ZLWKRXW PDNLQJ ZRUVH WKH
RWKHU´
8VXDOO\DPXOWLREMHFWLYHRSWLPL]DWLRQSUREOHPKDV
GLIIHUHQW RSWLPDO VROXWLRQV 7KH REMHFWLYH IXQFWLRQ
YDOXHV RI DOO WKHVH QRQGRPLQDWHG VROXWLRQ IRUP ZKDW
WKH VRFDOOHG WKH ³HIILFLHQW IURQWLHU´ )RU WKH SUREOHP
GHILQHG LQ HTXDWLRQV WKH HIILFLHQW IURQWLHU LV DQ
LQFUHDVLQJ FXUYH WKDW JLYHV WKH EHVW WUDGHRII EHWZHHQ
WKHPHDQUHWXUQDQGYDULDQFHULVN)LJXUHVKRZVDQ
H[DPSOHRIVXFKDFXUYHFRUUHVSRQGLQJWRWKHVPDOOHVW
EHQFKPDUN SUREOHP GHVFULEHG LQ VHFWLRQ 7KLV
HIILFLHQW IURQWLHU KDV EHHQ FRPSXWHG WDNLQJ GLIIHUHQWYDOXHVIRUWKHULVNDYHUVLRQSDUDPHWHU O DQG
VROYLQJ H[DFWO\ WKH FRUUHVSRQGLQJ SRUWIROLR VHOHFWLRQ
SUREOHPV 7KH REMHFWLYH IXQFWLRQ YDOXHV RI WKH
UHVXOWLQJVROXWLRQVJLYHSRLQWVWKDWIRUPWKHFXUYH
LQ)LJXUH:HFDOOWKLVFXUYHDVWKHVWDQGDUGHIILFLHQW
IURQWLHU LQ RUGHU WR GLVWLQJXLVK LW IURP WKH JHQHUDO
HIILFLHQW IURQWLHU FRUUHVSRQGLQJ WR WKH JHQHUDO PHDQ
YDULDQFH SRUWIROLR VHOHFWLRQ PRGHO ZKLFK ZH ZLOO EH
GHVFULEHVLQWKHFRPLQJSDUDJUDSKV
:LWK WKH SXUSRVH RI JHQHUDOL]LQJ WKH VWDQGDUG
0DUNRZLW]¶V PRGHO WR LQFOXGH FDUGLQDOLW\ DQG
ERXQGLQJ FRQVWUDLQWV WKH PRGHO IRUPXODWLRQ WKDW FDQ
DOVREHIRXQGLQ>@ZLOOEHDSSOLHG,QDGGLWLRQ
WRWKHSUHYLRXVO\GHILQHGYDULDEOHVOHW.EHWKHGHVLUHG
QXPEHURIGLIIHUHQWDVVHWVLQWKHSRUWIROLRZLWKQRQXOO
LQYHVWPHQW H L DQG G L EHWKHORZHUDQGXSSHUERXQGV
UHVSHFWLYHO\IRUWKHSURSRUWLRQRIFDSLWDOWREHLQYHVWHG
LQ WKH DVVHW L ZLWK d H L d G L d 7KH DGGLWLRQDO
GHFLVLRQYDULDEOHV ]L DUHLIDVVHWLLVLQFOXGHGLQWKH
SRUWIROLR DQG RWKHUZLVH 7KH JHQHUDO PHDQYDULDQFH
PRGHOIRUWKHSRUWIROLRVHOHFWLRQSUREOHPLV
1 1
1
PLQLPL]HO ª ¦ ¦ [ L V LM [ M º O ª ¦ P L [ L º »¼
«¬L M «¬ L »¼
1
VXEMHFW WR ¦ [ L
L 1
¦ ]L
L . H L ] L d [ L d G L ] L L 1 ] L  ^` L
1 7KLV IRUPXODWLRQ LV D PL[HG TXDGUDWLF DQG LQWHJHU
SURJUDPPLQJ SUREOHP IRU ZKLFK QR HIILFLHQW
DOJRULWKPVH[LVW$QRWKHUGLIIHUHQFHZLWKWKHVWDQGDUG
PRGHO LV WKDW LQ WKH SUHVHQFH RI FDUGLQDOLW\ DQG
ERXQGLQJ FRQVWUDLQWV WKH UHVXOWLQJ HIILFLHQW IURQWLHU
ZKLFK ZH DUH JRLQJ WR FDOO LW DV JHQHUDO HIILFLHQW
IURQWLHU FDQ EH TXLWH GLIIHUHQW IURP WKH RQH REWDLQHG
ZLWK WKH VWDQGDUG PHDQYDULDQFH PRGHO ,Q SDUWLFXODU
WKHJHQHUDOHIILFLHQWIURQWLHUPD\EHGLVFRQWLQXRXV>
@
$4XDQWXP%HKDYHG3DUWLFOH6ZDUP
2SWLPL]DWLRQ
7KH 362 DOJRULWKP ILUVWO\ SURSRVHG E\ .HQQHG\ DQG
(EHUKDUW >@ LV D SRSXODWLRQEDVHG HYROXWLRQDU\
VHDUFK WHFKQLTXH ,W LV XQGHUO\LQJ PRWLYDWLRQ IRU WKH
GHYHORSPHQW RI 362 ZDV VRFLDO EHKDYLRU RI DQLPDOV
VXFK DV ELUG IORFNLQJ ILVK VFKRROLQJ DQG DQLPDO
KHUGLQJDQGVZDUPWKHRU\,Q362ZLWK0LQGLYLGXDOV
D SRWHQWLDO VROXWLRQ WR D SUREOHP LV UHSUHVHQWHG DV D
SDUWLFOHIO\LQJLQ'GLPHQVLRQDOVHDUFKVSDFHZLWKWKH
SRVLWLRQ YHFWRU ;L [L [L«[L' DQG YHORFLW\
9L YLYL«YL' (DFK SDUWLFOH UHFRUGV LWV EHVW
SUHYLRXV SRVLWLRQ WKH SRVLWLRQ JLYLQJ WKH EHVW ILWQHVV
YDOXH DV SEHVWL SEHVWL SEHVWL « SEHVWL' FDOOHG
SHUVRQDO EHVW SRVLWLRQ $WHDFKLWHUDWLRQ HDFK SDUWLFOH
FRPSHWHVZLWKWKHRWKHUVLQWKHQHLJKERUKRRGRULQWKH
ZKROHSRSXODWLRQIRUWKHEHVWSDUWLFOHZLWKEHVWILWQHVV
YDOXH DPRQJ QHLJKERUKRRG RU WKH SRSXODWLRQ ZLWK
EHVWSRVLWLRQJEHVWL JEHVWLJEHVWL«JEHVWL'FDOOHG
JOREDO EHVW SRVLWLRQ DQG WKHQ PDNHV VWRFKDVWLF
DGMXVWPHQW DFFRUGLQJ WR WKH IROORZLQJ HYROXWLRQ
HTXDWLRQV
YLG
ZYLG F UDQG SEHVWLG [LG F UDQG JEHVW [LG [LG
[LG YLG )RU L «0 G «' ,Q HTXDWLRQ F DQG F
DUH SRVLWLYH FRQVWDQW UDQG DQG UDQG DUH WZR
UDQGRP IXQFWLRQV JHQHUDWLQJ XQLIRUPO\ GLVWULEXWHG
UDQGRP QXPEHUV ZLWKLQ > @ 3DUDPHWHU Z LV WKH
LQHUWLDZHLJKWLQWURGXFHGWRDFFHOHUDWHWKHFRQYHUJHQFH
VSHHGRIWKH362$WHDFKLWHUDWLRQWKHYDOXHRI9LGLV
UHVWULFWHGLQ>9PD[9PD[@
362 LV QRW D JOREDO FRQYHUJHQFHJXDUDQWHHG
RSWLPL]DWLRQ DOJRULWKP DV 9DQ 'HQ %HUJK KDV
GHPRQVWUDWHG >@ 7KHUHIRUH 6XQ HW DO > @
SURSRVHG D JOREDO FRQYHUJHQFHJXDUDQWHHG VHDUFK
WHFKQLTXH DOJRULWKP 4362 ZKRVH SHUIRUPDQFH LV
VXSHULRUWRWKH362,QWKHTXDQWXPPRGHORID362
WKHVWDWHRIDSDUWLFOHLVGHSLFWHGE\ZDYHIXQFWLRQȥ[
W LQVWHDG RI SRVLWLRQ DQG YHORFLW\ 7KH G\QDPLF
EHKDYLRXU RI WKH SDUWLFOHLV ZLGHO\ GLIIHUHQW IURP WKDW
RI WKH SDUWLFOH LQ WUDGLWLRQDO 362 V\VWHPV LQ WKDW WKH
H[DFW YDOXHV RI SRVLWLRQ DQG YHORFLW\ FDQQRW EH
GHWHUPLQHG VLPXOWDQHRXVO\ :H FDQ RQO\ OHDUQ WKH
SUREDELOLW\ RI WKH SDUWLFOH¶V DSSHDULQJ LQ SRVLWLRQ [
IURPSUREDELOLW\GHQVLW\IXQFWLRQ_< [ W _ WKHIRUPRI
ZKLFKGHSHQGVRQWKHSRWHQWLDOILHOGWKHSDUWLFOHOLHVLQ
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO1R0DUFK
7KHSDUWLFOHVPRYHDFFRUGLQJWRWKHIROORZLQJLWHUDWLYH
HTXDWLRQ>@
[LG W ^JLG r E _ PEHVWG [LG W _ OQ X ` ZKHUH
J LG
M SEHVW LG M JEHVW G DQG
PLQ = 0
PEHVW
G
¦ SEHVW
LG
0 L PEHVW PHDQ EHVW SRVLWLRQ RU PDLQVWUHDP WKRXJKW
SRLQWLVGHILQHGDVWKHPHDQYDOXHRIDOOSDUWLFOHV¶WKH
EHVWSRVLWLRQ M DQGXDUHUDQGRPQXPEHUGLVWULEXWHG
XQLIRUPO\RQ>@UHVSHFWLYHO\DQGPLVWKHQXPEHURI
SDUWLFOHV/ ȕ_PEHVWG[LGW_QXFDQEHYLHZHGDV
WKH VWUHQJWK RI FUHDWLYLW\ RU LPDJLQDWLRQ EHFDXVH LW
FKDUDFWHUL]HV WKH NQRZOHGJH VHHNLQJ VFRSH RI WKH
SDUWLFOHDQGWKHUHIRUHWKHODUJHUWKHYDOXH/WKHPRUH
OLNHO\ WKH SDUWLFOH ILQG RXW QHZ NQRZOHGJH 7KH
SDUDPHWHU ȕFDOOHG FRQWUDFWLRQH[SDQVLRQ FRHIILFLHQW
LV WKH RQO\ SDUDPHWHU LQ 4362 DOJRULWKP )URP WKH
UHVXOWV RI VWRFKDVWLF VLPXODWLRQV 4362 KDV UHODWLYHO\
EHWWHUSHUIRUPDQFHE\YDU\LQJWKHYDOXHRIȕIURP
DWWKHEHJLQQLQJRIWKHVHDUFKWRDWWKHHQGRIWKH
VHDUFKWREDODQFHWKHH[SORUDWLRQDQGH[SORLWDWLRQ>@
5HVHDUFK0HWKRGRORJ\
Q Q Q
¦ [L G L ¦ ¦ [L [ M G LM L L M ZKHUH G L DQG G LM DUHWKHYDULDQFHDQGFRYDULDQFHRI
WKHH[FHVVUHWXUQVUHVSHFWLYHO\
0LQLPL]LQJWKH6\VWHPDWLF/HYHORI5LVN
%HWD DV DQ LQGLFDWRU RI VHQVLWLYLW\ LV D FULWHULRQ IRU
PHDVXULQJWKHV\VWHPDWLFOHYHORIULVNZKLFKPHDVXUHV
SDUW RI WKH WRWDO ULVN WKDW GRHV QRW UHGXFH DV YDULHW\
LQFUHDVHV%HWDLVDUHODWLYHFULWHULRQRIDJLYHQVKDUHLQ
UHODWLRQWRWKHSRUWIROLRRIWKHZKROHVWRFN7KHDPRXQW
RIEHWDFDQEHFDOFXODWHGXVLQJWKHIROORZLQJHTXDWLRQ
>@7KHREMHFWLYHRIWKHPLQLPXPV\VWHPDWLFOHYHORI
ULVNFDQDOVREHGHILQHGDVWKHHTXDWLRQLQRUGHUWR
PLQLPL]HWKLVW\SHRIULVN
PLQ = Q
¦ [L E L
L ZKHUHȕLLVWKHV\VWHPDWLFULVNRIDVVHWV
0D[LPL]LQJWKH6WRFN5HWXUQ6NHZQHVV
7KH2EMHFWLYHVRI0RGHO
$V DOUHDG\ PHQWLRQHG WKH PDLQ REMHFWLYHV RI RXU
PRGHO IRU HVWLPDWLQJ WKH EHVW UHVXOWV IRU WKH SRUWIROLR
VHOHFWLRQLQFOXGH
0D[LPL]LQJWKH3RUWIROLR5HWXUQ
6LQFHLQYHVWPHQWLVFDUULHGRXWIRUREWDLQLQJUHWXUQDQG
LQYHVWRUVWU\WRLQYHVWLQD PDQQHUVRDVWREHDEOHWR
DFKLHYH WKH PD[LPXP OHYHO RI UHWXUQ DFFRUGLQJO\ WKH
SXUSRVH RI SRUWIROLR VHOHFWLRQ FDQ EH GHILQHG DV
³5HWXUQ RI LQYHVWPHQW LQ VWRFN LQFOXGLQJ DQ\ W\SH RI
FDVK ZLWKLQ D JLYHQ SHULRG RI WLPH DORQJ ZLWK WKH
IOXFWXDWLRQV RI SULFH GXULQJ WKH SHULRG GLYLGHG E\ WKH
SULFHRIVHFXULWLHVRUDVVHWVDWWKHWLPHRIEX\LQJ´>@
7RFDOFXODWHWKHUDWHRIUHWXUQWKHHTXDWLRQLVXVHG
Q
¦ [ L UL
L ZKHUH [L LV WKH SURSRUWLRQ LQYHVWHG LQ YDULRXV DVVHWV
ZKHQWKHEHVWWUDGHRIILVIRXQGDQGULLVWKHH[SHFWHG
UDWHRIWKHUHWXUQRIDVVHWV
0LQLPL]LQJWKH1RQ6\VWHPDWLF5LVN
PD[ = GLVWULEXWLRQ IRU PHDVXULQJ WKH DPRXQW RI ULVN >@
5HJDUGLQJWKHIDFWWKDWYDULDQFHUHYHDOVWKHGLVWULEXWLRQ
RI WKH GDWD DURXQG WKH PHDQ PLQLPL]LQJ RI WKH
VLJQLILFDQFH RI YDULDQFH DV DQ REMHFWLYH WR GHFUHDVH
WKH IOXFWXDWLRQ RI D SRUWIROLR UHWXUQ FDQ EH VWDWHG DV
HTXDWLRQ
6LQFHZHKDYHGHILQHGULVNDVWKHIOXFWXDWLRQRIUHWXUQ
WKHQWKHPRUHOLPLWHGWKHGLVWULEXWLRQRIWKHUHWXUQWKH
OHVV DPRXQW RI WKH ULVN ZH ZRXOG H[SHFW ,Q SUDFWLFH
ZH FDQ XVH ³VWDQGDUG GHYLDWLRQ RI WKH UDWH RI UHWXUQ´
ZKLFK VKRZV WKH FKDUDFWHULVWLFV RI SUREDELOLW\
&RQVLGHULQJWKHIDFWWKDWWKHLQYHVWRUORRNVIRUSRVLWLYH
UHWXUQ DQG WULHV WR VHOHFW D VWRFN ZKLW D SRVLWLYH
GLVWULEXWLRQ RI UHWXUQ DQG VLQFH WKH FRPSDQLHV XQGHU
LQYHVWLJDWLRQ KDG SRVLWLYH GLVWULEXWLRQ RI UHWXUQ
VNHZQHVV>@WKHIROORZLQJREMHFWLYHZDVGHILQHGIRU
VHOHFWLQJ D SRUWIROLR ZLWK D SRVLWLYH GLVWULEXWLRQ RI
UHWXUQVNHZQHVV
0D[= Q Q § Q
L ¦ 6 LLL ; L ¦ ¨ ¦ ; L ; M 6 LLM ¦ ; L ; M 6 LMM
L L © M L
M ·
¸
¹
L z M
ZKHUH 6 LLL LV WKH VNHZQHVV DQG 6LLM DQG 6LMM DUH FR
VNHZQHVVRIWKHH[FHVVUHWXUQV
0D[LPL]LQJWKH/HYHORI3RUWIROLR/LTXLGLW\
7KH DPRXQW RI OLTXLGLW\ VWRFN UHYHDOV WKH SRWHQWLDOLW\
RI FKDQJLQJ VWRFN LQWR RWKHU W\SHV RI HTXLWLHV VXFK DV
PRQH\6LQFHLQHPHUJHQF\FDVHVLQYHVWRUVWHQGWRVHOO
WKHLU VWRFN HDVLO\ LQ RUGHU WR FDOFXODWH WKH ULVN RI
FRPSDQ\OLTXLGLW\ZHFDQXVHWKHUDWLRRIWKHQXPEHU
RI GD\V LQ ZKLFK WKH FRPSDQ\
V VWRFN ZDV GHDOW RYHU
WKH QXPEHU RI WKH GD\V LQ ZKLFK WKH FRPSDQ\ ZDV
DFWLYH LQ WKH PDUNHW 7KHUHIRUH WKH REMHFWLYH RI
PD[LPL]LQJSRUWIROLROLTXLGLW\FDQEHVWDWHGDV
Q
¦ [L HL
L ZKHUHHL LVWKHOLTXLGLW\RIDVVHWV
PD[ = 8VLQJ4XDQWXP%HKDYHG3DUWLFOH6ZDUP2SWLPL]DWLRQIRU3RUWIROLR6HOHFWLRQ3UREOHP
0D[LPL]LQJWKH6KDUS5DWHLQ3RUWIROLR
7KH3URSRVHG$OJRULWKP
6KDUS LQWURGXFHG WKH FULWHULRQ RI DGGLWLRQDO
UHWXUQ WR WKH ULVN DV DQ LQGLFDWRU RI GHYHORSLQJ
SRUWIROLRHTXDWLRQ$VDOUHDG\H[SODLQHGDGGLWLRQDO
UHWXUQLVWKHGLIIHUHQFHEHWZHHQWKHUHWXUQZLWKRXWULVN
DQG WKH UHWXUQ RI WKH VWRFN DQG WKH LQYHVWRUV
DLP WR
LQYHVW LQ D ZD\ WR DFKLHYH WKH PD[LPXP RI WKLV OHYHO
DQGPRUHUHWXUQDWWKHH[SHQVHRIULVNWKH\DFFHSW
7KH IROORZLQJ LV WKH SURFHGXUH RI 43623RUWIROLR
6HOHFWLQJDOJRULWKP
Q
¦ [L 6 L
L PD[ = ZKHUH 6 L LVWKHOLTXLGLW\RIDVVHWV
x 6WHS,QLWLDOL]HWKHSRSXODWLRQE\UDQGRPO\JHQHUDWHWKH
SRVLWLRQYHFWRU;LRIHDFKSDUWLFOHDQGVHWSEHVWL ;L
x 6WHS (YDOXDWH WKH ILWQHVV YDOXH RI HDFK SDUWLFOH E\
HTXDWLRQ XSGDWH WKH SHUVRQDO EHVW SRVLWLRQ SEHVWL
DQG REWDLQ WKH JOREDO EHVW SRVLWLRQ JEHVW DFURVV WKH
SRSXODWLRQ
x 6WHS,IWKHVWRSFULWHULRQLVPHWJRWRVWHSKJRUHOVH
JRWRVWHS
x 6WHS 8SGDWH WKH SRVLWLRQ YHFWRU RI HDFK SDUWLFOH
DFFRUGLQJWRHTXDWLRQDQGJRWRVWHS
x 6HS 2XWSXW WKH JEHVW DV D VROXWLRQ IRU SRUWIROLR
VHOHFWLRQSUREOHP
7KH4XDQWXP%HKDYHG3DUWLFOH6ZDUP
2SWLPL]DWLRQIRU6ROYLQJ3RUWIROLR
6HOHFWLRQ3UREOHP
7KHUH DUH WZR DOWHUQDWLYHV IRU VWRS FULWHULRQ RI WKH
DOJRULWKP 2QH PHWKRG LV WKDW WKH DOJRULWKP VWRSV
ZKHQWKHREMHFWLYHIXQFWLRQYDOXHLVOHVVWKDQDJLYHQ
WKUHVKROG H ҏ WKH RWKHU LV WKDW LW WHUPLQDWHV DIWHU
H[HFXWLQJDSUHVSHFLILHGQXPEHURILWHUDWLRQV
,QRUGHUWRVROYHGHWHUPLQHWKHOHYHORILQYHVWPHQWLQD
SRUWIROLRZLWK4362ZHPXVWGHWHUPLQHDQHQFRGLQJ
RISDUWLFOH¶VSRVLWLRQDQGDILWQHVVIXQFWLRQDQGWKHQZH
PXVWLQWURGXFHDQDOJRULWKPEDVHGRQ4362
3DUWLFOH¶V3RVLWLRQ
7HVWRI5HVXOWVZLWK'LIIHUHQW5DWLRV
5XQQLQJWKH0RGHO
$SDUWLFOH¶VSRVLWLRQHQFRGLQJLVPRVWLPSRUWDQWIDFWRU
LQ 4362 WKDW LV DIIHFWHG RQ WKH VL]H RI WKH VHDUFK
VSDFH 7KH SDUWLFOH¶V SRVLWLRQ RI WKH FXUUHQW SUREOHP
KDV JHQHV 7KH GHFLPDO RI HDFK JHQH LQGLFDWHV D
FROOHFWLRQ RI DQVZHUV UHODWHG WR WKH DPRXQW RI
LQYHVWPHQW LQ HDFK FRPSDQ\ )LJXUH VKRZV WKH
SDUWLFOH¶VSRVLWLRQHQFRGLQJ
$VZDVPHQWLRQHGWKHREMHFWLYHZDVWRVHOHFWWKHEHVW
SRUWIROLR IURP DPRQJ WKH WRS FRPSDQLHV RI WKH
7HKUDQ 6WRFN ([FKDQJH 7DEOH VKRZV WKHVH
FRPSDQLHV DORQJ ZLWK WKH GHILQHG YDULDEOHV DQG WKH
QHFHVVDU\SDUDPHWHUVIRUDSSO\LQJWKHPRGHO
$V 7DEOH VKRZV WKH ILUVW FROXPQ OLVWV WKH
FRPSDQLHV LQ TXHVWLRQ WKH VHFRQG FROXPQ VKRZV WKH
GHFLGHG YDULDEOHV IRU HDFK FRPSDQ\ DQG WKH WKLUG
FROXPQLVWKHPRQWKO\UHWXUQIRUHDFKFRPSDQ\ZKLFK
ZDVFDOFXODWHGEDVHGRQWKHPHDQRIUHWXUQVLQWKHODVW
PRQWKV HQGLQJ LQ 0DUFK 7R PHDVXUH QRQ
V\VWHPDWLFULVNLQWKHIRXUWKFROXPQZHXVHGYDULDQFH
RI UHWXUQ 7KH ILIWK FROXPQ GHPRQVWUDWHV V\VWHPDWLF
ULVN EHWD VHQVLWLYLW\ LQGLFDWRU DQG WKH VL[WK FROXPQ
LQGLFDWHV WKH VNHZQHVV UHWXUQ RI VWRFN ZLWKLQ WKH
LQYHVWLJDWHG UDQJHV VLQFH WKH REMHFWLYH ZDV WR
PD[LPL]H WKHVNHZQHVV RI SRUWIROLRLQWKLVVWXG\WKH
WRS FRPSDQLHV LQ WKH VWRFN ZKLFK KDG SRVLWLYH
VNHZQHVV LQGLFDWRU ZHUH LQYHVWLJDWHG 7KH VHYHQWK
FROXPQ UHSUHVHQWV WKH OLTXLGLW\ RI HDFK FRPSDQ\ DQG
WKH ODVW FROXPQ LQGLFDWHV WKH VKDUS UDWH GHPRQVWUDWHV
WKH DGGLWLRQDO UHWXUQ RI WKH VWRFN LQ UHODWLRQ WR QRQ
V\VWHPDWLF ULVN 7R PHDVXUH WKH VKDUS UDWLR IUHHULVN
UHWXUQ ZDV FRQVLGHUHG DV DV WKH PHDQ UDWH RI
WKHFRPPHUFLDOVHFXULWLHV
)LJXUH$SDUWLFOH¶VSRVLWLRQHQFRGLQJ
)LWQHVV)XQFWLRQ
$QRWKHU LPSRUWDQW IDFWRU LV D ILWQHVV IXQFWLRQ 7KH
FRPSOHWHDQGDSSURSULDWHILWQHVVIXQFWLRQLVVKRZHGLQ
HTXDWLRQ
Q = = S = S Q = Q = Q = K
K
K
K
K
K
ZKHUH =L QLSL DQG KL DUH UHVSHFWLYHO\ WKH REMHFWLYH
IXQFWLRQVWKHILWQHVVDPRXQWVWKDWGHVFULEHGLQVHFWLRQ
DQGHXFOLGHDQQRUPDOL]HGLQGH[,QWKLVSDSHUZH
PXVWWU\WRPLQLPL]HILWQHVVIXQFWLRQ
) [
7DEOH&RHIILFLHQWRIWKHVWRFNVLQWKHPRGHO
6WRFNV
,UDQ.KRGUR
,UDQ.KRGUR'LHVHO
%DQN(JKWHVDGH1RYLQ
«
%HKUDQ2LO
3DUV2LO
9DULDEOH
;
;
;
«
;
;
5DWHRI5HWXUQ
«
1RQV\VWHPDWLFULVN
«
6\VWHPDWLFULVN
«
6NHZQHVVRIUHWXUQ
«
/LTXLGLW\
«
6KDUSUDWLR
«
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO1R0DUFK
7DEOH2SWLPDOSRUWIROLRVROXWLRQV
/LPLWDWLRQ/HYHOVDQG)LWQHVV$PRXQW
5HYLHZLQJ VLPLODU FDVHV DQG FRQGXFWLQJ LQWHUYLHZV
ZLWK VWRFN VSHFLDOLVWV DQG SUDFWLWLRQHUV ZH FRQFOXGHG
WKDW WKH PD[LPXP OHYHO RI LQYHVWPHQW LQ HDFK VWRFN
ZDV
7KH ILWQHVV DPRXQWV IRU WKH REMHFWLYHV VXFK DV
PD[LPL]LQJ WKH SRUWIROLR UHWXUQ Q PLQLPL]LQJ WKH
QRQV\VWHPDWLF ULVN S PD[LPL]LQJ WKH VWRFN UHWXUQ
VNHZQHVV Q PD[LPL]LQJ WKH OHYHO RI SRUWIROLR
OLTXLGLW\ Q DQG PD[LPL]LQJ WKH 6KDUS UDWH Q LQ
SRUWIROLR ZHUH PHDVXUHG DV DQGUHVSHFWLYHO\WKURXJKVROYLQJWKHVLQJOH
REMHFWLYHSURJUDPPLQJSUREOHPV
6LQFHWKHQRUPDOEHWDLQDPDUNHWLVDQGWKHVWRFNV
ZKRVHEHWDLVPRUHWKDQDUHULVN\VWRFNVDQGWKDWWKH
GLVWULEXWLRQ RI WKH UHWXUQ RI VXFK VWRFNV LV HQRUPRXV
DOVR FRQVLGHULQJ WKDW WKRVH VWRFNV ZKRVH EHWD LV OHVV
WKDQ DUH VDIH VWRFNV DQG WKH GLVWULEXWLRQ RI WKHLU
UHWXUQ LV OLPLWHG DFFRUGLQJO\ ZH FRQVLGHUHG DV WKH
ILWQHVVDPRXQWRIV\VWHPDWLFULVNREMHFWLYHS
7KH0RGHO¶V5HVSRQVH
9DULDEOH
5HVXOW
9DULDEOH
5HVXOW
9DULDEOH
5HVXOW
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
[
$OO DOJRULWKPV DUH FRGHG LQ -%XLOGHU DQG UXQV KDYH
EHHQ GRQH RQ D &HQWULQR *+] FRPSXWHU ZLWK
0% PHPRU\ $OVR WKH LQLWLDO SRSXODWLRQV RI DOO
DOJRULWKPV FRQVLVW RI UDQGRP LQGLYLGXDOV $QG HDFK
H[SHULPHQWIRUHDFKDOJRULWKPZDVUHSHDWHGWLPHV
ZLWK GLIIHUHQW UDQGRP VHHGV $OO DOJRULWKPV UXQ RQ
HTXLYDOHQW FRQGLWLRQV 6SHFLILF SDUDPHWHU VHWWLQJV RI
DOODOJRULWKPVDUHGHVFULEHGLQ7DEOH
7DEOH'HVLJQSDUDPHWHUVRI*$DQG4362
4362
*$
7HUPLQDWLRQFULWHULRQ0D[LWHUDWLRQ
6L]HRIWKHSRSXODWLRQ
7HUPLQDWLRQFULWHULRQ0D[LWHUDWLRQ
6L]HRIWKHSRSXODWLRQ
3UREDELOLW\RIFURVVRYHU
3UREDELOLW\RIPXWDWLRQ
6FDOHIRUPXWDWLRQV
7KH UHVXOW RI WKH DSSOLFDWLRQ RI 4362 LV VKRZQ LQ
7DEOH7KHSUHVHQWHGUHVXOWVVKRZWKHSURSRUWLRQRI
WKHVWRFNZKLFKVKRXOGEHLQYHVWHGLQWKHVKDUHRIHDFK
FRPSDQ\ )RU LQVWDQFH LQ WKH WKH UDZ DQG WKH
ODVW FROXPQ LQGLFDWH WKDW WR PLQLPL]H WKH ILWQHVV
IXQFWLRQ7KHLQYHVWRUVKRXOGLQYHVWRIKLVFDSLWDO
LQ WKH ; YDULDEOH %HKUDQ RLO FRPSDQ\ ,Q WKLV
VHFWLRQWRPHDVXUHWKHTXDOLW\RIWKHVHOHFWHGSRUWIROLR
E\ 4362 WKH UHWXUQ RI WKH VHOHFWHG SRUWIROLR LV
FRPSDUHGWR0DUNRZLW]0RGHODQG*HQHWLF$OJRULWKP
7R FRPSDUH WKH UHVXOWV ZH XVH WKH UHWXUQ RI WKH
SRUWIROLR ZLWKLQ WKH PRQWKV WLPH SHULRG HQGLQJ LQ
0DUFK)LJXUHVKRZVWKHDFFXPXODWHGUHWXUQRI
GLIIHUHQW SRUWIROLRV ZLWKLQ WKH WLPH UDQJH LQ TXHVWLRQ
)LJXUHFODULILHVWKDWWKH0DUNRZLW]SRUWIROLRJLYHVD
EHWWHU UHWXUQ LQ FRPSDULVRQ ZLWK PXOWLREMHFWLYHV
PRGHO ZKLFK KDV ZRUNHG EDVHG RQ WKH JHQHWLF
DOJRULWKPDQG4362
)LJXUH([SRVWSHUIRUPDQFHRISRUWIROLRVUHWXUQRISRUWIROLR
5HJDUGLQJ WKH IDFW WKDW LQYHVWRUV FRXQWHU ZLWK ULVN
PHUH UHOLDQFH RQ UHWXUQ LQ WKH HYDOXDWLRQ RI
SHUIRUPDQFH LV QRW D JRRG FULWHULRQ DOWKRXJK HYHU\
LQYHVWRU SUHIHU KLJKHU UHWXUQ WKH\ DOVR SUHIHU QRW WR
ULVN 7KHUHIRUH WR KDYH D IDLU HYDOXDWLRQ RI SRUWIROLR
SHUIRUPDQFHZHVKRXOGGHWHUPLQHZKHWKHUWKHUHWXUQLV
D IXQFWLRQ RI ULVN" +HQFH WR UHODWLYHO\ HYDOXDWH
SHUIRUPDQFH RI WKH SRUWIROLRV ZH VKRXOG XVH PHWKRGV
RI PRGLILHG HYDOXDWLRQ ZKLFK WDNH LQWR DFFRXQW WKH
DPRXQWRIULVNLQYROYHG$OVRWRFKHFNWKHYDULDWLRQV
RI WKH SRUWIROLRV ZH VKRXOG XVH FRUUHODWLRQFRHIILFLHQW
DQG WKH QXPEHU RI WKH VHOHFWHG VWRFNV 7DEOH LOOXVWUDWHVWKHLQGLFDWRUVIRUSHUIRUPDQFHHYDOXDWLRQRI
WKHSRUWIROLRV
7DEOHVKRZVWKDWQRQHRIWKHPRGHOVLVVXSHULRUWR
WKH RWKHU DVIDU DVDOO RIWKH LQGLFDWRUV DUH FRQFHUQHG
+RZHYHU WKH PXOWLSXUSRVH PRGHO ZKLFK KDV EHHQ
VROYHG E\ WKH XVH RI 4362 KDV JLYHQ KLJKO\ 1XPEHU
RIVWRFNVLQWKHSRUWIROLRZLWKOHVVDPRXQWRIQRQ
V\VWHPDWLFULVN'HVSLWHWKHIDFWWKDWWKHPRGHOVROYHG
E\4362UHVXOWVLQOHVVUHWXUQFRPSDUHGWR0DUNRZLW]
PRGHO FRQVLGHULQJ 7U\QRU LQGLFDWRU LW FDQ EH
8VLQJ4XDQWXP%HKDYHG3DUWLFOH6ZDUP2SWLPL]DWLRQIRU3RUWIROLR6HOHFWLRQ3UREOHP
XQGHUVWRRGWKDWWKHGHFUHDVHLQUHWXUQKDVEHHQFRXSOHG
ZLWK OHVV ULVN $OVR WKH PRGLILHG LQGLFDWRUV EDVHG RQ
WKH ULVN FRQILUP WKH VXSHULRULW\ RI WKH SRUWIROLRV
UHVXOWHG IURP 4362 LQ FRPSDULVRQ ZLWK WZR RWKHU
PRGHOV
7DEOH ([3RVW SHUIRUPDQFH RI SRUWIROLRV FRPSHWLWLRQV RI
PRGHOV
0RGHO
0DUNRZLW]
0RGHO
*$
0RGHO
4362
0RGHO
$YHUDJH5DWHRI5HWXUQ
6WDQGDUG'HYLDWLRQRIWKH5DWH
RI5HWXUQ1RQV\VWHPDWLF5LVN
-HQVHQ&RHIILFLHQW)UHHULVN
5HWXUQ
7UH\QRU5DWLR
6KDUSH5DWLR
&RHIILFLHQWRI'HWHUPLQDWLRQ
1XPEHURI6WRFNVLQWKH
3RUWIROLR
1XPEHURI0RQWKVZLWK
1HJDWLYH3RUWIROLR5HWXUQ
)LJXUH VKRZV WKH ILWQHVV YDOXH FXUYH RI WKH
SUREOHP VROYHG E\ WKH 4362 DQG *$ DIWHU LWHUDWLRQV 7KH PLQLPXP ILWQHVV YDOXH RI 4362
PHWKRG LV ( ZKHUHDV WKH PLQLPXP ILWQHVV
YDOXH RI *$ PHWKRG LV ( )LJXUH VKRZV
4362REWDLQHGEHWWHUVROXWLRQLQVKRUWHUWLPH
$FWLYDWLRQ)XQFWLRQ
$FWLYDWLRQIXQFWLRQILWQHVVYDOXH
*$
4362
1XPEHURILWHUDWLRQV
)LJXUH$FWLYDWLRQIXQFWLRQILWQHVVYDOXHFXUYH
&RQFOXVLRQVDQG'LVFXVVLRQV
&RQVLGHULQJ WKDW WKH 4362 DQG *$ PRGHOV DUH QRQ
OLQHDUDQGFDQEHHDVLO\DSSOLHGIRUQXPHURXVYDULDEOHV
DQG FDQ EH XSJUDGHG HIIRUWOHVVO\ LQ FDVH RI DGGLQJ D
QHZYDULDEOHFRPSDQ\WKH\FDQEHFODLPHGWKDWWKHVH
WZRPRGHOVDUHPRUHVXLWDEOHPRGHOIRUVHOHFWLQJVWRFN
SRUWIROLR LQ FRPSDULVRQ ZLWK 0DUNRZLW] PRGHO %XW
ILQDOO\ LQ VHOHFWLQJ EHWZHHQ WZR DUWLILFLDO PRGHOV
UHJDUGLQJ WR LQGH[HV WKH ILWQHVV YDOXH QXPEHU RI
LWHUDWLRQV DYHUDJH UDWH RI UHWXUQ QXPEHU RI VWRFNV LQ
WKH SRUWIROLR DQG VWDQGDUG GHYLDWLRQ RI WKH UDWH RI
UHWXUQ LW FRXOG EH FRQFOXGHG WKDW WKH EHVW PRGHO LV
4362LQSRUWIROLRVHOHFWLRQSUREOHPVROYLQJ
,Q WKLV VWXG\ WKH REMHFWLYHV RI WKH PRGHO ZHUH
FRQVLGHUHG DV H[SOLFLW QRQHWKHOHVV LQ VLPLODU VWXGLHV
RQH FDQ XVH IX]]\ PXOWLSXUSRVH PRGHOV LQ RUGHU WR
VHOHFW D SRUWIROLR 8VLQJ WKLV PRGHO RQH FDQ WDNH LQWR
DFFRXQWGLIIHUHQWGLPHQVLRQVRIWKHUHDOLW\RIWKHLVVXH
DQG LQ WXUQ DFKLHYH PRUH DFWXDO UHVSRQVHV 5HJDUGLQJ
WKH IDFW WKDW WKH UHWXUQ RI WKH VWRFN LV SUREDEOH LQ
QDWXUH ZH VXJJHVW IXWXUH UHVHDUFKHV DSSO\ SUREDEOH
PXOWLREMHFWLYHVLQVHOHFWLQJVWRFNSRUWIROLR
5HIHUHQFHV
>@ $OH[DQGHU * %DLOH\ - DQG 6KDUSH :
)XQGDPHQWDOV RI ,QYHVWPHQWV 3UHQWLFH+DOO
>@ %HVW0DQG-DURVODYD+³7KH(IILFLHQW)URQWLHU
IRU %RXQGHG $VVHWV´ 0DWKHPDWLFDO 0HWKRGV RI
2SHUDWLRQV5HVHDUFKYROQRSS
>@ &KDQJ / DQG <L / ³*HQHWLF $OJRULWKPV IRU
3RUWIROLR 6HOHFWLRQ 3UREOHPV ZLWK 0LQLPXP
7UDQVDFWLRQ /RWV´ -RXUQDO RI 2SHUDWLRQDO
5HVHDUFKYROQRSS
>@ &KDQJ70HDGH1DQG%HDVOH\-³+HXULVWLFV
IRU
&DUGLQDOLW\
&RQVWUDLQHG
3RUWIROLR
2SWLPLVDWLRQ´ &RPSXWHUV DQG 2SHUDWLRQV
5HVHDUFKYROQRSS
>@ &KDPEHUV / 7KH 3UDFWLFDO +DQG %RRN RI
*HQHWLF$OJRULWKP&KDPSDQ+DOO
>@ &DPSEHOO 5 +XLVPDQ 5 DQG .RHGLMN .
³2SWLPDO 3RUWIROLR 6HOHFWLRQ LQ D 9DOXH DW 5LVN
)UDPHZRUN´ -RXUQDO RI %DQNLQJ DQG )LQDQFH
YROQRSS
>@ &KHQ+DQG+XDQJ&³5HODWLYH5LVN$YHUVLRQ
DQG :HDOWK '\QDPLFV´ ,QIRUPDWLRQ 6FLHQFHV
YROQRSS
>@ (KUHQWUHLFK 1 ³7HFKQLFDO 7UDGLQJ LQ WKH 6DQWD
)H ,QVWLWXWH $UWLILFLDO 6WRFN 0DUNHW 5HYLVLWHG´
-RXUQDO RI (FRQRPLF %HKDYLRXU DQG
2UJDQL]DWLRQYROQRSS
>@ *ROGEHUJ ( *HQHWLF $OJRULWKPV LQ 6HDUFK
2SWLPL]DWLRQ DQG 0DFKLQH /HDUQLQJ $GGLVRQ
:HVOH\3XEOLVKLQJ&RPSDQ\86$
>@ +ROODQG - $GDSWDWLRQ LQ 1DWXUDO DQG $UWLILFLDO
6\VWHPV DQ ,QWURGXFWRU\ $QDO\VLV ZLWK
$SSOLFDWLRQV WR %LRORJ\ &RQWURO DQG $UWLILFLDO
,QWHOOLJHQFH8QLYHUVLW\RI0LFKLJDQ3UHVV86$
>@ +ROODQG + ³$GDSWDWLRQ LQ 5 5RVHQ )0
6QHOO (GV´ 3URJUHVV LQ 7KHRUHWLFDO %LRORJ\
$FDGHPLF3UHVV1HZ<RUNYROSS
>@ +XDQJ & DQG /LW]HQEHUJHU 5 )RXQGDWLRQV IRU
)LQDQFLDO (FRQRPLFV $FDGHPLF 3UHVV 1HZ
<RUN
>@ -REVW 1 +RUQLPDQ 0 DQG /XFDV &
³&RPSXWDWLRQDO $VSHFWV RI $OWHUQDWLYH 3RUWIROLR
6HOHFWLRQ 0RGHOV LQ WKH 3UHVHQFH RI 'LVFUHWH
7KH,QWHUQDWLRQDO$UDE-RXUQDORI,QIRUPDWLRQ7HFKQRORJ\9RO1R0DUFK
>@
>@
>@
>@
>@
>@
>@
>@
>@
>@
>@
>@
>@
>@
>@
$VVHW&KRLFH&RQVWUDLQWV´4XDQWLWDWLYH)LQDQFH
YROQRSS
.DL ) DQG :HQKXD ; ³7UDLQLQJ 1HXUDO
1HWZRUN ZLWK *HQHWLF $OJRULWKPV IRU
)RUHFDVWLQJ WKH 6WRFN 3ULFH ,QGH[´ LQ
3URFHHGLQJV RI WKH ,((( ,QWHUQDWLRQDO
&RQIHUHQFH RQ ,QWHOOLJHQW 3URFHVVLQJ 6\VWHPV
&KLQDSS
.HQQHG\ - DQG (EHUKDUW & ³3DUWLFOH 6ZDUP
2SWLPL]DWLRQ´ LQ 3URFHHGLQJV RI ,(((
,QWHUQDWLRQDO &RQIHUHQFH RQ 1HXUDO 1HWZRUN
:$SS
.RQQR + DQG 6X]XNL . ³$ 0HDQ9DULDQFH
6NHZQHVV 2SWLPL]DWLRQ 0RGHO´ -RXUQDO RI
2SHUDWLRQV 5HVHDUFK 6RFLHW\ RI -DSDQ YRO QRSS
/DKVDVQD $ DQG $LQRQ 5 ³&UHGLW 6FRULQJ
0RGHOV 8VLQJ 6RIW &RPSXWLQJ 0HWKRGV $
6XUYH\´ 7KH ,QWHUQDWLRQDO $UDE -RXUQDO RI
,QIRUPDWLRQ7HFKQRORJ\YROQR
0DUNRZLW] + ³3RUWIROLR 6HOHFWLRQ´ -RXUQDO RI
)LQDQFHYROQRSS
0DUNRZLW] + 3RUWIROLR 6HOHFWLRQ (IILFLHQW
'LYHUVLILFDWLRQRI,QYHVWPHQWV:LOH\1HZ<RUN
0DKIRXG6DQG0DQL*³)LQDQFLDOIRUHFDVWLQJ
XVLQJ JHQHWLF DOJRULWKPV´ $SSOLHG $UWLILFLDO
,QWHOOLJHQFHYROQRSS
0XKDPPDG$DQG.LQJ$³)RUHLJQ([FKDQJH
0DUNHW )RUHFDVWLQJ 8VLQJ (YROXWLRQDU\ )X]]\
1HWZRUNV´ LQ 3URFHHGLQJV RI WKH ,((( ,$)(
&RPSXWDWLRQDO ,QWHOOLJHQFH IRU )LQDQFLDO
(QJLQHHULQJ1HZ<RUNSS
0HUWRQ 5 ³$QDO\WLF 'HULYDWLRQ RIWKH (IILFLHQW
)URQWLHU´-RXUQDORI)LQDQFLDODQG4XDQWLWDWLYH
$QDO\VLVYROQRSS
1RHYHU'DQG%DVNDUDQ6³*HQHWLF$OJRULWKPV
7UDGLQJ RQ WKH 63´ 7KH 0DJD]LQH RI
$UWLILFLDO ,QWHOOLJHQFH LQ )LQDQFH YRO QR SS
2K-.LP<DQG0LQ+³3RUWIROLR$OJRULWKP
%DVHG RQ 3RUWIROLR %HWD 8VLQJ *HQHWLF
$OJRULWKP´ ([SHUW 6\VWHPV ZLWK $SSOLFDWLRQV
YROQRSS
6KDUS : ³$ 6LPSOLILHG 0RGHO IRU 3RUWIROLR
$QDO\VLV´ -RXUQDO 0DQDJHPHQW 6FLHQFH YRO QRSS
6DZDUDJL < 1DND\DPD + DQG 7DQLQR 7
7KHRU\RI0XOWL2EMHFWLYH2SWLPL]DWLRQ(OVHYLHU
6FLHQFH86$
6FKDHUI $ ³/RFDO 6HDUFK 7HFKQLTXHV IRU
&RQVWUDLQHG 3RUWIROLR 6HOHFWLRQ 3UREOHPV´
&RPSXWDWLRQDO(FRQRPLFVYROQRSS
6KRDI - DQG )RVWHU $ ³7KH (IILFLHQW 6HW *$
IRU 6WRFN 3RUWIROLRV´ LQ 3URFHHGLQJV RI ,(((
,QWHUQDWLRQDO &RQIHUHQFH RQ &RPSXWDWLRQDO
,QWHOOLJHQFH$.SS
>@ 6XQ - ³3DUWLFOH 6ZDUP 2SWLPL]DWLRQ ZLWK
3DUWLFOHV +DYLQJ 4XDQWXP %HKDYLRU´ LQ
3URFHHGLQJV RI &RQJUHVV RQ (YROXWLRQDU\
&RPSXWDWLRQYROSS
>@ 6XQ - ³$ *OREDO 6HDUFK 6WUDWHJ\ RI 4XDQWXP
%HKDYHG 3DUWLFOH 6ZDUP 2SWLPL]DWLRQ´ LQ
3URFHHGLQJVRI,(((&RQIHUHQFHRQ&\EHUQHWLFV
DQG ,QWHOOLJHQW 6\VWHPV YRO SS >@ 6XQ - ;X : DQG /LX- ³3DUDPHWHU 6HOHFWLRQ
RI
4XDQWXP%HKDYHG
3DUWLFOH
6ZDUP
2SWLPL]DWLRQ´ LQ 3URFHHGLQJV RI WKH VW
,QWHUQDWLRQDO&RQIHUHQFHRQ$GYDQFHVLQ1DWXUDO
&RPSXWDWLRQ%HUOLQYROSS
>@ 9RURV - ³3RUWIROLR $QDO\VLV$Q $QDO\WLF
'HULYDWLRQ RI WKH (IILFLHQW 3RUWIROLR )URQWLHU´
(XURSHDQ-RXUQDORI2SHUDWLRQDO5HVHDUFKYRO
QRSS
>@ 9DQ'HQ ) ³$Q $QDO\VLV RI 3DUWLFOH 6ZDUP
2SWLPL]HUV´3K'7KHVLV8QLYHUVLW\RI3UHWRULD
>@ ;LD < /LX % :DQJ 6 DQG /DL. ³$ PRGHO
IRU 3RUWIROLR 6HOHFWLRQ ZLWK 2UGHU RI ([SHFWHG
5HWXUQV´ &RPSXWHUV DQG 2SHUDWLRQV 5HVHDUFK
YROQRSS
>@ ;LD<:DQJ6DQG'HQJ;³$&RPSURPLVH
6ROXWLRQ WR 0XWXDO )XQGV 3RUWIROLR 6HOHFWLRQ
ZLWK 7UDQVDFWLRQ &RVWV´ (XURSHDQ -RXUQDO RI
2SHUDWLRQDO 5HVHDUFK YRO QR SS 6DHHG )DU]L LV D IDFXOW\ PHPEHU DW
WKH 'HSDUWPHQW RI &RPSXWHU
(QJLQHHULQJ
,VODPLF
$]DG
8QLYHUVLW\EHUDQFK RI .HUPDQVKDK
,UDQ +H UHFHLYHG KLV %6 GHJUHH LQ
FRPSXWHU HQJLQHHULQJ IURP 5D]L
8QLYHUVLW\ ,UDQ LQ DQG 06 LQ
$UWLILFLDO,QWHOOLJHQFHIURP ,VIHKDQ8QLYHUVLW\,UDQLQ
+LV FXUUHQW UHVHDUFK LQWHUHVWV LQFOXGH DUWLILFLDO
LQWHOOLJHQFH QHXUDO QHWZRUN VRIW FRPSXWLQJ DQG JULG
FRPSXWLQJ
$OLUH]D 5D\DWL 6KDYD]L LV D
JRYHUQPHQW PHPEHU DW \D]G
SURYLQFH ,UDQ +H UHFHLYHG KLV %6
GHJUHHLQFRPSXWHUHQJLQHHULQJIURP
0D\ERG8QLYHUVLW\,UDQLQDQG
06 LQ WUDGLQJ PDQDJHPHQW LQ WKH
IHLOG RI ILQDQFLDO IURP ,VIHKDQ
8QLYHUVLW\,UDQLQ+LVFXUUHQWUHVHDUFKLQWHUHVWV
LQFOXGH ILQDQFLDO PDUNHWLQJ LQWHUQDWLRQDO PDUNHWLQJ
DGPLQLVWUDWLRQDQGDUWLILFLDOLQWHOOLJHQFH
8VLQJ4XDQWXP%HKDYHG3DUWLFOH6ZDUP2SWLPL]DWLRQIRU3RUWIROLR6HOHFWLRQ3UREOHP
$EEDV 3DQGDUL LV D 3K'
FRQGLGDWHVLQ 7DUELDW 0RGDUUHV
8QLYHUVLW\,UDQ+HUHFHLYHGKLV%6
GHJUHH LQ LQGXVWUDLO PDQDJHPHQW
IURP <D]G 8QLYHUVLW\ ,UDQ LQ DQG06LQLQGXVWUDLOPDQDJHPHQWLQ
IHLOG RI PDQXIDFWXULQJ IURP 7DUELDW
0RGDUUHV 8QLYHUVLW\ ,UDQ LQ +LV FXUUHQW
UHVHDUFKLQWHUHVWVLQFOXGHILQDQFLDOPDQXIDFWULQJDQG
DUWLILFLDOLQWHOOLJHQFH