Anellini / Arco / Ginkgo / Intarsio / Nuvole / Stella / Tangram ...
Manual de GINKGO 1.4 - ENG - UBbiodiver.bio.ub.es/vegana/resources/help/ginkgo/Manual de GINKGO...
Transcript of Manual de GINKGO 1.4 - ENG - UBbiodiver.bio.ub.es/vegana/resources/help/ginkgo/Manual de GINKGO...
*,1.*2XVHU¶VPDQXDO
9HUVLRQ
0LTXHO'H&iFHUHV$LQVD
'HSW%LRORJLD9HJHWDO8QLWDWGH%RWjQLFD
8QLYHUVLWDWGH%DUFHORQD
,1'(;RI&217(176&KDSWHU,QWURGXFWLRQ 3URJUDPRYHUYLHZ :KDWLV*,1.*2 7HFKQLFDOLQIRUPDWLRQ
*HQHUDOIHDWXUHV 'DWDPDWUL[W\SHV 0XOWLYDULDWHDQDO\VLVW\SHV *,1.*2PDLQZLQGRZV :RUNLQJSURMHFWV
&KDSWHU'DWDPDQDJHPHQWDQGRSHUDWLRQV 'DWD(GLWRU:LQGRZ ,QWURGXFWLRQ 'DWD0DWUL[QDPHDQGW\SH &UHDWLQJQHZGDWDPDWULFHV ,PSRUWLQJH[SRUWLQJGDWDPDWULFHV 'HOHWLQJGDWDLWHPV 0RYLQJGDWDLWHPVEHWZHHQ*,1.*2ZLQGRZV (GLWLQJPDWULFHV
2SHUDWLRQVRQREMHFWGHVFULSWRUGDWD 7UDQVIRUPLQJREMHFWGHVFULSWRUPDWULFHV $QDO\VLVRIGHVFULSWRUV
6\PPHWULFPDWULFHV %XLOGLQJ6LPLODULW\'LVVLPLODULW\PDWULFHV 7UDQVODWLQJVLPLODULWLHVWRGLVWDQFHV
&KDSWHU2UGLQDWLRQPHWKRGV 2UGLQDWLRQFRQFHSWV 3ULQFLSDO&RPSRQHQWV$QDO\VLV3&$ 7KHPHWKRG 5XQQLQJ3&$ 3&$VWDQGDUGRXWSXW 3&$VFDOLQJVSORWVDQGSUHVHUYHGGLVWDQFHV 0HDQLQJIXOFRPSRQHQWV
0HWULF0XOWLGLPHQVLRQDO6FDOLQJFODVVLFDO0'6 ,QWURGXFWLRQ &ODVVLFDO0'6DOJRULWKP 1HJDWLYHHLJHQYDOXHV 5XQQLQJFODVVLFDO0'6LQ*,1.*2
1RQPHWULF0XOWLGLPHQVLRQDO6FDOLQJ10'6 ,QWURGXFWLRQ .UXVNDOV10'6DOJRULWKP 5XQQLQJ10'6LQ*,1.*2
*,1.*2XVHU¶VPDQXDO
&RUUHVSRQGHQFH$QDO\VLV&$ ,QWURGXFWLRQ 7KHPHWKRG 5XQQLQJ&$
5HGXQGDQF\$QDO\VLV5'$ ,QWURGXFWLRQWRFDQRQLFDODQDO\VLV ,QWURGXFWLRQWR5HGXQGDQF\DQDO\VLV $OJHEUDRI5'$ 5XQQLQJ5'$ 5'$SORWVDQGELSORWV
&DQRQLFDO&RUUHVSRQGHQFH$QDO\VLV&&$ ,QWURGXFWLRQWR&DQRQLFDOFRUUHVSRQGHQFHDQDO\VLV 0HWKRGDQGDOJHEUDRI&&$ 5XQQLQJ&&$ &&$SORWVDQGELSORWV
5HODWHG0XOWLGLPHQVLRQDO6FDOLQJ50'6 ,QWURGXFWLRQ 50'6IRXQGDWLRQVDQGPHWKRGGHVFULSWLRQ 50'6LQ*,1.*2
&KDSWHU&ODVVLILFDWLRQPHWKRGV &ODVVLILFDWLRQFRQFHSWV&OXVWHULQJDQG'LVFULPLQDQW$QDO\VLV &DQRQLFDOOLQHDUGLVFULPLQDQWDQDO\VLV ,QWURGXFWLRQ $OJHEUDDQGPHWKRGGHVFULSWLRQ 5XQQLQJ/') /')RXWSXW
4XDGUDWLFGLVFULPLQDQW 7KHTXDGUDWLFGLVFULPLQDQWUXOH 5XQQLQJTXDGUDWLFGLVFULPLQDQW
'LVWDQFHEDVHGGLVFULPLQDQWDQDO\VLV ,QWURGXFWLRQ 7KHRUHWLFDOIRXQGDWLRQV 7KH'%UXOH 5XQQLQJ'%GLVFULPLQDQWDQDO\VLV
$JJORPHUDWLYH+LHUDUFKLFDO&OXVWHULQJ ,QWURGXFWLRQ +LHUDUFKLFDODOJRULWKPV 5XQQLQJDQDJJORPHUDWLYHFOXVWHULQJPHWKRG 3ORWWLQJKLHUDUFKLFDOPHWKRGV¶UHVXOWV %XLOGLQJSDUWLWLRQVIURPGHQGURJUDPV
.PHDQV .PHDQVFOXVWHULQJPHWKRG 5XQQLQJ.PHDQV .PHDQVRXWSXW
)X]]\&PHDQV )X]]\VHWVIX]]\ORJLFDQGIX]]\SDUWLWLRQV )X]]\&PHDQV)&0 5XQQLQJ)X]]\&PHDQV
.PHGLDQV)X]]\&PHGLDQV &HQWURLGVDQGPHGRLGV 5XQQLQJ.PHGLDQV)X]]\&PHGLDQVLQ*,1.*2
9HUVLRQ
3RVVLELOLVWLF&PHDQV 7KH3&0PHWKRG 7ZR3&0LPSURYHPHQWV 5XQQLQJ3&0 3&0RXWSXW $FWLRQVRQRXWSXWDQGJUDSKLFV
5(%/2&. 7KHPHWKRG 5XQQLQJ5(%/2&.
&KDSWHU(YDOXDWLRQDQGLQWHUSUHWDWLRQRIFODVVLILFDWLRQV (YDOXDWLRQRIFODVVLILFDWLRQV ,QWURGXFWLRQ ,QWHUQDOFULWHULDRISDUWLWLRQHYDOXDWLRQ'HWHUPLQLQJWKHQXPEHURIJURXSV &RPSDULQJFODVVLILFDWLRQV &RPSDULVRQVLQ*,1.*2
)XUWKHULQWHUSUHWDWLRQRIFOXVWHUV $QDO\]LQJFOXVWHUSURSHUWLHVRQDGDWDPDWUL[ 0HDVXUHPHQWRIHFRORJLFDOGLYHUVLW\ &RPSXWLQJHFRORJLFDOGLYHUVLW\VWDWLVWLFV &RPSXWLQJVSHFLHVILGHOLWLHVDQGGLDJQRVWLFVSHFLHV
&KDSWHU*UDSKLFV ,QWURGXFWLRQWR*UDSKLFVLQ*,1.*2 2YHUYLHZ *UDSKLFW\SHV
&UHDWLQJJUDSKLFV &UHDWLQJ'DQG'VFDWWHUSORWV &UHDWLQJRWKHUSORWV
*UDSKLFPDQLSXODWLRQSULQWLQJDQGH[SRUWLQJ *UDSKLFFRQWUROV *UDSKLFSULQWLQJDQGH[SRUWLQJ
5HIHUHQFHV
&KDSWHU,QWURGXFWLRQ
3URJUDPRYHUYLHZ:KDWLV*,1.*2
*,1.*2 LV D FRPSXWHUSURJUDP WKDW WULHV WRPDNHPXOWLYDULDWH DQDO\VLVPHWKRGVHDVLHU WRUXQIRUQRQH[SHUWVLQVWDWLVWLFV,WKDVEHHQGHYHORSHGLQWKHFRQWH[WRIQXPHULFDOHFRORJ\EXWLWFDQ EH XVHG LQ RWKHU VFLHQWLILF GLVFLSOLQHV HJ VRFLRORJ\ SV\FKRORJ\ :KLOH LW UXQVLQGHSHQGHQWO\ LW LV WKH VWDWLVWLFDO PRGXOH RI 9(*$1$ SDFNDJH D ZRUNLQJ HQYLURQPHQW WKDWSURYLGHVVHYHUDOWRROVIRUHGLWLQJDQGDQDO\VLQJIORUDDQGYHJHWDWLRQ'H&iFHUHVHWDO
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
$V D ZKROH WKH SURJUDP PDNHV LW SRVVLEOH WR GR PXOWLYDULDWH DQDO\VHV RI PRGHUDWHFRPSOH[LW\7KLVVRUWRIHFRORJLFDOGDWDPLQLQJFDQEHGRQHLQVHYHUDOVHVVLRQVEHFDXVHFRPSOHWHZRUNLQJSURMHFWVDUHVDYHGLQFRPSUHVVHG]LSILOHV
7HFKQLFDOLQIRUPDWLRQ
7KH*,1.*2SURJUDPLVZULWWHQLQ-DYDSURJUDPPLQJODQJXDJH7KHUHIRUHFRPSLOHGFRGHFDQEHUXQXQGHUGLIIHUHQWRSHUDWLQJV\VWHPV:LQGRZV/LQX[0DFHWF,QIDFWDQ\SODWIRUPVXSSRUWLQJ-DYD5XQWLPH(QYLURQPHQWYHUVLRQRUKLJKHUKWWSZZZMDYDFRPLVVXLWHGWRUXQWKHSURJUDP/LNHDQ\RIWKH9(*$1$VRIWZDUHPRGXOHV*,1.*2LVIUHHO\GLVWULEXWHGDQGFRQWLQXRXVO\ LPSURYHG ,QVWDOODWLRQ LQVWUXFWLRQV SURJUDP GRZQORDGV DQG VDPSOH GDWD VHWV DUHDYDLODEOHDWWKH9(*$1$ZHEVLWHKWWSELRGLYHUELRXEHVYHJDQD
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
7KHPLQLPXPHVWLPDWHGKDUGZDUHUHTXLUHPHQWVDUHD3HQWLXP,,,SURFHVVRUDQG0%RIPHPRU\/DQJXDJHVFXUUHQWO\VXSSRUWHGDUH(QJOLVK6SDQLVKDQG&DWDODQ
*,1.*2XVHU¶VPDQXDO
*HQHUDOIHDWXUHV'DWDPDWUL[W\SHV
*,1*.2FDQ KDQGOH WZR W\SHVRI GDWDPDWULFHV REMHFWGHVFULSWRUPDWULFHV DQG V\PPHWULFPDWULFHV
2EMHFW'HVFULSWRU'DWD
1XPHULFDO GDWD LV RIWHQ LQ WKH IRUP RI D VHW RI Q YHFWRUV LQ WKH IHDWXUH VSDFH Sℜ RI SGHVFULSWRUVRUYDULDEOHV7KDWLVWKHPDWUL[WRDQDO\]HLVXVXDOO\DUHFWDQJXODUQ[SPXOWLYDULDWHGDWDPDWUL[; ^[[[Q`ZKHUH S
L ℜ∈[ LVDGHVFULSWRUYHFWRUUHSUHVHQWLQJREMHFW LL Q DQG ℜ∈LM[ M S LV WKH MWKPHDVXUHGGHVFULSWRURUYDULDEOHRIREMHFW L2EMHFWGHVFULSWRUPDWULFHVDUHWKHPRVWFRPPRQIRUPRIRULJLQDOXVHUGDWD
6\PPHWULF'DWD
6TXDUHV\PPHWULFGDWDPDWULFHVXVXDOO\UHSUHVHQWWKHDVVRFLDWLRQRUUHVHPEODQFHQRUPDOO\DVLPLODULW\RUGLVVLPLODULW\DPRQJREMHFWV7KUHHV\PPHWULFVXEFDWHJRULHVDUHDYDLODEOHXVHGWRODEHODQGGLVWLQJXLVKV\PPHWULFPDWULFHV
o 81.12:16<00(75,&o 6,0,/$5,7<0$75,;o ',66,0,/$5,7<0$75,;
/HW5 >UKO@GHQRWHDV\PPHWULFQ[QUHODWLRQDORUUHVHPEODQFHPDWUL[ZKHUHUKOPHDVXUHVWKHVWUHQJWKRIWKHUHODWLRQVKLSEHWZHHQHOHPHQWV KDQG O5PD\EHHLWKHUDVLPLODULW\6RUDGLVVLPLODULW\ 'PDWUL[ RU D V\PPHWULF UHODWLRQZLWKXQNQRZQSURSHUWLHV$GLVVLPLODULW\ RUGLVWDQFHQ[QPDWUL[' >GKO@VDWLVILHVWKHIROORZLQJWKUHHFRQGLWLRQV
=KKG IRUDQ\K Q D≥KOG IRUDQ\K QDQGO QDQG EOKKO GG = IRUDQ\K QDQGO Q F
&RQYHUVHO\DVLPLODULW\PDWUL[6 >VKO@IXOILOV≥KOV IRUDQ\K QDQGO Q DOKKO VV = IRUDQ\K QDQGO QDQG EKKKO VV ≤ IRUDQ\K QDQGO Q F
0XOWLYDULDWHDQDO\VLVW\SHV
*,1.*2GLYLGHV WKHSURYLGHGPXOWLYDULDWHPHWKRGV LQWRFDWHJRULHVRUDQDO\VLV W\SHV(DFKPXOWLYDULDWHDQDO\VLV W\SHKDVDFRUUHVSRQGLQJPHQXHOHPHQWLQWKH*,1.*2PHQXEDU8QGHUHDFKPHQXWKRVHDQDO\VHVUHODWHGWRWKHFRUUHVSRQGLQJW\SHDUHDYDLODEOHDVPHQXLWHPV
9HUVLRQ
2UGLQDWLRQV 7KHVH DQDO\VHV SXUVXH WKH UHSUHVHQWDWLRQ RIPXOWLYDULDWH REMHFWV LQ D UHGXFHGGLPHQVLRQVFDWWHUGLDJUDP2UGLQDWLRQVPD\EHFODVVHGDVFDQRQLFDORUQRQFDQRQLFDOGHSHQGLQJRQWKHQXPEHURILQSXWPDWULFHV6HHFKDSWHUIRUPRUHLQIRUPDWLRQRQRUGLQDWLRQPHWKRGV
&ODVVLILFDWLRQV7KHVHPXOWLYDULDWHPHWKRGVSXUVXHWKHJURXSLQJRIREVHUYDWLRQVLQWRFODVVHV&ODVVLILFDWLRQ FDQ EH GRQH E\FOXVWHULQJ XVLQJ GDWD VROHO\ RUGLVFULPLQDQW DQDO\VLV XVLQJ DQLQLWLDO FODVVLILFDWLRQ IRU OHDUQLQJ SXUSRVHV PHWKRGV 6HH FKDSWHU IRU PRUH LQIRUPDWLRQ RQFODVVLILFDWLRQPHWKRGV
&RPSDULVRQV $OORZ WKH FRPSDULVRQ RI PXOWLYDULDWH VWUXFWXUHV HLWKHU FODVVLILFDWLRQV RURUGLQDWLRQV6HHFKDSWHUIRUPRUHLQIRUPDWLRQRQWKRVHPHWKRGV
2WKHUDQDO\VHV7KLVFDWHJRU\LQFOXGHVUHVXOWVSURYLGHGE\*,1.*2PHWKRGVWKDWFDQQRWEHLQFOXGHGLQWRWKHSUHYLRXVFDWHJRULHV
*,1.*2PDLQZLQGRZV
*,1.*2KDVWKUHHPDLQZLQGRZV7KH\FDQEHRSHQHGDQGVHQWWRWKHIURQWE\VHOHFWLQJWKHFRUUHVSRQGLQJ PHQX LWHPV LQ WKH:LQGRZ PHQX RI WKH *,1.*2 PDLQ PHQX EDU RU XVLQJNH\ERDUGVKRUWFXWV(DFKZLQGRZKDVLWVRZQPHQXEDUZKLFKDOORZVDFWLRQVUHODWHGWRLW7KHWKUHHZLQGRZVDUH
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¶UHVXOWV7KH*UDSKLF(GLWRURUJDQL]HVLWVJUDSKLFVLQDWDEEHGSDQH,WPDNHVLWSRVVLEOHWRFKDQJHVRPHSORWIHDWXUHVDQGWRH[SRUWSORWVDVLPDJHILOHV7KHPHQXRSWLRQVDYDLODEOHFDQFKDQJHGHSHQGLQJRQWKHWDEVHOHFWHG
*,1.*2XVHU¶VPDQXDO
:RUNLQJSURMHFWV
*,1.*2DOZD\VUXQVXVLQJDZRUNLQJSURMHFW$ZRUNLQJSURMHFW LQFOXGHVERWK WKHVRXUFHGDWD PDWULFHV DQG WKH DQDO\VLV UHVXOWV VR IDU REWDLQHG IURP WKHP 3URMHFWV FDQ EH VDYHG DVFRPSUHVVHG ]LS ILOHV $V D UHVXOW WKH DQDO\VLV SURMHFW FDQ EH FRQWLQXHG LQ ODWHU VHVVLRQV*UDSKLFVJHQHUDWHGLQ*,1.*2DUHQRWVWRUHGLQWKHSURMHFWEXWFDQEHH[SRUWHGDVLPDJHILOHV
$OOSURMHFWDFWLRQVVXFKDVFUHDWLQJQHZSURMHFWVRURSHQLQJDQGVDYLQJSURMHFWVDUHKDQGOHGXVLQJ WKH3URMHFWPHQX LQ WKH *,1.*2PDLQ PHQX EDU 3URMHFW RSWLRQV FDQ EH FKDQJHG E\FOLFNLQJRQ(GLWSURMHFWRSWLRQVPHQXLWHP7KHDYDLODEOHSURMHFWRSWLRQVDUH
3URMHFW+RPH'LUHFWRU\'LUHFWRU\ZKHUHILOHVDUHVDYHGE\GHIDXOW/DQJXDJH/DQJXDJHXVHGLQPHQXV/RRN$QG)HHO3ODWIRUPORRNRIWKHSURJUDP:LQGRZV81,;0HWDO*UDSKLF,PDJHV'LUHFWRU\'LUHFWRU\ZKHUHJUDSKLFLPDJHILOHVDUHH[SRUWHGE\GHIDXOW'DWD6DYH2SWLRQV+HUHWKHXVHUFDQVHOHFWZKLFKGDWDW\SHVDQGDQDO\VLVUHVXOWVZLOOEHVDYHG(DFKGDWDRUDQDO\VLVW\SHKDVDGLIIHUHQWFKHFNER['HFLPDO)RUPDW2SWLRQV+HUHXVHUVFDQVSHFLI\ZKLFKGHFLPDOIRUPDWKDVWREHXVHGE\GHIDXOWWRGLVSOD\YDOXHVLQHDFKPDWUL[W\SH
;0/IRUPDWLVDOVRDYDLODEOH+RZHYHU=,3ILOHIRUPDWLVKLJKO\UHFRPPHQGHGGXHWRLWVGDWDFRPSUHVVLRQ7KHRQO\DQDO\VHVZKLFKDUHQRWVWRUHGLQZRUNLQJSURMHFWILOHVDUHWKRVHSHQGLQJLQWKHµ2WKHUDQDO\VHV¶QRGHLQ$QDO\VLV0DQDJHU
&KDSWHU'DWDPDQDJHPHQWDQGRSHUDWLRQV
'DWD(GLWRU:LQGRZ,QWURGXFWLRQ
'DWD(GLWRULVWKH*,1.*2ZLQGRZFRQWDLQLQJWKHGDWDWREHHGLWHGDQGDQDO\]HG1HDUO\DOODQDO\VHVVWDUWIURPDGDWDPDWUL[LQWKH'DWD(GLWRU$OOGDWDPDWULFHVDUHOLVWHGLQWKH(GLWRULQWKHIRUPRIDWUHHRQWKHOHIWSDUWRIWKHPRGXOH7ZRPDLQQRGHVDUHSUHVHQWRQWKHWUHHHDFKRQHFRUUHVSRQGLQJWRRQHGDWDW\SH3URMHFWGDWDLWHPVDUHRUJDQL]HGDVWUHHQRGHVKDQJLQJIURPRQHRIWKHVH:KHQDGDWDLWHPLVVHOHFWHGLQWKHWUHHWKHFRUUHVSRQGLQJGDWDPDWUL[LVGLVSOD\HGRQWKHULJKWDVDQHGLWDEOHWDEOH7KH'DWD(GLWRUFDQEHVKRZQZKHQQRWYLVLEOHE\SUHVVLQJ$OW)'DWD0DWUL[QDPHDQGW\SH
7KH 'DWD (GLWRU HQDEOHV HGLWLQJ QXPHULFDO GDWD PDWULFHV HLWKHU REMHFW GHVFULSWRU RUV\PPHWULFRQHV(DFKGDWDLWHPKDVDQDPHDQGDW\SH7KHLWHPQDPHLGHQWLILHVWKHGDWDPDWUL[DQG WKH W\SH UHVWULFWV WKHRSHUDWLRQV WKDWFDQEHSHUIRUPHGRQ WKHGDWD7KH WZRGDWD W\SHVDUHGLVWLQJXLVKHGLQWKH'DWD(GLWRUE\JURXSLQJGDWDLWHPVLQWRWZRFRUUHVSRQGLQJWUHHQRGHV7KHQDPHDQG W\SHRIDGDWD LWHPDUHGLVSOD\HGRQDSDQHORQ WRSRI WKHGDWD WDEOHDORQJZLWK WKHPDWUL[¶VGLPHQVLRQV³QXPEHURIURZV´[³QXPEHURIFROXPQV´
7KH GDWD LWHP¶V QDPH DQG W\SH FDQ EH FKDQJHG E\ XVLQJ WKH IROORZLQJ RSWLRQV LQ WKH ILOH
PHQX$OWHUQDWLYHO\WKHPDWUL[QDPHFDQEHHGLWHGE\GRXEOHFOLFNLQJRQWKHFRUUHVSRQGLQJWUHHQRGH
&RPPDQG 0HQX,WHP)LOH0HQX .H\VWURNH&KDQJHVGDWDW\SHRQO\IRUV\PPHWULFPDWULFHV &KDQJHPDWUL[W\SH &WUO7&KDQJHVGDWDLWHPQDPH &KDQJHPDWUL[QDPH &WUO1
*,1.*2XVHU¶VPDQXDO
&UHDWLQJQHZGDWDPDWULFHV
7KHVLPSOHVWZD\WRFUHDWHDQHZHPSW\GDWDLWHPLQWKHHGLWRU LVE\VHOHFWLQJ&UHDWHQHZPDWUL[LQWKH)LOHPHQX7KHGLDORJWKDWDSSHDUVHQDEOHVWKHXVHUWRVHOHFWWKHPDWUL[W\SHQDPHDQGPDWUL[GLPHQVLRQVRIWKHQHZGDWDLWHP2QFHFUHDWHGWKHQHZGDWDLWHPZLOOEHVKRZQLQWKH(GLWRU¶VWUHHDVDQHZWUHHQRGHDVDFKLOGRIWKHFRUUHVSRQGLQJGDWDW\SHQRGH
,PSRUWLQJH[SRUWLQJGDWDPDWULFHV
,PSRUWLQJ
'DWD LWHPVDUH W\SLFDOO\ LPSRUWHG WR*,1.*2IURPDQ$6&,,ILOH8VHUFDQFKRRVHDPRQJVHYHUDO LPSRUWLQJRSWLRQV WKHYDOXHVHSDUDWLRQFKDUDFWHU WKHGHFLPDOVHSDUDWLRQFKDUDFWHUDQGZKHWKHUFROXPQDQGRUURZQDPHVDUHLQFOXGHGLQWKH$6&,,LQSXWILOH
$6&,,REMHFWGHVFULSWRUPDWUL[ UHDGLQJ LVDV IROORZV7KHQXPEHURIREMHFWV Q LVHTXDO WR
WKHQXPEHURIQRQHPSW\OLQHVH[FOXGLQJWKHILUVWOLQHLILWLVFRPSRVHGRIFROXPQKHDGHUV)RUHDFKOLQHDQXPEHURIHOHPHQWVDUHLGHQWLILHGXVLQJWKHLQGLFDWHGVHSDUDWRUFKDUDFWHU7KHQWKHQXPEHURIGHVFULSWRUVSLVVHWWRWKHPD[LPXPRIURZOLQHHOHPHQWVIRXQGPLQXVRQHLIWKHILUVWFROXPQFRQVLVWVRIREMHFWQDPHV,IFROXPQKHDGHUVDUHLQFOXGHGLQWKHILUVWOLQHWKHODVWSHOHPHQWVDUHXVHGDVGHVFULSWRUQDPHV$6&,,V\PPHWULFPDWULFHVDUHUHDGVLPLODUO\
9HUVLRQ
$GGLWLRQDOLPSRUWLQJIDFLOLWLHVDUHSURYLGHGIRUXVHUVRI&$12&2WHU%UDDNRURWKHUSURJUDPV GHDOLQJZLWK LWV ILOH IRUPDW VLQFH LW LV SRVVLEOH WR LPSRUW &$12&2 VSHFLHV GDWD RUHQYLURQPHQWDOGDWDILOHVLQWRWKH*,1.*2'DWD(GLWRU
([SRUWLQJ
7KHVDPH$6&,,DQG&$12&2IRUPDWVDUHDYDLODEOH IRUH[SRUWLQJGDWD IURP*,1.*2WRRWKHUVRIWZDUHWRROV$QDOWHUQDWLYHZD\WRH[SRUWWDEOHVIURP*LQNJRFRQVLVWVRIVLPSO\VHOHFWLQJWKH GHVLUHG WDEOH URZV DQG SUHVVLQJ&WUO& WR FRS\ WKHP WR WKH V\VWHP FOLSERDUG 7KHZKROHPDWUL[FDQEHFRSLHGE\SUHVVLQJWKHµ&RS\¶EXWWRQRQWKH LWHPSDQHO2WKHUVRIWZDUHVXFKDV0LFURVRIW([FHOFDQWKHQUHDGWKHWDEOHFRSLHGRQWRWKHFOLSERDUG
,PSRUWLQJSK\WRVRFLRORJLFDOUHOHYpWDEOHV
48(5&86LVDQRWKHUFRPSXWHUSURJUDPEHORQJLQJWRWKH9(*$1$SDFNDJH5HOHYpWDEOHVLQ;0/48(5&86IRUPDWFDQEHLPSRUWHGWR*,1.*27KHSURFHGXUHLVWKHVDPHDVWKHRQHWKDWHQDEOHVH[SRUWLQJIURP48(5&86WR*,1.*27KHUHDGHULVUHIHUUHGWRWKHFRUUHVSRQGLQJVHFWLRQ LQ WKH 48(5&86 XVHU¶V PDQXDO ,PSRUW([SRUW FRPPDQGV DUH VXPPDUL]HG LQ WKHIROORZLQJWDEOH
&RPPDQG 0HQX,WHP)LOH0HQX,PSRUWVDWH[WILOH ,PSRUWGDWD$6&,,7H[W,PSRUWVD&$12&2VSHFLHVGDWDILOH ,PSRUWGDWD&$12&2'(&25$1$FRQGHQVHGVSHFLHVGDWD,PSRUWVD&$12&2HQYLURQPHQWDOGDWDILOH ,PSRUWGDWD&$12&2HQYLURQPHQWDOGDWD([SRUWVDVSDFHGWH[WILOH ([SRUWGDWD$6&,,7H[W([SRUWVD&$12&2VSHFLHVGDWDILOH ([SRUWGDWD&$12&2'(&25$1$FRQGHQVHGVSHFLHVGDWD([SRUWVD&$12&2HQYLURQPHQWDOGDWDILOH ([SRUWGDWD&$12&2HQYLURQPHQWDOGDWD,PSRUWVD48(5&865HOHYp7DEOH ,PSRUW;0/UHOHYpWDEOH
'HOHWLQJGDWDLWHPV
'DWDLWHPVFDQEHGHOHWHGIURPWKHSURMHFWE\VLPSO\SUHVVLQJ&WUO'HOHWHZKHQWKHGDWDLWHPLQTXHVWLRQLVVHOHFWHGRQWKH(GLWRU¶V WUHH7KHFRUUHVSRQGLQJPHQXRSWLRQLQWKH)LOHPHQXLVFDOOHG5HPRYHGDWDPDWUL[IURPSURMHFW0RYLQJGDWDLWHPVEHWZHHQ*,1.*2ZLQGRZV
6RPHWLPHVWKHXVHUPD\EHLQWHUHVWHGLQPRYLQJFODVVLILFDWLRQPDWULFHVIURPWKH'DWD(GLWRUWRWKH$QDO\VLV0DQDJHURUDOWHUQDWLYHO\LQSXWWLQJUHVXOWPDWULFHVEDFNLQWRWKH'DWD(GLWRULQRUGHU WRSHUIRUPVXEVHTXHQW DQDO\VLV7KH IROORZLQJ WDEOH LQGLFDWHVZKHUH WKHPHQX LWHPV WKDWODXQFKWKHVHDFWLRQVDUH
$FWLRQ 0HQX,WHP 0HQX :LQGRZ .H\VWURNH&RSLHVDGDWDPDWUL[RQWRWKHFOLSERDUGLQ*,1.*2IRUPDWQRWXVHGIRUH[SRUW
&RS\DOOPDWUL[WRFOLSERDUG
)LOH 'DWD(GLWRU &WUO$3DVWHVDGDWDPDWUL[IURPWKHFOLSERDUGLQWR'DWD(GLWRUQRWXVHGIRULPSRUW
3DVWHPDWUL[IURPFOLSERDUGWRHGLWRU
)LOH 'DWD(GLWRU &WUO13ODFHVDFRS\RIWKHVHOHFWHGPDWUL[LQWKH$QDO\VLV0DQDJHULQWKH'DWD(GLWRU
&RS\VHOHFWHGPDWUL[WR'DWD(GLWRU
(GLW $QDO\VLV0DQDJHU &WUO6KLIW&
3DVWHVPDWUL[IURPFOLSERDUGLQ*,1.*2IRUPDWLQWRWKH$QDO\VLV0DQDJHU
3DVWHFOLSERDUGPDWUL[DVQHZSDUWLWLRQ
(GLW $QDO\VLV0DQDJHU &WUO9
*,1.*2XVHU¶VPDQXDO
(GLWLQJPDWULFHV9DOXHHGLWLRQDQGYLVXDOL]DWLRQ
'DWDPDWUL[FHOOYDOXHVFDQEHHGLWHGPDQXDOO\DVLQDVSUHDGVKHHW:KHQHGLWLQJDFHOOLMLQD V\PPHWULF PDWUL[ WKH FRPSOHPHQWDU\ FHOO ML ZLOO EH DOVR EH DOWHUHG &ROXPQ ZLGWK DQGGHFLPDOIRUPDWLVFRQWUROOHGXVLQJWKHIROORZLQJPHQXLWHPVRIWKHPHQX(GLW
$FWLRQ 0HQX,WHP(GLW0HQX'HFLPDOSUHFLVLRQLVLQLWLDOO\VHWXVLQJSURMHFWGHIDXOWV,WFDQEHFKDQJHGXVLQJWKLVPHQXLWHP7KLVPHQXLWHPLVDOVRDYDLODEOHZKHQULJKWFOLFNLQJRQWKHWDEOH &KDQJHYDOXHIRUPDW&ROXPQZLGWKLVSL[HOVE\GHIDXOW,WFDQEHFKDQJHGXVLQJWKLVPHQXLWHP,QDGGLWLRQWKHXVHUFDQVHWWKLVSURSHUW\E\ULJKWFOLFNLQJRQWKHWDEOHZKHQRQHFROXPQLVVHOHFWHGRUE\SODFLQJPRXVHDUURZRQWKHFROXPQKHDGHUERUGHUDQGGUDJJLQJLW
&KDQJHFROXPQZLGWK:LGWKRIREMHFWODEHOFROXPQFDQEHFKDQJHGXVLQJWKLVPHQXLWHP,WLVDOVRDYDLODEOHZKHQULJKWFOLFNLQJRQWKHREMHFWODEHOFROXPQ &KDQJHODEHOZLGWK
5RZDQGFROXPQPDQLSXODWLRQ
7KH IROORZLQJ WDEOH OLVWV DOO PHQX LWHPV RI WKH PHQX (GLW UHODWHG WR URZ DQG FROXPQPDQLSXODWLRQ
$FWLRQ 0HQX,WHP(GLW0HQX$GGVQHZURZVWRDUHFWDQJXODUPDWUL[ $GG1HZURZV$GGVQHZFROXPQVWRDUHFWDQJXODUPDWUL[ $GG1HZFROXPQV$GGVQHZHOHPHQWVWRDV\PPHWULFPDWUL[ $GG1HZHOHPHQWV)LOWHUVHPSW\URZVLQDUHFWDQJXODUPDWUL[ )LOWHUQXOOURZV)LOWHUVHPSW\FROXPQVLQDUHFWDQJXODUPDWUL[ )LOWHUQXOOFROXPQV)LOWHUVVSHFLHVZLWKORZIUHTXHQF\LQWKHPDWUL[ )LOWHUORZFRQVWDQF\VSHFLHV'HOHWHVURZVLQDUHFWDQJXODUPDWUL[ 5HPRYHURZV'HOHWHVFROXPQVLQDUHFWDQJXODUPDWUL[ 5HPRYHFROXPQV'HOHWHVHOHPHQWVLQDV\PPHWULFPDWUL[ 5HPRYHHOHPHQWV
$OOWKHVHDFWLRQVFDQDOVREHGRQHE\VHOHFWLQJDURZRUFROXPQLQWKHWDEOHDQGULJKWFOLFNLQJ5RZFROXPQV FDQ EHPRYHG E\ VHOHFWLQJ WKHP DQG ULJKWFOLFNLQJ RQ WKH QHZ SRVLWLRQ GHVLUHGWKLV LV VLPLODU WRDFXWSDVWHDFWLRQ5RZFROXPQ ODEHOV QDPHVDUHFKDQJHG WKURXJKGRXEOHFOLFNLQJ RQ WKH GHVLUHG URZ RU FROXPQ 7DEOH URZV PD\ EH UHRUGHUHG IROORZLQJ WKH VHOHFWHGFROXPQYDOXHVLQFUHDVLQJRUIROORZLQJURZODEHODOSKDEHWLFDORUGHULQJ
$OOWDEOHDFWLRQV
2WKHU(GLWPHQXDFWLRQVDIIHFWWKHGDWDPDWUL[DVDZKROH$FWLRQ 0HQX,WHP
&ORQHVDGDWDPDWUL[DQGFUHDWHVDQHZLWHP$GLDORJLVSURPSWHGWRVHWWKHQDPHRIWKHQHZLWHP &ORQH0DWUL[7UDQVSRVHVDUHFWDQJXODUPDWUL[7KDWLVFKDQJLQJURZVE\FROXPQVDQGYLFHYHUVD7KLVPHDQVWUHDWLQJREMHFWVDVGHVFULSWRUVDQGGHVFULSWRUVDVREMHFWV 7UDQVSRVH0DWUL[&URSVDUHFWDQJXODUPDWUL[$GLDORJLVSURPSWHGWRVHOHFWZKLFKHOHPHQWVDUHWREHH[FOXGHG &URS0DWUL[
9HUVLRQ
(GLWDFWLRQVFRQFHUQLQJJURXSV
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
2QWKHRWKHUKDQGLIREMHFWSDUWLWLRQVDUHDYDLODEOHRQWKH$QDO\VLV0DQDJHULWLVSRVVLEOHWRVSOLWDJLYHQPDWUL[ LQWRJURXSVXEPDWULFHV XVLQJ*URXSV([WUDFWGDWDJURXSVIROORZLQJDSDUWLWLRQ RU WR UHPRYHREMHFWV URZV EHORQJLQJ WR D FHUWDLQJURXS XVLQJ*URXSV5HPRYHGDWDJURXSVIROORZLQJDSDUWLWLRQ
*,1.*2XVHU¶VPDQXDO
2SHUDWLRQVRQREMHFWGHVFULSWRUGDWD7UDQVIRUPLQJREMHFWGHVFULSWRUPDWULFHV
'DWDWUDQVIRUPDWLRQVDUHH[HFXWHGIURPWKH7UDQVIRUPPHQXLQWKH'DWD(GLWRU,QPRVWRIWKHVH WUDQVIRUPDWLRQV D GLDORJ LV SURPSWHG WR HQDEOH WKH XVHU WR VHOHFW ZKLFK YDULDEOHVGHVFULSWRUV ZLOO EH DIIHFWHG E\ WKH WUDQVIRUPDWLRQ DQG ZKLFK ZLOO QRW $OVR D FKHFN ER[ LVDYDLODEOH LQ WKH GLDORJ WR HQDEOH UHSODFLQJ WKH FXUUHQW GDWDPDWUL[ E\ WKH YDULDEOH WUDQVIRUPHGPDWUL[2WKHUZLVHDQHZGDWDPDWUL[ZLOOEHSRVWHGRQWKHSURMHFW7KHRSHUDWLRQVLQFOXGHGLQWKH7UDQVIRUP PHQX DUH GHVFULEHG EHORZ 1RWH WKDW DOO WUDQVIRUPDWLRQV H[FHSWLQJ µ7UDQVIRUPYDOXHV¶FDQRQO\EHDSSOLHGWRREMHFWGHVFULSWRUPDWULFHV
$FWLRQ 0HQX,WHP7UDQVIRUP0HQX .H\VWURNH$SSOLHVDVLPSOHQXPHULFDOWUDQVIRUPDWLRQVTXDUHURRWORJDULWKPH[SRQHQWLDOWRFHOOGDWDYDOXHV 7UDQVIRUPYDOXHV &WUO)6WDQGDUGL]HVYDULDEOHVLQDUHFWDQJXODUPDWUL[7KHDFWXDORSHUDWLRQFDQEHPRGLILHGE\VHOHFWLQJWKHYDOXHWRVXEWUDFWDQGWKHYDOXHWRGLYLGH$FRQVWDQWQXPEHUFDQDOVREHDGGHG
6WDQGDUGL]HYDULDEOHV &WUO)1RUPDOL]HV YDULDEOHV LQ D UHFWDQJXODU PDWUL[ +RZHYHU LW VNLSV]HURV IRU ERWK PHDQ DQG YDULDQFH FRPSXWDWLRQV DQG IRU WKHWUDQVIRUPDWLRQ
1RQ]HURQRUPDOL]DWLRQ )RUHYHU\URZVXEWUDFWVWKHJURXSDYHUDJHWRHDFKYDOXHZHLJKWHGE\WKHREMHFWPHPEHUVKLSWRWKHJURXS &HQWHUGDWDE\JURXSV 0RGLILHV YDOXHV LQ D UHFWDQJXODU GDWD PDWUL[ VR DV WR HPXODWH DJLYHQGLVWDQFH 'LVWDQFHHPXODWLQJWUDQVIRUPV 5HSODFHVQRQ]HURYDOXHVLQDUHFWDQJXODUGDWDPDWUL[E\VRDVWKHPDWUL[EHFRPHVDELQDU\3UHVHQFH$EVHQFHPDWUL[ &RQYHUWWR3$PDWUL[
'LVWDQFHHPXODWLQJWUDQVIRUPV/HJHQGUH*DOODJKHUFUHDWHDQHZPDWUL[RI<YDOXHVIURPDUHFWDQJXODUPDWUL[;VRWKDWZKHQFRPSXWLQJWKH(XFOLGHDQGLVWDQFHRQWKHWUDQVIRUPHGGDWD < WKH GLVWDQFHPDWUL[ REWDLQHGZLOO EH HTXDO WR WKHPDWUL[ REWDLQHG E\ FRPSXWLQJ WKHHPXODWHGGLVWDQFHRQWKHRULJLQDOGDWD;7KHDYDLODEOHGLVWDQFHHPXODWLQJWUDQVIRUPVDUH
'LVWDQFHHPXODWHG 7UDQVIRUPIRUPXOD 'HVFULSWLRQ
&KRUGGLVWDQFH ∑=
=S
OLOLMLM [[\
'LYLVLRQE\YHFWRUOHQJWK5RZVQRUPDOL]HGWR
XQLWOHQJWK
6SHFLHVSURILOHVGLVWDQFH ∑=
=S
OLOLMLM [[\
'LYLVLRQ E\ YHFWRU VXP 6SHFLHV DUH URZ
SURSRUWLRQV
+HOOLQJHUGLVWDQFH ∑=
=S
OLOLMLM [[\
6TXDUHURRWRIWKHVSHFLHVSURSRUWLRQ
FGLVWDQFHML
LMLM [[
[[\++
++ ⋅⋅= 'RXEOH WUDQVIRUP E\ URZ DQG FROXPQ VHHHTXDWLRQVIKIRUQRWDWLRQ
9HUVLRQ
$QDO\VLVRIGHVFULSWRUV
6RPH LQLWLDO GHVFULSWLRQ RI WKH YDULDEOH VWUXFWXUH LV H[HFXWHG IURP WKH9DULDEOH $QDO\VLVPHQXLQWKH'DWD(GLWRUPHQXEDU7KHDYDLODEOHPHQXLWHPVDUHGHVFULEHGLQWKHIROORZLQJ
'HVFULSWLYHVWDWLVWLFV&WUO)
&DOFXODWHVWKHFRPPRQHVWGHVFULSWLYHVWDWLVWLFVIRUWKHVHOHFWHGYDULDEOHVGHVFULSWRUVRIWKHFXUUHQW UHFWDQJXODU GDWD PDWUL[ $YHUDJH 0HGLDQ 9DULDQFH 6WDQGDUG 'HYLDWLRQ 9DULDWLRQ&RHIILFLHQW0LQLPXP0D[LPXP5DQJH6NHZDQG.XUWRVLV7KHUHVXOWVDUHSODFHGDWWKHµ2WKHUDQDO\VLV¶WUHHQRGHRIWKH$QDO\VLV0DQDJHUWUHH
&RYDULDWLRQPDWULFHV&WUO)
&DOFXODWHV FRYDULDWLRQ PDWULFHV IRU WKH VHOHFWHG YDULDEOHV GHVFULSWRUV RI WKH FXUUHQWUHFWDQJXODU GDWD PDWUL[ 7KH IROORZLQJ PDWULFHV FDQ EH REWDLQHG 6XP RI VTXDUHV PDWUL[&RYDULDQFH PDWUL[ 3HDUVRQ FRUUHODWLRQ PDWUL[ 6SHDUPDQ FRUUHODWLRQ PDWUL[ ,I FKHFNER[FRUUHODWLRQ SYDOXHV LV VHOHFWHG DGGLWLRQDO PDWULFHV RI W\SH, HUURU SUREDELOLWLHV SYDOXHV RIFRUUHODWLRQVLJQLILFDWLRQZLOOEHSURGXFHG
)UHTXHQF\KLVWRJUDP
&UHDWHV D EDU SORW RI YDOXH IUHTXHQFLHV KLVWRJUDP IURP D VHOHFWHG YDULDEOH RI WKH FXUUHQWREMHFWGHVFULSWRUPDWUL[8VHUPXVWLQGLFDWHWKHYDULDEOHWRSORWDQGWKHQXPEHURIYDOXHFODVVHVWREHPDGH7KHUHVXOWLQJEDUSORWLVSODFHGRQWKH'DWD(GLWRU
)UHTXHQF\KLVWRJUDPLQFOXVWHU
$VLQWKHSUHYLRXVLWHPFUHDWHVDEDUSORWRIYDOXHIUHTXHQFLHVIURPDVHOHFWHGYDULDEOHRIWKHFXUUHQW REMHFWGHVFULSWRU PDWUL[ +RZHYHU YDOXHV RI REMHFWV EHORQJLQJ WR D JLYHQ FOXVWHU DUHGLVWLQJXLVKHG IURPYDOXHVRIREMHFWVQRWEHORQJLQJ WR LW7KHXVHUPXVW LQGLFDWH WKHYDULDEOH WRSORWWKHFOXVWHUWREHXVHGDVUHIHUHQFHDQGWKHQXPEHURIYDOXHFODVVHVWREHPDGH7KHUHVXOWLQJEDU SORW FRPELQHV WZR KLVWRJUDPV RQH IRU WKH REMHFWV LQVLGH WKH JURXS DQG WKH RWKHU IRU WKHH[WHUQDOREMHFWV
*,1.*2XVHU¶VPDQXDO
6\PPHWULFPDWULFHV%XLOGLQJ6LPLODULW\'LVVLPLODULW\PDWULFHV
6\PPHWULFPDWULFHVDUHFRPPRQLQPRVWPXOWLYDULDWHDQDO\VHVVLQFH WKH\H[SUHVVUHODWLRQVEHWZHHQREMHFWVRUGHVFULSWRUV6RPHPXOWLYDULDWHDQDO\VHVFODVVLILFDWLRQVRURUGLQDWLRQVFDQRUPXVWEHUXQZLWKDV\PPHWULFGDWDPDWUL[DVLQSXWPDWUL[)RULQVWDQFH0HWULF0XOWLGLPHQVLRQDO6FDOLQJ 0'6QHHGVDGLVVLPLODULW\ JHQHUDOO\DGLVWDQFHPDWUL[ WREHH[HFXWHG2Q WKHRWKHUKDQG $JJORPHUDWLYH +LHUDUFKLFDO &OXVWHULQJ DOJRULWKPV FDQ EH DSSOLHG WR ERWK VLPLODULW\ DQGGLVVLPLODULW\PDWULFHV
5HPHPEHU WKDW V\PPHWULF PDWULFHV FDQ EH LPSRUWHG DV $6&,, ILOHV $OWHUQDWLYHO\ WRFRQVWUXFW VXFK V\PPHWULF PDWULFHV RU WR WUDQVIRUP VLPLODULWLHV RQWR GLVVLPLODULWLHV WKH5HVHPEODQFHPHQXRIWKH'DWD(GLWRUPXVWEHXVHG7KHPRVWLPSRUWDQWPHQXLWHPVDUH
%XLOG VLPLODULW\PDWUL[ &WUO) %XLOGV D VLPLODULW\PDWUL[ DQG SODFHV LW DV DQHZGDWDLWHPLQWKH'DWD(GLWRUWUHH
%XLOGGLVVLPLODULW\PDWUL[&WUO)%XLOGVDGLVVLPLODULW\GLVWDQFHPDWUL[DQGSODFHVLWDVDQHZGDWDLWHPLQWKH'DWD(GLWRUWUHH
0DQ\ GLVVLPLODULW\ DQG VLPLODULW\ PHDVXUHV IRU HFRORJLFDO GDWD DUH DOUHDG\ DYDLODEOH LQ*,1.*27KHLUIRUPXODHDQGVKRUWGHVFULSWLRQVDUHJLYHQLQWKHWDEOHVRQWKHQH[WWZRSDJHVIRUGLVVLPLODULW\ DQG VLPLODULW\PHDVXUHV UHVSHFWLYHO\7KH IROORZLQJ QRWDWLRQ KDV WR EH WDNHQ LQWRDFFRXQW >>= MM [[,D D =>= MM [[,E E >== MM [[,F F === MM [[,G G ∑ =+ =
SM M[[ H
∑ =+ =SM M[[ I
∑ =+ =QL LMM [[ J
∑ ∑= =++ =QL
SM LM[[ K
∑ ==⋅=
SM MM [,[$ L
∑ ==⋅=
SM MM [,[% M
∑ =>>⋅+=
SM MMMM [[,[[& N
∑ ==
SM MM [[: PLQ O
$SDUW IURP WKRVHRI WKH WDEOHV WZRDGGLWLRQDO LQGLFHVDUHSURYLGHGE\*,1.*2YHU
*RZHUDQG*RRGDOOSUREDELOLVWLFVLPLODULW\FRHIILFLHQWV6HH/HJHQGUH/HJHQGUHIRUDGHWDLOHGH[SODQDWLRQRIWKRVHDQGRWKHUUHVHPEODQFHPHDVXUHVIRUHFRORJLFDOGDWD
9HUVLRQ
'LVWDQFH )RUPXOD 6KRUWGHVFULSWLRQ
(XFOLGHDQ'LVWDQFH ( )∑=
−=S
MMM(' [[G
[[ 3\WKDJRUHDQ (XFOLGHDQ 'LVWDQFH IRUTXDQWLWDWLYHGDWD
6TXDUHG(XFOLGHDQ'LVWDQFH ( )∑
=
−=S
MMM64(' [[G
[[ 6TXDUHG 3\WKDJRUHDQ (XFOLGHDQ'LVWDQFHIRUTXDQWLWDWLYHGDWD
%LQDU\(XFOLGHDQ'LVWDQFH ( )∑
=
>−>=S
MMM%,1(' [,[,G
[[ 3\WKDJRUHDQ (XFOLGHDQ 'LVWDQFH IRUELQDU\GDWD,WEHKDYHVOLNHDGLVWDQFHFRPSOHPHQW IRU 6LPSOH 0DWFKLQJ&RHIILFLHQW
%LQDU\6TXDUHG(XFOLGHDQ'LVWDQFH ( )∑
=
>−>=S
MMM%,164(' [,[,G
[[ 6TXDUHG 3\WKDJRUHDQ (XFOLGHDQ'LVWDQFHIRUELQDU\GDWD
0DQKDWWDQ0HWULF ∑=
−=S
MMM0DQ [[G
[[ 0DQKDWWDQRUFLW\EORFNPHWULF
$EVROXWH9DOXH'LVWDQFH ∑=
−=S
MMM$%6 [[G
[[ 6TXDUHURRWRI0DQKDWWDQPHWULF
%UD\&XUWLV'LVWDQFH++
=
=
=
+
−=
+
−=
∑
∑
∑
[[
[[
[[
[[G
S
MMM
S
MMM
S
MMM
%& [[ %UD\ &XUWLV HFRORJLFDO GLVWDQFH ,WEHKDYHVDVDGLVWDQFHFRPSOHPHQWRI0RW\ND VLPLODULW\ IRU TXDQWLWDWLYHGDWD DQG 6|UHQVHQ LQGH[ IRU ELQDU\GDWD
χ'LVWDQFH ∑= +++++
−=
S
M
MM
M [[
[[
[[G
[[
χ
&KLVTXDUH GLVWDQFH DV WKH RQHSUHVHUYHG LQ &RUUHVSRQGHQFH$QDO\VLV 8VHV WDEOH PDUJLQVLQIRUPDWLRQ,WKDVDOLQHDUUHODWLRQWRWKH&KLVTXDUHPHWULF
χ0HWULF ∑= +++
−=
S
M
MM
MP [
[[[
[G
[[
χ &KLVTXDUHPHWULF8VHVWDEOHPDUJLQVLQIRUPDWLRQ,WKDVDOLQHDUUHODWLRQWRWKH&KLVTXDUHGLVWDQFH
0DKDODQRELV'LVWDQFH 0DKDODQRELV RQH JURXS GLVWDQFH/LNH (XFOLGHDQ GLVWDQFH EXW LW WDNHVLQWRDFFRXQWYDULDEOHFRUUHODWLRQVDQGH[WUDFWVWKHP
&DQEHUUD0HWULF ∑= +
−=
S
M MM
MM&DQE [[
[[G
[[ &DQEHUUDPHWULF
&DQEHUUD0HWULF$GNLQVIRUP ∑
=− +
−⋅
++=
S
M MM
MM$G&DQE [[
[[FEDG
[[ &DQEHUUD PHWULF QRUPDOL]HG E\ WKH
QXPEHURIVSHFLHV
&KRUG'LVWDQFH ∑ ∑∑= ==
−=
S
M
S
OOM
S
OOM&KRUG [[[[G
[[
&KRUG GLVWDQFH SURSRVHG E\ 2UORFL7KLVLVWKH(XFOLGHDQGLVWDQFHFRPSXWHGDIWHUGLYLGLQJ WKHYDOXHE\WKHQRUPRUOHQJWKRIWKHYHFWRU
+HOOLQJHU'LVWDQFH ∑= ++
−=
S
M
MM+HOO [
[[[G
[[ 7KH+HOOLQJHU GLVWDQFH GHVFULEHG E\5DR
6SHFLHV3URILOHV'LVWDQFH ∑
= ++
−=
S
M
MMRI6S [
[[[G
3U [[ 3\WKDJRUHDQ (XFOLGHDQ GLVWDQFHFRPSXWHG DIWHU WUDQVIRUPLQJ GDWDGLYLGLQJE\URZVXP
3HDUVRQFRUUHODWLRQFRPSOHPHQW [[[[ 3HDUVRQ&RPS3HDUV UG −= 2QH FRPSOHPHQW RI 3HDUVRQ
FRUUHODWLRQFRPSXWHGEHWZHHQURZV
*,1.*2XVHU¶VPDQXDO
6LPLODULW\ )RUPXOD 6KRUWGHVFULSWLRQ
-DFFDUG(OOHQEHUJ &%$
&V (OOHQ-DF ++=− [[ -DFFDUGVLPLODULW\LQGH[ZKHQDSSOLHGWR
ELQDU\ GDWD (OOHQEHUJ VLPLODULW\ LQGH[ZKHQDSSOLHGWRTXDQWLWDWLYHGDWD
6|UHQVHQ6WHLQKDXV
++− +
= [[:V 6WHLQ6RU [[ 6|UHQVHQ VLPLODULW\ LQGH[ ZKHQ DSSOLHG
WRELQDU\GDWD6WHLQKDXVVLPLODULW\LQGH[ZKHQDSSOLHGWRTXDQWLWDWLYHGDWD
*OHDVRQLQGH[ &%$&V*OHDVRQ ++
=[[
*OHDVRQ VLPLODULW\ LQGH[ ,W LV YHU\VLPLODU EXW JLYHV GRXEOH ZHLJKW WRFRPPRQVSHFLHV)RU3$GDWDLWEHKDYHVOLNH WKH 6RUHQVHQ LQGH[ +RZHYHU ZLWKTXDQWLWDWLYH GDWD LW LV GLIIHUHQW IURP0RW\NDLQGH[EHFDXVHLWGRHVQRWGRXEOHWKHPLQLPXPRIYDOXHV ,QVWHDG LW VXPVERWK
6LPSOH0DWFKLQJ&RHIILFLHQW GFED
DV60& +++= [[ 60& LV D ELQDU\FRHIILFLHQW DOVRNQRZQ
DVWKH6RNDO0LFKHQHULQGH[
6SlW]LQGH[ PD[PLQ
[[
[[
*OHDVRQS
M MM
MM
6SDWK
V[[[[
FED
V
⋅⋅++
=
∑=
6SlW] VLPLODULW\ LQGH[ 7KLV LV DQDOWHUQDWLYH TXDQWLILFDWLRQ RI WKH -DFFDUGLQGH[ ,WV IRUPXOD KDV WZR FRPSRQHQWVWKH OHIW SDUW LV DQ H[SUHVVLRQ RI WKHUHODWLYH VLPLODULW\ RI VWDQGV ZKLOH WKHULJKWSDUWLVWKH*OHDVRQLQGH[
.XOF]\QVNLLQGH[
+=
++
[:
[:V.XOF [[ .XOF]\QVNLVLPLODULW\LQGH[7KHVXPRI
PLQLPDLVFRPSDUHGWRWKHJUDQGWRWDORIHDFKVLWH
3HDUVRQFRUUHODWLRQ [[[[ 3HDUVRQ3HDUVRQ UV = &RPSXWHV 3HDUVRQ FRUUHODWLRQ DPRQJREMHFWV LQVWHDGRI WKHQRUPDOFRUUHODWLRQDPRQJYDULDEOHVGHVFULSWRUV
&KLVTXDUHVLPLODULW\ ∑= +++
−−=
S
M
MM
M [[
[[
[V
[[
χ
&KLVTXDUH VLPLODULW\ LQGH[ 7KLV LV WKHFRPSOHPHQW RI &KL6TXDUH 0HWULF $VWKH PHWULF H[FOXGHV GRXEOH]HURV WKLVLQGH[ GRHV WKH VDPH ,W QHHGV SRVLWLYHGDWD PDWULFHV EHFDXVH LW XVHV YDOXHV DVIUHTXHQFLHV
6LPLODULW\5DWLR∑∑∑
∑===
=
−+= S
M MMSM M
SM M
SM MM
65 [[[[[[V
[[ $QDQJXODUPHDVXUHRIVLPLODULW\
6LPSVRQLQGH[ PLQ FEDDV6LPSVRQ +
=[[ $ELQDU\LQGH[RIVLPLODULW\
7UDQVODWLQJVLPLODULWLHVWRGLVWDQFHV
0DQ\ RI WKH PXOWLYDULDWH PHWKRGV FDQQRW ZRUN ZLWK VLPLODULWLHV ,I RQH ZDQWV WR XVH WKHREMHFWUHODWLRQVSURYLGHGE\DVLPLODULW\PHDVXUHLQGLVWDQFHEDVHGFRPSXWDWLRQVLWLVQHFHVVDU\WRWUDQVIRUP VLPLODULW\ YDOXHV LQWRGLVWDQFHYDOXHV7UDQVIRUPDWLRQV DUH ODXQFKHGE\ VHOHFWLQJ WKH7UDQVIRUP '6 PHQX LWHP RQ WKH5HVHPEODQFHPHQX RU SUHVVLQJ&WUO) 7KH IROORZLQJWUDQVIRUPVDUHDYDLODEOH
KOKO VG −= DKOOOKKKO VVVG −+= E
KOKO VG −= F
&KDSWHU2UGLQDWLRQPHWKRGV
2UGLQDWLRQFRQFHSWV,QYLHZRIWKHREYLRXVGLIILFXOW\LQYROYHGLQJUDSKLFDOO\GLVSOD\LQJWKHLQIRUPDWLRQFRQWDLQHG
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
7UDGLWLRQDOO\ RUGLQDWLRQ PHWKRGV KDYH EHHQ GLYLGHG LQWR FDQRQLFDO DQG QRQFDQRQLFDOPHWKRGV,IRQO\RQHGDWDPDWUL[LVXVHGWKHPHWKRGLVUHIHUUHGWRDVµQRQFDQRQLFDO¶RULQGLUHFWJUDGLHQWDQDO\VLV,QDQRQFDQRQLFDORUGLQDWLRQPHWKRGWKHLQWHUSUHWDWLRQRIWKHUHVXOWLQJD[HVLVJLYHQE\WKHFRQWULEXWLRQRIWKHRULJLQDOYDULDEOHV2QWKHRWKHUKDQGLIWKHDQDO\VLVQHHGVWZRRUPRUHPDWULFHV LW LV EURDGO\ FDOOHG µFDQRQLFDO¶ RUGLUHFW JUDGLHQW DQDO\VLV LQ FDVHRI HFRORJLFDOGDWD ,Q FDQRQLFDOPHWKRGVZKLFK DUH XVXDOO\ EDVHGRQPXOWLSOH UHJUHVVLRQV LQWHUSUHWDWLRQRIRUGLQDWLRQLVGRQHE\FRQVLGHULQJWKHFRQWULEXWLRQRIH[SOLFDWLYHYDULDEOHVWRWKHFDQRQLFDOD[HV
2UGLQDWLRQPHWKRGVDYDLODEOHLQ*,1.*2DUHGLVSOD\HGDVPHQXLWHPVLQWKH2UGLQDWHPHQXRIWKHPDLQPHQXEDU,IWKHXVHUZDQWVWRODXQFKQRQFDQRQLFDORUGLQDWLRQVDGDWDPDWUL[PXVWEH VHOHFWHG LQ WKH'DWD (GLWRU 7KH W\SH RI GDWD VHOHFWHG LQ WKH'DWD (GLWRU¶V WUHH GHWHUPLQHVZKLFKDQDO\VLVFDQEHGRQH:KHQVHOHFWLQJRQHDQDO\VLVLQWKH2UGLQDWHPHQXDGLDORJZLOOEHSURPSWHG WR UHTXHVW DQDO\VLV RSWLRQV ,QPRVW QRQFDQRQLFDO RUGLQDWLRQPHWKRGV WKH XVHU FDQUHVWULFW WKH DQDO\VLV WR D VXEPDWUL[ RI WKH VHOHFWHG PDWUL[ E\ FOLFNLQJ RQ 6HW REMHFWV RU 6HWGHVFULSWRUV:KHQUXQQLQJRUGLQDWLRQDQDO\VLVRQV\PPHWULFPDWULFHVRQO\6HWREMHFWVZLOOEHDYDLODEOH ,I WKH8VH DOO FKHFNER[ LV VHOHFWHG WKHQ DOO REMHFWVYDULDEOHV ZLOO EH XVHG IRU WKHRUGLQDWLRQ
&DQRQLFDO PHWKRGV DUH UXQ VLPLODUO\ WKRXJK GDWD PDWULFHV DUH VHOHFWHG LQ WKH SURPSWHGGLDORJ1RUHVWULFWLRQRIREMHFWVRUGHVFULSWRUVFDQEHGRQHPDWUL[FURSSLQJKDYHEHHQSHUIRUPHGSUHYLRXVO\WKRXJK
$IWHUVHOHFWLQJWKHGHVLUHGSDUDPHWHUL]DWLRQDQGFOLFNLQJRQ2NWKHDQDO\VLVZLOOVWDUWDQGDQHZLWHPZLOOEHSRVWHGRQWKH$QDO\VLV0DQDJHUWUHH
*,1.*2XVHU¶VPDQXDO
3ULQFLSDO&RPSRQHQWV$QDO\VLV3&$7KHPHWKRG
8QGHU D PXOWLQRUPDO GLVWULEXWLRQ WKH ILUVW SULQFLSDO D[LV LV WKH OLQH WKDW JRHV WKURXJK WKHJUHDWHVWGLPHQVLRQRIWKHFRQFHQWUDWLRQK\SHUHOOLSVRLGGHVFULELQJWKHGLVWULEXWLRQ([WHQGLQJWKLVLGHDWKHSULQFLSDOD[HVDUHDVHWRID[HVUHVXOWLQJIURPDULJLGURWDWLRQRIWKHRULJLQDOFRRUGLQDWHV\VWHP DQG FRUUHVSRQGLQJ WR WKH VXFFHVVLYH GLUHFWLRQV RIPD[LPXPYDULDQFH RI WKH VFDWWHU RISRLQWV 7KH SULQFLSDO FRPSRQHQWV JLYH WKH SRVLWLRQV RI WKH REMHFWV LQ WKH QHZ V\VWHP RIFRRUGLQDWHV
3ULQFLSDO &RPSRQHQWV $QDO\VLV 3&$ +RWHOOLQJ LV WKH VLPSOHVW RI WKH RUGLQDWLRQPHWKRGV ,W ILQGV WKH SULQFLSDO D[HV WKURXJK WKH HLJHQYDOXH GHFRPSRVLWLRQ RI WKH GLVSHUVLRQPDWUL[6LHVROYLQJ X,6 =− NN ZKHUHWKHGLVSHUVLRQPDWUL[LVFRPSXWHGDV [ ] [ ][[[[6 −−
−=
Q
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
7KHHOHPHQWVXMNRIWKHHLJHQYHFWRUVDUHDOVRZHLJKWVRUORDGLQJVRIWKHRULJLQDOGHVFULSWRUVLQ WKH OLQHDU FRPELQDWLRQ RI GHVFULSWRUV IURP ZKLFK WKH SULQFLSDO FRPSRQHQWV DUH FRPSXWHG7KXVWKHSRVLWLRQRIREMHFW LRQWKHILUVWSULQFLSDOD[LVLVJLYHQE\WKHOLQHDUFRPELQDWLRQ [ ] X[[ ⋅−= LLI DQG WKHSRVLWLRQRI DOO REMHFWV LQ WKHQHZV\VWHPRIF D[HV)Q [ F LH WKHPDWUL[RISULQFLSDOFRPSRQHQWVRUVFRUHVLVFRPSXWHGXVLQJWKHPDWUL[RIHLJHQYHFWRUV8S[F [ ] 8[[) ⋅−= $VFDQEHVHHQIURPWKHSUHYLRXVHTXDWLRQVWKHV\VWHPRISULQFLSDOD[HVLVFHQWHUHGZLWKUHVSHFWWRWKHVFDWWHURISRLQWREMHFWV7KHTXDOLW\RIWKHUHSUHVHQWDWLRQLQDUHGXFHG(XFOLGHDQVSDFHZLWKPGLPHQVLRQVRQO\F≥PPD\EHDVVHVVHGE\WKHUDWLR YDU ∑∑ ==
=FN N
PN N λλ
1RWHWKDWWKHGHQRPLQDWRULVDFWXDOO\HTXDOWRWKHWUDFHRI6
9HUVLRQ
5XQQLQJ3&$
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
3&$VWDQGDUGRXWSXW
7KH 3&$ SURFHGXUH RXWSXWV D WH[W ZLWK D OLVW RI HLJHQYDOXHV DQG WKHLU FRUUHVSRQGLQJSHUFHQWDJH RI YDULDQFH LH WKH SURSRUWLRQ RI 6 WUDFH &XPXODWLYH SHUFHQWDJHV RI H[SODLQHGYDULDQFH DUH DOVR JLYHQ 2Q WKH RWKHU KDQG WZR PDWULFHV DUH JLYHQ WKH REMHFW SULQFLSDOFRPSRQHQWVPDWUL[)DQGWKHYDULDEOHORDGLQJVPDWUL[83&$VFDOLQJVSORWVDQGSUHVHUYHGGLVWDQFHV
$VPHQWLRQHG LQ VXEVHFWLRQHLJHQYHFWRUVDUHXVXDOO\ VFDOHG WRXQLW OHQJWK8QGHU WKLVVFDOLQJ(XFOLGHDQGLVWDQFHVFDOFXODWHGEHWZHHQREMHFWVXVLQJDOOSULQFLSDOFRPSRQHQWVDUHHTXDOWRWKH(XFOLGHDQGLVWDQFHVRQWKHRULJLQDOVSDFH,IRQO\WKHILUVWSULQFLSDOFRPSRQHQWVDUHXVHGWRWKH (XFOLGHDQ GLVWDQFHV RQ WKH RULJLQDO VSDFH DUH RQO\ DSSUR[LPDWHG 7KXV GLVWDQFHV EHWZHHQREMHFWVSORWWHGLQDVFDWWHUGLDJUDPRISULQFLSDOFRPSRQHQWVVKRXOGEHWDNHQFDXWLRXVO\ZKHQWKHFXPXODWLYHSHUFHQWDJHRIH[SODLQHGYDULDQFHLVQRWFORVHRUHTXDOWR
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
*,1.*2XVHU¶VPDQXDO
YDULDEOHV RQ WKH FRQVWUXFWLRQ RI WKH RUGLQDWLRQ D[HV :KHQ ERWK SULQFLSDO FRPSRQHQWV DQGYDULDEOHORDGLQJVDUHSORWWHGLQWKHVDPHGLDJUDPLWLVFDOOHGDGLVWDQFHELSORW
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⋅ 8QGHUWKLVVHFRQGVFDOLQJWKHSURMHFWLRQRID GHVFULSWRUD[LV RQ D SULQFLSDO D[LV VKRZV LWV FRYDULDQFH DQG WKXV LWV SRVLWLYH RU QHJDWLYHFRQWULEXWLRQ&RUUHODWLRQVDPRQJRULJLQDOGHVFULSWRUVDUHJLYHQE\WKHDQJOHEHWZHHQGHVFULSWRUD[HVRQWKHIXOOVSDFHQRWE\WKHSUR[LPLW\EHWZHHQDSLFHVRID[HV,IWKHUHSUHVHQWDWLRQLVQRWRQIXOOVSDFHWKHDQJOHVEHWZHHQD[HVRIGHVFULSWRUVRQO\DSSUR[LPDWHWKHLUFRUUHODWLRQV
2EMHFWV FDQ DOVR EH SORWWHG RQWR WKLV QHZ VFDOLQJ $SSO\LQJ WKH VDPH WUDQVIRUP WR D[HV[ ] 8[[* ⋅⋅−= GRHV WKLV (XFOLGHDQ GLVWDQFHV EHWZHHQ REMHFWV RQ WKLV VFDOLQJ GR QRW
DSSUR[LPDWH (XFOLGHDQ GLVWDQFHV RI WKH RULJLQDO VSDFH EXW UDWKHU DSSUR[LPDWH 0DKDODQRELVGLVWDQFHVRQWKHRULJLQDOVSDFH$JDLQSULQFLSDOFRPSRQHQWVDQGYDULDEOHORDGLQJVFDQEHSORWWHGWRJHWKHURQWKLVVFDOLQJ6XFKDELSORWLVFDOOHGDFRUUHODWLRQELSORW0HDQLQJIXOFRPSRQHQWV
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
7KHUHLVDQHPSLULFDOUXOHDOVRNQRZQDVWKH.DLVHU*XWWPDQFULWHULRQVXJJHVWLQJWKDWRQHVKRXOG RQO\ LQWHUSUHW D SULQFLSDO FRPSRQHQW LI WKH FRUUHVSRQGLQJ HLJHQYDOXH LV ODUJHU WKDQ WKHPHDQRIWKHHLJHQYDOXHV,IVWDQGDUGL]HGGHVFULSWRUVDUHXVHGLQ3&$6LVDFWXDOO\DFRUUHODWLRQPDWUL[WKHPHDQRIHLJHQYDOXHVLV
9HUVLRQ
0HWULF0XOWLGLPHQVLRQDO6FDOLQJFODVVLFDO0'6,QWURGXFWLRQ
&ODVVLFDO0'6DOVRFDOOHG3ULQFLSDO&RRUGLQDWHV$QDO\VLVZDVFUHDWHGE\*RZHUDVDPHWKRGWRREWDLQ(XFOLGHDQUHSUHVHQWDWLRQVLHLQD&DUWHVLDQVSDFHIURPDVHWRIREMHFWVZKRVHUHODWLRQVDUHREWDLQHGE\XVLQJDQ\GLVVLPLODULW\PHDVXUH7KXVLWLVSHUIRUPHGRQDGLVVLPLODULW\PDWUL['2QHLQWHUHVWLQJDVSHFWRIFODVVLFDO0'6LVWKDWLWPD\EHXVHGZLWKDOOW\SHVRIRULJLQDO; YDULDEOHV SURYLGHG WKDW D FRHIILFLHQW DSSURSULDWH WR WKH GDWD KDV EHHQ XVHG WR FRPSXWH WKHGLVWDQFHPDWUL[
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
:KHQXVLQJFODVVLFDO0'6RQDGLVVLPLODULW\PDWUL[QRWHPEHGGDEOHRQD(XFOLGHDQVSDFHQHJDWLYHHLJHQYDOXHVDUHREWDLQHGDQGWKXVVRPHRUGLQDWLRQD[HVDUHLPDJLQDU\VHHEHORZ1RQPHWULF 0XOWLGLPHQVLRQDO 6FDOLQJ 10'6 DOVR REWDLQV RUGLQDWLRQV IURP DQ\ GLVVLPLODULW\ RUVLPLODULW\ PDWUL[ VHH VHFWLRQ 2QH DGYDQWDJH RI 10'6 RYHU FODVVLFDO0'6 LV WKDW WKHIRUPHUDOZD\V\LHOGVUHDO(XFOLGHDQD[HVQRPDWWHUZKDWWKHRULJLQDOGLVVLPLODULW\PHDVXUHXVHGLV+RZHYHU10'6FDQEHFRPSXWDWLRQDOO\YHU\H[SHQVLYH&ODVVLFDO0'6DOJRULWKP
0'6VWDUWVIURPDV\PPHWULFGLVWDQFHPDWUL['7KHFODVVLFDO0'6DOJRULWKPLQFOXGHVWKHIROORZLQJVWHSV
0DWUL['LVWUDQVIRUPHGWR$DSSO\LQJWKHIROORZLQJHTXDWLRQIRUHDFKSDLURIREMHFWV OKOK GD −=
0DWUL[$ LV WKHQ FHQWHUHG WR WKH FRRUGLQDWHV¶ RULJLQ \LHOGLQJ WKH LQQHU SURGXFWPDWUL['= [δOK@ZKRVHHOHPHQWVDUH
DDDD KOOKOK +−−=δ ZKHUH WKH FROXPQ DQG URZPHDQV DUH VXEWUDFWHG IURP HDFK DOK HOHPHQW DQG WKH JUDQGPHDQLVDGGHG
&RPSXWHDQHLJHQYDOXHGHFRPSRVLWLRQ'REWDLQLQJDGLDJRQDOPDWUL[RIHLJHQYDOXHV/DQGDPDWUL[RIHLJHQYHFWRUV86FDOHHLJHQYHFWRUVWRKDYHDOHQJWKHTXDOWRWKHVTXDUHURRW RI WKH FRUUHVSRQGLQJ HLJHQYDOXH 7KHVH VFDOHG HLJHQYHFWRUV FRUUHVSRQG WR WKHSULQFLSDOFRRUGLQDWHVRIREMHFWV7KDWLVDVVXPLQJWKDW8LVLQLWLDOO\FROXPQVFDOHGWRXQLWOHQJWK
8; = ,IRQHKDVDV\PPHWULFVLPLODULW\PDWUL[6LWVYDOXHVPXVWEHWUDQVIRUPHGLQWRGLVWDQFHVVXEVHFWLRQ
*,1.*2XVHU¶VPDQXDO
'XHWRWKHFHQWHULQJVWHSPDWUL['KDVDOZD\VDWOHDVWRQH]HURHLJHQYDOXH1RWHWKDWDWPRVWQ±D[HVDUHQHFHVVDU\IRUUHSUHVHQWLQJQSRLQWVLQ(XFOLGHDQVSDFH7KHUHPD\EHPRUHWKDQ RQH ]HUR HLJHQYDOXH LQ WKH FDVHZKHUH WKH GLVWDQFHPDWUL[ LV GHJHQHUDWH LHZKHQ WKHQREMHFWVFDQEHUHSUHVHQWHGLQOHVVWKDQQ±GLPHQVLRQV,IPDWUL['LVWKH(XFOLGHDQ'LVWDQFHFRPSXWHG IURP D UHFWDQJXODU PDWUL[ ZLWK PRUH REMHFWV WKDQ GHVFULSWRUV Q ! S WKHQ WKHPD[LPXP QXPEHU RI QRQ]HUR HLJHQYDOXHV LV S 2WKHU UHVHPEODQFH FRHIILFLHQWV PD\ SURGXFHIHZHURUPRUHD[HV7KHWUDQVIRUPDWLRQRI$LQWR'VWHSLVQRWHVVHQWLDO,WLVVLPSO\PHDQWWRHOLPLQDWH RQH RI WKH HLJHQYDOXHV WXUQ LW LQWR FRQFUHWHO\ WKH HLJHQYDOXH WKDW ZRXOG RQO\DFFRXQWIRUWKHGLVWDQFHEHWZHHQWKHFHQWURLGDQGWKHRULJLQ
%\ FRQVWUXFWLRQ FODVVLFDO0'6 SUHVHUYHV WKH RULJLQDO GLVWDQFHV UHJDUGOHVV RI WKH IRUPXODXVHG WR FRPSXWH WKHP7KH UHSUHVHQWDWLRQ RI SULQFLSDO FRRUGLQDWHV LQ UHGXFHG VSDFH IRUPV WKHEHVW(XFOLGHDQDSSUR[LPDWLRQRIWKHRULJLQDOGLVWDQFHVLQWKHVHQVHWKDWWKHVXPRIVTXDUHVRIWKHSURMHFWLRQ GLVWDQFHV RI WKH REMHFWV RQWR WKH VHOHFWHG VXEVSDFH LVPLQLPXP$VZLWK 3&$ WKHTXDOLW\RIWKHUHSUHVHQWDWLRQFDQEHDVVHVVHGE\PHDQVRID6KHSDUGGLDJUDPRUE\DVFUHHSORW
$VSUHYLRXVO\PHQWLRQHGUXQQLQJDFODVVLFDO0'6VWDUWLQJIURPDPDWUL[RIWKH3\WKDJRUHDQ(XFOLGHDQ'LVWDQFHLVHTXLYDOHQWWRUXQQLQJD3&$+RZHYHU0'6GRHVQRWSURGXFHWKHUHODWLRQEHWZHHQRULJLQDOGHVFULSWRUVDQGWKHSULQFLSDOFRRUGLQDWHVDV3&$GRHVEHFDXVHLWGRHVQRWVWDUWIURP D UHFWDQJXODU GDWD PDWUL[ +RZHYHU RQH FRXOG D SRVWHULRUL FRPSXWH FRYDULDQFHV DQGFRUUHODWLRQVZLWKRULJLQDOGHVFULSWRUV
1HJDWLYHHLJHQYDOXHV
6RPHV\PPHWULFGLVVLPLODULW\PDWULFHVGRQRWDOORZDIXOOUHDO(XFOLGHDQUHSUHVHQWDWLRQ7KLVKDSSHQVLQWZRVLWXDWLRQV,IGLVVLPLODULWLHVGRQRWIXOILOOWKHWULDQJOHLQHTXDOLW\PHDVXUHGLVQRWDPHWULFRU,IWKHPHDVXUHLVDPHWULFEXWLWVUHVHPEODQFHYDOXHVDUHQRWIXOO\HPEHGGDEOHLQ D (XFOLGHDQ VSDFH :KHQ WUDQVIRUPLQJ VLPLODULWLHV ZH PXVW EH DZDUH RI WKH (XFOLGHDQSURSHUWLHVRIWKHWUDQVIRUPHGPHDVXUH)RUH[DPSOHWUDQVIRUPDFRXOG\LHOGPHWULFEXWQRQ(XFOLGHDQUHODWLRQV2QWKHRWKHUKDQGFZLOOQRUPDOO\\LHOGIXOO\HPEHGGDEOHVSDFHV
$GLVVLPLODULW\QRWIXOO\HPEHGGDEOHLQD(XFOLGHDQVSDFHZLOO\LHOGQHJDWLYHHLJHQYDOXHVLQWKH HLJHQYDOXH GHFRPSRVLWLRQ SKDVH RI FODVVLFDO 0'6 7KLV PHDQV WKHUH ZLOO EH LPDJLQDU\SULQFLSDOFRRUGLQDWHVZKLFKFDQQRWEHUHSUHVHQWHGDORQJZLWKWKHUHDOSDUW7RVROYHWKLVVRPHFRUUHFWLRQVIRUQRQHXFOLGHDQDULW\KDYHEHHQSURSRVHG
7KH/LQJRHVFRUUHFWLRQPHWKRGLVWKHRQHLPSOHPHQWHGLQ*,1.*2,QWKLVPHWKRGWKH ODUJHVW QHJDWLYH HLJHQYDOXH P \LHOGHG E\ FODVVLFDO 0'6 LV XVHG WR FRUUHFW WKH RULJLQDOGLVVLPLODULW\PDWUL[DVIROORZV PGG OKOK += $IWHU WKLV FRUUHFWLRQ RI GLVWDQFHV 0'6 LV UXQ DJDLQ DQG WKHQ QR QHJDWLYH HLJHQYDOXHV DUHSURGXFHG +RZHYHU FRUUHFWLRQV IRU QRQ(XFOLGHDQDULW\ FDQ EH SRWHQWLDOO\ GLVWRUWLQJ EHFDXVHVPDOOGLVWDQFHYDOXHVZLOOEH LQFUHPHQWHGPRUH WKDQ ODUJHGLVWDQFHYDOXHV7KLVKDVDQRYHUDOOHIIHFWRIPDNHSRVVLEOHFOXVWHUVWUXFWXUHVSUHVHQWLQGDWDPRUHIX]]\
9HUVLRQ
5XQQLQJFODVVLFDO0'6LQ*,1.*2
&ODVVLFDO0'6FDQRQO\EH UXQZKHQDGLVVLPLODULW\PDWUL[ LV VHOHFWHGRQ WKH'DWD(GLWRU2QFHWKH0'6GLDORJDSSHDUVWKHXVHUFDQFKDQJHVRPHDQDO\VLVRSWLRQV)LUVWVRPHHOHPHQWVIURPWKHRULJLQDOGLVVLPLODULW\PDWUL[PD\EHH[FOXGHGIURPWKHFRPSXWDWLRQVE\XQVHOHFWLQJWKHFKHFNER[ µXVH DOO REMHFWV¶ 6HFRQG WKH XVHU PD\ DVN IRU WKH /LQJRHV FRUUHFWLRQ RI QHJDWLYHHLJHQYDOXHVE\VHOHFWLQJFKHFNER[µ1HJDWLYH(9FRUUHFWLRQ¶)LQDOO\H[WUDRXWSXWPDWULFHVFDQEHUHTXHVWHGIURPWKHDQDO\VLVVHHEHORZ
6LPLODUO\ WR3&$ WKHURXWLQHIRUFODVVLFDO0'6OLVWVHLJHQYDOXHVDQGWKHLUDVVRFLDWHGRIYDULDQFHVDVZHOODVWKHFXPXODWLYHSHUFHQWDJHV7KHXVHUPXVWEHDZDUHWKDWZKHQHYHUQHJDWLYHHLJHQYDOXHV DUH SURGXFHG FXPXODWLYH SHUFHQWDJHV RI UHDO HLJHQYDOXHV FDQ H[FHHG VLQFHSURSRUWLRQVDUHFRPSXWHGXVLQJRYHUDOOYDULDQFH7KHUHIRUHWKHVHQXPEHUVPXVWEHUHJDUGHGZLWKFDXWLRQ$IWHUDGGLQJYDULDQFHRILPDJLQDU\D[HVWKHFXPXODWLYHSHUFHQWDJHDWWKHHQGLVQRWHWKDWYDULDQFHRILPDJLQDU\D[HVLVQHJDWLYH
$V QHJDWLYH HLJHQYDOXHVPD\EHSURGXFHG*,1.*2FDQEH DVNHG WR RXWSXW ERWK UHDO DQGLPDJLQDU\ SULQFLSDO FRRUGLQDWHV ,W DOVR RXWSXWV WKH FRUUHVSRQGLQJ GLVWDQFH VSDFHV UHDO DQGLPDJLQDU\VSDFH,IQRFRUUHFWLRQKDVEHHQGRQHWKHLQLWLDOGLVVLPLODULW\PDWUL[FDQEHUHFRYHUHGE\VXEWUDFWLQJWKHVTXDUHGLPDJLQDU\GLVWDQFHHOHPHQWVIURPWKHVTXDUHGUHDOGLVWDQFHHOHPHQWV
LPDJOKUHDOOKOK GGG −= WKHSURJUDPFDQDOVREHDVNHGWRSURGXFHWKHUHVXOWLQJPDWUL[2QWKHRWKHU
KDQGLIFRUUHFWLRQIRUQHJDWLYHHLJHQYDOXHVLVGRQHWKHGLVVLPLODULW\PDWUL[FRPSXWHGZLWKWKLVIRUPXODZLOOGLIIHUIURPWKHLQLWLDOGLVVLPLODULW\PDWUL[
$ ILQDO DGGLWLRQDO RXWSXW RSWLRQ IRU FODVVLFDO 0'6 LV WR FRPSXWH WKH SRVLWLRQ RI FOXVWHUFHQWURLGVLQWKHVSDFHRISULQFLSDOFRRUGLQDWHV2EYLRXVO\ WKHXVHU LV WKHQDVNHGWRFKRRVHRQHFODVVLILFDWLRQPDWUL[ DPRQJ WKRVH DYDLODEOH LQ WKH DQDO\VLVPDQDJHU ,GHDOO\ WKLV FODVVLILFDWLRQVKRXOG KDYH EHHQ REWDLQHG IURP WKH VDPH GLVVLPLODULW\ PDWUL[ EHLQJ XVHG LQ 0'6 3ORWWLQJFOXVWHUFHQWURLGVLQ0'6GLDJUDPVLVDJRRGZD\WRFRPELQHUHVXOWVIURPRUGLQDWLRQZLWKWKRVHRIFODVVLILFDWLRQ
*,1.*2XVHU¶VPDQXDO
1RQPHWULF0XOWLGLPHQVLRQDO6FDOLQJ10'6,QWURGXFWLRQ
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
10'6LVDQLWHUDWLYHVHDUFKIRUDUDQNLQJDQGSODFHPHQWRIQHQWLWLHVRQPGLPHQVLRQVD[HVWKDWPLQLPL]HV WKHVWUHVV RI WKHPGLPHQVLRQDOFRQILJXUDWLRQ6WUHVV LV DPHDVXUHRIGHSDUWXUHIURPPRQRWRQLFLW\ LQ UHODWLRQVKLSEHWZHHQ WKHGLVVLPLODULW\ LQ WKHRULJLQDOSGLPHQVLRQDOVSDFHDQGGLVWDQFHLQWKHUHGXFHGPGLPHQVLRQDORUGLQDWLRQVSDFH.UXVNDOV10'6DOJRULWKP
&RQVLGHUDJHQHUDOGLVVLPLODULW\PDWUL[>δKO@FRPSXWHGXVLQJDPHDVXUHDSSURSULDWHWRWKHGDWDDWKDQG7KHXVHUPXVWVSHFLI\ WKHQXPEHURIPGLPHQVLRQVIRUVFDOLQJWKHREMHFWV7KHRXWSXWZLOOSURYLGHFRRUGLQDWHVRIWKHQREMHFWVRQPD[HV10'6WKHQSURFHHGVDVIROORZV
&RQVWUXFWDQLQLWLDO;Q[PFRQILJXUDWLRQRIWKHQREMHFWVLQPGLPHQVLRQVWREHXVHGDVDVWDUWLQJSRLQWIRUWKHLWHUDWLYHDOJRULWKP 1RUPDOL]HFRQILJXUDWLRQ &DOFXODWH D PDWUL[ ' RI ILWWHG GLVWDQFHV GKO LQ WKH RUGLQDWLRQ VSDFH XVLQJ RQH RI WKH0LQNRZVNLVPHWULFVQGRUGHUPHWULFWKH(XFOLGHDQGLVWDQFHLQWKHFDVHRI*,1.*2,Q
WKHILUVWLWHUDWLRQGLVWDQFHVGKODUHFRPSXWHGIURPWKHLQLWLDOPVSDFHFRQILJXUDWLRQDQGLQWKHRWKHUVWKH\DUHWKHPRGLILFDWLRQVRIWKRVHGLVWDQFHV 2QH UHJUHVVLRQ PXVW WKHQ EH FKRVHQ WR UHJUHVV GKO RQ δKO 9DOXHV IRUHFDVWHG E\ WKH
UHJUHVVLRQOLQHDUHFDOOHG KOGÖ ,QFDVHRI*,1.*2DPRQRWRQHUHJUHVVLRQLVLPSOHPHQWHG0RQRWRQHUHJUHVVLRQLVDVWHSIXQFWLRQZKLFKLVFRQVWUDLQHGWRDOZD\VLQFUHDVHIURPOHIWWRULJKW,WLVHTXLYDOHQWWRDOLQHDUUHJUHVVLRQSHUIRUPHGDIWHUPRQRWRQLFWUDQVIRUPDWLRQRIWKHRULJLQDOGLVWDQFHV VRDV WRPD[LPL]H WKH OLQHDU UHODWLRQVKLSEHWZHHQGKODQG δKO7KHUHJUHVVLRQLVILWWHGE\OHDVWVTXDUHVVWUHVVIXQFWLRQ
0HDVXUHWKHJRRGQHVVRIILWRIWKHUHJUHVVLRQXVLQJDQREMHFWLYHIXQFWLRQ7KLVLVEDVHGRQWKHVXPRIVTXDUHGGLIIHUHQFHVEHWZHHQILWWHGYDOXHVGKODQGWKHIRUHFDVWHG KOGÖ YDOXHVE\WKHUHJUHVVLRQIXQFWLRQ
9HUVLRQ
∑
∑ −== Q
OK KO
KOQOK KO
GGG
766WUHVV
Ö
,PSURYHWKHFRQILJXUDWLRQE\PRYLQJLWVOLJKWO\LQDGLUHFWLRQRIGHFUHDVLQJVWUHVV7KLVLVGRQHE\PHWKRGVRIQXPHULFDORSWLPL]DWLRQEDVHGRQJUDGLHQW VXFKDVVWHHSHVWGHVFHQW7KH GLUHFWLRQ RI VWHHSHVW GHVFHQW LV WKH GLUHFWLRQ LQ WKH VSDFH RI VROXWLRQV DORQJZKLFKVWUHVVLVGHFUHDVLQJPRUHUDSLGO\:HILUVWFDOFXODWHWKHQHJDWLYHJUDGLHQWRIVWUHVVIRUHDFKSRLQWLLHWKHGLUHFWLRQRIPRYHPHQWRIHDFKSRLQWLLQWKHNWKGLPHQVLRQRIWKHPVSDFHLQZKLFKVWUHVVGHFUHDVHVIDVWHU7KHJUDGLHQWYHFWRUJLVFDOFXODWHGE\
∑∑= =
−
−
−−⋅=
Q
K
Q
O KO
MNKNKOKOKOLOLKLN G
[[7G
6GG6WUHVVJ
Ö δδ
7KH OHWWHUK LQGH[HV RQH RI WKHQ SRLQWV O LQGH[HV DQRWKHU RI WKHQSRLQWVN LQGH[HV DSDUWLFXODUGLPHQVLRQDQGLLQGH[HVDWKLUGSRLQWWKHSRLQWRILQWHUHVWZKLFKLVPRYHGRQGLPHQVLRQN 6RJLN LQGLFDWHV D VKLIW IRUSRLQW L DORQJGLPHQVLRQN+HUH δLK DQGδLO DUH.URQHFNHUGHOWDVZKLFKKDYHWKHYDOXHLILDQGKRULDQGOLQGLFHVDUHHTXDORWKHUZLVHWKH\KDYHYDOXH7KHDPRXQWRIPRYHPHQWLQWKHGLUHFWLRQRIWKHQHJDWLYHJUDGLHQWLVVHWE\WKHVWHSVL]HαZKLFKLVLQLWLDOO\VHWDWEXWFDQFKDQJHGXULQJWKHLWHUDWLRQV7KHQH[WFRQILJXUDWLRQ;¶LVREWDLQHGE\
LNLNLN JJPDJ[[ α+=
ZKHUHPDJJ PHDQV WKH UHODWLYH PDJQLWXGH RI J DQG LV JLYHQ E\ DVVXPLQJ WKDW [ LVQRUPDOL]HG
∑ ∑=QL
PN LNJQJPDJ
:HUHSHDWVWHSVXQWLOFRQYHUJHQFHLVDFKLHYHGDPLQLPXP7KHODVWVWHSFRRUGLQDWHVRIVWHSDUHWKHRUGLQDWLRQD[HVRIWKHQREMHFWVLQWKHPGLPHQVLRQV
5XQQLQJ10'6LQ*,1.*2
10'6RSWLRQV
10'6 LV UXQ VWDUWLQJ IURP D V\PPHWULF GLVVLPLODULW\ PDWUL[ LI WKH VWDUWLQJ PDWUL[ LV DV\PPHWULF VLPLODULW\ PDWUL[ D WUDQVIRUP VKRXOG EH DSSOLHG ILUVW $V ZLWK RWKHU V\PPHWULFVWDUWLQJPHWKRGVFKDQJLQJWKHREMHFWVLQFOXGHGLQWKHDQDO\VLVUHVXOWVLQXVLQJDVXEPDWUL[IRUWKHFRPSXWDWLRQ7KHRWKHU10'6RSWLRQVDUH1XPEHU RI GLPHQVLRQV 7KH QXPEHU RI GLPHQVLRQV WR EH VHDUFKHG 7KH ORZHU WKH QXPEHU RIGLPHQVLRQVVHOHFWHGWKHKLJKHUWKHVWUHVVZLOOEH
*,1.*2XVHU¶VPDQXDO
6WDUWLQJPRGH$VZLWK.PHDQV VHFWLRQ VWDUWLQJPRGH LVYHU\ LPSRUWDQW LQ10'67KLVVWDUWLQJSRLQWLVFULWLFDODVLWLVLQPRVWRSWLPL]DWLRQDOJRULWKPVOLNH.PHDQVVSDFHPD\FRQWDLQVHYHUDOPLQLPDEHVLGHVWKHRYHUDOOPLQLPXP7ZRRSWLRQVDUHSURYLGHGLQ*,1.*2DVVWDUWLQJRSWLRQV
• 5DQGRPVWDUW5XQWKHSURJUDPVHYHUDOWLPHVVWDUWLQJIURPGLIIHUHQWUDQGRPSODFHPHQWRIREMHFWV
•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
10'6RXWSXW
10'6 RXWSXW LV GLIIHUHQW GHSHQGLQJ RQ WKH VWDUWLQJ PRGH DQG ZKHWKHU D ILQDO 3&$ LVSHUIRUPHGRUQRW+RZHYHU10'6SURFHGXUHDOZD\V\LHOGVWKHILQDOREMHFWFRRUGLQDWHVDQGWKH(XFOLGHDQ GLVWDQFH PDWUL[ RQ WKH 10'6 VSDFH 7KH SURFHGXUH DOVR RXWSXWV WKH QXPEHU RI10'6LWHUDWLRQVXVHGDQGWKHILQDO10'6675(66YDOXH
6HHVHFWLRQIRUDGHVFULSWLRQRIKRZPHWULFVFDOLQJZRUNV
9HUVLRQ
&RUUHVSRQGHQFH$QDO\VLV&$,QWURGXFWLRQ
&RUUHVSRQGHQFH DQDO\VLV ZDV GHYHORSHG LQGHSHQGHQWO\ E\ VHYHUDO DXWKRUV ,W ZDV ILUVWSURSRVHGIRUDQDO\VLQJWZRZD\FRQWLQJHQF\WDEOHVZKHUHWKHVWDWHVRIDILUVWGHVFULSWRUURZVDUHFRPSDUHGWRWKHVWDWHVRIDVHFRQGGHVFULSWRUFROXPQV'DWDLQHDFKFRQWLQJHQF\WDEOHFHOODUHIUHTXHQFLHVLHQXPEHUVRIREMHFWVFRGHGZLWKDFRPELQDWLRQRIVWDWHVRIWKHWZRGHVFULSWRUV7KHVHIUHTXHQFLHVDUHWKXVSRVLWLYHLQWHJHUVRU]HURV
,QHFRORJ\&$LVRIWHQXVHGWRDQDO\]HVSHFLHVGDWDDWGLIIHUHQWVDPSOLQJVLWHVZKHUHYDOXHVDUHDOVR]HURRUSRVLWLYHQXPEHUVRIVSHFLHVDEXQGDQFHV7KHURZVDQGFROXPQVWKHQFRUUHVSRQGWRVLWHVDQGVSHFLHVUHVSHFWLYHO\6XFKDWDEOHFDQEHWUHDWHGDQDORJRXVO\WRDFRQWLQJHQF\WDEOH&$FDQDOVREHXVHGRQFRQWLQJHQF\WDEOHV WKDWFRPSDUH WZRJURXSVRIGHVFULSWRUV ,QJHQHUDO&$ FDQ EH DSSOLHG WR DQ\ GDWD WDEOH WKDW LV GLPHQVLRQDOO\ KRPRJHQHRXV DQG RQO\ FRQWDLQVSRVLWLYHLQWHJHUVRU]HURYDOXHV
&$LVSULPDULO\DPHWKRGRIRUGLQDWLRQ$VVXFKLWLVVLPLODUWR3&$,WSUHVHUYHVLQWKHVSDFHRISULQFLSDOD[HVWKH(XFOLGHDQGLVWDQFHEHWZHHQSURILOHVRIZHLJKWHGFRQGLWLRQDOSUREDELOLWLHV,QRWKHUZRUGVWKHχGLVWDQFHLVXVHGWRTXDQWLI\WKHUHODWLRQVKLSVEHWZHHQURZVDQGFROXPQVZKLFKLQWKLVDQDO\VLVDUHWUHDWHGV\PPHWULFDOO\7KXVWKH(XFOLGHDQGLVWDQFHEHWZHHQREMHFWVRQWKHRUGLQDWLRQD[HVHTXDOVWKHχGLVWDQFHRQWKHRULJLQDOFRQWLQJHQF\WDEOH
%HVLGHVLWVUROHDVDQRUGLQDWLRQPHWKRG&$PD\EHXVHGWRVWXG\WKHSUR[LPLWLHVEHWZHHQURZV RU FROXPQV RI WKH FRQWLQJHQF\ WDEOH DV ZHOO DV WKH FRUUHVSRQGHQFH EHWZHHQ URZV DQGFROXPQV7KHPHWKRG
/HW;EH D FRQWLQJHQF\ WDEOHZLWK U URZV DQG F FROXPQV 7KHUHIRUH WKHLU FHOO YDOXHV [LMVKRXOGEHUHJDUGHGDVIUHTXHQFLHV[LM ILM7KHQDPDWUL[3 >SLM@RIUHODWLYHIUHTXHQFLHVFDQEHFRPSXWHG$VVXPHWKDWWKHWDEOHLVZULWWHQLQVXFKDZD\WKDWU≥FLWPD\EHWUDQVSRVHGVLQFHURZVDQGFROXPQVDUHWUHDWHGV\PPHWULFDOO\LQ&$7KHVWHSVLQ&RUUHVSRQGHQFH$QDO\VLVDUHDVIROORZV
5HPHPEHUWKDW3HDUVRQχVWDWLVWLFLVDVXPRIVTXDUHGχLMYDOXHVFRPSXWHGIRUHYHU\FHOO LM RI WKH FRQWLQJHQF\ WDEOH (DFK χLM YDOXH LV WKH VWDQGDUGL]HG UHVLGXDO RI DIUHTXHQF\ ILMDIWHU ILWWLQJDQXOOPRGHO WRWKHFRQWLQJHQJ\WDEOH7KHQXOOPRGHOVWDWHVWKDWWKHUHLVQRUHODWLRQVKLSEHWZHHQURZVDQGFROXPQVRIWKHWDEOH&$LVEDVHGXSRQDPDWUL[4U[FZKRVHFHOOVDUHGHILQHGYHU\VLPLODUO\WRχLMYDOXHV7KXV4LVDPDWUL[RIGHSDUWXUHVUHVLGXDOVIURPWKHQXOOPRGHO
[ ]
⋅
−=
−==
++++
++++
++
++
ML
MLLM
ML
MLLMLM [[[
[[[[SSSSST4
*,1.*2XVHU¶VPDQXDO
ZKHUH ∑ =+ =FM LML [[ DQG ∑ =+ =
UL LMM [[ DUH WKH URZ DQG FROXPQPDUJLQDOV UHVSHFWLYHO\
WKHVDPHIRUUHODWLYHIUHTXHQFLHVSLMDQG ∑ ∑= =++ =UL
FM LM[[ LVWKHJUDQGWRWDO7KHVXP
RIVTXDUHVRIDOOYDOXHVLQPDWUL[4∑ LMT PHDVXUHVWKHWRWDOLQHUWLDLQ4
6LQJXODUYDOXHGHFRPSRVLWLRQLVDSSOLHGWRPDWUL[4ZLWKWKHIROORZLQJUHVXOW Ö F[FU[FU[FU[F 8:84 =
ZKHUHERWK8 DQG 8Ö DUHFROXPQRUWKRQRUPDOPDWULFHVDQG: LVDGLDJRQDOPDWUL[RIVLQJXODUYDOXHV6LQFH8Ö LVRUWKRQRUPDO ,88 =ÖÖ DQG
ÖÖ :88::8888:44 ==
7KHGLDJRQDOPDWUL[:¶:ZKLFKFRQWDLQVVTXDUHGVLQJXODUYDOXHVRQLWVGLDJRQDOLVWKHGLDJRQDO PDWUL[ RI HLJHQYDOXHV RI 4¶4 ,Q DGGLWLRQ 8 LV HTXDO WR WKH PDWUL[ RIHLJHQYHFWRUV RI 4¶4 7KHUHIRUH LGHQWLFDO UHVXOWV FDQ EH REWDLQHG DSSO\LQJHLJHQDQDO\VLVWR4¶4%RWKVLQJXODUYDOXHGHFRPSRVLWLRQRI4DQGHLJHQYDOXHDQDO\VLVRI4¶4 DOZD\V \LHOG RQH QXOO HLJHQYDOXH GXH WR WKH FHQWHULQJ VWHS LPSOLFLW LQ WKHFRQVWUXFWLRQRI47KXVWKHUHDUHF±SRVLWLYHHLJHQYDOXHVRUVLQJXODUYDOXHVZKHQU≥F
0DWULFHV8 DQG8Ö PD\EHXVHGDV VFRUHV WRSORW WKHSRVLWLRQVRI WKH URZDQGFROXPQYHFWRUV LQ WZR VHSDUDWH VFDWWHU GLDJUDPV )RU MRLQW SORWV YDULRXV VFDOLQJV KDYH EHHQSURSRVHG)LUVWPDWULFHV8DQG8Ö FDQEHZHLJKWHGE\WKHLQYHUVHRIWKHVTXDUHURRWVRIWKHFROXPQDQGURZVFRUHV
8'9 −
+= MF[F S
8'9 ÖÖ
−+= LF[F S
0DWUL[ ) ZKLFK JLYHV WKH SRVLWLRQV RI WKH URZV RI WKH FRQWLQJHQF\ WDEOH LQ WKHFRUUHVSRQGHQFH\ DQDO\VLV VSDFH LV REWDLQHG IURP WKH WUDQVIRUPHG PDWUL[ RIHLJHQYHFWRUV9ZKLFKJLYHVWKHSRVLWLRQVRIWKHFROXPQVLQWKDWVSDFH7KLVLVGRQHE\DSSO\LQJWKHXVXDOHTXDWLRQIRUFRPSRQHQWVFRUHVWR4LQFOXGLQJDGLYLVLRQE\WKHURZZHLJKWV
49') −
+= LU[F S
,QWKHVDPHZD\PDWUL[)Ö ZKLFKJLYHVWKHSRVLWLRQVRIWKHFROXPQVRIWKHFRQWLQJHQF\WDEOHLQWKHFRUUHVSRQGHQFHDQDO\VLVVSDFHLVREWDLQHGIURPWKHWUDQVIRUPHGPDWUL[RIHLJHQYHFWRUV9Ö ZKLFKJLYHVWKHSRVLWLRQVRIWKHURZVLQWKDWVSDFH
94') ÖÖ
−+= MF[F S
9HUVLRQ
)URPWKHODVW&$FRPSXWDWLRQVWHSLWVKRXOGEHFOHDUWKDWWKHUHDUHWZRSRVVLEOHVFDOLQJVWRGUDZELSORWVRIURZVDQGFROXPQV
• 6FDOLQJW\SH'UDZDMRLQWSORWZLWKWKHURZV)DWWKHFHQWURLGVRIWKHFROXPQV9 ,Q WKLVSORW GLVWDQFHVEHWZHHQ URZV LH VLWHV LQ HFRORJ\SUHVHUYH WKHLUχGLVWDQFHV1RWHWKDWSRVLWLRQVRIWKHFHQWURLGVDUHFDOFXODWHGXVLQJZHLJKWVHTXDOWRWKHUHODWLYHIUHTXHQFLHVRIWKHFROXPQVVSHFLHVVRWKHRUGLQDWLRQRIURZVVLWHVLVPHDQLQJIXO
• 6FDOLQJW\SH'UDZDMRLQWSORWZLWKWKHFROXPQV)Ö DWWKHFHQWURLGVRIWKHURZV9Ö ,QWKLVSORWGLVWDQFHVEHWZHHQFROXPQVLHVSHFLHVLQHFRORJ\SUHVHUYHWKHLUχGLVWDQFHV
5XQQLQJ&$
&$FDQRQO\EH UXQ IURPD UHFWDQJXODUREMHFWGHVFULSWRUPDWUL[FRQWDLQLQJSRVLWLYHRU]HURYDOXHV$VLQ3&$VRPHREMHFWVRUGHVFULSWRUVFDQEHH[FOXGHGIURPFRPSXWDWLRQV7KHXVHUFDQDOVROLPLWWKHQXPEHURID[HVWREHNHSWXQVHOHFWLQJWKHµ$OOHLJHQYDOXHV¶FKHFNER[DQGHQWHULQJDVXLWDEOHQXPEHU
$V WH[W RXWSXW *,1.*2 JLYHV D WDEOH RI VLQJXODU YDOXHV DORQJ ZLWK WKHLU FRUUHVSRQGLQJHLJHQYDOXHVDQGWKHLUFRQWULEXWLRQWRWKHWRWDOLQHUWLDRI4
%\GHIDXOW WKH&$URXWLQHJLYHVPDWULFHVIRUVFDOLQJ9DQG)EXWFDQEHDVNHGWRDOVRJLYHWKHPDWULFHVIRUVFDOLQJ9Ö DQG)Ö 'HSHQGLQJRQWKHILQDODYDLODEOHPDWULFHVWKH&$SORWVWKDWFDQEHEXLOWRQWKH3ORWPHQXDUH
• 6FUHHSORW3ORWRIHLJHQYDOXHVVHH• 2EMHFW¶VVSDFHSORW6FDWWHUSORWRIPDWUL[)• &KDUDFWHU¶VVSDFH6FDWWHUSORWRIPDWUL[)Ö • &$ELSORWVFDOLQJ6FDWWHUELSORWRIPDWULFHV9DQG)• &$ELSORWVFDOLQJ6FDWWHUELSORWRIPDWULFHV9Ö DQG)Ö
*,1.*2XVHU¶VPDQXDO
5HGXQGDQF\$QDO\VLV5'$,QWURGXFWLRQWRFDQRQLFDODQDO\VLV
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
,QWURGXFWLRQWR5HGXQGDQF\DQDO\VLV
5HGXQGDQF\$QDO\VLV 5'$YDQGHQ:ROOHQEHUJ LV WKHGLUHFW H[WHQVLRQRIPXOWLSOHUHJUHVVLRQWRWKHPRGHOLQJRIPXOWLYDULDWHUHVSRQVHGDWD7KHWHUPµUHGXQGDQF\¶LVV\QRQ\PRXVKHUHZLWKµH[SODLQHGYDULDQFH¶7KHDQDO\VLV LVDV\PPHWULF ,Q5'$HDFKFDQRQLFDORUGLQDWLRQD[LVFRUUHVSRQGVWRDGLUHFWLRQLQWKHUHVSRQVHVSDFHRI<ZKLFKLVPD[LPDOO\UHODWHGWRDOLQHDUFRPELQDWLRQRIWKHH[SODQDWRU\YDULDEOHV;,QIDFWWKUHHRUGLQDWLRQVRIWKHREMHFWVDUHREWDLQHGLQ5'$
2UGLQDWLRQRIREMHFWV LQ WKHVSDFHRIYDULDEOHV<6FRUHVDUH OLQHDUFRPELQDWLRQVRIWKH<YDULDEOHVDVLQ3&$EXWXVLQJFDQRQLFDOD[HVDVORDGLQJV
2UGLQDWLRQRIREMHFWV LQWKHVSDFHRIYDULDEOHV;RU LQWKHVSDFHRIILWWHGYDOXHV <Ö 6FRUHV DUH OLQHDU FRPELQDWLRQV RI WKH ILWWHG <Ö YDULDEOHV ZKLFK DUH DOVR OLQHDUFRPELQDWLRQVRIWKH;YDULDEOHV
2UGLQDWLRQRIREMHFWVLQWKHVSDFHRIUHVLGXDOV << Ö− 5'$SUHVHUYHV WKH(XFOLGHDQGLVWDQFHEHWZHHQREMHFWV LQPDWUL[ <Ö FRQWDLQLQJYDOXHVRI<
ILWWHGE\UHJUHVVLRQWRWKHH[SODQDWRU\YDULDEOHV;
$OJHEUDRI5'$
/HW;Q[PEHWKHH[SODQDWRU\PDWUL[RIPH[SODQDWRU\GHVFULSWRUVRQQREMHFWVDQGOHW<Q [ S EH WKH UHVSRQVHPDWUL[ RIS GHVFULSWRUV RQ WKH VDPHQ REMHFWV )RU FRQYHQLHQFH WKHVHPDWULFHVDUHDVVXPHGWREHFROXPQFHQWHUHG3UREOHPVRIFDQRQLFDODQDO\VLVPD\EHSUHVHQWHGE\WKHIROORZLQJSDUWLWLRQHGFRYDULDQFHPDWUL[UHVXOWLQJIURPWKHIXVLRQRIWKH<DQG;GDWDVHWVWKHMRLQWGLVSHUVLRQPDWUL[6<;FRQWDLQVEORFNVWKDWDUHLQGHQWLILHGDVIROORZVIRUFRQYHQLHQFH
9HUVLRQ
=
=+
;;<;
<;<<
;;;<
<;<<;< 66
6666666
ZKHUH VXEPDWULFHV6<< S [ S DQG6;; P [P FRQFHUQ HDFK RI WKH WZR VHWV RI GHVFULSWRUVZKHUHDV6<;S[PDQGLWVWUDQVSRVH6¶<; 6;<P[SDFFRXQWIRUWKHFRYDULDQFHVDPRQJWKHGHVFULSWRUVRIWKHWZRJURXSV7KHHLJHQDQDO\VLVHTXDWLRQIRUUHGXQGDQF\DQDO\VLVLV
X,666 <;;;<; =−−LL
DQG PD\ EH GHULYHG WKURXJK PXOWLSOH OLQHDU UHJUHVVLRQ IROORZHG E\ SULQFLSDO FRPSRQHQWGHFRPSRVLWLRQ 3&$7KLVFDQEHSURYHQDV IROORZV ,IZHGRDPXOWLSOH OLQHDU UHJUHVVLRQ IRUHDFKYDULDEOHLQWDEOH<RQDOOYDULDEOHVRI;WKHPDWUL[RIUHJUHVVLRQFRHIILFLHQWVFRUUHVSRQGLQJWRWKHZKROHVHWRIUHJUHVVLRQVLHIRUDOOUHVSRQVHYDULDEOHVLV [ ] <;;;% −= DQGWKHPDWUL[RIILWWHGYDOXHVZKLFKZHZLOOFDOO<Ö LV [ ] <;;;;%;< Ö −== %HFDXVHYDULDEOHVLQ;DQG<DUHFHQWHUHGRQWKHLUPHDQVWKHUHLVQRLQWHUFHSWSDUDPHWHULQWKHYHFWRUVRI%>,IP Q;LVVTXDUHLQWKDWFDVHWKHPXOWLSOHUHJUHVVLRQZLOODOZD\VH[SODLQWKHYDULDEOHVLQPDWUL[<HQWLUHO\VRWKDW << =Ö @7KHFRYDULDQFHPDWUL[FRUUHVSRQGLQJWRWKHILWWHGYDOXHV<Ö LVFRPSXWHGIURP ( ) ( ) [ ] [ ] <;;;<;<< 666<;;;;;;;;<<<6 ÖÖ
ÖÖ−−− =−=−= QQ
VRWKXVLWLVVKRZQWKDW5'$DSSOLHV3&$RQWKHFRYDULDQFHPDWUL[RIWKHWDEOHRIILWWHGYDOXHV<Ö X,6 << =− LL ÖÖ
7KHPDWUL[FRQWDLQLQJQRUPDOL]HGFDQRQLFDOHLJHQYHFWRUV LVFDOOHG8 S[S7KH\JLYHWKHFRQWULEXWLRQVRIWKHGHVFULSWRUVLQ<Ö WRWKHYDULRXVFDQRQLFDOD[HV,WFRQWDLQVRQO\PLQ>SPQ±@HLJHQYHFWRUVZLWKQRQ]HURHLJHQYDOXHV7KH\VKRXOGEHLQWHUSUHWHGDVLQ3&$7KHRUGLQDWLRQRIREMHFWVLQWKHVSDFHRIWKHUHVSRQVHYDULDEOHVFDQEHREWDLQHGGLUHFWO\IURPWKHFHQWHUHGPDWUL[<E\SURMHFWLQJRQWKHFDQRQLFDOD[HV <8) = 2UGLQDWLRQYHFWRUVDUHVRPHWLPHVFDOOHG³VLWHVFRUHV´7KH\KDYHYDULDQFHVWKDWDUHFORVHEXWQRWHTXDOWRWKHFRUUHVSRQGLQJHLJHQYDOXHVVLQFHHLJHQYDOXHGHFRPSRVLWLRQKDVEHHQSHUIRUPHGRQWKHPDWUL[<Ö RIILWWHGYDOXHVDQGQRWRQWKHRULJLQDOUHVSRQVHPDWUL[7KHRUGLQDWLRQRIREMHFWVLQVSDFH;RU<Ö LVREWDLQHGVLPLODUO\ ;%88<= == Ö
*,1.*2XVHU¶VPDQXDO
7KHVHRUGLQDWLRQYHFWRUVDUHVRPHWLPHVFDOOHG³ILWWHGVLWHVFRUHV´7KH\KDYHYDULDQFHVHTXDOWRWKHFRUUHVSRQGLQJHLJHQYDOXHV
7KHFRQWULEXWLRQRIH[SODQDWRU\YDULDEOHV & WR WKH IRUPDWLRQRIFDQRQLFDORUGLQDWLRQD[HVFDQEHNQRZQE\FRPSXWLQJ& %8
5HGXQGDQF\ DQDO\VLV GRHV QRW FRPSOHWHO\ H[SODLQ WKH YDULDWLRQ LQ WKH UHVSRQVH YDULDEOHVPDWUL[<'XULQJWKHUHJUHVVLRQVWHSUHJUHVVLRQUHVLGXDOVPD\EHFRPSXWHGIRUHDFKYDULDEOH\7KHUHVLGXDOVDUHREWDLQHGDVWKHGLIIHUHQFHEHWZHHQREVHUYHGYDOXHVDQGWKHFRUUHVSRQGLQJILWWHGYDOXHV7KHPDWUL[RIUHVLGXDOV<UHVQ[SLVWKXVREWDLQHGE\ <<<UHV Ö−= 5HVLGXDOVPD\ EH DQDO\]HG E\ 3ULQFLSDO &RPSRQHQWV$QDO\VLV OHDGLQJ WRPLQ>S Q ± @ QRQFDQRQLFDOHLJHQYDOXHVDQGHLJHQYHFWRUV8UHV1RQFDQRQLFDOREMHFWVFRUHVDUHWKHQREWDLQHGE\SURMHFWLQJ<UHVRQWKHQRQFDQRQLFDOD[HV )UHV <UHV8UHV
:KHQWKHYDULDEOHVLQ;DUHJRRGSUHGLFWRUVRIWKHYDULDEOHVLQ<WKHFDQRQLFDOHLJHQYDOXHVPD\ EH ODUJHU WKDQ WKH ILUVW QRQFDQRQLFDO HLJHQYDOXHV EXW WKLV LV QRW DOZD\V WKH FDVH ,I WKHYDULDEOHVLQ;DUHQRWJRRGSUHGLFWRUVRI<WKHILUVWQRQFDQRQLFDOHLJHQYDOXHVFRPSXWHGRQWKHUHVLGXDOVPD\EHODUJHUWKDQWKHLUFDQRQLFDOFRXQWHUSDUWV
1RWH WKDW WKH ³VLWH VFRUHV´ DSSUR[LPDWH WKH REVHUYHG GDWD ZKLFK FRQWDLQV UHVLGXDOV UHV<<< += Ö 2QWKHRWKHUKDQGWKH³ILWWHGVLWHVFRUHV´DSSUR[LPDWHRQO\WKHILWWHGGDWD(LWKHUPD\EHXVHGLQELSORWV
,QWKHFDVHZKHUH<FRQWDLQVDVLQJOHUHVSRQVHYDULDEOHUHGXQGDQF\DQDO\VLVLVQRWKLQJEXWPXOWLSOHOLQHDUUHJUHVVLRQDQDO\VLV
5XQQLQJ5'$
:KHQUXQQLQJ5'$LQ*,1.*2WKHXVHUPXVWVSHFLI\ZKLFKGDWDLWHPVLQWKH'DWD(GLWRUZLOOEHXVHGDVH[SODQDWRU\DQG UHVSRQVH1RWH WKDW LI WKHUHDUH OHVV WKDQ WZRREMHFWGHVFULSWRUPDWULFHV5'$FDQQRWEHFRPSXWHG6RPHRWKHURSWLRQVDUHDYDLODEOH
• $OOHLJHQYDOXHV7KLVRSWLRQLVVHOHFWHGE\GHIDXOWVRDOOHLJHQYDOXHVDUHVRXJKW7KHXVHUFDQVSHFLI\KRZPDQ\HLJHQYDOXHVDUHWREHNHSWLQWKHILQDOUHVXOWV
• 6WDQGDUGL]H H[SODQDWRU\ ; &HQWHULQJ RI ; LV DOZD\V GRQH ,I WKH H[SODQDWRU\YDULDEOHVDUHVWDQGDUGL]HG WKHSRVVLEOHHIIHFWVRI WKHLUGLIIHUHQWSK\VLFDOGLPHQVLRQVDUH UHPRYHG7KLV WXUQV UHJUHVVLRQFRHIILFLHQWV LQWRVWDQGDUG UHJUHVVLRQFRHIILFLHQWVZKLFKPDNHVWKHPFRPSDUDEOHWRRQHDQRWKHU
• 6WDQGDUGL]HUHVSRQVH<&HQWHULQJRI<LVDOZD\VGRQHEXWWKHXVHUFDQVWDQGDUGL]HFROXPQVRI WKH UHVSRQVHPDWUL[ZKLFK LV DGYLVDEOHZKHQ WKHGLIIHUHQWYDULDEOHVDUHQRWGLPHQVLRQDOO\KRPRJHQHRXV
9HUVLRQ
(LJHQYDOXHRXWSXWLQIRUPDWLRQLVOLVWHGLQWZRVHSDUDWHEORFNVRQHIRUFDQRQLFDOD[HVDQGWKH
RWKHU IRU WKHQRQFDQRQLFDORQHV7KHSDUWLWLRQRI WKH WRWDOYDULDQFHRI<EHWZHHQ WKHYDULDQFHH[SODLQHG E\ UHJUHVVLRQ DQG WKH UHVLGXDO YDULDQFH LV DOVR JLYHQ 7KH DYDLODEOH 5'$ RXWSXWPDWULFHVDUH
• &DQRQLFDO(LJHQ9HFWRUV8(LJHQYHFWRUVUHVXOWLQJIURPWKHGHFRPSRVLWLRQRIILWWHGUHVSRQVHYDOXHVFRYDULDQFHPDWUL[
• &DQRQLFDO6FRUHV ) <82EMHFW VFRUHV DOVRFDOOHG³VLWHVFRUHV´ UHVXOWLQJ IURPSURMHFWLQJRULJLQDOUHVSRQVHYDOXHVRQFDQRQLFDOD[HV
• )LWWHG &DQRQLFDO 6FRUHV ;%88<= == Ö 2EMHFW VFRUHV DOVR FDOOHG ³ILWWHG VLWHVFRUHV´UHVXOWLQJIURPSURMHFWLQJILWWHGUHVSRQVHYDOXHVRQFDQRQLFDOD[HV
• 1RQ&DQRQLFDO(LJHQ9HFWRUV8UHV(LJHQYHFWRUVUHVXOWLQJIURPWKH'HFRPSRVLWLRQRI5HVLGXDO5HVSRQVH9DOXHV&RYDULDQFH0DWUL[• 1RQ&DQRQLFDO 6FRUHV )UHV <UHV8UHV 2EMHFW VFRUHV UHVXOWLQJ IURP SURMHFWLQJUHVLGXDOUHVSRQVHYDOXHVRQQRQFDQRQLFDOD[HV• )LWWHG5HVSRQVH9DOXHV %;< =Ö )LWWHG9DOXHVUHVXOWLQJIURP0XOWLSOH5HJUHVVLRQV• 6WDQGDUGL]HG5HJUHVVLRQ&RHIILFLHQWV%6WDQGDUGL]HGUHJUHVVLRQFRHIILFLHQWVIRU
VWDQGDUGL]HGH[SODQDWRU\YDULDEOHVUHVXOWLQJIURPPXOWLSOHUHJUHVVLRQV• &DQRQLFDO &RHIILFLHQWV & %8 :HLJKWV RI WKH H[SODQDWRU\ YDULDEOHV; RQ WKH
IRUPDWLRQRIWKHFDQRQLFDOD[HV• &RUUHODWLRQV ; YV ) 3HDUVRQ FRUUHODWLRQV EHWZHHQ H[SODQDWRU\ YDULDEOHV DQG
FDQRQLFDOVFRUHV5'$SORWVDQGELSORWV
$VLQ3&$5'$SORWVDQGELSORWVFRXOGEHEDVHGRQWZRW\SHVRIVFDOLQJEHFDXVHFDQRQLFDOD[HVFDQEHVFDOHGWROHQJWKHTXDOWRRUWROHQJWKHTXDOWRLWVVWDQGDUGGHYLDWLRQ L 7KHVDPHDSSOLHVWRWKHQRQFDQRQLFDOD[HV,Q*,1.*2VFDOLQJWROHQJWKLVWKHRQO\VFDOLQJDYDLODEOHIRU5'$
&DQRQLFDORUGLQDWLRQSORWVFDQEHEXLOWLQ*,1.*2XVLQJHLWKHU)=RU8$GGLWLRQDOO\)DQG8RU=DQG8FDQEHXVHGWRJHWKHULQELSORWVEHFDXVHWKHSURGXFWVRIWKHHLJHQYHFWRUVZLWKWKH REMHFW VFRUHPDWULFHV UHFRQVWUXFW WKH RULJLQDOPDWULFHV HLWKHU< RU <Ö 7KHVH ELSORWV DUHFDOOHGGLVWDQFHELSORWV LQ WKH VFDOLQJ WR OHQJWK DQGDOORZ WKH LQWHUSUHWDWLRQ WR IRFXVRQ WKHRUGLQDWLRQRI REMHFWV EHFDXVH(XFOLGHDQGLVWDQFHV DSSUR[LPDWH WKHLU(XFOLGHDQGLVWDQFHV LQ WKHVSDFHRIUHVSRQVHYDULDEOHV6LPLODUO\QRQFDQRQLFDORUGLQDWLRQSORWVFDQEHEXLOWXVLQJ)UHVRU8UHVDQGDQRQFDQRQLFDOGLVWDQFHELSORWLVDYDLODEOHVKRZLQJWKHLQIRUPDWLRQRQERWKPDWULFHV
*,1.*2XVHU¶VPDQXDO
&DQRQLFDO&RUUHVSRQGHQFH$QDO\VLV&&$,QWURGXFWLRQWR&DQRQLFDOFRUUHVSRQGHQFHDQDO\VLV
&DQRQLFDO FRUUHVSRQGHQFH DQDO\VLV &&$ WHU %UDDN LV WKH FDQRQLFDO IRUP RIFRUUHVSRQGHQFHDQDO\VLVVHFWLRQ$Q\GDWDWDEOHWKDWFRXOGEHVXEMHFWHGWRFRUUHVSRQGHQFHDQDO\VLVIRUPVDVXLWDEOHUHVSRQVHPDWUL[<IRU&&$VHH
7KHPDWKHPDWLFVRI&&$ LV HVVHQWLDOO\ WKH VDPHDV LQ UHGXQGDQF\DQDO\VLV VHH VXEVHFWLRQ 7KXV &&$ LV HVVHQWLDOO\ D PXOWLSOH UHJUHVVLRQ IROORZHG E\ DQ RUGLQDWLRQ DQDO\VLV+RZHYHUWKHUHDUHVRPHGLIIHUHQFHV7KHGHSHQGHQWGDWDWDEOHLQ&&$LVQRWPDWUL[<FHQWHUHGE\ YDULDEOHV DV LQ 5'$ &&$ XVHV PDWUL[ 4 RI FRQWULEXWLRQV WR WKH χ VWDWLVWLF VHHFRUUHVSRQGHQFH DQDO\VLV VHFWLRQ 5HODWLYH IUHTXHQFLHV LQ < DUH DOVR XVHG LQ WKH VFDOLQJRSHUDWLRQV $QRWKHU GLIIHUHQFH LV WKDW ZHLJKWHG PXOWLSOH UHJUHVVLRQ LV XVHG LQVWHDG RI DFRQYHQWLRQDOOLQHDUPXOWLSOHUHJUHVVLRQ&&$DSSUR[LPDWHVχGLVWDQFHVEHWZHHQWKHURZVRIWKHGHSHQGHQWGDWDPDWUL[VXEMHFWWRWKHFRQVWUDLQWWKDWWKHFDQRQLFDORUGLQDWLRQYHFWRUVKDYHWREHPD[LPDOO\UHODWHGWRZHLJKWHGOLQHDUFRPELQDWLRQVRIWKHH[SODQDWRU\YDULDEOHV0HWKRGDQGDOJHEUDRI&&$
+HUH<PXVWEHUHJDUGHGDVDFRQWLQJHQF\WDEOHZLWKQURZVDQGSFROXPQV7KHUHIRUHWKHLUFHOOYDOXHV \LM VKRXOGEH UHJDUGHGDV IUHTXHQFLHV \LM ILM7KHQDPDWUL[3 >SLM@RI UHODWLYHIUHTXHQFLHVFDQEHFRPSXWHG,QDGGLWLRQWKHPDUJLQDOVKDYHWREHFDOFXODWHG
∑ =+ =SM LML \\ DQG ∑ =+ =
QL LMM \\ DUHWKHURZREMHFWDQGFROXPQYDULDEOHPDUJLQDOV
∑ ∑= =++ =QL
SM LM\\ LVWKHJUDQGWRWDO
7KH&&$PHWKRGLVDVIROORZV &RPSXWH4 WKHPDWUL[ RI GHSDUWXUHV UHVLGXDOV RI WKH UHVSRQVHPDWUL[< IURP WKH
QXOOPRGHO
[ ]
⋅
−=
−==
++++
++++
++
++
ML
MLLM
ML
MLLMLM \\\
\\\\SSSSST4
$V LQ FRUUHVSRQGHQFH DQDO\VLV WKH VXPRI VTXDUHV RI DOO YDOXHV LQPDWUL[4 ∑ LMT
PHDVXUHVWKHWRWDOLQHUWLDLQ4 7KHH[SODQDWRU\PDWUL[;LVVWDQGDUGL]HGXVLQJZHLJKWV'\L :HLJKWHGPXOWLSOHUHJUHVVLRQLVXVHGLQVWHDGRIWKHFRQYHQWLRQDOPXOWLSOHUHJUHVVLRQ
7RGRDZHLJKWHGPXOWLSOHUHJUHVVLRQWKHZHLJKWVJLYHQE\GLDJRQDOPDWUL['SLPXVWEHDSSOLHGWRPDWUL[;HYHU\ZKHUHLWRFFXUV7KHPXOWLSOHUHJUHVVLRQFRHIILFLHQWVRI5'$DUHLQ&&$FRPSXWHGDV
[ ] 4';;';% +−
+= LL SS DQGWKHHTXDWLRQIRUFRPSXWLQJ<Ö LV
9HUVLRQ
%;'< Ö+= LS
(LJHQYDOXHGHFRPSRVLWLRQLVFDUULHGRXWRQWKHFRYDULDQFHPDWUL[ <<6 ÖÖ ZKLFKLQWKLVFDVHLVVLPSO\
<<6 <<ÖÖÖÖ =
(LJHQYDOXHGHFRPSRVLWLRQSURGXFHVDGLDJRQDOPDWUL[RIHLJHQYDOXHV/DQGDPDWUL[8RIHLJHQYHFWRUV
7KHQRUPDOL]HGPDWUL[8Ö LVREWDLQHGXVLQJ Ö 488 =
7KLVPDWUL[GRHVQRWFRQWDLQWKHORDGLQJVRIWKHURZVRI <Ö RQWKHFDQRQLFDOD[HVEXWWKHORDGLQJVRIWKHURZVRI4RQWKHFDQRQLFDOD[HVDVLQFRUUHVSRQGHQFHDQDO\VLV,WLVXVHG WR ILQG WKH³VLWHVFRUHV´ LQ WKHVSDFHRI WKHRULJLQDOYDULDEOHV&DQRQLFDOFROXPQDQG URZ VFRUHV IRU WKH WZR &$ VFDOLQJV PDWULFHV9&DQ 9Ö &DQ )&DQ DQG ) &DQ DUHREWDLQHGXVLQJWKHWUDQVIRUPDWLRQVRIDQG
7KH³ILWWHGVLWHVFRUHV´OLQHDUFRPELQDWLRQVRIWKHHQYLURQPHQWDOYDULDEOHVDUHIRXQGIURP<Ö XVLQJWKHIROORZLQJHTXDWLRQV
8<'= Ö
−+= LVFDOLQJ S
Ö −−
+= 8<'= LVFDOLQJ S
5HVLGXDOV <4<UHV Ö−= FDQ EH DQDO\]HG E\ DSSO\LQJ HLJHQYDOXH GHFRPSRVLWLRQ WRFRYDULDQFHPDWUL[ UHVUHV<< <<6 = SURGXFLQJPDWULFHVRIQRQFDQRQLFDOHLJHQYDOXHVDQGHLJHQYHFWRUV7KHQDQRQFDQRQLFDOPDWUL[8Ö LVREWDLQHGXVLQJDQGWKHQRQFDQRQLFDOVFRUHVIRUERWKURZVDQGFROXPQVDUHFRPSXWHGDJDLQXVLQJHTXDWLRQV DQG 2Q WKHVH HTXDWLRQV WKH URZ DQG FROXPQ VXPV −
+LS' DQG −
+ MS' IURPWKHRULJLQDOPDWUL[<KDYHWREHXVHG5XQQLQJ&&$
$VZLWKLWVOLQHDUFRXQWHUSDUWZKHQUXQQLQJ&&$LQ*,1.*2WKHXVHUPXVWVSHFLI\ZKLFKWZRGDWDLWHPVLQWKH'DWD(GLWRUZLOOEHXVHGDVH[SODQDWRU\DQGUHVSRQVHPDWULFHV1RWHWKDWLIWKHUH DUH OHVV WKDQ WZR REMHFW GHVFULSWRU PDWULFHV &&$ FDQQRW EH FRPSXWHG 2WKHU RSWLRQVLQFOXGHZKHWKHUDOOHLJHQYDOXHVKDYHWREHNHSWDQGZKLFKRXWSXWPDWULFHVDUHGHVLUHG
(LJHQYDOXHRXWSXWLQIRUPDWLRQLVOLVWHGLQWZRVHSDUDWHEORFNVRQHIRUFDQRQLFDOD[HVDQGWKHRWKHU IRU WKH QRQFDQRQLFDO RQHV 7KH SDUWLWLRQ RI WKH WRWDO LQHUWLD RI4 EHWZHHQ WKH LQHUWLDH[SODLQHGE\UHJUHVVLRQDQGWKHUHVLGXDOLQHUWLDLVDOVRJLYHQ
*,1.*2XVHU¶VPDQXDO
7KHDYDLODEOHRXWSXWPDWULFHVRI&&$DUH• &DQRQLFDOVLWHVFRUHVVFDOLQJ)&DQ5RZVFRUHVRQWKHFDQRQLFDOD[HVIRUVFDOLQJ• &DQRQLFDOVLWHVFRUHVVFDOLQJ9Ö &DQ5RZVFRUHVRQWKHFDQRQLFDOD[HVIRUVFDOLQJ• &DQRQLFDOVSHFLHVVFRUHVVFDOLQJ9&DQ&ROXPQVFRUHVRQWKHFDQRQLFDOD[HVIRUVFDOLQJ• &DQRQLFDOVSHFLHVVFRUHVVFDOLQJ) &DQ&ROXPQVFRUHVRQWKHFDQRQLFDOD[HVIRUVFDOLQJ• 1RQFDQRQLFDOVLWHVFRUHVVFDOLQJ)1RQ&DQ6LWH6FRUHVRQWKHQRQFDQRQLFDOD[HVIRU6FDOLQJ• 1RQFDQRQLFDOVLWHVFRUHVVFDOLQJ9Ö 1RQ&DQ5RZVFRUHVRQWKHQRQFDQRQLFDOD[HVIRUVFDOLQJ• 1RQFDQRQLFDO VSHFLHV VFRUHV VFDOLQJ 91RQ&DQ &ROXPQ VFRUHV RQ WKH QRQFDQRQLFDO D[HV IRUVFDOLQJ• 1RQFDQRQLFDO VSHFLHV VFRUHV VFDOLQJ ) 1RQ&DQ&ROXPQ VFRUHVRQ WKHQRQFDQRQLFDO D[HV IRU6FDOLQJ• &DQRQLFDO HLJHQYHFWRUV 8&DQ (LJHQYHFWRUV UHVXOWLQJ IURP WKH GHFRPSRVLWLRQ RI ILWWHG UHVSRQVH
YDOXHVFRYDULDQFHPDWUL[ <<6 <<ÖÖÖÖ =
• 1RQFDQRQLFDO HLJHQYHFWRUV 81RQ&DQ (LJHQYHFWRUV UHVXOWLQJ IURP WKH GHFRPSRVLWLRQ RI WKHUHVLGXDOUHVSRQVHFRYDULDQFHPDWUL[ UHVUHV<< <<6 = • ([SODQDWRU\YDULDEOHZHLJKWV & %8&DQ:HLJKWVFRQWULEXWLRQRIH[SODQDWRU\YDULDEOHVLQWKH
IRUPDWLRQRIWKHPDWUL[RIILWWHGVLWHVFRUHV• &RUUHODWLRQ;YV9Ö &DQ&RUUHODWLRQVEHWZHHQH[SODQDWRU\YDULDEOHVDQGVLWHVFRUHV• )LWWHGUHVSRQVHYDOXHV<Ö )LWWHGYDOXHVUHVXOWLQJIURPZHLJKWHGPXOWLSOHUHJUHVVLRQV• 5HJUHVVLRQFRHIILFLHQWV%9DULDEOHFRHIILFLHQWVUHVXOWLQJIURPZHLJKWHGPXOWLSOHUHJUHVVLRQV
&&$SORWVDQGELSORWV
*,1.*2DOORZV&&$SORWVRIURZVLWHV)&DQVSDFHRUFROXPQVSHFLHV) &DQVSDFH:LWKVFDOLQJW\SHFDQRQLFDOELSORWVFDQEHGUDZQXVLQJHLWKHU)&DQDQG9&DQRU=6FDOLQJDQG9&DQ$QDORJRXVO\ZLWKVFDOLQJW\SHFDQRQLFDOELSORWVFDQEHGUDZQXVLQJHLWKHU) &DQDQG9Ö &DQRU=6FDOLQJ DQG ) &DQ 2QHPDWUL[ SORWV RI WKH QRQFDQRQLFDO FRQWULEXWLRQ DUH EXLOW XVLQJ HLWKHU)1RQ&DQRU) 1RQ&DQ%LSORWVRIWKHQRQFDQRQLFDOFRQWULEXWLRQFDQEHGRQHXVLQJHLWKHU)1RQ&DQDQG91RQ&DQIRUVFDOLQJRU) 1RQ&DQDQG9Ö 1RQ&DQIRUVFDOLQJ
9HUVLRQ
5HODWHG0XOWLGLPHQVLRQDO6FDOLQJ50'6,QWURGXFWLRQ
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
,I WKH SULQFLSDO FRRUGLQDWHV REWDLQHG IURP '$ DQG WKRVH REWDLQHG IURP '% DUHRUWKRJRQDOWKHQG$% G$G% F.QRZLQJKRZFODVVLFDO0'6ZRUNVWKH50'6PHWKRGLVVLPSO\DVIROORZV /HW '$ DQG '% EH WKH LQQHU SURGXFW PDWULFHV DVVRFLDWHG ZLWK'$ DQG'% UHVSHFWLYHO\7KHVHLQQHUSURGXFWPDWULFHVDUHREWDLQHGDSSO\LQJHTXDWLRQVDQGWRPDWULFHV'$DQG'% 7KHLQQHUSURGXFWPDWUL['$%DVVRFLDWHGZLWKWKHPDWUL['$%RIMRLQWGLVWDQFHVLVJLYHQE\
$%%$%$$% +−+=
ZKHUH αααα ;; ⋅⋅= EHLQJ α; WKH SULQFLSDO FRRUGLQDWHV DQG α WKH GLDJRQDO
PDWUL[RIHLJHQYDOXHVα $%,WFDQEHSURYHGWKDWWKHPDWUL['$%RIMRLQWGLVWDQFHVZKRVH FRUUHVSRQGLQJ LQQHU SURGXFW PDWUL[ LV '$% IXOILOV WKH SURSHUWLHV RI DFSURYLGHGWKDW'$DQG'%KDYHWKHVDPHJHRPHWULFYDULDELOLW\VHHLHLI
∑∑==
=Q
ML%
Q
ML$ MLGQMLGQ
1RWH WKDW WKLV FRQGLWLRQ FDQ DOZD\V EH DVVXPHG WR KROG VLQFH PXOWLSO\LQJ RQH RI WKHPDUJLQDOGLVWDQFHVE\DQDSSURSULDWHFRQVWDQWDPRXQWVWRDFKDQJHRIPHDVXUHPHQWXQLW
*,1.*2XVHU¶VPDQXDO
)LQDOO\ WKH UHODWHG PHWULF VFDOLQJ VROXWLRQ ;$% LV FRPSXWHG IURP WKH VSHFWUDOGHFRPSRVLWLRQ RI '$% ZKLFK JLYHV WKH PDWUL[ RI HLJHQYDOXHV $% DQG WKH PDWUL[ RIHLJHQYHFWRUV $%8
$%$%$% 8; =
50'6LQ*,1.*2
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
7KH50'6URXWLQHRXWSXWVDOLVWRIHLJHQYDOXHV $% DQGWKHLUDVVRFLDWHGRIYDULDQFHRIWKH MRLQW$% VSDFH DVZHOO DV WKH FXPXODWLYH SHUFHQWDJHV 2XWSXWPDWULFHV DUH WKHPDWUL[ RIHLJHQYHFWRUV $%8 WKH50'6REMHFWSULQFLSDOFRRUGLQDWHV;$%DQGWKH50'6GLVWDQFHVLQWKHIXOORUGLQDWLRQVSDFH
&KDSWHU&ODVVLILFDWLRQPHWKRGV
&ODVVLILFDWLRQFRQFHSWV&OXVWHULQJDQG'LVFULPLQDQW$QDO\VLV7KH QHFHVVLW\ RI HVWDEOLVKLQJ FODVVHV DPRQJ D VHW RI HOHPHQWV LVPRWLYDWHG E\ WKHDSULRUL
EHOLHI WKDW WKH REVHUYHG YDULDELOLW\ RI GDWD PDNHV LW SRVVLEOH WR GLYLGH WKH VHW LQWR FDWHJRULHVZKLFK DUH H[SHFWHG WR EH XVHIXO LQ IXUWKHU VWXGLHV +RZHYHU WKH ZD\ RQH VKRXOG WDFNOH WKHFODVVLILFDWLRQSUREOHPZLOOEHGLIIHUHQWGHSHQGLQJRQWKHDSULRULNQRZOHGJHRIGDWD
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
$QXVXDOVWHSLQHFRORJLFDODQDO\VLVLVWRVWDUWZLWKDQDOUHDG\NQRZQJURXSLQJRIWKHREMHFWVDQG WU\ WR GHWHUPLQH WR ZKDW H[WHQW D VHW RI TXDQWLWDWLYH GHVFULSWRUV FDQ DFWXDOO\ H[SODLQ WKLVJURXSLQJ,WPD\EHWKHUHVXOWRIDFOXVWHUDQDO\VLVFRPSXWHGIURPDGLIIHUHQWGDWDVHWRUUHIOHFWDK\SRWKHVLV WREH WHVWHG7KXV DSDUW IURPEHLQJDEOH WRFODVVLI\QHZREVHUYDWLRQVGLVFULPLQDQWDQDO\VLV KHOSV WR LQWHUSUHW DOUHDG\ GHILQHG JURXSV 6RPH UHIHUHQFH PDQXDOV RQ GLVFULPLQDQWDQDO\VLVDUH0F/DFKODQ0DUGLDHWDORU'XGDHWDO
,Q WKHZRUVW FDVH WKHFODVVLILFDWLRQRI WKH WUDLQLQJVHWFDQDOVREHXQNQRZQ7KHQ WKHUH LVDFWXDOO\QRWUDLQLQJVHWDQGGLVFULPLQDQWDQDO\VLVFDQQRWEHXVHG/XFNLO\WKHUHLVDVHFRQGJURXSRIFODVVLILFDWLRQPHWKRGVWKDWFDQEHXVHGFOXVWHUDQDO\VLVRUFOXVWHULQJPHWKRGV,QFRQWUDVWWRGLVFULPLQDQWDQDO\VLVWKHODFNRIDSULRULNQRZOHGJHDERXWGDWDFDXVHVFOXVWHULQJPHWKRGVWREHYHU\KHXULVWLFLQWKHLUDSSURDFKWRFODVVLILFDWLRQ+DUWLJDQVWDWHGLQUHIHUHQFHWRWKRVHPHWKRGV µWKH\ DUH QRW \HW DQ DFFHSWHG LQKDELWDQW RI WKH VWDWLVWLFDOZRUOG¶ 5HIHUHQFHPDQXDOVIRFXVLQJRQFOXVWHUDQDO\VLVDUH-DLQ'XEHV(YHULWWRU*RUGRQ
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
*,1.*2XVHU¶VPDQXDO
&DQRQLFDOOLQHDUGLVFULPLQDQWDQDO\VLV,QWURGXFWLRQ
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
$QDO\VLVRIYDULDQFHLVRIWHQXVHGIRUVFUHHQLQJYDULDEOHVSULRUWROLQHDUGLVFULPLQDQWDQDO\VLV+RZHYHU DQ\ VLQJOH YDULDEOHPD\QRW GLVFULPLQDWH EHWZHHQJURXSVZHOO DOWKRXJK LWPD\KDYHKLJKGLVFULPLQDWLQJSRZHULQFRPELQDWLRQZLWKRWKHUYDULDEOHV7KHUHIRUHRQHVKRXOGEHFDUHIXOZKHQ XVLQJ XQLYDULDWH DQDO\VLV WR HOLPLQDWH YDULDEOHV0HWKRGV RI YDULDEOH VHOHFWLRQ IRUZDUGEDFNZDUGRU VWHSZLVHVHOHFWLRQDUHDEHWWHUZD\ WRVHOHFW VHWVRIYDULDEOHVZLWKGLVFULPLQDWLQJSRZHU +RZHYHU WKHVH YDULDEOH VHOHFWLRQ PHWKRGV GR QRW JXDUDQWHH WKDW WKH ³EHVW´ VHW RIH[SODQDWRU\YDULDEOHVLVQHFHVVDULO\JRLQJWREHIRXQG
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
:LWKLQJURXSVXPRIVTXDUHVSURGXFW ∑=
−−=Q
LNLNL
PLMN X
[[[[: ∑
=
=F
NN
::
$PRQJJURXSIX]]\VXPRIVTXDUHVSURGXFW
[[[[$ −−⋅
= ∑
=NN
Q
L
PLMN X ∑
=
=F
NN
$$
7RWDOVXPRIVTXDUHVSURGXFW7 $: 1RWHWKDWLIIX]]\PHPEHUVKLSVDUHXVHGDQGWKHIX]]LQHVVH[SRQHQWLVJUHDWHUWKDQWKHVXPRI:DQG$GRHVQRWHTXDOWKHXVXDOWRWDOVXPRIVTXDUHVPDWUL[RIGDWD
7KHVROXWLRQWRWKHSUREOHPRIPD[LPL]LQJWKHYDULDWLRQDPRQJJURXSVZKLOHPLQLPL]LQJWKDWZLWKLQJURXSVFDOOV IRU WKHHLJHQYDOXHVDQGHLJHQYHFWRUVRIDPDWUL[FRUUHVSRQGLQJ WR WKH UDWLR
9HUVLRQ
EHWZHHQWKHDPRQJJURXSDQGEHWZHHQJURXSVXPRIVTXDUHVDQGFURVVSURGXFWVPDWULFHV7KDWLVWKHFKDUDFWHULVWLFHTXDWLRQLV =−−
NN X,$: λ
1RWH WKDW WKH HLJHQYHFWRUV XN ZLOO QRW EH RUWKRJRQDO LQ WKH UHIHUHQFH VSDFH RI RULJLQDOYDULDEOHV 7KXV ZKHQ WKHVH QRQRUWKRJRQDO HLJHQYHFWRUV DUH SORWWHG DW ULJKW DQJOHV WKH\VWUDLJKWHQ WKH UHIHUHQFH VSDFH DQG WKH HOOLSVRLGV RI ZLWKLQJURXS VFDWWHUV RI REMHFWV ,I WKHHLJHQYHFWRUVDUHQRUPDOL]HGLQDQDSSURSULDWHPDQQHUWKHZLWKLQJURXSVFDWWHUVRIREMHFWVFDQEHPDGH FLUFXODU LQVRIDU DV WKH ZLWKLQJURXS FURVVSURGXFW PDWULFHV DUH KRPRJHQHRXV VDPHGLVSHUVLRQLQDOOJURXSV7KHVHQRUPDOL]HGFRHIILFLHQWVHLJHQYHFWRUVDUH −= 9888& ZKHUHWKHQRUPDOL]LQJIDFWRULV 988
0DWULFHV RI QRUPDOL]HG & FRHIILFLHQWV FDQ WKHQ EH XVHG WR REWDLQ WKH REMHFW FDQRQLFDOFRRUGLQDWHVSURMHFWLQJFHQWHUHG;YDOXHVRQWKHFDQRQLFDOVSDFH)RUHDFKREMHFW &[[) −= LL 6LPLODUO\WKHJURXSFHQWURLGVFDQDOVREHSURMHFWHGWRWKHFDQRQLFDOVSDFHIRUHDFKNJURXS &[[) −= NN 1RWH WKDW FDQRQLFDO FRRUGLQDWHV FRXOG DOVR EH FRPSXWHG XVLQJ PDWUL[ 8 RI QRQQRUPDOL]HGHLJHQYHFWRUV
&DQRQLFDOFRRUGLQDWHVDUHXVHGWREXLOGWKHFODVVLILFDWLRQRULGHQWLILFDWLRQUXOHRUIXQFWLRQXVHGWRFODVVLI\REMHFWV(DFKREMHFWLVDVVLJQHGWRWKHFODVVZKRVHFHQWURLGLVFORVHVWLQWHUPVRI(XFOLGHDQ'LVWDQFHWRWKHREMHFWRQWKHFDQRQLFDOVSDFH,IWKHQXPEHURIJURXSVLVWZRF WKLVUXOHFRUUHVSRQGVWRFODVVLI\LQJHDFKREMHFWWRWKHFORVHVWJURXSLQWKHRULJLQDOVSDFHXVLQJDVSUR[LPLW\PHDVXUHWKH0DKDODQRELVGLVWDQFHIURPWKDWREMHFWWRHDFKRQHRIWKHJURXS5XQQLQJ/')
,QSXWGDWDDQGWUDLQLQJFODVVHV
/LQHDUGLVFULPLQDQWDQDO\VLVFDQRQO\EHH[HFXWHGZKHQDQREMHFWGHVFULSWRUPDWUL[ LWHPLVVHOHFWHGRQWKH'DWD(GLWRUWUHH$VXVXDOWKLVPDWUL[FDQEHFURSSHGLQRUGHUWRHOLPLQDWHWKRVHREMHFWVRUYDULDEOHVQRWGHVLUHGIRUWKHDQDO\VLV,QDGGLWLRQ/')QHHGVDVWDUWLQJFODVVLILFDWLRQSDUWLWLRQRIREMHFWV8VHUVFDQWDNHDVHOHFWHGFROXPQRIWKHRULJLQDOPDWUL[DVWKHFODVVLILFDWLRQFROXPQ$OWHUQDWLYHO\ D VHOHFWHG FODVVLILFDWLRQPDWUL[ IURP WKH$QDO\VLV0DQDJHU FDQ DOVR EHXVHG
*,1.*2XVHU¶VPDQXDO
$GYDQFHGRSWLRQV
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
9HUVLRQ
/')RXWSXW
/')PD\RXWSXWD ORWRI LQIRUPDWLRQ7RVWDUWZLWKXQLYDULDWH$129$WHVWUHVXOWVPD\EHZULWWHQ ,I WKH XVHU UHTXHVWV D YDULDEOH VHOHFWLRQ SURFHGXUH WKH GLIIHUHQW SURFHGXUH VWHSV DUHVKRZQLQWKHWH[WRXWSXWLQFOXGLQJWKHWHVWVGRQHWRLQFOXGHRUH[FOXGHYDULDEOHV
$IWHUVHOHFWLQJWKHRULJLQDOYDULDEOHVWREHLQFOXGHGLQWKH/')DQDO\VLVD0$129$:LON¶VWHVWFDQEHSHUIRUPHG7KHQWKHHLJHQYDOXHVRI $: − DUHSUHVHQWHGDVZHOODVWKHLUFRQWULEXWLRQWRYDULDQFHDQGWKHLUDVVRFLDWHG:LON¶VUDWLR
7KHRXWSXWPDWULFHVWKDW*,1.*2PD\RXWSXWDUH• 3RROHG ZLWKLQJURXS GLVSHUVLRQ :LWKLQJURXS FRYDULDQFH PDWUL[ SRROLQJ ZLWKLQ
JURXSVXPRIVTXDUHV• %HWZHHQJURXSGLVSHUVLRQ%HWZHHQJURXSFRYDULDQFHPDWUL[• 7RWDOGLVSHUVLRQ2YHUDOOFRYDULDQFHPDWUL[• 3RROHGZLWKLQJURXSVXPRIVTXDUHV3RROHGZLWKLQJURXSVXPRIVTXDUHVPDWUL[• %HWZHHQJURXSVXPRIVTXDUHV%HWZHHQJURXSVXPRIVTXDUHVPDWUL[• 7RWDOVXPRIVTXDUHV2YHUDOOVXPRIVTXDUHVPDWUL[• &DQRQLFDO FRHIILFLHQWV &DQRQLFDO HLJHQYHFWRUV QRUPDOL]HG LI UHTXHVWHG GHILQLQJ
FDQRQLFDOD[HV• &DQRQLFDOREMHFWFRRUGLQDWHV2EMHFWVFRUHVRQFDQRQLFDOD[HV• &DQRQLFDOJURXSFHQWURLGV&HQWURLGFRRUGLQDWHVRQFDQRQLFDOD[HV• &DQRQLFDO FHQWURLGV LQWHUGLVWDQFHV (XFOLGHDQ GLVWDQFHV EHWZHHQ FHQWURLGV RQ
FDQRQLFDOVSDFH• ;)FRUUHODWLRQV3HDUVRQFRUUHODWLRQVEHWZHHQFDQRQLFDOFRRUGLQDWHVDQGWKHRULJLQDO
GHVFULSWRUV,IUHFODVVLILFDWLRQRIREMHFWVZDVUHTXHVWHGE\WKHXVHUDGGLWLRQDOFODVVLILFDWLRQSDUWLWLRQVDUH
SUHVHQWHGREWDLQHGIURPUHVXEVWLWXWLRQRU/22SURFHGXUHV7KHVHFODVVLILFDWLRQPDWULFHVFDQEHFRPSDUHGZLWK WKH RULJLQDO FODVVLILFDWLRQPDWUL[ XVHG WR EXLOG GLVFULPLQDQW DQDO\VLV DIWHUZDUGVVHH VHFWLRQ&RPSDULQJ FODVVLILFDWLRQV3HUFHQWDJHVRI FRUUHFW UHFODVVLILFDWLRQ DUHJLYHQ LQWKHWH[WRXWSXW)LQDOO\DQDGGLWLRQDOO\FODVVLILFDWLRQPDWUL[ZLOODSSHDULIWKHXVHUDVNHGIRUWKHFODVVLILFDWLRQRIDQH[WHUQDOGDWDPDWUL[FRQWDLQLQJQHZREMHFWREVHUYDWLRQV
7KH FDQRQLFDO REMHFW FRRUGLQDWHVPDWUL[ FDQ EH SORWWHG GLUHFWO\ IURP/')DQDO\VLV ,Q WKLVVFDWWHUJUDSKLFJURXSVIURPHLWKHU WKHRULJLQDOFODVVLILFDWLRQRU UHFODVVLILFDWLRQVFDQEHXVHG WRJURXSVDPSOHSRLQWV7RGLVSOD\RWKHUPDWULFHVWKH\PXVWEHUHFRSLHGLQWRWKH'DWD(GLWRUVHH*UDSKLFVFKDSWHUIRUPRUHLQIRUPDWLRQ
*,1.*2XVHU¶VPDQXDO
4XDGUDWLFGLVFULPLQDQW7KHTXDGUDWLFGLVFULPLQDQWUXOH
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ΩNLV NNLNNL[4') πOQOQ −Σ+∆=Ω [ ZKHUH Mπ LVWKHSURSRUWLRQRIJURXSΩNDQG
LN [∆ LVWKH0DKDODQRELVGLVWDQFHIURPREMHFW LWRJURXSΩN
MLMMLLN [[[[[ −Σ−=∆ −
.QRZQDV4')WKHTXDGUDWLFGLVFULPLQDQWUXOHFDQEHVLPSO\VWDWHGDV³$VVLJQREMHFW LWRJURXSΩNLI PLQ KLKNL [4')[4') Ω=Ω ´
5XQQLQJTXDGUDWLFGLVFULPLQDQW
$V LQ OLQHDUGLVFULPLQDQWDQDO\VLV4')QHHGVDVHOHFWHGGDWD LWHP WREH UXQ$VXVXDO WKHDQDO\VLVGLDORJVPDNHFURSSLQJWKH LQSXWPDWUL[SRVVLEOH LQRUGHU WRHOLPLQDWHWKRVHREMHFWVRUYDULDEOHVQRWGHVLUHG4')DJDLQQHHGVDVWDUWLQJFODVVLILFDWLRQLHDIX]]\RUFULVSFSDUWLWLRQRIREMHFWV8VHUVFDQWDNHDVHOHFWHGFROXPQRIWKHRULJLQDOPDWUL[DVWKHFODVVLILFDWLRQFROXPQ$OWHUQDWLYHO\DVHOHFWHGFODVVLILFDWLRQPDWUL[IURPWKH$QDO\VLV0DQDJHUFDQDOVREHXVHG
5XOHHYDOXDWLRQFDQEHGRQHE\OHDYHRQHRXWH[WUDFWLQJHDFKREMHFWEHIRUHUHFODVVLI\LQJLWRUE\UHVXEVWLWLWXWLRQUHFODVVLI\LQJWKHREMHFWVXVHGWREXLOGWKHUXOHZLWKRXWH[WUDFWLRQ$OVRDQDGGLWLRQDOREMHFWGHVFULSWRUPDWUL[FDQEHXVHGWRFODVVLI\QHZREVHUYDWLRQV
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
9HUVLRQ
'LVWDQFHEDVHGGLVFULPLQDQWDQDO\VLV,QWURGXFWLRQ
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
/HW;EHDSGLPHQVLRQDOUDQGRPYHFWRUGHILQHGRQDSUREDELOLW\VSDFHΠ$3DQGWDNLQJYDOXHVLQ 36 ℜ⊂ ZLWKDGHQVLW\SUREDELOLW\IXQFWLRQ IZLWKUHIHUHQFHWRDQDGHTXDWHPHDVXUHλ)XUWKHUPRUHOHW ⋅⋅G EHDGLVVLPLODULW\IXQFWLRQGHILQHGRYHUSDLUVRIHOHPHQWVLQΠVRWKDWLWVVTXDUHLVLQWHJUDEOHLQ67KHQWKHJHRPHWULFYDULDELOLW\RI;ZLWKUHVSHFWWR ⋅⋅G LVGHILQHGDV&XDGUDV)RUWLDQD
[ ] ∫ ×=∈= 66G GGIIG6G(9
[[[[[[;;;;; λλ
*LYHQ 3ℜ∈R[ ZH GHILQH WKH SUR[LPLW\ RI R[ WR WKH SRSXODWLRQΠ ZLWK UHVSHFW WR ⋅⋅G DV&XDGUDVHWDO RR ;[[[[[ G6G 9GIG −=Π ∫ λφ
,I D UHSUHVHQWDWLRQ RI ⋅⋅G H[LVWV LH LI WKHUH LV D IXQFWLRQ /5 3 →ψ ZKHUH ⋅⋅/ V\PEROL]HVDQ(XFOLGHDQRU+LOEHUWVSDFHILOOHGZLWKDVFDODUSURGXFW ⋅⋅ VXFKDV XXX ____ = LVWKHQDWXUDOQRUPIRUHYHU\ /∈X DQGDVVXPLQJWKDW ;ψ( DQG ____ ;ψ( DUHILQLWHWKHQWKHJHRPHWULFYDULDELOLW\RI;DQGWKHSUR[LPLW\RI R[ WRWKHSRSXODWLRQΠDUH
____ ;;; ψψ ((9G −= D
RR ;[[ ψψφ (G −= E
7KH'%UXOH
7KHNH\RIWKHGLVWDQFHEDVHG'%DSSURDFKLVWRFRPSXWHWKHGLVWDQFHIURPDQREMHFWWRDJURXSIURPDPDWUL['Q[Q >GLM@RIREMHFWLQWHUGLVWDQFHV7KLVDSSURDFKLVSRVVLEOHERWKIRUFULVSDQGIX]]\SDUWLWLWLRQVVHH:HZLOOILUVWHQXQFLDWHWKH'%UXOHIRUWKHFULVSFDVHDQGODWHUJLYHWKHIX]]\JHQHUDOL]DWLRQ/HW NQNN [[ EHWKHQNYHFWRUVRIREMHFWVEHORQJLQJWRDJURXSΩN7KHVTXDUHGGLVWDQFHRIDJLYHQREMHFW LWRWKHJURXSΩNLV&XDGUDVHWDO
Ö
N9NGQG GKLQ
KNNL
N−=Ω ∑
=
[[[
*,1.*2XVHU¶VPDQXDO
ZKHUH Ö N9G LVWKHJHRPHWULFYDULDELOLW\RIΩN
Ö
OKQ
OKNG NNGQN9
N[[∑=
7KHVHHTXDWLRQVVKRXOGEHFRPSXWHGIRUHDFKREMHFWYHFWRU L[ L «QDQGHDFKΩNJURXSN «FXQWLOREWDLQLQJDPDWUL[RIVTXDUHGGLVWDQFHVIURPDOOREMHFWVWRDOOJURXSFHQWHUV1RZWKHGLVWDQFHEDVHG'%UXOHLVVWDWHGDVIROORZV ³$VVLJQ LWRWKHJURXSΩNLI `^PLQ
FLLLNL GGGG ΩΩΩ=Ω [[[[ ´ $VVWDWHGDERYHHTXDWLRQV DQG FDQEHJHQHUDOL]HGWRWKHFDVHRIKDYLQJDIX]]\
SDUWLWLRQ VHH *LYHQ D IX]]\ SDUWLWLRQ PDWUL[8Q [ F DQG D IX]]LQHVV H[SRQHQWP WKHGLVWDQFHIURPDQREMHFWWRDIX]]\JURXSΩNDQGWKHIX]]\JURXSJHRPHWULFDOYDULDELOLW\DUH Ö
NIGKL
Q
K
PKNQ
K
PKN
NL 9GXX
G Ω−=Ω ∑∑ =
=
[[[
Ö
OKQ
OK
PON
PKNQ
L
PLN
NIG GXXX
9 [[∑∑
⋅⋅
=Ω
=
1RWHWKDWWKHVHODVWHTXDWLRQVUHGXFHWRHTXDWLRQVDQGZKHQWKHFODVVLILFDWLRQWUDLQLQJPDWUL[LVDFULVSSDUWLWLRQ5XQQLQJ'%GLVFULPLQDQWDQDO\VLV
8QOLNH/')DQG4')'%GLVFULPLQDQWDQDO\VLVQHHGVDVHOHFWHGDV\PPHWULFGLVVLPLODULW\LWHPWREHUXQ$VXVXDOWKH'%GLVFULPLQDQWDQDO\VLVGLDORJPDNHVLWSRVVLEOHWRFURSWKHLQSXWPDWUL[ LQ RUGHU WR HOLPLQDWH WKRVH REMHFWV 7KH DQDO\VLV DOVR QHHGV D VWDUWLQJ FODVVLILFDWLRQSDUWLWLRQRIREMHFWV,QWKLVFDVHRQO\DVHOHFWHGFODVVLILFDWLRQPDWUL[IURPWKH$QDO\VLV0DQDJHUFDQEHXVHG,IWKHVHOHFWHGFODVVLILFDWLRQPDWUL[LVIX]]\WKHQHTXDWLRQVDQGZLOOEHXVHGWRREWDLQVTXDUHGGLVWDQFHVWRFHQWURLGV2WKHUZLVHWKHLUFULVSFRXQWHUSDUWVZLOOEHXVHGLQWKH'%UXOH
$VRXWSXW'%GLVFULPLQDQWDQDO\VLV\LHOGVWKHJHRPHWULFYDULDELOLW\RIHDFKJURXSFRPSXWHGWKURXJK RU ,I UHFODVVLILFDWLRQ RI REMHFWV KDV EHHQ UHTXHVWHG E\ WKH XVHU DGGLWLRQDOFODVVLILFDWLRQ SDUWLWLRQV DUH SUHVHQWHG REWDLQHG IURP UHVXEVWLWXWLRQ RU /22 SURFHGXUHV 7KHVHFODVVLILFDWLRQ PDWULFHV FDQ EH FRPSDUHG ZLWK WKH RULJLQDO FODVVLILFDWLRQ PDWUL[ XVHG WR EXLOGGLVFULPLQDQW DQDO\VLV DIWHUZDUGV VHH VHFWLRQ &RPSDULQJ FODVVLILFDWLRQV 3HUFHQWDJHV RIFRUUHFWUHFODVVLILFDWLRQDUHJLYHQLQWKHWH[WRXWSXW
9HUVLRQ
$JJORPHUDWLYH+LHUDUFKLFDO&OXVWHULQJ,QWURGXFWLRQ
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
+LHUDUFKLFDO DJJORPHUDWLYH PHWKRGV FDQ EH YHU\ XVHIXO IRU JUDSKLFDOO\ VXPPDUL]LQJ WKHUHODWLRQV FRQWDLQHG LQ D UHVHPEODQFH PDWUL[ +RZHYHU WKHVH FOXVWHULQJ DOJRULWKPV EHFRPHSUREOHPDWLF ZKHQ GHDOLQJ ZLWK PDQ\ REMHFWV EHFDXVH GHQGURJUDP WUHHV EHFRPH GLIILFXOW WRXQGHUVWDQG,QDGGLWLRQDWWKHKLJKHVWOHYHOVRIWKHKLHUDUFK\WKHEUDQFKHVDUHWRWDOO\GHSHQGHQWRQ WKH ORZHU OLQNV DQG FDQ DFFXPXODWH HUURUV *HQHUDOO\ VSHDNLQJ DOPRVW DOO KLHUDUFKLFDODJJORPHUDWLYH DOJRULWKPV DUH VDIH ZKHQ WKH LQWHUHVW LV SODFHG RQ WKH VPDOO ORZ OHYHOV RI WKHKLHUDUFK\ DQG WKH\ EHFRPH XQVDIH DW KLJK OHYHOV 3UHFLVHO\ WKH GLIIHUHQW KLHUDUFKLFDODJJORPHUDWLYH DOJRULWKPV QRUPDOO\ GLIIHU LQ WKH VROXWLRQV JLYHQ DW WKRVH KLJK OHYHOV 6HH/HJHQGUH/HJHQGUHIRUDGHWDLOHGH[SODQDWLRQRQWKLVNLQGRIDOJRULWKPV7KHIROORZLQJVXEVHFWLRQEULHIO\LQWURGXFHVWKRVHDOJRULWKPVLPSOHPHQWHGLQ*,1.*2
+LHUDUFKLFDODOJRULWKPV
6LQJOH/LQNDJHWKHEDVLFPRGHO
7KH EDVLF DJJORPHUDWLYH PRGHO LV 6LQJOH /LQNDJH 6QHDWK DOVR FDOOHG QHDUHVWQHLJKERU ,W FDQ VWDUW IURP D UHVHPEODQFHPDWUL[ DPRQJ REMHFWV GLVWDQFHPDWUL[ RU VLPLODULW\PDWUL[ ,WRUGHUVREMHFWSDLUVDFFRUGLQJ WR VLPLODULW\ LQDGHVFHQGLQJRUGHU DQG IRUPVFOXVWHUVKLHUDUFKLFDOO\VWDUWLQJIURPWKHPRVWVLPLODUSDLUV
,QVLQJOHOLQNDJH WRMRLQDQREMHFWWRDQDOUHDG\H[LVWLQJFOXVWHULWPXVWKDYHDVLPLODULW\DWOHDVW HTXDO WR WKH FRQVLGHUHG VLPLODULW\ OHYHOZLWK21( RI WKH REMHFWV DOUHDG\ LQFOXGHG LQ WKHFOXVWHU 7KHUHIRUH DQ HOHPHQW ZLOO EH JURXSHG WR D FOXVWHU DW WKH OHYHO FRUUHVSRQGLQJ WR WKHPD[LPXPVLPLODULW\EHWZHHQLWDQGWKHHOHPHQWVLQWKHFOXVWHU'XHWRLWVQDWXUHVLQJOHOLQNDJHSUHVHQWV D SURSHUW\ZKDW LV FDOOHGFKDLQLQJ$V D UHVXOW LWPD\EH LQDGHTXDWH LQPDQ\FDVHV&KDLQLQJPHDQVWKDWWKHREMHFWVMRLQDFOXVWHUHDVLO\LIWKHUHDUHLQWHUPHGLDWHREMHFWVWKDWEULGJHWKH FOXVWHU WR RWKHU REMHFWV $V FKDLQLQJ DSSHDUV ZKHQ WKHUH DUH LQWHUPHGLDWH SRLQWV VLQJOHOLQNDJHLVDJRRGZD\WRGHWHFWWKHP2QWKHRWKHUKDQGFKDLQLQJPDNHVVLQJOHOLQNDJHSURQHWRGDWDQRLVH7KHELJJHUWKHFOXVWHULVWKHHDVLHVWLWLVWRMRLQPRUHDQGPRUHHOHPHQWVEHFDXVHWKHSUREDELOLW\RIILQGLQJLQWHUPHGLDWHREMHFWVLQFUHDVHV7KXVVLQJOHOLQNDJHLVVDLGWRFRQWUDFWWKHVSDFHRIUHODWLRQVDPRQJREMHFWVLQWKHQHDUE\RIFOXVWHUV
&RPSOHWH/LQNDJH
,QFRPSOHWH OLQNDJH WZRFOXVWHUV IXVHGHSHQGLQJRQ WKHPRVWGLVWDQWSDLU RIREMHFWV DPRQJWKHP ,QRWKHUZRUGV DQREMHFW MRLQVD FOXVWHUZKHQ LWV VLPLODULW\ WR$// WKHHOHPHQWV LQ WKDWFOXVWHULVHTXDOWRRUKLJKHUWKDQWKHFRQVLGHUHGOHYHO,QDJURZLQJFOXVWHUQHZREMHFWVKDYHOLWWOH
*,1.*2XVHU¶VPDQXDO
FKDQFHWRMRLQEHFDXVHWKH\PXVWEHFORVHWRDOOREMHFWVLQWKHFOXVWHUVRWKH\MRLQODWHUZKHQWKHOHYHO RI VLPLODULW\ FRQVLGHUHG LV ORZHU7KXVZKHQ D FOXVWHU JURZV LWPRYHV DSDUW IURPRWKHUREMHFWV&RPSOHWHOLQNDJHLVVDLGWRH[SDQGWKHVSDFHLQHDFKFOXVWHUVXUURXQGV7KLVDOJRULWKPPD\EHDGHTXDWHZKHQRQHZDQWVWRLQVSHFWFOHDUGLVFRQWLQXLWLHV
$OO WKH IROORZLQJPHWKRGV DUH VDLG WRFRQVHUYH WKHPHWULF UHODWLRQVRI WKH UHIHUHQFH VSDFH7KH\DUHQRWREMHFWOLQNPHWKRGV LQ WKHVHQVHRISUHYLRXVPHWKRGV$OWHUQDWLYHO\ WKH\DYHUDJHWKHVLPLODULWLHVDWHDFKDJJORPHUDWLYHVWHS
83*0$8QZHLJKWHGDULWKPHWLFDYHUDJHFOXVWHULQJ
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
:3*0$:HLJKWHGDULWKPHWLFDYHUDJHFOXVWHULQJ
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
83*0&8QZHLJKWHGFHQWURLGFOXVWHULQJ
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
9HUVLRQ
LKLK
LKJL
LK
LJK
LK
KJKL 6ZZ
ZZ6ZZZ6ZZ
Z6 −+
++
++
=
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
83*0&FDQEHXVHGZLWKDQ\VLPLODULW\PHDVXUHEXW*RZHUVIRUPXODUHPDLQVYDOLGRQO\IRUVLPLODULWLHV FRUUHVSRQGLQJ WRPHWULFGLVWDQFHV7KH VDPSOLQJ DVVXPSWLRQVRI WKLVPRGHO DUH WKHVDPHDV83*0$EHFDXVHDOOWKHRULJLQDOREMHFWVDUHJLYHQWKHVDPHZHLJKW83*0&FDQ\LHOGUHYHUVDOV
:3*0&:HLJKWHGFHQWURLGFOXVWHULQJ
:3*0&LVWKHFHQWURLGFRXQWHUSDUWRI:3*0$:KHQWKHUHDUHWZRXQHTXDOVL]HGFOXVWHUVWKDW MRLQ WKHELJJHURQHZLOOGUDJ WKHQHZFHQWURLGWRLWVHOI,I WKHVDPSOLQJLVQRWUDQGRPWKLVPD\EHXQGHVLUDEOH7RJLYHHTXDOZHLJKWWRERWKEUDQFKHVZHPXVWXVHWKHIROORZLQJIRUPXOD
LKJLJKJKL 6666 −++=
$IWHUHDFKVWHSWKHQHZO\IRUPHGFOXVWHUKDVDFHQWURLGWKDWUHSUHVHQWVWKHJHRPHWULFFHQWHURIWKHOLQHMRLQLQJWKHSUHYLRXVFHQWURLGV:3*0&FDQSURGXFHUHYHUVDOV
:DUG¶VPHWKRGRUPLQLPXPVXPRIVTXDUHVPHWKRG:DUG
7KLVPHWKRG LV UHODWHG WR WKH WZRSUHYLRXVRQHV LQ WKHVHQVH WKDW WKH WZRFHQWURLGVSOD\DQLPSRUWDQWUROH:DUG¶VPHWKRGPLQLPL]HVDWHDFKVWHSWKHVXPRITXDGUDWLFHUURUV&RQFUHWHO\LWIXVHVWKRVHQRGHV\LHOGLQJDORZHULQFUHDVHLQTXDGUDWLFHUURU1RWHWKDWWKLVREMHFWLYHIXQFWLRQLVVLPLODUWRWKDWRI.PHDQVVHHQH[WVHFWLRQ
)OH[LEOHPHWKRG
/DQFH:LOODPV SURSRVHG D JHQHUDOL]HG KLHUDUFKLFDOPHWKRG WKDW LQFOXGHV DOO WKHDERYHPHWKRGV/HWKDQGLEHWKHHOHPHQWVRIWKHQHZO\IRUPHGJURXSDQGJDQH[WHUQDOREMHFW7KHGLVWDQFHIURPJWRWKHJURXSKLLVFRPSXWHGXVLQJ JMJLLMJMMJLLLMJ GGGGGG −⋅+⋅+⋅+⋅= λβαα
*,1.*2XVHU¶VPDQXDO
$VVLJQLQJGLIIHUHQWYDOXHVWRWKHIRXUPRGHOSDUDPHWHUVRIWKHPRGHOLWLVSRVVLEOHWRREWDLQDOOWKHKLHUDUFKLFDODOJRULWKPVGHVFULEHGVRIDU,QDGGLWLRQ/DQFH:LOODPVSURSRVHGWROHWRQH RI WKH SDUDPHWHUV YDU\ EHWZHHQ ± DQG LQ RUGHU WR REWDLQ LQWHUPHGLDWH VROXWLRQVEHWZHHQVLQJOHOLQNDJHDQGFRPSOHWHOLQNDJH7KLVPHWKRGZDVODWHUFDOOHG IOH[LEOHFOXVWHULQJ7KHUHIHUHQFHVSDFHLVFRQVHUYHGIRU §YDOXHUHFRPPHQGHGE\0LOOLJDQ5XQQLQJDQDJJORPHUDWLYHFOXVWHULQJPHWKRG
$JJORPHUDWLYH FOXVWHULQJ PHWKRGV LQ *,1.*2 FDQ EH UXQ IURP HLWKHU VLPLODULW\ RUGLVVLPLODULW\V\PPHWULFPDWULFHV$IWHUVHOHFWLQJWKHGHVLUHGPDWUL[RQWKH'DWD(GLWRUWKHPHQXRSWLRQ$JJORPHUDWLYHKLHUDUFKLFDOFOXVWHULQJPXVWEHVHOHFWHG$GLDORJLVSURPSWHGDQGWKHXVHUPXVWVHOHFWWKHDJJORPHUDWLYHPHWKRGWKDWLVWREHUXQ6RPHREMHFWVLQWKHLQLWLDOVLPLODULW\PDWUL[FDQEHH[FOXGHGIURPWKHFRPSXWDWLRQV
7KH UHVXOWLQJ RXWSXW SDQHO RI DQ DJJORPHUDWLYH PHWKRG FRQWDLQV WZR PDWULFHV WKH LQSXWV\PPHWULFPDWUL[DQGWKHFRSKHQHWLFPDWUL[ZKLFKLVWKHPDWUL[UHSUHVHQWDWLRQRIWKHUHVXOWLQJKLHUDUFKLFDO FODVVLILFDWLRQ 7KUHH PHDVXUHV RI JRRGQHVVRIILW EHWZHHQ WKH FOXVWHULQJ UHVXOWVFRSKHQHWLFPDWUL[DQGWKHRULJLQDOV\PPHWULFPDWUL[DUHDOVRSURYLGHG
• 3HDUVRQ U &RSKHQHWLF &RUUHODWLRQ 3HDUVRQ FRUUHODWLRQ FRPSXWHG E\FRPSDULQJWKHPDWULFHV¶RUGHUHGFHOOSDLUV
• 6SHDUPDQU&RSKHQHWLF&RUUHODWLRQ6SHDUPDQUDQNFRUUHODWLRQFRPSXWHGE\FRPSDULQJWKHPDWULFHV¶RUGHUHGFHOOSDLUV
• *RZHU'LVWDQFH 6WUHVV 6XP RI VTXDUHG GLIIHUHQFHV EHWZHHQ YDOXHV LQWKHFRSKHQHWLFPDWUL[DQGWKHRULJLQDOV\PPHWULFPDWUL[
3ORWWLQJKLHUDUFKLFDOPHWKRGV¶UHVXOWV
*,1.*2HQDEOHVWKHXVHUWREXLOGWZRGLIIHUHQWSORWVIURPDKLHUDUFKLFDOFOXVWHULQJPHWKRGUHVXOWWKHGHQGURJUDPDQGWKH6KHSDUGGLDJUDP7KHILUVWJUDSKLFDOO\GLVSOD\VWKHFRSKHQHWLFUHODWLRQV DPRQJ REMHFWV ZKLOH WKH VHFRQG FRPSDUHV LQ D WZR GLPHQVLRQDO VFDWWHU JUDSKLF WKHRULJLQDO VLPLODULWLHV RU GLVWDQFHVZLWK WKH FRSKHQHWLF VLPLODULWLHV RU GLVWDQFHV REWDLQHG7KHGLDJRQDOUHSUHVHQWV WKHHTXLYDOHQFHEHWZHHQERWKYDOXHV ,QD6KHSDUGSORW WKHXVHUFDQFKHFNWZRWKLQJV)LUVWDJUDSKLFDO LGHDRI WKHVWUHVV LVSUHVHQWHG6HFRQG LWFDQEHVHHQZKHWKHUWKHUHIHUHQFHVSDFHKDVEHHQFRQVHUYHGH[SDQGHGRUFRQWUDFWHGGHSHQGLQJRQZKHWKHUWKHSRLQWVIDOOQHDUEHORZRUDERYHWKHGLDJRQDOUHVSHFWLYHO\%XLOGLQJSDUWLWLRQVIURPGHQGURJUDPV
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
9HUVLRQ
.PHDQV.PHDQVFOXVWHULQJPHWKRG
.PHDQV0DF4XHHQLVDFODVVLILFDWLRQDOJRULWKPZKLFKSDUWLWLRQVDVHWRIQREMHFWVLQF JURXSV RU FOXVWHUV 7KH .PHDQV FULWHULRQ IRU GHILQLQJ WKH JURXSV LV WKDW WKH\ PXVW KDYH DPLQLPXPGLVSHUVLRQ7KHIXQFWLRQDOWREHPLQLPL]HGLVWKH7RWDO(UURU6XPRI6TXDUHV7(66
[ ]∑∑∑= ==
Ω⊂==F
N
Q
LLNNL
F
NNF H,(7(66
ω
ZKHUH N( LVWKHVXPRIVTXDUHHUURUV(66IRUJURXS NΩ DQG [ ] =Ω⊂ NL, ω LIREMHFW Lω EHORQJVWR NΩ DQG [ ] =Ω⊂ NL, ω RWKHUZLVH
LNH LVWKHVTXDUHGLVWDQFHIURPWKHREMHFW Lω WRFHQWURLGRINΩ ,QRWKHUZRUGV
LNH LVWKHVFDWWHURIREMHFW Lω ZLWKUHVSHFWWRWKHFHQWURLG
NLS
MNLMNLMNLLN [[GH [[[[ −−=−=Ω= ∑
=
ω
1RWH WKDW DV WKHUH LV D OLPLWHGQXPEHURISRVVLEOHSDUWLWLRQVRIREMHFWV LQWRJURXSV RQH FRXOGLGHDOO\H[SORUHWKHPWRHQGXSNHHSLQJWKHSDUWLWLRQZLWKORZHVWFRUUHVSRQGLQJ7(66+RZHYHUWKH QXPEHU RI SRVVLEOH SDUWLWLRQV FDQ EH H[WUHPHO\ KLJK HYHQ IRU PRGHUDWH YDOXHV RI Q RU F7KHUHIRUHDOJRULWKPVRSWLPL]LQJ7(66DUHQHHGHG
7KHFRQFUHWHLPSOHPHQWDWLRQDOJRULWKPRI.PHDQVFDQWDNHVHYHUDOIRUPVEXWLQ*,1.*2LWLVDVIROORZV6WDUWLQJIURPDQLQLWLDOSDUWLWLRQ
&DOFXODWHWKHFOXVWHUFHQWHUVFHQWURLGV &DOFXODWHVTXDUHGLVWDQFHVIURPDOOREMHFWVWRDOOFHQWURLGVZLWK 5HDVVLJQHDFKREMHFWWRLWVQHDUHVWFOXVWHU ,WHUDWHXQWLOQRPRUHPRYHVRFFXU
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
*,1.*2XVHU¶VPDQXDO
5XQQLQJ.PHDQV
.PHDQV LQ *,1.*2 FDQ EH UXQ IURP HLWKHU D UHFWDQJXODU GDWD PDWUL[ RU D V\PPHWULFGLVVLPLODULW\ PDWUL[ WKRXJK LW FDQQRW EH UXQ IURP D VLPLODULW\ PDWUL[ 7KLV KDV WR EH ILUVWFRQYHUWHGWRDGLVWDQFHPDWUL[$VZLWKRWKHUDQDO\VHVVRPHREMHFWVDQGRUVRPHGHVFULSWRUVFDQEHH[FOXGHGIURPFRPSXWDWLRQV7KHRWKHURSWLRQVLQWKH.PHDQVGLDORJDUH
6WDUWLQJ0RGH$VH[SODLQHGLQWKHDOJRULWKPVHFWLRQ.PHDQVFDQEHVWDUWHGIURPGLIIHUHQWSDUWLWLRQFRQILJXUDWLRQV7KLVRSWLRQLVFULWLFDOVRWKHXVHUPXVWEHDZDUHRIWKHDGYDQWDJHVDQGGLVDGYDQWDJHV RI HDFK VWDUWLQJ PRGH )LYH VWDUWLQJ PRGHV FDQ EH XVHG LQ *,1.*2 $ JRRGVWUDWHJ\LVWRUXQ.PHDQVZLWKWKHVDPHGDWDVHYHUDOWLPHVXVLQJDGLIIHUHQWVWDUWLQJPRGHHDFKWLPHDQGWRILQDOO\NHHSWKHUHVXOWVRIWKHUXQZKLFK\LHOGHGDORZHU7(667KHDYDLODEOHVWDUWLQJPRGHVIRU.PHDQVDQG)X]]\&PHDQVDUHJLYHQKHUHDVZHOODVVRPHUHFRPPHQGDWLRQVIRUWKHLUXVH
5$1'206(('6*,1.*2ZLOOSHUIRUPVHYHUDO.PHDQVUXQVHDFKWLPHFKRRVLQJGLIIHUHQWREMHFWVDVVWDUWLQJFOXVWHUFHQWHUVVHHGV7KHQXPEHURIUDQGRPUXQVDQGWKHQXPEHU FOXVWHUV FDQ EH FKDQJHG:KHQ ORRNLQJ IRU D KLJK QXPEHU RI FOXVWHUV WKHQXPEHURIUXQVVKRXOGDOVREHKLJKLQRUGHUWRH[SORUHPRUHFRPSOHWHO\WKHVSDFHRI.PHDQVVROXWLRQV7KLVRSWLRQFDQEHYHU\VORZDQGLQHIIHFWLYHZKHQWKHQXPEHURIREMHFWVRUFOXVWHUVLVKLJKEXWLWLVVDIHWRUXQLWDQGWKHQFRPSDUHLWVUHVXOWVZLWKRWKHUVWDUWLQJPRGHV
)$57+(6732,176*,1.*2ZLOO WU\ WRGHWHUPLQH WKHSRLQWV WKDW OLH IDUWKHU DQGXVHWKHPDVVWDUWLQJVHHGV$VLQJOHUXQLVPDGHZLWKWKLVVWDUWLQJPRGH
&+26(16(('67KHXVHUFDQFKRRVH WKHREMHFWV WKDWZLOOEHXVHGE\.PHDQVDVVWDUWLQJ FOXVWHU FHQWHUV VHHGV 7KH QXPEHU RI FOXVWHUVZLOO EH WKH QXPEHU RI VHHGVFKRVHQ$VLQJOH.PHDQVUXQLVPDGHZLWKWKLVVWDUWLQJPRGH
&+26(13$57,7,2167KHXVHUFDQFKRRVHWKHSDUWLWLRQVIURPWKHRQHVDYDLODEOHLQ WKH$QDO\VLV0DQDJHUZKLFKZLOOEHXVHGE\.PHDQVDV VWDUWLQJSDUWLWLRQV7KHQXPEHURIFOXVWHUVZLOOEHWKHQXPEHURIJURXSVLQHDFKFKRVHQSDUWLWLRQ
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
9HUVLRQ
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
.PHDQV WH[W RXWSXW ZLOO YDU\ GHSHQGLQJ RQ WKH .PHDQV VWDUWLQJ PRGH DQG ZKHWKHU WKHGHWDLOHG RXWSXW RSWLRQ KDV EHHQ VHOHFWHG RU QRW +RZHYHU LW DOZD\V LQFOXGHV WKH IROORZLQJLQIRUPDWLRQRQWKHSDUWLWLRQIRXQG
• 7(66)LQDOWRWDOVXPRIVTXDUHVHUURU• 7(66/22 )LQDO WRWDO VXP RI VTXDUHV HUURU ZLWK /22 FRUUHFWLRQ RQO\
VKRZQZKHQ/22FRUUHFWLRQKDVEHHQUHTXHVWHG• 7RWDO9DU7RWDOGDWDYDULDQFH7KLVZLOOEHDOZD\VJUHDWHUWKDQ7(66,WLV
WKHWRWDOGLVSHUVLRQRIGDWDSRLQWV• &+ SVHXGR ) &DOLQVNL+DUDEDV] SVHXGR ) VWDWLVWLF VHH 7KLV
PHDVXUHPD\SURYHWREHXVHIXOIRUGHFLGLQJKRZPDQ\FOXVWHUVFRXOGH[LVWLQWKHGDWDDQDO\]HG
1H[WDWDEOHGHVFULELQJHDFKJURXSLVZULWWHQ,WLQFOXGHV• *URXSJURXSQXPEHU• )UHT1XPEHURIREMHFWVLQIORDWIRUPDWLQFOXGHGLQWKHJURXS• (666XPRIVTXDUHVHUURURIWKHJLYHQJURXS• 0D['0D[LPXPGLVWDQFHEHWZHHQREMHFWVEHORQJLQJWRWKLVJURXS• 1HDU1HDUHVWJURXSQXPEHU• 1HDU'1HDUHVWJURXSGLVWDQFH
7RKHOSLQWHUSUHWWKHUHVXOWLQJJURXSVLI.PHDQVZDVUXQXVLQJDGLVVLPLODULW\PDWUL[RULIVWDUWLQJ ZDV +,(5$5&+,&$/&/867(502'( .PHDQV RXWSXWV D6LOKRXHWWH DQDO\VLV RIWKHVH JURXSV VHH VXEVHFWLRQ IRU PRUH LQIRUPDWLRQ ,I .PHDQV KDV EHHQ UXQ XVLQJ DUHFWDQJXODU PDWUL[ WKH XVHU PD\ DVN IRU XQLYDULDWH $129$V LQ RUGHU WR WHVW IRU GLIIHUHQFHVDPRQJJURXSVIRUHDFKRIWKHRULJLQDOYDULDEOHV
.PHDQVDYDLODEOHRXWSXWPDWULFHVDUHWKHIROORZLQJ• 2EMHFWPHPEHUVKLSV'LVSOD\VWKHRXWSXWSDUWLWLRQRIWKHREMHFWVHW2EMHFWV
DUH LQ URZV DQG JURXSV LQ FROXPQV 9DOXHV DUH HLWKHU IRU DQ REMHFW
*,1.*2XVHU¶VPDQXDO
EHORQJLQJWRWKHJLYHQJURXSFROXPQRUIRUDQREMHFWQRWEHORQJLQJWRWKHJLYHQJURXSFROXPQ7KLVPDWUL[FDQEHXVHGLQSDUWLWLRQFRPSDULVRQVRUWRJURXSSRLQWVLQSORWV
• 3URWRW\SHV 2QO\ DYDLODEOH ZKHQ UXQQLQJ .PHDQV IURP D UHFWDQJXODUREMHFWGHVFULSWRU PDWUL[ 3URYLGHV WKH ILQDO FHQWURLG FRRUGLQDWHV IRU DOOJURXSV LQ WKH SDUWLWLRQ 5HFWDQJXODU PDWUL[ ZLWK JURXSV LQ URZV DQG WKHGHVFULSWRUVLQFROXPQV
• 'LVWDQFHWRFOXVWHUV5HFWDQJXODUPDWUL[ZLWKREMHFWV LQURZVDQGFOXVWHUVLQFROXPQVDVZLWKPHPEHUVKLSPDWUL[0DWUL[FHOOVDUHWKHGLVWDQFHVIURPWKHREMHFWVWRWKHFOXVWHUFHQWHUV
• 6TXDUHGGLVWDQFHWRFOXVWHUV5HFWDQJXODUPDWUL[ZLWKREMHFWVLQURZVDQGFOXVWHUV LQ FROXPQV DV ZLWK PHPEHUVKLS PDWUL[ 0DWUL[ FHOOV DUH WKHVTXDUHGGLVWDQFHVIURPWKHREMHFWVWRWKHFOXVWHUFHQWHUV
• ,QWHUFOXVWHU GLVWDQFHV 6\PPHWULF GLVWDQFH PDWUL[ &HOOV DUH GLVWDQFHVEHWZHHQSDLUVRIFOXVWHUV7KLVPDWUL[UHIOHFWV WKHVSDFHUHODWLRQVEHWZHHQFOXVWHUFHQWHUVFHQWURLGV
9HUVLRQ
)X]]\&PHDQV)X]]\VHWVIX]]\ORJLFDQGIX]]\SDUWLWLRQV
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
$ IX]]\ SDUWLWLRQ LV D SDUWLWLRQ RI REMHFWV LQWR JURXSV RU FODVVHV DOORZLQJ LQWHUPHGLDWHPHPEHUVKLSV ,Q D IX]]\ SDUWLWLRQ HDFK REMHFW VSOLWV LWV RYHUDOOPHPEHUVKLS RI EHWZHHQ WKHGLIIHUHQWFOXVWHUV)RUPDOO\VSHDNLQJPDWUL[8Q[F >XLN@LVDQRQGHJHQHUDWHIX]]\FSDUWLWLRQLIVDWLVILHV ≤≤ LNX IRUDOOL QDQGN F D
=∑
=
F
LLNX IRUDOOL Q E
>∑=
Q
LLNX IRUDOON F F
1RWH WKDW KDUG RU FULVS FSDUWLWLRQV OLNH WKRVH RI .PHDQV LPSO\ WKH VDPH FRQGLWLRQVH[FHSWLQJDZKLFKKDVWREHUHSODFHGE\ ∈LMX IRUL QDQGM F D¶
)X]]\&PHDQV)&0
)X]]\&PHDQV)&0LVDQH[WHQVLRQRIFODVVLF.PHDQVXVLQJWKHFRQFHSWVRIIX]]\ORJLF2QHRIWKHZD\VWRLQWURGXFHIX]]\ORJLFLQ.PHDQVIXQFWLRQDOLV%H]GHNNHHSLQJ.WRQRWHWKHQXPEHURIFOXVWHUV
∑ ∑∑= ==
==F
N
Q
LLN
PLN
F
NPNPF HX-)7(66
ZKHUH LNX LVWKHIX]]\PHPEHUVKLSRIREMHFW Lω WRWKHIX]]\VHW NΩ DQG ∞∈P LVDIX]]LQHVVH[SRQHQWZKLFKGHWHUPLQHVWKHLQFLGHQFHRIIX]]\YDOXHVRQWKHFRPSXWDWLRQV+HUH
LNH KDVWKHVDPHPHDQLQJDVLQ.PHDQVWKRXJKWKHFHQWURLGFRRUGLQDWHVDUHQRZFRPSXWHGDV
∑
∑
=
=
⋅= Q
L
PLN
Q
LLM
PLN
NMX
[X[
*,1.*2XVHU¶VPDQXDO
)URPWKHPLQLPL]DWLRQRIWKHIXQFWLRQDOHTXDWLRQRQHFDQREWDLQWKHIROORZLQJH[SUHVVLRQWRFRPSXWHPHPEHUVKLSV
−
=∑
= PF
O LO
LNLN
HH
X
)X]]\&PHDQVDOJRULWKPZRUNV LQHVVHQWLDOO\ WKHVDPHZD\DV.PHDQV:HPXVWVSHFLI\WKHVWDUWLQJFRQGLWLRQVDQGOHWWKHDOJRULWKPPLQLPL]HLWVIXQFWLRQDOSURYLGHGWKDWFHQWURLGVDUHFRPSXWHG XVLQJ DQG REMHFWV DUH UHDVVLJQHG XVLQJ ,Q DGGLWLRQ )&0 QHHGV DPRUHFRPSOH[ VWRSSLQJ UXOH 7KLV LV GRQH KHUH E\ FRPSDULQJ WKH IX]]\ SDUWLWLRQV RI WZR VXFFHVVLYHLWHUDWLRQV,WVWRSVZKHQ8WDQG8WGLIIHUOHVVWKDQDVSHFLILHGYDOXH5XQQLQJ)X]]\&PHDQV
$V .PHDQV )&0 FDQ EH UXQ IURP ERWK UDZ GDWD PDWULFHV DQG V\PPHWULF GLVVLPLODULW\PDWULFHV )&0 GLDORJ LV PDLQO\ WKH VDPH DV .PHDQV VHH IRU GHWDLOHG LQIRUPDWLRQ RQLQSXW2QO\RQHQHZSDUDPHWHU WKH IX]]LQHVVH[SRQHQWPPXVWEHVXSSOLHG+LJKHUYDOXHVRIIX]]LQHVVZLOOFDXVH)&0WR\LHOGIX]]LHUFODVVLILFDWLRQPDWULFHV)RUQRUPDOGDWDDQP FDQEHXVHGPRVWRIWKHWLPH:LWKHFRORJLFDOFRPPXQLW\GDWDWKHUHLVDKLJKGHJUHHRIQRLVHDQGPPXVWEHORZHULQRUGHUWRLQFUHDVHSDUWLWLRQKDUGQHVVP >@/HDYHRQHRXWYDOLGDWLRQLVQRWDYDLODEOHLQ)&0
2EYLRXVO\RXWSXW WH[WDQGPDWULFHVSURGXFHG LQ)&0DUHDOVRVLPLODU WR WKRVHRI.PHDQVVHHIRUGHWDLOHGLQIRUPDWLRQRQRXWSXW,QWKLVFDVHREMHFWPHPEHUVKLSVDUHIX]]\VRERWKWKHPHPEHUVKLSPDWUL[DQGWKHFOXVWHUQXPEHURIREMHFWVIX]]\VHWFDUGLQDOLW\DUHUHDOQXPEHUV
6RPHDGGLWLRQDOPHDVXUHVRIILWDUHSURYLGHGZKHQUXQQLQJ)&0WKHVHDUHIXOO\H[SODLQHGLQVHFWLRQ
• 'XQQFRHIILFLHQW0HDVXUHVWKH³FULVSQHVV´LQDIX]]\SDUWLWLRQ,WVPD[LPXPYDOXHLVFULVS
• 1RUPDOL]HG 'XQQ FRHIILFLHQW 1RUPDOL]HV WKH SUHYLRXV PHDVXUH ,W LV UDQJHGEHWZHHQDQG
• 3DUWLWLRQHQWURS\$QLQGLFDWRURIWKHLQIRUPDWLRQFRQWHQW• 3DUWLWLRQHIILFLHQF\1RUPDOL]HVSDUWLWLRQHQWURS\,WLVUDQJHGEHWZHHQDQG
9HUVLRQ
.PHGLDQV)X]]\&PHGLDQV&HQWURLGVDQGPHGRLGV
%RWK.PHDQVDQG)&0DVVXPHWKDWWKHEHVWZD\RIUHSUHVHQWLQJWKHSURWRW\SHRIDFOXVWHULVE\PHDQV RI LWV FHQWURLG LH WKH DYHUDJH YHFWRU DQG WKDW GLVWDQFHV IURP HYHU\ REMHFW WR WKHFOXVWHUPXVWEHFRPSXWHGWKURXJKWKH(XFOLGHDQ'LVWDQFHWRWKHFHQWURLG1RWHWKDWWKLVVWLOOKROGVWUXH ZKHQ UXQQLQJ WKHVH FOXVWHULQJ PHWKRGV XVLQJ GLVVLPLODULW\ PDWULFHV $OWKRXJK WKHGLVVLPLODULW\ PD\ EH QRQ(XFOLGHDQ LQ WKH 'LVWDQFHEDVHG DSSURDFK WKH FHQWURLG LV LPSOLFLWO\SODFHGLQDSRVLWLRQDVVXPLQJ(XFOLGLDQLW\
,W LV SRVVLEOH WRGHILQH.PHDQV)&0FRXQWHUSDUWV IRU WKH/QRUP LQVWHDGRI/8QGHUWKLV QRUP WKHSURWRW\SHV DUH GHILQHG DV WKHYHFWRU RIPHGLDQV PHGRLGV DQG WKHGLVWDQFHV WRWKHP DUH FRPSXWHG XVLQJ WKH0DQKDWWDQPHWULF LH E\ VXP RI GLIIHUHQFHV LQ DEVROXWH YDOXH7KHVHFRXQWHUSDUWPHWKRGVDUHFDOOHG.PHGLDQV.PHGDQG)X]]\&PHGLDQV)&0HG7KHGLIIHUHQFHEHWZHHQWKHPLVWKHVDPHDVLQWKHFDVHRI.PHDQV)&01RGLVWDQFHEDVHGDSSURDFKLVDYDLODEOHLQWKLVFDVH5XQQLQJ.PHGLDQV)X]]\&PHGLDQVLQ*,1.*2
.PHG)&0HGPHWKRGV DUH VWDUWHG RQO\ IURP DQ REMHFWGHVFULSWRUPDWUL[ $V XVXDO VRPHREMHFWVRUGHVFULSWRUVPD\EHH[FOXGHGIURPWKHDQDO\VLV7KHDYDLODEOHRSWLRQVDUHVLPLODUWR.PHDQVRU)&0%RWKDQDO\VHVVKDUHWKHVDPHPHQXLWHP7KHUHIRUH)X]]\&PHGLDQVPXVWEHLQGLFDWHG WKURXJK D FKHFNER[ LQ WKH GLDORJ 7KH RXWSXW LV VLPLODU WR WKH SUHYLRXV FOXVWHULQJPHWKRGV H[FHSW IRU WKH RSWLPL]DWLRQ IXQFWLRQ ZKLFK LV QRZ D PHDVXUH RI0HGLDQ $EVROXWH'HYLDWLRQV0$'DQGWKHRXWSXWSURWRW\SHVZKLFKDUHPHGRLGV
*,1.*2XVHU¶VPDQXDO
3RVVLELOLVWLF&PHDQV7KH3&0PHWKRG
&RQVWUDLQWERQIX]]\SDUWLWLRQVFDXVHV)&0WRJHQHUDWHIX]]\PHPEHUVKLSVWKDWFDQEHLQWHUSUHWHGDVGHJUHHVRIVKDULQJRUUHODWLYHPHPEHUVKLSVEXWQRWDVGHJUHHVRIWUXHW\SLFDOLW\LHWKHFRPSDWLELOLW\EHWZHHQWKHREMHFWDQGWKHFODVVSURWRW\SH7KHPRVWVHULRXVGLVDGYDQWDJHRIXVLQJ UHODWLYHPHPEHUVKLSV LV WKDW WKHSHUIRUPDQFHRI)&0FDQEH LQDGHTXDWHZKHQQRLVHDQGRXWOLHUVFRQWDPLQDWH WKHGDWDVHW7KLVSUREOHPPRWLYDWHG WKHVHDUFKIRUPRUHUREXVWFOXVWHULQJPHWKRGV)ULJXL.ULVKQDSXUDP'DYp.ULVKQDSXUDP
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
∑∑==
−+=Q
L
PLNN
Q
LLN
PLNN XHX-
η
ZKHUHηNLVDVXLWDEOHSRVLWLYHQXPEHUD³EDQGZLGWK´SDUDPHWHUFDOOHGUHIHUHQFHGLVWDQFHXNLVWKHYHFWRUFRQWDLQLQJDOOWKHSRVVLELOLVWLFPHPEHUVKLSYDOXHVDVVRFLDWHGZLWKFOXVWHUΩN7KHQXNPD\EHDORFDOPLQLPXPRI-NRQO\LIPHPEHUVKLSVDUHFRPSXWHGXVLQJ
−
+
= P
N
LNLN HX
η
$VHTXDWLRQVKRZVWKHPHPEHUVKLSYDOXHRIREMHFW LLQFOXVWHUΩ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
&RUUHFWLRQIRUERXQGHGGLVVLPLODULWLHV
%RXQGHG GLVVLPLODULWLHV DUH WKRVH GLVVLPLODULW\ PHDVXUHV ZLWK DQ XSSHU ERXQG PD[LPXPYDOXHUHJDUGOHVVRIWKHLUPHWULFRU(XFOLGHDQSURSHUWLHV/HWGEEHWKHXSSHUGLVVLPLODULW\ERXQGRI RQH RI VXFK PHDVXUHV ,Q WKH FDVH RI GLVVLPLODULW\ PDWULFHV REWDLQHG XVLQJ D ERXQGHGGLVVLPLODULW\ LW LV HDV\ WR VHH WKDW D SUREOHP DULVHV FRQFHUQLQJ WKH SRVVLELOLVWLF PHPEHUVKLSIXQFWLRQZKHQ UXQQLQJ3&0QRPDWWHUZKDW WKH IX]]LQHVV OHYHO LV WKHFDOFXODWHGPHPEHUVKLS
9HUVLRQ
YDOXH IRU WKH XSSHU GLVWDQFH ERXQG XGE ZLOO DOZD\V EH QRQ]HUR ,Q RWKHUZRUGV WKH XVXDOSRVVLELOLVWLFPHPEHUVKLSIXQFWLRQRQO\DV\PSWRWLFDOO\\LHOGVQXOOYDOXHVIRUODUJHGLVWDQFHV,QRUGHUWRVROYHWKLVSUREOHPRQHFDQVLPSO\FRUUHFW'H&iFHUHVHWDOVXEPLWWHGIXQFWLRQ
E\UHVFDOLQJLWWRWKHLQWHUYDO>XGE@7KDWLVZHGHILQHDQHZSRVVLELOLVWLFPHPEHUVKLSIXQFWLRQQRWHGX DV LNLNNENELNLN DXGXGXXX ⋅=−−=
ZKHUH WKH ULJKW SURGXFWPHPEHU −−= PELNLN GHD LV WKHPHPEHUVKLS IXQFWLRQ¶V FRUUHFWLQJ
IDFWRU7KHFORVHU LNH JHWVWR
EG WKHFORVHUWR]HURIDFWRUDLNZLOOEHDQGVRZLOOX :KHQXVLQJHTXDWLRQ LQVWHDG RI LQ WKH 3&0 DOJRULWKP RQH REWDLQV D QHZ DOJRULWKPLF YDULDQWZKLFKPLQLPL]HVWKHIROORZLQJREMHFWLYHIXQFWLRQ
∑∑==
−+⋅=Q
L
PLN
PLNLNN
Q
L
PLNLN
PLNN DXDDHX-
η
(VWLPDWLQJVXLWDEOHUHIHUHQFHGLVWDQFHV
5HIHUHQFHGLVWDQFHηNFDQEHLQWHUSUHWHGDVD³VFDOH´RU³EDQGZLGWK´SDUDPHWHU,QJHQHUDOLW LV GHVLUDEOH IRU ηN WR EH UHODWHG WR WKH RYHUDOO VL]H RI WKH FOXVWHUΩN 7KLV SDUDPHWHU DOVRGHWHUPLQHVWKH]RQHRILQIOXHQFHRIDFOXVWHU7KHODUJHUηNLVLQDFOXVWHUWKHPRUHPRELOLW\LWKDVLQ3&0VLQFHLWFDQ³VHH´PRUHSRLQWV7KHUHIRUHRYHUHVWLPDWLQJηNIRUD³VPDOO´FOXVWHUORFDWHGEHVLGHD³ODUJHU´RQHLQFUHDVHVWKHSUREDELOLW\RIPLVVLQJWKHVPDOORQH7KXVLWLVREYLRXVWKDWJRRGHVWLPDWLRQVRIWKLVSDUDPHWHUDUHFUXFLDOIRUWKHVXFFHVVRI3&0
:KHQWKHQDWXUHRIFOXVWHUVLVNQRZQYDOXHVIRUηNPD\EHIL[HGDSULRUL.ULVKQDSXUDP.HOOHUSURYLGHWZRZD\VRILQLWLDOL]LQJηN
∑∑==
⋅⋅=Q
L
PLN
Q
LLN
PLNN XHX.η
( )ααη N[ LNN H Ω= ∑ Π∈
ZKHUH ( )αNΩ LV DQ DSSURSULDWH FXW RIΩN+RZHYHU HVWLPDWLQJ UHIHUHQFH GLVWDQFH IURP)&0DQG XVLQJ WKH DERYH HTXDWLRQV FDQ RYHUHVWLPDWH RU XQGHUHVWLPDWH WKLV SDUDPHWHU GXH WR WKHLQFOXVLRQ RI RXWOLHUV DQG LQOLHUV LQ WKH LQLWLDO SDUWLWLRQ ,Q DGGLWLRQ FOXVWHU YDULDQFH PD\ QRWSURYLGHJRRGηNHVWLPDWHVZKHQFOXVWHUVH[KLELWODUJHGHYLDWLRQVIURPPXOWLQRUPDOLW\ZKLFKLVH[SHFWHGWREHWKHFDVHLQPDQ\DUELWUDU\GLVVLPLODULW\PDWULFHV
:KDW LV QHHGHG LV D IXQFWLRQ WR SURYLGH VXLWDEOH YDOXHV IRU ηN WKDW LV YDOXHV WKDW \LHOGFRPSDFW DQG LVRODWHG FOXVWHUV $ KHXULVWLF FULWHULRQ WR SURYLGH VXLWDEOHηN YDOXHV ZRXOG EH WRVHDUFK IRU WKRVH YDOXHV WKDW FRUUHVSRQG WR ORFDO PLQLPXP YDOXHV RI WKH SDUWLDO GHULYDWLYH RIFOXVWHU YDULDQFH VHH VHFWLRQZLWK UHVSHFW WR UHIHUHQFHGLVWDQFH NNIG9 η∂Ω∂ Ö +RZHYHUFOXVWHUYDULDQFHLQFUHDVHVTXDGUDWLFDOO\DQGQRWOLQHDUO\LQDQLVRWURSLFVSDFH7KHVROXWLRQWRWKLVLV WR XVH FOXVWHU ³VWDQGDUG GHYLDWLRQ´ Ö NIGNIG 96WG Ω=Ω LQVWHDG RI FOXVWHU YDULDQFH 7KHSDUWLDOGHULYDWLYHRIFOXVWHUVWDQGDUGGHYLDWLRQZLWKUHVSHFWWRUHIHUHQFHGLVWDQFHLV
*,1.*2XVHU¶VPDQXDO
Ö NIGNNIGNNIG 6WG96WG Ω⋅∂Ω∂=∂Ω∂ ηη
ZKHUH ÖÖ
∑∑∑∑====
⋅⋅Ω−⋅⋅=∂Ω∂Q
L
PLN
Q
LLN
PLNNIG
Q
L
PLN
Q
LLN
PLNLNNNIG XX9XXH9 ααη
DQG −− ⋅⋅⋅−= PNLNLNNLN HXPP ηηα
)LQDOO\UHIHUHQFHGLVWDQFHLQLWLDOL]DWLRQVWUDWHJ\LVDVIROORZV'H&iFHUHVHWDOVXEPLWWHG• 6WDUWLQJ IURP D VXLWDEOH LQLWLDO PHPEHUVKLS PDWUL[ FDOFXODWH IRU HDFK FOXVWHU WKH XVXDO
HVWLPDWHRIUHIHUHQFHGLVWDQFHXVLQJHTXDWLRQ• )RUHDFKFOXVWHUILQGWKHFORVHVWUHIHUHQFHGLVWDQFHWKDW\LHOGVDPLQLPXPRI$YRLG
WKHWULYLDOVROXWLRQVηN DQGηN GELQWKHFDVHRIERXQGHGPLQLPD5XQQLQJ3&0
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
9HUVLRQ
'HWDLOHGRXWSXW6HOHFWLQJWKLVRSWLRQLQFUHDVHVWKHDPRXQWRIWH[WRXWSXWSURGXFHGLQ3&0
3&0RXWSXW
7KH IOH[LELOLW\ RI WKH FOXVWHU FRQFHSW LQ 3&0 PDNHV LW FDSDEOH RI GHWHFWLQJ VWUXFWXUHV DWGLIIHUHQW FOXVWHULQJ OHYHOV+RZHYHU WKH VDPHSURSHUW\PD\EH UHJDUGHG DV D GUDZEDFNRI WKHDOJRULWKPVLQFHQHVWHGFOXVWHUVPD\EHSURGXFHG7KHUHIRUH3&0FOXVWHUVFDQEHUHSUHVHQWHGLQWKH IRUP RI D WUHH RI QHVWHG FOXVWHUV 7KLV LV WKH RXWSXW IRUP FKRVHQ LQ *,1.*2 7KH 3&0RXWSXWSDQHOKDVWKUHHVXESDQHOV
• 2XWSXWWH[WSDQHO3DQHOZLWKDOOWKHWH[WRXWSXW\LHOGHGE\3&0SURFHGXUH• &OXVWHU WUHHSDQHO3DQHOZLWK WKUHHSDUWV2Q WKH OHIWSDUW WKHUH LVD WUHHRI3&0
FOXVWHUV:KHQ VHOHFWLQJ D FOXVWHU QRGH RQ WKH WUHH WKHSDQHO EHORZ WKH WUHHZLOOVKRZ LQIRUPDWLRQ DERXW WKH3&0FOXVWHU VHOHFWHG UHIHUHQFHGLVWDQFH FDUGLQDOLW\FOXVWHU VWDQGDUG GHYLDWLRQ« $W WKH VDPH WLPH RQ WKH ULJKW SDUW WKH YHFWRU RIREMHFWSRVVLELOLVWLFPHPEHUVKLSVZLOOEHVKRZQ
• &OXVWHUGHVFULSWRUVSDQHO3DQHO VKRZLQJ WKH LQIRUPDWLRQRQDOO3&0FOXVWHUV LQWKHIRUPRIDQREMHFWGHVFULSWRUPDWUL[
*,1.*2XVHU¶VPDQXDO
$FWLRQVRQRXWSXWDQGJUDSKLFV
6RPHDFWLRQVDUHSRVVLEOHDIWHUWKH3&0FDOFXODWLRQVKDYHEHHQGRQH7KHIROORZLQJRSWLRQVDUHDYDLODEOHRQWKH3&0PHQXLQWKH$QDO\VLV0DQDJHU
• 5HEXLOG FOXVWHU WUHH &RQVWUXFWV RU UHFRQVWUXFWV WKH WUHH RI 3&0 FOXVWHUVDQDO\]LQJZKLFKFOXVWHUVDUHQHVWHGRURYHUODSSHG:KHQVRPHFOXVWHUVKDYHEHHQGHOHWHGVRPHWLPHVWKHFOXVWHUWUHHQHHGVWREHUHEXLOW
• 5HEXLOG FODVVLILFDWLRQ PDWUL[ &RQVWUXFWV RU UHFRQVWUXFWV D SRVVLELOLVWLFFODVVLILFDWLRQPDWUL[PHUJLQJWKHGLIIHUHQW3&0FOXVWHUPHPEHUVKLSYHFWRUV
• %XLOG IX]]\ SDUWLWLRQ %XLOGV D IX]]\ SDUWLWLRQ IURP WKH 3&0FOXVWHUV8VHUPXVWGHFLGH :KLFK FRPELQDWLRQ RI FOXVWHUV IURP WKH RQHV DYDLODEOH LQ WKH FXUUHQWFOXVWHUWUHHZLOOEHXVHGWREXLOGWKHSDUWLWLRQV:KLFKOHYHORIIX]]LQHVVZLOOEHXVHG :KHWKHU WKH UDWLR EHWZHHQ SRVVLELOLVWLF PHPEHUVKLSV RU WKH GLVWDQFH WRHDFKFOXVWHUFHQWHUZLOOEHXVHGWRFRPSXWHIX]]\PHPEHUVKLSYDOXHV
• 6KRZLQWHUVHFWLRQPDWUL[%XLOGVDV\PPHWULFPDWUL[RI3&0FOXVWHULQWHUVHFWLRQ• 6KRZLQFOXVLRQPDWUL[%XLOGVDVTXDUHPDWUL[RILQFOXVLRQEHWZHHQFOXVWHUV• 6KRZ EHVW VXLWHG FRPELQDWLRQV )LQGVZKLFK FOXVWHU FRPELQDWLRQV IURP WKH RQHV
DYDLODEOHLQWKHFXUUHQWFOXVWHUWUHHDUHEHWWHUVXLWHGWRSDUWLWLRQGDWD• &RPSDUH WR FODVVLILFDWLRQ PDWUL[ &RPSXWHV 3HDUVRQ FRUUHODWLRQ DPRQJ WKH
PHPEHUVKLSYHFWRUVRIWKHVHOHFWHGFODVVLILFDWLRQPDWUL[DQGWKH3&0FOXVWHUV• 'HOHWHFOXVWHUQRGH'HOHWHVWKHWUHHVHOHFWHGFOXVWHUQRGH• 'HOHWH ORZ FDUGLQDOLW\ QRGHV 'HOHWHV FOXVWHUV KDYLQJ FDUGLQDOLWLHV ORZHU WKDQ D
VSHFLILHGWKUHVKROGYDOXH*,1.*2 DOORZV XVHUV RI 3&0 WR EXLOG DQ LQWHUDFWLYH SORW WKURXJK WKHPHQX LWHP IX]]\
LQWHUDFWLYHJUDSKLF6XFKDSORWLVPDGHXSRIDFOXVWHUWUHHDQGDVFDWWHUGLDJUDP)RUWKHODWWHUWKHXVHUPXVWLQGLFDWHZKLFKFRRUGLQDWHPDWUL[KDVWREHXVHGDVWKHVRXUFHIRURUGLQDWLRQD[HV2QFHEXLOWHDFKWUHHQRGHVHOHFWLRQKLJKOLJKWVWKHFRUUHVSRQGLQJFOXVWHURQWKHVFDWWHUGLDJUDP,IWZRRUPRUHQRGHVDUHVHOHFWHGWKHFRUUHVSRQGLQJFOXVWHUVDUHLQGLFDWHGLQGLIIHUHQWFRORUV
9HUVLRQ
5(%/2&.7KHPHWKRG
5(%/2&. 3RGDQL )HROL LV D FOXVWHULQJ DOJRULWKP WKDW SHUIRUPV D GRXEOHFODVVLILFDWLRQ RI REMHFWV DQG GHVFULSWRUV ,W KDV EHHQ GHVLJQHG LQ WKH FRQWH[W RI QXPHULFDOSK\WRVRFLRORJ\ IRU FODVVLI\LQJ SODQW FRPPXQLWLHV DQG DW WKH VDPH WLPH LGHQWLI\LQJ VSHFLHVJURXSV,QLWVRULJLQDOFRQFHSWLRQLWPDNHVLWSRVVLEOHWRRSWLPL]HWKUHHGLIIHUHQWIXQFWLRQVEXWLQ*,1.*2 WKH RQO\ IXQFWLRQ RSWLPL]HG LV D VWDWLVWLF 7KH DFWXDO DLP LV WR PD[LPL]H WKHFRQWLQJHQF\RIEORFNVGHILQHGE\REMHFWJURXSVDQGGHVFULSWRUJURXSVWKURXJKWKHVWDWLVWLF
∑∑= = ⋅
⋅−
=
ÂÂÂÂ
ÂÂÂÂ
F
L
F
M ML
MLLM
FF
IIIIIII
χ
ZKHUHFDQGFDUHWKHQXPEHURIREMHFWDQGGHVFULSWRUJURXSVUHVSHFWLYHO\ILMLVWKHQXPEHURISUHVHQFHV [OV ! LQ EORFN LM 7KH VWDWLVWLF PHDVXUHV WKH GLYHUJHQFH RI VSHFLHV SUHVHQFHGLVWULEXWLRQLQWKHEORFNVIURPWKHH[SHFWHGUDQGRPRQH$Q LPSRUWDQWGUDZEDFNRI5(%/2&. LV WKDW LWQHHGV WKHGHVFULSWRUDQGREMHFWQXPEHURI
JURXSVWREHVSHFLILHGDSULRUL6WDUWLQJIURPDQLQLWLDOGRXEOHSDUWLWLRQWKHDOJRULWKPUHDVVLJQVWKHYDULDEOHRUREMHFWWKDWWXUQVLQWRDODUJHULQFUHDVHRIWKHIXQFWLRQDO$VLQ.PHDQVDQGUHODWHGPHWKRGVWKHILQDOVROXWLRQRI5(%/2&.GHSHQGVRQWKHLQLWLDOGRXEOHSDUWLWLRQXVHGVRVHYHUDOVWDUWVDUHUHFRPPHQGHG
7R HYDOXDWH LWV UHVXOWV 3RGDQL)HROL SURSRVHG WR XVH$QDO\VLV RI&RQFHQWUDWLRQV$2&)HROL2UOyFL ,Q WKDWSDSHU WKH
FFχ VWDWLVWLFZDVXVHG WRHYDOXDWH WKH UHODWLYHVKDUSQHVV RI SK\WRVRFLRORJLFDO GRXEOH SDUWLWLRQV )HROL 2UOyFL DOVR SURSRVHG WKHIROORZLQJPHDVXUHRIVKDUSQHVV [ ]PLQ ÂÂ
−−⋅= FFI6 FFχ
7KHJUHDWHU6ZDV WKHEHWWHU WKHGRXEOHSDUWLWLRQZRXOGEH ,QRXURSLQLRQ WKLVPHDVXUHKDVDELDVEHFDXVHLWZRXOGEHPLQLPXPZKHQF F,Q*,1.*2WKHIROORZLQJPRGLILHGPHDVXUHRIUHODWLYHVKDUSQHVVLVJLYHQWREHXVHGDVDVRXUFHIRUHYDOXDWLRQV ( ) ÂÂ
−⋅−⋅= FFI6 FFχ
*,1.*2XVHU¶VPDQXDO
5XQQLQJ5(%/2&.
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
$VWH[WRXWSXW WKH5(%/2&.SURFHGXUH\LHOGVWKHFKLVTXDUHYDOXHRIHDFKUXQ7KHVROXWLRQZLWKODUJHUIXQFWLRQDOLVNHSW7KHUHODWLYHVKDUSQHVVRIHDFKVROXWLRQLVDOVRJLYHQ2XWSXWPDWULFHV DUH WKH REMHFW DQG GHVFULSWRUPHPEHUVKLSV WR WKHLU UHVSHFWLYH JURXSV WKH WZRSDUWLWLRQVDQGWKHDEVROXWHDQGUHODWLYHFRQWULEXWLRQVWRWKHFKLVTXDUHVWDWLVWLF
&KDSWHU(YDOXDWLRQDQGLQWHUSUHWDWLRQRIFODVVLILFDWLRQV
(YDOXDWLRQRIFODVVLILFDWLRQV,QWURGXFWLRQ
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³HOERZ´ LQ WKH 7(66SORW LVZKDWPDQ\VWDWLVWLFV WU\WRGHWHFWHOERZSUREOHP
*,1.*2LQFRUSRUDWHV WZR LQGLFHV WKDWPD\EHXVHGDVYDOLGDWLQJ LQWHUQDOFULWHULD IRUFULVSDQG IX]]\ SDUWLWLRQV &DOLQVN\+DUDEDV] SVHXGR) VWDWLVWLF DQG WKH QRQSDUDPHWULFVLOKRXHWWH 5RXVVHXZ 7KH ODWWHU FDQ DOVR EH XVHG WR GHWHFW LQGLYLGXDO REMHFWPLVFODVVLILFDWLRQV
*,1.*2XVHU¶VPDQXDO
3VHXGR)
2QH RI WKHPRVW FRPPRQO\ XVHG FULWHULD IRU WKH VHOHFWLRQ RI D QXPEHU RI JURXSVF LV WKHPD[LPL]DWLRQRIDSVHXGR)VWDWLVWLF&DOLQVN\+DUDEDV]
FQFF)
−−
= :$
ZKHUH$ DQG: DUH JLYHQ E\ HTXDWLRQV DQG UHVSHFWLYHO\ 7KLV VWDWLVWLF LV EDVHG RQPXOWLYDULDWHQRUPDOGLVWULEXWLRQRIGDWD7KHUHIRUHLWZRUNVEHVWZLWKFOXVWHUVVKRZLQJWKLVNLQGRIGLVWULEXWLRQ'HSDUWXUHVIURPQRUPDOLW\ZLOOWHQGWRORZHUWKHSHUIRUPDQFHRIWKLVVWDWLVWLF7KHKLJKHU WKH YDOXH RI SVHXGR) LV WKHPRUH YDULDQFH DPRQJ JURXSV WKHUH ZLOO EH FRPSDUHG WRZLWKLQJURXSYDULDQFHDQGWKHEHWWHUWKHSDUWLWLWLRQZLOOEH1RWHWKDW3VHXGR)FDQEHFRPSXWHGXVLQJIX]]\SDUWLWLRQV
6LOKRXHWWHV
$QRWKHUSRVVLELOLW\ LV WRXVHDQRQSDUDPHWULFJHRPHWULF DSSURDFK6LOKRXHWWHV 5RXVVHXZWU\WRPDNHDJUDSKLFDOUHSUHVHQWDWLRQRIWKHSDUWLWLRQLQGLFDWLQJIRUHDFKREMHFWZKHWKHULWLVFORVHVWWRWKHJURXSLWEHORQJVWRRULVFORVHUWRDQRWKHUFOXVWHU)RUHDFKHOHPHQW Lω VLOKRXHWWHLV LVFRPSXWHGDVIROORZV
/HW D EH WKH FOXVWHU FRQWDLQLQJ Lω :H ILUVW GHILQH LD DV WKH DYHUDJH GLVVLPLODULW\EHWZHHQ Lω DQGWKHRWKHUHOHPHQWVLQ D
:HQH[WGHILQH NG L DVWKHDYHUDJHGLVVLPLODULW\EHWZHHQ Lω DQGWKHHOHPHQWVRI N:HFRPSXWHIRUDOON F DN ≠
:HVHOHFWWKHPLQLPXP NGPLQE LDNL ≠= 7KHFOXVWHUFRUUHVSRQGLQJWRWKLVPLQLPXPLV
WKHQHLJKERUFOXVWHU E LV LVREWDLQHGFRPELQLQJ LD DQG LE
`^ LL
LLL EDPD[
DEV −=
)URPWKLVGHILQLWLRQRQHFDQVHHWKDW ≤≤− LV 9DOXHVRI LV QHDU]HURLQGLFDWHLW LVQRWFOHDUZKHWKHUREMHFW Lω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
∑
∑
=
=
⋅= Q
MMD
Q
MLMMD
LX
GXD
⋅
=
∑
∑
=
=
≠ Q
MMN
Q
MLMMN
DNLX
GXE
PLQ
9HUVLRQ
)X]]LQHVVPHDVXUHVIRUIX]]\SDUWLWLRQV
,Q SDUDOOHO WR WKH GHYHORSPHQW RI IX]]\ SDUWLWLYH FOXVWHULQJ DOJRULWKPV VRPH SDUWLWLRQIX]]LQHVVLQGLFHVKDYHEHHQSURSRVHG'XQQ6HH.LPHWDOIRUDUHFHQWUHYLHZRQWKH VXEMHFW 7KHSDUWLWLRQRU'XQQ FRHIILFLHQW %H]GHN PHDVXUHV WKH GHJUHH RIµKDUGQHVV¶RUµIX]]LQHVV¶RIDSDUWLWLRQ
∑ ∑= =
=F
N
Q
LLNXQF3&
8
:KHQDSDUWLWLRQLVFRPSOHWHO\IX]]\ FF3& =8 ZKLOHIRUDFULVSSDUWLWLRQ =8F3& $QRUPDOL]HGYHUVLRQRIWKH'XQQFRHIILFLHQWLV
−
−⋅=
−−
= FF3&F
FFF3&F3& QRUP
888
$QRWKHULQWHUQDOPHDVXUHRIIX]]LQHVVLVSDUWLWLRQHQWURS\5XVSLQLZKLFKPHDVXUHVWKHLQIRUPDWLRQFRQWHQWRIWKHIX]]\SDUWLWLRQ ∑ ∑
= =
⋅⋅
−=F
N
Q
LLNDLN
DXXFQF+
ORJORJ
8
7KH IX]]LHU WKHSDUWLWLRQ WKHPRUHHQWURS\ GLVRUGHUZLOO DSSHDU$QDORJRXVO\ WR WKHSUHYLRXVFRHIILFLHQWSDUWLWLRQHQWURS\FDQEHDOVRQRUPDOL]HGE\GLYLGLQJE\LWVPD[LPXPYDOXH7KLVLVFDOOHGQRUPDOL]HGHQWURS\RUSDUWLWLRQHIILFLHQF\'XQQ
( )QFF+F+ QRUP
−
=88
%RWK WKH QRUPDOL]HG SDUWLWLRQ FRHIILFLHQW DQG QRUPDOL]HG HQWURS\ DUH VWDWLVWLFV WKDW FDQ EHXVHG WR GHFLGH WKH QXPEHU RI JURXSV LQ IX]]\ SDUWLWLRQLQJ 'XQQ 0DUVLOL/LEHOOL (TXLKXD 2QH PXVW FKRRVH WKH F YDOXH ZLWK D KLJKHVW SDUWLWLRQ FRHIILFLHQW RU ORZHVWSDUWLWLRQHIILFLHQF\5HPHPEHUWKRXJKWKDWWKHVHFRHIILFLHQWVXVHRQO\WKHPHPEHUVKLSYDOXHVWRHYDOXDWHSDUWLWLRQVDQGQRWWKHJHRPHWULFDOVWUXFWXUHRIGDWD
&RPSDULQJFODVVLILFDWLRQV
,QRUGHU WRHYDOXDWHFULVSSDUWLWLRQVXVLQJH[WHUQDOFULWHULD*,1.*2SURYLGHVWKHFRUUHFWHG5DQG5DQG+XEHUW$UDELHDQG)RZONHV0DOORZV LQGLFHV7KHVH LQGLFHVFDQ DVVHVV WKH OHYHO RI DJUHHPHQW VKRZQ EHWZHHQ WZR FULVS SDUWLWLRQV 7R FRPSDUH IX]]\SDUWLWLRQVXVLQJWKHVHLQGLFHVWKH\PXVWILUVWEH³GHIX]]LILHG´$OWHUQDWLYHO\*,1.*2ERDVWVDPRGLILFDWLRQRIWKHFRUUHFWHG5DQGLQGH[ZKLFKGLUHFWO\FRPSDUHVIX]]\PDWULFHVXQSXEOLVKHGUHVXOWV
*,1.*2XVHU¶VPDQXDO
&RQIXVLRQWDEOHV
/HW8Q[FDQG9Q[F¶EHWZRSDUWLWLRQVLQWRFDQGF¶FOXVWHUVUHVSHFWLYHO\RIWKHVDPHGDWDVHW7KHUH DUH GLIIHUHQW DSSURDFKHV WR WKH UHVHPEODQFH EHWZHHQ SDUWLWLRQV ,Q D ILUVW DSSURDFK RQHEXLOGVDFURVVFODVVLILFDWLRQWDEOHRUFRQIXVLRQWDEOH7F[F¶ZKHUHWKHWZRSDUWLWLRQVDUHFURVVHG(DFKWNN¶HOHPHQWFRQWDLQVWKHQXPEHURIREMHFWVFODVVLILHGLQJURXSNRI8DQGLQJURXSN¶RI97KHVLPSOHLQVSHFWLRQRIPDWUL[7JLYHVDORWRILQIRUPDWLRQUHODWHGWRWKHUHODWLRQEHWZHHQWKHWZRSDUWLWLRQV
,QFLGHQFHPDWULFHV5DQGLQGH[
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
=
∑∑<
Q5DQG
Q
L
Q
LMLMγ
98 ZKHUH
D LM LI LDQG MEHORQJWRWKHVDPHJURXSLQERWK8DQG9F8LM DQGF9LM E LM LI LDQG MEHORQJWRDGLIIHUHQWJURXSLQ8DQGWRWKHVDPHJURXSLQ9F8LM DQGF9LM F LM LI LDQG MEHORQJWRWKHVDPHJURXSLQ8DQGWRDGLIIHUHQWJURXSLQ9F8LM DQGF9LM G LM LI LDQG MEHORQJWRDGLIIHUHQWJURXSLQERWK8DQG9F8LM DQGF9LM ,W LV UDWKHU HDV\ WR VKRZ WKDW WKH 5DQG LQGH[ FDQ DOVR EH FRPSXWHG IURP WKH FURVV
FODVVLILFDWLRQWDEOH7
+−+
=∑∑∑∑
=⋅
=⋅
=
QWWWQ
5DQG
F
MM
F
LL
F
L
F
MLM
987 ZKHUH −⋅=
[[[
8VLQJ WKLV ODVW DSSURDFK +XEHUW $UDELH SURSRVHG WR FRUUHFW WKH 5DQG LQGH[ WRH[WUDFWWKHDJUHHPHQWWKDWZRXOGRFFXURQO\GXHWRFKDQFHHIIHFWV7KHFRUUHFWHG5DQGLQGH[LV
5DQG([SHFWHG5DQG0D[LPXP
5DQG([SHFWHG5DQGDQG&RUUHFWHG5−
−=987
⋅
−
+
⋅
−
=
∑∑∑∑
∑∑∑∑
=
⋅
=
⋅
=
⋅
=
⋅
=
⋅
=
⋅
=
QWWWW
QWWW
F
M
MF
L
LF
M
MF
L
L
F
M
MF
L
LF
L
F
M
LM
ZKHUH −⋅=
[[[
9HUVLRQ
7KHFRUUHFWHG5DQG LQGH[ LVZKHQ WKHQXPEHURIFRLQFLGHQFHV LVHTXDO WR WKRVHH[SHFWHGE\FKDQFHQXOOPRGHO ,QFRQWUDVW WKHYDOXHRI LPSOLHVDV LQ WKHFDVHRI WKHXQFRUUHFWHG5DQGLQGH[ D SHUIHFW FRUUHVSRQGHQFH EHWZHHQ WKH FRPSDUHG SDUWLWLRQV $Q DGYDQWDJH RI WKH 5DQGLQGH[ZKHWKHUFRUUHFWHGRUQRWLVWKDWLWFDQEHFRPSXWHGHYHQLIWKHQXPEHURIFOXVWHUVFDQGF¶DUHGLIIHUHQW
0,1'07
$QRWKHU DSSURDFK WR WKHPHDVXUH RI SDUWLWLRQ DJUHHPHQW FRQVLVW LQ H[SUHVVLQJ WKH GLVWDQFHEHWZHHQSDUWLWLRQV LQ WHUPVRI WKHPLQLPXPFKDQJHVQHHGHGWR WUDQVIRUPRQHSDUWLWLRQ LQWR WKHRWKHU7KLVLVZKDWWKH0,1'07PLQLPXPQXPEHURIGLYLVLRQVPHUJHQFHVDQGWUDQVIHUV'D\3RGDQLLQGH[GRHV
&RPSDULQJIX]]\SDUWLWLRQV
,Q RUGHU WR FRPSDUH IX]]\ SDUWLWLRQV WKH VLPSOHU DSSURDFK LV WR µGHIX]]LI\¶ WKHP EHIRUHDSSO\LQJFULVSFRPSDULVRQLQGLFHV'HIX]]LILFDWLRQFDQEHGRQHLQWZREDVLFZD\V&UHDWLQJDFULVSSDUWLWLRQE\FKRRVLQJIRUHDFKREMHFWWKHJURXSWKDWKDVDKLJKHUPHPEHUVKLS&UHDWLQJDFULVSSDUWLWLRQIURPDQ FXWLHGHILQLQJDFULVSPHPEHUVKLSPDWUL[ZKHUHYDOXHVDUHRQO\LIWKHFRUUHVSRQGLQJIX]]\YDOXHLVDERYHDVSHFLILHG WKUHVKROG$VWKHVHFRQGPHWKRGFDQ\LHOGGHJHQHUDWH SDUWLWLRQV QRW IXOILOOLQJ FRQGLWLRQ E WKH PRVW IUHTXHQWO\ XVHG GHIX]]LILFDWLRQPHWKRGLVWKHILUVW
,Q*,1.*2IX]]\SDUWLWLRQVPD\EHGHIX]]LILHGWKURXJKWKHPHQXLWHP'HIX]]LI\SDUWLWLRQLQ WKH $QDO\VLV 0DQDJHU E\ FKRRVLQJ DQ YDOXH +RZHYHU ZKHQ VHYHUDO JURXSV KDYH DPHPEHUVKLSDERYHWKHWKUHVKROGQRQGHJHQHUDF\LVDYRLGHGE\FKRRVLQJWKHKLJKHVWPHPEHUVKLSJURXS7KXVVHWWLQJ WRWKHILUVWGHIX]]LILFDWLRQPHWKRGLVXVHG
0,1'07
,I RQH ZDQWV WR FRPSDUH WZR IX]]\ SDUWLWLRQV ZLWKRXW ORVLQJ WKH LQIRUPDWLRQ FRQWDLQHG LQIX]]\PHPEHUVKLSVPHDVXUHV RI DJUHHPHQW IRU IX]]\ YDOXHV DUH QHHGHG ,Q WKLV VHQVH 3RGDQLSURSRVHGWRH[WHQG0,1'07WRWKHIX]]\FDVH&RQFUHWHO\DOOWKHSRVVLEOHSHUPXWDWLRQVRIFROXPQVLQ8ZLWKUHVSHFWWR9DUHWHVWHGWRILQGWKHSHUPXWDWLRQWKDWPLQLPL]HVWKHGLVWDQFH
∑∑= =
−=Q
L
F
NLMLM YXG
98
)X]]\5DQGLQGH[
7KH0,1'07DSSURDFKKDVWKHGUDZEDFNRIQRWDOORZLQJGLIIHUHQWQXPEHUVRIJURXSVLQ8DQG9 ,QRUGHU WRFRPSDUH IX]]\SDUWLWLRQVZLWKRXW WKLV OLPLWDWLRQZHPXVW VHHN WRJHQHUDOL]HLQGLFHVDOORZLQJGLIIHUHQWQXPEHUVRIJURXSV7KLVJHQHUDOL]DWLRQLVSRVVLEOHIRUWKH5DQGLQGH[LIZHH[SUHVV7DQG&LQPDWUL[QRWDWLRQ 98987 ⋅=
888& ⋅= 1RWHWKDWXVLQJPDWUL[QRWDWLRQ8DQG9FDQKDYHIX]]\YDOXHV&RPSXWLQJ&DVRQHFDQWKHQFRPSXWHWKHIRXUFHOOVDGRIWKH5DQGLQGH[DV
*,1.*2XVHU¶VPDQXDO
( )
( ) ( ) ( )∑ ∑∑ ∑
∑ ∑∑ ∑
= +== +=
= +== +=
−⋅−=−⋅=
⋅−=⋅=
1
L
1
LMLMLM
1
L
1
LMLMLM
1
L
1
LMLMLM
1
L
1
LMLMLM
FFGFFF
FFEFFD
9898
9898
,W LV HDV\ WR VKRZ WKDW WKLV GHILQLWLRQ JHQHUDOL]HV WKH FULVS FDVH DQG WKDW LQ FDVH RI QRQGHJHQHUDWH SDUWLWLRQV IXOILOOV WKH HTXDWLRQ DEFG Q ÂQ $QDORJRXVO\ WKLVJHQHUDOL]DWLRQ LV H[WHQVLEOH WR WKH FRUUHFWHG5DQG LQGH[7KH ILJXUHV EHORZ VKRZ WZRFDVHV WRH[HPSOLI\WKHJHQHUDOL]DWLRQ
3DUWLWLRQ8 3DUWLWLRQ9
8 8 9 9 S S
S
LQGH[
YDOXH
5DQG)X]]\5DQG&RUUHFWHG5DQG)X]]\&RUUHFWHG5DQG
([DPSOH 3DUWLWLRQV 8 DQG9 RI GLPHQVLRQV [ DUH RQ WKH OHIW 7KH RQO\ GLIIHUHQFH EHWZHHQ WKHP LV WKHFODVVLILFDWLRQRIWKHODVWREMHFW ZKLFKLQ9GHSHQGVRQWKHYDOXHRISDUDPHWHUS7KHGLDJUDPRQWKHULJKWVKRZVWKH5DQGLQGH[YDOXHVLQWKHFDVHVRIFRPELQLQJFRUUHFWLRQDQGIX]]\JHQHUDOL]DWLRQ,QWKHH[WUHPHFDVHVS DQGS WKHIX]]\DQGFULVSYHUVLRQVDUHFRLQFLGHQW)RULQWHUPHGLDWHYDOXHVRISWKHIX]]\PHPEHUVKLSRI PDNHVWKHIX]]\5DQGLQGH[FKDQJHJUDGXDOO\2QWKHRWKHUKDQGWKHFRUUHFWHGYHUVLRQVRIERWKLQGLFHVVKRZORJLFDOO\WKHVDPHSDWWHUQEXWLQORZHUYDOXHV
3DUWLWLRQ8 3DUWLWLRQ9
8 8 9 9 S S Q Q S S
Q Q S S
Q Q S S
S
LQGH[
YDOXH
)X]]\5DQG)X]]\&RUUHFWHG5DQG1 )X]]\&RUUHFWHG5DQG1 )X]]\&RUUHFWHG5DQG1
([DPSOH3DUWLWLRQV8DQG9RIGLPHQVLRQVQ[DUHRQWKHOHIW8LVDWZRJURXSSDUWLWLRQHDFKRIVL]HQ,Q9WKHPHPEHUVKLS WR WKHVHVDPHJURXSVGHSHQGVRQSDUDPHWHUµS¶7KHGLDJUDPRQWKHULJKWVKRZVWKHIX]]\5DQGLQGH[YDOXHV,QWKHH[WUHPHVS DQGS WKHLQGH[LV)RUWKHLQWHUPHGLDWHFRQIXVLRQ]RQHRI9SDURXQGWKHXQFRUUHFWHGLQGH[LVDQGWKHFRUUHFWHGLQGH[LVLQGHSHQGHQWO\RIWKHQXPEHURIREMHFWV7KLVZRXOGUHIOHFWWKDWWKHLQGHWHUPLQDWLRQLQ9FRUUHVSRQGVLQDFULVSVHQVHWRWKHUDQGRPDVVLJQPHQWRIREMHFWV
9HUVLRQ
&RPSDULQJDJJORPHUDWLYHKLHUDUFKLFDOWUHHV
&RPSDULVRQV EHWZHHQ KLHUDUFKLFDO FODVVLILFDWLRQV LH GHQGURJUDPV FDQ EH PDGH E\JHQHUDWLQJSDUWLWLRQVDWGLIIHUHQWFXWWLQJOHYHOVDQGWKHQDVVHVVLQJWKHLUDJUHHPHQWZLWKDQ\RIWKHDIRUHPHQWLRQHG LQGLFHV 0RUHRYHU WKLV VWUDWHJ\ LV DSSOLFDEOH WR FRPSDULVRQV EHWZHHQGHQGURJUDPVDQGSDUWLWLRQV
&RPSDULVRQVLQ*,1.*2
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
,QRUGHUWRIDFLOLWDWHYDOLGDWLRQE\PHDQVRIH[WHUQDOFULWHULDH[WHUQDOFODVVLILFDWLRQPDWULFHVFDQEHLPSRUWHGLQWRWKH$QDO\VLV¶0DQDJHUE\UHDGLQJUHFWDQJXODU$6&,,WH[WILOHV5HPHPEHUWKDWFODVVLILFDWLRQPDWULFHVFDQEHFUHDWHGIURPGDWDPDWULFHVLQWKH'DWD(GLWRUVHHVXEVHFWLRQ ,Q DGGLWLRQ *,1.*2 LV FDSDEOH RI UHDGLQJ 7:,163$1¶V GRXEOH SDUWLWLRQV LH RQHSDUWLWLRQ RI UHOHYpV DQG RQH RI VSHFLHV DV JHQHUDWHG E\ WKH SURJUDP 3&25' 0F&XQH 0HIIRUG
*,1.*2XVHU¶VPDQXDO
)XUWKHULQWHUSUHWDWLRQRIFOXVWHUV$QDO\]LQJFOXVWHUSURSHUWLHVRQDGDWDPDWUL[
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
• 9DULDQFHGHVFULSWLRQ2'*LYHVWKHHUURUVXPRIVTXDUHV(66RIHDFKFOXVWHUDVZHOODVLWVYDULDQFHDQGSHUFHQWDJHRIWKHWRWDOHUURUVXPRIVTXDUHV7(66
• &HQWURLG FRRUGLQDWHV 2 *LYHV WKH YHFWRU RI DYHUDJH YDOXHV IRU HDFK FOXVWHU DZHLJKWHGDYHUDJHLQWKHFDVHRIIX]]\SDUWLWLRQV
• (XFOLGHDQ'LVWDQFHV WR &HQWURLGV 2'*LYHV WKHPDWUL[ RI (XFOLGHDQ GLVWDQFHVEHWZHHQREMHFWVDQGFHQWURLGV
• 0HGRLGFRRUGLQDWHV2*LYHVWKHYHFWRURIPHGLDQYDOXHVIRUHDFKFOXVWHUDIX]]\PHGLDQLQWKHFDVHRIIX]]\SDUWLWLRQV
• 0DQKDWWDQ'LVWDQFHVWR0HGRLGV2*LYHVWKHPDWUL[RI0DQKDWWDQPHWULFGLVWDQFHVEHWZHHQREMHFWVDQGPHGRLGV
• &OXVWHUIRUP2''LIIHUHQWVWDWLVWLFVRIFOXVWHUVSKHULFLW\DUHJLYHQLQWKHIROORZLQJ0 PD\ EH DQ LQQHU SURGXFW PDWUL[ IRU ' FDOFXOXV RU D FRYDULDQFH PDWUL[ IRU 6FDOFXOXV
GHW0GHWHUPLQDQWVTXDUHGYROXPHRI0GHW0AS([SHFWHGPHDQWUDFHSHUGLPHQVLRQRI0WU0WUDFHRI0WU0SPHDQWUDFHSHUGLPHQVLRQRI0>WU0S@ASH[SHFWHGGHWHUPLQDQWVTXDUHGYROXPHXQGHUVSKHULFLW\+\SHU9ROXPH5DWLR GHW0>WU0S@ASPHDVXUHVWKHGHSDUWXUHIURPVSKHULFDOFRQGLWLRQ
DVDUDWLRLQSGLPHQVLRQV9DULDQFH5DWLR >GHW0AS@>WU0S@PHDVXUHVWKHGHSDUWXUHIURPVSKHULFDOFRQGLWLRQ
DVDUDWLRLQRQHGLPHQVLRQ• ,VRODWLRQ VWDWLVWLFV '*LYHV DPDWUL[ RI FOXVWHU LVRODWLRQ VWDWLVWLFV FRPSXWHG IURP
HDFK FOXVWHU YHFWRU RQ GLVWDQFH WR FHQWURLG PDWUL[ $YHUDJH PHGLDQ VWDQGDUGGHYLDWLRQVNHZQHVVPHDQFOXVWHUVLOKRXHWWH
• ,QWHUJURXSGLVWDQFHV2'*LYHVDPDWUL[RI(XFOLGHDQGLVWDQFHVEHWZHHQFOXVWHUFHQWURLGV
• ,QWHUJURXSDGMDFHQF\2'*LYHVDPDWUL[RIDGMDFHQF\EHWZHHQFOXVWHUV)LQGVWKHQHDUHVWJURXSIRUHDFKREMHFWH[FOXGLQJWKHDFWXDOJURXS7KHVDPHPDWUL[LVJLYHQLQJURXSSHUFHQWDJHV
• 6XPRIVTXDUHVJURXSPDWULFHV2*LYHVWKHVXPRIVTXDUHVPDWUL[IRUHDFKJURXS• &RYDULDQFHJURXSPDWULFHV2*LYHVWKHFRYDULDQFHPDWUL[IRUHDFKJURXS• &RUUHODWLRQJURXSPDWULFHV2*LYHVWKHFRUUHODWLRQPDWUL[IRUHDFKJURXS• 8QLYDULDWH$129$V 2*LYHV DPDWUL[ZLWK XQLYDULDWH$129$FRPSXWDWLRQV IRU
HDFK GHVFULSWRU LQFOXGLQJ VXP RI VTXDUHV GHJUHHV RI IUHHGRP PHDQ VTXDUHV )VWDWLVWLFVDQGSYDOXHV
9HUVLRQ
0HDVXUHPHQWRIHFRORJLFDOGLYHUVLW\
7KHPHDVXUHPHQWRIHFRORJLFDOGLYHUVLW\ LVDQREMHFWRI VWXG\ LQ VHYHUDO UHIHUHQFHPDQXDOVVHHIRULQVWDQFH0DUJDOHI0DJXUUDQR/HJHQGUH/HJHQGUH:HZLOOEULHIO\LQWURGXFHKHUHVRPHVWDWLVWLFVUHODWHGWRGLYHUVLW\7KHUHDUHWZRPDLQIDFWRUVLQWKHPHDVXUHPHQWRIHFRORJLFDOGLYHUVLW\WKHQXPEHURIVSHFLHV6DQGWKHLUDEXQGDQFHVQQQ67KHHQWURS\RU6KDQQRQ:LHQHU6KDQQRQ:HDYHUGLYHUVLW\LQGH[LVRQHRIWKHFRPPRQHVWZD\VWRPHDVXUHWKHELRORJLFDOGLYHUVLW\LQDVDPSOH ∑
=
−=6
MMM SS+
ORJ
ZKHUHSMLVWKHSUREDELOLW\RIV\PEROLHVSHFLHVM,QSUDFWLFHSUREDELOLWLHVDUHHVWLPDWHVXVLQJUHODWLYHIUHTXHQFLHVLQWKHVDPSOH7D\ORUVWDWHVWKDWLI+LVREWDLQHGIRUVHYHUDOVDPSOHVWKHYDOXHVWHQGWREHGLVWULEXWHGDFFRUGLQJWRQRUPDOLW\7KLVSURSHUW\PDNHVSRVVLEOHWKHXVHRISDUDPHWULFVWDWLVWLFV0DJXUUDQ6KDQQRQ¶VHQWURS\LVDVSHFLILFFDVHRI5pQ\LJHQHUDOL]HGHQWURS\5pQ\L ∑
=−=
6
M
DMD SD+
ORJ
)RUHDFKHQWURS\RIRUGHUDWKHUHLVDFRUUHVSRQGLQJYDOXHRIVSHFLILFULFKQHVVGLYHUVLW\QXPEHU'1RIWKHVDPHRUGHU2UGHUD (QWURS\+D 'LYHUVLW\QXPEHU'1D
ORJ 6+ = 6'1 = +SS+
6
MMM =⋅−= ∑
= ORJ 6KDQQRQ¶V+ +'1 H[S =
∑=
−=6
MMS+
ORJ
−
=
= ∑
S'1 &RQFHQWUDWLRQ
,QFUHDVLQJWKHRUGHUDOHVVHQVWKHLQIOXHQFHRIUDUHVSHFLHVDVFRPSDUHGWRWKHGRPLQDQWRQHV7KHUHIRUHGHSHQGHQFHRIGLYHUVLW\PHDVXUHVZLWKUHVSHFWWRWKHQXPEHURIVSHFLHVLVKLJKHUIRUORZYDOXHVRID
,IRQHFDOFXODWHVWKHGLYLVLRQEHWZHHQWKHREVHUYHG+YDOXHDQGWKHYDOXHLWZRXOGKDYHLIDOOVSHFLHVZHUHHTXLSUREDEOH+PD[ ORJ6 +RQHREWDLQVDPHDVXUHRIHYHQQHVVRUHTXLWDELOLW\LQWKHSURSRUWLRQRIV\PEROV3LHORX PD[ ++++- == 3LHORX¶VHYHQQHVVLVWRRGHSHQGHQWRQWKHVDPSOLQJHIIRUWVLQFHLWLQFOXGHV+7RRYHUFRPHWKLVOLPLWDWLRQ+LOOSURSRVHGDIDPLO\RIXQLIRUPLW\PHDVXUHV EDED '1'1( = D!E
:KHQGLYHUVLW\LVPHDVXUHGRQWKHVSHFLHVDEXQGDQFHYDOXHVVDPSOHGRQDVSHFLILFVLWHLWLVDPHDVXUHRIDOSKDαGLYHUVLW\RIWKHFRPPXQLW\6WXG\LQJGLYHUVLW\LVPRUHGLIILFXOWZKHQRQH
*,1.*2XVHU¶VPDQXDO
ZDQWVWRSRROGLIIHUHQWVDPSOHVEHORQJLQJWRDJLYHQJURXSRUFOXVWHU7KHVLPSOHVWRSWLRQLVWRDYHUDJH WKH DOSKD GLYHUVLW\ YDOXHV RI DOO JURXS VLWH PHPEHUV $OWHUQDWLYHO\ LW LV SRVVLEOH WRFRPSXWH GLYHUVLW\ PHDVXUHV WDNLQJ DV VDPSOH WKH JURXS SRROHG GDWD :KHQ WKH XQLW RIPHDVXUHPHQW LV D JHRJUDSKLFDO UHJLRQ RQH FDQ VSHDN RI JDPPD γ RU UHJLRQDO GLYHUVLW\+RZHYHULIWKHJURXSGRHVQRWKDYHDJHRJUDSKLFDOVHQVHWKLVQRPHQFODWXUHLVHUURQHRXVDQGLWFDQVLPSO\EHFDOOHGJURXSGLYHUVLW\
7R VXP XS LW LV LPSRUWDQW WR GLVWLQJXLVK VLWH DOSKD GLYHUVLW\ YDOXHV WKH DYHUDJHGLYHUVLW\YDOXHV IRUDJURXSDQG WKHJURXSGLYHUVLW\FRPSXWHG WDNLQJJURXSSRROHGGDWDDVVDPSOLQJXQLW&RPSXWLQJHFRORJLFDOGLYHUVLW\VWDWLVWLFV
*,1.*2 PDNHV LW SRVVLEOH WR FRPSXWH VHYHUDO GLYHUVLW\ VWDWLVWLFV XVLQJ WKH PHQX LWHP&OXVWHU VSHFLHV GLYHUVLW\ IURP WKH PHQX *URXS LQIR 1RWH WKDW WKH GDWD VHW KDV WR EH DUHFWDQJXODUREMHFWGHVFULSWRUPDWUL[$VZLWKRWKHUDQDO\VHVVRPHREMHFWVRUGHVFULSWRUVPD\EHH[FOXGHGIURPFRPSXWDWLRQV7KHXVHUPXVWDOVRVSHFLI\ZKLFKFODVVLILFDWLRQSDUWLWLRQZLOOEHXVHGDVVRXUFHIRUFOXVWHUV
%\GHIDXOWWKHGLYHUVLW\SURFHGXUHSHUIRUPVDQDO\VLVRIYDULDQFHRQWKUHHSDUDPHWHUVVSHFLHVULFKQHVV 6 VLWH WRWDO DEXQGDQFHDQG6KDQQRQ¶VHQWURS\ + ,W ILUVWRXWSXWV DPDWUL[ZLWK WKHIROORZLQJVWDWLVWLFVFRPSXWHGIRUHDFKJURXSRUFOXVWHU
• 1VS$9(5$*($YHUDJHVLWHVSHFLHVULFKQHVVZLWKLQVLWHVRIWKHVDPHJURXS• 1VS666XPRIVTXDUHVRIVLWHVSHFLHVULFKQHVVZLWKLQVLWHVRIWKHVDPHJURXS• 1VS67''(96WDQGDUGGHYLDWLRQRIVLWHVSHFLHVULFKQHVVZLWKLQVLWHVRIWKHVDPHJURXS• 1VS&99DULDWLRQFRHIILFLHQWRIVLWHVSHFLHVULFKQHVVZLWKLQVLWHVRIWKHVDPHJURXS• $EXQGDQFH$9(5$*($YHUDJHWRWDOVLWHDEXQGDQFHZLWKLQVLWHVRIWKHVDPHJURXS• $EXQGDQFH666XPRIVTXDUHVRIWRWDOVLWHDEXQGDQFHZLWKLQVLWHVRIWKHVDPHJURXS• $EXQGDQFH67''(96WDQGDUGGHYLDWLRQRIWRWDOVLWHDEXQGDQFHZLWKLQVLWHVRIWKHVDPHJURXS• $EXQGDQFH&99DULDWLRQFRHIILFLHQWRIWRWDOVLWHDEXQGDQFHZLWKLQVLWHVRIWKHVDPHJURXS• +'LY$9(5$*($YHUDJHVLWH6KDQQRQV+GLYHUVLW\ZLWKLQVLWHVRIWKHVDPHJURXS• +'LY666XPRIVTXDUHVRIVLWH6KDQQRQV+GLYHUVLW\ZLWKLQVLWHVRIWKHVDPHJURXS• +'LY67''(96WDQGDUGGHYLDWLRQRIVLWH6KDQQRQV+GLYHUVLW\ZLWKLQVLWHVRIWKHVDPHJURXS• +'LY&99DULDWLRQFRHIILFLHQWRIVLWH6KDQQRQV+GLYHUVLW\ZLWKLQVLWHVRIWKHVDPHJURXS
7KH$129$VUHVXOWVDUHSUHVHQWHGLQWKHRXWSXWWH[W)RXUDGGLWLRQDODQDO\VHVFDQEHSHUIRUPHG• $OSKDVLWHGLYHUVLW\YDOXHV2XWSXWVGLYHUVLW\VWDWLVWLFYDOXHVFRPSXWHGDWHDFKVLWH
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
• *DPPD JURXS GLYHUVLW\ YDOXHV *URXS GLYHUVLW\ VWDWLVWLFV FRPSXWHG WDNLQJ JURXSSRROHGGDWD DV VDPSOLQJXQLW 3RROLQJ FDQEHGRQHE\FRXQWLQJ VSHFLHVRFFXUUHQFHV
9HUVLRQ
FRQVWDQF\RUVXPPLQJXSDEXQGDQFHVWRWDODEXQGDQFH7KHRXWSXWPDWUL[KDVWKHIROORZLQJGHVFULSWRUV
1N1XPEHURIVLWHVLQJURXSN1N1XPEHURIVSHFLHVLQJURXSN+N(QWURS\RIRUGHU]HUR HA1N+N&RQVWDQFLHV (QWURS\ RI RUGHU RQH 6KDQQRQV HQWURS\ PHDVXUH FRPSXWHG XVLQJ
VSHFLHVIUHTXHQF\LQGDWD1N&RQVWDQFLHV 'LYHUVLW\ QXPEHU RI RUGHU WZR ,QYHUVH RI VSHFLHV FRQFHQWUDWLRQ
FRPSXWHGXVLQJVSHFLHVIUHTXHQF\LQGDWD+N&RQVWDQFLHV (QWURS\ RI RUGHU WZR ORJVSHFLHV FRQFHQWUDWLRQ FRPSXWHG XVLQJ
VSHFLHVIUHTXHQF\LQGDWD- ++N&RQVWDQFLHV3LHORXVPHDVXUHRI(YHQQHVVFRPSXWHGXVLQJVSHFLHVIUHTXHQF\
LQGDWD11N&RQVWDQFLHV0HDVXUH RI HYHQQHVV 5DWLR EHWZHHQ 1 DQG 1 FRPSXWHG XVLQJ
VSHFLHVIUHTXHQF\LQGDWD++N&RQVWDQFLHV0HDVXUH RI HYHQQHVV 5DWLR EHWZHHQ+ DQG+ FRPSXWHG XVLQJ
VSHFLHVIUHTXHQF\LQGDWD11N&RQVWDQFLHV0HDVXUH RI HYHQQHVV 5DWLR EHWZHHQ 1 DQG 1 FRPSXWHG XVLQJ
VSHFLHVIUHTXHQF\LQGDWD+N7RW$E (QWURS\ RI RUGHU RQH 6KDQQRQV HQWURS\ PHDVXUH FRPSXWHG XVLQJ WRWDO
DEXQGDQFHRIVSHFLHVLQGDWD1N7RW$E'LYHUVLW\ QXPEHU RI RUGHU WZR ,QYHUVHRI VSHFLHV FRQFHQWUDWLRQ FRPSXWHG
XVLQJWRWDODEXQGDQFHRIVSHFLHVLQGDWD+N7RW$E (QWURS\ RI RUGHU WZR ORJVSHFLHV FRQFHQWUDWLRQ FRPSXWHG XVLQJ WRWDO
DEXQGDQFHRIVSHFLHVLQGDWD- ++N7RW$E 3LHORXV PHDVXUH RI (YHQQHVV FRPSXWHG XVLQJ WRWDO DEXQGDQFH RI
VSHFLHVLQGDWD11N7RW$E0HDVXUH RI HYHQQHVV 5DWLR EHWZHHQ1 DQG1 FRPSXWHG XVLQJ WRWDO
DEXQGDQFHRIVSHFLHVLQGDWD++N7RW$E0HDVXUH RI HYHQQHVV5DWLR EHWZHHQ+ DQG+ FRPSXWHG XVLQJ WRWDO
DEXQGDQFHRIVSHFLHVLQGDWD11N7RW$E0HDVXUH RI HYHQQHVV 5DWLR EHWZHHQ1 DQG1 FRPSXWHG XVLQJ WRWDO
DEXQGDQFHRIVSHFLHVLQGDWD9DU+&RQVWDQFLHV 0HDVXUH RI HYHQQHVV 9DULDQFH RI VLWH 6KDQQRQ HQWURS\ YDOXHV
FRPSXWHGXVLQJVSHFLHVIUHTXHQF\LQGDWD9DU+7RW$E0HDVXUHRI HYHQQHVV9DULDQFHRI VLWH6KDQQRQHQWURS\YDOXHV FRPSXWHG
XVLQJWRWDODEXQGDQFHRIVSHFLHVLQGDWD• &RQVWDQF\DQDO\VLV&RPSXWHVVSHFLHVYDULDEOHFRQVWDQF\YDOXHVIRUHDFKJURXSRI
VLWHVREMHFWVDVZHOODVWKHDEVROXWHDQGUHODWLYHIUHTXHQF\RIFRQVWDQF\FODVVHVILYHFODVVHVIRUHDFKJURXS
• 0HDQDEXQGDQFHDQDO\VLV&RPSXWHVVSHFLHVYDULDEOHDYHUDJHDEXQGDQFHYDOXHVIRUHDFKJURXSRIVLWHVREMHFWVDVZHOODV WKHDEVROXWHDQGUHODWLYHIUHTXHQF\RIPHDQDEXQGDQFHFODVVHVILYHFODVVHVIRUHDFKJURXS
*,1.*2XVHU¶VPDQXDO
&RPSXWLQJVSHFLHVILGHOLWLHVDQGGLDJQRVWLFVSHFLHV
'LDJQRVWLFVSHFLHVDUH WKRVHVSHFLHVVKRZLQJDSUHIHUHQFHIRUDJLYHQYHJHWDWLRQXQLW$VDFRQVHTXHQFH WKH\ DUH XVHIXO IRU SRLQWLQJ WR D VSHFLILF YHJHWDWLRQ W\SH DPRQJ RWKHUV WKXVUHVHPEOLQJ WKH FRQFHSW RI LQGLFDWRU VSHFLHV 7KH GHJUHH RI SUHIHUHQFH VKRZQ E\ D VSHFLHV LVFDOOHGµILGHOLW\¶LQWKH(XURSHDQDSSURDFKWRSK\WRVRFLRORJ\)LGHOLW\ZDVLQLWLDOO\GHILQHGDVWKHGHJUHHRISUHIHUHQFHRIDVSHFLHVIRUDJLYHQSK\WRVRFLRORJLFDODVVRFLDWLRQEXWWKHFRQFHSWFDQEHH[WHQGHGWRPHDQWKHGHJUHHRISUHIHUHQFHRIDWD[RQIRUDJLYHQV\QWD[RQ
*,1.*2IRFXVHVRQ ILGHOLW\PHDVXUHPHQWV VXLWDEOH IRUFDWHJRULFDOGDWD ,QYHJHWDWLRQGDWDVHWVVSHFLHVSUHVHQFHVDEVHQFHVJLYHPRUHUREXVWILGHOLW\HVWLPDWLRQVWKDQFRYHUVDEXQGDQFHVDVWKH\DUHOHVVDIIHFWHGE\WHPSRUDOIOXFWXDWLRQVDQGREVHUYHUELDV&K\WUê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
• 1 QXPEHURIUHOHYpVLQWKHGDWDVHW• 1$ QXPEHURIUHOHYpVEHORQJLQJWR$• Q QXPEHURIWD[RQRFFXUUHQFHVLQWKHGDWDVHW• Q$ QXPEHURIWD[RQRFFXUUHQFHVLQUHOHYpVEHORQJLQJWR$
:LWK NQRZQ YDOXHV IRU WKHVH SDUDPHWHUV VHYHUDO ILGHOLW\ VWDWLVWLFV PD\ EH FRPSXWHG 7KHIROORZLQJDUHDYDLODEOHLQ*,1.*2
+\SHUJHRPHWULFXYDOXH%UXHOKHLGH ( )
−−⋅−⋅⋅⋅−⋅
=−⋅−⋅−⋅⋅
⋅−= 111Q11Q
1QQ11111Q11Q
1Q1QX$$
$$
$$
$$K\S
%LQRPLDOXYDOXH%UXHOKHLGH ( )
−−⋅=
−⋅⋅⋅−⋅
=−⋅⋅
⋅−= 1Q1X111Q
1QQ11111Q
1Q1QX K\S$$
$$
$$
$$ELQ
&KLVTXDUH 6RNDO5RKOI)URPWKHFHOOVRIDFRQWLQJHQF\WDEOH[RQHFDQEXLOG
GEFDGFED
EFDG1++++
−=χ
ZKHUH $QD = $QQE −= $$ Q1F −= DQG $$ Q1Q1G −−−= %\VXEVWLWXWLRQ WXUQVRXWWREH 111X11Q11Q
1QQ11K\S
$$
$$ ⋅Φ=−⋅=−⋅−⋅⋅
⋅−⋅⋅=
χ
3KLFRHIILFLHQWΦ6RNDO5RKOI ( )
11X11Q11Q1QQ1
111Q11Q1Q1Q
K\S$$
$$
$$
$$
χ
=Φ−=−⋅−⋅⋅
⋅−⋅=
−⋅−⋅⋅
⋅−=Φ
9HUVLRQ
%LQDU\LQGLFDWRUYDOXH'XIUrQH/HJHQGUH&K\WUêHWDO
( )$
$
$$$$
$$ELQ 1
Q1Q1Q1Q
11Q,QG9DO ⋅+−⋅
−=
%LQDU\IUHTXHQFHILGHOLW\
$
$$ELQ 1
Q11Q)UHT)LG ⋅
−=
%LQDU\6SHFLILFLW\9DOXH ( )
1Q1Q1Q11Q6SHF9DO
$$$$
$$ELQ +−⋅
−=
7KH PHQX LWHP&OXVWHU VSHFLHV ILGHOLW\ IURP WKH PHQX*URXS LQIR PDNHV LW SRVVLEOH WR
FRPSXWHWKHVHLQGLFHVRQWKHGDWDLWHPFXUUHQWO\VHOHFWHGLQWKH'DWD(GLWRU1RWHWKDWWKHGDWDVHWKDV WR EH D UHFWDQJXODU REMHFWGHVFULSWRU PDWUL[ $V ZLWK RWKHU DQDO\VHV VRPH REMHFWV RUGHVFULSWRUVPD\EHH[FOXGHGIURPFRPSXWDWLRQV7KHXVHUPXVWDOVRVSHFLI\ZKLFKFODVVLILFDWLRQSDUWLWLRQZLOOEHXVHGDVVRXUFHIRUFOXVWHUV7KHRWKHURSWLRQVRIWKLVSURFHGXUHDUH
• )LGHOLW\ LQGH[ 6WDWLVWLF WR EH FRPSXWHG DPRQJ WKRVH SUHVHQWHG DERYH$PDWUL[ RIGLPHQVLRQV S [ F QXPEHU RI VSHFLHV E\ QXPEHU RI JURXSVZLOO EH WKH RXWSXW RIILGHOLW\YDOXHV
• /LVW RUGHUHG ILGHOLWLHV&KHFNER[ WKDW SHUPLWV OLVWLQJ IRU HDFKJURXS RI WKH ILGHOLW\YDOXHVJRLQJLQRUGHUIURPWKHPRUHGLDJQRVWLFKLJKHVWYDOXHWRWKHOHDVWGLDJQRVWLFORZHVWYDOXH
• *HQHUDWH ILGHOLW\ SURILOHV0DNHV SRVVLEOH FRPSXWLQJ RI ILGHOLW\ SURILOHV 7KHVH DUHREWDLQHG VWDUWLQJ IURP WKH VLWHVEHORQJLQJ WR WKHFOXVWHUE\DGGLQJRQHVLWHDW HDFKVWHSWRWKHUHIHUHQFHVHWRIVLWHVXVHGWRFRPSXWHILGHOLW\
• &RPPXQLW\ RUGHULQJ GLVWDQFH 'LVWDQFH PHDVXUH XVHG WR RUGHU WKH H[WHUQDO VLWHVEHIRUHVWDUWLQJWKHDGGLQJVHTXHQFHLQWKHSURILOHJHQHUDWLRQSURFHVV
&KDSWHU*UDSKLFV
,QWURGXFWLRQWR*UDSKLFVLQ*,1.*22YHUYLHZ
7KHUHVXOWVRIRUGLQDWLRQPHWKRGVFDQEHGLVSOD\HGLQ'RU'VFDWWHUGLDJUDPVLQFOXGLQJRUGLQDWLRQELSORWVDQG6KHSDUGGLDJUDPV6KHSDUG ,QDGGLWLRQDQ\DYDLODEOHSDUWLWLRQ LQWKH$QDO\VHV0DQDJHUZKHWKHUIX]]\RUFULVSPD\EHXVHGWRODEHOREMHFWVLQVFDWWHUGLDJUDPV,WLV WKHUHIRUH SRVVLEOH WR LQWHUSUHW GDWD VWUXFWXUH E\ FRPELQLQJ WKH SDWWHUQV UHYHDOHG XVLQJ ERWKFODVVLILFDWLRQDQGRUGLQDWLRQPHWKRGV
7KH JHQHUDWHG JUDSKLFV DUH GLVSOD\HG LQ *,1.*2¶V *UDSKLFV (GLWRU ZKHUH HDFK SORW LVGLVSOD\HGLQDGLIIHUHQWWDE*UDSKLFV(GLWRUPDNHVLWSRVVLEOHWRHGLWVRPHSORWSURSHUWLHVH[SRUWLPDJHILOHVDQGVHQGSULQWMREV*UDSKLFW\SHV
7KHIROORZLQJJUDSKLFVDUHDYDLODEOHLQ*,1.*2• 6FDWWHUJUDSKLFV6FDWWHUJUDSKLFVWKDWGLVSOD\SRLQWVDQGDUURZVLQD'RU'VSDFH
XVLQJREMHFWDQGVRPHWLPHVGHVFULSWRUFRRUGLQDWHVDVLQSXW7KHXVHUFDQGHFLGHWRVKRZODEHOVRUFOXVWHUUHVXOWVRQWKHGLVSOD\
• &RQQHFWHGVFDWWHUJUDSKLFV6FDWWHUJUDSKLFVWKDWGLVSOD\FRQQHFWHGSRLQWVLQD'RU'VSDFHXVLQJREMHFWFRRUGLQDWHVDVLQSXW7KHXVHUFDQGHFLGHWRVKRZODEHOVRQWRWKHGLVSOD\
• 'VHULHVJUDSKLFV*UDSKLFVWKDWGLVSOD\RUGHUHGVHULHVRIYDOXHVRQD'SORWXVLQJREMHFWGHVFULSWRUFRRUGLQDWHVDVLQSXW2EMHFWODEHOVDUHXVHGLQWKHDEVFLVHV¶D[LVDQGHDFKGHVFULSWRUYHFWRULVXVHGWRGLVSOD\DGLIIHUHQWVHULHVRIRUGLQDWHYDOXHV
• %DUJUDSKLFV*UDSKLFVWKDWGLVSOD\RQHRUWZRVHULHVRIYDOXHVLQD'SORW7KHVHDUHXVHGLQ*,1.*2RQO\WRUHSUHVHQWYDULDEOHIUHTXHQF\KLVWRJUDPV
• 6KHSDUGGLDJUDPV ' VFDWWHUJUDSKLFZKHUH FRRUGLQDWHV DUHJLYHQE\YDOXHV LQ WKHVDPHFHOORIWZRV\PPHWULFPDWULFHV
• 'HQGURJUDPV+LHUDUFKLFDOSORWRIFOXVWHUUHODWLRQVDYDLODEOHRQO\IURPWKHRXWSXWRIKLHUDUFKLFDODJJORPHUDWLYHFOXVWHULQJPHWKRGV
• 6FUHHSORW*UDSKLFWKDWGLVSOD\VWKHRUGHUHGVHULHVRIGHFUHDVLQJHLJHQYDOXHVFRPLQJIURPWKHHLJHQDQDO\VLVLQPDQ\RUGLQDWLRQPHWKRGV
*,1.*2XVHU¶VPDQXDO
&UHDWLQJJUDSKLFV&UHDWLQJ'DQG'VFDWWHUSORWV
6FDWWHUSORWVFDQEHFUHDWHGLQWZRZD\V)URPUDZGDWDLQWKH'DWD(GLWRURU)URPWKH UHVXOWV RI D PXOWLYDULDWH DQDO\VLV PHWKRG \LHOGLQJ REMHFW FRRUGLQDWHV LQ WKH $QDO\VLV0DQDJHU,QWKHILUVWFDVHWKHXVHUPXVWVHOHFWWKHGDWDPDWUL[ZKHUHWKHSRLQWFRRUGLQDWHVDUHEHIRUH VHOHFWLQJ 6FDWWHU JUDSKLF LQ WKH'UDZ PHQX ,Q WKH FDVH RI DQ DQDO\VLV PHQX LWHPVHQDEOLQJ WKH SRVVLEOH VFDWWHU SORWVZLOO DSSHDU RQ WKHPHQX EDU RI WKH$QDO\VLV0DQDJHU 7KHVDPHGLDORJSURPSWVLQERWKFDVHV7KHIROORZLQJRSWLRQVDUHDYDLODEOH
• 7LWOH 7KH WLWOH RI WKH JUDSKLF ,WZLOO EH XVHG WR ODEHO WKH FRUUHVSRQGLQJ WDE LQ WKH*UDSKLF(GLWRUZLQGRZ
• )LUVWD[LV7KHGHVFULSWRUYDULDEOHWREHXVHGDVILUVWD[LVLQWKHVFDWWHUSORW• 6HFRQGD[LV7KHGHVFULSWRUYDULDEOHWREHXVHGDVVHFRQGD[LVLQWKHVFDWWHUSORW• 'SORW&KHFNER[WRHQDEOH'SORWV• 7KLUGD[LV7KHGHVFULSWRUYDULDEOHWREHXVHGDVWKLUGD[LVLQWKHVFDWWHUSORW• 6KRZODEHOV&KHFNER[WRHQDEOHSRLQWODEHOV• 3URSRUWLRQDO ;<= $[HV &KHFNER[ WR PDNH DOO VFDWWHU D[HV ERXQGHG LQ WKH VDPH
UDQJH• $SSO\ FODVVLILFDWLRQ PDWUL[ &KHFNER[ WR HQDEOH JURXSLQJ SRLQWV IROORZLQJ WKH
LQIRUPDWLRQJLYHQE\DFODVVLILFDWLRQPDWUL[LIDQ\IURPWKH$QDO\VLV0DQDJHU• $SSO\IX]]\VHW&KHFNER[WRHQDEOHH[SUHVVLRQRIWKHPHPEHUVKLSGHJUHHVKRZQE\
WKHUHSUHVHQWHGREMHFWVWRDJLYHQIX]]\VHWDVDV\PERORISURSRUWLRQDOVL]HDQGFRORULQWHQVLW\
&UHDWLQJRWKHUSORWV
&RQQHFWHGVFDWWHUSORWVDUHRQO\GUDZQE\FKRRVLQJDQREMHFWGHVFULSWRUGDWDLWHPLQWKH'DWD(GLWRU DQG WKHQVHOHFWLQJ WKHPHQX LWHP&RQQHFWHGVFDWWHUJUDSKLF IURP WKH'UDZPHQX ,QWKLV FDVH GDWD LV H[SHFWHG WR EH DGHTXDWHO\ RUGHUHG RWKHUZLVH WKH FRQQHFWLRQV GUDZQZLOO EHPHDQLQJOHVV7KHSURPSWHGGLDORJLVVLPLODUWRWKDWRIXQFRQQHFWHGVFDWWHUSORWVH[FHSWIRUWKHIDFWWKDWLQIRUPDWLRQIURPFODVVLILFDWLRQPDWULFHVRUIX]]\VHWVFDQQRWEHUHSUHVHQWHGRQWKHSORW
,QRUGHU WRGUDZD'VHULHVJUDSKLFDQREMHFWGHVFULSWRUGDWD LWHPPXVWEH VHOHFWHG LQ WKH'DWD(GLWRU7KHRSWLRQVLQWKLVFDVHLQFOXGHVSHFLI\LQJWKHJUDSKLFWLWOHDVZHOODVWKHWLWOHVIRUWKH;DQG<D[LVDQGWKHYDULDEOHVLQWKHGDWDPDWUL[WREHLQFOXGHGDVVHULHVRIYDOXHV
9HUVLRQ
%DUJUDSKLFVDUHFUHDWHGIURPWKH9DULDEOH$QDO\VLVPHQXRIWKH'DWD(GLWRUPHQXEDUVHHVXEVHFWLRQ
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
'HQGURJUDPV DUH RQO\ DYDLODEOH IURP WKH UHVXOWV RI KLHUDUFKLFDO DJJORPHUDWLYH FOXVWHULQJPHWKRGV:KHQVHOHFWLQJ'HQGURJUDPLQWKH3ORWPHQXRIWKH$QDO\VLV0DQDJHUPHQXEDUWKHLQIRUPDWLRQFRQWDLQHGLQWKHXOWUDPHWULFPDWUL[LVXVHGWREXLOGWKHGHQGURJUDP
6FUHHSORWVDUHDYDLODEOHIURPWKHRXWSXWRIRUGLQDWLRQPHWKRGVLQFOXGLQJHLJHQDQDO\VLV$QLWHPPHQXQDPHG6FUHHSORWZLOODSSHDUDPRQJWKHPHQXLWHPVRIWKH$QDO\VLV0DQDJHUPHQXEDU1RGLDORJZLOOEHSURPSWHG7KHSORWSURGXFHGLVVLPLODUWRWKDWRID'VHULHVJUDSKLF
*,1.*2XVHU¶VPDQXDO
*UDSKLFPDQLSXODWLRQSULQWLQJDQGH[SRUWLQJ*UDSKLFFRQWUROV
7KH IROORZLQJ RSWLRQV FDQ EH XVHG WR FKDQJH WKH DSSHDUDQFH RI D FHUWDLQ SORW 7KH\ DUHDYDLODEOHLQWKH2SWLRQVPHQXRIWKH*UDSKLFV(GLWRUPHQXEDU1RWDOORSWLRQVDUHDSSOLFDEOHLQDOOSORWV
• 5HVL]HJUDSKLF(QDEOHVFKDQJLQJ WKHJUDSKLFVL]H LQSL[HOV7KHGLDORJ LQFOXGHVDFKHFNER[RSWLRQ WR HQVXUHPDLQWHQDQFHRI WKHSURSRUWLRQVEHWZHHQ WKHSORW¶VZLGWKDQGKHLJKW
• &KDQJHD[HVUDQJH3HUPLWVFKDQJLQJWKHUDQJHPLQLPXPDQGPD[LPXPRIVFDWWHUD[HV
• 6KRZJULG&KHFNER[PHQXLWHPWRLQFOXGHWKHJULGLQDVFDWWHUSORW• (GLW VHULHV 7KH SURPSWLQJ GLDORJ RI WKLV RSWLRQ DOORZV WKH XVHU WR FKDQJH WKH
DSSHDUDQFH RI HDFK VHULHV RI GDWD EHLQJ GLVSOD\HG&KDQJHDEOH RSWLRQV DUH V\PEROW\SHVL]HDQGFRORUODEHOV$VSHFLDORSWLRQLVWKHDSSOLFDWLRQPXOWLSOLFDWLYHIDFWRUWRGDWD YDOXHV PDNHV VHQVHZKHQGHVFULSWRUV DQGREMHFWV DUH GLVSOD\HG LQ D ELSORW LQRUGHUWRUHVFDOHWKHVHULHVLQUHODWLRQWRWKHRWKHUV
• (GLWWLWOHV3HUPLWVDFKDQJHLQWKHJUDSKLFWLWOHDVZHOODVD[LVWLWOHV• $QWLDOLDVLQJ&KHFNER[PHQXLWHPWRPDNHWKHRYHUDOOJUDSKLFDSSHDUDQFHVRIWHU
6FDWWHUJUDSKLFVZKHWKHUFRQQHFWHGRUQRWHQDEOHWKHXVHUWRµQDYLJDWH¶LQVLGHWKHP7KLVLVGRQHXVLQJWKHPRXVHDQGWKHNH\V&75/DQG6+,)7,QD'VFDWWHUSORWSUHVVLQJ&75/OHIWEXWWRQDQGGUDJJLQJDOORZVWKHXVHUWRVHOHFWDQDUHDWREH]RRPHGLQRQ2QFHRQO\DSDUWRIWKHSORW LW LV VKRZQ WKH XVHUPD\ µPRYH¶ WKHZLQGRZ E\ XVLQJ GUDJJLQJ WKHPRXVHZLWK WKH OHIWEXWWRQSUHVVHG ,I&75/OHIW EXWWRQ LVSUHVVHG DJDLQZLWKRXWGUDJJLQJ LWPDNHV WKHSORW ]RRPRXW,QD'VFDWWHUSORWWKHOHIWEXWWRQRQWKHPRXVHLVXVHGWRURWDWHWKHSORW7KHULJKWEXWWRQFDQEHXVHGWRPRYHWKHSORWLQVLGHWKHJUDSKLFSDQHO,QWKHVDPHSORWGUDJJLQJWKHPRXVHZLWK6+,)7ULJKWEXWWRQDOORZVWKHXVHUWR]RRPLQDQGRXWRIWKHSORW
*UDSKLFSULQWLQJDQGH[SRUWLQJ
*UDSKLFVFDQEHH[SRUWHGDVLPDJHILOHVVHOHFWLQJWKHPHQXRSWLRQ([SRUWWRLPDJHILOHLQWKHPHQX)LOH RI WKH*UDSKLFV (GLWRU 2XWSXW IRUPDWV GHSHQG RQ WKH FDSDELOLWLHV RI WKH RSHUDWLQJV\VWHPW\SLFDOO\*,)-3*31*LPDJHIRUPDWVDUHDOORZHG7RSULQWWKHFXUUHQWJUDSKLFVHOHFWWKHPHQXRSWLRQ3ULQW IURP WKHPHQX)LOH RI WKH*UDSKLFV(GLWRU$GLDORJZLOOEHSURPSWHGDVNLQJWKHXVHUWRVHOHFWDSULQWHULIPRUHWKDQRQHLVDYDLODEOHDVZHOODVVRPHRWKHURSWLRQV
5HIHUHQFHV%H]GHN-&1XPHULFDOWD[RQRP\ZLWK)X]]\VHWV-0DWK%LRO%H]GHN-&3DWWHUQ5HFRJQLWLRQZLWK)X]]\2EMHFWLYH)XQFWLRQ3OHQXP3UHVV%H]GHN -& 6RPH QRQVWDQGDUG FOXVWHULQJ DOJRULWKPV LQ /HJHQGUH 3 /HJHQGUH /
'HYHORSPHQWVLQ1XPHULFDO(FRORJ\1$72$6,6HULHV9RO*6SULQJHU9HUODJ%UXHOKHLGH+³$QHZPHDVXUHRIILGHOLW\DQGLWVDSSOLFDWLRQWRGHILQLQJVSHFLHVJURXSV´-RXUQDO
RI9HJHWDWLRQ6FLHQFH&DOLQVNL7+DUDEDV]-³$GHQGULWHPHWKRGIRUFOXVWHUDQDO\VLV´&RPPXQLFDWLRQVLQ6WDWLVWLFV
&K\WUê07LFKê/+ROW-%RWWD'XNiW=³'HWHUPLQDWLRQRIGLDJQRVWLFVSHFLHVZLWKVWDWLVWLFDO
ILGHOLW\PHDVXUHV´-RXUQDORI9HJHWDWLRQ6FLHQFH&XDGUDV&0)RUWLDQD-³$FRQWLQXRXVPHWULFVFDOLQJVROXWLRQIRUDUDQGRPYDULDEOH´-RXUQDO
RI0XOWLYDULDWH$QDO\VLV&XDGUDV&0)RUWLDQD-³9LVXDOL]LQJFDWHJRULFDOGDWDZLWKUHODWHGPHWULFVFDOLQJ´LQ%ODVLXV-
*UHHQDFUH09LVXDOL]DWLRQRI&DWHJRULFDO'DWD/RQGRQ$FDGHPLF3UHVV&XDGUDV &0 )RUWLDQD - 2OLYD ) 7KH SUR[LPLW\ RI DQ LQGLYLGXDO WR D SRSXODWLRQ ZLWK
DSSOLFDWLRQVLQGLVFULPLQDQWDQDO\VLV-RXUQDORI&ODVVLILFDWLRQ'DYp51.ULVKQDSXUDP5³5REXVWFOXVWHULQJPHWKRGV$XQLILHGYLHZ´,(((7UDQV)X]]\
6\VW'D\:+(³7KHFRPSOH[LW\RIFRPSXWLQJPHWULFGLVWDQFHVEHWZHHQSDUWLWLRQV´0DWKHPDWLFDO
6RFLDO6FLHQFHV'H&iFHUHV02OLYD))RQW;6XEPLWWHG´2QUHODWLRQDOSRVVLELOLVWLFFOXVWHULQJ´'H&iFHUHV0)RQW;*DUFtD52OLYD) ³9(*$1$XQSDTXHWHGHSURJUDPDVSDUD OD
JHVWLyQ \ DQiOLVLV GH GDWRV HFROyJLFRV´ 9,, &RQJUHVR 1DFLRQDO GH OD $VRFLDFLyQ (VSDxROD GH(FRORJtD7HUUHVWUHSS
'XGD52+DUW3(6WRUN'*3DWWHUQ&ODVVLILFDWLRQQGHGQ:LOH\6RQV1HZ<RUN'XQQ-&$)X]]\5HODWLYHRIWKH,62'$7$3URFHVVDQGLWV8VHLQ'HWHFWLQJ&RPSDFW:HOO
6HSDUDWHG&OXVWHUV-&\EHUQ'XQQ-&,QGLFHVRISDUWLWLRQIX]]LQHVVDQGWKHGHWHFWLRQRIFOXVWHUVLQODUJHGDWDVHWVLQ*XSWD
0HG)X]]\DXWRPDWDDQGGHFLVLRQSURFHVVHV(OVHYLHU'XIUrQH0/HJHQGUH3 ³6SHFLHV DVVHPEODJHV DQG LQGLFDWRU VSHFLHV 7KH QHHG IRU D IOH[LEOH
DV\PHWULFDODSSURDFK´(FRORJLFDO0RQRJUDSKV(TXLKXD0³)X]]\FOXVWHULQJRIHFRORJLFDOGDWD´-RXUQDORIHFRORJ\
*,1.*2XVHU¶VPDQXDO
(YHULWW%6³&OXVWHU$QDO\VLV´(GZDOG$UQROG/RQGRQ0HOERXUQH$XFNODQG)HROL(2UOyFL/³$QDO\VLVRIFRQFHQWUDWLRQDQGGHWHFWLRQRIXQGHUO\LQJIDFWRUVLQVWUXFWXUHG
WDEOHV´9HJHWDWLR)RZONHV(%0DOORZV&/$PHWKRGIRUFRPSDULQJWZRKLHUDUFKLFDODOJRULWKPV-RXUQDORI
WKH$PHULFDQ6WDWLVWLFDO$VVRFLDWLRQ)ULJXL + .ULVKQDSXUDP 5 ³$ UREXVW DOJRULWKP IRU DXWRPDWLF H[WUDFWLRQ RI DQ XQNQRZQ
QXPEHURIFOXVWHUVIURPQRLV\GDWD´3DWWHUQ5HFRJQLWLRQ/HWWHUV*RUGRQ$'&ODVVLILFDWLRQQGHGQ&KDSPDQDQG+DOO&5&/RQGRQ*RZHU -& ³6RPH GLVWDQFH SURSHUWLHV RI ODWHQW URRWV DQG YHFWRUPHWKRGV XVHG LQPXOWLYDULDWH
DQDO\VLV´%LRPHWULND+DUWLJDQ-&OXVWHULQJ$OJRULWKPV-RKQ:LOOH\DQG6RQV1HZ<RUN+DWKDZD\ 5- 'DYHQSRUW -: %H]GHN -& ³5HODWLRQDO GXDOV RI WKH FPHDQV FOXVWHULQJ
DOJRULWKPV´3DWWHUQ5HFRJQLWLRQ+LOO02³'LYHUVLW\DQGHYHQQHVVDXQLI\LQJQRWDWLRQDQGLWVFRQVHTXHQFHV´(FRORJ\
+RWHOOLQJ + ³$QDO\VLV RI FRPSOH[ VWDWLVWLFDO YDULDEOHV LQWR SULQFLSDO FRPSRQHQWV´ - (GXF
3V\FKRO+XEHUW/$UDELH3³&RPSDULQJSDUWLWLRQV´-RXUQDORI&ODVVLILFDWLRQ-DLQ$.'XEHV5& $OJRULWKPV IRUFOXVWHULQJGDWD3UHQWLFH+DOO(QJOHZRRG&OLIIV1HZ
-HUVH\.LP':/HH.+/HH'³2QFOXVWHUYDOLGLW\LQGH[IRUHVWLPDWLRQRIWKHRSWLPDOQXPEHU
RIIX]]\FOXVWHUV´3DWWHUQ5HFRJQLWLRQ.ULVKQDSXUDP5.HOOHU-0³$SRVVLELOLVWLFDSSURDFKWRFOXVWHULQJ´,(((7UDQVDFWLRQVRQ
)X]]\6\VWHPV.ULVKQDSXUDP 5 .HOOHU -0 ³7KH 3RVVLELOLVWLF &0HDQV $OJRULWKP ,QVLJKWV DQG
5HFRPPHQGDWLRQV´,(((7UDQVDFWLRQVRQ)X]]\6\VWHPV.UXVNDO-%D³0XOWLGLPHQVLRQDOVFDOLQJE\RSWLPL]LQJJRRGQHVVRIILWWRDQRQPHWULFK\SRWKHVLV´
3V\FKRPHWULND.UXVNDO-%E³1RQPHWULF0XOWLGLPHQVLRQDOVFDOLQJ$QXPHULFDOPHWKRG´3V\FKRPHWULND
/DQFH*1:LOOLDPV:7³0L[HGGDWDFODVVLILFDWRU\SURJUDPV,$JJORPHUDWLYHV\VWHPV´
$XVWU&RPSXW-RXUQDO/HJHQGUH3/HJHQGUH/1XPHULFDO(FRORJ\6HFRQG(QJOLVK(GLWLRQ(G(OVHYLHUSS/HJHQGUH3*DOODJKHU('³(FRORJLFDOO\PHDQLQJIXOWUDQVIRUPDWLRQVIRURUGLQDWLRQRIVSHFLHV
GDWD´2HFRORJLD
9HUVLRQ
/LQJRHV - ³6RPH ERXQGDU\ FRQGLWLRQV IRU D PRQRWRQH DQDO\VLV RI V\PPHWULF PDWULFHV´3V\FKRPHWULND
0DJXUUDQ$('LYHUVLGDGHFROyJLFD\VXPHGLFLyQ(G9HUGUD%DUFHORQD0DUJDOHI5(FRORJLD(G2PHJD%DUFHORQDSS0DUVLOL/LEHOOL6³)X]]\FOXVWHULQJRIHFRORJLFDOGDWD´&RHQRVHV0LOOLJDQ * : ³$ VWXG\ RI WKH EHWDIOH[LEOH FOXVWHULQJ PHWKRG´ 0XOWLYDULDWH %HKDYLRUDO
5HVHDUFK0LOOLJDQ *: 6RNRO /0 ³$ WZR VWDJH FOXVWHULQJ DOJRULWKP ZLWK UREXVW UHFRYHU\
FKDUDFWHULVWLFV´(GXFDWLRQDODQG3V\FKRORJLFDO0HDVXUHPHQW0DF4XHHQ-³6RPHPHWKRGVIRUFODVVLILFDWLRQDQGDQDO\VLVRIPXOWLYDULDWHREVHUYDWLRQ´SS
LQ /0 /H &DP - 1H\PDQ HGV 3URFHHGLQJV RI WKH ILIWK %HUNHOH\ V\PSRVLXP RQPDWKHPDWLFDOVWDWLVWLFVDQGSUREDELOLW\9RO8QLYHUVLW\RI&DOLIRUQLD3UHVV%HUNHOH\
0DUGLD.9.HQW-7%LEE\-00XOWLYDULDWHDQDO\VLV$FDGHPLF3UHVV/RQGRQ8QLWHG.LQJGRPSS
0F&XQH%0HIIRUG0-3&25'0XOWLYDULDWHDQDO\VLVRIHFRORJLFDOGDWD9HUVLRQ0M06RIWZDUH'HVLJQ*OHQHGHQ%HDFK258685/KWWSKRPHFHQWXU\WHOQHWaPMP
0F/DFKODQ* - 'LVFULPLQDQWDQDO\VLVDQGVWDWLVWLFDOSDWWHUQ UHFRJQLWLRQ:LOH\6RQV1HZ<RUN
2OLYD)&iFHUHV0GH)RQW;&XDGUDV&0³&RQWULEXFLRQHVGHVGHXQDSHUVSHFWLYDEDVDGDHQSUR[LPLGDGHVDOIX]]\.PHDQVFOXVWHULQJ´;;,9&RQJUHVR6(,2ÒEHGD6SDLQSHUVFRPP
2UORFL/³$QDJJORPHUDWLYHPHWKRGIRUFODVVLILFDWLRQRISODQWFRPPXQLWLHV´-RXUQDORI(FRORJ\
3LHORX(&³7KHPHDVXUHPHQWRIGLYHUVLW\LQGLIIHUHQWW\SHVRIELRORJLFDOFROOHFWLRQV´-RXUQDORI7KHRUHWLFDO%LRORJ\
3RGDQL-³&RPSDULVRQRISDUWLWLRQVLQYHJHWDWLRQVWXGLHV´$EVWUDFWD%RWDQLFD3RGDQL-³&RPSDULVRQRIIX]]\FODVVLILFDWLRQV´&RHQRVHV3RGDQL - )HROL ( ³$ JHQHUDO VWUDWHJ\ IRU WKH VLPXOWDQHRXV FODVVLILFDWLRQ RI YDULDEOHV DQG
REMHFWVLQHFRORJLFDOGDWDWDEOHV´-RXUQDORI9HJHWDWLRQ6FLHQFH5DQG :0 ³2EMHFWLYH &ULWHULD IRU WKH (YDOXDWLRQ RI &OXVWHULQJ 0HWKRGV´ -RXUQDO RI WKH
$PHULFDQ6WDWLVWLFDO$VVRFLDWLRQ5DR( ³$ UHYLHZRI FDQRQLFDO FRRUGLQDWHV DQGDQDOWHUQDWLYH WR FRUUHVSRQGHQFHDQDO\VLVXVLQJ
+HOOLQJHUGLVWDQFH´4HVWLLy4XDGHUQVG(VWDGLVWLFDL,QYHVWLYDFLy2SHUDWLYD5pQ\L$³2QPHDVXUHVRIHQWURS\DQGLQIRPDWLRQ´,Q-1H\PDQHG3URFHHGLQJVRI
WKHIRXUWK%HUNHOH\V\PSRVLXPRQPDWKHPDWLFDOVWDWLVWLFVDQGSUREDELOLW\8QLYHUVLW\RI&DOLIRUQLD3UHVV%HUNHOH\
*,1.*2XVHU¶VPDQXDO
5RXVVHXZ 3- ³6LOKRXHWWHV D JUDSKLFDO DLG WR WKH LQWHUSUHWDWLRQ DQG YDOLGDWLRQ RI FOXVWHUDQDO\VLV´-RXUQDORI&RPSXWDWLRQDQG$SSOLHG0DWKHPDWLFV
5XVSLQL(³$1HZ$SSURDFKWR&OXVWHULQJ´,QI&RQWURO6KDQQRQ&(:HDYHU:7KH0DWKHPDWLFDO7KHRU\RI&RPPXQLFDWLRQ8QLYHUVLW\RI,OOLQRLV
3UHVV8UEDQD,/6KHSDUG51³7KHDQDO\VLVRISUR[LPLWLHVPXOWLGLPHQVLRQDOVFDOLQJZLWKDQXQNQRZQGLVWDQFH
IXQFWLRQ´3V\FKRPHWULND6QHDWK3+$6RNDO551XPHULFDOWD[RQRP\±7KHSULQFLSOHVDQGSUDFWLFHRIQXPHULFDO
FODVVLILFDWLRQ:+)UHHPDQ6DQ)UDQFLVFRSS6RNDO 5 50LFKHQHU & ' ³$ VWDWLVWLFDOPHWKRG IRU HYDOXDWLQJ V\VWHPDWLF UHODWLRQVKLSV´
8QLY.DQV6FL%XOO6RNDO 5RKOI %LRPHWU\ WKH SULQFLSOHV DQG SUDFWLFH RI VWDWLVWLFV LQ ELRORJLFDO UHVHDUFK UG
HGLWLRQ1HZ<RUN)UHHPDQ7D\ORU /5 ³%DWHV :LOOLDPV +XWFKLQVRQ ± D YDULHW\ RI GLYHUVLWLHV ,Q 'LYHUVLW\ RI ,QVHFW
)DXQDV´ /$ 0RXQG 1 :DUORII HGV WK 6\PSRVLXP RI WKH 5R\DO (QWRPRORJLFDO 6RFLHW\%ODFNZHOO2[IRUGSS
WHU %UDDN &-) ³&DQRQLFDO FRUUHVSRQGHQFH DQDO\VLV $ QHZ HLJHQYHFWRU WHFKQLTXH IRUPXOWLYDULDWHGLUHFWJUDGLHQWDQiOLVLV´(FRORJ\
WHU%UDDN&-)³&DQRQLFDOFRUUHVSRQGHQFHDQDO\VLVDQGUHODWHGPXOWLYDULDWHPHWKRGVLQDTXDWLFHFRORJ\´$TXDWLF6FLHQFHV
WHU %UDDN &-) âPLODXHU 3 &$12&2 UHIHUHQFH PDQXDO DQG XVHU¶V JXLGH WR &DQRFR IRU:LQGRZV 6RIWZDUH IRU &DQRQLFDO &RPPXQLW\ 2UGLQDWLRQ YHUVLRQ &HQWUH RI %LRPHWU\:DJHQLQJHQ85/KWWSZZZPLFURFRPSXWHUSRZHUFRP
7LEVKLUDQL5:DOWKHU*+DVWLH7³(VWLPDWLQJWKHQXPEHURIFOXVWHUVLQDGDWDVHWYLDWKHJDSVWDWLVWLF´-RXUQDORIWKH5R\DO6WDWLVWLFDO6RFLHW\%
YDQGHQ:ROOHQEHUJ$/³5HGXQGDQF\DQDO\VLVDQDOWHUQDWLYHIRUFDQRQLFDOFRUUHODWLRQDQDO\VLV´3V\FKRPHWULND
:DUG -+ ³+LHUDUFKLFDO JURXSLQJ WR RSWLPL]H DQ REMHFWLYH IXQFWLRQ´ -RXQDO RI WKH$PHULFDQ6WDWLVWLFDO$VVRFLDWLRQ
=DGHK/$³)X]]\VHWV´,QIRUPDWLRQDQG&RQWURO