thermal conductivity and thermal diffusivity of liquid copper · 2015-09-28 · ˆ &kdswhu...
TRANSCRIPT
7KHUPDO&RQGXFWLYLW\DQG7KHUPDO'LIIXVLYLW\RI/LTXLG&RSSHU
',3/20$7+(6,6
&ODXV&DJUDQ
,QVWLWXWIU([SHULPHQWDOSK\VLN)HEUXDU\
7HFKQLVFKH8QLYHUVLWlW*UD]
0HLQHQ(OWHUQPHLQHQEHLGHQ%UGHUQXQG
$QJHOLNDJHZLGPHW
$EVWUDFW
$ JHQHUDOVXUYH\RIGLIIHUHQW WKHUPRSK\VLFDOPHDVXUHPHQWPHWKRGVLVJLYHQZLWKLQ
WKLV ZRUN IRFXVLQJ PDLQO\ RQ WHFKQLTXHV ZKLFK DUH XVHG WR GHWHUPLQH WKHUPDO
FRQGXFWLYLW\ DQG WKHUPDOGLIIXVLYLW\RIPHWDOV DQGDOOR\VERWK LQ WKH VROLG VWDWH DV
ZHOODVDW WKHPHOWLQJSRLQWDQG LQWR WKHOLTXLGSKDVH%\XVLQJDVXEVHFRQGRKPLF
SXOVHKHDWLQJWHFKQLTXHLWLVSRVVLEOHWRPHDVXUHWKHUPRSK\VLFDOSURSHUWLHVRIPHWDOV
DQGDOOR\VDWWHPSHUDWXUHUHJLRQVWKDWDUHLQDFFHVLEOHWRPRVWRWKHUWHFKQLTXHV7KLV
WHFKQLTXHHQDEOHVKHDWLQJUDWHVXSWR.VDQGWKXVLVDSSOLHGIRUVKRUWWLPHµV
PHDVXUHPHQWV RI WKHUPRSK\VLFDO SURSHUWLHV RI HOHFWULFDO FRQGXFWLQJ PDWHULDOV
%HFDXVHRI WKH VKRUW WLPHRI WKHH[SHULPHQWVQRFKHPLFDO LQWHUDFWLRQVEHWZHHQ WKH
VDPSOH DQG LWV HQYLURQPHQW RFFXU 8VLQJ SXOVHKHDWLQJ PHDVXUHPHQWV RQ ZLUH
VKDSHG&RSSHU&XVSHFLPHQVRIPPGLDPHWHUDQGDQDYHUDJHOHQJWKRIPP
ZHUH SHUIRUPHG DQG WKH UHVXOWV HVSHFLDOO\ WKHUPDO FRQGXFWLYLW\ DQG WKHUPDO
GLIIXVLYLW\ XS WR . LQWR WKH OLTXLG SKDVH DUH GLVFXVVHG DQG FRPSDUHG WR
OLWHUDWXUHYDOXHV
,Q GHU YRUOLHJHQGHQ $UEHLW ZLUG HLQ JHQHUHOOHU hEHUEOLFN EHU YHUVFKLHGHQH
0HWKRGHQ]XU0HVVXQJ WKHUPRSK\VLNDOLVFKHU'DWHQYRQ0HWDOOHQXQG/HJLHUXQJHQ
JHJHEHQ*DQ] EHVRQGHUHV$XJHQPHUNZXUGH GDEHL DXI7HFKQLNHQ JHOHJW GLH HLQH
0HVVXQJ GHU :lUPHOHLWIlKLJNHLW XQG GHU 7HPSHUDWXUOHLWIlKLJNHLW VRZRKO YRQ
)HVWN|USHUQDOVDXFKYRQ)OVVLJNHLWHQHUP|JOLFKHQ(LQHGLHVHU0HWKRGHQLVWGLH
2KPVFKH 3XOVKHL]XQJ HOHNWULVFK OHLWHQGHU 0DWHULDOLHQ GLH HLQH (UPLWWOXQJ GHU
WKHUPRSK\VLNDOLVFKHQ 'DWHQ ELV LQ 7HPSHUDWXUEHUHLFKH HUODXEW GLH PLW
KHUN|PPOLFKHQ7HFKQLNHQ]%0HVVXQJHQ LPRGHUQDKHGHPWKHUPRG\QDPLVFKHQ
*OHLFKJHZLFKWQLFKWHUUHLFKWZHUGHQN|QQHQ'DPLWZHUGHQ$XIKHL]UDWHQELV]X
.V HUUHLFKW ZRGXUFK 0HVVXQJHQ LP µV%HUHLFK HUP|JOLFKW XQG FKHPLVFKH
:HFKVHOZLUNXQJHQ PLW GHU 8PJHEXQJ QDKH]X DXVJHVFKORVVHQ ZHUGHQ N|QQHQ ,Q
GLHVHU$UEHLWZXUGHQ0HVVXQJHQDQKRFKUHLQHQ.XSIHUGUlKWHQ&XPLW
HLQHP 'XUFKPHVVHU YRQ PP XQG HLQHU GXUFKVFKQLWWOLFKHQ /lQJH YRQ PP
GXUFKJHIKUW XQG GLH GDUDXV HUPLWWHOWHQ'DWHQ YRU DOOHP:lUPHOHLWIlKLJNHLW XQG
7HPSHUDWXUOHLWIlKLJNHLW ELV . LQ GLH IOVVLJH 3KDVH GLVNXWLHUW XQG PLW
/LWHUDWXUZHUWHQYHUJOLFKHQ
&RQWHQWV
&KDSWHU,QWURGXFWLRQ
&KDSWHU)XQGDPHQWDO7KHRU\
'HILQLWLRQVRIWKHUPDOFRQGXFWLYLW\DQGWKHUPDOGLIIXVLYLW\
([SHULPHQWDOGHWHUPLQDWLRQ
&RQYHFWLRQ
5HODWLRQVKLSRIWKHUPDOFRQGXFWLYLW\ZLWKHOHFWULFDOFRQGXFWLYLW\
WKH:,('(0$11)5$1=ODZ
6XPPDU\RILPSRUWDQWHTXDWLRQVIURPWKHGHULYDWLRQ
&KDSWHU6XUYH\RI0HWKRGV
&ODVVLILFDWLRQRIPHWKRGVXVHGWRPHDVXUHWKHUPDOFRQGXFWLYLW\DQG
WKHUPDOGLIIXVLYLW\
6WHDG\VWDWHWHFKQLTXHV
1RQVWHDG\VWDWHWHFKQLTXHV
7UDQVLHQWWHFKQLTXHV
3XOVHKHDWLQJWHFKQLTXHV
&KDSWHU([SHULPHQWDOVHWXSDQGGDWDHYDOXDWLRQ
([SHULPHQWDOGHWDLOVRIWKHSXOVHKHDWLQJVHWXS
0HDVXUHGDQGFDOFXODWHGSURSHUWLHV
'DWDHYDOXDWLRQ
$GGLWLRQDOPHDVXUHPHQWV
([SHULPHQWDOSDUDPHWHUVDQGVSHFLILFYDOXHVXVHGIRUFDOFXODWLRQ
&KDSWHU5HVXOWV
([SHULPHQWDOUHVXOWV
7DEXODUVXPPDU\RIWKHH[SHULPHQWDOUHVXOWV
&RPSDULVRQWROLWHUDWXUH
&KDSWHU(VWLPDWLRQRIXQFHUWDLQW\
&KDSWHU&RQFOXVLRQDQGRXWORRN
&KDSWHU5HIHUHQFHV
&KDSWHU
,QWURGXFWLRQ
)RU VHYHUDO \HDUV QRZ WKH 6XEVHFRQG7KHUPRSK\VLFV*URXS RI WKH ,QVWLWXWH IRU([SHULPHQWDO
3K\VLFV SHUIRUPV WKHUPRSK\VLFDO SURSHUWLHV PHDVXUHPHQWV E\ XVLQJ D RKPLF SXOVHKHDWLQJ
WHFKQLTXH:LWK WKLV WHFKQLTXH JRRG UHVXOWVKDYHEHHQREWDLQHG IRUERWK SXUHPHWDOV VXFKDV
$X1E:RU1LDVZHOODVIRUDOOR\VVXFKDV,QFRQHORU,QYDU)H1L
7KH GDWD REWDLQHG E\ RXU PHDVXUHPHQWV DUH RI WKH JUHDWHVW LQWHUHVW IRU WKH PHWDOZRUNLQJ
LQGXVWU\LHDVLQSXWGDWDIRUFRPSXWHUVLPXODWLRQVWRPRGHOOLTXLGPHWDOSURFHVVLQJRSHUDWLRQV
VXFKDVFDVWLQJRUZHOGLQJ0$*0$VRIWWRXQGHUVWDQGDQGGHVLJQSURFHVVLQJHTXLSPHQWVXFK
DV IDFLOLWLHV IRU WKH JURZWK RI VLQJOH FU\VWDOV IURP WKH PHOW WR REWDLQ PRUH DFFXUDWH SKDVH
GLDJUDPVIRUEHWWHUDVVHVVPHQWRISRWHQWLDODFFLGHQWVLQWKHGHVLJQRIVDIHUQXFOHDUUHDFWRUVIRU
DHURVSDFHWHFKQLTXHVRUMXVWIRUIXQGDPHQWDOPDWHULDOVUHVHDUFKUHDVRQV
7KLVSUHVHQWZRUNGHDOVZLWKWKHGHWHUPLQDWLRQRIWKHUPDOFRQGXFWLYLW\DQGWKHUPDOGLIIXVLYLW\RI
SXUH&RSSHU&X&RSSHULWVHOIKDVDOUHDG\EHHQPHDVXUHGDWWKH,QVWLWXWHDFRXSOHRI\HDUVDJR
ZLWK JRRG UHVXOWV EXW WKLV WLPH ZH PDLQO\ IRFXVHG RQ GLIIHUHQW SURSHUWLHV OLNH WKHUPDO
FRQGXFWLYLW\DQGWKHUPDOGLIIXVLYLW\%DFNLQWKHS\URPHWHUZDVDEOHWRSURSHUO\GHWHFWWKH
PHOWLQJSODWHDXRI&RSSHUDOWKRXJKWKHVXUIDFHUDGLDWLRQRI&RSSHULVORZZKLFKLVE\XVLQJ
3/$1&.VODZRQEODFNERG\UDGLDWLRQDUHVXOWRIWKHORZPHOWLQJWHPSHUDWXUHRI&RSSHU%\
ZD\RIFRQWUDVWDOOWKHVLJQDOVDQGGDWDIURPWKHVROLGVWDWHEHIRUHPHOWLQJZHUHFRYHUHGE\WKH
QRLVH RI WKH DPSOLI\LQJ HOHFWURQLF DQGZHUH WKHUHIRUH LQDFFHVVLEOH$V DPDWWHU RI IDFWV VRPH
TXDQWLWLHV VXFKDV WKHHQWKDOS\RU WKHHOHFWULFDO UHVLVWLYLW\DW WKHPHOWLQJ WUDQVLWLRQ OHG WRJRRG
UHVXOWVZKHUHDVPHDVXUHPHQWVLQWKHVROLGVWDWHZHUHQHDUO\XQSUDFWLFDEOH
0HDQZKLOHWKLVSUREOHPKDVEHHQUHPRYHGE\UHQHZLQJDQGLPSURYLQJRXUDSSDUDWXV:HKDYH
D QHZ LQWHUIHUHQFH ILOWHU LQ WKH S\URPHWHU ZLWK D ZLGHU EDQGZLWK DQG QHZ DPSOLILFDWLRQ
HOHFWURQLFVZLWKEHWWHUVLJQDO WRQRLVHUDWLR7KHUHIRUHZHIHOWDEOHWRPHDVXUHWKHSURSHUWLHVRI
&RSSHUDJDLQ%XWZHGLGQRWWKLQNDERXWUHPHDVXULQJWKHSURSHUWLHVRIOLTXLG&RSSHUXQWLOZH
JRW DQ LQTXLU\ IURP'U -RKQ5HGJURYH+HDGRI7KHUPRSK\VLFDO3URSHUWLHV6HFWLRQ1DWLRQDO
3K\VLFDO /DERUDWRU\ 13/ /RQGRQ ZKR KDYH EHHQ FRPPLVVLRQHG WR GHYHORS D QDWLRQDO
VWDQGDUG IRU PHDVXUHPHQW RI WKH WKHUPDO GLIIXVLYLW\ DQG WKHUPDO FRQGXFWLYLW\ RI PROWHQ
PDWHULDOV7KHREMHFWLYHVRIWKHLU\HDUSURMHFWZKLFKEHJDQ-XO\DUHWR
• VXSSRUW WKH SURFHVV LQGXVWULHV E\ SURYLGLQJ D WKHUPDO FRQGXFWLYLW\GLIIXVLYLW\
PHDVXUHPHQWVWDQGDUGIRUPROWHQPDWHULDOV
• SURYLGHGDWDRQNH\UHIHUHQFHPDWHULDOV
$VDSDUWRIWKHYDOLGDWLRQWKH\ZDQWWRLQWHUFRPSDUHPHDVXUHPHQWVRQVHOHFWHGPDWHULDOVZLWK
RWKHUODERUDWRULHVDQGGLIIHUHQWPHDVXUHPHQWWHFKQLTXHVWRJHWDQHVWLPDWLRQRIWKHDFFXUDF\RI
ERWKWKHPHDVXUHGYDOXHVDVZHOODVWKHGLIIHUHQWWHFKQLTXHV13/DVNHGXVWRSDUWLFLSDWHLQWKH
LQWHUFRPSDULVRQ RI DERXW GLIIHUHQW ODERUDWRULHV ZRUOGZLGH DQG WR FRQWULEXWH WKH
WKHUPRSK\VLFDO SURSHUWLHV PDLQO\ WKH WKHUPDO FRQGXFWLYLW\ DQG WKH WKHUPDO GLIIXVLYLW\ RI
&RSSHUDW.WR.WRWKHLUPROWHQPDWHULDOVLQWHUFRPSDULVRQ
&RSSHULWVHOILVFRPPRQO\XVHGDVDUHIHUHQFHPDWHULDOEHFDXVHRIVHYHUDOUHDVRQVWKHORZDQG
ZHOONQRZQPHOWLQJWHPSHUDWXUHJRRGPHFKDQLFDOSURSHUWLHVJRRGHOHFWULFDOSURSHUWLHVVXFKDV
KLJK HOHFWULFDO FRQGXFWLYLW\ RQO\ VLOYHU $J KDV D EHWWHU HOHFWULFDO FRQGXFWLYLW\ WKDQ&RSSHU
DQGWKHUHIRUHDORZUHVLVWLYLW\DQGRIFRXUVHLWVDYDLODELOLW\WRQDPHMXVWDIHZ13/DOVRDLPVWR
SXEOLVKWKHILQDOUHVXOWVDIWHUWKH\HDUVLQWKHVFLHQWLILFOLWHUDWXUHWRPDNHWKHGDWDDFFHVVLEOHWR
WKHVFLHQWLILFFRPPXQLW\
$OWKRXJKZHNQHZWKDW WKHVDPHUHDVRQVWKDWPDNH&RSSHUVXFKDJRRGUHIHUHQFHPDWHULDODUH
WKHRQHV WRPDNHPHDVXUHPHQWVPRUHFRPSOLFDWHGDQGGLIILFXOWZHDJUHHGDQGSDUWLFLSDWHG LQ
WKHLQWHUFRPSDULVRQSURMHFWZLWK13/1RWDWOHDVWWKHVHQHZ&RSSHUPHDVXUHPHQWVDUHDTXLWH
JRRGLQGLFDWRUIRUWKHSUHVHQWDELOLWLHVRIRXUPHDVXUHPHQWV\VWHP
&KDSWHU
)XQGDPHQWDO7KHRU\
'HILQLWLRQV RI WKHUPDO FRQGXFWLYLW\ DQG WKHUPDOGLIIXVLYLW\
$VDVWDUWLQJSRLQWIRUDVKRUWGHULYDWLRQDF\OLQGULFDOURGZKLFKLVLVRODWHGDJDLQVWKHDWORVVHV
DORQJWKHVXUIDFHLVFKRVHQ:HORRNDWWKHKHDWWUDQVIHUSDUDOOHOWRWKHF\OLQGHUD[LV
)LJ6FKHPDWLFGLVSOD\LQJ WKHEDVLFVRIKHDW FRQGXFWLRQ.H\7 WHPSHUDWXUH[ GLVWDQFHGTKHDW
IOX[$DUHD9YROXPH
)RXULHUVSULQFLSOHODZRIWKHKHDWWUDQVIHUUHDGV
JUDG7T ⋅−= λ
ZKHUHTLVWKHKHDWIOX[7WKHWHPSHUDWXUHDQGλWKHWKHUPDOFRQGXFWLYLW\
DGLDEDWLFLQVXODWLRQ$
'LVWDQFH[
7
[ [G[
7[
7[G[
G[
9GT
[GT
[G[
)RXULHUPDGH WKH DVVXPSWLRQ WKDW WKH SHUSHQGLFXODU KHDW IORZ DFURVV WKH XQLW DUHD$SHUXQLW
WLPHPXVWEHSURSRUWLRQDOWRWKHXQLWDUHD$DQGWKHWHPSHUDWXUHJUDGLHQWG7G[ZKLFKOHDGVWR
G[G7
$G7GT ⋅⋅−==Φ λ
ZKHUHΦLVWKHKHDWFXUUHQWDQG$WKHXQLWDUHD
,QWKLVHTXDWLRQWKHUPDOFRQGXFWLYLW\λLVDSURSRUWLRQDOFRQVWDQW,WKDVWREHVWDWHGKHUHWKDWλ
LWVHOI FRXOG EH D WHPSHUDWXUH GHSHQGHQW TXDQWLW\ DQG WKHUHIRUH FRXOG QRW ORQJHU EH VHHQ DV D
FRQVWDQW
,IZHPDNHVRPHVLPSOHFRQYHUVLRQVZLWK(TZHILQGWKHZHOONQRZQGHVFULSWLRQ
G[G7
$
T
⋅−=λ
2QHFDQVHH WKDW WKHUPDOFRQGXFWLYLW\λFDQEHGHILQHGDVWKHKHDWIOX[TFRQGXFWHGDFURVVDQ
XQLWDUHD$SHUVHFRQGSHUXQLWWHPSHUDWXUHJUDGLHQWDQGKDVWKHGLPHQVLRQ>:P.@
6LPLODUWRWKHGHULYDWLRQRIWKHHTXDWLRQIRUGLIIXVLRQWKHHQWLUHPDWKHPDWLFDOVROXWLRQFDQRQO\
EHIRXQG LI WKHWHPSHUDWXUH7ZLWKLQWKHF\OLQGHULVNQRZQDVDIXQFWLRQRIWLPHWDQGSODFH[
7[\]W7KHHTXDWLRQFRQVLGHULQJWKRVHSRLQWVLVNQRZQDVWKHGLIIHUHQWLDOHTXDWLRQRIKHDW
WUDQVIHU
[7
FGGWG7
S ∂∂⋅
⋅= λ
ZKHUHGLVWKHGHQVLW\DQGFSWKHKHDWFDSDFLW\
&RPELQLQJWKHFRQVWDQWVIURP(TRQHJHWVWKHWKHUPDOGLIIXVLYLW\DZKLFKLVGHILQHGDV
SFGD
⋅= λ
7KHUPDO GLIIXVLYLW\ UHSUHVHQWV WKH UDWH RI KHDW GLIIXVLRQ SHU XQLW WLPH DQG KDV WKH GLPHQVLRQ
>PV@ (T HTXDOV ),&.V QG ODZ RI GLIIXVLRQ ZKLFK UHIOHFWV LQ WKH QDPH WKHUPDO
GLIIXVLYLW\
$VRQHFDQVHH(TFUHDWHVDUHODWLRQEHWZHHQWKHUPDOFRQGXFWLYLW\DQGWKHUPDOGLIIXVLYLW\
7KLV LV YHU\ LPSRUWDQW IRU GLIIHUHQWPHDVXUHPHQWV EHFDXVH LQ VRPHPHWKRGV LW LV QRW WKHUPDO
FRQGXFWLYLW\ λ EXW WKHUPDO GLIIXVLYLW\ D ZKLFK LV GHWHUPLQHG DV ZLWK WKH NQRZOHGJH RI RQH
TXDQWLW\LWVSRVVLEOHWRGHWHUPLQHWKHRWKHUTXDQWLW\
([SHULPHQWDOGHWHUPLQDWLRQ
%HIRUHWKHYDULRXVGLIIHUHQWPHWKRGVXVHGWRPHDVXUHWKHUPDOFRQGXFWLYLWLHVDQGGLIIXVLYLWLHVDUH
GLVFXVVHGLQWKHQH[WFKDSWHU,ZDQWWRFDOO\RXUDWWHQWLRQWRWZRWKLQJVZKLFKVKRXOGDOZD\VEH
NHSWLQPLQGZKLOHGLVFXVVLQJWKHVHPHWKRGV
• 7KHILUVWSRLQW LVKRZFRQYHFWLRQDIIHFWV WKHVSHFLILFPHDVXUHPHQWRUKRZRQHFDQSUHYHQW
WKHHIIHFWRIFRQYHFWLRQ
• 7KH VHFRQG SRLQW LV WKH FORVH UHODWLRQVKLS RI WKHUPDO FRQGXFWLYLW\ ZLWK HOHFWULFDO
FRQGXFWLYLW\7KHVHVLPLODULWLHVOHDGWRVRPHWRWDOO\GLIIHUHQWSRVVLELOLWLHVRIPHDVXULQJWKHVH
TXDQWLWLHV
&RQYHFWLRQ
:KHQWKHUPDOFRQGXFWLYLW\PHDVXUHPHQWVDUHFDUULHGRXWRQOLTXLGV WKHKHDWIOX[TFDQREWDLQ
VXEVWDQWLDO FRQWULEXWLRQV IURP FRQYHFWLRQ DQG FDQ OHDG WR HUURQHRXVO\ KLJK YDOXHV IRU WKHUPDO
FRQGXFWLYLW\DQGDOVRIRUWKHUPDOGLIIXVLYLW\&RQVHTXHQWO\JUHDWHIIRUWVDUHPDGHWRPLQLPL]H
FRQYHFWLRQE\
L DFFXUDWHWHPSHUDWXUHFRQWURORIWKHVDPSOH
LL HQVXLQJWKDWWKHIUHHVXUIDFHRIWKHOLTXLGLVDWPDUJLQDOO\KLJKHUWHPSHUDWXUHWKDQWKDWRI
WKHEDVHRIWKHVDPSOH
+RZHYHU PDQ\ PHWDOV PHOW DW YHU\ KLJK WHPSHUDWXUHV DQG LQ SUDFWLFH LW LV YHU\ GLIILFXOW WR
SURYLGH WKH QHFHVVDU\ FRQWURO RI WHPSHUDWXUH XQGHU WKHVH FRQGLWLRQV &RQVHTXHQWO\ LQ UHFHQW
\HDUV WUDQVLHQW DQG QRQVWHDG\ VWDWH PHWKRGV VHH &KDSWHU KDYH EHHQ LQFUHDVLQJO\ XVHG WR
FDUU\RXWPHDVXUHPHQWVRQOLTXLGPHWDOVDQGDOOR\V,QWKHVHH[SHULPHQWVWKHPHDVXUHPHQWVDUH
FDUULHGRXWUDSLGO\ZLWKDYLHZWRFRPSOHWHWKHHQWLUHH[SHULPHQWEHIRUHWKHRQVHWRIFRQYHFWLRQ
5HODWLRQVKLS RI WKHUPDO FRQGXFWLYLW\ ZLWK HOHFWULFDOFRQGXFWLYLW\WKH:,('(0$11)5$1=/DZ
,Q PDQ\ GLIIHUHQW SUDFWLFDO FDVHV HOHFWULFDO FRQGXFWLYLW\ σ RU HOHFWULFDO UHVLVWLYLW\ σ
PHDVXUHPHQWV DUH D ORW HDVLHU WR SHUIRUP WKDQ WKH GHWHUPLQDWLRQ RI WKH WKHUPDO FRQGXFWLYLW\
LWVHOI WKXV D UHODWLRQ EHWZHHQ WKHVH YDOXHV LV QHHGHG WR GHULYHλ HLWKHU IURPσ RU σ WKH
:,('(0$11)5$1=/25(17=ODZ:)/>.OHPHQVDQG:LOOLDPV@KDYHVKRZQLWV
WKHRUHWLFDOGHULYDWLRQZKLFKLVVXPPHGXSRQWKHIROORZLQJSDJHV
7KHRU\
7KH WKHUPDO FRQGXFWLYLW\ RI PHWDOV DQG DOOR\V LV FRPSRVHG RI WZR FRPSRQHQWV D ODWWLFH
FRPSRQHQW λO DQG DQ HOHFWURQLF FRPSRQHQW λH ,Q ERWK FDVHV KHDW LV WUDQVSRUWHG E\ PRELOH
FDUULHUVDQGWKHUPDOFRQGXFWLYLW\GXHWRHDFKFDUULHUFDQEHH[SUHVVHGLQWKHIRUP
LLLL OY& ⋅⋅⋅=λ
+HUH&L LV WKH FRQWULEXWLRQ RI FDUULHUV RI W\SH L WR WKH VSHFLILF KHDW SHU XQLW YROXPH YL LV WKH
DYHUDJHVSHHGRIWKRVHFDUULHUVDQGOLWKHLUPHDQIUHHSDWK7KLVHTXDWLRQKDVWKHVDPHIRUPDV
WKHH[SUHVVLRQIRUWKHUPDOFRQGXFWLYLW\LQWKHNLQHWLFWKHRU\RIJDVHVDQGFDQEHGHULYHGIURPD
%2/7=0$11HTXDWLRQ6LQFHWKHFRQWULEXWLRQVRIWKHVHWZRW\SHVRIFDUULHUVFRXOGEHGLYLGHG
IXUWKHULQWRVXEJURXSVWKHRYHUDOOWKHUPDOFRQGXFWLYLW\EHFRPHVWKHVXPRIWKHVHFRQWULEXWLRQV
∑=L
Lλλ
$V PHQWLRQHG EHIRUH WKHUPDO FRQGXFWLRQ LQ PHWDOV DQG DOOR\V FRQVLVWV RI D ODWWLFH DQG DQ
HOHFWURQLF FRPSRQHQW 6HYHUDO LQYHVWLJDWRUV KDYH VKRZQ H[SHULPHQWDOO\ WKDW DOWKRXJK WKH
PHFKDQLVP RI SKRQRQ RU ODWWLFH FRQGXFWLRQ FDQ PDNH D VLJQLILFDQW FRQWULEXWLRQ DW ORZHU
WHPSHUDWXUHVHOHFWURQLFFRQGXFWLRQLVGRPLQDQWDWWHPSHUDWXUHVDURXQGWKHPHOWLQJSRLQW>13/
5HSRUW@:LWKWKHVHDVVXPSWLRQVWKHRU\OHDGVWRWKH:)/E\MXVWORRNLQNDWWKHHOHFWURQLF
FRPSRQHQW
(OHFWURQLFFRPSRQHQWWKH/25(17=UDWLR
(TKROGVIRUWKHHOHFWURQLFFRPSRQHQWDVZHOODVIRUWKHODWWLFHFRPSRQHQWEXWLWLVPRUH
XVHIXOWRUHODWHλHWRWKHHOHFWULFDOFRQGXFWLYLW\σ,QSDUWWKLVIROORZVEHFDXVH&HWKHHOHFWURQLF
FRPSRQHQWRIWKHVSHFLILFKHDWLVRQO\DVPDOOSDUWRIWKHWRWDOVSHFLILFKHDWDQGWKXVQRWHDVLO\
GHGXFHG IURPPHDVXUHPHQWV7KHPDLQ DGYDQWDJHRI H[SUHVVLQJλH LQ WHUPVRIσ LV WKDWERWK
TXDQWLWLHV DUH GLUHFWO\ SURSRUWLRQDO WR WKH HOHFWURQPHDQ IUHH SDWK OH VR WKDW WKH UDWLRλHσ LV
LQGHSHQGHQWRIOHIXUWKHUPRUHσLVUHODWLYHO\HDV\WRPHDVXUH7KLVDVVXPHVRIFRXUVHWKDWWKH
PHDQ IUHH SDWK OH DV SURSHUO\ GHILQHG WKURXJK D %2/7=0$11 HTXDWLRQ LV WKH VDPH IRU
HOHFWULFDODVIRUWKHUPDOFRQGXFWLRQ:KLOHWKLVLVE\QRPHDQVXQLYHUVDOO\WUXHGLIIHUHQFHVLQWKH
WZRPHDQIUHHSDWKVDUHLPSRUWDQWPDLQO\DWORZWHPSHUDWXUHVZKHUHHOHFWURQVFDWWHULQJLVERWK
LQHODVWLFDQGDQLVRWURSLF
,QWKHILUVWLQVWDQFHOHWXVDVVXPHDPHDQIUHHSDWKZKLFKLVWKHVDPHIRUHOHFWULFDODQGWKHUPDO
FRQGXFWLRQ (DFK HOHFWURQ LV WUHDWHG DV EHLQJ LQ D GHILQLWH VWDWH RI PRWLRQ VSHFLILHG E\ LWV
PRPHQWXPSEXWKDYLQJLWVSRVLWLRQFRPSOHWHO\XQVSHFLILHGZLWKLQWKHYROXPHRIWKHVROLG)RU
HDFKSYDOXH WKHUH DUH WZRSRVVLEOH YDOXHVRI VSLQ WKH VWDWHRI WKH HOHFWURQ LV VSHFLILHGE\ LWV
PRPHQWXP VSLQ $FFRUGLQJ WR WKH 3DXOL H[FOXVLRQ SULQFLSOH WKHUH FDQQRW EH PRUH WKDQ RQH
HOHFWURQ LQ HDFK VXFK VWDWH7KH DYHUDJH QXPEHU RI HOHFWURQV SHU VWDWH GHILQHV WKH GLVWULEXWLRQ
IXQFWLRQIS7KHHOHFWURQGRHVQRWPRYHLQIUHHVSDFHEXWLQWKHSHULRGLFSRWHQWLDORIWKHFU\VWDO
ODWWLFH KHQFH(S WKH HQHUJ\ RI WKH HOHFWURQ RI WKHPRPHQWXPS GLIIHUV IURP WKDW RI D IUHH
HOHFWURQ
,QDSHUIHFWO\SHULRGLFODWWLFHHDFKHOHFWURQFRQVHUYHVLWVPRPHQWXPYDOXHSDVLILWZRXOGPRYH
LQ IUHH VSDFH'HYLDWLRQV IURP SHULRGLFLW\ ODWWLFH YLEUDWLRQV LPSHUIHFWLRQV ERXQGDULHV FDXVH
HOHFWURQVWREHVFDWWHUHGIURPRQHSVWDWHWRDQRWKHUXQRFFXSLHGVWDWH,QWKHUPDOHTXLOLEULXPWKH
RFFXSDWLRQQXPEHUDWWDLQVLQDYHUDJHWKHYDOXHJLYHQE\WKH)(50,',5$&GLVWULEXWLRQIS
( ) ( )
S
+
= −7N
(
%H
I ζ
&
ZKHUH N% LV WKH %2/7=0$11 FRQVWDQW DQG ζ WKH )(50, HQHUJ\ LV VLPLODU WR D FKHPLFDO
SRWHQWLDODQGLVGHWHUPLQHGE\WKHHOHFWURQGHQVLW\
,I WKHGLVWULEXWLRQ IXQFWLRQ IS GHSDUWV V\VWHPDWLFDOO\ LH IRUD ODUJHJURXSRI VWDWHV IURP LWV
HTXLOLEULXP YDOXH I WKH VDPH VFDWWHULQJ SURFHVVHV ZLOO WHQG WR UHVWRUH WKH HTXLOLEULXP
GLVWULEXWLRQ 7KH UDWH RI UHWXUQ WRZDUGV HTXLOLEULXP FDQ EH FKDUDFWHUL]HG E\ D UHOD[DWLRQ WLPH
τSWKHUDWHRIFKDQJHRIISGXHWRWKHLQWHUDFWLRQLQWSURFHVVHVLVH[SUHVVHGDV
( ) ( )( )
( )( )SSJ
SSISI
GWGI
&
&
&
&&
ττ−=−−=
LQW_
ZKHUHJSLVWKHGHSDUWXUHRIWKHGLVWULEXWLRQIXQFWLRQIURPLWVHTXLOLEULXPYDOXH7KHPHDQIUHH
SDWKLVGHILQHGDVOH YHτZKHUHYH G(GSLVWKHHOHFWURQYHORFLW\
$QHOHFWULFILHOG)RUDWHPSHUDWXUHJUDGLHQW7ZLOOWHQGWRFKDQJHWKHGLVWULEXWLRQIXQFWLRQDW
DUDWH
G7GI
Y7G(GI
Y)HGWGI
HH7)
_&&&
⋅∇−⋅−=∇
ZKHUHHWKHHOHFWURQFKDUJH
7KH%2/7=0$11HTXDWLRQVWDWHVWKDWWKHQHWUDWHRIFKDQJHGXHWRHTXDWLRQVDQG
LV]HURLQDVWHDG\VWDWHVRWKDW
( ) ( )
∇
+−⋅−= 7
G7G
NN)HY
G(GI
SSJ%
%H
ζετ &&&&
ZKHUHε (ζN%7LVWKH%2/7=0$11WHUP
,QWKHUPDOHTXLOLEULXPWKHHOHFWULFFXUUHQWGHQVLW\MDQGWKHKHDWFXUUHQWGHQVLW\4YDQLVK%RWK
RIWKHVHFXUUHQWVWKXVFDQEHH[SUHVVHGDV
( )
( ) ( )∫
∫−=
=
SGSJ(YK
4
SGSJYKH
M
H
H
&&&
&&&
ζ
VLQFHKGS LVWKHQXPEHURITXDQWXPVWDWHVSHUXQLWYROXPHLQDQHOHPHQWGSRISVSDFHKLV
3/$1&.VFRQVWDQW
2QH QRZ FDQ DUUDQJH WKH LQWHJUDWLRQ RYHU SVSDFH LQ WHUPV RI LQWHJUDWLQJ RYHU VXUIDFHV RI
FRQVWDQW HQHUJ\ ( LQ SVSDFH DQG WKHQ RYHU ( 1RZ G( N%7Gε 7KH IDFWRU
GIG( N%7GIGεRFFXUVLQERWKLQWHJUDOVLQ(TDQGGIGεLVDQHYHQIXQFWLRQRIε
7KHYDULRXV WHUPV LQHTXDWLRQDQGFDQEHJURXSHGDFFRUGLQJWRWKHLUSRZHURIε
5HWDLQLQJWHUPVHYHQLQεZHDUULYHDWWKHIROORZLQJUHVXOWV
7KHLVRWKHUPDOHOHFWULFDOFRQGXFWLYLW\GHILQHGDVσ M)ZKHQ∇7 FDQEHZULWWHQDV
( )∫
== ε
εεσσ G
GGI
0
DQGLVWKXVWKH]HURWKPRPHQWRIDSDUWLDOFRQGXFWLYLW\WHQVRUσLMεGIGεZKHUH
( ) ( ) ( ) ( ) ( )∫ −= G6SYSYSYSKH
HMLLM
&&&τεσ
ZKHUH L M GHQRWH &DUWHVLDQ FRPSRQHQWV G6 LV D VXUIDFH HOHPHQW RI WKH FRQWRXU(S ( LQ
SVSDFHDQGWKHLQWHJUDWLRQLVRYHUWKHHQWLUHFRQWRXU( N%7εζ
2QHFDQGHILQHWKHILUVWDQGVHFRQGPRPHQWRIWKHVDPHSDUWLDOFRQGXFWLYLW\E\
( ) εε
εεσ GGGI
0 QQ ∫
=
7KH3HOWLHUFRHIILFLHQW∏LVGHILQHGDV4MZKHQ∇7 DQGRQHFDQVKRZWKDW
=∏
00
H7N%
7KHHOHFWURQLFFRPSRQHQWRIWKHUPDOFRQGXFWLYLW\LVGHILQHGDVλH 4∇7XQGHUWKHFRQGLWLRQ
M 7KHODWWHUFRQGLWLRQGHWHUPLQHVWKHWKHUPRHOHFWULFSRZHU6H ∏7 >)N%GζG7@∇7
DQGRQHILQDOO\REWDLQV
−
=
000
7HN%
Hλ
7KH HOHFWURQLF WKHUPDO FRQGXFWLYLW\ FDQ EH UHODWHG WR WKH HOHFWULFDO FRQGXFWLYLW\ E\ WKH
/25(17=UDWLR
H%%H 6
00
HN
00
00
HN
7/ −
=
−
==
σλ
:KLOH (T KROGV IRU VHPLFRQGXFWRUV DQG VHPLPHWDOV DV ZHOO DV IRU JRRG PHWDOOLF
FRQGXFWRUV ZH DUH SDUWLFXODUO\ LQWHUHVWHG LQ WKH FDVH RI KLJK GHJHQHUDF\ ZKHUH WKH HOHFWURQ
GHQVLW\ LV VR KLJK DQG WKH )(50, HQHUJ\ VR ODUJH WKDWσ( FDQ EH H[SDQGHG DV D 7$</25
VHULHVDERXWζ
( ) ( ) ( ) +
+
+=
ζζ
σεσεζσσ
G(G
7NG(G
7N( %%
VR WKDW HOHFWULFDO FRQGXFWLYLW\ WKHUPRHOHFWULF SRZHU WKHUPDO FRQGXFWLYLW\ DQG WKH/25(17=
UDWLRDUHJLYHQE\
( ) ( ) ( )ζ
σπζσσ
+=
G((G
7N%
( ) ( )ζ
σσ
π
=
G((G
7NH
N6 %
%H
7/H ⋅⋅= σλ
DQG
( ) ( )
H%%% 6
G((G
7NHN
HN
/ −
×
+
=
ζ
σσ
ππ
7KHOHDGLQJWHUPLQ(T/ πN%HLVWKH6200(5)(/'YDOXHRIWKH/25(17=
UDWLR
,QWHJUDOVRIWKHW\SH
( )∫∞
∞−
−+= εεεε G, QQ
H[SH[S
KDYH EHHQ H[SDQGHG DQG H[SUHVVHG LQ WHUPVRI WKH5,(0$11]HWD IXQFWLRQ7KXV , π
, πDQGIRUKLJKHUHYHQYDOXHVRIQ,Q≈Q
7KHVH DERYH UHODWLRQV ZHUH GHULYHG XQGHU WKH DVVXPSWLRQ WKDW WKH UHOD[DWLRQ WLPH τS LV D
IXQFWLRQRISEXW LV LQGHSHQGHQWRI WKHIXQFWLRQDOIRUPRIJS WKXVτS LVDVVXPHGWREHWKH
VDPH IRU HOHFWULFDO DQG WKHUPDO FRQGXFWLRQ VR WKDW σε LV DOVR XQLTXH ,Q FDVHV ZKHQ WKLV
FRQGLWLRQ LVQRW VDWLVILHG(TZRXOGQRWKROGEHFDXVH WKHPDJQLWXGHRIσ(ZRXOGQRW
FDQFHORXWLQWKHUDWLRRIPRPHQWVRI(T
1HYHUWKHOHVV WKHVH UHVXOWVDUH LQJRRGDJUHHPHQWZLWK WKHH[SHULPHQWDOO\REWDLQHG UHVXOWVDQG
XVHGIRUGDWDHYDOXDWLRQ
6XPPDU\RILPSRUWDQWHTXDWLRQVIURPWKHGHULYDWLRQ
:,('(0$11)5$1=/25(17=ODZ:)/
6LPSOHPDQLSXODWLRQVZLWK(TOHDGWRWKH:,('(0$11)5$1=ODZLQWKHGHVFULSWLRQ
RI//25(17=
7/
⋅=
σλ
RU 7/ ⋅⋅= σλ
ZKHUH/LVWKH/25(17=QXPEHUλLVWKHUPDOFRQGXFWLYLW\σLVHOHFWULFDOFRQGXFWLYLW\DQG7
LVWHPSHUDWXUH
/25(17=QXPEHU
$VPHQWLRQHGEHIRUHWKHOHDGLQJWHUPLQ(T
⋅=HN
/ %π
LV WKH 6200(5)(/' YDOXH RI WKH /25(17= UDWLR $V ZH FDQ VHH LW GHSHQGV RQO\ RQ
FRQVWDQWVDQGDVDPDWWHURIIDFWVLVDFRQVWDQWLWVHOI,WVXQLYHUVDOYDOXHFDQEHFDOFXODWHGZLWK
WKHXVHRIVRPHTXDQWXPPHFKDQLFVDQGVKRXOGUHDG>%HUJPDQQ6FKDHIHU@
.9
/ ⋅=
7DEOH(OHFWULFDOFRQGXFWLYLWLHVσDQG/25(17=QXPEHUV/IRUGLIIHUHQWPHWDOVDWGLIIHUHQW
WHPSHUDWXUHV>%HUJPDQQ6FKDHIHU@
(OHFWULFDOFRQGXFWLYLW\V>:FP@
/25(17=QXPEHUOV7>9.@
7HPSHUDWXUH>.@
6LOYHU
&RSSHU
*ROG
$OXPLQXP
=LQF
1LFNHO
3ODWLQXP
/HDG
7DEOHVKRZVWKHYDOLGLW\RIWKH:)/IRUKLJKHU!.WHPSHUDWXUHVDOWKRXJKWKHHOHFWULFDO
FRQGXFWLYLW\YDOXHVDUHGLIIHULQJLQWKHUDQJHRI8QIRUWXQDWHO\WKHYDOXHVIRUWKH/25(17=
QXPEHUDUHQRWH[DFWWKHVDPHDVWKHWKHRUHWLFDOYDOXHZKLFKOHDGVWRDXQFHUWDLQW\ZKLOHXVLQJ
WKH:)/IRUGLIIHUHQWPDWHULDOV
8QVXUSULVLQJO\DVWKH:)/ZDVGHULYHGXQGHURPLVVLRQRIWKHODWWLFHRUSKRQRQFRPSRQHQWRI
FRQGXFWLRQZKLFKLVGRPLQDQWDWORZWHPSHUDWXUHV7DEOHVKRZVWKHIDLOXUHRIWKH:)/LQWKH
ORZWHPSHUDWXUHUDQJH
&KDSWHU
6XUYH\RIPHWKRGV
&ODVVLILFDWLRQ RI PHWKRGV XVHG WR PHDVXUH WKHUPDOFRQGXFWLYLW\DQGGLIIXVLYLW\RIPHWDOV
0RVW RI WKH WHFKQLTXHV XVHG WR GHWHUPLQH WKHUPDO FRQGXFWLYLW\ DQG WKHUPDO GLIIXVLYLW\ FDQ EH
FODVVLILHG LQWR VWHDG\ VWDWH QRQVWHDG\ VWDWH DQG WUDQVLHQW WHFKQLTXHV HYHQ WKRXJK WKLV
FODVVLILFDWLRQ LVQRW DOZD\V HDV\ DQGFOHDU(VSHFLDOO\ WKHGLIIHUHQFHVEHWZHHQQRQVWHDG\VWDWH
DQGWUDQVLHQWWHFKQLTXHVDUHYHU\VPDOO
• 6WHDG\ VWDWH PHDQV D VWHDG\ WHPSHUDWXUH JUDGLHQW DFURVV WKH ZKROH VSHFLPHQ 7KHVH
WHFKQLTXHV UHTXLUH YHU\ DFFXUDWH WHPSHUDWXUH FRQWURO WKURXJKRXW WR PLQLPL]H FRQYHFWLRQ
7KLV EHFRPHV SURJUHVVLYHO\ PRUH GLIILFXOW DV WKH WHPSHUDWXUH LQFUHDVHV DQG FRQVHTXHQWO\
WKHVHPHWKRGVKDYHPRVWO\EHHQXVHGRQORZPHOWLQJPHWDOVVXFKDVWLQDQGOHDG
• 1RQVWHDG\VWDWHWHFKQLTXHVDQGDVZHOOWUDQVLHQWWHFKQLTXHVKDYHEHHQXVHGZLWKDYLHZWR
FRPSOHWLQJWKHH[SHULPHQWVEHIRUHWKHRQVHWRIFRQYHFWLRQ,QQRQVWHDG\VWDWHH[SHULPHQWV
WKLV LV DFFRPSOLVKHG E\ XVLQJ YHU\ KLJK KHDWLQJ UDWHV XS WR .V DQG DERYH VR WKH
GXUDWLRQRIH[SHULPHQWVIRU WKHOLTXLGSKDVHLVVHFRQG7KHPHWKRGVVXPPHGXSLQWR
WKLV FDWHJRU\ DUH KLVWRULFDOO\ WKH ILUVW RQHV WR DEDQGRQ WKHZHOO NQRZQ HQYLURQPHQW RI WKH
VWHDG\ VWDWH PHDVXUHPHQWV EXW QRQVWHDG\ VWDWH H[SHULPHQWV EHFDPH PRUH DQG PRUH OHVV
LPSRUWDQWDVWLPHZHQWRQ7KHVHGD\VWUDQVLHQWWHFKQLTXHVDQGPHWKRGVDUHDPRUHSRZHUIXO
DQGUHOLDEOHWRROIRUG\QDPLFPHDVXUHPHQWV
• 7UDQVLHQWPHWKRGVRQOLTXLGVKDYHLQGLFDWHGWKDWFRQYHFWLRQRFFXUVDIWHUFDVHFRQGEXWWKH
WHPSHUDWXUH GLIIHUHQFHV LQ WKH WUDQVLHQW WHFKQLTXHV DUHRI WKHRUGHURI. FRPSDUHGZLWK
!.LQWKHQRQVWHDG\VWDWHH[SHULPHQWV7KHVHODUJHWHPSHUDWXUHJUDGLHQWVPD\JLYHULVH
WR FRQYHFWLRQDO IORZV GXH WR EXR\DQF\ DQG WKHUPRFDSLOODU\ IRUFHV 7KXV FRQYHFWLRQDO
FRQWULEXWLRQV WR WKH WKHUPDO FRQGXFWLYLW\ FDQ QRW EH UXOHG RXW LQ WKHVH QRQVWHDG\ VWDWH
H[SHULPHQWVLQGHHGWKHUHDUHVRPHFDVHVLH)HZKHUHWKLVDSSHDUVWRKDYHRFFXUHG$VD
PDWWHU RI IDFWV WUDQVLHQW PHWKRGV PRUH RU OHVV KDYH UHSODFHG QRQVWHDG\ VWDWH WHFKQLTXHV
EHFDXVHRIWKHVPDOOHUWHPSHUDWXUHJUDGLHQWVDQGWKHEHWWHUUHVXOWV
7UDQVLHQW WHFKQLTXHV KDYH EHFRPHZLGHO\ XVHG IRUPHDVXUHPHQWV RQ RUJDQLF OLTXLGV VLQFH
WKH PHDVXUHPHQW FDQ EH FDUULHG RXW UDSLGO\ LQ RUGHU WR PLQLPL]H FRQYHFWLRQ 7KHVH
WHFKQLTXHV DSSHDU WR KDYH D GLVWLQFW DGYDQWDJH EXW PD\ EH OLPLWHG LQ WKHLU DSSOLFDWLRQ WR
WHPSHUDWXUHV RI OHVV WKDQ . GXH WR WKH IDFW WKDW L LQVXODWRUV EHFRPH HOHFWULFDO
FRQGXFWRUV DW KLJK WHPSHUDWXUHV DQG LL UHDFWLRQVPD\RFFXUEHWZHHQ WKH OLTXLGPHWDODQG
WKHFRDWLQJDWKLJK WHPSHUDWXUHEHFDXVHPRVWPHWDOVEHFRPHYHU\UHDFWLYHDVWKH\EHFRPH
OLTXLG
0RVW RI WKH IROORZLQJ WHFKQLTXHV FDQ EH DSSOLHG WR PHDVXUHPHQWV RQ VROLGV DV ZHOO DV RQ
OLTXLGVZKHUHDVVRPHWHFKQLTXHVRUDSSDUDWXVDUHVSHFLDOO\GHVLJQHGMXVWIRUPHDVXUHPHQWVRQ
VROLGVRUOLTXLGV,IWKLVDSSOLHVWRDPHWKRGDVHSDUDWHDQQRWDWLRQZLOOEHPDGH
6WHDG\VWDWHWHFKQLTXHV7UDGLWLRQDOFODVVLILFDWLRQGLVWLQJXLVKHVIRXUDEVROXWHVWHDG\VWDWHWHFKQLTXHVIRUPHDVXULQJD[LDO
KHDWIORZUDGLDOKHDWIORZJXDUGHGKRWSODWHDQGGLUHFWHOHFWULFDOKHDWLQJ
$[LDOKHDWIORZPHWKRG
,QWKHD[LDOKHDWIORZPHWKRGDNQRZQWKHUPDOIOX[TLVDSSOLHGWRRQHHQGRIWKHVDPSOHDQG
UHPRYHGDWWKHRWKHUHQGE\DKHDWVLQN
)LJ6FKHPDWLFUHSUHVHQWDWLRQRIWKHD[LDOKHDWIORZPHWKRG
7KHUPDOFRQGXFWLYLW\FDQEHFDOFXODWHGE\WKHIROORZLQJHTXDWLRQ
7]
$T
∆∆⋅=λ
ZKHUHTLVWKHKHDWIOX[WUDYHUVLQJWKURXJKWKHVSHFLPHQRIFURVVVHFWLRQDODUHD$DQG∆7∆]LV
WKHFRQVWDQWWHPSHUDWXUHJUDGLHQWDORQJWKHVSHFLPHQXVXDOO\GHWHUPLQHGIURPWKHWHPSHUDWXUHV
7 DQG7 ∆7 7] 7] RI VHQVRUV ORFDWHG DW ] DQG ] 7KH HYDOXDWLRQ RIλ WKHUHIRUH
LQYROYHVWKHIROORZLQJ
7KHGHWHUPLQDWLRQRIWKHJHRPHWULFDOSDUDPHWHUV$DQG∆] ]]
$VVXUDQFH WKDW WKH KHDW IORZ SDWWHUQ LV LQGHHG XQLGLUHFWLRQDO 7KLV XVXDOO\ LQYROYHV ERWK
FDUHIXOGHVLJQRIH[SHULPHQWDOFRQILJXUDWLRQVDQGDFWLYHWHPSHUDWXUHPDWFKLQJRIYDULRXV
FRPSRQHQWVRIWKHDSSDUDWXVGXULQJWKHH[SHULPHQW
&RPSOLDQFHZLWKWKHUHTXLUHPHQWVRIVWHDG\VWDWHFRQGLWLRQV
T T∆]
∆7
$
0HDVXUHPHQW RI T XVXDOO\ JHQHUDWHG LQ VRPH KHDWHU DWWDFKHG WR RU HPEHGGHG LQ WKH
VSHFLPHQ 7KLV PHDVXUHPHQW LWVHOI LV QRUPDOO\ D VWDQGDUG RSHUDWLRQ EXW GLIILFXOWLHV DUH
HQFRXQWHUHG LQ HQVXULQJ WKDW DOO WKH PHDVXUHG SRZHU KHDW IOX[ LV UHVSRQVLEOH IRU WKH
PHDVXUHGWHPSHUDWXUHJUDGLHQW∆7∆]
7KHPHDVXUHPHQWRIWKHWHPSHUDWXUHRIWKHWZRRULQVRPHPHWKRGVPRUHVHQVRUV7DQG
7 $V ZLWK WKH SRZHU PHDVXUHPHQW WKLV E\ LWVHOI LV DJDLQ VWUDLJKWIRUZDUG KRZHYHU
HQVXULQJ WKDW WKHPHDVXUHG VHQVRU WHPSHUDWXUH FRUUHVSRQGV WR WKH VSHFLPHQ WHPSHUDWXUH DW
WKHSUHVXPHGORFDWLRQV]DQG]LVQRWWULYLDO
7KHVHILYHSRLQWVDUHFRPPRQWRDOOXQLGLUHFWLRQDOVWHDG\VWDWHPHWKRGVDOWKRXJKWKHLUUHODWLYH
LPSRUWDQFHPD\YDU\IURPWHFKQLTXHWRWHFKQLTXH,QJHQHUDODQGDUHVWUDLJKWIRUZDUGWKH
RWKHUWKUHHWURXEOHVRPH)RUWKHD[LDOKHDWIORZWHFKQLTXHLVWKHPRVWLPSRUWDQWIDFWRUDWORZ
WHPSHUDWXUHVDQGDWKLJKWHPSHUDWXUHV
7KLV SULQFLSDO SUREOHP DW KLJK WHPSHUDWXUHV LV UHODWHG WR WKH SUHYHQWLRQ RI KHDW ORVVHV E\
FRQYHFWLRQDQGUDGLDWLRQLWLVXVXDOO\RYHUFRPHE\XVLQJLQVXODWLRQPDWHULDOVDQGKHDWHGJXDUG
VKLHOGV%\XVLQJLQVXODWLRQPDWHULDOVRUKHDWHGJXDUGVKLHOGV(TKDVWREHUHDUUDQJHG
−
∆∆= FF$7]T
$λλ
7KHVXEVFULSWFGHQRWHVSURSHUWLHVRIWKHVXUURXQGLQJFHOO
7KHELJJHVWDGYDQWDJHRIWKHD[LDOKHDWIORZLVWKHVLPSOHJHRPHWU\DQGWKHPRUHRUOHVVVLPSOH
VHWXS7KLVPHWKRGKDVEHHQXVHG WRGHWHUPLQH WKH WKHUPDOFRQGXFWLYLW\QRWRQO\RIVROLGVEXW
DOVR RI YDULRXV OLTXLG PHWDOV ZLWK ORZ PHOWLQJ SRLQWV LQFOXGLQJ +J 3E ,Q DQG *D
>13/5HSRUW@
5DGLDOKHDWIORZPHWKRG
)RXULHUV ODZIRUVWHDG\VWDWHKHDW WUDQVIHUKROGV UHJDUGOHVVZKHWKHUWKHWHPSHUDWXUHJUDGLHQW LV
OLQHDURUF\OLQGULFDO
)RXULHUVODZIRUGLPHQVLRQUHDGV
G[G7
T ⋅−= λ
)RXULHUVODZFDQEHWUDQVODWHGWRDF\OLQGULFDOJHRPHWU\E\UHFRJQL]LQJWKDWWKHVXUIDFHDUHDRID
F\OLQGHULV⋅π⋅U⋅/7KHKHDWIORZVIURPWKHLQQHUUWRWKHRXWHUUUDGLXVDWWHPSHUDWXUHV7
DQG 7 UHVSHFWLYHO\ %\ UHDUUDQJLQJ (T XQGHU FRQVLGHUDWLRQ RI WKHVH IDFWV RQH JHWV WKH
IROORZLQJ
( )
OQ
77
UU
/T
−
⋅=π
λ
)LJ6FKHPDWLF RI D IXQGDPHQWDO UDGLDO KHDW IORZ DSSDUDWXV 7KH WHPSHUDWXUH VHQVRU SRVLWLRQV DUH
GHQRWHGE\•>0DJOLü@
)LJVKRZVWKHVFKHPDWLFRIDQDSSDUDWXVXVHGIRUUDGLDOKHDWIORZPHDVXUHPHQWV7KHWKHUPDO
FRQGXFWLYLW\LVFDOFXODWHGE\XVLQJ(TZKHUHT/LVWKHKHDWIOX[SHUXQLWOHQJWKIURPWKH
FRUHKHDWHURYHUWKHVSHFLPHQPLGSODQHDQG7QLVWKHWHPSHUDWXUHDWUDGLXVUQ
7KLV FRQILJXUDWLRQZLOO \LHOG DFFXUDWH GDWD LI WKH UDWLR RI VSHFLPHQ OHQJWK / WR GLDPHWHU G LV
VXIILFLHQWO\ODUJHWRHQVXUHWKDWDOOKHDWIORZDWWKHVSHFLPHQPLGSODQHLVUDGLDO
7KH JUHDWHVW DGYDQWDJH RI D UDGLDO KHDW IORZ DSSDUDWXV LV LWV KLJK DFFXUDF\ DW HOHYDWHG
WHPSHUDWXUHV$ VHFRQGDU\ DGYDQWDJH DULVHV IURP WKH IDFW WKDW WKHVH V\VWHPV FDQ EH RSHUDWHG
ZLWKUHODWLYHO\VLPSOHLQVWUXPHQWDWLRQ$QDGGLWLRQDODGYDQWDJHLVLWVDSSOLFDELOLW\RQVSHFLPHQV
ZLWKYHU\KLJKDQGYHU\ORZWKHUPDOFRQGXFWLYLWLHV
7KHJUHDWHVWGLVDGYDQWDJHRIWKHUDGLDOKHDWIORZWHFKQLTXHLVWKHODUJHVSHFLPHQVL]HZKLFKFDQ
OHDGWRXQGHVLUDEOHKLJKVSHFLPHQFRVWDVVHPEO\GLIILFXOWLHVDQGVORZRSHUDWLRQ
7KH UDGLDO KHDW IORZPHWKRG FDQ DOVR EH DGDSWHG IRUPHDVXUHPHQWVZLWKPROWHQPHWDOV 7KLV
PHWKRGLVVRPHWLPHVFDOOHGFRQFHQWULFF\OLQGHUPHWKRGLQVWHDGRIUDGLDOKHDWIORZPHWKRG
)LJ6FKHPDWLFGLDJUDPRIWKHFRQFHQWULFF\OLQGHUPHWKRG
7KH DGDSWHG DSSDUDWXV FRQVLVWV RI WKH WZRFRQFHQWULF F\OLQGHUVZLWK DJDSEHWZHHQ WKHP7KH
PROWHQ PHWDO LV SODFHG LQ WKH DQQXOXV EHWZHHQ WKH F\OLQGHUV DQG WKH NQRZQ KHDW IOX[ T LV
VXSSOLHG WR WKH LQQHU F\OLQGHU DQG WKH WHPSHUDWXUH GLIIHUHQFH∆7EHWZHHQ WKH WZRF\OLQGHUV LV
PRQLWRUHG
(QG&DS
7KHUPRFRXSOH:HOOV
+HDWHU:HOO
2XWHU&\OLQGHU
*DS
,QQHU&\OLQGHU
(QG&DS
$V RQH FDQ VHH WKH UDGLDO KHDW IORZ PHWKRG LV DGDSWHG IRU PROWHQ PHWDOV E\ SURGXFLQJ D
FRQWDLQHUIRU WKHOLTXLGEXW WKHUHVWRIWKHPHDVXUHPHQWVWD\VH[DFWO\WKHVDPH8QVXUSULVLQJO\
DV WKHWHFKQLTXHHTXDOV WKHUDGLDOKHDWIORZPHWKRGWKHWKHUPDOFRQGXFWLYLW\LVDOVRFDOFXODWHG
E\(T$VDVRUWRIKHUHGLW\WKHFRQFHQWULFF\OLQGHUPHWKRGVXIIHUVIURPWKHVDPHSUREOHPV
VXFKDVDVVHPEO\GLIILFXOWLHVRUVORZRSHUDWLRQDVLWVRULJLQ
'LUHFWKHDWLQJPHWKRG
7KHUH LV D JHQHUDO FODVV RI WKHUPRSK\VLFDO GHWHUPLQDWLRQV ZKLFK XWLOL]H -RXOHDQ KHDWLQJ
JHQHUDWHG E\ HOHFWULFDO FXUUHQW IORZLQJ WKURXJK WKH VDPSOH WR FRQWURO WKH VDPSOH WHPSHUDWXUH
JUDGLHQWVGXULQJWKHSURSHUW\PHDVXUHPHQWV7KLVFODVVLVFRPELQHGDVGLUHFWHOHFWULFDOKHDWLQJ
PHWKRGV 7KH\ DUH GLVWLQJXLVKHG E\ WKH ODFN RI H[WHUQDO IXUQDFHV WR FRQWURO WKH VSHFLPHQ
WHPSHUDWXUH7KLVLQWXUQJUHDWO\VKRUWHQVWKHWLPHWRDWWDLQDQHTXLOLEULXPWHPSHUDWXUHDQGHDVLO\
SHUPLWV WUDQVLHQWPHDVXUHPHQWV7KHVHPHWKRGV DUH OLPLWHG WR UHDVRQDEOHHOHFWULFDOFRQGXFWRUV
EXWDOORZWKHXVHRIGLIIHUHQWVSHFLPHQIRUPVVXFKDVZLUHVURGVWXEHVRUVKHHWV
7KHJUHDWHVWDGYDQWDJHRIWKLVPHWKRGH[FHSWRIWKHODFNRIDQH[WHUQDOIXUQDFHLVWKHRSSRUWXQLW\
WR\LHOGPRUHWKDQRQHSURSHUW\E\PHDVXULQJVHYHUDOSURSHUWLHVVLPXOWDQHRXVO\
7KHPHDVXUHPHQWVRI WKLVZRUNZHUHSHUIRUPHGZLWKDGLUHFWHOHFWULFKHDWLQJVHWXSEXWZLWKD
G\QDPLFPHDVXUHPHQWWHFKQLTXHLQVWHDGRIWKHVWHDG\VWDWHPHDVXUHPHQW6HHWKHSXOVHKHDWLQJ
VHFWLRQDWWKHHQGRIWKLVFKDSWHUIRUPRUHVSHFLILFGHWDLOVRQWKLVPHWKRG
*XDUGHGKRWSODWHPHWKRG
7KH JXDUGHG KRW SODWH PHWKRG LV D VWHDG\ VWDWH D[LDO KHDW IORZ PHDVXUHPHQW RI WKHUPDO
FRQGXFWLYLW\IRUGLVNVKDSHGVSHFLPHQV7KHKHDWIORZLVPHDVXUHGLQDVLPLODUZD\DVWKHUDGLDO
KHDWIORZDQGWKHKRWZLUHWHFKQLTXHWKHUPDOGLVVLSDWLRQGXHWR-RXOHDQ,⋅5KHDWLQJRIDFHQWUDO
KHDWHU7KLV WHFKQLTXH LVJHQHUDOO\ UHJDUGHG WREH WKHPRVWDFFXUDWHPHDVXUHPHQW WHFKQLTXH LQ
WKHILHOGRIVWHDG\VWDWHH[SHULPHQWV
7KHUHDUH WZRGLIIHUHQWDSSDUDWXV IRU WKLVPHWKRG7KHILUVWDQGPRUHFRPPRQRQHLV WKHWZR
VSHFLPHQ VHWXS WKH VHFRQGRQH LV WKH VLQJOHVSHFLPHQ VHWXS7KH H[SHULPHQWDO FRQILJXUDWLRQV
IRUWKHWHFKQLTXHDUHVKRZQLQ)LJXUHVDE
D E
)LJ*HQHUDOIHDWXUHVRIWZRVSHFLPHQDQGVLQJOHVSHFLPHQKRWSODWHDSSDUDWXV
D WZRVSHFLPHQDSSDUDWXV
E VLQJOHVSHFLPHQDSSDUDWXV
.H\$PHWHULQJDUHDKHDWHU%PHWHULQJDUHDVXUIDFHSODWHV&JXDUGKHDWHU'JXDUGKHDWHU
VXUIDFH SODWHV ( FRROLQJ XQLW (V FRROLQJ XQLW VXUIDFH SODWHV ) GLIIHUHQWLDO WKHUPRFRXSOHV
*KHDWLQJXQLWVXUIDFHWKHUPRFRXSOHV+FRROLQJXQLWVXUIDFHWKHUPRFRXSOHV,WHVWVSHFLPHQ
/JXDUGSODWH0JXDUGSODWHLQVXODWLRQ1JXDUGSODWHGLIIHUHQWLDOWKHUPRFRXSOHV
,Q WKH FDVHRI WKH WZR VSHFLPHQVPHWKRG)LJD WKH WHVW VSHFLPHQVDUH V\PPHWULFDOO\SODFHG
DERYHDQGEHORZWKHPDLQKHDWHUDQGWKHWHPSHUDWXUHGURSDFURVVWKHVSHFLPHQV∆7LVPHDVXUHG
E\ WZR WKHUPRFRXSOHV LPPHUVHG LQ HDFK VSHFLPHQ VSDFHGGLVWDQFH/DSDUW$VVXPLQJSHUIHFW
V\PPHWU\LQGLPHQVLRQVWKHUPRFRXSOHMXQFWLRQSODFHPHQWDQGKHDWIORZWKURXJKWKHXSSHUDQG
ORZHUVSHFLPHQRQHJHWV
7$T/∆
=
λ
,QRUGHUWRJXDUDQWHHWKDWWKHKHDWIORZIURPWKHPHWHUHGDUHDLVRQHGLPHQVLRQDOWKDWPHDQVLW
IORZV VWULFWO\ WKURXJK WKH VSHFLPHQV DQG QRW RXW RI WKH VLGHZDOOV RI WKHPDLQ KHDWHU DQG WKH
VSHFLPHQVVHYHUDOJXDUGKHDWHUVDQGJXDUGSODWHVZLWKLQVXODWLRQDUHXVHG
*
+
)
( (
(6 (6
$
, ,
& ''
& ''
% %
*
+
1
)
(
,
/$ 0
&''
% %
,Q WKH FDVH RI WKH VLQJOH VSHFLPHQPHWKRG)LJE RQH RI WKH FROG SODWHV LV UHPRYHGDQG WKH
DX[LOLDU\ KHDWHU RQ WKDW VLGH LV KHDWHG WRPDWFK WKH WHPSHUDWXUH RI WKHPHWHUHG DUHD6LQFHQR
WHPSHUDWXUH JUDGLHQW H[LVWV LQ WKDW GLUHFWLRQ KHDW JHQHUDWHG IURP WKH PHWHUHG DUHD IORZV
XQLD[LDOO\ WKURXJK WKH VLQJOH VSHFLPHQ %\ ORVLQJ WKH PXOWLSOLFLW\ IDFWRU IURP (T WKH
WKHUPDOFRQGXFWLYLW\LVFDOFXODWHGE\
7$T/∆
=λ
,QVRPHSXEOLFDWLRQVDVLPLODUWHFKQLTXHLVPHQWLRQHGWRSHUIRUPPHDVXUHPHQWVRQOLTXLGPHWDOV
FDOOHGSDUDOOHOSODWHPHWKRG7KLVPHWKRGLVPRVWO\WKHVDPHDVWKHVLQJOHVSHFLPHQJXDUGHGKRW
SODWHPHWKRGDQGXVHVDOVR(TWRFDOFXODWHWKHUPDOFRQGXFWLYLW\7KHRQO\PDMRUGLIIHUHQFH
LQ WKH VHWXS DUH WKH H[SDQVLRQ YROXPHV XVHG WR FRPSHQVDWH WKHUPDO H[SDQVLRQV WKURXJK WKH
PHDVXUHPHQWSURFHVV
)LJ6FKHPDWLFGLDJUDPRISDUDOOHOSODWHDSSDUDWXV
&DORULPHWHUPHWKRG
$Q DGGLWLRQDOPHWKRG WR WKH IRXU WUDGLWLRQDO WHFKQLTXHV LV WKH FDORULPHWHUPHWKRG 7KLV LV DQ
ROGHU WHFKQLTXH ZKLFK LV D GLUHFW PHDVXUHPHQW RI WKH )RXULHUV ODZ ,W LV RQH RI WKH $670
$PHULFDQ 6RFLHW\ IRU 7HVWLQJ DQG 0DWHULDOV VWDQGDUG WHVWV IRU WKHUPDO FRQGXFWLYLW\ 7KH
H[SHULPHQWDOFRQILJXUDWLRQLVVKRZQEHORZ
VWDLQOHVVVWHHO
VWDLQOHVVVWHHO
WKHUPRFRXSOHV
WLQ
H[SDQVLRQYROXPH
)LJ 6FKHPDWLF RI WKH FDORULPHWHU PHWKRG RI PHDVXULQJ WKHUPDO FRQGXFWLYLW\ 6SHFLPHQ VL]HV DUH
DSSUR[LPDWHO\WKUHHEULFNVRIGLPHQVLRQ[[FP>6SH\HU@
$6L&VODEDFWV WRGLVWULEXWHWHPSHUDWXUHJUDGLHQWVIURPWKHKHDWVRXUFHXVXDOO\6L&RU0R6L
KHDWLQJHOHPHQWV7KHWHVWVSHFLPHQLVERUGHUHGE\WZRLQVXODWLQJJXDUGEULFNVDQGWKHVHJXDUG
EULFNV DV ZHOO DV WKH VSHFLPHQ DUH LQ WKHUPDO FRQWDFW ZLWK D ZDWHUFRROHG &RSSHU EDVH 7KH
&RSSHU EDVH LV PDGH XS RI VHYHUDO VHSDUDWHG ZDWHU FRROLQJ V\VWHPV $ FHQWHU V\VWHP LV WKH
FDORULPHWHUZKLFK LV VXUURXQGHGE\ WKH LQQHU DQGRXWHUJXDUGV7KH FDORULPHWHUKDVD VPDOOHU
DUHDWKDQWKHWHVWEULFN7KHFRQILJXUDWLRQLVGHVLJQHGVRWKDWWKHUHDUHQRWHPSHUDWXUHJUDGLHQWV
LQWKHKRUL]RQWDOSODQHVDORQJWKHKHDWIORZSDWKWRWKHFDORULPHWHU7KXVWKHKHDWIORZLQWRWKH
FDORULPHWHULVRQHGLPHQVLRQDO
7ZR WKHUPRFRXSOHV VHSDUDWHG E\ GLVWDQFH / DUH LPEHGGHG LQ WKH WHVW VSHFLPHQ RQH GLUHFWO\
DERYHWKHRWKHUZKHUHE\WKHWHPSHUDWXUHGURS77EHWZHHQWKHPLVPHDVXUHG$GLIIHUHQWLDO
WKHUPRFRXSOHPHDVXUHVWKHWHPSHUDWXUHULVHRIWKHH[LWZDWHURIWKHFDORULPHWHUDVFRPSDUHGWR
LWVHQWUDQFHWHPSHUDWXUH7KHPDVVIORZUDWHRIZDWHULQWRWKHFDORULPHWHULVPRQLWRUHGVRWKDW
RYHU D VSHFLILF WLPH LQWHUYDO∆W WKH WRWDO KHDW DEVRUEHGE\ WKH FDORULPHWHUPD\EH FDOFXODWHG
NQRZLQJ WKH VSHFLILF KHDW FS RIZDWHU'LYLGLQJ E\ WKH WLPH LQWHUYDOZLOO JLYH WKH UDWHRIKHDW
IORZ LQWR WKH FDORULPHWHU XQGHU VWHDG\ VWDWH FRQGLWLRQV +HQFH WKHUPDO FRQGXFWLYLW\ PD\ EH
GHWHUPLQHGE\DUHDUUDQJHPHQWRI)RXULHUVHTXDWLRQ
( ) 77$
/GWGT
−=λ
ZKHUH $ LV WKH FURVV VHFWLRQDO DUHD RI WKH FDORULPHWHU DQG / WKH GLVWDQFH EHWZHHQ WKH WZR
HPEHGGHGWKHUPRFRXSOHVMXQFWLRQV6LQFHWKHKHDWIORZLVFRQVWDQWWKURXJKRXWDYHUWLFDOVHFWLRQ
RIWKHVSHFLPHQVWHDG\VWDWHFRQGLWLRQVWKHUPRFRXSOHMXQFWLRQVPHDVXULQJ7DQG7FDQKDYH
YHUWLFDOSRVLWLRQVDQ\ZKHUHDORQJWKHVSHFLPHQZKLFKLVRQHRIWKHDGYDQWDJHVRIWKLVPHWKRG
1RQVWHDG\VWDWHWHFKQLTXHV
%RWK PHWKRGV GHVFULEHG LQ WKLV VHFWLRQ DUH QRW YHU\ FRPPRQ EHFDXVH RWKHU PHDVXUHPHQWV
LHWUDQVLHQWPHWKRGVDUHHDVLHUWRFDUU\RXW1HYHUWKHOHVVWKH\DUHLQFOXGHGWRGHPRQVWUDWHWKH
RYHUDOO SULQFLSOHV RI QRQVWHDG\ VWDWH WHFKQLTXHV DV WKH\ DUH FKDUDFWHUL]LQJ IRU WKLV JURXS RI
WHFKQLTXHV
5DGLDOWHPSHUDWXUHZDYH57:WHFKQLTXH
,QWKLVPHWKRGWKHVDPSOHLVXVXDOO\F\OLQGULFDOO\VKDSHGDQGDPRGXODWHGKHDWVXSSO\LVDSSOLHG
DORQJWKHFHQWHURIWKHVSHFLPHQ7KHYDULDWLRQVLQWHPSHUDWXUHDUHPRQLWRUHGRQWKHRXWVLGHRI
WKHVDPSOH7KHUHLVDSKDVHODJEHWZHHQWKHLQSXWDQGWKHRXWSXWDQGWKLVLVUHODWHGWRWKHUPDO
GLIIXVLYLW\ D RI WKH VDPSOH 7KHUPDO GLIIXVLYLWLHV FDQ EH GHULYHG IURP WKH DPSOLWXGH RI
WHPSHUDWXUHRVFLOODWLRQV DQG IURP WKHSKDVHGLIIHUHQFHVEHWZHHQ WKHP WKHUPDO FRQGXFWLYLW\ LV
FDOFXODWHGYLDWKH:)/DQGWKHYDOXHVFDOFXODWHGZLWKGDWDIURPWKLVPHWKRGZHUHIRXQGWREHLQ
JRRGDJUHHPHQW>13/5HSRUW@
3ODQHWHPSHUDWXUHZDYH37:WHFKQLTXH
7KLVPHWKRGXVHVGLVFVKDSHGVSHFLPHQVW\SLFDOO\PPWKLFNDQGSODQHWHPSHUDWXUHZDYHV
DUH GHULYHG E\ ERPEDUGLQJ WKH VSHFLPHQ ZLWK D KDUPRQLFDOO\PRGXODWHG HOHFWURQ EHDP DQG
PRQLWRULQJ WKH SKDVH FKDQJH RI WKH WHPSHUDWXUH WUDQVLHQW UHFRUGHG RQ WKH RWKHU IDFH RI WKH
VSHFLPHQ0HDVXUHPHQWV FDQ EH REWDLQHG HLWKHU DW FRQVWDQW WHPSHUDWXUHV RU G\QDPLFDOO\ZLWK
KHDWLQJ UDWHV XS WR .⋅VHF 7KH UHVXOWVRI WKH WZRH[SHULPHQWVZHUH DOVR IRXQG WREH LQ
JRRG DJUHHPHQW )RU PHDVXUHPHQWV LQ WKH OLTXLG SKDVH RQO\ D VPDOO SRUWLRQ RI WKH GLVF LV
DOORZHG WRPHOW DQG UHDGLQJV DUH REWDLQHG IRU WHPSHUDWXUHV XS WR . DERYH WKH OLTXLGXV
7KHUPDOGLIIXVLYLWLHVIRUWKHOLTXLGSKDVHRIKLJKPHOWLQJPHWDOVVXFKDV0R7L,U5K3WDQG
3G ZHUH REWDLQHG ZLWK WKLV PHWKRG >13/ UHSRUW @ ,W FRXOG EH DUJXHG WKDW FRQYHFWLRQDO
FRQWULEXWLRQVZRXOGWHQGWREHVPDOOGXHWRVKRUWGXUDWLRQRIH[SHULPHQWVLQWKHOLTXLGVWDWHEXW
DVVXPSWLRQV PD\ QRW EH YDOLG VLQFH FLUFXODWLRQ IORZV FRXOG DULVH IURP EXR\DQF\ DQG
WKHUPRFDSLOODU\ IRUFHV FDXVHG E\ WKH ODUJH WHPSHUDWXUH JUDGLHQWV 7KLV PHWKRG LV VRPHWLPHV
UHIHUUHGWRDVWKHPRGXODWHGEHDPWHFKQLTXH
7UDQVLHQWWHFKQLTXHV
7KH WUDQVLHQW WHFKQLTXHVDUHWKHKLVWRULFDOO\QHZHVWPHDVXUHPHQWPHWKRGV7KH\DUHHDVLHUDQG
IDVWHUWRFDUU\RXWWKDQWKHQRQVWHDG\VWDWHPHWKRGVDQGHYHQSURYLGHPRUHDFFXUDF\
7UDQVLHQWKRWZLUHPHWKRG
7KH KRW ZLUH WKHUPDO FRQGXFWLYLW\ PHWKRG LQYROYHV WKH SODFHPHQW RI D WKLQ UHIUDFWRU\ ZLUH
EHWZHHQWZRLGHQWLFDOUHIUDFWRU\SODWHVXQGHULQYHVWLJDWLRQ+LVWRULFDOO\WKLVLVDQDSSOLFDWLRQRI
DKRWZLUHPHWKRGXVHGLQWKHGHWHUPLQDWLRQRIWKHUPDOFRQGXFWLYLWLHVRIOLTXLGVDQGJDVHV
$FRQVWDQWHOHFWULFDOSRZHULVGLVVLSDWHGE\WKHZLUHDVKHDWLQWRWKHVXUURXQGLQJUHIUDFWRU\DQG
WKH WHPSHUDWXUH RI WKHZLUH LVPRQLWRUHG ,I WKH UHIUDFWRU\ LV KLJKO\ WKHUPDOO\ FRQGXFWLQJ WKH
ZLUHWHPSHUDWXUHZLOOEHORZHUFRPSDUHGWRWKHFDVHZKHQWKHUHIUDFWRU\LVKLJKO\LQVXOWLQJ
)LJ6FKHPDWLFRIWKHKRWZLUHWKHUPDOFRQGXFWLYLW\WHVW5HIUDFWRU\EULFNVZRXOGEHRIWKHVDPHVL]H
DVLQ)LJ>6SH\HU@
7KHWKHRUHWLFDOPRGHODVVXPHVDOLQHDUKHDWVRXUFHGLVVLSDWLQJKHDWUDGLDOO\LQWRDQLQILQLWHVROLG
LQLWLDOO\ DW XQLIRUP WHPSHUDWXUH 7KH IXQGDPHQWDO KHDW FRQGXFWLRQ HTXDWLRQ LQ F\OLQGULFDO
FRRUGLQDWHVLVVROYHGZLWKWKHLQLWLDOFRQGLWLRQWKDWWKHWHPSHUDWXUHRIWKHZLUHDW]HURWLPHLV7
DQG DIWHU VRPH WLPH W ERXQGDU\ FRQGLWLRQV DW LQILQLWH UDGLDO GLVWDQFH IURP WKH ZLUH WKH
WHPSHUDWXUHLVVWLOO7DWDUDGLDOSRVLWLRQZLWKLQWKHUHIUDFWRU\DSSURDFKLQJWKHUDGLXVRIWKH
ZLUHVWHDG\VWDWHUDGLDOKHDWWUDQVIHURFFXUV7KHVROXWLRQREWDLQHGE\/$3/$&(WUDQVIRUPVLV
( )
⋅=∆
γπλ H[S
OQ
UDWT
WU7
7KHUPDOFRQGXFWLYLW\LVJLYHQE\WKLVHTXDWLRQZKHUHTLVWKHKHDWLQSXWSHUXQLWOHQJWKRI
ZLUHULVWKHUDGLXVRIWKHZLUHDLVWKHWKHUPDOGLIIXVLYLW\RIWKHPDWHULDOXQGHULQYHVWLJDWLRQγ
LV(8/(5VFRQVWDQWγ >%URQVWHLQ@DQGWLVWLPH7KHWHPSHUDWXUHRIWKHZLUH
LV DVVXPHG WR EH FRQVWDQW WKURXJKRXW LWV YROXPH%DVHG RQ WKLV H[SUHVVLRQ D SORW RI∆7U W
YHUVXV OQ WLPH VKRXOG EH D OLQHDU LQFUHDVLQJ IXQFWLRQ ZKHUH WKH WKHUPDO FRQGXFWLYLW\ RI WKH
UHIUDFWRU\ FDQ EH GLUHFWO\ FDOFXODWHG IURP WKH VORSH LI T LV NQRZQ 1RWH WKDW (T RQO\
DSSOLHVZKHQUDW
,QSUDFWLFHRQO\DSRUWLRQRI WKH OQ WLPHWHPSHUDWXUHSORW LV OLQHDU$QRQOLQHDUSRUWLRQDW WKH
VWDUW RI WKH FXUYH LV D UHVXOW RI VWHDG\ VWDWH FRQGLWLRQV QRW LPPHGLDWHO\ EHLQJPHW DW WKHZLUH
VXUIDFH$QGWKHQRQOLQHDUSRUWLRQDIWHUORQJHUWLPHVUHVXOWVIURPWKHUHIUDFWRU\EORFNQRWDFWXDO
EHLQJRILQILQLWHGLPHQVLRQV
7KHUPDOFRQGXFWLYLW\PHDVXUHPHQWVDUHWDNHQDWDVHULHVRILVRWKHUPDOWHPSHUDWXUHVFUHDWHGE\
DQ H[WHUQDO IXUQDFH 7KH IXUQDFH PXVW SURYLGH HQRXJK VWDELOLW\ VR WKDW WKHUH DUH QHJOLJLEOH
WHPSHUDWXUHJUDGLHQWVZLWKLQWKHUHIUDFWRU\EORFNV
7HPSHUDWXUHLVPHDVXUHGYLDDWKHUPRFRXSOHMXQFWLRQZHOGHGWRWKHFHQWHURIWKHKRWZLUH7KH
OHJVRI WKH WKHUPRFRXSOHVH[WHQGSHUSHQGLFXODU LQHLWKHUGLUHFWLRQWRWKHKRWZLUHDQGJURRYHV
PXVW EH FXW LQ WKH UHIUDFWRU\ IRU WKHVH ZLUHV $ GLVDGYDQWDJH RI WKLV WHFKQLTXH LV WKDW WKH
WKHUPRFRXSOHZLUHVPD\DFWDVKHDWVLQNVIRUWKHKRWZLUHZKLFKFDQEHDYRLGHGRUPLQLPL]HG
E\XVLQJWKHUPRFRXSOHZLUHRIPLQLPDOGLDPHWHUDQGDMXQFWLRQEHDGDVVPDOODVSRVVLEOH
,QDQRWKHUFRPPRQO\XVHGFRQILJXUDWLRQRIWKHKRWZLUHPHWKRGWKHZLUHDFWVERWKDVDKHDWLQJ
HOHPHQWDQGDUHVLVWDQFHWKHUPRPHWHU7KLVVSHFLDOFRQILJXUDWLRQH[SDQGVWKHEDVLFPHWKRGDQG
DOORZVWRPHDVXUHPROWHQPHWDOVDQGOLTXLGVZLWKLW(TKROGVIRUDOOGLIIHUHQWW\SHVRIKRW
ZLUH FRQILJXUDWLRQV DQG WKH GHWHUPLQDWLRQ RI WKH WKHUPDO FRQGXFWLYLW\ YLD WKH VORSH RI WKH∆7
YHUVXVOQWLPHSORWVWD\VWKHVDPHWRR6HH)LJXUHIRUDVFKHPDWLFGLDJUDPRIWKLVVHWXS
)LJ6FKHPDWLFGLDJUDPVKRZLQJWKHWUDQVLHQWKRWZLUHPHWKRGIRUOLTXLGV
:KHQWKLVPHWKRGLVDSSOLHGWRHOHFWULFDOO\FRQGXFWLQJPHOWVLWLVQHFHVVDU\WRDSSO\DFRDWLQJWR
WKH ZLUH WR SUHYHQW HOHFWULFDO OHDNDJH LQWR WKH PHOW 9DULRXV LQVXODWLRQ WHFKQLTXHV KDYH EHHQ
HPSOR\HGVXFKDV
• XVLQJDJODVVFDSLOODU\FRQWDLQLQJOLTXLG+JRU*D
• DSSOLFDWLRQRI$O2RURWKHULQVXODWLQJR[LGHOD\HUV
• WKHR[LGDWLRQRIWKHPHWDOZLUHWRSURYLGHDSURWHFWLYHFRDWLQJ
+RZHYHU WKHDSSOLFDWLRQRI WKLVFRQILJXUDWLRQPD\EH UHVWULFWHG WR WHPSHUDWXUHVXS WR.
VLQFHZLWK LQFUHDVLQJ WHPSHUDWXUHV WKH FRDWLQJVEHFRPHSURJUHVVLYHO\ LPRUHFRQGXFWLQJ LL
PRUH YXOQHUDEOH WR FKHPLFDO DWWDFN DQG LLL WKHPLVPDWFK LQ WKHUPDO H[SDQVLRQRIPHWDO DQG
FRDWLQJEHFRPHPRUHSURQRXQFHGDQGFDQOHDGWRVSDOOLQJ
/DVHUIODVKRUSXOVHPHWKRG
7KHODVHUIODVKPHWKRGGLIIHUVIURPWKHRWKHUPHWKRGVGLVFXVVHGDERYHLQWKLVFKDSWHULQVRIDUDV
LW LV D PHWKRG RI PHDVXULQJ WKH WKHUPDO GLIIXVLYLW\ LQVWHDG RI WKH WKHUPDO FRQGXFWLYLW\ 7KH
WKHUPDO FRQGXFWLYLW\PD\EH REWDLQHG IURP WKH WKHUPDO GLIIXVLYLW\ LI WKH VSHFLILFKHDW DQG WKH
GHQVLW\RI WKHPDWHULDO XQGHU LQYHVWLJDWLRQ DUHNQRZQ 6HH WKH&KDSWHU([SHULPHQWDO VHWXS
DQGGDWDHYDOXDWLRQIRUPRUHGHWDLOV
7KHIODVKPHWKRGHQWDLOVDVKRUWSXOVHRIKLJKLQWHQVLW\HQHUJ\DEVRUEHGE\WKHIURQWVXUIDFHRID
VPDOO VSHFLPHQ VKDSHG LQ WKH IRUPRI D GLVN7KH UDGLDQW HQHUJ\ VRXUFH FDQEH D[HQRQ IODVK
ODPSDQHOHFWURQEHDPRUPRVWFRPPRQD ODVHU7KHHQHUJ\SURSDJDWHVGXHWRFRQGXFWLRQ
DQG DWKLJKHU WHPSHUDWXUHV UDGLDWLRQ WRZDUG WKHEDFNVXUIDFHRI WKH VSHFLPHQ%\PRQLWRULQJ
WKHWHPSHUDWXUHULVHRIWKHEDFNIDFHRIWKHVDPSOHWKHUPDOGLIIXVLYLW\FDQEHREWDLQHG
$QXPEHURIVLPSOLI\LQJDVVXPSWLRQVDUHQHHGHGIRUDPDWKHPDWLFDOPRGHOIRUWKLVPHWKRGOLNH
7KHIODVKLVXQLIRUPO\GLVWULEXWHGDFURVVWKHIURQWIDFHDQGDEVRUEHGZLWKLQDWKLQOD\HUUHODWLYH
WRLWVRYHUDOOWKLFNQHVVRUWKHKHDWSURSDJDWHVRQHGLPHQVLRQDOO\WRZDUGWKHEDFNIDFHHWF7KH
ZKROH PDWKHPDWLFDO PRGHO LV H[SODLQHG LQ GLIIHUHQW SXEOLFDWLRQV HJ >5) 6SH\HU 7KHUPDO
DQDO\VLVRIPDWHULDOV@
'XULQJ WKH GHULYDWLRQ RQH REWDLQV WKH ODWHU RQ XVHG UHVXOW WKDW WKH WHPSHUDWXUH WUDQVLHQW DW WKH
EDFN IDFH H[KLELWV DPD[LPXP∆7PD[ DV D FRQVHTXHQFHRI UDGLDWLRQ ORVVHV$VVXPLQJ WKDW WKH
DVVXPSWLRQV RI WKH PRGHO KDYH EHHQ PHW H[SHULPHQWDOO\ E\ GHWHUPLQLQJ WKH WLPH W
FRUUHVSRQGLQJWRWKHWHPSHUDWXUHDWKDOIPD[LPXP∆7PD[WKHUPDOGLIIXVLYLW\FDQEHFDOFXODWHG
E\
W
OD
⋅=
ZKHUHDLVWKHWKHUPDOGLIIXVLYLW\DQGOWKHWKLFNQHVVRIWKHVDPSOH
,QSUDFWLFHRWKHUIUDFWLRQVWγFDQDOVREHXVHGEXWDGLIIHUHQWFRQVWDQWPXVWEHHPSOR\HG7KHVH
FRQVWDQWVDUHWDEXODWHGIRUGLIIHUHQWIUDFWLRQV
7KLVPHWKRGKDVEHHQZLGHO\XVHGIRUPHDVXUHPHQWVRQVROLGV)RUWKHXVHRQOLTXLGVLWPXVWEH
PRGLILHGVLQFHLWLVQHFHVVDU\LWRFRQWDLQWKHVDPSOHDQGLLWRPRXQWWKHGLVFKRUL]RQWDOO\
$ODVHULVXVHGWRVXSSO\WKHKHDWSXOVHDQGWKHWHPSHUDWXUHRIWKHEDFNIDFHLVPRQLWRUHGE\DQ
LQIUDUHG GHWHFWRU LH ,Q6E 7KH VDPSOH LV FRQWDLQHG LQ VLOLFD RU VDSSKLUH FHOOV ZKLFK DUH
WUDQVSDUHQWWRLQIUDUHGUDGLDWLRQ7KHWKLFNQHVVRIWKHVSHFLPHQPXVWEHFDUHIXOO\VHOHFWHGZLWK
UHJDUGWRWKHWKHUPDOFRQGXFWLYLW\RIWKHVDPSOH&DUERQLVIUHTXHQWO\DSSOLHGWRWKHVXUIDFHRI
WKHPHWDO WR LPSURYH WKHDEVRUSWLRQRI WKHHQHUJ\SXOVH ,W LVGLIILFXOW WRPDLQWDLQGLVF VKDSHG
JHRPHWU\ IRU OLTXLG PHWDOV ZKLFK DUH QRQZHWWLQJ RQ VDSSKLUH RU VLOLFD DQG FRQVHTXHQWO\
UHOLDEOHPHDVXUHPHQWVFDQQRWEHREWDLQHGIRUWKHVHFRQGLWLRQV&RUUHFWLRQVDUHXVXDOO\DSSOLHG
WRDFFRXQWIRUH[SDQVLRQVRIWKHPHWDO
)LJ 6FKHPDWLF GLDJUDP LOOXVWUDWLQJ L W\SLFDO ODVHU SXOVH DSSDUDWXV XVHG WR GHWHUPLQH WKHUPDO
GLIIXVLYLW\RIOLTXLGPHWDOVDQGLLW\SLFDOWUDQVLHQWGLVSOD\
7KHSULQFLSOHDGYDQWDJHVRIWKLVWHFKQLTXHDUH
• LWLVUREXVWDQGLQYROYHVQRFRQWDFWEHWZHHQWKHSUREHDQGWKHPHOW
• WKHPHWKRGLVZHOOSURYHQDQGZLGHO\XVHGRQVROLGV
3RVVLEOHGLVDGYDQWDJHVRIWKHPHWKRGDUH
• WUDQVLHQW WLPHV LQ OLTXLGPHWDOVDUHXSWRVHFRQGVDQGVRPHFRQYHFWLRQDOIORZVPD\EH
LQLWLDWHGZKLFKFRXOGDIIHFWWKHUHVXOWV
• UHDFWLRQVEHWZHHQWKHOLTXLGPHWDODQGWKHFRQWDLQHUPD\DOVRDIIHFWWKHUHVXOWV
• WKHDSSOLFDWLRQRIFDUERQWRLPSURYHHQHUJ\DEVRUSWLRQLVQRWGHVLUDEOHIRUPHWDOVVXFKDV)H
ZKLFKKDYHDSSUHFLDEOHFDUERQVROXELOLW\
7P
W WLPH
WHPS
7 P
)ODVKVRXUFH
'HWHFWRU
6LJQDOFRQGLWLRQHU
'DWDFROOHFWLRQV\VWHP
'DWDSURFHVVRU
/LQHSULQWHU
6DPSOH
+HDWHU
9LVXDOGLVSOD\
9DFXXPRULQHUW
DWPRVSKHUHHQFORVXUH
3XOVHKHDWLQJWHFKQLTXHV
&ODVVLILFDWLRQ
7KHSXOVHKHDWLQJPHWKRGLVQRZJRLQJWREHGLVFXVVHGWKHWHFKQLTXHWKHPHDVXUHPHQWVRIWKLV
ZRUNZHUHPDGHZLWK7KHUHDUHWZRGLIIHUHQWUHDVRQVZK\WKLVPHWKRGZDVQRWKDQGOHGHDUOLHU
LQ WKH VXUYH\ L LWV WKHPHWKRGZKRVH WKHRU\DQGH[SHULPHQWDOGHWDLOVDUHEHVWNQRZQZLWKLQ
RXUZRUNJURXS LL VRPHKRZSXOVHKHDWLQJGRHVQRW ILW LQDQ\RI WKHFDWHJRULHVGHDOWZLWKLQ
WKLVFKDSWHU
7KHFODVVLILFDWLRQRIWKHSXOVHKHDWLQJPHWKRGLVDOLWWOHELWGLIILFXOWDQGFRQIXVLQJRQRQHVLGHLW
GRHV QRW DSSO\ WR WKH WUDQVLHQW WHFKQLTXHV EHFDXVH WHPSHUDWXUH JUDGLHQWV DUH RI WKH RUGHU RI
VRPH.DQGRQ WKHRWKHU VLGH LW FDQWEHDQRQVWHDG\VWDWH WHFKQLTXHEHFDXVHRI WKHVKRUW
WLPHUHJLPHRIDERXWWRVHF7RKDQGOHWKLVXQFOHDUQHVVZHGHFLGHGWRH[SODLQSXOVH
KHDWLQJDVDVWDQGDORQHWHFKQLTXH
3ULQFLSDOFRQVLGHUDWLRQV
$VPHQWLRQHG EHIRUH WKH SULQFLSOHPHWKRG RI -RXOHDQ ,⋅5 KHDWLQJ JHQHUDWHG E\ DQ HOHFWULFDO
FXUUHQWIORZLQJWKURXJKDVDPSOHLVQRWUHVWULFWHGWRVWHDG\VWDWHWHFKQLTXHVRQWKHFRQWUDU\LWV
ZLGHO\XVHGLQG\QDPLFPHDVXUHPHQWVEHFDXVHRIWKHDELOLW\WRUHDFKWHPSHUDWXUHUHJLRQVZKLFK
DUH LPSRVVLEOH WR JHW WR ZLWK VWHDG\ VWDWH PHWKRGV 7UDGLWLRQDO VWHDG\ VWDWH WHFKQLTXHV DUH
JHQHUDOO\ OLPLWHG WR WHPSHUDWXUHV XS WR DERXW . 7KLV OLPLWDWLRQ UHVXOWV IURP GLIIHUHQW
UHDVRQV
• FKHPLFDOLQWHUDFWLRQVRIWKHVSHFLPHQVZLWKLWVFRQWDLQHUV
• WKHORVVRIPHFKDQLFDOVWUHQJWK
• LQFUHDVLQJO\ PRUH SUREOHPV ZLWK KHDW WUDQVIHU HYDSRUDWLRQ DQG HOHFWULFDO LQVXODWLRQ DV
WHPSHUDWXUH ULVHVZKLOH WKH VDPSOHV DQG LWV HQYLURQPHQW DUH NHSW IRU WLPHV XS WR KRXUV DW
KLJKWHPSHUDWXUHV
$VDZD\RXW IDVWG\QDPLFPHWKRGVVXFKDVSXOVHKHDWLQJKDYHEHHQGHYHORSHG WRDYRLG WKHVH
GLIILFXOWLHVDQGSHUPLWWKHH[WHQVLRQRIWKHH[SHULPHQWDOUDQJHVRPH.LQWRWKHOLTXLGSKDVH
([SHULPHQWDOGHWDLOV
5DSLG YROXPH KHDWLQJ PHWKRGV LQYROYH UHVLVWLYH VHOIKHDWLQJ RI WKH VSHFLPHQ E\ SDVVLQJ DQ
HOHFWULFDOFXUUHQWSXOVHWKURXJKLW6WDUWLQJDWURRPWHPSHUDWXUHPHDVXUHPHQWVFDQEHSHUIRUPHG
IDU LQWR WKH OLTXLG SKDVH RI WKH PDWHULDO XQGHU LQYHVWLJDWLRQ 'HSHQGLQJ RQ WKH KHDWLQJ UDWH
UHTXLUHG WKH HOHFWULFDO HQHUJ\ LV VWRUHG LQ D EDWWHU\EDQN VORZ RU LQ D FDSDFLWRUEDQN IDVW
0HDVXUHPHQWVFDQEHSHUIRUPHGHLWKHULQDQDLURUDQLQHUWJDVDWPRVSKHUH
)LJ6FKHPDWLFGLVSOD\RIDVWDQGDUGUHVLVWLYHSXOVHKHDWLQJV\VWHP
)LJXUH VKRZVDIXQFWLRQDOGLDJUDPRID W\SLFDOSXOVHKHDWLQJV\VWHPZKLFKVKRXOGKHOSWR
H[SODLQ WKHPDMRU SDUWV IRU VXFK DPHDVXUHPHQW7KH GHWDLOV RI WKH FRPSRQHQWV YDU\ZLWK WKH
WLPHVFDOHRIWKHPHDVXUHPHQW
7KHGLVFKDUJHFLUFXLWFRQVLVWVRI WKHHQHUJ\VWRUDJHWKHPDLQVZLWFKLHKLJKYROWDJHPHUFXU\
YDSRU LJQLWURQ WXEH DQG RI WKH VSHFLPHQ FKDPEHU ZLWK ZLQGRZV IRU RSWLFDO GLDJQRVWLFV$Q
DGGLWLRQDOUHTXLUHPHQWLVWKHFURZEDUVZLWFKWRVWRSWKHH[SHULPHQWDWDQ\GHVLUHGPRPHQW
7KHPHDVXUHGTXDQWLWLHVDUHWKHFXUUHQWWKURXJKWKHVDPSOHWKHYROWDJHGURSDFURVVWKHVDPSOH
WKH WHPSHUDWXUHRI WKH VDPSOHZKLFK LVGHWHFWHGE\XVLQJRSWLFDO S\URPHWHUV DQGRWKHURSWLFDO
&KDUJLQJXQLW
(QHUJ\VWRUDJH
&URZEDUVZLWFK
0DLQVZLWFK
&XUUHQW3UREH
6WDUW
7LPHUDQG&RQWURO
&RPSXWHU
IRU
HYDOXDWLRQ
5HF
RUGLQJ
V\VWHP
3UHVVXUHFRQWURO
6SHFLPHQFKDPEHU
ZLWK
RSWLFDOZLQGRZV
&LUFXLW,QGXFWLYLW\
&LUFXLW5HVLVWLYLW\
6KLHOGHG5RRP
9ROWDJH0HDVXUHPHQW
&XUUHQW0HDVXUHPHQW
7HPSHUDWXUH0HDVXUHPHQW
2WKHURSWLFDO0HDVXUHPHQWV
PHDVXULQJ LQVWUXPHQWV VXFK DV D FDPHUDV\VWHP ZLWK D &&'DUUD\ WR GHWHUPLQH YROXPH
H[SDQVLRQRIWKHVDPSOHGXULQJWKHH[SHULPHQW
'XHWRWKHKHDWLQJUDWHVXVHGYHU\IDVWDQGUHOLDEOHGDWDDFTXLVLWLRQHTXLSPHQWLVDPXVW$OORI
WKLVHTXLSPHQWKDVWREHSODFHGLQDVKLHOGHGURRPDVRFDOOHG)$5$'$<FDJH
3XOVHKHDWLQJ PHWKRGV KDYH EHHQ XVHG WR PHDVXUH WKHUPDO FRQGXFWLYLW\ HOHFWULFDO UHVLVWLYLW\
VSHFLILFKHDWKHPLVSKHULFDOWRWDOHPLVVLYLW\QRUPDOVSHFWUDOHPLVVLYLW\WKHUPDOH[SDQVLRQDQG
SURSHUWLHVGHULYHGIURPWKHSULPDU\SURSHUWLHVVXFKDVHQWKDOS\WKHUPDOGLIIXVLYLW\FRHIILFLHQW
RIOLQHDUH[SDQVLRQDQG:)/UDWLR
3URVDQGFRQWUDVRIWKHSXOVHKHDWLQJPHWKRG
7KHJUHDWHVWDGYDQWDJHRISXOVHKHDWLQJDQGRIFRXUVHRIDOOGLUHFWKHDWLQJWHFKQLTXHVLVVXUHO\
WKHIDFWWKDWWKLVWHFKQLTXH\LHOGVPRUHWKDQRQHSURSHUW\GHWHUPLQHGDWRQFHDQGLQIDFWDOOWKH
SURSHUWLHVOLVWHGDERYHFDQEHPHDVXUHGVLPXOWDQHRXVO\RUFRQVHFXWLYHO\ZLWKVWHDG\VWDWHGLUHFW
KHDWLQJPHWKRGVRQWKHVDPHVSHFLPHQ$QRWKHUDGYDQWDJHLVWKDWVDPSOHVFDQEHXVHGLQDORW
RIGLIIHUHQWIRUPVVXFKDVURGVWXEHVSODWHVDQGZLUHV
2Q WKH FRQWUDU\ WKHJUHDWHVW GLVDGYDQWDJH LV WKH IDFW WKDW WKLVPHWKRG LV OLPLWHG WRHOHFWULFDOO\
FRQGXFWLQJ PDWHULDOV $ VHFRQG GLVDGYDQWDJH LV WKH H[WHQVLYH H[SHULPHQWDO VHWXS QHHGHG IRU
PHDVXUHPHQWVLQWKHµVWLPHUHJLPH
&KDSWHU
([SHULPHQWDOVHWXSDQGGDWDHYDOXDWLRQ
([SHULPHQWDOGHWDLOVRIWKHSXOVHKHDWLQJVHWXS
$VPHQWLRQHGLQWKHODVWFKDSWHUWKHPHDVXUHPHQWVRIWKLVZRUNDUHSHUIRUPHGZLWKDUHVLVWLYH
SXOVHKHDWLQJ DSSDUDWXV RXU VR FDOOHG VORZ GLVFKDUJH FLUFXLW 7KHZRUG VORZ UHIHUV WR WKH
WLPH UHJLPH WR µV FRYHUHG E\ RXUPHDVXUHPHQWV :HDOVRKDYH D IDVWGLVFKDUJH
FLUFXLWZKLFKPHDQVDGXUDWLRQIRURQHPHDVXUHPHQWRIDERXWWRµV7KHSULQFLSOHRIWKLV
DSSDUDWXVLVPRUHRU OHVV WKHVDPHDVVKRZQLQ)LJEXWGLIIHUVLQH[SHULPHQWDOGHWDLOVOLNH
WKH RSWLFDO GHWHFWLRQ RU WKH YROWDJH PHDVXUHPHQW )RU EHWWHU XQGHUVWDQGLQJ WDNH D ORRN DW
)LJDWWKHHQGRIWKLVVHFWLRQZKLFKVKRZVDVFKHPDWLFGLDJUDPRIWKHGLVFKDUJHFLUFXLWXVHG
LQRXUODERUDWRU\
'XULQJDPHDVXUHPHQWYHU\KLJKFXUUHQWVDERXW$FDQRFFXUGHSHQGLQJRQWKHVSHFLPHQ
DQGWKHFKDUJLQJYROWDJH'XHWRWKLVIDFWYHU\DSSURSULDWHHOHFWULFDOVKLHOGLQJLVQHHGHGIRUDOO
WKH LQVWUXPHQWV OHDGV DQG GHWHFWRUV$OO HOHFWULFDO OHDGV DUH SURYLGHGZLWK FRD[LDO FDEOHV DQG
VKLHOGHGZLWKLQ&RSSHU WXEHV WRPLQLPL]HHOHFWULFDO LQWHUIHUHQFHRQ WKHVLJQDOV 7KHDPSOLILHU
HOHFWURQLFLVVKLHOGHGWZLFHWRSUHYHQWLQWHUIHUHQFH7KHODUJHVFDOHVKLHOGLQJSD\VRIIDVZHFDQ
UHDFKKHDWLQJUDWHVXSWR.V7KHHQHUJ\VWRUDJHILWWHGLQWRWKHFLUFXLWLVDµ)FDSDFLWRU
EDQNZKLFKFRXOGEHFKDUJHGXSWRDERXWN9XVLQJDQKLJKYROWDJHSRZHUVXSSO\
)LJ6FKHPDWLFGLDJUDPRIWKHGLVFKDUJHFLUFXLWLQ*UD]
.H\+936 KLJK YROWDJH SRZHU VXSSO\& FDSDFLWRU EDQN6 VZLWFK5FURZ FURZEDU UHVLVWRU
5Y YDULDEOH UHVLVWRU ,* LJQLWURQV 3* SXOVH JHQHUDWRU $ DPSOLILHU 33 3HDUVRQ SUREH
'& GLVFKDUJH FKDPEHU .( NQLIHHGJHV 55 RKPLF YROWDJH GLYLGHU UHVLVWRUV
3<S\URPHWHU/OHQV,)LQWHUIHUHQFHILOWHU)OLJKWILEHU'SKRWRGLRGH
0HDVXUHGDQGFDOFXODWHGSURSHUWLHV
2XU SXOVHKHDWLQJ DSSDUDWXV HQDEOHV XV WR PHDVXUH GLIIHUHQW WLPH UHVROXWHG TXDQWLWLHV
VLPXOWDQHRXVO\GXULQJRQHVLQJOHH[SHULPHQW$GGLWLRQDOO\ZHFDQPDNHVXSSOHPHQWDU\RSWLFDO
PHDVXUHPHQWV OLNH VWDELOLW\ LQYHVWLJDWLRQV RQ WKH ZLUH ZLWKRXW DIIHFWLQJ WKH SULQFLSOH
PHDVXUHPHQW7KHVHTXDQWLWLHVZHEDVLFDOO\PHDVXUHDUH
• WKHFXUUHQWWKURXJKWKHZLUH
• WKHYROWDJHGURSDORQJWKHZLUH
• WKHUDGLDQFHRIWKHZLUHVXUIDFH
• WKHYROXPHH[SDQVLRQRIWKHZLUH
$V WKH QHZHVW DGGLWLRQ WR RXU H[SHULPHQWDO VHWXS ZH JRW D 'LYLVLRQ RI $PSOLWXGH /DVHU
3RODULPHWHU'2$3ZKLFKDOORZVXVWRPHDVXUHWKHHPLVVLYLW\εDWλ QPWLPHUHVROYHG
3&,
8+27
8&2/'
-
5
5
59
,*
,*
5&52:
&
5 5
6
33
'&
3*
)
3<
,) /
.(
.(
'
$$
$
$'
7ULJJHU
DQGVLPXOWDQHRXVO\ZLWKDOOWKHRWKHUVLJQDOV8SWRQRZWKHHPLVVLYLW\PHDVXUHPHQWLVVWLOOLQ
LWVWHVWSKDVHDQGKDVQRWEHFRPHRQHRIRXUVWDQGDUGSURSHUWLHVWRPHDVXUH)LUVWUHVXOWVDUHYHU\
HQFRXUDJLQJ DQG KRSHIXOO\ ZH FDQ DGG WKH HPLVVLYLW\ WR WKH OLVW RI FRQVWDQWO\ GHWHUPLQHG
SURSHUWLHVGXULQJWKHQH[W\HDU
)LJ 3ORWRIWKHHOHFWULFDOUDZVLJQDOVGHWHFWHGGXULQJRQHH[SHULPHQW6LJQDOVJUHHQFXUUHQWUHG
EODFNYROWDJHVEOXHVXUIDFHUDGLDQFH7KHQHDUO\KRUL]RQWDOOLQHLQWKHUDGLDQFHVLJQDOEHWZHHQ
DQGµVLVWKHVRFDOOHGPHOWLQJSODWHDXWKHVROLGOLTXLGWUDQVLWLRQRIWKHZLUH&URZEDU
DWµV1RWH)RUHDVHRIJUDSKLFDOUHSUHVHQWDWLRQWKHUDGLDQFHVLJQDORIWKHS\URPHWHUKDV
EHHQGLYLGHGE\DIDFWRU
6WDUWLQJZLWK WKHVH IRXUTXDQWLWLHVZHREWDLQPRVWRI WKHGHVLUHG WKHUPRSK\VLFDO SURSHUWLHVE\
VLPSOHFDOFXODWLRQV$VXUYH\RIWKHSURSHUWLHVZHDUHDEOHWRGHWHUPLQHLVJLYHQLQWKHIROORZLQJ
SDUDJUDSKV
6LJQD
OV9
7LPHµV
)LJ 6FKHPDWLFGLDJUDPRI WKHPHDVXUHGTXDQWLWLHVDQG WKHSURSHUWLHVFDOFXODWHGIURPWKHRULJLQDO
VLJQDOV 4XDQWLWLHV LQ \HOORZ FLUFOHV DUH WKH PHDVXUHG RQHV JUHHQ FLUFOHV DUH LQGLFDWLQJ WKH
GHULYHGSURSHUWLHV1RWHLQWKLVJUDSKLFWKHHPLVVLYLW\εDSSHDUVDVDILIWKPHDVXUHGSURSHUW\
DOWKRXJKZHGRQRWPHDVXUHLWSHUPDQHQWO\\HW,WLVSDUWRIWKHFXUUHQWSURMHFWZHDUHUXQQLQJ
ULJKWDWWKHPRPHQW
7KHIROORZLQJVHFWLRQGLVSOD\VLQVKRUWWHUPVWKHPHDVXUHPHQWRIHDFKRIWKHIRXUSURSHUWLHVDQG
WKHUHODWLRQVXVHGWRFDOFXODWHDOORWKHUSURSHUWLHVIURPWKHPHDVXUHGRQHV
'DWDHYDOXDWLRQ
7KHFXUUHQW
$ UHVLVWRU5Y WR Ω LV XVHG WR UHDOL]H D UHVRQDQW FLUFXLW WR VKDSH WKH FXUUHQW SXOVH DV
UHFWDQJXODU DVSRVVLEOH 6HH FXUUHQW VLJQDO LQ)LJ7KHGLVFKDUJH LVSURPSWO\ VWDUWHG DQG
DERUWHG E\ WZR LJQLWURQV ZKLFK DUH YHU\ IDVW VZLWFKHV 7KH ILUVW RQH VWDUWV WKHPHDVXUHPHQW
ZKHUHDVWKHVHFRQGLJQLWURQFURZEDUVWKHGLVFKDUJHZLWKDQRWKHUUHVLVWRU5FURZ
7KH FXUUHQW LQ WKH GLVFKDUJH FLUFXLW DQG WKURXJK WKH ZLUH LV PHDVXUHG YLD D 3HDUVRQ SUREH
3HDUVRQ(OHFWURQLFV W\SHXVLQJWKHLQGXFWLRQSULQFLSOH7RJHWDFXUUHQWVLJQDOZKLFKLV
GLUHFWSURSRUWLRQDOWRWKHYROWDJHWKURXJKWKHSUREHD5&FRPSRQHQWLVLQWHJUDWHGLQWKHSUREH
7KHFDOLEUDWLRQIDFWRUIRUWKHSUREHLV$9
α7
λ7F3
-W ,W8WεW UW
7W ρ0W+W W99
ρ7 ρ++7 +99
799
$OOHOHFWULFDOVLJQDOVUHFRUGHGZLWKWKHGDWDDFTXLVLWLRQHTXLSPHQWKDYHWREHLQWKHUDQJHRI±
YROWVQRW WRRYHUORDG WKHGDWDDFTXLVLWLRQFDUGV LQ WKHFRPSXWHUZKLFK LVJXDUDQWHHGE\XVLQJ
FDOLEUDWHGRKPLFYROWDJHGLYLGHUV
7KHYROWDJHGLYLGHUIDFWRUIRUWKHFXUUHQWKDVEHHQGHWHUPLQHGDV
'LYLGHU5DWLR ±
7KHYROWDJH
$FWXDOO\ LWVQRW WKHYROWDJHZHPHDVXUHEXW WKHYROWDJHGURSEHWZHHQ WZRNQLIHHGJHSUREHV
DQG JURXQG7KHVH NQLIHHGJHSUREHV DUHPP7DQWDOXPVWULSVZKLFK DUHYVKDSHGRQRQH
HQG 7KH NQLIHHGJH SUREHV DUH SODFHG DW ERWK VLGHV RI WKH ZLUH ZLWK WKH VSHFLPHQ UXQQLQJ
WKURXJK WKHYVKDSHGFXWWLQJ7KHGLVWDQFHEHWZHHQ WKH WZRSUREHVKDV WREHPHDVXUHGZLWKD
WUDYHOOLQJ PLFURVFRSH EHFDXVH WKLV DFWXDO OHQJWK LV XVHG IRU WKH FDOFXODWLRQ RI WKH VSHFLILF
FRQGXFWLYLW\
7KHGHVLUHGUHVXOWLVWKHYROWDJHGURSDFURVVWKHZLUHZKLFKLVREWDLQHGE\VXEWUDFWLQJWKHWZR
YROWDJHVLJQDOV7KLVPHWKRGKHOSVXVWRFDQFHORXWWKHDUELWUDU\UHVLVWDQFHDWWKHFRQWDFWSRLQWV
RIWKHNQLIHHGJHSUREHVZLWKWKHZLUHZKLFKZRXOGEHQHDUO\LPSRVVLEOHWRGHWHUPLQH
)LJ6FKHPDWLFGUDZLQJRIWKHNQLIHHGJHSUREHV2QHRIWKHSUREHVFDQEHVHHQLQ)LJD
$V ZLWK WKH FXUUHQW VLJQDO ERWK YROWDJH VLJQDOV KDYH WR SDVV WKURXJK YROWDJHGLYLGHUV WR
JXDUDQWHH WKDW WKH\DUH LQ WKHUDQJHRIRXUPHDVXUHPHQWHOHFWURQLFVHHWKHSDUDJUDSKKDQGOLQJ
WKHFXUUHQWVLJQDODERYH7KHIDFWRUVIRUWKHGLYLGHUVKDYHEHHQFDOLEUDWHGWR
'LYLGHU5DWLRKRW ±
'LYLGHU5DWLRFROG ±
aPP
aPP
7KH VXEVFULSW KRWPDUNV WKHYROWDJH VLJQDOQH[W WR WKHFXUUHQW LQMHFWLRQ WKH VXEVFULSWFROG WKH
YROWDJHVLJQDORQWKHRWKHUVLGHRIWKHZLUH
7KHPHDVXUHGYROWDJHVLJQDOFRQVLVWVRIWKHIROORZLQJWKUHHWHUPVDQGKDVWREHWUHDWHGDOLWWOHELW
WRJHWWKHGHVLUHGUHVXOW
( ) ( ) ( ) ( ) ( ) ( ) ( )GW
WG/W,
GWWG,
//W5W,W8 VFVV ⋅+⋅++⋅=
ZKHUH8WLVWKHPHDVXUHGYROWDJHVLJQDO,WLVWKHFXUUHQW5VLVWKHUHVLVWLYLW\RIWKHVDPSOH
/VLVWKHLQGXFWDQFHRIWKHVDPSOHDQG/FLVWKHLQGXFWDQFHRIWKHFHOO
7KHILUVWWHUPLQ(TLVWKHGHVLUHGYROWDJHGURSDFURVVWKHZLUH7KHVHFRQGWHUPUHSUHVHQWV
WKH LQGXFWLYH FRPSRQHQWRI WKHYROWDJH VLJQDO FDXVHGE\ WKH LQGXFWDQFHRI WKHFLUFXLW DQG WKH
VDPSOH ZKLOH EHLQJ WUHDWHG ZLWK D FKDQJLQJ FXUUHQW SXOVH 7KLV WHUP KDV WR EH FRPSHQVDWHG
ZKLFK LV GRQHZLWK D FRPSXWHU HYDOXDWLRQ SURJUDPE\ DSSUR[LPDWLQJ WKH DFWXDO FRXUVH RI WKH
VLJQDO ZLWK D SRO\QRPLDO ILW DQG VXEWUDFWLQJ WKH WZR FXUYHV )RU IXUWKHU GHWDLOV VHH
>6DFKVHQKRIHU @ 7KH WKLUG WHUP WDNHV WKH FKDQJH RIZLUHLQGXFWDQFH LQWR FRQVLGHUDWLRQ
ZKLFKLVFDXVHGE\WKHYROXPHH[SDQVLRQRIWKHVDPSOH7KLVWHUPLVRQO\DVPDOOFRQWULEXWLRQWR
WKHWRWDOYROWDJHVLJQDODQGFDQEHQHJOHFWHGZLWKRXWDIIHFWLQJWKHUHVXOWDWDOO6HH&KDSWHU
(VWLPDWLRQRIXQFHUWDLQW\IRUPRUHGHWDLOV
7KHVXUIDFHUDGLDQFH
7KHRQO\ZD\WRPHDVXUHWHPSHUDWXUHVLQDUDQJHIURPWRVRPH.LVE\XVLQJDQRSWLFDO
S\URPHWHU1RWRQO\LV WKHS\URPHWHUWKHRQO\UHOLDEHOPHWKRGRIPHDVXULQJKLJKWHPSHUDWXUHV
EXW LW DOVR KDV DOO WKH DGYDQWDJHV RI DQ RSWLFDO PHWKRG LWV IDVW HQRXJK WR IROORZ UDSLG
WHPSHUDWXUHFKDQJHV LWGRHVQRWQHHGGLUHFWFRQWDFWZLWKWKHVSHFLPHQDQGGRHVQRWDIIHFWWKH
HOHFWULFDOPHDVXUHPHQWV
7KHSULQFLSOHRI WKHS\URPHWHUXVHG FDQEH H[SODLQHGDV IROORZV7KH OLJKW YLVLEOHDVZHOO DV
LQIUDUHGHPLWWHGIURPWKHKHDWHGVXUIDFHSDVVHVWKURXJKDQLQWHUIHUHQFHILOWHUWRVHOHFWDVSHFLILF
ZDYHOHQJWKDQGDOHQVFROOHFWVWKHOLJKWDQGSURMHFWVDQLPDJHRIWKHZLUHRQWKHHQWUDQFHVOLWRI
D OLJKWILEHU 7KURXJK WKLV ILEHU WKH OLJKW LV WUDQVSRUWHG WR WKH S\URPHWHU FLUFXLWU\ ZKHUH LWV
GHWHFWHG E\ DQ ,Q*D$VSKRWRGLRGH DQG WKH YROWDJH VLJQDO LV DPSOLILHG ZLWK DQ RSDPS 7KLV
DPSOLILHGVLJQDOLVGHWHFWHGDQGUHFRUGHGZLWKDFRPSXWHU
7DEOH6SHFLILFDWLRQVRIWKHLQWHUIHUHQFHILOWHUXVHGIRUWKHPHDVXUHPHQWVRQ&RSSHU
)LOWHUW\SH&HQWHUZDYHOHQJWK
>QP@%DQGZLGWK
>QP@%ORFNLQJ>QP@
EDQGSDVV 89WR
,Q )LJ WKH QHDUO\ KRUL]RQWDO DUHD EHWZHHQ DQG µV LQ WKH VXUIDFH UDGLDQFH VLJQDO
LQGLFDWHV WKHPHOWLQJRI WKHZLUHZKHUH WKH WHPSHUDWXUHVWD\VPRUHRU OHVVFRQVWDQWXQOHVV WKH
HQWLUHVSHFLPHQLVPROWHQ
7KHYROXPHH[SDQVLRQ
7KHZLUHLVLOOXPLQDWHGE\DIODVKODPSDQGWKHSLFWXUHLVSURMHFWHGYLDDOHQVRQDPXOWLFKDQQHO
SODWH 0&3$VSHFLDO WHFKQLTXHRIVKLIWLQJ WKHH[SRVHGDUHDRQ WKH&&'DUUD\HQDEOHVXV WR
WDNHHYHU\µVDSLFWXUHRIWKHH[SDQGLQJZLUHIURPZKLFKZHGHWHUPLQHWKHYROXPHH[SDQVLRQ
GXULQJWKHH[SHULPHQW
7KHVH SUHVHQW PHDVXUHPHQWV RQ &RSSHU KDYH EHHQ SHUIRUPHG ZLWKRXW WKH H[SDQVLRQ
PHDVXUHPHQWEHFDXVHRIWKHIROORZLQJUHDVRQVLWKH&&'FDPHUDZDVDWWKHPDQXIDFWXUHUIRU
UHSDLUDQG LPSURYHPHQW LL WKH&&'DUUD\UHDGRXWSURFHVVRIRXUVHFRQGFDPHUDLV WRRVORZ
IRUDFFXUDWHPHDVXUHPHQWVRQO\RQHSLFWXUHSHUµVSRVVLEOHLLLVHYHUDOLQYHVWLJDWRUVKDYH
VWXGLHGWKHYROXPHH[SDQVLRQGXULQJKHDWLQJRISXUH&RSSHUVRWKDWWKHUHVXOWVDUHZHOONQRZQ
DQGIRXQG WREHFRUUHFW6LQFHHYHU\PHDVXUHPHQWFRQWDLQVV\VWHPDWLFHUURUVDQGXQFHUWDLQWLHV
ZKLFK DUH GLIILFXOW WR HVWLPDWHZH GHFLGHG WR XVH WKH UHFRPPHQGHG YDOXHV IURPZHOO NQRZQ
VRXUFHV HJ >7RXORXNLDQ @ RU >1,67 @ ZKLFK DUH YHU\ DFFXUDWH DQGZHOO SURYHQ
LQVWHDGRIPHDVXULQJWKHYROXPHH[SDQVLRQRXUVHOYHVDWDOOFRVWV
7KHWHPSHUDWXUH
7KH WHPSHUDWXUH LV FDOFXODWHG E\ XVLQJ DQ DGDSWHG YHUVLRQ RI 3/$1&.V ODZ RI EODFN ERG\
UDGLDWLRQ
( )( )
( )( )
−
⋅
⋅⋅+⋅
=
H[SOQ
P
PP
P 7F
7-7-
77
F7
λεελ
ZKHUHFLV3/$1&.VVHFRQGFRQVWDQWF ⋅P.>%HUJPDQQ6FKDHIHU@λLV
WKHZDYHOHQJWK VHOHFWHG E\ WKH LQWHUIHUHQFH ILOWHU λ QP ε LV WKH HPLVVLYLW\ - LV WKH
UDGLDQFH LQWHQVLW\ GHWHFWHG E\ WKH S\URPHWHU WKH VXEVFULSW P GHQRWHV WKH WHPSHUDWXUH DW WKH
PHOWLQJSRLQW
6LQFH WKHHPLVVLYLW\ε7RIPRVW OLTXLGPHWDOV LVXQNQRZQDQDVVXPSWLRQKDVWREHPDGHIRU
WKH UDWLRεWε7P LQ WKH OLTXLGSKDVHRI WKHPHWDOε7P LV WKHYDOXHRI WKHHPLVVLYLW\RI WKH
VDPSOH DW WKHPHOWLQJ WHPSHUDWXUH7PZKHUH WHPSHUDWXUHV DUH FDOFXODWHG E\ IRUPLQJ UDWLRV RI
UDGLDQFH -7 DWD WHPSHUDWXUH7 WR WKH UDGLDQFH-P7P DW7P7KHPHOWLQJ WHPSHUDWXUH7P LV
WDNHQIURPOLWHUDWXUHGDWD
8S WR QRZ D FRQVWDQW HPLVVLYLW\ εWε7P ZDV DVVXPHG IRU WKH OLTXLG SKDVH IRU SXOVH
KHDWLQJH[SHULPHQWV6LPXODWLRQVVKRZHG>6HLIWHU@WKDWDFKDQJHRIHPLVVLYLW\GXULQJWKH
OLTXLGSKDVHGRHVQRWDIIHFWWKHWHPSHUDWXUHUHVXOWVWRRPXFK
$W WKHPRPHQWZH DUH IRUFLQJ HPLVVLYLW\PHDVXUHPHQWVZLWK RXU ODVHU SRODULPHWU\ DSSDUDWXV
:LWKWKLVV\VWHPZHDUHDEOHWRGHWHUPLQHWKHDEVROXWHYDOXHRIHPLVVLYLW\εRIWKHVSHFLPHQDW
PHOWLQJDQGWKURXJKRXWWKHOLTXLGSKDVHRQRQHZDYHOHQJWKDWQP
7KHHQWKDOS\
:LWK WKHGHWHFWHGHOHFWULFDOVLJQDOVYROWDJHDQGFXUUHQW LW LVSRVVLEOH WRGHWHUPLQH WKHHQWKDOS\
LQGXFHGLQWRWKHZLUHE\-RXOHDQKHDWLQJ7KHHQWKDOS\LVFDOFXODWHGZLWK
( ) ( ) ( )∫ ⋅⋅⋅=−W
. GWW8W,P
+W+
ZKHUH +. LV WKH HQWKDOS\ DW URRP WHPSHUDWXUH DQG LV FRPPRQO\ VHW WR WKH DUELWUDU\ YDOXH
+. DQGFDQKHQFHEHRPLWWHGPLVWKHPDVVRIWKHZLUHGHWHUPLQHGIURPWKHGHQVLW\RIWKH
PHWDO DQG WKH OHQJWKRI WKHZLUH OHQJWKPHDVXUHPHQWRI WKHZLUHEHWZHHQ WKH WZRNQLIHHGJH
SUREHV
7KH HQWKDOS\ GHWHUPLQDWLRQ LV RQH RI WKH ELJJHVW DGYDQWDJHV RI WKH SXOVHKHDWLQJ PHWKRG
EHFDXVH WKH HQWKDOS\ E\ -RXOHDQ SXOVHKHDWLQJ H[SHULPHQWV HTXDOV WKH HQHUJ\ DEVRUEHG E\ WKH
ZLUH7KHUHIRUHZHFDQFDOFXODWHGLUHFWO\WKHDEVRUEHGHQHUJ\RIWKHZLUHDWDQ\JLYHQWLPH
7KHVSHFLILFKHDW
$VZHKDYHVHHQ(TDOORZVWRFDOFXODWHHQWKDOS\+RIWKHZLUHE\PHDVXULQJWKHFXUUHQW
DQGWKHYROWDJHDFURVVWKHVDPSOH%XWWKHUHLVDQRWKHUUHODWLRQWKDWKROGVIRUWKHHQWKDOS\
( ) ( )∫ ⋅=7
.S G77F7+
ZKHUHF3LVWKHVSHFLILFKHDWRIWKHVSHFLPHQXQGHUFRQVWDQWSUHVVXUH
5HDUUDQJLQJOHDGVWR
( ) ( )77+
7F3 ∂∂=
%\WDNLQJDFORVHUORRNDW(TRQHFDQVHHWKDWWKHVSHFLILFKHDWFDQEHGHWHUPLQHGIURPWKH
VORSHRIWKHOLQHDUVHFWLRQVRIWKHFXUYHHQWKDOS\+YHUVXVWHPSHUDWXUH7
7KHHOHFWULFDOUHVLVWLYLW\
7KHXQFRUUHFWHG HOHFWULFDO UHVLVWLYLW\ρR QR DFWXDOYROXPHH[SDQVLRQFRQVLGHUHGFDQDJDLQEH
FDOFXODWHG IURPRXURULJLQDOO\PHDVXUHGSURSHUWLHVFXUUHQWDQGYROWDJHE\XVLQJ WKH IROORZLQJ
UHODWLRQ
( ) ( )( ) O
UW,W8
Wπρ ⋅
⋅=
ZKHUHURLVWKHUDGLXVRIWKHZLUHDWURRPWHPSHUDWXUHDQGOLWVOHQJWK
6LQFHWKHUDGLXVRIWKHZLUHFKDQJHVGXULQJWKHH[SHULPHQWEHFDXVHRIWKHYROXPHH[SDQVLRQLW
FRXOG QRW EH UHJDUGHG DV FRQVWDQW ,IZH QHJOHFW WKH UDGLDO H[SDQVLRQZH JHW WKH XQFRUUHFWHG
HOHFWULFDO UHVLVWLYLW\&RQVHTXHQWO\ E\ FRQVLGHULQJ WKH UDGLDO H[SDQVLRQ RQH JHWV WKH FRUUHFWHG
HOHFWULFDOUHVLVWLYLW\ZLWK
( ) ( ) ( )
UWU
WWFRUU ⋅= ρρ
ZKHUHUWULVWKHUDGLDORUYROXPHH[SDQVLRQRIWKHZLUH
)RU IXUWKHUFDOFXODWLRQV WKHHOHFWULFDOFRQGXFWLYLW\σ LVQHHGHGZKLFK LVFOHDUO\FRQQHFWHGZLWK
WKHHOHFWULFDOUHVLVWLYLW\WURXJKWKHHOHPHQWDU\UHODWLRQ
FRUUρσ =
7KHWKHUPDOFRQGXFWLYLW\
$V DOUHDG\ VKRZQ LQ &KDSWHU HOHFWULFDO FRQGXFWLYLW\ DQG WKHUPDO FRQGXFWLYLW\ DUH WLHG
WRJHWKHUWKURXJKWKH:,('(0$11)5$1=/25(17=:)/ODZ
FRUU
7/ρ
λ ⋅=
7KHSXEOLVKHGYDOXHV IRU WKH/25(17=QXPEHUDW WKHPHOWLQJ WHPSHUDWXUHGLIIHU LQ WKHUDQJH
EHWZHHQ⋅9.IRUGLIIHUHQWPHWDOV$OWKRXJKZHPRVWFRPPRQO\XVHWKHYDOXH
⋅9.>:HLPDQWHODQG+DPDQQ@IRUWKH/25(17=QXPEHUZHGHFLGHGWRXVH
DQRWKHU KLJKHU YDOXH LQ WKLV ZRUN RQ WKH EDVLV RI WKH ZRUN RI >7\H +D\GHQ @ 7KH\
GHWHUPLQHG /25(17=QXPEHUV IRU &RSSHU DW GLIIHUHQW WHPSHUDWXUHV ZKLFK DUH FRQVHTXHQWO\
!⋅9.$VWKHVHYDOXHVFKDQJHIRUGLIIHUHQW WHPSHUDWXUHVZHDVVXPHWKDWWKHYDOXH
IRU WKH/25(17=QXPEHUIRU&RSSHULV LQWKHLQYHVWLJDWHGWHPSHUDWXUHUDQJHIURP.WR
.
/ 9.
7KHWKHUPDOGLIIXVLYLW\
7KH HTXDWLRQ IRU GHWHUPLQDWLRQ RI WKHUPDO GLIIXVLYLW\D KDV DOUHDG\ EHHQPHQWLRQHG EHIRUH LQ
&KDSWHU%\SURFHHGLQJIURPWKHWKHUPDOFRQGXFWLYLW\λWKHVSHFLILFKHDWF3DQGWKHGHQVLW\
GRIWKHZLUHRQHJHWV
GFD
3 ⋅= λ
7KHGHWHUPLQDWLRQRI7W+WρRW+7DQGρR7LVFDUULHGRXWZLWKDQHZGDWDHYDOXDWLRQ
VRIWZDUHSURJUDPPHGE\>6DFKVHQKRIHU@DVDSDUWRIKLVIRUWKFRPLQJGLSORPDWKHVLV$OO
RWKHUFDOFXODWLRQVDUHGRQHE\XVLQJFRPPHUFLDOFDOFXODWLRQVRIWZDUHVXFKDV2ULJLQRU([FHO
$GGLWLRQDOPHDVXUHPHQWV
6WDELOLW\RIWKHZLUHGXULQJWKHKHDWLQJSURFHVV
7KH VWDELOLW\ RI WKHZLUH GXULQJ WKH KHDWLQJ SURFHVV LV RQHRI WKHPRVW LPSRUWDQW WKLQJVZKLOH
XVLQJWKLVVRUWRISXOVHKHDWLQJWHFKQLTXH7KHZLUHKDVWREHKHDWHGVRIDVWWKDWJUDYLW\FDQQRW
HIIHFWWKHJHRPHWU\RIWKHZLUHDVDUHVXOWRILQHUWLDRIPDVV,QRWKHUZRUGVWKHZLUHPDLQWDLQV
KLVLQLWLDOUDGLDOJHRPHWU\WKURXJKRXWWKHHQWLUHWLPHRIPHDVXUHPHQWZKLFKLVDERXWWRµV
7KLVEHKDYLRUKDVWRSURYHQE\VKRUWWLPHSLFWXUHVPRQLWRULQJWKHZKROHZLUHVDPSOH
7KHUHDUHWZRGLIIHUHQWFRPSOH[HVRISUREOHPVWKDWPLJKWRFFXULIWKHZLUHLVXQVWDEOH
• WKHVXUIDFHUDGLDQFHPHDVXUHPHQW
• WKHYROXPHH[SDQVLRQPHDVXUHPHQWV
7KHILUVWSRLQWRQHKDVWRFRQVLGHULV WKHPHDVXUHPHQWRIWKHVXUIDFHUDGLDWLRQ$VVDLGEHIRUH
WKHUDGLDWLRQHPLWWHGE\WKHKRWZLUHLVPHDVXUHGZLWKDQRSWLFDOS\URPHWHU7KLVS\URPHWHUKDV
WREHDGMXVWHGLQVXFKDZD\WKDWWKHVXUIDFHRIWKHZLUHLVLQWKHIRFDOSODQHRIWKHS\URPHWHU
OHQV 2WKHUZLVH WKH PHDVXUHPHQWV ZRXOG EH QRW LQWHUFRPSDUDEOH 7KHUHIRUH D PRUH RU OHVV
SHUIHFW RSWLFDO DGMXVWPHQW LV WKH RQO\ ZD\ WRPDNH FRUUHVSRQGLQJPHDVXUHPHQWV ,I IRU DQ\
UHDVRQWKHZLUHPRYHVGXULQJWKHPHDVXUHPHQWZKLFKPHDQVLWPRYHVRXWRIWKHIRFXVRIWKH
OHQVWKHS\URPHWHUGHWHFWVXVHOHVVDQGDUELWUDU\UDGLDWLRQLQWHQVLWLHV
7KH VHFRQG LV WKH GHWHUPLQDWLRQ RI WKH YROXPH H[SDQVLRQ2XU&&'FDPHUD IRU GHWHFWLQJ WKH
YROXPHH[SDQVLRQFDQRQO\WDNHGLPHQVLRQDOSLFWXUHVRIWKHZLUH7KHUHIRUHZHFDQQRWGLUHFWO\
PHDVXUHWKHYROXPHH[SDQVLRQEXWRQO\WKHUDGLDOH[SDQVLRQRIWKHZLUH)XUWKHUPRUHZHKDYH
WRDVVXPHWKDWWKHZLUHPDLQWDLQVLWVUDGLDOJHRPHWU\WRFDOFXODWHWKHYROXPHH[SDQVLRQZLWKKHOS
RI WKH UDGLDO H[SDQVLRQ7KLVPHDQV LQ RWKHUZRUGV WKDW WKH VSHFLPHQ VKRXOG QRW EH JLYHQ
HQRXJK WLPH IRU OLQHDU H[SDQVLRQ GXULQJ WKH KHDWLQJ SURFHVV 6R LI WKHZLUHPRYHV WKH UDGLDO
JHRPHWU\LVQRORQJHUJXDUDQWHHGDQGDOOFDOFXODWHGSURSHUWLHVFDQQRWEHH[SHFWHGWREHFRUUHFW
,QVWDELOLWLHVDUHPDLQO\FDXVHGE\
L LQVXIILFLHQW FKDUJLQJYROWDJH WKH VDPSOH LV KHDWHG WRR VORZ DQG
JHWV
HQRXJKWLPHIRUOLQHDUH[SDQVLRQ
LL LUUHJXODULWLHV RI WKH VDPSOHJHRPHWU\ LI WKH VDPSOHV
GLDPHWHULVQRWFRQVWDQWWKURXJKRXWWKHOHQJWKWKLQQHUVHFWLRQVDUH
KHDWHGIDVWHU
LLL GLVFKDUJHVEHWZHHQWKHZLUHDQGWKHKROGLQJGHYLFH
7KH IROORZLQJ VHFWLRQ VKRXOG VKRUWO\ GHVFULEH KRZ ZH DYRLG DOO RI WKH EHIRUHPHQWLRQHG
LQVWDELOLWLHV ZKLFK ZRXOG FDXVH XQZDQWHG WURXEOHV ,W KDV WR EH VDLG JHQHUDOO\ WKDW QRW DOO
PDWHULDOVHTXDOO\ WHQG WRZDUGV LQVWDELOLW\HIIHFWV1LRELXPLVRQHRI WKHPRUHKDUPOHVVVDPSOH
PDWHULDOVUHODWLQJWRLQVWDELOLWLHV&RSSHURQWKHRWKHUKDQGLVYHU\GLIILFXOWWRKDQGOHEHFDXVHRI
LWVORZPHOWLQJSRLQWDQGLWVJRRGHOHFWULFDOFRQGXFWLYLW\
7KHYHU\ORZUHVLVWLYLW\RI&RSSHULVWKHPDLQUHDVRQIRUWKHGLIILFXOWLHVZKLOHSXOVHKHDWLQJWKLV
PHWDO VLQFH WKHHOHFWULFDOSRZHUDEVRUEHGE\WKHVDPSOHLVGLUHFWSURSRUWLRQDO WRWKHVTXDUHRI
WKHFXUUHQWDQGWRWKHUHVLVWLYLW\3 ,⋅57KHUHIRUHZHKDGWRXVHYHU\KLJKFKDUJLQJYROWDJHV
RIDERXWN9IRURXUH[SHULPHQWVWRDYRLGWKRVHLQVWDELOLWLHV7KHVHKLJKYROWDJHVOHDGWR
FXUUHQWSXOVHVDFURVVWKHZLUHDQGWKHGLVFKDUJHFKDPEHULQWKHUDQJHRIN$&RQVHTXHQWO\
WKHVHKLJKFXUUHQWSXOVHVKHDYLO\VXSSRUWWKHSURGXFWLRQRIGLVFKDUJHVDQGIODVKRYHUVVHHVHFWLRQ
IRULLLEHORZ
7KHRQO\ WKLQJZHFDQGRFRQFHUQLQJLL LV WRWUHDW WKHZLUHDVFDUHIXOO\DVSRVVLEOH6LQFHZH
KDYH WRSXUFKDVH WKHZLUHDQG LW LV FRLOHGXSRQD VSLQGOHZHKDYH WRVWUHWFK LW VOLJKWO\EHIRUH
XVLQJ LW $QRWKHU LPSRUWDQW WKLQJ LV QRW WR EHQG WKHZLUHZKLOH EXLOGLQJ LW LQWR WKH GLVFKDUJH
FKDPEHU,WLVUHFRPPHQGHGQRWWRWRXFKWKHZLUHZLWKEDUHKDQGV$OVRZHUHFRPPHQGWRFOHDQ
WKHVXUIDFHRIWKHZLUHZLWK$FHWRQHZKLFKOHDGVWREHWWHUVLJQDOVEHFDXVHRIDFOHDQHUVXUIDFH
$WOHDVWZHKDYHWRKDQGOHLLLWKHJORZGLVFKDUJHVDQGWKHIODVKRYHUVEHWZHHQWKHZLUHDQGWKH
KROGLQJGHYLFHV7KHUHLVQRWPXFKZHFDQGRDERXWLWH[FHSWVDQGWKHKROGLQJGHYLFHVPDGHRI
EURQ]HZLWKKLJKJUDGHSDSHU WR UHPRYHGHSRVLWLRQV IURPSUHFHGLQJH[SHULPHQWVDQGWRPDNH
WKHVXUIDFHDVVPRRWKDVSRVVLEOH(GJHVDQGVSLNHVDUHWKHSULPDU\VRXUFHRIIODVKRYHUV
2QFH \RX JRW XVHG WR DOO RI WKLV LW LV QRW WKDW GLIILFXOW WR PDLQWDLQ WKH VWDELOLW\ RI WKH ZLUH
DOWKRXJKLWGHPDQGVDOLWWOHELWRISDWLHQFHWRKDQGOHDOORIWKHDERYH
D E
)LJ D&RSSHUZLUHZLWKPDVVLYHLQVWDELOLWLHVGXULQJWKHKHDWLQJEVWDEOHOLTXLG&RSSHUZLUHDIWHU
µVDWDERXW.1RWHWKHQDUURZVHFWLRQRIWKHZLUHLQWKHXSSHUKDOIRIELVQRWDQ
LUUHJXODULW\RI WKHZLUHEXW DQRYHUH[SRVHGDUHD DW WKH&&'DUUD\GXH WR WKH LQWHQVLW\RI WKH
EDFNJURXQGIODVK
(PLVVLYLW\PHDVXUHPHQW
$VPHQWLRQHGEHIRUHDWWKHEHJLQQLQJRIWKLVFKDSWHUZHKDYHJRWDODVHUSRODULPHWU\V\VWHPWR
PHDVXUH WKH FKDQJH RI HPLVVLYLW\ ε WLPH UHVROYHG GXULQJ WKH HQWLUH SXOVHKHDWLQJ H[SHULPHQW
7KH QH[W SDUDJUDSK GHDOV ZLWK WKLVPHDVXUHPHQW WR SURYLGH DQ LGHD RI WKH WHFKQLTXH DQG WKH
UHVXOWV )RU IXUWKHU LQIRUPDWLRQ DERXW ODVHU SRODULPHWU\ DQG WKH '2$3 V\VWHP VHH HJ
>6DFKVHQKRIHU@
7KH'2$3FRQVLVWVPRUHRUOHVVRIWKHIROORZLQJFRPSRQHQWVDPRGXODWHG0+]ODVHUGLRGH
DSRODUL]HU ILYHGHWHFWRUV XVLQJ/RFN,Q WHFKQRORJ\DVHSDUDWHGGDWDDFTXLVLWLRQDFRPSXWHU
ZLWK WKH GDWD HYDOXDWLRQ SURJUDP DQG OLJKWILEHUV IRU VLJQDO WUDQVSRUWDWLRQ $OO SDUWV DUH
VHSDUDWHO\EXLOGLQWRWKHVWDQGDUGSXOVHKHDWLQJVHWXSQRWWRDIIHFWWKHRULJLQDOH[SHULPHQW
:HSHUIRUPHGVRPHH[SHULPHQWZLWKWKH'2$3RQ&RSSHUWRVHHLIZHJHWSUDFWLFDEOHUHVXOWV
6HH)LJIRUDW\SLFDOVLJQDORIWKHH[SHULPHQW
)LJ (PLVVLYLW\εRI&RSSHUYHUVXVWLPHGXULQJDSXOVHKHDWLQJH[SHULPHQW7KHPHOWLQJRIWKHZLUHLV EHWZHHQ DQG µV 1RWH 3RODULPHWHU PHDVXUHPHQWV DUH SHUIRUPHG DW RQO\ RQHZDYHOHQJWKDWQP
(PLVVLYLW\ε
7LPHµV
7KH YDOXH IRU HPLVVLYLW\ ε EHIRUH PHOWLQJ LV DUELWUDU\ GHSHQGLQJ RQO\ RQ WKH SUHYLRXV
SUHSDUDWLRQ RI WKH VXUIDFH ,Q )LJ WKH VLJQDO IRU HPLVVLYLW\ GHFUHDVHV VWURQJO\ DV WKHZLUH
UHDFKHV 7P 7KH OLWHUDWXUH YDOXH IRU ε DW WKLV ZDYHOHQJWK LV ε7P >.ULVKQDQ @
)LJVKRZVFOHDUO\WKDWRXUPHDVXUHPHQWPDWFKHVWKLVYDOXHDWWKHPHOWLQJWHPSHUDWXUH7P
7KHPRVW LQWHUHVWLQJ IDFW LV WKDWε ULVHVDJDLQ LQ WKH OLTXLGSKDVHDV WHPSHUDWXUH LQFUHDVHVDQG
UHDFKHVDYDOXHRIDW.
([SHULPHQWDO SDUDPHWHUV DQG VSHFLILF YDOXHV XVHG IRUFDOFXODWLRQV
7DEOH&RSSHUVSHFLILFYDOXHVDQGH[SHULPHQWDOSDUDPHWHUV
6SHFLPHQPDWHULDO &RSSHU&X
0DQXIDFWXUHU$GYHQW5HVHDUFK0DWHULDOV/GW(\QVKDP(QJODQG
6KDSH :LUH
'LDPHWHU PP
3XULW\ QRQR[\JHQIUHH
+DUGQHVV 7HPSHUDVGUDZQ
'HQVLW\DW. NJ⋅P
0HOWLQJSRLQW .
%RLOLQJSRLQW .
6SHFLPHQOHQJWK 9DULDEOHPP
&KDUJLQJYROWDJH N9
:DYHOHQJWKO QP
&KDSWHU
5HVXOWV
([SHULPHQWDOUHVXOWV
7KH H[SHULPHQWDO SDUDPHWHUV IRU &RSSHU FDQ EH VHHQ LQ 7DE ,Q WKH WHPSHUDWXUH UDQJH
EHWZHHQ.DQG.WKHIROORZLQJSURSHUWLHVDUHGHWHUPLQHGIURPWKHPHDVXUHGVLJQDOV
L HQWKDOS\+
LL VSHFLILFKHDWXQGHUFRQVWDQWSUHVVXUHF3
LLL HOHFWULFDOUHVLVWLYLW\ZLWKRXWFRUUHFWLRQRIWKHYROXPH
H[SDQVLRQρ
LY YROXPHH[SDQVLRQ
Y HOHFWULFDOUHVLVWLYLW\LQFOXGLQJFRUUHFWLRQRIWKHYROXPH H[SDQVLRQρFRUU
YL WKHUPDOFRQGXFWLYLW\λ
YLL WKHUPDOGLIIXVLYLW\D
3OHDVHQRWHWKDWDOOJUDSKVLQWKLVFKDSWHUVKRZWKHVHSURSHUWLHVYHUVXVWHPSHUDWXUH7$OWKRXJK
JUDSKV SURSHUW\ YHUVXV HQWKDOS\ZRXOG EHPRUH DFFXUDWH LW LV FRPPRQO\ RIPRUH LQWHUHVW IRU
WHFKQLFDO XVH WR SORW WKH SURSHUWLHV YHUVXV WHPSHUDWXUH (UURU EDUV DW VLJQLILFDQW WHPSHUDWXUHV
DERXW..DQG.DUHDOVRVKRZQLQWKHJUDSKV
(QWKDOS\+
)LJXUHVKRZVHQWKDOS\+YHUVXVWHPSHUDWXUH77KHUHVXOWVRIWKHPHDVXUHPHQWVDUHJLYHQ
E\ WKH IROORZLQJ OLQHDU SRO\QRPLDO ILWV RI DSSUR[LPDWHO\ VHSDUDWHPHDVXUHPHQWV7KH QRQ
OLQHDUFXUYHGXULQJPHOWLQJLVDVZHWKLQNDUHVXOWRIVXUIDFHHIIHFWVDFKDQJHLQHPLVVLYLW\DQG
DVOLJKWRVFLOODWLRQRIWKHDPSOLILHUHOHFWURQLF
)LJ 6SHFLILF HQWKDOS\+ YHUVXV WHPSHUDWXUH 7 RI&RSSHU DUH GDWD SRLQWV RI WKHPHDVXUHPHQW
VROLGOLQHVDUHWKHOHDVWVTXDUHVILWV
3RO\QRPLDOILWUHVXOWVIRUWKHHQWKDOS\+7LQWKHVROLGVWDWHDQGLQWKHOLTXLGSKDVH
3RO\QRPLDOILWV+7N-NJ 7HPSHUDWXUHUDQJHRIYDOLGLW\
VROLG +7 ⋅7 .7.
OLTXLG +7 ⋅7 .7.
$WWKHPHOWLQJWUDQVLWLRQWKHFKDQJHLQHQWKDOS\∆+PLV
'+P N-NJ
(QWKD
OS\N
- NJ
7HPSHUDWXUH.
6SHFLILFKHDW
$VPHQWLRQHG LQ WKH ODVWFKDSWHU WKHVSHFLILFKHDWRI&RSSHU LVGHULYHGIURPWKHVORSHVRI WKH
OLQHDUVHFWLRQVRIWKHHQWKDOS\YHUVXVWHPSHUDWXUHSORW)URPWKHSRO\QRPLDOILWVRIWKHHQWKDOS\
ZHREWDLQIRUWKHVSHFLILFKHDW
6SHFLPHQ &36ROLG &3OLTXLG
&RSSHUZLUH -⋅NJ. -⋅NJ.
)LJ6SHFLILFKHDWF3YHUVXVWHPSHUDWXUH7FDOFXODWHGIURPWKHHQWKDOS\+ZLWK(T
1RWH)LJLVGHULYHGIURPRXUPHDVXUHPHQWVDQGQRWGLUHFWO\PHDVXUHG$OWKRXJKWKHYDOXHV
IRUF3DUHQRWDVVWHDG\DVWKHRQHVREWDLQHGE\D'6&PHDVXUHPHQWWKHSORWVKRZVWKHFRUUHFW
IXQFWLRQDOIRUPRIF3DWWKHPHOWLQJWUDQVLWLRQ
6SH
FLILF
+HD
WF
SN
- NJ
.
7HPSHUDWXUH.
(OHFWULFDOUHVLVWLYLW\ZLWKRXWFRUUHFWLRQRIYROXPHH[SDQVLRQ
7KHHOHFWULFDOUHVLVWLYLW\ZLWKRXWFRUUHFWLRQLVFDOFXODWHGE\XVLQJ(T
)LJ (OHFWULFDOUHVLVWLYLW\ρYHUVXVWHPSHUDWXUH7 DUHGDWDSRLQWVRIWKHPHDVXUHPHQWVROLGOLQHV
DUHWKHOHDVWVTXDUHVILWV
3RO\QRPLDOILWVU7P:P 7HPSHUDWXUHUDQJHRIYDOLGLW\
VROLG ρ7 [⋅7 .7.
OLTXLG ρ7 [⋅7 .7.
$WPHOWLQJWKHFKDQJHLQHOHFWULFDOUHVLVWLYLW\ZLWKRXWYROXPHFRUUHFWLRQLV
'U P:P
(OHFWULF
DOUHV
LVWLY
LW\ρ
µ
ΩP
7HPSHUDWXUH.
9ROXPHH[SDQVLRQ
$VH[SODLQHGHDUOLHUWKHYROXPHH[SDQVLRQRI&RSSHUKDVQRWEHHQPHDVXUHGZLWKLQWKLVZRUN
6HYHUDO LQYHVWLJDWRUV HJ >1XEDXPHU @ LQ RXU ODERUDWRU\ RU >*DWKHUV @ KDYH
GHWHUPLQHGUHOLDEOHDQGDFFXUDWHSRO\QRPLDOILWVIRUWKHYROXPHH[SDQVLRQRISXUH&RSSHU:H
GHFLGHGWRXVHWKHVHGDWDLQVWHDGRIPHDVXUHLWRXUVHOYHV
7KH YROXPH H[SDQVLRQ LQ WKH VROLG SKDVH LV FDOFXODWHG IURP OLQHDU H[SDQVLRQ GDWD IRU SXUH
&RSSHU SXEOLVKHG E\ >*ROGVPLWK @ DQG >1,67@ :KHUHDV (T SXEOLVKHG E\
>%OXPP DQG +HQGHUVRQ @ ZDV XVHG WR GHULYH WKH YROXPH H[SDQVLRQ 99 IURP OLQHDU
H[SDQVLRQ//
∆+
∆⋅+
∆⋅=∆//
//
//
99
7KHEHVWZD\WRILWWKHFDOFXODWHGGDWDIRU99LVDUGRUGHUSRO\QRPLDOILWVKRZQEHORZ
)RU WKH OLTXLG SKDVH ZH XVHG WKH SRO\QRPLDO ILW IURP WKH ZRUN RI >1XEDXPHU @ ZKR
GHWHUPLQHG WKH YROXPH H[SDQVLRQ 99+ :H DGDSWHG WKH SRO\QRPLDO ILW DQG REWDLQHG
997
3RO\QRPLDOILWV99 7HPSHUDWXUHUDQJHRIYDOLGLW\
VROLG997 [
⋅7[⋅7[⋅7
.7.
OLTXLG 997 [⋅7 .7.
)LJ 9ROXPH H[SDQVLRQ99 YHUVXV WHPSHUDWXUH7Ì DUH YDOXHV IURP >*ROGVPLWK @ DUH
>1,67@YDOXHVDQG UHSUHVHQWWKHYDOXHVPHDVXUHGE\>1XEDXPHU@7KHVROLGOLQH
LVWKHSRO\QRPLDOILWIRUWKHYROXPHH[SDQVLRQ
)RU SXUHPHWDOV VHYHUDO H[SHULPHQWDO LQYHVWLJDWLRQV HVWLPDWHG D YDOXH IRU WKH YROXPH FKDQJH
GXULQJPHOWLQJLQWKHUDQJHEHWZHHQSHUFHQW7KHFKDQJHGXULQJPHOWLQJREWDLQHGE\RXU
SRO\QRPLDOILWVLV/LWHUDWXUHYDOXHVIRUWKHYROXPHFKDQJHDWWKHVROLGOLTXLGWUDQVLWLRQRI
SXUH &RSSHU DUH >$VNHODQG @ DQG >%OXPP +HQGHUVRQ @ 7KH DFWXDO
GHQVLWLHVDUHOLVWHGLQ7DE
9ROXP
H([S
DQVLRQ
99
S
HUFHQ
W
7HPSHUDWXUH.
(OHFWULFDOUHVLVWLYLW\ZLWKFRUUHFWLRQRIWKHYROXPHH[SDQVLRQ
%\ XVLQJ WKH ILWV IRU WKH YROXPH H[SDQVLRQ RQH FDQ FDOFXODWH WKH YROXPHFRUUHFWHG HOHFWULFDO
UHVLVWLYLW\ZLWK(T
)LJ9ROXPHFRUUHFWHGHOHFWULFDOUHVLVWLYLW\ρFRUUYHUVXVWHPSHUDWXUH7
3RO\QRPLDOILWVUFRUU7P:P 7HPSHUDWXUHUDQJHRIYDOLGLW\
VROLG ρFRUU7 [⋅7 .7.
OLTXLG ρFRUU7 [⋅7 .7.
%\FRQVLGHULQJWKHYROXPHFRUUHFWLRQWKHFKDQJH∆ρFRUUDWPHOWLQJLV
'UFRUU P:P
(OHFWULF
DOUHV
LVWLY
LW\ρ
FRUU
µΩ
P
7HPSHUDWXUH.
7KHUPDOFRQGXFWLYLW\
$V VKRZQ LQ (T WKHUPDO FRQGXFWLYLW\ LV FDOFXODWHG E\ XVLQJ WHPSHUDWXUH FRUUHFWHG
HOHFWULFDOUHVLVWLYLW\DQGWKH/25(17=QXPEHU
)LJ 7KHUPDOFRQGXFWLYLW\λYHUVXVWHPSHUDWXUH7 DUHWKHPHDVXUHGGDWDSRLQWVVROLGOLQHVDUHWKH
OHDVWVTXDUHVILWV DUHIURP>3RWWODFKHU@ DUHIURP>=LQRY\HY@DQG DUHIURP
>7\H@
7KHOHDVWVTXDUHVILWVIRUWKHWKHUPDOFRQGXFWLYLW\DUH
3RO\QRPLDOILWVO:.P 7HPSHUDWXUHUDQJHRIYDOLGLW\
VROLG λ7 ⋅7 .7.
OLTXLG λ7 ⋅7 .7.
7KH
UPDOFRQ
GXFWLYLW\
λ:.
P
7HPSHUDWXUH.
7KHUPDOGLIIXVLYLW\
)RUFDOFXODWLQJWKHUPDOGLIIXVLYLW\ZLWK(TWKHGHQVLW\GDWDJLYHQWHPSHUDWXUHLVQHHGHG
ZKLFKFDQEHREWDLQHGE\
( )( )7
99
7G
=
ZKHUH997LVWKHUHODWLYHYROXPHH[SDQVLRQDWDJLYHQWHPSHUDWXUH7DQGLVWKHGHQVLW\
RI&RSSHULQNJ⋅PDW.
)LJ 7KHUPDO GLIIXVLYLW\ D YHUVXV WHPSHUDWXUH7 DUH WKH GDWD SRLQWV WKH VROLG OLQH LV WKH OHDVW
VTXDUHVILWDQG DUHYDOXHVIURP>&XVFR0RQDJKDQ@
7KH
UPDOGLIIXV
LYLW\D
P
V
7HPSHUDWXUH.
3RO\QRPLDOILWVIRUWKHWKHUPDOGLIIXVLYLW\D7IRU&RSSHU
3RO\QRPLDOILWVDPV 7HPSHUDWXUHUDQJHRIYDOLGLW\
VROLG D7 [[⋅7 .7.
OLTXLG D7 [[⋅7 .7.
7DEXODUVXPPDU\RIWKHH[SHULPHQWDOUHVXOWV
7RVXPXSWKHUHVXOWVRIWKLVFKDSWHU7DEZKLFKLVVKRZQRQWKHQH[WSDJHOLVWVLQWKHUDQJH
EHWZHHQ.DQG.LQ.VWHSVYDOXHVIRUDOORIWKHSURSHUWLHVFDOFXODWHGIURPWKH
SRO\QRPLDOILWV
7DE 7KHUPRSK\VLFDOSURSHUWLHVRIFRSSHUDWJLYHQWHPSHUDWXUHV77HPSHUDWXUH+(QWKDOS\ρVSHF5HVLVWLYLW\XQFRUUHFWHG999ROXPHH[SDQVLRQG'HQVLW\ρFRUUVSHF5HVLVWLYLW\FRUUHFWHGλ7KHUPDOFRQGXFWLYLW\D7KHUPDOGLIIXVLYLW\
7.
+N-NJ
UP:P
99G
NJPUFRUUP:P
O:.P
DPV
[ [ [ [ [V [O [ [ [ [ [ [ [ [ [ [ [ [ [ [
&RPSDULVRQZLWKOLWHUDWXUH
7DE&RPSDULVRQ RI HQWKDOS\ + VSHFLILF KHDW FS DQG HOHFWULFDO UHVLVWLYLW\ ρ ZLWK OLWHUDWXUH GDWD
VXEVFULSWV V LQGLFDWHVVROLGVWDWHYDOXHV OYDOXHVLQWKHOLTXLGSKDVHDQG VOYDOXHVDWWKHVROLG
OLTXLGWUDQVLWLRQ1RWH LQGLFDWHVQRQYROXPHFRUUHFWHGYDOXHV
+V +O '+VO FSV FSO UV UO 'UVO 5HIHUHQFH
WKLVZRUN
>1XEDXPHU@
>*DOORE@
>*DWKHUV@
7DE&RPSDULVRQ RI WKHUPDO FRQGXFWLYLW\λ DQG WKHUPDO GLIIXVLYLW\ D ZLWK OLWHUDWXUH GDWD 1RWH
LQGLFDWHVYDOXHVDW.
OV OO DV DO 5HIHUHQFH
[ [ WKLVZRUN
>3RWWODFKHU@
[ >&XVFR@
>=LQRY\HY@
>13/UHSRUW@
[ >7RXORXNLDQ@
:LWKLQRXUHVWLPDWHGXQFHUWDLQW\DOORIWKHJLYHQOLWHUDWXUHGDWDVKRZDQH[FHOOHQWDJUHHPHQWIRU
WKHUPDOFRQGXFWLYLW\DQGWKHUPDOGLIIXVLYLW\RI&RSSHU
&KDSWHU
(VWLPDWLRQRIXQFHUWDLQW\
7KHVH IROORZLQJ SDUDJUDSKV DUH GHDOLQJZLWK WKH SUREOHP RI GHWHUPLQLQJ WKH DFFXUDF\ RI RXU
UHVXOWVDQGWKHEHORQJLQJHUURUV%HIRUHKDQGLWKDVWREHVDLGWKDWPRVWRIWKHNQRZQV\VWHPDWLF
HUURUVDUHFRPSHQVDWHGGXULQJWKHGDWDHYDOXDWLRQZKHUHDVWKHXQNQRZQV\VWHPDWLFHUURUVRIRXU
PHDVXUHPHQWV DUH QRW LQFOXGHGZLWKLQ WKH JLYHQ XQFHUWDLQW\ UDQJHV7KH GHYLDWLRQ RI WKH RZQ
UHVXOW IURPSURYHQ OLWHUDWXUHGDWD LVDJRRG LQGLFDWRU IRU WKHV\VWHPDWLFHUURU6LQFHRXUUHVXOWV
FRUUHVSRQG TXLWH ZHOO ZLWK OLWHUDWXUH GDWD DQG UHFRPPHQGHG YDOXHV ZH WKLQN WKDW ZH KDYH
FDQFHOHGRXWPRVWRIWKHVHHUURUV7KHVWDWHGXQFHUWDLQWLHVFRYHUWKHDFFLGHQWDOHUURUVZKLFKPD\
DQG GR DULVH GXULQJ WKHPHDVXUHPHQWV DQG WKH HYDOXDWLRQ SURFHVVHV 1RWH VXEVFULSWV V DQG O
GHQRWHVROLGVWDWHOLTXLGSKDVHSURSHUWLHV
7KH FXUUHQW VLJQDO 7ZR GLIIHUHQW HUURUV FDQ RFFXUZLWKLQ WKH FXUUHQWPHDVXUHPHQW 3HDUVRQ
HOHFWURQLFV FDOLEUDWH WKHLU FXUUHQWSUREHV DQG JXDUDQWHH DPD[LPDO GHYLDWLRQ RI± 7KH
VHFRQGXQFHUWDLQW\ LV WKH VLJQDOGLJLWDOL]DWLRQZLWKLQ WKHGDWD UHJLVWUDWLRQRI WKHFRPSXWHU:H
KDYHELWGDWDDFTXLVLWLRQFDUGVZKHUHDVWKHHUURU LVDWPRVW LQWKHODVWGLJLWKHQFHOHVVWKDQ
±$WKLUGEXWQHJOLJLEOHSRLQWLVWKHXQFHUWDLQW\RIWKHRKPLFYROWDJHGLYLGHUVEHFDXVH
RILWVVPDOOFRQWULEXWLRQRIOHVVWKDQ7KHVDPHDSSOLHVWRWKHYROWDJHPHDVXUHPHQW7KH
WRWDOHUURURIWKHFXUUHQWPHDVXUHPHQWLV
∆, ±
7KHYROWDJHVLJQDOV7KHHUURURIWKHYROWDJHVLJQDOVLVPRUHGLIILFXOWWRHVWLPDWHWKDQWKHRQHRI
WKHFXUUHQWVLJQDO7KHYROWDJHLVFDOFXODWHGE\(T$VVDLGHDUOLHUWKHWKLUGWHUPG/GWFDQ
EH RPLWWHG EHFDXVH LW LV D VPDOO FRQWULEXWLRQ WR WKH RYHUDOO YDOXH EXW WKLV OHDGV WR D VPDOO
XQFHUWDLQW\$QRWKHU HUURU FDQRFFXU LI WKHFRUUHFWLRQRI WKH VHFRQG WHUP/⋅G,GW LQ WKH VDPH
HTXDWLRQ LV QRW GRQH DFFXUDWHO\ )RU VRPH RWKHU PDWHULDOV WKH YROWDJH VLJQDOV DUH QRW YHU\
VHQVLWLYH RQ WKH VL]H RI WKLV FRUUHFWLRQ EXW ZLWK &RSSHU WKLV FRUUHFWLRQ VKRXOG EH GRQH DV
DFFXUDWHDVSRVVLEOH$QRWKHUSUREOHPZKLOHXVLQJWKHVHKLJKFXUUHQWVFRXOGEHWKHDULVLQJVNLQ
HIIHFW(DUOLHUHVWLPDWLRQVKDYHVKRZQ WKDW WKLV LQIOXHQFHFRXOGEHQHJOHFWHGZLWKRXWDIIHFWLQJ
WKH VLJQDOV WRR PXFK $QG DV D ODVW SRLQW WKH YROWDJH PHDVXUHPHQW LV DIIHFWHG E\ WKH VDPH
GLJLWDOL]DWLRQSUREOHPDVWKHFXUUHQWVLJQDOV,IDOORIWKHDERYHHUURUVDUHHVWLPDWHGZLWK±
DQGDUHVXPPHGXSWKHWRWDOHUURURIWKHYROWDJHPHDVXUHPHQWLV
∆8 ±
7KH WHPSHUDWXUHPHDVXUHPHQW 7KHUH DUHPDLQO\ WZRGLIIHUHQW UHDVRQV WKDW DUH UHVSRQVLEOH
IRUDQXQFHUWDLQW\RIWKHWHPSHUDWXUHPHDVXUHPHQW)LUVWWKHLQWHUIHUHQFHILOWHULQWKHS\URPHWHU
KDV D EDQGZLGWK RI QPZKLOH WKH IRUPDOLVP IRU FDOFXODWLQJ WKH WHPSHUDWXUH XVHV DQ H[DFW
ZDYHOHQJWK6LPXODWLRQVIURP>6DFKVHQKRIHU@VKRZHGWKDWWKHHUURULVDWOHDVWOHVVWKDQ±
7KHVHFRQGHUURURFFXUVE\VHWWLQJWKHUDWLRRIWKHHPLVVLYLWLHVεεP :HZHUHDEOHWR
VKRZ WKDW WKH HPLVVLYLW\ RI &RSSHU VOLJKWO\ ULVHV ZKLOH RYHUKHDWLQJ WKH OLTXLG PHWDO %XW
VLPXODWLRQV LQFOXGLQJ WKLV FKDQJH LQHPLVVLYLW\ >6HLIWHU@ VKRZHG WKDW WKLV IRUFHGHUURU LV
QHJOLJLEOH1HZVLPXODWLRQVIRU&RSSHUOHDGDW.WRDQHUURUOHVVWKDQ7KHUHIRUHWKH
WRWDOHUURURIWKHWHPSHUDWXUHPHDVXUHPHQWLVJLYHQE\
∆7 ±
7KHPDVVRIWKHZLUH7KHPDVVLVFDOFXODWHGE\WKHGHQVLW\DQGWKHYROXPHRIWKHZLUHVDPSOH
ZKHUHDV WKH YROXPH LWVHOI KDV WR EH FDOFXODWHG IURP WKH OHQJWK RI WKH ZLUH DQG WKH GLDPHWHU
6LQFH WKH ZLUH LV GUDZQ DQG LWV GLDPHWHU LV FRQWUROOHG WKURXJKRXW WKH ZKROH SURFHVV WKH
XQFHUWDLQW\ RI WKH GLDPHWHU FDQ EH RPLWWHG 7KH RQO\ HUURU ZH FDQ HVWLPDWH LV DQ XQFHUWDLQW\
ZLWKLQ WKH OHQJWK GHWHUPLQDWLRQ 7KH OHQJWK RI WKH ZLUH FDQ EH PHDVXUHG ZLWK DQ HUURU RI
±PP&RQVLGHULQJDQDYHUDJHOHQJWKRIWKHZLUHVRIPPWKHHUURULV±7KXVWKH
HUURURIWKHPDVVLVDOVR
∆P ±
7KHHQWKDOS\7KHHQWKDOS\LVILUVWFDOFXODWHGIURPWKHPHDVXUHGYDOXHVE\XVLQJ(T7KH
HUURU RI+ LV FDOFXODWHG E\ VXPPLQJ XS WKH HUURUV RI HDFK RI WKH VLJQDOV XVHG WR FDOFXODWH+
7KXV WKH WRWDOHUURU LV±%XW WKHFDOFXODWHGHUURURI+ LVDOZD\V OHVV WKDQ WKUHHSHUFHQW
EHFDXVH ZH DYHUDJH VHYHUDO HQWKDOS\FXUYHV WRPLQLPL]H WKH VWDWLVWLF HUURUV1HYHUWKHOHVVZH
GHFLGHGWRVHWWKHHUURUIRUWKHHQWKDOS\WR
∆+ ±
7KHVSHFLILFKHDW6LQFHWKHVSHFLILFKHDW LVFDOFXODWHGIURPWKHVORSHRI WKHOLQHDUVHFWLRQVRI
WKHHQWKDOS\FXUYHWKHHUURUFDQRQO\EHDSSUR[LPDWHGVWDWLVWLFDOO\7KHHUURURIWKHVSHFLILFKHDW
LV WKHXQFHUWDLQW\RI WKH VORSHRI WKH OLQHDU ILW6LQFH WKHUHDUHPRUH DQGHYHQPRUHDFFXUDWH
GDWDSRLQWV IRUFDOFXODWLQJ WKH OLQHDU ILWRI WKH OLTXLGSKDVHF3O LVPRUHDFFXUDWH WKDQF3V7KH
HUURUVIRUWKHVSHFLILFKHDWDUH
∆F3V ±
∆F3O ±
7KH XQFRUUHFWHG HOHFWULFDO UHVLVWLYLW\ 7KH VDPH SRLQWV DV VDLG EHIRUH ZKLOH KDQGOLQJ WKH
HUURURIWKHHQWKDOS\DUHDSSO\LQJWRρDVZHOO7KXVWKHXQFHUWDLQW\LVWKHVDPH
∆ρ ±
7KHYROXPHH[SDQVLRQ6LQFHZHXVHGOLWHUDWXUHGDWDIRUWKHYROXPHH[SDQVLRQZHKDYHWRXVH
HUURU HVWLPDWLRQV 7KH YROXPH H[SDQVLRQ GDWD IRU WKH VROLG VWDWH DUH YHU\ DFFXUDWH DQG RIWHQ
SURYHGE\GLIIHUHQWPHDVXUHPHQWVVR WKHHVWLPDWHGYDOXHIRU WKHXQFHUWDLQW\LV±)RUWKH
OLTXLG SKDVHZHXVHGDSRO\QRPLDO ILWZKLFKZDVPHDVXUHG LQRXURZQ ODERUDWRU\ DQGZKRVH
XQFHUWDLQW\ZDVGHWHUPLQHGWR±$VDUHVXOWZHKDYHIRUWKHHUURURIWKHYROXPHH[SDQVLRQ
∆99V ±
∆99O ±
7KHFRUUHFWHGHOHFWULFDOUHVLVWLYLW\ρFRUULVFDOFXODWHGIURPWKHXQFRUUHFWHGHOHFWULFDOUHVLVWLYLW\
DQGWKHYROXPHH[SDQVLRQ7KHUHIRUHWKHHUURUVRIERWKTXDQWLWLHVDUHVXPPHGXSDQGUHVXOWLQ
WKHWRWDOXQFHUWDLQW\RIρFRUUZKLFKLV
ρFRUUV ±
ρFRUUO ±
7KHWKHUPDOFRQGXFWLYLW\7KLVTXDQWLW\LVFDOFXODWHGE\XVLQJ(T7KHELJJHVWSUREOHP
ZKLOHKDQGOLQJWKLVHTXDWLRQLVWKHHUURUHVWLPDWLRQRIWKH/25(17=QXPEHU/VLQFHWKHYDOXHV
UHSRUWHGIRU/DUHYDU\LQJLQWKHUDQJHEHWZHHQDQG[9.:HGHFLGHGWRUHJDUG
/DVDFRQVWDQWZKLFKKDVWKHHUURU]HUREHFDXVHLIDQ\RQHLVDEOHWRGHWHUPLQHWKHFRUUHFWYDOXH
RI / IRU &RSSHU ZH ZLOO XVH LW IRU RXU FDOFXODWLRQV DQG DUH DEOH WR FKDQJH RXU UHVXOWV
LPPHGLDWHO\ 7KHUHIRUH WKH WRWDO HUURU RI λ FRQVLVWV RI WKH HUURUV RI WKH WHPSHUDWXUH DQG WKH
FRUUHFWHGHOHFWULFDOUHVLVWLYLW\%\IROORZLQJWKHUXOHVRIWKHEDVLFHUURUSURSDJDWLRQFDOFXODWLRQV
RQHJHWV
FRUU
FRUU
77
ρρ
λλ ∆
+∆=∆
6LQFHWKHGHWHUPLQDWLRQRIERWKTXDQWLWLHVLVLQGHSHQGHQWIURPWKHRWKHUZHFDQUHDUUDQJHWKLV
HTXDWLRQDQGREWDLQ
∆+
∆=∆
FRUU
FRUU
77
ρρ
λλ
,IWKLVFDOFXODWLRQLVFDUULHGRXWRQHJHWVIRUWKHWRWDOXQFHUWDLQW\RIWKHWKHUPDOFRQGXFWLYLW\
∆λV ±
∆λO ±
7KH WKHUPDO GLIIXVLYLW\ /DVW EXW QRW OHDVW ZH KDYH WR GHDOZLWK WKH XQFHUWDLQW\ RI WKHUPDO
GLIIXVLYLW\ZKLFKLVFDOFXODWHGE\XVLQJ(T)RUFDOFXODWLQJWKHHUURURIWKLVTXDQWLW\LWLV
QHFHVVDU\ WR UHDUUDQJH WKH HTXDWLRQ WR VHH WKDW WKHUPDO GLIIXVLYLW\ LV LQGHSHQGHQW IURP WKH
YROXPHH[SDQVLRQ
≠
⋅⋅⋅=
⋅
⋅⋅
=⋅
=
99
DGF
7/
99
GF
997/
GFD
SS
S ρρλ
2WKHUZLVHWKHYROXPHH[SDQVLRQ99ZRXOGEHFRQVLGHUHGWZLFHDQGWKHHUURUZRXOGEHFRPH
HUURQHRXVO\ODUJH%\DSSO\LQJWKHVDPHIRUPDOLVPDVIRUWKHUPDOFRQGXFWLYLW\WR(TRQH
JHWVVLQFH/DQGGDUHFRQVWDQWV
S
S
F
F
77
DD ∆
+∆
+∆=∆
ρρ
7KHRQO\GLIIHUHQFHEHWZHHQWKHHUURUFDOFXODWLRQRIWKHUPDOFRQGXFWLYLW\DQGGLIIXVLYLW\LVWKDW
WKHGLIIHUHQWWHUPVRI(TDUHQRWLQGHSHQGHQWIURPHDFKRWKHUDQGPXVWQRWEHVXPPHGXS
JHRPHWULFDOO\%\FDOFXODWLQJWKHWRWDOHUURURIWKHUPDOGLIIXVLYLW\RQHREWDLQV
∆DV ±
∆DO ±
7DEXODUVXPPDU\RIWKLVFKDSWHU
7DE0HDVXUHGDQGFDOFXODWHGSURSHUWLHVRI&RSSHUZLWKWKHLUEHORQJLQJHUURUV
VROLGVWDWH.7.OLTXLGSKDVH.7.
(UURU
4XDQWLW\ VROLGVWDWH OLTXLGSKDVH
&XUUHQW, ±9ROWDJH8 ±7HPSHUDWXUH7 ±0DVVP ±(QWKDOS\+ ±∆+P ±6SHFLILFKHDWF3 ± ±XQFRUU5HVLVWLYLW\ρ ±9ROXPHH[SDQVLRQ99 ± ±'HQVLW\G ± ±FRUU5HVLVWLYLW\ρFRUU ± ±∆ρFRUU ±WKHUP&RQGXFWLYLW\λ ± ±WKHUP'LIIXVLYLW\D ± ±
&KDSWHU
&RQFOXVLRQDQGRXWORRN
7KHWKHUPRSK\VLFDOSURSHUWLHVRI&RSSHUXSWR.LQWRWKHOLTXLGSKDVHKDYHEHHQPHDVXUHG
ZLWKLQWKHFXUUHQWZRUNE\XVLQJDQRKPLFSXOVHKHDWLQJWHFKQLTXH$PRQJWKHVHSURSHUWLHVDUH
WZRZKLFKZHUHRISDUWLFXODULQWHUHVWWKHUPDOFRQGXFWLYLW\DQGWKHUPDOGLIIXVLYLW\
$VDILUVWSRLQWZHVKRZHGWKDWRXUSXOVHKHDWLQJDSSDUDWXVFDQEHDGDSWHGIRUPHDVXUHPHQWVRQ
ORZPHOWLQJPHWDOVZLWKRXWH[SDQGLQJWKHXQFHUWDLQW\RIWKHH[SHULPHQWDOGDWD:HDUHDEOHWR
VKRZ WKDW RXU YDOXHV IRU HQWKDOS\ HOHFWULFDO UHVLVWLYLW\ DQG VSHFLILFKHDW LQ WKH VROLG VWDWH DV
ZHOO DV LQ WKH OLTXLG SKDVH FRUUHVSRQG YHU\ ZHOO ZLWK OLWHUDWXUH GDWD ZLWKLQ WKH XQFHUWDLQW\
UDQJHV:HXVHGWKH:,('(0$11)5$1=/25(17=ODZWRGHWHUPLQHWKHUPDOFRQGXFWLYLW\
DQG WKHUPDO GLIIXVLYLW\ 1RUPDOO\ WKHVH SURSHUWLHV DUH PHDVXUHG GLUHFWO\ DV VKRZQ LQ PRVW
SXEOLFDWLRQV E\ XVLQJ HJ D ODVHU IODVK DSSDUDWXV 2XU REWDLQHG UHVXOWV DUH LQ H[FHOOHQW
DJUHHPHQWZLWKOLWHUDWXUHYDOXHVLH>&XVFR@DOWKRXJKZHFDOFXODWHGWKHVHSURSHUWLHV
$V D IXWXUH SURMHFW DFFXUDWH HPLVVLYLW\ PHDVXUHPHQWV ZLWK RXU '2$3 V\VWHP VKRXOG EH
SHUIRUPHGRQ&RSSHUIRUYDULRXVUHDVRQV
L IXUWKHUWHVWLQJRIWKH'2$3V\VWHP
LL PLQLPL]DWLRQRIWKHXQFHUWDLQW\RIWKHWHPSHUDWXUHLQWKHOLTXLGSKDVH
LLL EDVLFUHVHDUFKUHDVRQV
3DUWLFXODUO\ LL LV RI JUHDW LQWHUHVW IRU RXU PHDVXUHPHQWV ZLWK UHJDUG WR PDNH WKH UHVXOWV DV
DFFXUDWH DV SRVVLEOH $V PHQWLRQHG EHIRUH LLL VKRXOG EH DOVR RI JUHDW LQWHUHVW EHFDXVH WKH
HPLVVLYLW\εIRU&RSSHUVHHPVWRULVHDJDLQLQWKHOLTXLGSKDVHDVWHPSHUDWXUHLQFUHDVHV
6HYHUDO \HDUV DJR ZH ZHUH DEOH WR GHWHUPLQH ZLWK RXU DSSDUDWXV WKH SURSHUWLHV RI *ROG
>1XEDXPHU @ 1RZZH DSSOLHG ZLWK HTXDOO\ VXFFHVV WKH SXOVHKHDWLQJ WHFKQLTXH WR
&RSSHUDQGZHUHDOVRDEOHWRDGGWKHUPDOFRQGXFWLYLW\GLIIXVLYLW\WRWKHGHWHUPLQHGSURSHUWLHV
7KHUHIRUH WKH QH[W ORJLFDO VWHS VKRXOG EH WR ILJXUH RXW LI ZH DUH DEOH WR H[SDQG RXU
PHDVXUHPHQWVWRWKHQH[WORZHUPHOWLQJPHWDO6LOYHU
)LJ 7KH GHWHFWHG VLJQDOV RI 6LOYHU 6LJQDOV JUHHQ FXUUHQW UHG EODFN YROWDJH EOXH VXUIDFH
UDGLDQFH7KHKRUL]RQWDOOLQHDUVHFWLRQRIWKHUDGLDQFHVLJQDOEHWZHHQDQGµVLQGLFDWHV
WKHPHOWLQJRIWKHZLUH
)LJ DV D ILUVW DWWHPSW FOHDUO\ VKRZV WKHPHOWLQJ SODWHDX RI6LOYHU 7P . WLPH
UHVROYHGWRJHWKHUZLWKDOOWKHRWKHUHOHFWULFDOVLJQDOV7KLVILUVWDQGYHU\HQFRXUDJLQJH[SHULPHQW
RQ6LOYHUVKRXOGEHXVHGDVDVWDUWLQJSRLQWIRUPHDVXUHPHQWVRQ6LOYHUDVDIXWXUHSURMHFW7KHVH
PHDVXUHPHQWVZRXOGQRWRQO\EHD IXUWKHU WHVW IRU WKHDELOLWLHVRI WKHS\URPHWHUEXWDOVRYHU\
FKDOOHQJLQJEHFDXVHXSWRQRZQRDFFXUDWHPHDVXUHPHQWVRQ6LOYHUKDYHEHHQSHUIRUPHGZLWK
WKHSXOVHKHDWLQJWHFKQLTXH
6LJQD
OV9
7LPHµV
&KDSWHU
5HIHUHQFHV
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±(OHPHQWV3HUJDPRQ3UHVV2[IRUG+XOWJUHQ5'HVDL 3'+DZNLQV'7*OHLVHU0.HOOH\.. DQG:DJPDQ'' 6HOHFWHG9DOXHVRIWKHUPRG\QDPLF3URSHUWLHVRIWKH(OHPHQWV$PHULFDQ6RFLHW\IRU0HWDOV.OHPHQV 3 * DQG :LOOLDPV 5 . 7KHUPDO FRQGXFWLYLW\ RI PHWDOV DQG DOOR\V,QWHUQDWLRQDO0HWDOV5HYLHZV9RO1RS
.ULVKQDQ6SULYDWHFRPPXQLFDWLRQ0DJOLü . ' &H]DLUOL\DQ $ DQG 3HOHWVN\ 9 ( &RPSHQGLXP RI 7KHUPRSK\VLFDO3URSHUW\0HDVXUHPHQW0HWKRGV9ROXPH3OHQXP3UHVV1HZ<RUN0DJOLü . ' &H]DLUOL\DQ $ DQG 3HOHWVN\ 9 ( &RPSHQGLXP RI 7KHUPRSK\VLFDO3URSHUW\0HDVXUHPHQW0HWKRGV9ROXPH3OHQXP3UHVV1HZ<RUN0LOOV.&0RQDJKDQ%-DQG.HHQH%-7KHUPDO&RQGXFWLYLWLHVRI0ROWHQ0HWDOV3DUW3XUH0HWDOV13/5HSRUW&007$1DWLRQDO,QVWLWXWHRI6WDQGDUGVDQG7HFKQRORJ\1,67&HUWLILFDWHRI6WDQGDUG5HIHUHQFH0DWHULDO&RSSHU7KHUPDO([SDQVLRQ6WDQGDUG5HIHUHQFH0DWHULDOV3URJUDP1XVVEDXPHU * :HLWHUHQWZLFNOXQJ GHU ]HLWDXIJHO|VWHQ ([SDQVLRQV XQG 6SDQQXQJVPHVVXQJ EHL0LNURVHNXQGHQ 3XOVKHL]H[SHULPHQWHQ %HVWLPPXQJ WKHUPRSK\VLNDOLVFKHU'DWHQYRQ.XSIHUXQG*ROG'LSORPDUEHLW3RWWODFKHU * %HLWUl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
:HLPDQWHO&KXQG+DPDQQ&*UXQGODJHQGHU)HVWN|USHUSK\VLN$XIODJH6SULQJHU9HUODJ%HUOLQ=LQRY\HY9(7DOXWV6*.DPDVKHY0*9ODVRY%93RO\NRYD93.RUHQRYVNLL1,&KLSLQD/ ,=DJUHELQ/' 7KHUPDO3URSHUWLHVDQG/RUHQW]1XPEHUVRI&RSSHUDQG6LOYHUDW+LJKDQG$YHUDJH7HPSHUDWXUHV3K\V0HW0HWDOOS
'LH YRUOLHJHQGH$UEHLWZXUGH DP ,QVWLWXW IU([SHULPHQWDOSK\VLN GHU7HFKQLVFKHQ8QLYHUVLWlW
*UD] XQWHU GHU /HLWXQJ YRQ +HUUQ DR 8QLY 3URI 'U *HUQRW 3RWWODFKHU GXUFKJHIKUW ,KP
JHEKUW PHLQH YROOVWH +RFKDFKWXQJ XQG VHL DQ GLHVHU 6WHOOH PHLQ JDQ] EHVRQGHUV 'DQN
DXVJHGUFNW 1LFKW QXU IU GLH %HUHLWVWHOOXQJ GHU DSSDUDWLYHQ0LWWHO ]XU 'XUFKIKUXQJ GLHVHU
$UEHLW VRQGHUQ DXFK IU VRYLHOH DQGHUH'LQJHGD HLQHYROOVWlQGLJH$XIOLVWXQJGHQ5DKPHQ
GLHVHU6HLWHVSUHQJHQZUGH6HLQH+LOIVEHUHLWVFKDIWZDUVRJURGDHUDXFKLQVHLQHU)UHL]HLW
QRFK=HLWIUPLFKHUEULJWHXQGLPPHUHLQJXWHV:RUWRGHUHLQHQJXWHQ9RUVFKODJSDUDWKDWWH
2KQHVHLQ=XWXQZlUHGLHVH$UEHLWQLH]XVWDQGHJHNRPPHQ
(EHQVR]X'DQNYHUSIOLFKWHW IKOH LFKPLFKPHLQHQEHLGHQ)UHXQGHQXQG.ROOHJHQ',$FKLP
6HLIWHUXQG)UDQ]6DFKVHQKRIHU6LHVLQGPLUZlKUHQGGHU$UEHLWQLFKWQXUPLWVHKU]DKOUHLFKHQ
XQG ZHUWYROOHQ 5DWVFKOlJHQ ]XU 6HLWH JHVWDQGHQ VRQGHUQ KDOIHQ PLU DXFK LPPHU ZLHGHU DXV
H[SHULPHQWHOOHQ 6DFNJDVVHQ $XHUGHP VRUJWHQ VLH QHEHQ GHU $UEHLW IU HLQ ZLUNOLFK
DQJHQHKPHV.OLPDXQGGHQQ|WLJHQ6SDLP/DERU
'DZlKUHQGPHLQHU'LSORPDUEHLW GHU ,QVWLWXWVYRUVWDQGZHFKVHOWHP|FKWH LFKPLFKEHLEHLGHQ
9RUVWlQGHQ +HUUQ 8QLY3URI 'U +HOPXW -lJHU XQG +HUUQ DR 8QLY3URI 'U /DXUHQWLXV
:LQGKRO]KHU]OLFKEHGDQNHQVRZLHEHLDOOGHQDQGHUHQXQJHQDQQWHQ0LWJOLHGHUQGHV,QVWLWXWHV
IUGLH+LOIVEHUHLWVFKDIWXQGGDVDQJHQHKPH$UEHLWVNOLPD
)U DOO GLH )UHXQGVFKDIW XQG GLH VFK|QHQ 0RPHQWH ZlKUHQG GHV 6WXGLXPV P|FKWH LFK DXFK
PHLQH6WXGLHQNROOHJLQQHQXQG.ROOHJHQGDQNHQGLHPLU VWHWVKDOIHQGHQ ULFKWLJHQ:HJGXUFK
GLH8QWLHIHQGHU3K\VLN]XILQGHQ
=X JXWHU /HW]W VHL DQ GLHVHU 6WHOOH PHLQHQ (OWHUQ *HVFKZLVWHUQ 9HUZDQGWHQ XQG )UHXQGHQ
JHGDQNW GLH PLFK ZlKUHQG GHV 6WXGLXPV XQWHUVWW]W KDEHQ DXFK ZHQQ VLH VLFK QLFKW LPPHU
JHQDXYRUVWHOOHQNRQQWHQZDV LFKJHUDGHPDFKH0HLQJDQ]EHVRQGHUHU'DQNJLOWDEHUPHLQHU
)UHXQGLQ$QJHOLND6LHZDUZLUNOLFKLPPHUIUPLFKGDXQGPXWHDXFK|IWHUVPHLQHQ0LPXW
QDFK)HKOVFKOlJHQHUWUDJHQ
'$1.(