Advanced Application Guidelines for Ground Fault Protection

Advanced Application Guidelines for
Ground Fault Protection
George E. Alexander, Joe Mooney, and William Tyska
Schweitzer Engineering Laboratories, Inc.
Presented at the
28th Annual Western Protective Relay Conference
Spokane, Washington
October 23–25, 2001
$'9$1&('$33/,&$7,21*8,'(/,1(6)25
*5281')$8/73527(&7,21
*HRUJH($OH[DQGHU-RH0RRQH\DQG:LOOLDP7\VND
6FKZHLW]HU(QJLQHHULQJ/DERUDWRULHV,QF
3XOOPDQ:$86$
,1752'8&7,21
$SUHYLRXVSDSHU>@GHVFULEHGDSSOLFDWLRQJXLGHOLQHVIRUJURXQGIDXOWGHWHFWLRQRQ
XQFRPSHQVDWHGRYHUKHDGSRZHUOLQHV,QWKDWSDSHUWKHGLVFXVVLRQIRFXVHGRQWKHSURWHFWLRQ
HOHPHQWVDQGFRPSDULVRQVZHUHEDVHGXSRQVHQVLWLYLW\DQGVHFXULW\
7KHGLVFXVVLRQLQWKLVSDSHUH[SDQGVRQWKHVDPHWRSLFDQGLQFOXGHVGLVFXVVLRQRQWKHIROORZLQJ
œ 6HULHV&RPSHQVDWHG/LQHV
œ 6LQJOH3ROH7ULSSLQJ
œ 8QGHUJURXQG&DEOHV
3UREOHPDUHDVRIJURXQGIDXOWGHWHFWLRQLQFOXGHGLVWDQFHHOHPHQWRYHUUHDFKRQVHULHV
FRPSHQVDWHGOLQHVGLUHFWLRQDOVWDELOLW\RQVHULHVFRPSHQVDWHGOLQHVGLUHFWLRQDORYHUFXUUHQW
VHQVLWLYLW\LQVLQJOHSROHWULSSLQJDSSOLFDWLRQVDSSOLFDWLRQRIJURXQGGLVWDQFHRQFDEOHVDQG
GLUHFWLRQDORYHUFXUUHQWVHQVLWLYLW\RQFDEOHV
7KLVSDSHURIIHUVUHFRPPHQGDWLRQVRQVHWWLQJDQGVHOHFWLRQRIWKHDSSURSULDWHJURXQGIDXOW
SURWHFWLRQHOHPHQWVLQWKHDERYHDSSOLFDWLRQV:HDOVRLQFOXGHJXLGHOLQHVIRUVHWWLQJJURXQGIDXOW
GHWHFWLQJHOHPHQWV,QRWKHUFDVHVZHRIIHUUHFRPPHQGDWLRQVRQHOHPHQWVHOHFWLRQDQGLGHQWLI\
RWKHUSRVVLEOHSUREOHPDUHDV
6(5,(6&203(16$7('/,1($33/,&$7,216
6HULHVFDSDFLWRUVUHGXFHWKHRYHUDOOLQGXFWLYHUHDFWDQFHRIDWUDQVPLVVLRQOLQH$GGLWLRQDO
LQIRUPDWLRQUHJDUGLQJWKHEHQHILWVRIVHULHVFRPSHQVDWLRQDUHGLVFXVVHGLQGHWDLOLQYDULRXVWH[W
ERRNVDQGQXPHURXVWHFKQLFDOSDSHUV,QWKLVGRFXPHQWVHULHVFRPSHQVDWLRQLVVLPSO\DFFHSWHG
DVDFKDOOHQJHWRWKHSURWHFWLRQHQJLQHHU
7KHWHUP³VHULHVFDSDFLWRU´UHIHUVWRD³EDQN´RIPXOWLSOHLQGLYLGXDOFDSDFLWRUFDQVFRQQHFWHGLQD
VHULHVSDUDOOHODUUDQJHPHQW)RUVLPSOLFLW\LQWKLVSDSHUZHXVH³VHULHVFDSDFLWRU´LQSODFHRIWKH
PRUHFXPEHUVRPH³VHULHVFDSDFLWRUEDQN´7KHFDSDFLWRUFDQVDQGUHODWHGSURWHFWLYHHTXLSPHQW
DUHSK\VLFDOO\PRXQWHGRQDUDLVHGSODWIRUPWKDWLVLQVXODWHGIURPJURXQG
6LQFHWKHFDSDFLWLYHUHDFWDQFH;FLVLQVHULHVZLWKWKHWUDQVPLVVLRQOLQHLQGXFWLYHUHDFWDQFH;O
DQG;F;ODVXEKDUPRQLFQDWXUDOIUHTXHQF\WUDQVLHQWUHVXOWVIROORZLQJIDXOWVRUFDSDFLWRU
VZLWFKLQJ7KLVFDQUHVXOWLQSURWHFWLRQSUREOHPVRYHUUHDFKDQGJHQHUDWRUSUREOHPV
VXEV\QFKURQRXVUHVRQDQFH
$OOVHULHVFDSDFLWRUVHPSOR\VRPHW\SHRIE\SDVVSURWHFWLRQWRSUHYHQWGDPDJHFDXVHGE\
RYHUYROWDJHUHVXOWLQJIURPKLJKIDXOWFXUUHQWOHYHOV7KLVE\SDVVSURWHFWLRQPD\EHDVLPSOH
WULJJHUHGDLUJDSRUPHWDOR[LGHYDULVWRUV029V7KHRSHUDWLRQRIDWULJJHUHGJDSSURGXFHV
KLJKIUHTXHQF\WUDQVLHQWV'LJLWDORUQXPHULFUHOD\VZLWKWKHLUDQDORJDQWLDOLDVLQJILOWHUVDQG
GLJLWDOILOWHUVHIIHFWLYHO\PLWLJDWHWKHVHKLJKIUHTXHQF\WUDQVLHQWVEXWWKHVHVDPHGHYLFHVPXVW
GHDOZLWKWKHVXEKDUPRQLFWUDQVLHQWV029VSDUDOOHOWKHFDSDFLWRUEDQNZLWKDUHVLVWDQFHZKRVH
YDOXHLVGHSHQGHQWXSRQWKHPDJQLWXGHRIYROWDJHGHYHORSHGDFURVVWKHFDSDFLWRUEDQNGXULQJD
IDXOW7KHHIIHFWLVWRSURGXFHDQRQVLQXVRLGDOZDYHIRUPDQGWRPRGLI\EXWQRWHOLPLQDWHWKH
QDWXUDOIUHTXHQF\VXEKDUPRQLFWUDQVLHQW029E\SDVVSURWHFWLRQLQFRUSRUDWHVDQDLUJDSWKDWLV
WULJJHUHGZKHQWKHHQHUJ\H[FHHGVWKH029UDWLQJ7KXVWKH029SURWHFWVWKHFDSDFLWRUIURP
RYHUYROWDJHZKLOHWKHDLUJDSSURYLGHVWKHUPDOSURWHFWLRQRIWKH029,QHLWKHUE\SDVVVFKHPH
WKHFDSDFLWRULVVKRUWHGZKHQWKHDLUJDSLVWULJJHUHG
3UREOHP6FRSH
0XFKRIWKHH[LVWLQJVHULHVFRPSHQVDWHGOLQHSURWHFWLRQOLWHUDWXUHIRFXVHVRQWKHSUREOHPV
DVVRFLDWHGZLWKGLVWDQFHDQGGLUHFWLRQDOIXQFWLRQV:KLOHGLUHFWLRQDOLQWHJULW\DQGRYHUUHDFKDUH
LPSRUWDQWLVVXHVWKHYLDELOLW\RIWKHGLUHFWLRQDOFRPSDULVRQVFKHPHORJLFLVHTXDOO\LPSRUWDQW
)RULQVWDQFHDGGLWLRQDOWUDQVLHQWEORFNLQJORJLFPD\KDYHWREHDGGHGWRSURYLGHDGHTXDWH
VHFXULW\DJDLQVWPLVRSHUDWLRQVZKHUHGLUHFWLRQDOLQWHJULW\FDQQRWEHPDLQWDLQHGIRUVORZFOHDULQJ
IDXOWV
1DWXUDO)UHTXHQF\7UDQVLHQWV
)RUXQFRPSHQVDWHGWUDQVPLVVLRQOLQHVSURWHFWLRQHQJLQHHUVRIWHQIHHOFRPIRUWDEOHDSSO\LQJ
JURXQGGLVWDQFHUHOD\VEDVHGRQVWHDG\VWDWHIDXOWLPSHGDQFHVSORWWHGWRJHWKHUZLWKDUHOD\
FKDUDFWHULVWLFRQDQ5;GLDJUDP:HGRQRWUHFRPPHQGWKLVDSSURDFKIRUVHULHVFRPSHQVDWHG
WUDQVPLVVLRQOLQHVEHFDXVHRIWKH³LPSHGDQFHVSLUDO´SURGXFHGE\WKHVXEKDUPRQLFWUDQVLHQWV
PHQWLRQHGDERYH)RUWXQDWHO\WKLVLPSHGDQFHVSLUDOFDQEHUHDGLO\DQDO\]HGIRUJURXQGGLVWDQFH
IXQFWLRQVLPSOHPHQWHGLQGLJLWDORUQXPHULFUHOD\VWKDWHPSOR\DFRVLQHGLVFUHWH)RXULHU
WUDQVIRUPRURWKHUGLJLWDOILOWHU
7KHIROORZLQJDQDO\VLVGHVFULEHVWKHLPSHGDQFHVSLUDOSKHQRPHQRQ1RWHWKDWWKHHIIHFWVRI
E\SDVVSURWHFWLRQDUHQRWFRQVLGHUHG²WKHFDSDFLWDQFHYDOXHQHYHUFKDQJHV)LJXUHGHSLFWVRQH
SKDVHRIDVHULHVFRPSHQVDWHGWUDQVPLVVLRQOLQH7KHVZLWFKFORVHVDWW WRDSSO\DQ$*IDXOW
DWWKHUHPRWHEXVRIWKHWUDQVPLVVLRQOLQH
=V
=F
=O
YEXV
YW
=V
=F
=O
6RXUFH,PSHGDQFH
6HULHV&DSDFLWRU,PSHGDQFH
5HSOLFD/LQH,PSHGDQFH
)LJXUH 6HULHVFRPSHQVDWHGWUDQVPLVVLRQOLQHV
7KHVROXWLRQLVREWDLQHGE\VROYLQJHTXDWLRQIRUWKHIDXOWFXUUHQWLWDQGVXEVHTXHQWO\VROYLQJ
IRUWKHEXVYROWDJHYEXVW
YW = 9 ‡ VLQ ‡ W + = LW ‡ 5 +
GLW
‡ / + ‡ LW ‡ GW
&
GW
×
7KHIROORZLQJYDOXHVZHUHXVHG
6RXUFH
=V = =V = µ•=V = µ• /LQH
=O = =O = µ•=O = µ• &DSDFLWRU
=F = µ ± • 9ROWDJH
9 = » YROWV 7KH$SKDVHIDXOWFXUUHQWLWLVVKRZQLQ)LJXUH
)DXOW&XUUHQW
IW
IW
±
±
±
7LPHVHFRQGV
)LJXUH )DXOW&XUUHQW:DYHIRUPV
,Q)LJXUHIWLVWKH+]FRPSRQHQWRIWKH$SKDVHIDXOWFXUUHQWDQGIWWKHEROGHGOLQH
LVWKH+]QDWXUDOIUHTXHQF\WUDQVLHQW
7KH$SKDVHYROWDJHYEXVWLVVKRZQLQ)LJXUH
%XV9ROWDJH
IW
IW
±
±
7LPHVHFRQGV
)LJXUH %XV9ROWDJH:DYHIRUPV
,Q)LJXUHIWLVWKH+]FRPSRQHQWDQGIWWKHEROGHGOLQHLVWKH+]QDWXUDO
IUHTXHQF\WUDQVLHQW
7KHQH[WVWHSLVWRVROYHIRUWKHDSSDUHQWLPSHGDQFHVHHQE\WKH$SKDVHJURXQGGLVWDQFHUHOD\
)LUVWWKHWLPHGRPDLQVROXWLRQIRULWDQGYEXVWDUHVDPSOHGWLPHVSHUF\FOH$IXOOF\FOH
QRQUHFXUVLYHGLJLWDOILOWHUWKHQFRQYHUWVWKHVDPSOHGYDOXHVWRSKDVRUV7KHFXUUHQWSKDVRUVDUH
WKHQFRPSHQVDWHGE\DGGLQJ>=±==@Â,WRWKHSKDVHFXUUHQWDQGWKHDSSDUHQWLPSHGDQFH
LVFDOFXODWHGZKHUH, Â,$,%,&
)LJXUHVKRZVWKHVSLUDOLQJLPSHGDQFHFDXVHGE\WKHQDWXUDOIUHTXHQF\WUDQVLHQWVKRZQLQ
)LJXUHDQG)LJXUH1RWHWKDWLPPHGLDWHO\DIWHUWKHIDXOWLVDSSOLHGWKHVSLUDOFKDUDFWHULVWLFLV
ODUJHDQGSDVVHVWKURXJKWKHVWHDG\VWDWHLPSHGDQFHFKDUDFWHULVWLF$VWKHWUDQVLHQWGHFD\VWKH
VSLUDOLVUHGXFHGXQWLOLWUHDFKHVDVWHDG\VWDWHYDOXHDIWHUDSSUR[LPDWHO\F\FOHV7KHFLUFOHWKDW
SDVVHVWKURXJKWKHRULJLQRIWKH5;GLDJUDPUHSUHVHQWVWKHVWHDG\VWDWHFKDUDFWHULVWLFIRUD
=RQH$SKDVHJURXQGGLVWDQFHPKRIXQFWLRQVHWZLWKDRKPUHDFK7KLVVHWWLQJUHSUHVHQWVD
EHVWJXHVVWRSUHYHQW=RQHRYHUUHDFKIRUDUHPRWHEXVIDXOWEDVHGRQWKHVWHDG\VWDWH
LPSHGDQFH,WLVDSSDUHQWWKDWWKLVUHDFKVHWWLQJPXVWEHUHGXFHGWRSUHYHQW=RQHRSHUDWLRQ
EHFDXVHRIWKHVSLUDOLQJLPSHGDQFH
,PSHGDQFH6SLUDOIRU$*IDXOW
,P]
,PV]
,PPKR
5H]5HV]5HPKR
)LJXUH 5;'LDJUDP
'LUHFWLRQDO,QWHJULW\
'LUHFWLRQDOLQWHJULW\LVGHILQHGKHUHDVWKHDELOLW\RIDGLUHFWLRQDOIXQFWLRQ²DGLUHFWLRQDOJURXQG
GLVWDQFHIXQFWLRQDQHJDWLYHVHTXHQFHGLUHFWLRQDOIXQFWLRQRUD]HURVHTXHQFHGLUHFWLRQDO
IXQFWLRQ²WRRSHUDWHDQGVWD\RSHUDWHGIRUWKHIDXOWGXUDWLRQIRUDIRUZDUGJURXQGIDXOW
GHSHQGDELOLW\DQGWRQRWRSHUDWHIRUDUHYHUVHJURXQGIDXOWVHFXULW\'LUHFWLRQDOLQWHJULW\LVDQ
LVVXHHYHQZLWKXQFRPSHQVDWHGWUDQVPLVVLRQOLQHDSSOLFDWLRQV6HULHVFRPSHQVDWHGWUDQVPLVVLRQ
OLQHVH[DFHUEDWHWKHSUREOHPEHFDXVHRIWKHSRVVLELOLW\RIYROWDJHDQGFXUUHQWUHYHUVDOV
$YROWDJHUHYHUVDORFFXUVIRUDJURXQGIDXOWQHDUDVHULHVFDSDFLWRUZKHQWKHLPSHGDQFHIURPWKH
YROWDJHWUDQVIRUPHUORFDWLRQWRWKHIDXOWLVFDSDFLWLYHUDWKHUWKDQLQGXFWLYH7KLVUHYHUVDORIWKH
YROWDJHSKDVHDQJOHFDQFUHDWHERWKGHSHQGDELOLW\DQGVHFXULW\SUREOHPV
)LJXUHVKRZVWZRSDUDOOHOWUDQVPLVVLRQOLQHV,QHDFKOLQHDVHULHVFDSDFLWRULVSK\VLFDOO\
ORFDWHGDWWKHOHIW/EXV)RUDJURXQGIDXOWDW)RQWKHWRSOLQHWKDWLVFORVHWRWKHVHULHV
FDSDFLWRUWKHYROWDJHVHHQE\WKHUHOD\VDW/RQERWKWKHWRSDQGERWWRPOLQHVPD\EHUHYHUVHG$
JURXQGGLVWDQFHUHOD\RQWKHWRSOLQHFRXOGGHWHUPLQHWKDWWKHIDXOWLVH[WHUQDOUDWKHUWKDQLQWHUQDO
DQGEORFNWULSSLQJ$JURXQGGLVWDQFHUHOD\RQWKHERWWRPOLQHFRXOGGHWHUPLQHWKDWWKHIDXOWLV
LQWHUQDOUDWKHUWKDQH[WHUQDODQGWULSLQFRUUHFWO\$VLPLODUVFHQDULRFRXOGRFFXUIRUHLWKHU
QHJDWLYHRU]HURVHTXHQFHGLUHFWLRQDOIXQFWLRQVXVHGLQDGLUHFWLRQDOFRPSDULVRQVFKHPH
5HOD\
5HOD\
)
5HOD\
5HOD\
/
5
)LJXUH ([DPSOH6\VWHP
$QHIIHFWLYHPHDQVWRPLWLJDWHWKHHIIHFWVRIDYROWDJHUHYHUVDOLQDJURXQGGLVWDQFHUHOD\LVWRXVH
WKHDSSURSULDWHSRVLWLYHVHTXHQFHYROWDJH9DVWKH³SRODUL]LQJ´TXDQWLW\DQGWRXVHWKHSUHIDXOW
YDOXHRI97KHSUHIDXOWRU³PHPRU\´YDOXHRI9UHVXOWVLQDG\QDPLFFKDUDFWHULVWLFWKDW
DVVXUHVSURSHUGLUHFWLRQDOVHQVLQJXQWLO9WUDQVLWLRQVWRWKHIDXOWYDOXH:LWKGLJLWDORUQXPHULF
UHOD\VPHPRU\DOJRULWKPVPD\EHLPSOHPHQWHGZLWKPHPRU\SHUVLVWHQFHUDQJLQJIURPVHYHUDO
F\FOHVWRLQILQLW\7KHPHPRU\IHDWXUHHQVXUHVWKDWJURXQGGLVWDQFHIXQFWLRQVVHQVHWKHFRUUHFW
GLUHFWLRQDWIDXOWLQLWLDWLRQ.QRZLQJWKHPHPRU\SHUVLVWHQFHLQWHUYDODOORZVWKHXVHURU
PDQXIDFWXUHUWRDGGWKHUHTXLUHGWUDQVLHQWEORFNLQJORJLFWRWKHRYHUDOOVFKHPHORJLFWRDVVXUH
SURSHURSHUDWLRQRIWKHGLUHFWLRQDOFRPSDULVRQVFKHPHORJLF
$FXUUHQWUHYHUVDORFFXUVIRUDJURXQGIDXOWRQWKHSURWHFWHGVHULHVFRPSHQVDWHGOLQHZKHQWKH
IDXOWFXUUHQWHQWHUVDWRQHHQGDQGOHDYHVDWWKHRWKHUHQGDVZRXOGRFFXUIRUDQH[WHUQDOIDXOW
)RUWKHV\VWHPLQ)LJXUHLIWKHERWWRPOLQHLVUHPRYHGDFXUUHQWUHYHUVDOFDQRFFXUIRUD
JURXQGIDXOWDW)LIWKHOHIWVRXUFHLPSHGDQFHLVOHVVWKDQWKHUHDFWDQFHRIWKHVHULHVFDSDFLWRU,I
WKHJURXQGIDXOWDW)ZHUHDEROWHGIDXOWWKHQWKHODUJHIDXOWFXUUHQWZRXOGPRVWOLNHO\FDXVHUDSLG
E\SDVVLQJRIWKHVHULHVFDSDFLWRU+RZHYHUDKLJKUHVLVWDQFHIDXOWPLJKWUHGXFHWKHIDXOWFXUUHQW
VRWKHVHULHVFDSDFLWRULVQRWE\SDVVHG
&HUWDLQQHJDWLYHDQG]HURVHTXHQFHGLUHFWLRQDOIXQFWLRQVFDQPLVRSHUDWHRUIDLOWRRSHUDWHIRU
FXUUHQWUHYHUVDOVDQGYROWDJHUHYHUVDOV7KHORFDWLRQRIWKHYROWDJHWUDQVIRUPHUVRQHLWKHUWKH
³EXVVLGH´RU³OLQHVLGH´RIWKHVHULHVFDSDFLWRULVRQHIDFWRUWKDWGHWHUPLQHVZKDWKDSSHQV7KH
GHVLJQRIWKHGLUHFWLRQDOIXQFWLRQFDQPLWLJDWHRUHOLPLQDWHWKHVHSUREOHPV³&RPSHQVDWHG´
GLUHFWLRQDOIXQFWLRQVSURYLGHWKHXVHUZLWKVHWWLQJVWKDWYLUWXDOO\³PRYH´WKHIXQFWLRQDORQJWKH
OLQHWRZKHUHFRUUHFWGLUHFWLRQDOVHQVLQJLVDVVXUHG>@
$VDQH[DPSOHWKHVHWWLQJVIRUWKHFRPSHQVDWHGQHJDWLYHVHTXHQFHGLUHFWLRQDOHOHPHQWV
GHVFULEHGLQUHIHUHQFH>@DUHJLYHQIRURQHUHOD\ORFDWLRQLQ)LJXUH&RQVLGHUWKHUHOD\ORFDWHG
RQWKHERWWRPOLQHDWWKHOHIWEXVYROWDJHWUDQVIRUPHUORFDWHGRQWKHOLQHVLGHRIWKHVHULHV
FDSDFLWRU)LUVWDVVXPHWKHFDSDFLWRUEDQNLVVKRUWHGXQFRPSHQVDWHGOLQH7KHVXJJHVWHG
LPSHGDQFHWKUHVKROGVHWWLQJVDUH
=
=5 = =) +
,UDWHG
=) =
/
ZKHUH = LVWKHSRVLWLYHVHTXHQFHLPSHGDQFHRI WKHOLQH
,UDWHGLVWKHUDWHGFXUUHQWRI WKHUHOD\RUA
/
7KHGLUHFWLRQDOHOHPHQWGHFODUHVDIRUZDUGIDXOWLIWKHFDOFXODWHG=QHJDWLYHVHTXHQFH
LPSHGDQFHLVOHVVWKDQ=)DQGDUHYHUVHIDXOWLIWKHFDOFXODWHG=LVJUHDWHUWKDQ=5
1RZDVVXPHWKDWWKHVHULHVFDSDFLWRULVLQVHUYLFH%HFDXVHWKHUHOD\YROWDJHLVVXSSOLHGIURPWKH
OLQHVLGHRIWKHVHULHVFDSDFLWRUWKHFDSDFLWRULPSHGDQFHPXVWEHFRQVLGHUHGDVSDUWRIWKHVRXUFH
LPSHGDQFHEHKLQGWKHUHOD\,I;&LVJUHDWHUWKDQWKHVRXUFHLPSHGDQFHDYROWDJHUHYHUVDOFRXOG
RFFXUIRUIRUZDUGGLUHFWLRQIDXOWVUHVXOWLQJLQLPSURSHUGLUHFWLRQDOVHQVLQJ7RSUHYHQWWKLVWKH
=)VHWWLQJPXVWEHJUHDWHUWKDQ;&7KHVXJJHVWHGLPSHGDQFHWKUHVKROGVHWWLQJVDUH
= - ; +;
=5 = =) +
,UDWHG
=) =
/
&
&
ZKHUH = LVWKHSRVLWLYHVHTXHQFHLPSHGDQFHRI WKHOLQH
,UDWHGLVWKHUDWHGFXUUHQWRI WKHUHOD\RUA
; LVWKHSRVLWLYHVHTXHQFHLPSHGDQFHRI WKHVHULHVFDSDFLWRU
/
&
=HUR6HTXHQFH&RPSHQVDWLRQ)DFWRUIRU*URXQG'LVWDQFH)XQFWLRQV
$JURXQGGLVWDQFHIXQFWLRQDSSOLHGRQDWUDQVPLVVLRQOLQHZLWKRXWVHULHVFDSDFLWRUVUHTXLUHV
³]HURVHTXHQFHFXUUHQWFRPSHQVDWLRQ´RIWKHSKDVHFXUUHQWWRFRUUHFWO\GHWHUPLQHWKHWUXH
SRVLWLYHVHTXHQFHLPSHGDQFHIURPWKHUHOD\WRDJURXQGIDXOW$FRQFLVHGHULYDWLRQRIWKH]HUR
VHTXHQFHFXUUHQWFRPSHQVDWLRQIDFWRULVSUHVHQWHGLQ$SSHQGL[$
7KH]HURVHTXHQFHFXUUHQWFRPSHQVDWLRQLVGHILQHGDVIROORZV
,D + N ‡ ,
N=
= - =
=
,DLVWKHSKDVHFXUUHQWDWWKHUHOD\DQG,LVWKH]HURVHTXHQFHFXUUHQWDWWKHUHOD\=LVWKH]HUR
VHTXHQFHLPSHGDQFHDQG=LVWKHSRVLWLYHVHTXHQFHLPSHGDQFHRIWKHSURWHFWHGOLQH)RUD
VHULHVFDSDFLWRUFRPSHQVDWHGWUDQVPLVVLRQOLQHVKRXOGWKHHYDOXDWLRQRINXVHXQFRPSHQVDWHG
LPSHGDQFHV=DQG=RUFRPSHQVDWHGLPSHGDQFHV=±M;FDQG=±M;F";FLVWKHUHDFWDQFH
RIWKHVHULHVFDSDFLWRUVORFDWHGEHWZHHQWKHUHOD\DQGWKHHQGRIWKHOLQH9ROWDJHWUDQVIRUPHU
ORFDWLRQGHWHUPLQHVUHOD\ORFDWLRQ:HQH[WHYDOXDWHDQ$*IDXOWDWWKHUHPRWHEXVIRUWKHVHULHV
FRPSHQVDWHGWUDQVPLVVLRQOLQHV\VWHPLQ)LJXUHWRKHOSDQVZHUWKLVTXHVWLRQ
$VVXPHWKDWWKHVHULHVFDSDFLWRULVQRWE\SDVVHGGXULQJWKHIDXOWDQGWKDWXQFRPSHQVDWHGYDOXHV
RI=DQG=DUHXVHGWRFDOFXODWHN
N=
µ• - µ•
= µ - •
µ•
,D = µ - •
, = µ - •
9D = µ - •
9D
= µ•
,D + N ‡ ,
$VVXPLQJWKHYROWDJHWUDQVIRUPHULVORFDWHGRQWKHEXVVLGHRIWKHVHULHVFDSDFLWRUZHNQRZWKDW
WKHSRVLWLYHVHTXHQFHLPSHGDQFHIURPWKHUHOD\WRWKHIDXOWLVµƒµ±ƒ µƒ
7KHJURXQGGLVWDQFHUHOD\GRHVQRWFDOFXODWHWKHH[SHFWHGYDOXHRISRVLWLYHVHTXHQFHLPSHGDQFH
1H[WDVVXPHWKDWNLVFDOFXODWHGXVLQJFRPSHQVDWHGYDOXHVRI=DQG=
N=
(µ• + µ - •) - (µ• + µ - •) = µ - •
(µ• + µ - •)
9D
= µ•
,D + N ‡ ,
7KHGHVLUHGUHVXOWLVREWDLQHG,QIDFWWKHVSLUDOLQJLPSHGDQFHSORWWHGLQ)LJXUHZDVFDOFXODWHG
XVLQJN µ±ƒ
7KHUHIRUHWKHDSSDUHQWDQVZHUWRWKHTXHVWLRQLVWRFDOFXODWHNXVLQJ=±M;FDQG=±M;FIRU
JURXQGGLVWDQFHIXQFWLRQVWKDWDUHH[SHFWHGWRRSHUDWHEHIRUHWKHVHULHVFDSDFLWRULVE\SDVVHGDQG
WRFDOFXODWHNXVLQJ=DQG=IRUJURXQGGLVWDQFHIXQFWLRQVWKDWDUHH[SHFWHGWRRSHUDWHDIWHUWKH
VHULHVFDSDFLWRULVE\SDVVHG7KLVLVRQHRIWKRVHORJLFDODQVZHUVWKDWKDVQRYDOXHLQSUDFWLFHWKH
SULPDU\YDULDEOHWKDWGHWHUPLQHVZKHQRULIDVHULHVFDSDFLWRULVE\SDVVHGRUWKHGHJUHHRI
UHVLVWRUVKXQWLQJLI029¶VDUHXVHGLVWKHPDJQLWXGHRIIDXOWFXUUHQW%HFDXVHDJURXQGIDXOWDW
DSDUWLFXODUORFDWLRQPD\EHDGLUHFWJURXQGRUDKLJKLPSHGDQFHJURXQGGHSHQGLQJXSRQZKDW
FDXVHVWKHIDXOWJURXQGIDXOWFXUUHQWPDJQLWXGHVPD\YDU\IRUDJLYHQIDXOWORFDWLRQ
)RUWKH)LJXUHH[DPSOHXVLQJN µ±ƒFRXOGFDXVHD=RQHJURXQGGLVWDQFHIXQFWLRQ
WRRYHUUHDFKIRUDUHPRWHEXVIDXOWLIWKHWUDQVPLVVLRQOLQHZDVRSHUDWHGZLWKWKHVHULHVFDSDFLWRU
UHPRYHGIURPVHUYLFHVKRUWHG&RQVHTXHQWO\WKHEHVWSUDFWLFHLVWRFDOFXODWHNXVLQJWKH
XQFRPSHQVDWHGYDOXHVRI=DQG=
6HWWLQJDQG6HOHFWLRQ*XLGHOLQHV
:KDWLVWKHEHVWUHOD\VFKHPHWRXVHIRUVHULHVFRPSHQVDWHGWUDQVPLVVLRQOLQHSURWHFWLRQ²FXUUHQW
GLIIHUHQWLDORUGLUHFWLRQDOFRPSDULVRQ"%HIRUHWKHDGYHQWRIVRSKLVWLFDWHGVWDWLFDQDORJDQG
GLJLWDOQXPHULFUHOD\GHVLJQVWKHPRVWSRSXODUDQVZHUZDVSKDVHFRPSDULVRQDVXEVHWRI
FXUUHQWGLIIHUHQWLDO7RGD\ERWKFXUUHQWGLIIHUHQWLDODQGGLUHFWLRQDOFRPSDULVRQVFKHPHVDUH
DYDLODEOHIRUVHULHVFRPSHQVDWHGWUDQVPLVVLRQOLQHSURWHFWLRQ²RIWHQIURPWKHVDPH
PDQXIDFWXUHU1RWDOOFXUUHQWGLIIHUHQWLDOUHOD\VDUHVXLWDEOH1RWDOOGLVWDQFHGLUHFWLRQDOIXQFWLRQ
EDVHGGLUHFWLRQDOFRPSDULVRQVFKHPHVDUHVXLWDEOH7KHNH\LVWRNQRZDQGHYDOXDWHWKH
FDSDELOLWLHVDQGOLPLWDWLRQVRIDJLYHQUHOD\V\VWHP6RPHUHOD\VFRPELQHFXUUHQWGLIIHUHQWLDODQG
GLUHFWLRQDOFRPSDULVRQVFKHPHVLQRQHSDFNDJH
7KHUHTXLUHGFRPPXQLFDWLRQVFKDQQHOFDSDELOLWLHVVKRXOGEHFORVHO\VFUXWLQL]HG,QJHQHUDO
GLUHFWLRQDOFRPSDULVRQVFKHPHVUHTXLUHOHVVFKDQQHOFDSDELOLW\WKDQGRFXUUHQWGLIIHUHQWLDO
VFKHPHV:LWKWKHLQFUHDVLQJDYDLODELOLW\RIILEHURSWLFVZLGHUEDQGZLGWKFKDQQHOVDUHRIWHQ
DYDLODEOHWRDOORZWKHXVHRIFXUUHQWGLIIHUHQWLDOVFKHPHV
:KHQDXVHULVFRQVLGHULQJDSSOLFDWLRQRIDSDUWLFXODUUHOD\RUUHOD\VFKHPHRQDVHULHV
FRPSHQVDWHGOLQHIRUWKHILUVWWLPHSUHDQGSRVWSXUFKDVHWHVWLQJRQDPRGHOSRZHUV\VWHP
VLPXODWRUVKRXOGEHFRQVLGHUHG,QWKHSUHSXUFKDVHRUHYDOXDWLRQVWDJHVXFKWHVWLQJSHUPLWV
VFUHHQLQJEHWZHHQFRPSHWLQJSURGXFWVDQGE\LQFUHDVLQJWKHXVHU¶VJHQHUDONQRZOHGJHRIWKH
VXEMHFWDLGVLQWKHSXUFKDVHGHFLVLRQ,QWKHSRVWSXUFKDVHVWDJHVXFKWHVWLQJLQFUHDVHV
FRQILGHQFHLQWKHVHOHFWHGVHWWLQJVIRUDJLYHQDSSOLFDWLRQ
6,1*/(3+$6(75,33,1*$1'5(&/26,1*
7RGD\PDQ\XWLOLWLHVDUHIDFHGZLWKWKHQHHGIRUVXSSO\LQJPRUHUHOLDEOHSRZHUZLWKIHZHUDGGHG
WUDQVPLVVLRQOLQHV2QHRIWKHPHDQVWRDFKLHYHWKLVJRDOLVWKHLQFUHDVHGXVHRIVLQJOHSKDVH
WULSSLQJRIWKHWUDQVPLVVLRQFLUFXLWV,QDVLQJOHSKDVHWULSSLQJVFKHPHRQO\WKHIDXOWHGSKDVHRI
WKHWUDQVPLVVLRQOLQHLVLQWHUUXSWHGIRUVLQJOHOLQHWRJURXQGIDXOWV7KLVDOORZVSRZHUWREH
WUDQVPLWWHGRYHUWKHOLQHRQWKHWZRKHDOWK\SKDVHVZKLOHWKHIDXOWLVFOHDUHG7KLVLPSURYHVERWK
WKHUHOLDELOLW\RISRZHUWUDQVPLVVLRQDQGWKHVWDELOLW\RIWKHV\VWHPDJDLQVWSRZHUVZLQJV)RUDOO
IDXOWVLQYROYLQJPRUHWKDQRQHSKDVHDOOWKUHHSKDVHVRIWKHOLQHDUHRSHQHG7KHUHLVDOVRD
PRGLILFDWLRQRIWKLVVFKHPHUHIHUUHGWRDVVHOHFWLYHSKDVHWULSSLQJ,QDVHOHFWLYHSKDVHWULSSLQJ
VFKHPHRQO\WKHIDXOWHGSKDVHVDUHLQWHUUXSWHGIRUPXOWLSKDVHIDXOWV7KLVVFKHPHLVUDUHO\
DSSOLHGDVWKHDGYDQWDJHVRIWUDQVPLWWLQJSRZHURYHUDVLQJOHSKDVHDUHOLPLWHG
7KHVHVFKHPHVDUHRIWHQUHIHUUHGWRDVVLQJOHSKDVHWULSSLQJDQGUHFORVLQJEHFDXVHDXWRPDWLF
UHFORVLQJPXVWDOZD\VEHXVHGWRUHHVWDEOLVKWKHWKUHHSKDVHWUDQVPLVVLRQOLQHIROORZLQJDVLQJOH
SKDVHWULS5HFORVLQJIRUPXOWLSKDVHIDXOWVLVRSWLRQDODQGYDULHVZLWKHDFKDSSOLFDWLRQ
6FKHPH'HVLJQ
$OOSURWHFWLYHUHOD\VFKHPHVDUHGHVLJQHGWRGHWHFWLIDIDXOWLVZLWKLQLWV]RQHRISURWHFWLRQDQGLI
LWLVWRLVVXHDWULSRXWSXWVRWKDWWKHIDXOWPD\EHUHPRYHGIURPWKHSRZHUV\VWHP,QVLQJOH
SKDVHWULSSLQJDSSOLFDWLRQVWKHUHOD\PXVWDGGLWLRQDOO\GHWHUPLQHZKLFKSKDVHRUSKDVHVDUH
LQYROYHGLQWKHIDXOWDQGWKHQLVVXHWKHSURSHUWULSRXWSXWVWRRSHQHLWKHUDVLQJOHSROHRIWKH
EUHDNHURUDOOWKUHHSROHV7KXVDVLQJOHSKDVHWULSSLQJVFKHPHPXVWKDYHERWKIDXOWGHWHFWLRQ
FDSDELOLW\DQGIDXOWHGSKDVHVHOHFWLRQFDSDELOLW\7UDGLWLRQDOO\WKHUHDUHWZRGHVLJQDSSURDFKHV
WRPHHWWKHVHUHTXLUHPHQWV
7KHILUVWLVWKH³&RPELQHG´RU³,QWHJUDWHG´VFKHPH,QWKLVW\SHRIVFKHPHWKHVDPHPHDVXULQJ
HOHPHQWVDUHXVHGIRUERWKIDXOWGHWHFWLRQDQGSKDVHVHOHFWLRQ$QH[DPSOHRIWKLVW\SHRIVFKHPH
PLJKWEHDQLQGLYLGXDOSKDVHOLQHFXUUHQWGLIIHUHQWLDOUHOD\7KHLQGLYLGXDOSKDVHGLIIHUHQWLDO
HOHPHQWVZLOOGHWHFWWKHIDXOWDQGGHWHUPLQHZKLFKSKDVHVDUHLQYROYHGLQWKHIDXOW
7KHVHFRQGDSSURDFKLVD³6HSDUDWHG´VFKHPH,QWKLVVFKHPHGLIIHUHQWHOHPHQWVDUHXVHGWR
GHWHFWWKHIDXOWDQGWRGHWHUPLQHWKHIDXOWHGSKDVH$QH[DPSOHRIWKLVLVDWKUHHSKDVHWULSSLQJ
VFKHPHWKDWLVFRQYHUWHGWRVLQJOHSKDVHWULSSLQJE\WKHDGGLWLRQRISKDVHVHOHFWRUHOHPHQWVDQG
DVVRFLDWHGORJLF
:LWKWRGD\¶VPXOWLIXQFWLRQUHOD\VDVLQJOHSKDVHWULSSLQJVFKHPHLVPRVWOLNHO\WREHD
FRPELQDWLRQRIWKHWUDGLWLRQDOVFKHPHV6RPHRIWKHPHDVXULQJHOHPHQWVSRVVLEO\JURXQG
GLVWDQFHIXQFWLRQVDUHGHVLJQHGWRUHVSRQGRQO\WRVLQJOHOLQHWRJURXQGIDXOWV+RZHYHURWKHU
HOHPHQWVLQWKHUHOD\VXFKDV]HURDQGQHJDWLYHVHTXHQFHRYHUFXUUHQWHOHPHQWVDUHLQKHUHQWO\
QRQSKDVHVHOHFWLYHDQGPXVWLQFOXGHVHSDUDWHSKDVHVHOHFWLRQHOHPHQWVZKHQDSSOLHGLQVLQJOH
SKDVHWULSSLQJDSSOLFDWLRQV
(IIHFWVRIDQ2SHQ3KDVH
$QRSHQSKDVHRQDWUDQVPLVVLRQOLQHFUHDWHVXQEDODQFHVWKDWFDQDIIHFWQRWRQO\WKHUHOD\VRQWKH
OLQHZLWKWKHRSHQSKDVHEXWDOVRRWKHUUHOD\VWKURXJKRXWWKHV\VWHP(LWKHUWKHSURWHFWLRQ
HOHPHQWVPXVWEHGHVLJQHGWREHLPPXQHWRWKHHIIHFWVRIXQEDODQFHVRUWKH\PXVWEHGHVHQVLWL]HG
RUUHPRYHGIURPVHUYLFHGXULQJWKHRSHQSROHSHULRGIROORZLQJDVLQJOHSKDVHWULS&RQVLGHU
WKHVLPSOHV\VWHPRI)LJXUH7KLVVLPSOHV\VWHPLVXVHGWRVKRZWKHXQEDODQFHVUHVXOWLQJIURP
DQRSHQSKDVHZLWKORDG0RGHOLQJRIDQRSHQSKDVHLVGLVFXVVHGLQ$SSHQGL[%
/
5
/LQH
/LQH
/LQH
/LQH
)LJXUH 3DUDOOHO/LQH6\VWHP
7DEOH $OO3KDVHV&ORVHG
&XUUHQW6HFRQGDU\$PSHUHV
/LQH
/LQH
/LQH
,$
µƒ
µƒ
µƒ
,%
µ±ƒ
µ±ƒ
µ±ƒ
,&
µƒ
µƒ
µƒ
,
µƒ
µƒ
µƒ
,
,
9ROWDJHV6HFRQGDU\
%XV/
%XV5
9$
µƒ
µƒ
9%
µ±•
µ±ƒ
9&
µƒ
µƒ
9
µƒ
µƒ
9
9
7DEOH $3KDVH2SHQLQ/LQH
&XUUHQW6HFRQGDU\$PSHUHV
/LQH
/LQH
/LQH
,$
µƒ
µƒ
,%
µ±ƒ
µ±ƒ
µ±ƒ
,&
µƒ
µƒ
µƒ
,
µƒ
µƒ
µƒ
,
µ±ƒ
µƒ
µ±ƒ
,
µ±ƒ
µƒ
µ±ƒ
9ROWDJHV6HFRQGDU\
%XV/
%XV5
9$
µƒ
µƒ
9%
µ±•
µ±ƒ
9&
µƒ
µƒ
9
µƒ
µƒ
9
µƒ
µ±ƒ
9
µƒ
µ±ƒ
,IWKHUHOD\SRWHQWLDOLVREWDLQHGIURPWKHOLQHUDWKHUWKDQWKHEXVDQG]HURYROWDJHLVDVVXPHGIRU
$SKDVHWKHQWKHUHOD\RQ/LQHLVSUHVHQWHGZLWKWKHIROORZLQJDQDORJVLJQDOV
9ROWDJHV6HFRQGDU\
%XV/
%XV5
9$
9%
µ±•
µ±ƒ
9&
µƒ
µƒ
9
µƒ
µƒ
9
µ±ƒ
µ±ƒ
9
µ±ƒ
µ±ƒ
0KR'LVWDQFH(OHPHQWV
7KHSKDVHPKRGLVWDQFHHOHPHQWVDVVRFLDWHGZLWKWKHRSHQSKDVHRQWKHOLQHVKRXOGEHUHPRYHG
IURPVHUYLFHGXULQJWKHWLPHWKDWWKHEUHDNHUSROHLVRSHQ)RUH[DPSOHZKHQWKH$SKDVHLV
RSHQWKHSKDVHGLVWDQFHHOHPHQWVIRU$%DQG&$DUHEORFNHG7KLVLVGXHWRWKHPDJQLWXGHDQG
SKDVHDQJOHVKLIWRIWKHSKDVHWRSKDVHUHVWUDLQWYROWDJHGXULQJWKHRSHQSROH
7KHJURXQGGLVWDQFHHOHPHQWDVVRFLDWHGZLWKWKHRSHQSKDVHVKRXOGDOVREHUHPRYHGIURPVHUYLFH
EHFDXVHLWPD\KDYHQRUHVWUDLQWYROWDJH+RZHYHUWKHHOHPHQWPD\VWLOOKDYH]HURVHTXHQFH
RSHUDWLQJFXUUHQW'HSHQGLQJRQWKHW\SHRISRODUL]LQJYROWDJHXVHGLQWKHGHVLJQRIWKHJURXQG
GLVWDQFHHOHPHQWVWKHGLVWDQFHHOHPHQWVRQWKHXQRSHQHGSKDVHVPD\EHDIIHFWHG)RUH[DPSOH
LITXDGUDWXUHSRODUL]LQJYROWDJHLVXVHGDQGWKH$SKDVHLVRSHQWKHQWKHSRODUL]LQJYROWDJHIRU
WKH%DQG&SKDVHJURXQGGLVWDQFHHOHPHQWVDUHSKDVHVKLIWHGVLPLODUWRWKHHIIHFWRIDEORZQ
IXVHRQWKH$SKDVH977KLVFRXOGUHVXOWLQDPLVRSHUDWLRQRIWKRVHGLVWDQFHHOHPHQWV
7KHUHVXOWLQJSKDVHVKLIWDQGPDJQLWXGHFKDQJHVIRUWKHTXDGUDWXUHSRODUL]LQJYROWDJHDUHVKRZQ
LQ)LJXUH7KHSRODUL]LQJYROWDJHIRUWKH$*JURXQGPKRGLVWDQFHHOHPHQWVDUHVKLIWHG
“GHJUHHVDQGUHGXFHGLQPDJQLWXGHIRUDQRSHQ%RU&SKDVH3RVLWLYHVHTXHQFHSRODUL]LQJ
YROWDJHDQJOHLVUHODWLYHO\XQDIIHFWHGE\WKHRSHQSKDVH
3KDVH%2SHQ
1RUPDO&RQGLWLRQV
3KDVH&2SHQ
9$
µ
9%
µ
µ
ƒ
9%&
±ƒ
ƒ
µ
ƒ
9%&
±ƒ
ƒ
9%
9&
µ
µ
µ
µ
9&
9$
9$
ƒ
µ
±ƒ
9%&
±ƒ
µ
±ƒ
)LJXUH (IIHFWRI2SHQ3ROHRQ4XDGUDWXUH3RODUL]LQJ9ROWDJH
7KHUHVXOWLQJSKDVHVKLIWDQGPDJQLWXGHFKDQJHVIRUWKHSRVLWLYHVHTXHQFHYROWDJHDUHVKRZQLQ
)LJXUH7KHSRODUL]LQJYROWDJHIRUWKH$*JURXQGPKRGLVWDQFHHOHPHQWVLVUHGXFHGLQ
PDJQLWXGHEXWWKHSKDVHDQJOHGRHVQRWFKDQJH
3RVLWLYHVHTXHQFHSRODUL]LQJYROWDJHLVUHFRPPHQGHGIRUPKRGLVWDQFHHOHPHQWVXVHGLQVLQJOH
SKDVHWULSSLQJDSSOLFDWLRQV
1RUPDO&RQGLWLRQV
3KDVH%2SHQ
9$
9$
µ
9%
ƒ
9
9$
µ
ƒ
9&
µ
3KDVH&2SHQ
µ
±ƒ
µ
ƒ
µ
ƒ
9&
9%
µ
µ
ƒ
9
ƒ
µ
ƒ
9
±ƒ
µ
ƒ
)LJXUH (IIHFWRI2SHQ3ROHRQ3RVLWLYH6HTXHQFH9ROWDJH
4XDGULODWHUDO*URXQG'LVWDQFH(OHPHQWV
%HFDXVH TXDGULODWHUDO JURXQG GLVWDQFH HOHPHQWV GR QRW XVH D SRODUL]LQJ YROWDJH WKH\ DUH QRW
DIIHFWHGE\WKHYROWDJHSKDVHVKLIWVGHVFULEHGLQWKHSUHYLRXVVHFWLRQ+RZHYHUWKHSRODUL]LQJ
VLJQDO IRU D W\SLFDO TXDGULODWHUDO JURXQG GLVWDQFH HOHPHQW LV GHULYHG IURP ]HUR DQG QHJDWLYH
VHTXHQFHFXUUHQWV7KHXQEDODQFHGSKDVHFXUUHQWVFUHDWHGE\DQRSHQSKDVHRQWKHWUDQVPLVVLRQ
V\VWHPKDYHDGLUHFWLPSDFWRQWKHSHUIRUPDQFHRIWKHVHTXDGULODWHUDOJURXQGGLVWDQFHHOHPHQWV
)RUWKDWUHDVRQLWLVUHFRPPHQGHGWKDWDQ\TXDGULODWHUDOJURXQGGLVWDQFHHOHPHQWVEHEORFNHGRU
UHPRYHGIURPVHUYLFHGXULQJWKHRSHQSKDVHSHULRGIROORZLQJDVLQJOHSKDVHWULS
'LUHFWLRQDO(OHPHQWV
7KHXQEDODQFHGYROWDJHVDQGFXUUHQWVLQWURGXFHGLQWRWKHSRZHUV\VWHPE\WKHRSHQSKDVHDIIHFW
WKHSHUIRUPDQFHRIERWK]HURDQGQHJDWLYHVHTXHQFHGLUHFWLRQDOHOHPHQWV:KHQWKHSRWHQWLDO
VRXUFHIRUWKHUHOD\LVRQWKHOLQHWKHXQEDODQFHGYROWDJHVKDYHWKHJUHDWHVWHIIHFW,WLVW\SLFDO
SUDFWLFHWRGLVDEOHWKHVWDQGDUG]HURDQGQHJDWLYHVHTXHQFHGLUHFWLRQDOHOHPHQWVGXULQJWKH
SHULRGWKDWWKHEUHDNHUSROHLVRSHQWRSUHYHQWPLVRSHUDWLRQVRIWKHVFKHPH$VVKRZQ
SUHYLRXVO\WKHXQEDODQFHGFXUUHQWVDQGYROWDJHVPD\DOVRDIIHFWUHOD\VRQOLQHVWKDWGRQRWKDYH
DQRSHQSKDVH
2YHUFXUUHQW(OHPHQWV
7KHRSHQSKDVHKDVPLQLPDOHIIHFWRQSKDVHRYHUFXUUHQWIXQFWLRQV+RZHYHUWKHXQEDODQFHV
DVVRFLDWHGZLWKWKHRSHQSKDVHDIIHFWVWKHSHUIRUPDQFHDQGVHWWLQJVRI]HURDQGQHJDWLYH
VHTXHQFHRYHUFXUUHQWIXQFWLRQV$JDLQWKHXQEDODQFHGFXUUHQWVDUHW\SLFDOO\KLJKHVWLQWKHOLQH
ZLWKWKHRSHQSKDVHKRZHYHULQVRPHV\VWHPFRQILJXUDWLRQVVXFKDVWKHFRQILJXUDWLRQGHSLFWHG
LQ)LJXUHWKHVDPHOHYHORIXQEDODQFHPD\RFFXULQDGMDFHQWOLQHV
/
5
3KDVH$2SHQ
/LQH
/LQH
/LQH
)LJXUH 6LQJOH/LQH6\VWHP
7KHUHOD\VRQWKHOLQHZLWKWKHRSHQSKDVHDUHDEOHWRGHWHUPLQHWKDWWKHSKDVHLVRSHQ7KLV
LQIRUPDWLRQFDQEHXVHGE\WKHSURWHFWLYHVFKHPHWRPRGLI\WKHPHDVXULQJHOHPHQWVDQGVFKHPH
ORJLFWKHUHE\SUHYHQWLQJDQ\PLVRSHUDWLRQVFDXVHGE\WKHXQEDODQFHGFXUUHQWV+RZHYHUWKH
UHOD\VWKDWDUHQRWDVVRFLDWHGZLWKWKHRSHQSKDVHOLQHW\SLFDOO\GRQRWKDYHWKDWLQIRUPDWLRQ
DYDLODEOHWRWKHP7KHUHIRUHWKH\PXVWEHGHVHQVLWL]HGWRSUHYHQWPLVRSHUDWLRQVIURPWKH
XQEDODQFHGFXUUHQWVWKDWDUHFDXVHGE\DQRSHQSKDVHDQ\ZKHUHLQWKHV\VWHP
6HQVLWLYLW\&RQVLGHUDWLRQV
7KHUHDUHWZRSULPDU\DUHDVRIVHQVLWLYLW\WRFRQVLGHU7KHILUVWLVWKHUHODWLYHVHQVLWLYLW\RIWKH
IDXOWGHWHFWLRQHOHPHQWVDQGWKHSKDVHVHOHFWLRQHOHPHQWV)RUWKHEHVWVHOHFWLYLW\WKHSKDVH
VHOHFWLRQHOHPHQWVVKRXOGEHPRUHVHQVLWLYHWKDQWKHIDXOWGHWHFWLRQHOHPHQWV,IWKHIDXOW
GHWHFWLRQLVPRUHVHQVLWLYHWKHUHOD\PD\WULSWKHLQFRUUHFWSKDVHRUDOOWKUHHSKDVHVLQDQ
DWWHPSWWRFOHDUDORZOHYHOVLQJOHOLQHWRJURXQGIDXOW7KLVFDQEHDSDUWLFXODUSUREOHPZKHUH
KLJKUHVLVWDQFHJURXQGIDXOWVPD\RFFXU
$VHFRQGDUHDRIVHQVLWLYLW\FRQFHUQLVWKHUHVSRQVHRIWKHUHOD\WRWKHXQEDODQFHFXUUHQWV7KH
IDXOWGHWHFWLQJHOHPHQWVPXVWEHVHWVRWKH\GRQRWUHVSRQGLQFRUUHFWO\WRWKHXQEDODQFHGFXUUHQWV
FDXVHGE\DQRSHQSKDVHLQDQRWKHUOLQHVHFWLRQ7KLVUHGXFHGVHQVLWLYLW\FDQUHVWULFWWKHIDXOW
UHVLVWDQFHIRUZKLFKWKHUHOD\FRUUHFWO\WULSV7KHIROORZLQJWDEOHVKRZVWKHQHJDWLYHDQG]HUR
VHTXHQFHPDJQLWXGHVIRUVHYHUDOFRQGLWLRQVEDVHGRQWKHVLPSOHV\VWHPRI)LJXUH
7DEOH &XUUHQWVDQG9ROWDJHV6HFRQGDU\6HHQE\5HOD\DW/
&RQGLWLRQ
,
,
9
9
1RRSHQ3KDVHV$*IDXOWSXIURP/5) W
1RRSHQ3KDVHV$*IDXOWSXIURP/5) W
1RRSHQ3KDVHV$*IDXOWSXIURP/5) W
1RRSHQ3KDVHV$*IDXOWSXIURP/5) W
$SKDVHRSHQLQ/LQH
7KHVLJQDOPDJQLWXGHVIRULQWHUQDOIDXOWFRQGLWLRQVPD\EHRIDVLPLODUPDJQLWXGHRUHYHQOHVV
WKDQWKDWFDXVHGE\DQRSHQSKDVHLQWKHSDUDOOHOOLQH7KHXQEDODQFHVRIWKHRSHQSKDVHPD\
FDXVHODUJHHUURUVLQWKHPHDVXUHPHQWVLIWKHUHOD\LVVHWWRRVHQVLWLYH
'HVHQVLWL]LQJ2YHUFXUUHQW(OHPHQWV
5DLVLQJWKHJURXQGRYHUFXUUHQWRUQHJDWLYHVHTXHQFHFXUUHQWWKUHVKROGSUHYHQWVRSHUDWLRQGXULQJ
DQRSHQSKDVHFRQGLWLRQ)XUWKHUPRUHUDLVLQJWKHSLFNXSWKUHVKROGDOVRUHGXFHVWKHDELOLW\RIWKH
RYHUFXUUHQWHOHPHQWWRGHWHFWKLJKUHVLVWDQFHIDXOWV
8VLQJDYROWDJHWKUHVKROGRQWKHGLUHFWLRQDOHOHPHQWLVDQRWKHUZD\WRUHGXFHWKHGLUHFWLRQDO
HOHPHQWVHQVLWLYLW\3ODFLQJDYROWDJHWKUHVKROGRQWKHGLUHFWLRQDOGHFLVLRQGUDPDWLFDOO\UHGXFHV
WKHIDXOWUHVLVWDQFHFRYHUDJHRIWKHUHOD\>@DQGPD\FDXVHFRRUGLQDWLRQGLIILFXOWLHV6HOHFWLQJ
DQDUELWUDU\WKUHVKROGZRUNVLQVRPHFDVHVEXWQRWDOOWKHUHIRUHWKHWDVNLVWRGHWHUPLQHZKHUH
WKHYROWDJHWKUHVKROGVKRXOGEHVHW)URPWKHSUHYLRXVH[HUFLVHWKHQHJDWLYHDQG]HURVHTXHQFH
YROWDJHPDJQLWXGHVFKDQJHGZLWKUHVSHFWWRVRXUFHDQGORDGIORZ&RQVHTXHQWO\LWLVGLIILFXOWWR
GHWHUPLQHDVHWWLQJIRUWKHYROWDJHWKUHVKROGWKDWDGGUHVVHVDOOV\VWHPVDQGFRQGLWLRQV7KHUHIRUH
WKHUHFRPPHQGHGVROXWLRQLVWRLQFUHDVHWKHVHWWLQJRIWKHJURXQGDQGQHJDWLYHVHTXHQFH
RYHUFXUUHQWHOHPHQWV
6SHFLDO&RQGLWLRQV
(YROYLQJ)DXOWV
7KHWHUPHYROYLQJIDXOWLVDSSOLHGZKHQDIDXOWEHJLQVDVVLQJOHOLQHWRJURXQGEXWLQYROYHVDQ
DGGLWLRQDOSKDVHRUSKDVHVVKRUWO\DIWHUIDXOWLQLWLDWLRQ7KHIDXOWPD\HYROYHEHIRUHWKHLQLWLDO
VLQJOHOLQHWRJURXQGIDXOWLVFOHDUHGRUGXULQJWKHRSHQSROHSHULRGIROORZLQJDVXFFHVVIXOVLQJOH
SKDVHWULS:KHQDQHYROYLQJIDXOWRFFXUVWKHSURWHFWLYHUHOD\V\VWHPPXVWEHDEOHWRFRUUHFWO\
GHWHUPLQHWKHIDXOWW\SHDQGLQLWLDWHWKUHHSKDVHWULSSLQJZLWKQRVLJQLILFDQWWLPHGHOD\DGGHG
EHFDXVHRIWKHFKDQJHRIIDXOWHGSKDVHLQIRUPDWLRQ7KHSURWHFWLRQVFKHPHPXVWDOVRSURYLGHWKH
SURSHULQIRUPDWLRQWRWKHDVVRFLDWHGDXWRUHFORVLQJORJLF7KHIDXOWW\SHVHOHFWLRQORJLFVKRXOG
UXQHYHU\SURWHFWLRQSURFHVVLQJLQWHUYDOWRHQVXUHKLJKVSHHGIDXOWW\SHGHWHUPLQDWLRQLQWKHHYHQW
RIDQHYROYLQJIDXOW
&URVV&RXQWU\)DXOWV
7KHWHUPFURVVFRXQWU\IDXOWLVDSSOLHGZKHQPXOWLSOHIDXOWVRFFXURQWKHV\VWHPDWWKHVDPHWLPH
DQGDWGLIIHUHQWORFDWLRQV)RUH[DPSOHDQ$SKDVHWRJURXQGIDXOWPD\RFFXURQWKHSURWHFWHG
OLQHDWWKHVDPHWLPHWKDWD%SKDVHWRJURXQGIDXOWRFFXUVRQDQDGMDFHQWRUSDUDOOHOOLQH$
FURVVFRXQWU\IDXOWPD\KDYHPLQLPDOHIIHFWRQDWKUHHSKDVHWULSSLQJDSSOLFDWLRQEXWPD\
SUHVHQWDPDMRUSUREOHPWRDVLQJOHSKDVHWULSSLQJDSSOLFDWLRQ
&RQVLGHUWKHVLPSOHV\VWHPRI)LJXUHZLWKGLVWDQFHW\SHSURWHFWLRQ
5HOD\
5HOD\
$*
/
5
5HOD\
/
5HOD\
%*
/
5
5
)LJXUH &URVV&RXQWU\)DXOW
)RUPRVWDSSOLFDWLRQVWKHUHOD\DW5FRUUHFWO\LGHQWLILHVWKHIDXOWDVDVLQJOHOLQHWRJURXQGIDXOW
RQ$SKDVHDQGWKHUHOD\DW5FRUUHFWO\LGHQWLILHVWKHIDXOWDVDVLQJOHOLQHWRJURXQGIDXOWRQ%
SKDVH7KHVLWXDWLRQLVQRWWKDWVLPSOHIRUWKHUHOD\VDW%XV/%RWKRIWKHVHUHOD\VVHQVHWKHIDXOW
DVDQ$%*GRXEOHOLQHWRJURXQGIDXOWEHFDXVHWKHWZRVLQJOHOLQHWRJURXQGIDXOWVDUHDW
HVVHQWLDOO\WKHVDPHHOHFWULFDOSRLQWRQWKHV\VWHP$VWKHIDXOWORFDWLRQLVPRYHGDZD\IURPWKH
%XV5WRZDUGVWKHFHQWHURIWKHOLQHWKHUHOD\VFDQPRUHHDVLO\GLVWLQJXLVKWKHLQWHUQDOIDXOWHG
SKDVHIURPWKHH[WHUQDOIDXOWHGSKDVH,QDVLPSOHSLORWVFKHPHWKHIDXOWGHSLFWHGLQ)LJXUH
PD\UHVXOWLQFRUUHFWVLQJOHSKDVHWULSSLQJE\WKHUHOD\VDW5DQG5EXWLQFRUUHFWWKUHHSKDVH
WULSSLQJE\WKHUHOD\VDW/DQG/7KLVLVEHFDXVHWKHSLORWFKDQQHOLQIRUPDWLRQLVRQO\WZR
VWDWHHLWKHUWKHUHOD\VVHHDIDXOWRUWKH\GRQRWVHHDIDXOW7KHIDXOWHGSKDVHVHOHFWLRQPXVWEH
DFFRPSOLVKHGE\WKHORFDOUHOD\V,QWKLVFDVHWKHUHOD\VDW/DQG/VHOHFWDQ$%*IDXOWW\SH
UHVXOWLQJLQDWKUHHSKDVHWULSIRUDVLQJOHOLQHWRJURXQGIDXOW6HYHUDODSSURDFKHVPD\EH
HPSOR\HGWRDYRLGWKLVPLVRSHUDWLRQ
œ 7KHSLORWWULSSLQJFDQEHGHOD\HGORQJHQRXJKWKDWWKH=RQHHOHPHQWVDW%XV5LQLWLDWH
VLQJOHSKDVHWULSSLQJ$IWHUWKHEUHDNHUVDW%XV/RSHQWKHIDXOWHGSKDVHVWKHUHOD\VDW/
DQG/VHHRQO\WKHLQWHUQDOVLQJOHOLQHWRJURXQGIDXOWV
œ 0XOWLSOHWZRVWDWHSLORWFRPPXQLFDWLRQVFKDQQHOVFDQEHXVHGWRWUDQVPLWSKDVH
LGHQWLILFDWLRQLQDGGLWLRQWRWULSSHUPLVVLRQ
œ $GLJLWDOSLORWFRPPXQLFDWLRQVFKDQQHOFDQEHXVHGWRWUDQVPLWPXOWLSOHELWVRI
LQIRUPDWLRQVXFKDVIDXOWHGSKDVHVHOHFWLRQLQDGGLWLRQWRWKHSHUPLVVLYHVLJQDO
7KHILUVWVROXWLRQLQWURGXFHVWLPHGHOD\DQGUHTXLUHVWKDWWKHSURWHFWLRQRQWKHSDUDOOHOOLQH
RSHUDWHWRFOHDUWKHIDXOWRQWKHSDUDOOHOOLQH7KHVHFRQGVROXWLRQLPSURYHVXSRQWKHILUVW
KRZHYHUWKHVFKHPHUHTXLUHVWKDWWKHFKDQQHOVVZLWFKVWDWHVVLPXOWDQHRXVO\DQGDVZLWFKLQJ
WUDQVLWLRQPD\EHLQWHUSUHWHGDVDGLIIHUHQWIDXOWW\SH7KHODVWVROXWLRQLVWKHEHVWRSWLRQ$
GLJLWDOSLORWFRPPXQLFDWLRQVFKDQQHOSURYLGHVWKHEHVWSHUIRUPDQFH>@
$SHUSKDVHOLQHFXUUHQWGLIIHUHQWLDOVFKHPHPD\EHDEOHWRFRUUHFWO\LGHQWLI\WKHLQWHUQDOVLQJOH
OLQHWRJURXQGIDXOWVLQWKLVFDVH+RZHYHULWPD\QRWEHVHQVLWLYHWRKLJKUHVLVWDQFHIDXOWV
7KHFURVVFRXQWU\IDXOWPD\DOVREHDQHYROYLQJIDXOW,Q)LJXUHWKH$*IDXOWRQ/LQHPD\
RFFXUEHIRUHWKH%*RQ/LQH:KHQWKLVRFFXUVWKHUHOD\DW/PD\VHOHFW$*DVWKHLQLWLDO
IDXOWHGSKDVH7KLVPD\FDXVHDGGLWLRQDOSKDVHVHOHFWLRQSUREOHPVZKHQWKHLQWHUQDO%*IDXOW
RFFXUV,QVRPHFDVHVWKHUHOD\DW5PD\HYHQLQLWLDWHDQLQFRUUHFWVLQJOHSKDVHWULSRQ
%SKDVH7KHGLJLWDOFRPPXQLFDWLRQVFKDQQHOZKHQXVHGZLWKDIDVWIDXOWW\SHVHOHFWLRQORJLF
FDQSUHYHQWWKLVPLVRSHUDWLRQ
81'(5*5281'68%0$5,1(&$%/($33/,&$7,216
3URWHFWLYHUHOD\LQJUHTXLUHPHQWVIRUFDEOHVDUHGLIIHUHQWIURPWKRVHIRURYHUKHDGOLQHV7KH
LPSHGDQFHFKDUDFWHULVWLFVIRUFDEOHVDUHVLJQLILFDQWO\GLIIHUHQWIURPWKHLPSHGDQFHFKDUDFWHULVWLFV
RIRYHUKHDGOLQHV7KHVKXQWFDSDFLWDQFHIRUFDEOHVLVJUHDWHUWKDQRYHUKHDGOLQHVWKXVUHVXOWLQJ
LQPRUHOLQHFKDUJLQJFXUUHQWRQDSHUXQLWGLVWDQFHEDVLV7\SLFDOO\WKHOHQJWKRIWKHFDEOHLV
UHODWLYHO\VKRUWOHVVWKDQNPZKHQFRPSDUHGWRRYHUKHDGWUDQVPLVVLRQOLQHV
&DEOHLPSHGDQFHVYDU\JUHDWO\ZLWKUHVSHFWWRWKHFDEOHFRQVWUXFWLRQLQVXODWLQJPHGLXPDQG
VKLHOGLQJPHWKRG>@2QHRIWKHPRUHZHOONQRZQFDEOHFKDUDFWHULVWLFVLVWKDWWKHVHTXHQFH
LPSHGDQFHVKDYHORZDQJOHV7\SLFDORYHUKHDGWUDQVPLVVLRQOLQHVKDYHLPSHGDQFHDQJOHVJUHDWHU
WKDQGHJUHHV&DEOHLPSHGDQFHDQJOHVDUHW\SLFDOO\OHVVWKDQGHJUHHV7KH]HURVHTXHQFH
OLQHLPSHGDQFHFDQYDU\ZLWKUHVSHFWWRWKH]HURVHTXHQFHFXUUHQWUHWXUQSDWK,QVRPH
FRQILJXUDWLRQVWKH]HURVHTXHQFHLPSHGDQFHFKDQJHVZLWKUHVSHFWWRWKHPDJQLWXGHRIWKH]HUR
VHTXHQFHFXUUHQW
7KHVKXQWFDSDFLWLYHUHDFWDQFHFKDUDFWHULVWLFVDUHVLJQLILFDQWO\GLIIHUHQWIURPWKRVHRIRYHUKHDG
OLQHV,QVRPHFDEOHFRQILJXUDWLRQVWKHSRVLWLYHQHJDWLYHDQG]HURVHTXHQFHVKXQWFDSDFLWDQFH
DUHDOOWKHVDPH7KHLQVXODWLQJPHGLXPFDQDOVRKDYHDVLJQLILFDQWLPSDFWRQWKHVKXQW
FDSDFLWDQFH7KHVKXQWFDSDFLWDQFHIRURYHUKHDGOLQHVLVDIXQFWLRQRIWKHFRQGXFWRUKHLJKWIURP
JURXQGDQGWKHFRQGXFWRUVSDFLQJZKHUHDVWKHVKXQWFDSDFLWDQFHYDOXHIRUDFDEOHLVSULPDULO\D
IXQFWLRQRIWKHVLQJOHFRQGXFWRUJHRPHWU\VKLHOGLQJDQGWKHGLHOHFWULF
3URWHFWLRQRI&DEOHV
/LQHGLIIHUHQWLDOUHOD\VKDYHWUDGLWLRQDOO\EHHQDSSOLHGIRUSURWHFWLRQRIFDEOHV7KLVSDSHU
IRFXVHVRQGLVWDQFHDQGGLUHFWLRQDOHOHPHQWDSSOLFDWLRQV1HJDWLYHVHTXHQFHGLUHFWLRQDOHOHPHQWV
KDYHEHHQXVHGDVDQDOWHUQDWHWROLQHFXUUHQWGLIIHUHQWLDOSURWHFWLRQ>@'XHWRWKHXQFHUWDLQW\RI
WKH]HURVHTXHQFHLPSHGDQFHRIVRPHXQGHUJURXQGFDEOHFRQILJXUDWLRQV]HURVHTXHQFH
GLUHFWLRQDOHOHPHQWVDUHQRWUHFRPPHQGHG1HJDWLYHVHTXHQFHHOHPHQWVSURYLGHYHU\JRRGIDXOW
UHVLVWDQFHFRYHUDJHDQGGLUHFWLRQDOVHFXULW\VLQFHWKHQHJDWLYHVHTXHQFHLPSHGDQFHVDUHVWDEOH
DQGSUHGLFWDEOH
*URXQGGLVWDQFHSURWHFWLRQVFKHPHVKDYHDOVREHHQDSSOLHGRQXQGHUJURXQGFDEOHV8VLQJ
JURXQGGLVWDQFHUHOD\VUHTXLUHVH[WHQGHGVHWWLQJUDQJHVIRUWKH]HURVHTXHQFHFRPSHQVDWLRQ
IDFWRU,QDGGLWLRQWKHVKRUWGLVWDQFHVDQGWKXVORZLPSHGDQFHVXVHGIRUFDEOHVPD\PDNH
DSSOLFDWLRQRIGLVWDQFHUHOD\VSURKLELWLYHLQPDQ\FDVHV
*URXQG'LVWDQFH5HOD\$SSOLFDWLRQ
&DUHIXOFRQVLGHUDWLRQPXVWEHJLYHQWRDSSO\LQJJURXQGGLVWDQFHUHOD\VRQFDEOHV7KH]HUR
VHTXHQFHLPSHGDQFHFDQYDU\GHSHQGLQJXSRQWKHHDUWKUHWXUQSDWK,QVRPHFDVHVWKH]HUR
VHTXHQFHLPSHGDQFHPD\FKDQJHZLWKUHVSHFWWRWKHPDJQLWXGHRIWKH]HURVHTXHQFHFXUUHQW
$VDQH[DPSOHOHWXVORRNDWWKHFDEOHLPSHGDQFHIRUDSDUWLFXODUNFPLOFRSSHUSDSHU
LQVXODWHGOHDGVKHDWKFDEOH
= WNPµ•
= WNPµ•
6KHDWK5HWXUQ2QO\
= WNPµ•
6KHDWKDQG(DUWK5HWXUQ
= WNPµ•
(DUWK5HWXUQ2QO\
8VLQJ(TXDWLRQWKH]HURVHTXHQFHFRPSHQVDWLRQIDFWRUVIRUHDFK]HURVHTXHQFHLPSHGDQFH
DUHOLVWHGEHORZ
N µ±•
6KHDWK5HWXUQ2QO\
N µ±•
N µ•
6KHDWKDQG(DUWK5HWXUQ
(DUWK5HWXUQ2QO\
:HQH[WPRGHOHGDNPVHFWLRQRIWKHDERYHFDEOHLQDVLPSOHWZRVRXUFHV\VWHPZLWKWKH
VRXUFHLPSHGDQFHVVHWHTXDOWRHDFKRWKHU*URXQGIDXOWVDUHWDNHQDWSHUFHQWRIWKHOLQH
OHQJWKXVLQJWKHWKUHHGLIIHUHQW]HURVHTXHQFHOLQHLPSHGDQFHVDQG]HURVHTXHQFHFRPSHQVDWLRQ
IDFWRUV7KHDSSDUHQWJURXQGIDXOWLPSHGDQFHLVFDOFXODWHGIRUHDFKHDUWKUHWXUQSDWKDQG]HUR
VHTXHQFHFRPSHQVDWLRQIDFWRU:HDOVRFDOFXODWHGGLVWDQFHHOHPHQWPHDVXUHPHQWVIRUDJURXQG
PKRDJURXQGTXDGULODWHUDOZLWK]HURVHTXHQFHFXUUHQWSRODUL]LQJDQGDJURXQGTXDGULODWHUDO
ZLWKQHJDWLYHVHTXHQFHFXUUHQWSRODUL]LQJ
7DEOH7DEOHDQG7DEOHOLVWWKHUHVXOWLQJGLVWDQFHHOHPHQWPHDVXUHPHQWVLQSHUXQLWRIOLQH
OHQJWK$SHUXQLWPHDVXUHPHQWRIOHVVWKDQRQHLQGLFDWHVWKDWWKHGLVWDQFHHOHPHQWRYHUUHDFKHV
$SHUXQLWPHDVXUHPHQWJUHDWHUWKDQRQHLQGLFDWHVWKDWWKHGLVWDQFHHOHPHQWXQGHUUHDFKHV$OO
IDXOWVDQGPHDVXUHPHQWVDUHWDNHQDWSHUFHQWRIWKHOLQHLPSHGDQFH
7DEOH =HUR6HTXHQFH&RPSHQVDWLRQ)DFWRU8VLQJ6KHDWK5HWXUQ2QO\
6KHDWK5HWXUQ2QO\N µ±•
$SSDUHQW=
0KR 4XDG±,5
=,PSHGDQFH
4XDG±,
6KHDWK5HWXUQ2QO\
Wµ•
6KHDWKDQG(DUWK5HWXUQ
Wµ•
(DUWK5HWXUQ
Wµ•
7DEOH =HUR6HTXHQFH&RPSHQVDWLRQ)DFWRU8VLQJ6KHDWKDQG(DUWK5HWXUQ
=,PSHGDQFH
6KHDWKDQG(DUWK5HWXUQN µ±•
$SSDUHQW=
0KR 4XDG±,5
4XDG±,
6KHDWK5HWXUQ2QO\
Wµ•
6KHDWKDQG(DUWK5HWXUQ
Wµ•
(DUWK5HWXUQ
Wµ•
7DEOH =HUR6HTXHQFH&RPSHQVDWLRQ)DFWRU8VLQJ(DUWK5HWXUQ2QO\
=,PSHGDQFH
(DUWK5HWXUQ2QO\N µ•
$SSDUHQW=
0KR 4XDG±,5
4XDG±,
6KHDWK5HWXUQ2QO\
Wµ±•
6KHDWKDQG(DUWK5HWXUQ
Wµ•
(DUWK5HWXUQ
Wµ•
7KHUHVXOWVVKRZQLQ7DEOH7DEOHDQG7DEOHGHPRQVWUDWHWKDWVHOHFWLRQRIWKHDSSURSULDWH
]HURVHTXHQFHFRPSHQVDWLRQIDFWRULVFULWLFDOLQHQVXULQJFRUUHFWGLVWDQFHHOHPHQWUHDFK8VLQJ
WKHZURQJ]HURVHTXHQFHFRPSHQVDWLRQIDFWRUFDQUHVXOWLQVHYHUHXQGHURURYHUUHDFK
7KHWHVWUHVXOWVDOVRVKRZWKDWXVLQJDGLVWDQFHEDVHGVFKHPHIRUWKLVSDUWLFXODUFDEOHPD\QRWEH
WKHEHVWFKRLFH+RZHYHURIWKHWKUHHJURXQGGLVWDQFHHOHPHQWVVWXGLHGWKHPKRJURXQGHOHPHQW
SURYLGHGWKHEHVWSHUIRUPDQFHLQWHUPVRIPLQLPL]LQJXQGHUDQGRYHUUHDFK
)RUWKLVFDEOHFRQILJXUDWLRQWKHEHVWVHOHFWLRQIRUWKH]HURVHTXHQFHFRPSHQVDWLRQIDFWRUIRUDQ
XQGHUUHDFKLQJGLVWDQFHHOHPHQWLVWKHVKHDWKUHWXUQRQO\1RWHWKDWLIWKHFXUUHQWUHWXUQSDWKLV
QRWWKHVKHDWKWKHXQGHUUHDFKLQJJURXQGGLVWDQFHHOHPHQWPD\QRWRSHUDWH8VLQJWKHHDUWKRU
VKHDWKDQGHDUWKUHWXUQZRXOGUHVXOWLQVHYHUHRYHUUHDFKZKHQWKHJURXQGFXUUHQWUHWXUQSDWKLV
QRWWKHSDWKVHOHFWHGIRUVHWWLQJWKH]HURVHTXHQFHFRPSHQVDWLRQIDFWRU
7KHEHVWVHOHFWLRQIRUDQRYHUUHDFKLQJJURXQGGLVWDQFHHOHPHQWZRXOGEHWKHHDUWKUHWXUQRQO\
+RZHYHUWKLVFKRLFHPD\QRWEHDSSURSULDWHIRUWLPHGHOD\HGEDFNXSSURWHFWLRQZKHUHWKHUHOD\
PD\KDYHDWHQGHQF\WRXQGHUUHDFKIRUH[WHUQDOIDXOWVLIWKHUHWXUQSDWKLVQRWWKHHDUWKUHWXUQ,I
WKHRYHUUHDFKLQJHOHPHQWLVXVHGLQDSLORWVFKHPHWKHQXVLQJWKHHDUWKUHWXUQLVWKHDSSURSULDWH
FKRLFHDVWKHHOHPHQWDOZD\VRSHUDWHVFRUUHFWO\IRULQWHUQDOIDXOWVUHJDUGOHVVRIWKHJURXQG
FXUUHQWUHWXUQSDWK
8VLQJJURXQGGLVWDQFHLQFDEOHDSSOLFDWLRQVUHTXLUHVFDUHIXODQDO\VLV,IWKH]HURVHTXHQFH
LPSHGDQFHLVNQRZQDQGIL[HGHJWKH]HURVHTXHQFHLPSHGDQFHGRHVQRWFKDQJHZLWKUHVSHFW
WRUHWXUQSDWKRUIDXOWPDJQLWXGHWKHQJURXQGGLVWDQFHUHOD\VPD\EHXVHGLQWKHDSSOLFDWLRQ
+RZHYHULQPRVWFDEOHDSSOLFDWLRQVWKH]HURVHTXHQFHLPSHGDQFHPD\QRWEHNQRZQWKXV
PDNLQJLWGLIILFXOWWRDSSO\JURXQGGLVWDQFHSURWHFWLRQ
'LUHFWLRQDO2YHUFXUUHQW
'LUHFWLRQDORYHUFXUUHQWUHOD\VSURYLGHDJRRGDOWHUQDWLYHWRWUDGLWLRQDOOLQHFXUUHQWGLIIHUHQWLDORU
GLVWDQFHEDVHGSURWHFWLRQ8VLQJGLUHFWLRQDORYHUFXUUHQWUHOD\VLQDGLUHFWLRQDOFRPSDULVRQ
VFKHPHFDQSURYLGHVHFXUHKLJKVSHHGWULSSLQJ>@
8VHRIGLUHFWLRQDORYHUFXUUHQWHOHPHQWVUHTXLUHVVWXG\DQGFRQVLGHUDWLRQRIWKHFDEOHVKXQW
FDSDFLWDQFH7KHFDEOHVKXQWFDSDFLWDQFHFDQLPSDFWWKHRYHUFXUUHQWHOHPHQWLQWZRZD\V
GLUHFWLRQDOVHFXULW\DQGVHQVLWLYLW\
)LJXUHVKRZVWKHQHJDWLYHVHTXHQFHFXUUHQWGLVWULEXWLRQIRUDQH[WHUQDOJURXQGIDXOW1RWH
WKDWWKHVKXQWFDSDFLWDQFHFXUUHQWRIWKHFDEOHVXEWUDFWVIURPWKHIDXOWFXUUHQWIORZIURP7HUPLQDO
5WR7HUPLQDO6
,6 ,5±,&5±,&6
ZKHUH , 1HJDWLYHVHTXHQFHIDXOWFXUUHQWVXSSOLHGIURP6RXUFH5
5
, 1HJDWLYHVHTXHQFHIDXOWFXUUHQWIORZLQJWKURXJKWKHOLQHWHUPLQDODW
6WDWLRQ6
, 1HJDWLYHVHTXHQFHVKXQWFXUUHQWDW6WDWLRQ5
6
&5
,
,6
&6
1HJDWLYHVHTXHQFHVKXQWFXUUHQWDW6WDWLRQ6
6
5
5HOD\
,&6
,&5
,5
5HOD\
)LJXUH 1HJDWLYH6HTXHQFH&XUUHQW'LVWULEXWLRQ²([WHUQDO)DXOW
7KHSLFNXSRIWKHUHYHUVHHOHPHQWDW6WDWLRQ6PXVWEHVHWPRUHVHQVLWLYHO\WKDQWKHIRUZDUG
HOHPHQWDW6WDWLRQ57KLVLVWRHQVXUHSURSHUFRRUGLQDWLRQIRUH[WHUQDOIDXOWLQWKHGLUHFWLRQDO
FRPSDULVRQVFKHPH,IWKHIRUZDUGHOHPHQWSLFNVXSDW6WDWLRQ5ZLWKRXWRSHUDWLRQRIWKHUHYHUVH
HOHPHQWDW6WDWLRQ6XQZDQWHGWULSSLQJPD\RFFXUDW6WDWLRQ57KHUHIRUHWKHSLFNXSWKUHVKROGV
DW6WDWLRQV5DQG6PXVWEHVHWWRDFFRPPRGDWHWKHFDSDFLWLYHFXUUHQWVXSSOLHGE\WKHFDEOH
7KHGLUHFWLRQDOHOHPHQWLVDOVRDIIHFWHGE\WKHFDEOHVKXQWFDSDFLWDQFH2QHGLUHFWLRQDOHOHPHQW
GHVLJQ>@>@XVHVDQLPSHGDQFHEDVHGWHFKQLTXHIRUGHWHUPLQLQJIDXOWGLUHFWLRQV)RUUHYHUVH
IDXOWVUHIHUWR)LJXUHWKHHTXLYDOHQWLPSHGDQFHLQFOXGHVWKHVKXQWFDSDFLWDQFHRIWKHFDEOH
>@7KHFDEOHFDSDFLWDQFHFDQPRGLI\WKHFKDUDFWHULVWLFDVVKRZQLQ)LJXUH
;
=
5=/
&
%
5HYHUVH)DXOWV
5
$
±=
)RUZDUG)DXOWV
)LJXUH 1HJDWLYH6HTXHQFH,PSHGDQFH0HDVXUHPHQW
3RLQW$LOOXVWUDWHVWKHPHDVXUHGQHJDWLYHVHTXHQFHLPSHGDQFHIRUDIRUZDUGIDXOWDW6WDWLRQ6
3RLQW%LOOXVWUDWHVWKHPHDVXUHGQHJDWLYHVHTXHQFHLPSHGDQFHIRUDUHYHUVHIDXOWEHKLQG6WDWLRQ6
ZLWKRXWFRQVLGHULQJWKHVKXQWFDSDFLWDQFH3RLQW&LOOXVWUDWHVWKHPHDVXUHGQHJDWLYHVHTXHQFH
LPSHGDQFHIRUDUHYHUVHIDXOWZLWKWKHVKXQWFDSDFLWDQFH
)LJXUHVKRZVWKDWDQLPSHGDQFHEDVHGGLUHFWLRQDOHOHPHQWLVQRWDIIHFWHGE\WKHFDEOHVKXQW
FDSDFLWDQFH7KHPHDVXUHGLPSHGDQFHIRUDUHYHUVHIDXOWPRYHVLQWKHODWHUDOGLUHFWLRQDQGGRHV
QRW³UHGXFH´WKHPHDVXUHGLPSHGDQFHYDOXH>@+RZHYHURWKHUGLUHFWLRQDOHOHPHQWGHVLJQV
VKRXOGEHHYDOXDWHGFDUHIXOO\WRHQVXUHFRUUHFWRSHUDWLRQ
&21&/86,216
8QGHUUHDFKLQJJURXQGGLVWDQFHHOHPHQWVFDQRYHUUHDFKZKHQDSSOLHGRQVHULHVFRPSHQVDWHG
OLQHVEHFDXVHRIWKHORZIUHTXHQF\WUDQVLHQWVJHQHUDWHGGXULQJDIDXOW7KHRYHUUHDFKLV
PD[LPL]HGZKHQWKHFDSDFLWRULVEHWZHHQWKHIDXOWDQGWKHUHOD\
'LUHFWLRQDOHOHPHQWVDQGGLVWDQFHHOHPHQWSRODUL]LQJTXDQWLWLHVPXVWEHGHVLJQHGWR
DFFRPPRGDWHYROWDJHLQYHUVLRQVFDXVHGE\VHULHVFDSDFLWRUV
6LQJOHSROHWULSSLQJVFKHPHVUHTXLUHVHFXUHSKDVHVHOHFWLRQDOJRULWKPVWRHQVXUHFRUUHFW
VLQJOHSKDVHWULSSLQJ2YHUFXUUHQWHOHPHQWVFDQEHXVHGLQVLQJOHSROHWULSSLQJVFKHPHVLI
WKHSKDVHVHOHFWLRQORJLFLVGHVLJQHGWRVXSHUYLVHWKHRYHUFXUUHQWHOHPHQWV
2YHUFXUUHQWHOHPHQWVXVHGRQRUQHDUVLQJOHSROHWULSSLQJDSSOLFDWLRQVPXVWEHVHWVRWKH\GR
QRWRSHUDWHGXULQJWKHRSHQSROHSHULRGRQDGMDFHQWOLQHV
6RPHFDEOHFRQILJXUDWLRQVFDXVHWKH]HURVHTXHQFHLPSHGDQFHWRFKDQJHZLWKUHVSHFWWRWKH
FXUUHQWUHWXUQSDWKRUWKHPDJQLWXGHRIWKH]HURVHTXHQFHFXUUHQW*URXQGGLVWDQFHUHOD\V
XVHGRQFDEOHVPXVWKDYHGLIIHUHQW]HURVHTXHQFHFRPSHQVDWLRQIDFWRUVIRUXQGHUDQG
RYHUUHDFKLQJHOHPHQWV
'LUHFWLRQDODQGVHQVLWLYHRYHUFXUUHQWHOHPHQWVDSSOLHGWRFDEOHSURWHFWLRQPXVWEHVHWWR
DFFRPPRGDWHWKHFDEOHVKXQWFDSDFLWDQFHWRHQVXUHSURSHURSHUDWLRQ
5()(5(1&(6
>@ -HII5REHUWVDQG$UPDQGR*X]PiQ³'LUHFWLRQDO(OHPHQW'HVLJQDQG(YDOXDWLRQ´
VW$QQXDO:HVWHUQ3URWHFWLYH5HOD\&RQIHUHQFH6SRNDQH:DVKLQJWRQ2FWREHU
>@ -HVXV9DUJDV$UPDQGR*X]PiQ-RUJH5REOHV³8QGHUJURXQG6XEPDULQH&DEOH3URWHFWLRQ
8VLQJ$1HJDWLYH6HTXHQFH'LUHFWLRQDO&RPSDULVRQ6FKHPH´WK$QQXDO:HVWHUQ
3URWHFWLYH5HOD\&RQIHUHQFH6SRNDQH:$2FWREHU
>@ (26FKZHLW]HU,,,DQG-5REHUWV³'LVWDQFH5HOD\(OHPHQW'HVLJQ´WK$QQXDO:HVWHUQ
3URWHFWLYH5HOD\&RQIHUHQFH6SRNDQH:$2FWREHU
>@ -RH0RRQH\DQG-DFNLH3HHU³$SSOLFDWLRQ*XLGHOLQHVIRU*URXQG)DXOW3URWHFWLRQ´
WK$QQXDO:HVWHUQ3URWHFWLYH5HOD\&RQIHUHQFH6SRNDQH:$2FWREHU
>@ -HII5REHUWV(GPXQG26FKZHLW]HU5HQX$URUDDQG(UQLH3RJJL³/LPLWVWRWKH6HQVLWLYLW\
RI*URXQG'LUHFWLRQDODQG'LVWDQFH3URWHFWLRQ´QG$QQXDO:HVWHUQ3URWHFWLYH5HOD\
&RQIHUHQFH6SRNDQH:$2FWREHU
>@ .HQQHWK&%HKUHQGW³5HOD\WR5HOD\'LJLWDO/RJLF&RPPXQLFDWLRQIRU/LQH3URWHFWLRQ
0RQLWRULQJDQG&RQWURO´UG$QQXDO:HVWHUQ3URWHFWLYH5HOD\&RQIHUHQFH6SRNDQH:$
2FWREHU
>@ $QGHUVRQ30DQG)DUPHU5*6HULHV&RPSHQVDWLRQRI3RZHU6\VWHPV3%/6+,QF
(QFLQLWDV&$
$33(1',;$ *5281'',67$1&((/(0(17N)$&725
'HULYDWLRQRIWKHSKDVHFXUUHQWFRPSHQVDWLRQIDFWRUNIRUJURXQGGLVWDQFHIXQFWLRQV
5HOD\
)
5
/
$JURXQGGLVWDQFHUHOD\LVORFDWHGDW%XV/DQGDQ$*IDXOWLVDSSOLHGDW%XV5
= SRVLWLYHVHTXHQFHLPSHGDQFHRI/LQH/5
= QHJDWLYHVHTXHQFHLPSHGDQFHRI/LQH/5 = =
= ]HURVHTXHQFHLPSHGDQFHRI/LQH/5
,D = , + , + ,
9D = , ‡ = + , ‡ = + , ‡ =
= , ‡ = + , ‡ = + , ‡ = + (, ‡ = - , ‡ =)
= ,D ‡ = + , ‡ (= - =)
=DSSDUHQW =
9D
,
= = + ‡ (= - =)
,D
,D
9D = ,D ‡ = + , ‡ (= - =)
9D
Ë = - = Û
= ,D + Ì
Ü ‡ ,
=
Í = Ý
= =
6HW N =
9D
= - =
,D +
‡ ,
=
= - =
=
7KHUHIRUH = =
9D
,D+ N ‡,
1RWHWKDWµN¶LVDFRPSOH[QXPEHUEXW_N_LVRIWHQXVHGLQVWHDGWR\LHOGDQDSSUR[LPDWHUDWKHU
WKDQDQH[DFWFRPSHQVDWLRQRIWKHSKDVHFXUUHQW
$33(1',;% 02'(/,1*23(13+$6(&21'8&7256
$VVXPHWKDWDFRQGXFWRUFDQRSHQDQ\ZKHUHDORQJWKHSURWHFWHGOLQHVHFWLRQ,QWKHVHFDVHVDQ\
RQHVROXWLRQPXVWQRWEHGHSHQGHQWXSRQWKHORFDWLRQRIWKHRSHQFRQGXFWRU)RUVLPSOLFLW\
DVVXPHWKHRSHQLVLQWKHPLGGOHRIWKHOLQHDWP IRUWKHV\VWHPVKRZQLQ)LJXUHZKHUH
P SHUXQLWOLQHOHQJWK
=/
=/
=6
=5
(6
(5
5HOD\
5HOD\
)LJXUH 6LQJOH/LQH'LDJUDPRI([DPSOH6\VWHP
7KHV\PPHWULFDOFRPSRQHQWVFRQQHFWLRQIRUDVLQJOHSKDVHRSHQFRQGLWLRQLVVKRZQLQ)LJXUH
7KHFRQQHFWLRQGLDJUDPVKRZQLQ)LJXUHLVYHU\VLPLODUWRWKDWRIDPLGOLQHSKDVHWRSKDVH
WRJURXQGIDXOW)LJXUH
,Q)LJXUHWKHWKURXJKORDGSRVLWLYHVHTXHQFHFXUUHQWGLYLGHVEHWZHHQWKHQHJDWLYHDQG]HUR
VHTXHQFHQHWZRUNVLH, ±,,7KHUHODWLRQVKLSRI, ±,,LVLGHQWLFDOWRWKDW
REWDLQHGIRUDSKDVHWRSKDVHWRJURXQGIDXOWRQDUDGLDOV\VWHPZLWKWKHUHPRWHEUHDNHURSHQ
7KHUHOD\VDWERWKHQGVRIWKHOLQHDUHDOVRVXEMHFWHGWRWKHVDPHVHTXHQFHFXUUHQWVVLQFH,,
DQG,DUHWKHHTXLYDOHQWIRUERWKHQGVRIWKHOLQH
)LJXUH 6\PPHWULFDO&RPSRQHQWV&RQQHFWLRQIRU6LQJOH3KDVH2SHQ&RQGLWLRQ
)LJXUH 6\PPHWULFDO&RPSRQHQWV&RQQHFWLRQIRU3KDVHWR3KDVHWR*URXQG)DXOW
7KHV\PPHWULFDOFRPSRQHQWFRQQHFWLRQLQ)LJXUHFDQEHUHGXFHGWRDSDUDOOHOFRQQHFWLRQRI
WKHQHJDWLYHDQG]HURVHTXHQFHQHWZRUNVLQVHULHVZLWKWKHSRVLWLYHVHTXHQFHOLQHDQGVRXUFH
LPSHGDQFHVVKRZQLQ)LJXUH5HGXFLQJWKHQHWZRUNVKRZVWKDWWKHQHJDWLYHDQG]HUR
VHTXHQFHFXUUHQWVDUHIORZLQJLQRSSRVLWHGLUHFWLRQVRQWKHVXSSO\EXVWKHEXVVXSSO\LQJSUHIDXOW
ORDGFXUUHQWDQGWKHORDGEXVIRUWKLVV\VWHP
)LJXUH 6LPSOLILHG3DUDOOHO&RQQHFWLRQ1HJDWLYHDQG=HUR6HTXHQFH1HWZRUNV
$VLQJOHSKDVHRSHQFRQGLWLRQGXULQJORDGSUHVHQWVWKHUHOD\VDWERWKHQGVRIWKHOLQHZLWK
QHJDWLYHDQG]HURVHTXHQFHFXUUHQWVDQGYROWDJHV7KHPDJQLWXGHVRIQHJDWLYHDQG]HUR
VHTXHQFHFXUUHQWVDQGYROWDJHVSURGXFHGDUHGHWHUPLQHGE\WKHORDGIORZDQGWKHVWUHQJWK
PDJQLWXGHDQGDQJOHRIWKHVRXUFHV,IWKHORDGIORZLV]HURQRVHTXHQFHFXUUHQWRSHUDWLQJ
TXDQWLWLHVDUHVXSSOLHGWRWKHUHOD\V$VORDGIORZLQFUHDVHVWKHVHTXHQFHFXUUHQWRSHUDWLQJ
TXDQWLWLHVDYDLODEOHWRWKHUHOD\VEHFRPHODUJHU
%,2*5$3+,(6
*HRUJH($OH[DQGHUKROGVD%6((GHJUHHIURP9LOODQRYD8QLYHUVLW\DQGDQ06((GHJUHH
IURP'UH[HO8QLYHUVLW\+HLVDUHJLVWHUHGSURIHVVLRQDOHQJLQHHULQWKHVWDWHRI3HQQV\OYDQLD+H
KDVRYHU\HDUVH[SHULHQFHLQWKHGHVLJQDQGDSSOLFDWLRQRIWUDQVPLVVLRQOLQHUHOD\LQJDQG
KROGVVHYHUDO86SDWHQWVLQWKLVDUHD0U$OH[DQGHUKDVEHHQLQYROYHGLQWKHGHYHORSPHQWDQG
0RGHO3RZHU6\VWHPWHVWLQJRIVROLGVWDWHK\EULGDQDORJGLJLWDODQGIXOO\GLJLWDOSURWHFWLYH
UHOD\LQJV\VWHPV+HMRLQHG6(/LQDQGLVFXUUHQWO\UHJLRQDOVHUYLFHPDQDJHUIRUWKH1RUWK
86DQG(DVWHUQ&DQDGD
-RVHSK%0RRQH\3(UHFHLYHGKLV%6FLQ(OHFWULFDO(QJLQHHULQJIURP:DVKLQJWRQ6WDWH
8QLYHUVLW\LQ+HMRLQHG3DFLILF*DVDQG(OHFWULF&RPSDQ\XSRQJUDGXDWLRQDVD6\VWHP
3URWHFWLRQ(QJLQHHU,QKHOHIW3DFLILF*DVDQG(OHFWULFDQGZDVHPSOR\HGE\%RQQHYLOOH
3RZHU$GPLQLVWUDWLRQDVD6\VWHP3URWHFWLRQ0DLQWHQDQFH'LVWULFW6XSHUYLVRU,QKHOHIW
%RQQHYLOOH3RZHU$GPLQLVWUDWLRQDQGMRLQHG6FKZHLW]HU(QJLQHHULQJ/DERUDWRULHVDVDQ
$SSOLFDWLRQ(QJLQHHU6KRUWO\DIWHUVWDUWLQJZLWK6(/KHZDVSURPRWHGWR$SSOLFDWLRQ
(QJLQHHULQJ0DQDJHU,QKHEHFDPH0DQDJHURIWKH3RZHU(QJLQHHULQJ*URXSRIWKH
5HVHDUFKDQG'HYHORSPHQWGHSDUWPHQWDW6FKZHLW]HU(QJLQHHULQJ/DERUDWRULHV+HLVD
UHJLVWHUHG3URIHVVLRQDO(QJLQHHULQWKHVWDWHVRI&DOLIRUQLDDQG:DVKLQJWRQ
:LOOLDP7\VNDUHFHLYHGD%6((IURP&ODUNVRQ8QLYHUVLW\DQGVXEVHTXHQWO\FRPSOHWHG*(¶V
3RZHU6\VWHP(QJLQHHULQJ&RXUVH+LVZRUNH[SHULHQFHLQFOXGHVGHVLJQDQGDSSOLFDWLRQRI
SURWHFWLYHUHOD\HTXLSPHQWIRU\HDUVZLWK*(+HLVWKHDXWKRURUFRDXWKRURIUHOD\
FRQIHUHQFHSDSHUVUHODWHGWRSRZHUV\VWHPSURWHFWLRQ3UHVHQWO\KHLVHPSOR\HGDVDSRZHU
HQJLQHHULQWKH.LQJRI3UXVVLD3$RIILFHRI6FKZHLW]HU(QJLQHHULQJ/DERUDWRULHV,QF
&RS\ULJKW‹6(/
$OOULJKWVUHVHUYHG
3ULQWHGLQ86$