Aalborg Universitet
On the Inherent Segment Length in Music
Jensen, Karl Kristoffer
Published in:
Machine Audition
DOI (link to publication from Publisher):
10.4018/978-1-61520-919-4.ch013
Publication date:
2011
Document Version
Early version, also known as pre-print
Link to publication from Aalborg University
Citation for published version (APA):
Jensen, K. K. (2011). On the Inherent Segment Length in Music. In W. Wang (Ed.), Machine Audition:
Principles, Algorithms and Systems (Chapter 13, pp. 317-333). USA: IGI global. DOI: 10.4018/978-1-61520-9194.ch013
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners
and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.
? You may not further distribute the material or use it for any profit-making activity or commercial gain
? You may freely distribute the URL identifying the publication in the public portal ?
Take down policy
If you believe that this document breaches copyright please contact us at [email protected] providing details, and we will remove access to
the work immediately and investigate your claim.
Downloaded from vbn.aau.dk on: juni 17, 2017
&KDSWHU
2QWKH,QKHUHQW6HJPHQW
/HQJWKLQ0XVLF
.ULVWRIIHU-HQVHQ
$DOERUJ8QLYHUVLW\(VEMHUJ'HQPDUN
$%675$&7
,QWKLVZRUN DXWRPDWLFVHJPHQWDWLRQLVGRQHXVLQJGLIIHUHQWRULJLQDOUHSUHVHQWDWLRQVRIPXVLFFRU
UHVSRQGLQJWRUK\WKPFKURPDDQGWLPEUHDQGE\FDOFXODWLQJDVKRUWHVWSDWKWKURXJKWKHVHOIVLPLODU
LW\FDOFXODWHGIURPHDFKWLPHIHDWXUHUHSUHVHQWDWLRQ%\YDU\LQJWKHFRVWRILQVHUWLQJQHZVHJPHQWV
VKRUWHU VHJPHQWV FRUUHVSRQGLQJ WR JURXSLQJ RU ORQJHU FRUUHVSRQGLQJ WR IRUP FDQ EH UHFRJQL]HG
(DFKVHJPHQWDWLRQVFDOHTXDOLW\LVDQDO\]HGWKURXJKWKHXVHRIWKHPHDQVLOKRXHWWHYDOXH7KLVSHUPLWV
DXWRPDWLFVHJPHQWDWLRQRQGLIIHUHQWWLPHVFDOHVDQGLWJLYHVLQGLFDWLRQRQWKHLQKHUHQWVHJPHQWVL]HVLQ
WKHPXVLFDQDO\]HG'LIIHUHQWPHWKRGVDUHHPSOR\HGWRYHULI\WKHTXDOLW\RIWKHLQKHUHQWVHJPHQWVL]HV
E\FRPSDULQJWKHPWRWKHOLWHUDWXUHJURXSLQJFKXQNVE\FRPSDULQJWKHPDPRQJWKHPVHOYHVDQGE\
PHDVXULQJWKHVWUHQJWKRIWKHLQKHUHQWVHJPHQWVL]HV
,1752'8&7,21
0XVLFFRQVLVWVRIVRXQGVRUJDQL]HGLQWLPH7KHVH
VRXQGVFDQEHXQGHUVWRRGIURPDUK\WKPLFWLP
EUDORUKDUPRQLFSRLQWRIYLHZDQGWKH\FDQEH
XQGHUVWRRGRQGLIIHUHQWWLPHVFDOHVJRLQJIURP
WKHYHU\VKRUWQRWHRQVHWVWRWKHPHGLXPJURXS
LQJWRWKHODUJHVFDOHZLWKPXVLFDOIRUP1RWH
RQVHWVJURXSLQJDQGIRUPDUHFRPPRQPXVLFDO
WHUPVZKLFKFDQEHFRPSDUHGWRGLIIHUHQWDVSHFWV
'2,FK
RI DXGLWLRQ PHPRU\ DQG JURXSLQJ EHKDYLRU
7KHVH WHUPV FDQ EH FRPSDUHG WR FKXQNV ULIIV
DQGRWKHUWHPSRUDOVHJPHQWDWLRQWHUPVFXUUHQWO\
XVHGLQPXVLF
:KHQLGHQWLI\LQJFKXQNVULIIVVHFWLRQVIRUPV
RURWKHUVWUXFWXUDOHOHPHQWVGRWKH\UHDOO\H[LVW
RU GRHV WKH LGHQWLILFDWLRQ SURFHVV FUHDWH WKHP"
7KLVZRUNSUHVHQWVDPHWKRGEDVHGRQDXWRPDWLF
VHJPHQWDWLRQWKDWLGHQWLILHVWKHLQKHUHQWVWUXFWXUH
VL]HVLQPXVLFLHJLYHVLQGLFDWLRQVDVWRZKDW
DUHWKHRSWLPDOVHJPHQWDWLRQVL]HVLQWKHPXVLF
7KLV ZRUN KDV LPSOLFDWLRQV IRU UK\WKPLFDO DQG
&RS\ULJKW‹,*,*OREDO&RS\LQJRUGLVWULEXWLQJLQSULQWRUHOHFWURQLFIRUPVZLWKRXWZULWWHQSHUPLVVLRQRI,*,*OREDOLVSURKLELWHG
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
FODVVLFDO PXVLF XQGHUVWDQGLQJ DQG SURFHVVLQJ
6WUXFWXUHLVDQHFHVVDU\GLPHQVLRQLQPRVWLIQRW
DOO PXVLF DQG LI WKLV VWUXFWXUH VKRXOG EH PDGH
YLVLEOHIRUDQ\SXUSRVHWKHPHWKRGVSUHVHQWHG
KHUHFDQKHOSLGHQWLI\LQJWKHRSWLPDOVWUXFWXUH
:KLOHWKLVIXQGDPHQWDOUHVHDUFKJLYHVDPHWKRG
IRUILQGLQJWKHRSWLPDOVHJPHQWVL]HLQPXVLFDQG
UHVXOWVXVLQJWKLVPHWKRGPRUHZRUNLVQHHGHG
LQ RUGHU WR DVVHVV WKH LQKHUHQW VWUXFWXUH ZLWK
FHUWDLQW\IRUDOOPXVLF8QWLOWKHQUHVHDUFKDQG
GHYHORSPHQWRIDXWRPDWLFVHJPHQWDWLRQRIPXVLF
VKRXOGSRVVLEO\DVFHUWDLQWKHLQKHUHQWVWUXFWXUHLQ
WKHPXVLFJHQUHVWKDWLVWKHDLPRIWKHZRUNSULRU
WRSHUIRUPLQJWKHVHJPHQWDWLRQ
$Q\IHDWXUHWKDWFDQEHFDOFXODWHGIURPWKH
DFRXVWLFVRIWKHPXVLFFDQEHSUHVHQWHGLQDPDQ
QHUIRULQVWDQFHE\WDNLQJWKHWLPHGHULYDWLYHVR
DVWRJLYHLQGLFDWLRQRIWKHORFDOFKDQJHVLQWKH
PXVLF6XFKDQH[LVWHQFHRIDORFDOFKDQJHLVQRW
DJXDUDQWHHRIDQLQKHUHQWVWUXFWXUHKRZHYHU,Q
RUGHUWRDVVHVVWKHTXDOLW\RIWKHVHJPHQWDWLRQ
WKHUHODWLYHGLVWDQFHRUDQ\PHDVXUHRIVLPLODU
LW\ZLWKLQDVHJPHQWVKRXOGEHFRPSDUHGWRWKH
GLVWDQFH WR WKH RWKHU VHJPHQWV ,I WKH VHJPHQW
LV ZHOO JURXSHG DQG IDU LQ VRPH VHQVH WR WKH
RWKHUVHJPHQWVWKHQLWLVDJRRGVHJPHQWDWLRQ
$PHWKRGIRUDVVHVVLQJWKHVHJPHQWDWLRQLVWKH
VLOKRXHWWH.DXIPDQ5RXVVHHXZ*LYHQ
DVHJPHQWDWLRQWKHPHDQRIWKHVLOKRXHWWHYDOXH
IRUDOOVHJPHQWVLVDJRRGPHDVXUHRIWKHTXDOLW\
RI WKH VHJPHQWDWLRQ 7KHUHIRUH LI DOO SRVVLEOH
VHJPHQWDWLRQVDUHFDOFXODWHGWKHDVVRFLDWHGPHDQ
VLOKRXHWWHYDOXHVFDQEHXVHGWRDVFHUWDLQWKHEHVW
LHWKHLQKHUHQWVWUXFWXUHVL]HV
$VWRWKHTXHVWLRQRIZKLFKIHDWXUHLVXVHGIRU
WHPSRUDO SHUFHSWLRQ RI PXVLF 6FKHLUHU GHWHUPLQHGLQVHYHUDODQDO\VLVE\V\QWKHVLVH[
SHULPHQWV WKDW UK\WKP FRXOG QRW EH SHUFHLYHG
E\DPSOLWXGHDORQHEXWQHHGHGVRPHIUHTXHQF\
GHSHQGHQW LQIRUPDWLRQ ZKLFK KH FRQVWUXFWHG
XVLQJ VL[ EDQGSDVV ILOWHUV 6HYHUDO RWKHU VWXG
LHVKDYHLQYHVWLJDWHGWKHLQIOXHQFHRIWLPEUHRQ
VWUXFWXUH 0F$XOH\ $\DOD IRXQG WKDW
WLPEUHGLGQRWDIIHFWWKHUHFRJQLWLRQRIIDPLOLDU
PHORGLHVEXWWKDWLWKDGLPSRUWDQFHHQRXJKWRKXUW
UHFRJQLWLRQRQQRQIDPLOLDUPHORGLHV0F$GDPV
VWXGLHGFRQWHPSRUDU\DQGWRQDOPXVLFDQG
IRXQGWKDWWKHRUFKHVWUDWLRQDIIHFWVWKHSHUFHLYHG
VLPLODULW\RIPXVLFDOVHJPHQWVVWURQJO\LQVRPH
FDVHV+HDOVRIRXQGWKDWPXVLFDOO\WUDLQHGOLVWHQ
HUVILQGVWUXFWXUHWKURXJKVXUIDFHIHDWXUHVOLQNHG
WRWKHLQVWUXPHQWDWLRQZKHUHDVXQWUDLQHGOLVWHQ
HUVIRFXVHGRQPRUHDEVWUDFWIHDWXUHVPHORGLF
FRQWRXUUK\WKP
'HOLqJHDQG0pOHQSRVWXODWHVWKDWPXVLF
LVVHJPHQWHGLQWRVHFWLRQVRIYDU\LQJOHQJWKXVLQJ
FXHDEVWUDFWLRQPHFKDQLVPDQGWKHSULQFLSOHRI
VDPHQHVVDQGGLIIHUHQFHDQGWKDWWKHRUJDQL]DWLRQ
RIWKHVHJPHQWDWLRQUHLWHUDWHGDWGLIIHUHQWKLHUDU
FKLFDOOHYHOVSHUPLWVWKHVWUXFWXUHWREHJUDVSHG
7KHFXHVHVVHQWLDOO\PRWLIVLQFODVVLFDOPXVLF
DQGDFRXVWLFLQVWUXPHQWDORUWHPSRUDORWKHUZLVH
DFWDVUHIHUHQFHSRLQWVGXULQJORQJWLPHVSDQV
'HOLqJHDQG0pOHQIXUWKHUPRUHLOOXVWUDWHWKLVFXH
DEVWUDFWLRQSURFHVVWKURXJKVHYHUDOH[SHULPHQWV
ILQGLQJDPRQJRWKHUWKLQJVWKDWPXVLFLDQVDUH
PRUHVHQVLWLYHWRVWUXFWXUDOIXQFWLRQVDQGWKDWWKH
VWUXFWXULQJSURFHVVLVXVHGIRUUHPHPEHULQJLQ
SDUWLFXODUWKHILUVWDQGODVWVHJPHQW,QRUGHUWR
HQVXUHWKDWDWOHDVWSDUWRIWKHIXOOGLPHQVLRQDOLW\RI
PXVLFLVWDNHQLQWRDFFRXQWLQWKHZRUNSUHVHQWHG
KHUHWKUHHGLIIHUHQWIHDWXUHVDUHXVHG2QHIHDWXUH
LVEHOLHYHGWREHUHODWHGWRWHPSRDQGUK\WKPDQG
LWLVFDOOHGWKHUK\WKPRJUDP$QRWKHUIHDWXUHLV
FRQVLGHUHG UHODWHG WR WKH WLPEUH SHUFHSWLRQ DW
OHDVWWKHWLPHYDU\LQJSHUFHSWLYHVSHFWUXPDQGLW
LVFDOOHGWKHWLPEUHJUDP)LQDOO\DQRWKHUIHDWXUH
LVUHODWHGWRWKHQRWHYDOXHVLQWKHPXVLFDQGLWLV
FDOOHGFKURPDJUDP%\XVLQJWKUHHIHDWXUHVZLWK
GLVWLQFWO\GLIIHUHQWFRQWHQWLWLVWKHDLPWRIXUWKHU
DVVHVVWKHUHVXOWVRQLQKHUHQWDQGRSWLPDOVHJPHQW
VL]HSUHVHQWHGKHUH
6HJPHQWDWLRQ RI PXVLF LV RIWHQ GRQH IRU
WKXPEQDLOLQJPXVLFVXPPDU\SXUSRVHV7KLVLV
VXSSRVHGO\DPHDQVIRUSUHVHQWLQJPXVLFSULRU
WRVHOOLQJLWIRULQVWDQFHLQRQOLQHVWRUHV2WKHU
XVHV RI VHJPHQWDWLRQ DUH DUWLVWLF IRU LQVWDQFH
IRUOLYHPL[LQJRIPXVLFIRUIDVWHUQDYLJDWLRQ
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
ZKHUHWKHNQRZOHGJHRIVWUXFWXUDOHOHPHQWVFDQ
EHXVHGIRUVNLSSLQJVLPLODUHOHPHQWVRUUHODWHG
WR PXVLF LGHQWLILFDWLRQ )LQDOO\ VHJPHQWDWLRQ
DXWRPDWLFODEHOLQJRIPXVLFFDQEHEHQHILFLDOIRU
PXVLFDQDO\VLV
$VIRUWKHPHWKRGVIRUDXWRPDWLFVHJPHQWDWLRQ
)RRWHLQWURGXFHGWKHXVHRIVHOIVLPLODULW\
PDWULFHVE\FRQYROYLQJWKHVHOIVLPLODULW\PDWUL[
ZLWKDFKHFNHUNHUQHOWKXVFDOFXODWLQJWKHQRYHOW\
PHDVXUHZKLFKJLYHVLQGLFDWLRQVRIWKHGHJUHH
RI QRYHOW\ RYHU WLPH %DUWVFK DQG :DNHILHOG
XVHGWKHFKURPDUHSUHVHQWDWLRQIRUDXGLR
WKXPEQDLOLQJE\VHOHFWLQJWKHPD[LPXPRIWKH
WLPHODJPDWUL[ZKLFKLVWKHVHOIVLPLODULW\PDWUL[
ILOWHUHGDORQJWKHGLDJRQDOLQRUGHUWRUHYHDOVLPL
ODULWLHVDORQJH[WHQGHGUHJLRQVRIWKHVRQJV*RWR
DQG&KDL9HUFRHDOVRLGHQWLI\
UHSHDWLQJVHJPHQWVXVLQJFKURPDUHSUHVHQWDWLRQ
*RWR XVLQJ D VLPLODULW\ PHDVXUH RI WKH
GLVWDQFHEHWZHHQYHFWRUVWRJHWKHUZLWKDPHWKRG
IRULQWHJUDWLQJYHFWRUVLQWRVHJPHQWVDQG&KDL
9HUFRHE\LGHQWLI\LQJORFDOPLQLPDLQWKH
G\QDPLFSURJUDPPLQJZKLFKLVDQLQGLFDWRURI
UHSHWLWLRQRIVHJPHQWV3DXOXVDQG.ODSXUL
LQDGGLWLRQXVH0DUNRYPRGHOVWRDVVLJQODEHOV
&KRUXV9HUVHHWFWRWKHVHJPHQWV
,Q WKLV ZRUN IRFXV ZLOO EH RQ GHWHUPLQLQJ
LI WKHUH H[LVWV DQ LQKHUHQW VHJPHQW VL]H LQ WKH
PXVLF,QGHHGPRVWVHJPHQWDWLRQPHWKRGVDUH
DEOHWRFRPSXWHVHJPHQWDWLRQDWGLIIHUHQWWLPH
VFDOHVZKLOHWKHFKRVHQVHJPHQWDWLRQVL]HLVOHIW
WRWKHDSSOLFDWLRQGHYHORSPHQWVWDJH.QRZLQJ
WKH LQKHUHQW WLPH VFDOH LQ PXVLF LV GRQH LQ WKH
IROORZLQJPDQQHU)LUVWWKHIHDWXUHHVWLPDWLRQLV
SUHVHQWHGWKHQWKHVHJPHQWDWLRQXVLQJG\QDPLF
SURJUDPPLQJ LV SHUIRUPHG IRU DOO WLPH VFDOH
WKHQDPHDVXUHRIWKHTXDOLW\RIWKHVHJPHQWDWLRQ
LVFDOFXODWHGDQGWKHSHDNVRIWKLVPHDVXUHDUH
LGHQWLILHGDQGXVHGDVDQLQGLFDWRURIWKHLQKHUHQW
VHJPHQWDWLRQVL]H6HYHUDOPHWKRGVIRUDVVHVVLQJ
WKHLPSRUWDQFHRIWKHRSWLPXPVHJPHQWVL]HVDUH
HPSOR\HGDQGGLVFXVVHGLQWKHFRQFOXVLRQV
)($785((67,0$7,21
,QRUGHUWRSHUIRUPDJRRGVHJPHQWDWLRQRIWKH
VRQJV D UREXVW IHDWXUH LV QHHGHG ,QGHHG WKH
IHDWXUH XVHG IRU VHJPHQWDWLRQ FDQ FKDQJH WKH
VHJPHQWDWLRQUHVXOWVLJQLILFDQWO\7KUHHGLIIHUHQW
IHDWXUHVDUHLQYHVWLJDWHGKHUHWKHUK\WKPLFIHDWXUH
WKHUK\WKPRJUDP-HQVHQLVEDVHGRQWKH
DXWRFRUUHODWLRQ RI WKH SHUFHSWXDO VSHFWUDO IOX[
36)-HQVHQ7KH36)KDVKLJKHQHUJ\LQ
WKHWLPHSRVLWLRQZKHUHSHUFHSWXDOO\LPSRUWDQW
VRXQGFRPSRQHQWVVXFKDVQRWHVKDYHEHHQLQ
WURGXFHG7KHWLPEUHIHDWXUHWKHWLPEUHJUDPLV
EDVHGRQWKHSHUFHSWXDOOLQHDUSUHGLFWLRQ3/3
D VSHHFK IURQWHQG +HUPDQVN\ DQG WKH
KDUPRQ\IHDWXUHWKHFKURPDJUDPLVEDVHGRQWKH
FKURPD%DUWVFK:DNHILHOGFDOFXODWHG
RQWKHVKRUWWLPH)RXULHUWUDQVIRUP67)77KH
*DXVVLDQ ZHLJKWHG VSHFWURJUDP *:6 LV SHU
IRUPHGLQRUGHUWRLPSURYHUHVLOLHQFHWRQRLVHDQG
LQGHSHQGHQFHRQEORFNVL]HIRUWKHWLPEUHJUDP
DQGFKURPDJUDP$VSHHFKIURQWHQGVXFKDVWKH
3/3DOWHUVWKH67)7GDWDE\VFDOLQJWKHLQWHQVLW\
DQGIUHTXHQF\VRWKDWLWFRUUHVSRQGVWRWKHZD\
WKH KXPDQ DXGLWRU\ V\VWHP SHUFHLYHV VRXQGV
7KH FKURPD PDSV WKH HQHUJ\ RI WKH ))7 LQWR
WZHOYHEDQGVFRUUHVSRQGLQJWRWKHWZHOYHQRWHV
RI RQH RFWDYH %\ XVLQJ WKH UK\WKPLF WLPEUDO
DQGKDUPRQLFIHDWXUHVWRLGHQWLI\WKHVWUXFWXUHRI
WKHPXVLFVRPHRIWKHGLIIHUHQWDVSHFWVRIPXVLF
SHUFHSWLRQDUHEHOLHYHGWREHWDNHQLQWRDFFRXQW
0RUHLQIRUPDWLRQRIWKHIHDWXUHHVWLPDWLRQXVHG
KHUHFDQEHIRXQGLQ-HQVHQ
5K\WKPRJUDP
$Q\PRGHORIUK\WKPVKRXOGKDYHDVEDVLVVRPH
NLQGRIIHDWXUHWKDWUHDFWVWRWKHQRWHRQVHWV7KH
QRWHRQVHWVPDUNWKHPDLQFKDUDFWHULVWLFVRIWKH
UK\WKP,QDSUHYLRXVZRUN-HQVHQDODUJH
QXPEHURIIHDWXUHVZHUHFRPSDUHGWRDQDQQR
WDWHGGDWDEDVHRIWZHOYHVRQJVDQGWKHSHUFHSWXDO
VSHFWUDOIOX[36)ZDVIRXQGWRSHUIRUPEHVW
7KH36)LVFDOFXODWHGZLWKDVWHSVL]HRIPLO
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
OLVHFRQGVDQGWKHEORFNVL]HRIPLOOLVHFRQGV
$V WKH VSHFWUDO IOX[ LQ WKH 36) LV ZHLJKWHG VR
DVWRFRUUHVSRQGURXJKO\WRWKHHTXDOORXGQHVV
FRQWRXUERWKORZIUHTXHQF\VRXQGVVXFKDVEDVV
GUXPDQGKLJKIUHTXHQF\VRXQGVVXFKDVKLKDW
DUHHTXDOO\ZHOOWDNHQLQWRDFFRXQW
7KLVIUHTXHQF\ZHLJKWLQJLVREWDLQHGLQWKLV
ZRUNE\DVLPSOHHTXDOORXGQHVVFRQWRXUPRGHO
7KHSRZHUIXQFWLRQLVLQWURGXFHGLQRUGHUWRVLPX
ODWHWKHLQWHQVLW\ORXGQHVVSRZHUODZDQGUHGXFH
WKHUDQGRPDPSOLWXGHYDULDWLRQV7KHVHWZRVWHSV
DUHLQVSLUHGIURPWKH3/3IURQWHQG+HUPDQVN\
XVHGLQVSHHFKUHFRJQLWLRQ7KH36)ZDV
FRPSDUHGWRRWKHUQRWHRQVHWGHWHFWLRQIHDWXUHV
ZLWKJRRGUHVXOWVRQWKHSHUFXVVLYHFDVHLQDUHFHQW
VWXG\&ROOLQV,QRUGHUWRREWDLQDPRUH
UREXVWUK\WKPIHDWXUHWKHDXWRFRUUHODWLRQRIWKH
IHDWXUHLVQRZFDOFXODWHGRQRYHUODSSLQJEORFNV
RIVHFRQGVZLWKKDOIDVHFRQGVWHSVL]H+]
IHDWXUHVDPSOHUDWH2QO\WKHLQIRUPDWLRQEHWZHHQ
]HURDQGWZRVHFRQGVLVUHWDLQHG7KHDXWRFRUUHOD
WLRQLVQRUPDOL]HGVRWKDWWKHDXWRFRUUHODWLRQDW
]HURODJHTXDOVRQH,IYLVXDOL]HGZLWKODJWLPH
RQWKH\D[LVWLPHSRVLWLRQRQWKH[D[LVDQGWKH
DXWRFRUUHODWLRQYDOXHVYLVXDOL]HGDVLQWHQVLWLHVLW
JLYHVDIDVWRYHUYLHZRIWKHUK\WKPLFHYROXWLRQRI
DVRQJ7KLVUHSUHVHQWDWLRQFDOOHGUK\WKPRJUDP
-HQVHQ SURYLGHV LQIRUPDWLRQ DERXW WKH
UK\WKPDQGWKHHYROXWLRQRIWKHUK\WKPLQWLPH
7KHDXWRFRUUHODWLRQKDVEHHQFKRVHQLQVWHDGRI
WKHIDVW)RXULHUWUDQVIRUP))7IRUWZRUHDVRQV
)LUVWLWLVEHOLHYHGWREHPRUHLQDFFRUGDQFHZLWK
WKHKXPDQSHUFHSWLRQRIUK\WKP'HVDLQ
DQGVHFRQGLWLVEHOLHYHGWREHPRUHHDVLO\XQ
GHUVWRRGYLVXDOO\7KHUK\WKPRJUDPILUVWO\JLYHV
LQIRUPDWLRQDERXWWKHWHPSRRIWKHVRQJDORQJ
ZLWKWKHVWUHQJWKRIWKHWHPSRDQGVHFRQGO\JLYHV
LQIRUPDWLRQDERXWWKHWLPHVLJQDWXUHDOWKRXJKWKLV
LQIRUPDWLRQLVQRWDOZD\VFOHDUO\YLVLEOH
7LPEUHJUDP
7KH WLPEUH LV XQGHUVWRRG KHUH DV WKH VSHFWUDO
HVWLPDWH DQG GRQH KHUH XVLQJ WKH SHUFHSWXDO
OLQHDUSUHGLFWLRQ3/3+HUPDQVN\7KLV
LQYROYHVXVLQJWKHEDUN6HNH\+DQVRQ
VFDOH WRJHWKHU ZLWK DQ DPSOLWXGH VFDOLQJ WKDW
JLYHV DQ DSSUR[LPDWLRQ RI WKH KXPDQ DXGLWRU\
V\VWHP7KH3/3LVFDOFXODWHGZLWKDEORFNVL]H
RI DSSUR[LPDWHO\ PLOOLVHFRQGV DQG ZLWK D
VWHSVL]HRIPLOOLVHFRQG7KHWLPEUHJUDPLVD
IHDWXUHWKDWLVEHOLHYHGWRFDSWXUHRUFKHVWUDWLRQRI
WKHPXVLFPDLQO\,QWKHWLPEUHJUDPLQIRUPDWLRQ
DERXWZKLFKLQVWUXPHQWVDUHSDUWLFLSDWLQJLQWKH
PXVLFDWWKHFXUUHQWWLPHVWHSLVJLYHQDORQJZLWK
LQGLFDWLRQVRIZKDWG\QDPLFOHYHOWKHLQVWUXPHQWV
DUHSOD\HG,WUHSUHVHQWVWKHSHUFHSWXDOIUHTXHQF\
D[LVLQVWHSV:KHQDQLQVWUXPHQWLVLQWURGXFHG
LQWKHPXVLFLWLVRIWHQYLVLEOHLQWKHWLPEUHJUDP
,WFDQDOVRVKRZWKHRYHUDOOIUHTXHQF\FRQWHQWLH
ROGHUPXVLFODFNVLQEDVVDQGWUHEOHSRSPXVLF
JHQHUDOO\KDVHQHUJ\RQDOOIUHTXHQFLHVZKLOHVRPH
GDQFHPXVLFWHFKQRRQO\KDVHQHUJ\LQWKHWUHEOH
DQG EDVV UHJLRQV 7KH WLPEUHJUDP DOVR UHYHDOV
ZKHQVHFWLRQVDUHUHSHDWHGDQGLQSDUWLFXODUZKHQ
VHFWLRQVDUHFOLPD[HGZLWKVWURQJHULQVWUXPHQWV
WKURXJKRXW7KLVLVUHIOHFWHGZLWKVWURQJHUYDOXHV
LQWKHSDUWLFXODUEDUNWLPHORFDWLRQV
&KURPDJUDP
1RWHHVWLPDWLRQLVQRWRULRXVO\HUURUSURQHHYHQLI
DORWRISURJUHVVLVGRQHLQWKHGRPDLQFXUUHQWO\
7KHUHH[LVWVRQHHVWLPDWHWKDWLVUREXVWDQGUHODWHG
WRWKHQRWHYDOXHVWKHFKURPDZKLFKLVXVHGKHUH
,QWKHFKURPDRQO\WKHUHODWLYHFRQWHQWRIHQHUJ\
LQ WKH WZHOYH QRWHV RI WKH RFWDYH LV IRXQG 1R
LQIRUPDWLRQRIWKHRFWDYHRIWKHQRWHVLVLQFOXGHG
7KHFKURPDLVFDOFXODWHGIURPWKH67)7XVLQJD
EORFNVL]HRIPLOOLVHFRQGVDQGDVWHSVL]HRI
PLOOLVHFRQGV7KHFKURPDLVREWDLQHGE\VXPPLQJ
WKHHQHUJ\RIDOOSHDNVRIORJRIWKHIUHTXHQ
FLHV KDYLQJ PXOWLSOHV RI 7KH FKURPDJUDP
JLYHVLQIRUPDWLRQDERXWWKHQRWHYDOXHZLWKRXW
LQIRUPDWLRQDERXWWKHRFWDYH7KLVLVDUDWKHUJRRG
PHDVXUHRIZKLFKFKRUGVDUHSOD\HGDQGDOVRRI
WKHPXVLFDOVFDOHDQGWRQDOLW\,IVHYHUDOQRWHVDUH
SOD\HGIRUDPRPHQWWKHQWKLVLVFOHDUO\YLVLEOH
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
LQWKHFKURPDJUDP$OVRZKHQDQRWHLVGURSSHG
DQGDQRWKHUQRWHLVLQVWHDGSOD\HGPRUHWKLVLV
DOVRFOHDUO\UHIOHFWHGLQWKHFKURPDJUDPYDOXHV
*DXVVLDQ:LQGRZHG6SHFWURJUDP
,IWKHUDZIHDWXUHVDUHXVHGLWKDVEHHQIRXQGWKDW
WKHGHWDLOHGLQIRUPDWLRQVRPHWLPHVRYHUVKDGRZV
WKHORQJWHUPFKDQJHVLQWKHPXVLF,IWKHIHDWXUHV
DUHFDOFXODWHGRQVKRUWVHJPHQWVWRPLO
OLVHFRQGVWKH\JLYHGHWDLOHGLQIRUPDWLRQLQWLPH
WRRYDU\LQJWREHXVHGLQWKHVHJPHQWDWLRQPHWKRG
XVHGKHUH,QVWHDGWKHIHDWXUHVDUHFDOFXODWHGRQD
ODUJHVHJPHQWEXWORFDOL]HGLQWLPHE\XVLQJWKH
DYHUDJHRIPDQ\67)7EORFNVPXOWLSOLHGZLWKD
*DXVVLDQ7KLVLVFDOOHGWKH*DXVVLDQ:HLJKWHG
6SHFWUDJUDP*:68VLQJWKH*:6DOOVHJPHQWV
DUHXVHGDWDOOWLPHVWHSVEXWWKHFXUUHQWEORFN
YDOXHVDUHZHLJKWHGKLJKHUWKDQWKHPRUHGLVWDQW
EORFNV%\DYHUDJLQJXVLQJWKH*DXVVLDQDYHU
DJHQRVSHFLILFWLPHORFDOL]DWLRQLQIRUPDWLRQLV
REWDLQHG RI WKH LQGLYLGXDO QRWHV RU FKRUGV EXW
LQVWHDGDJHQHUDOYDOXHRIWKHWLPHDUHDLVJLYHQ
,QWKLVZRUNWKHDYHUDJLQJLVGRQHFRUUHVSRQGLQJ
WRDíG%ZLQGRZRIDSSUR[LPDWHO\VHFRQG
$IWHUWKH*:6WKHWLPEUHJUDPDQGFKURPDJUDP
KDVDVWHSVL]HRIòVHFRQG
$VDQH[DPSOHRIWKHIHDWXUHVWKHUK\WKPR
JUDP WLPEUHJUDP DQG FKURPDJUDP RI $XJXVW
(QJNLOGH ± %HDXWLIXO 1RLVH %UXPWRQH LV VKRZQ LQ )LJXUH $OO WKUHH IHDWXUHV VHHP
LQIRUPDWLYH DOWKRXJK WKH\ GR QRW JLYH VLPLODU
LQIRUPDWLRQ :KLOH WKH UK\WKP HYROXWLRQ LV LO
OXVWUDWHGLQWKHUK\WKPRJUDPLWLVWKHHYROXWLRQ
RIWKHWLPEUHWKDWLVVKRZQZLWKWKHWLPEUHJUDP
DQGWKHHYROXWLRQRIWKHQRWHYDOXHVWKDWFDQEH
VHHQLQWKHFKURPDJUDP%HDXWLIXO1RLVHLVQRWD
W\SLFDOUK\WKPLFSLHFHRIPXVLFDVFDQEHVHHQ
IURP WKH ODFN RI FOHDU UK\WKP LQIRUPDWLRQ LQ
ODUJHSDUWRIWKHPXVLF:KLOHWKHUK\WKPRJUDP
YDOXHVDUHQRUPDOL]HGEXWLQVWHDGWKHORZWLPH
ODJYDOXHVDUHVHWWR]HUR$VWKHVHDUHDOVRWKH
DXWRFRUUHODWLRQYDOXHZKLFKLVE\GHILQLWLRQVHW
WRRQHWKHUHODWLYHVWUHQJWKRIWKHKLJKHUWLPHODJ
FRUUHODWLRQVDUHUHIOHFWHGLQWKHUK\WKPRJUDP,Q
WKHFDVHRI%HDXWLIXO1RLVHWKHYHU\IDVWDOPRVW
YLEUDWLQJUK\WKPVKDYHYHU\VLPLODUUHSHWLWLRQV
ZKLFKDUHUHIOHFWHGDVVWURQJHUYDOXHVLQWKHFRU
UHVSRQGLQJWLPHVHJPHQWVLQWKHUK\WKPRJUDP
7KHWLPEUHJUDPUHYHDOVWKDWWKLVVRQJKDVHQHUJ\
LQWZRGLVWLQFWIUHTXHQF\UDQJHVRQHORZDQGRQH
KLJKXQWLODOPRVWWKUHHPLQXWHV7KHQWKHKLJK
IUHTXHQF\FRPSRQHQWDQRLVHZLQG\VRXQGGLV
DSSHDUV7KHWLPEUHJUDPLVQRWQRUPDOL]HGVRWKH
FUHVFHQGRVDUHYLVLEOHDWDOLWWOHDIWHUWZRPLQXWHV
DWWZRDQGDKDOIPLQXWHDQGDIWHUILYHPLQXWHV
7KH FKURPDJUDP LV QRUPDOL]HG DQG UHYHDOV D
VLQJOHQRWHSOD\HGDWWKHWLPHWKURXJKWKLVVRQJ
,WFKDQJHVIURPµ*¶WRµ'¶DQGEDFNDWDURXQG
RQHPLQXWHDQGWRRWKHUQRWHYDOXHVHOVHZKHUHLQ
WKHVRQJ%RWKWKHUK\WKPRJUDPWKHWLPEUHJUDP
DQGWKHFKURPDJUDPJLYHSHUWLQHQWLQIRUPDWLRQ
DERXWWKHHYROXWLRQLQWLPHRIWKHPXVLFDQGLW
VHHPVMXGLFLRXVWRLQYHVWLJDWHDOOWKUHHKHUH
6(*0(17$7,21
$XWRPDWLFVHJPHQWDWLRQXVLQJG\QDPLFSURJUDP
PLQJKDVEHHQSURSRVHGSUHYLRXVO\)RRWH
%DUWVFK:DNHILHOG*RWR&KDL
-HQVHQ-HQVHQHWDO-HQVHQ,QDQ
DXWRPDWLFVHJPHQWDWLRQWDVNDGMDFHQWEORFNVDUH
JURXSHGWRJHWKHUIRUPLQJVHJPHQWV7KLVFDQIRU
LQVWDQFHFRUUHVSRQGWRWKHFKRUXVYHUVHVWUXFWXUH
IRXQGLQPRVWUK\WKPLFPXVLFRUWRFKDQJHVLQ
WKH UK\WKPLF SDWWHUQ LQ WKH RUFKHVWUDWLRQ RU LQ
WKHQRWHVSOD\HG
7KHG\QDPLFSURJUDPPLQJXVHGKHUHLVEDVHG
RQWKHVKRUWHVWSDWKDOJRULWKP&RUPHQHWDO
DQGGRQHRQVHOIVLPLODULW\PDWULFHVFUHDWHGIURP
WKHRULJLQDOIHDWXUHVUK\WKPFKURPDRUWLPEUH
-HQVHQE\FDOFXODWLQJWKH/QRUPRIHDFK
WLPHYHFWRUFRPSDUHGWRDOORWKHUWLPHYHFWRUV
XVLQJDVHTXHQFHRI1YHFWRUVRIHDFKVRQJWKDW
VKRXOG EH GLYLGHG LQWR D QXPEHU RI VHJPHQWV
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
)LJXUH5K\WKPRJUDPWRSWLPEUHJUDPDQGFKURPDJUDPERWWRPRI%HDXWLIXO1RLVH
)LUVWOHWWKHFRVWFLMRIDVHJPHQWIURPEORFN
LWRMEHWKHZHLJKWHGVXPRIWKHVHOIVLPLODULW\
DQGWKHFRVWRIDQHZVHJPHQWEHDIL[HGFRVWĮ
6HFRQGO\ LQ RUGHU WR FRPSXWH D EHVW SRVVLEOH
VHJPHQWDWLRQDQHGJHZHLJKWHGGLUHFWHGJUDSK
*LVFRQVWUXFWHGZLWKWKHVHWRIQRGHVEHLQJDOO
WKH EORFN RI WKH VRQJ )RU HDFK SRVVLEOH VHJ
PHQWDQHGJHH[LVWV7KHZHLJKWRIWKHHGJHLV
ĮFLM$SDWKLQ*IURPQRGHWRQRGH1
FRUUHVSRQGVWRDFRPSOHWHVHJPHQWDWLRQZKHUH
HDFKHGJHLGHQWLILHVWKHLQGLYLGXDOVHJPHQW7KH
ZHLJKWRIWKHSDWKLVHTXDOWRWKHWRWDOFRVWRIWKH
FRUUHVSRQGLQJVHJPHQWDWLRQ7KHUHIRUHDVKRUWHVW
SDWKRUSDWKZLWKPLQLPXPWRWDOZHLJKWIURP
QRGHWRQRGH1JLYHVDVHJPHQWDWLRQZLWK
PLQLPXPWRWDOFRVW6XFKDVKRUWHVWSDWKFDQEH
FRPSXWHGLQWLPH21
7KH G\QDPLF SURJUDPPLQJ ZLOO FOXVWHU WKH
WLPHYHFWRUVLQWRVHJPHQWVDVORQJDVWKHYHFWRUV
DUHVLPLODU%\YDU\LQJWKHLQVHUWLRQFRVWĮRIQHZ
VHJPHQWVVHJPHQWERXQGDULHVFDQEHIRXQGDWGLI
IHUHQWWLPHVFDOHV$ORZLQVHUWLRQFRVWZLOOFUHDWH
ERXQGDULHVFRUUHVSRQGLQJWRPLFUROHYHOFKXQNV
ZKLOHDKLJKLQVHUWLRQFRVWZLOORQO\FUHDWHIHZ
PHVROHYHOFKXQNV7KXVWKHVDPHVHJPHQWDWLRQ
PHWKRGFDQFUHDWHVHJPHQWVRIYDU\LQJVL]HIURP
VKRUWWRORQJIURPWKHJURXSLQJWRWKHIRUPRI
WKH PXVLF$Q H[DPSOH RI WKH VHJPHQWDWLRQ LV
VKRZQLQ)LJXUHIRU$XJXVW(QJNLOGH±%HDXWLIXO
1RLVH%UXPWRQH$VWKHVHJPHQWFRVWĮ
LVLQFUHDVHGOHVVDQGOHVVVHJPHQWVDUHFUHDWHG
ZKLFKLQWXUQJLYHVORQJHUPHDQVHJPHQWOHQJWKV
7KHFRPSDULVRQRIWKHVHJPHQWDWLRQGRQHXVLQJ
WKHPHWKRGSUHVHQWHGKHUHEDVHGRQWKHWKUHHIHD
WXUHVUK\WKPRJUDPWLPEUHJUDPDQGFKURPDJUDP
UHYHDOVD)YDOXHRIDSSUR[LPDWHO\-HQVHQ
FRUUHVSRQGLQJ WR D PDWFKLQJ UHFDOO DQG
SUHFLVLRQ YDOXH RI 7KH FRPSDULVRQ WR
PDQXDO VHJPHQWDWLRQ JLYHV ) YDOXHV VOLJKWO\
KLJKHUDWDSSUR[LPDWHO\-HQVHQ7KLVLV
DQLQGLFDWLRQWKDWWKHPDQXDOVHJPHQWDWLRQLVGRQH
XVLQJGLIIHUHQWUK\WKPLFWLPEUDODQGFKURPDFXHV
DVWKHIHDWXUHVDUHEHWWHUPDWFKHGWRWKHPDQXDO
VHJPHQWDWLRQWKDQDPRQJWKHPVHOYHV7KHUHIRUH
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
)LJXUH6HJPHQWDWLRQXVLQJWKHWLPEUHJUDPIHDWXUHIRUDOOVHJPHQWFRVWVIRU$XJXVW(QJNLOGH±%HDX
WLIXO1RLVH
LWVHHPVWKDWDOOIHDWXUHVVKRXOGEHHPSOR\HGLQ
D VHJPHQWDWLRQ WDVN$V WKH ILQDO VHJPHQWDWLRQ
LVQRWWKHWDUJHWJRDOWKLVKDVQRWEHHQGHHPHG
LPSRUWDQWKHUH
:KLOH PDQ\ PHWKRGV IRU VHJPHQWDWLRQ RI
PXVLFH[LVWWKHSUREOHPRIILQGLQJWKHLQKHUHQW
QXPEHURIVHJPHQWVVWLOOH[LVWV.XKOUHODWHGWKLV
WRWKHQRWLRQRIFKXQNV$FFRUGLQJWRKLPWKH
FKXQNLVDQLPSRUWDQWHOHPHQWRIPXVLF$FKXQN
LVDVKRUWVHJPHQWRIDOLPLWHGQXPEHURIVRXQG
HOHPHQWVDFKXQNFRQVLVWVRIDEHJLQQLQJDIRFDO
SRLQWSHDNDQGDQHQGLQJ.XKOH[WHQGV
WKHFKXQNVWRLQFOXGHPLFURVWUXFWXUHEHORZ
VHFPHVRVWUXFWXUHFKXQNVWKHSUHVHQWDSSU
VHFVDQGPDFURVWUXFWXUH6XSHUFKXQNV.XKODQG
-HQVHQDWVHFV
%(676(*0(176,=(
7KHTXHVWLRQLQYHVWLJDWHGKHUHLVDERXWZKHWKHU
WKHUHH[LVWDQLQKHUHQWVHJPHQWVL]HLQWKHPXVLF
DQGLIVRLILWLVWKHVDPHIRUGLIIHUHQWPXVLFDQGLI
LWLVUHODWHGWRWKHFKXQNWKHRU\VL]HV7KLVTXHVWLRQ
KDVEHHQDQDO\]HGIURPGLIIHUHQWSRLQWVRIYLHZ
LQWKHOLWHUDWXUH+XURQLQYHVWLJDWHGWKH
PHORGLFDUFKDQGIRXQGDVLQJOHDUFKXSWR
QRWHVPHORGLHVZKLOHPHORGLHVFRQVLVWLQJRI
RUPRUHQRWHVSUHVHQWDGRXEOHDUFK7KLVLVRI
FRXUVHUHODWHGWRWKHVKRUWWLPHPHPRU\WKHRU\
RI“0LOOHUEXWLWGRHVQRWJLYHLQIRU
PDWLRQDERXWWKHWLPHRQO\WKHQXPEHURIQRWHV
,QRUGHUWRLQYHVWLJDWHWKLVIXUWKHUDGDWDEDVH
RIYDULHGPXVLFKDVEHHQFROOHFWHGDQGVHJPHQWHG
XVLQJWKHVKRUWHVWSDWKDOJRULWKPZLWKWKHUK\WKP
WLPEUHDQGFKURPDUHODWHGSDUDPHWHUV7KHIUHH
YDULDEOHĮLVYDULHGLQRUGHUWRSURGXFHVHJPHQW
VL]HVEHWZHHQRQHEORFNWRWKHIXOOVRQJLHDOO
SRVVLEOHVHJPHQWVL]HV7KHFODVVLFDOZD\RILQ
YHVWLJDWLQJWKHFOXVWHULQJTXDOLW\KDVWRGRZLWK
FRPSDULQJWKHLQWHUGLVWDQFHWKHVL]HRIHDFKFOXV
WHUWRWKHH[WUDGLVWDQFHWKHGLVWDQFHEHWZHHQWKH
FOXVWHUV8QIRUWXQDWHO\WKLVFDQQRWEHFRPSXWHG
IRUWKHRQHFOXVWHUVROXWLRQRUWKHRQHFOXVWHUIRU
HDFKEORFNVROXWLRQDQGLWJHQHUDOO\SURGXFHVD
µ8¶VKDSHVROXWLRQZLWKEHVWYDOXHVIRUVPDOORU
ODUJHFOXVWHUVL]HV$UREXVWHVWLPDWHRIWKHFOXVWHU
TXDOLW\LVWKHVLOKRXHWWH.DXIPDQ5RXVVHHXZ
FDOFXODWHGIRUHDFKREVHUYDWLRQLDV
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
)LJXUH6LOKRXHWWHSORWIRU%HDXWLIXO1RLVH$KLJKSRVLWLYHYDOXHVLQGLFDWHWKDWWKHREVHUYDWLRQLVZHOO
FOXVWHUHGZKLOHDODUJHQHJDWLYHYDOXHVLQGLFDWHDEDGFOXVWHULQJIRUWKHREVHUYDWLRQ
s=
bi − ai
max(ai , bi )
,
ZKHUHDLVWKHDYHUDJHGLVVLPLODULW\WRDOORWKHU
SRLQWVLQLWVRZQFOXVWHUDQGELVWKHPLQLPXP
RIWKHDYHUDJHGLVVLPLODULWLHVRILWRDOOREMHFWV
LQDQRWKHUFOXVWHU7KHVLOKRXHWWHYDOXHIRUHDFK
REVHUYDWLRQLVDOZD\VFRPSULVHGEHWZHHQDQG
,IWKHVLOKRXHWWHYDOXHLVODUJHLHFORVHWRWKH
REVHUYDWLRQLVFHQWHUHGLQWKHFOXVWHUZKLOHLIWKH
YDOXHLVORZWKHREVHUYDWLRQLVDOVRFORVHWRRWKHU
FOXVWHUV7KHVLOKRXHWWHIRUDFOXVWHULQJVROXWLRQFDQ
EHFDOFXODWHGDVWKHDYHUDJHRIHDFKREVHUYDWLRQV
VLOKRXHWWHYDOXH$QH[DPSOHRIWKHVLOKRXHWWHIRU
WKHVHJPHQWDWLRQXVLQJWKHWLPEUHJUDPIHDWXUHRI
%HDXWLIXO1RLVHLVVKRZQLQ)LJXUH7KHUHDUH
HLJKWFOXVWHUVZLWKDQDYHUDJHOHQJWKRIVHFRQGV
7KHDYHUDJHVLOKRXHWWHYDOXHLV6RPHRIWKH
FOXVWHUVWKHILUVWDQGILIWKLQSDUWLFXODUKDYHKLJK
VLOKRXHWWHYDOXHVWKURXJKRXWZKLOHVRPHRIWKH
RWKHUVKDYHQHJDWLYHVLOKRXHWWHYDOXHVIRUVRPH
RIWKHREVHUYDWLRQVRIWKHFOXVWHU
6HJPHQWDWLRQ$QDO\VLV
7KHPHDQVLOKRXHWWHYDOXHLVQRZFDOFXODWHGIRU
HDFKQHZVHJPHQWDWLRQFRVWLQRUGHUWRDQDO\]H
WKH TXDOLW\ RI WKH GLIIHUHQW VHJPHQWDWLRQV 2QH
VLOKRXHWWHYDOXHLVUHWDLQHGIRUHDFKDYHUDJHFOXVWHU
OHQJWKFDOFXODWHGDVWKHWRWDOOHQJWKGLYLGHGE\
WKHQXPEHURIFOXVWHUV$QH[DPSOHRIWKHPHDQ
VLOKRXHWWHYDOXHDVDIXQFWLRQRIDYHUDJHFOXVWHU
VL]HIRU%HDXWLIXO1RLVHLVVKRZQLQ)LJXUH7KH
DYHUDJHVLOKRXHWWHLVSORWWHGIRUWKHUK\WKPRJUDP
WLPEUHJUDPDQGFKURPDJUDPDORQJZLWKLQGLFD
WLRQVRIWKHSHDNVLQHDFKVLOKRXHWWHSORWXVLQJ
SOXV µ¶ VLJQV 7KLV VRQJ KDV VLOKRXHWWH SHDNV
IRUGLIIHUHQWVHJPHQWOHQJWKVLQFOXGLQJIRUWKH
FKXQNVL]HDWDSSUR[LPDWHO\VHFRQGVDQGWKH
VXSHUFKXQN VL]H DW DSSUR[LPDWHO\ VHFRQGV
2WKHURSWLPXPFKXQNVL]HVDUHDOVRYLVLEOH
1LQHVRQJVRIFODVVLFDOSRSUDSDQGMD]]JHQUHV
KDYHEHHQVHJPHQWHGXVLQJWKHUK\WKPRJUDPWLP
EUHJUDPDQGFKURPDJUDPIHDWXUHVIRUYDU\LQJQHZ
VHJPHQWFRVW(DFKVRQJKDVDQXPEHURIVLOKRXHWWH
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
)LJXUH0HDQVLOKRXHWWHYDOXHDVDIXQFWLRQRIDYHUDJHVHJPHQWOHQJWKIRU%HDXWLIXO1RLVH3HDNVDUH
LQGLFDWHGZLWKSOXVµ¶VLJQV
SHDNVIRUHDFKIHDWXUHJLYLQJDQLQGLFDWLRQRIWKH
LQKHUHQWVHJPHQWVL]HDVDIXQFWLRQRIWKHDYHUDJH
VHJPHQWOHQJWK9LVXDOO\WKHUK\WKPRJUDPVHHPV
WRJLYHDEHWWHUUHVXOW7RFRPSDUHWRWKHFKXQN
WKHRU\RI.KOWKHSHDNVRIWKHDYHUDJH
VLOKRXHWWHYDOXHVFDQEHLGHQWLILHVDVEHORQJLQJWR
WKHUDQJHVHFRQGVFRUUHVSRQGLQJWRWKHFKXQN
VL]HDQGEHWZHHQVHFRQGVFRUUHVSRQGLQJ
WRWKHVXSHUFKXQNVL]H)RUWKHQLQHVRQJVWKHUH
KDV EHHQ IRXQG FKXQN PDWFKHV IRU
UK\WKPRJUDPVXSHUFKXQNPDWFKHV
FKXQNPDWFKHVIRUWLPEUHJUDP
VXSHUFKXQNPDWFKHVDQGFKXQNPDWFKHV
IRUFKURPDJUDPVXSHUFKXQNPDWFKHV
7KHUK\WKPRJUDPSHUIRUPVVLJQLILFDQWO\EHWWHU
WKDQ WKH RWKHU IHDWXUHV IRU WKLV SDUWLFXODU WDVN
7KLVLVDOVRYLVLEOHLIWKHPHDQRIWKHQLQHVRQJV
LVFDOFXODWHGDQGSORWWHG)LJXUH,QGHHGWKH
UK\WKPRJUDP VLOKRXHWWH SORW SUHVHQWV D SURPL
QHQW SHDN DW WKH FKXQN OHYHO DURXQG VHFRQG
DYHUDJHVHJPHQWOHQJWKDQGDOVRRQHSHDNDWDS
SUR[LPDWHO\VHFRQGVDYHUDJHVHJPHQWOHQJWK
7KHWLPEUHJUDPDQGFKURPDJUDPKDVDPRUHµ8¶
VKDSHGVLOKRXHWWHYDOXHHIIHFWLYHO\SUHYHQWLQJDQ\
VLOKRXHWWHSHDNDWWKHFKXQNOHYHO6HYHUDORWKHU
SRVVLEOH SHDN SRVLWLRQV DOVR H[LVW IRU LQVWDQFH
DURXQGVHFRQGVDQGDURXQGVHFRQGV
$QRWKHU GLVWLQFWLRQ WKDW FDQ EH PDGH LV EH
WZHHQWKHVKRUWWHUPPHPRU\DQGWKHORQJWHUP
PHPRU\ 6Q\GHU UHODWHV WKH VKRUWWHUP
PHPRU\WRPHORGLFDQGUK\WKPLFJURXSLQJDQG
VLWXDWHVLWEHWZHHQVHFRQGWRVHFRQGDQG
WKH ORQJWHUP PHPRU\ WR PXVLFDO IRUP DQG
VLWXDWHVWKLVDERYHVHFRQGV,IWKHTXHVWLRQLV
ZKDWLVPRUHSURPLQHQWJURXSLQJRUIRUPWKHQ
WKHVWXG\SHUIRUPHGKHUHJLYHVLQGLFDWLRQVWKDW
IRUPLVPRVWSURPLQHQWDVWKHUHLV
DQGSHDNVEHORZVHF
RQGV FRUUHVSRQGLQJ WR JURXSLQJ IRU UK\WKP
WLPEUHDQGFKURPDUHVSHFWLYHO\7KXVJURXSLQJ
LVVHHPLQJO\PRUHUHODWHGWRUK\WKPDQGOHVVWR
WLPEUHDQGFKURPD
$VWRWKHTXHVWLRQRIWKHVLPLODULW\RIWKHSHDN
SRVLWLRQRIWKHVLOKRXHWWHDVDIXQFWLRQRIDYHU
DJH VHJPHQW OHQJWK WKH QRUPDOL]HG KLVWRJUDP
RIWKHVHJPHQWDWLRQSHDNVDUHFDOFXODWHGDORQJ
ZLWKDPHDVXUHRIWKHSHDNHGQHVVRIHDFKSHDN
7KH QRUPDOL]HG KLVWRJUDP JLYHV YDOXHV RI WKH
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
)LJXUH7KHPHDQVLOKRXHWWHYDOXHVIRUQLQHVRQJVDQGUK\WKPRJUDPWLPEUHJUDPDQGFKURPDJUDP
UHODWLYHRFFXUUHQFHVRIGLIIHUHQWRSWLPDOVHJPHQW
OHQJWKV7KHSHDNHGQHVVLVFDOFXODWHGDVWKHUHOD
WLYHVWUHQJWKRIWKHSHDNGLYLGHGE\WKHZLGWKRI
WKHWZRVXUURXQGLQJVDPSOHV
p=
si
4 ⋅ (si −1 + si +1 ) ⋅ (li +1 − li −1 )
ZKHUHVLLVWKHVLOKRXHWWHYDOXHDWLQGH[LDQGOLLV
WKHDYHUDJHOHQJWKDWLQGH[L7KLVQRUPDOL]DWLRQE\
WKHZLGWKLVQHFHVVDU\DVWKHVLOKRXHWWHYDOXHVDUH
QRWXQLIRUPO\VDPSOHGDORQJWKHDYHUDJHVHJPHQW
OHQJWKD[LV,QDGGLWLRQWKHSHDNVLOKRXHWWHYDOXH
LVDOVRUHWDLQHG7KHVLOKRXHWWHSHDNGLVWUXEXWLRQ
YDOXHVDQGSHDNHGQHVVIRUQLQHVRQJVDUHVKRZQ
LQ)LJXUH
7KHUHDUHUK\WKPRJUDPVLOKRXHWWHSHDNV
WLPEUHJUDPDQGFKURPDJUDPSHDNVLQDOO
LQWKHQLQHVRQJV,QWKHKLVWRJUDP)LJXUHWRS
WKHUK\WKPRJUDPKDYHDQDSSDUHQWSHDNDWDS
SUR[LPDWHO\DQGVHFRQGVDYHUDJH
VHJPHQWOHQJWKWKHWLPEUHJUDPKDVSHDNVDW
DQGVHFRQGVDQGWKHFKURPDJUDPKDV
SHDNVDWDQGVHFRQGVDYHUDJHVHJPHQW
OHQJWK ,Q WKH SHDN YDOXH VXESORW PLGGOH WKH
UK\WKPRJUDPVLOKRXHWWHYDOXHVVHHPKLJKHUWKDQ
WKHRWKHUYDOXHV7KHPHDQVLOKRXHWWHSHDNYDOXHV
DUHDQGVKRZLQJDVLJQLILFDQWO\
EHWWHU YDOXH IRU WKH UK\WKPRJUDP DQG D UDWKHU
XQXVDEOHYDOXHIRUWKHFKURPDJUDP$VIRUWKH
SHDNHGQHVV )LJXUH ERWWRP WKH SHDNHGQHVV
YDOXHVDUHGHFUHDVLQJZLWKWKHDYHUDJHOHQJWKRI
WKHVHJPHQWVH[FHSWIRUDIHZSHDNVZLWKKLJK
SHDNHGQHVVYDOXHVDWYHU\KLJKVHJPHQWOHQJWKV
7KHWLPEUHJUDPKDVDSSDUHQWO\WKHKLJKHVWSHDN
HGQHVVYDOXHVDQGWKHFKURPDJUDPWKHORZHVW
7KHPHDQRIWKHSHDNHGQHVVLVDQG
IRU UK\WKPRJUDP WLPEUHJUDP DQG FKUR
PDJUDPUHVSHFWLYHO\+RZHYHUWKHDFWXDOSHDN
YDOXHVDUHGHHPHGPRUHLPSRUWDQWDQGWKH\DUH
VKRZLQJWKHUK\WKPRJUDPWREHWKHEHVWIHDWXUH
IRUVHJPHQWDWLRQ
$&78$/,1+(5(17
6(*0(17%281'$5,(6
*LYHQWKHPHWKRGSUHVHQWHGKHUHLWLVQRZSRV
VLEOHWRLGHQWLI\WKHRSWLPDOVHJPHQWDWLRQVL]HV
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
)LJXUH+LVWRJUDPRIVLOKRXHWWHSHDNSRVLWLRQWRSWKHSHDNVLOKRXHWWHYDOXHVPLGGOHDQGWKHVLOKRXHWWH
SHDNHGQHVVERWWRPDVIXQFWLRQIRUDYHUDJHVHJPHQWOHQJWKIRUQLQHVRQJV7KHUK\WKPRJUDPYDOXHVDUH
GHSLFWHGZLWKDµ¶WKHWLPEUHJUDPDµ[¶DQGWKHFKURPDJUDPDµR¶LQWKHPLGGOHDQGORZHUVXESORW
7KHTXHVWLRQLVQRZZKDWGRWKHVHVL]HVUHSUHVHQW
LQWKHPXVLF$VDQH[DPSOHWKHVRQJ+ROG2Q
E\-DPLH:DOWHUV$WODQWLFLVIXUWKHULQYHV
WLJDWHG7KHPHDQVLOKRXHWWHYDOXHVDVIXQFWLRQ
RIDYHUDJHVHJPHQWDWLRQOHQJWKIRUWKLVVRQJLV
VKRZQ LQ )LJXUH $V IRU WKH RWKHU VRQJV WKH
UK\WKPRJUDPPHDQVLOKRXHWWHYDOXHVKDYHDULV
LQJSHDNIRUVKRUWDYHUDJHVHJPHQWOHQJWKVDQG
WKHQGHFUHDVLQJZKLOHERWKWKHWLPEUHJUDPDQG
WKHFKURPDJUDPEDVHGVLOKRXHWWHYDOXHVKDYHD
µ8¶VKDSHLHWKHVLOKRXHWWHYDOXHVGHFUHDVHWR
DPLQLPXPDQGWKHQULVHDJDLQZLWKRQO\ORFDO
PD[LPD7KHPD[LPDRIVLOKRXHWWHIRUUK\WKPR
JUDP DUH IRXQG DW DSSUR[LPDWHO\ DQG VHFRQGVZKLOHWKHWLPEUHJUDPVLOKRXHWWHPD[LPD
DUHIRXQGDWDQGZKLOHIRU
WKHFKURPDJUDPWKHPD[LPDRIWKHVLOKRXHWWHDUH
IRXQGDWDQG7KHVHFRQGVDUH
WKHSHDNVDWWKHFDVHVZKHUHDOOREVHUYDWLRQVKDYH
DVHSDUDWHVHJPHQWDOOREVHUYDWLRQVDJURXSHG
LQWRLQGLYLGXDOVHJPHQWVDQGWKXVWKHDYHUDJH
VHJPHQWOHQJWKLVHTXDOWRWKHVDPSOLQJUDWHRI
WKHIHDWXUHV
7KHPXVLJUDPSORWVDORQJZLWKWKHDXWRPDWLF
VHJPHQWDWLRQERXQGDULHVIRUWKHVDPHVRQJDUH
IRXQGLQ)LJXUH7KHUK\WKPRJUDPLVVKRZQLQ
WKHXSSHUVXESORWWKHWLPEUHJUDPLQWKHPLGGOH
VXESORWDQGWKHFKURPDJUDPLQWKHORZHUVXESORW
7KHHQVHPEOHLVFDOOHGPXVLJUDP.XKO-HQ
VHQ7KHUK\WKPRJUDPUHYHDOVDOWHUQDWLQJ
VHFWLRQVZLWKPRUHRUOHVVVWURQJSXOVH7KHWLP
EUHJUDPUHYHDOVDZHDNLQWURDQGILUVWVHFWLRQVD
VWURQJHUVHFWLRQZKLFKLVUHSHDWHGPLQDQG
PLQDQGSRVVLEO\UHSHDWHGLQDFUHVFHQGRDW
PLQ6LPLODUREVHUYDWLRQVFDQEHPDGHLQWKH
FKURPDJUDP+RZHYHUWKHVHJPHQWDWLRQVIRXQG
XVLQJWKHDXWRPDWLFVHJPHQWDWLRQGRQRWQHFHV
VDULO\ILQGWKHVDPHVHJPHQWVZKLFKLVSRVVLEO\
LPSHGLQJ RQ WKH TXDOLW\ RI WKHVH H[SHULPHQWV
+RZHYHULWLVQRWEHOLHYHGWREHYHU\LQIOXHQWLDO
LQWKHUHVXOWVRIWKHH[SHULPHQWV
7KHDYHUDJHVHJPHQWOHQJWKVIRUWKHDXWRPDWLF
VHJPHQWDWLRQERXQGDULHVLQ)LJXUHDUH
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
)LJXUH0HDQVLOKRXHWWHYDOXHDVDIXQFWLRQRIDYHUDJHVHJPHQWVOHQJWKIRU+ROG2Q±-DPLH:DOWHU
DQGVHFRQGV,WLVFOHDUIURPWKHDQDO\VLVRI
PRUH VRQJV WKDW WKH DXWRPDWLF VHJPHQWDWLRQ
JLYHV DW WKH VDPH WLPH VKRUWHU DQG ORQJHU VHJ
PHQWV)RUWKHVHDYHUDJHVHJPHQWDWLRQOHQJWKV
WKHUK\WKPRJUDPJLYHVVHJPHQWOHQJWKVEHWZHHQ
DQGVHFRQGVVWDQGDUGGHYLDWLRQLV
WKHWLPEUHJUDPUHQGHUVVHJPHQWOHQJWKVEHWZHHQ
DQGVWG VHFRQGVDQGWKHFKURPDJUDP
VHJPHQWOHQJWKVEHWZHHQDQGVHFRQGV
VWG ,WLVWKHUHIRUHGLIILFXOWWRVD\ZKHWKHU
WKHRSWLPXPVHJPHQWOHQJWKVFRUUHVSRQGRUQRWWR
RWKHUWKHRULHVVXFKDVWKHFKXQNWKHRU\RI.XKO
+RZHYHULQGLFDWLRQVWRZDUGVVXFKDFRU
UHVSRQGHQFHLVQRQHWKHOHVVREVHUYHG)LUVWWKHUH
LVRIWHQSHDNVLQWKHVLOKRXHWWHYDOXHVIRUGLIIHUHQW
VHJPHQWOHQJWKVZKLFKFRUUHVSRQGVVRPHZKDWWR
WKHPLFURPHVRDQGVXSHUFKXQNVRI.XKOZKLFK
KDVVL]HVDWDQGVHFRQGV+RZHYHU
RIWHQ WKH VHJPHQWDWLRQ EDVHG RQ WKH GLIIHUHQW
IHDWXUHVUHQGHUVGLIIHUHQWRSWLPDOVHJPHQWDWLRQ
OHQJWKVXVLQJWKHVLOKRXHWWHPHWKRG
$OEXP6WXG\
2QWKHTXHVWLRQRIKRZUHSURGXFLEOHWKHUHVXOWV
RIWKHVWXG\RILQKHUHQWVHJPHQWVL]HVLQPXVLF
D VHFRQG H[SHULPHQW KDV EHHQ SHUIRUPHG$UH
WKH LQKHUHQW VHJPHQW VL]HV VLPLODU DFURVV WKH
PXVLFJHQUHVRUZLWKLQDPXVLFVW\OHRUDUHWKH
LQKHUHQW VHJPHQW VL]HV FKDQJLQJ WR D GHJUHH LI
WKHUH DUH QR V\VWHPDWLF YDOXHV WR EH IRXQG" ,Q
RUGHUWRLQYHVWLJDWHWKLVIXUWKHUDIXOODOEXP7KH
%HDWOHV±6JW3HSSHUV/RQHO\+HDUWV&OXE%DQG
3DUORSKRQH&DSLWRO KDV EHHQ DQDO\]HG
LQWKHVDPHPDQQHUDVDERYH7KHWKUHHIHDWXUHV
UK\WKPRJUDPWLPEUHJUDPDQGFKURPDJUDPKDYH
EHHQFDOFXODWHGIURPWKHDFRXVWLFVRIHDFKVRQJ
RI WKH DOEXP WKHQ WKH DXWRPDWLF VHJPHQWDWLRQ
KDVEHHQGRQHIRUDOOSRVVLEOHVHJPHQWVL]HV)L
QDOO\WKHVLOKRXHWWHYDOXHVKDYHEHHQFDOFXODWHG
DVDPHDVXUHRIWKHTXDOLW\RIHDFKVHJPHQWVL]H
,IWKHVHVLOKRXHWWHYDOXHVKDYHSHDNVRQVLPLODU
VHJPHQWVL]HVIRUWKHGLIIHUHQWVRQJVWKLVLVDQ
LQGLFDWLRQ WKDW WKH LQKHUHQW VHJPHQW VL]HV DUH
VLPLODUDFURVVWKLVSDUWLFXODUDOEXPZKLFKFDQ
EHVHHQDVDVDPSOHRIDJHQUH,IWKHVLOKRXHWWH
SHDNVDUHVFDWWHUHGDURXQGWKHLQKHUHQWVHJPHQW
VL]HVDUHLQGLYLGXDOIRUHDFKVRQJ
,QRUGHUWRLQYHVWLJDWHWKLVWKHUHODWLYHQXPEHU
RIVLOKRXHWWHSHDNVIRUGLIIHUHQWVHJPHQWVL]HVKDV
EHHQFDOFXODWHGIRUWKH%HDWOHVDOEXPDORQJZLWK
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
)LJXUH0XVLJUDPUK\WKPRJUDPWRSWLPEUHJUDPDQGFKURPDJUDPERWWRPDORQJZLWKDXWRPDWLF
VHJPHQWDWLRQERXQGDULHVLOOXVWUDWHGZLWKYHUWLFDOOLQHVREWDLQHGXVLQJHDFKIHDWXUHIRU+ROG2Q-DPLH
:DOWHU
WKHSHDNYDOXHVDQGWKHSHDNHGQHVVYDOXHVDQG
DUHVKRZQLQ)LJXUH
7KHWLPEUHJUDPDQGFKURPDJUDPDOZD\VUHQ
GHUVDSHDNDWWKHVKRUWHVWSRVVLEOHVHJPHQWVL]H
VHFRQG7KLVKDVQRWEHHQWDNHQLQWRDFFRXQW
KHUH:KHQFRPSDUHGZLWKWKHVLPLODUGDWDIRUWKH
QLQHVRQJVRIYDULHGJHQUHV)LJXUHWKHGLI
IHUHQFHVDUHVHHPLQJO\PLQRU7KHUK\WKPRJUDP
UHQGHUVSHDNVDWDQGVHFRQGVEXWQRWDW
DQGVHFRQGV7KHWLPEUHJUDPUHQGHUVSHDNVDW
DQGVHFRQGVDQGWKHFKURPDJUDPSHDNV
DWDQGVHFRQGV7KHUK\WKPRJUDP
VLOKRXHWWHSHDNYDOXHVDUHVLJQLILFDQWO\KLJKHUWKDQ
WKH WLPEUHJUDP YDOXHV ZKLFK DUH VLJQLILFDQWO\
KLJKHUWKDQWKHFKURPJUDPYDOXHVZLWKDYHUDJH
VLOKRXHWWHSHDNVWUHQJWKRIDQG
IRUUK\WKPJRUDPWLPEUHJUDPDQGFKURPDJUDP
$VIRUWKHQLQHVRQJVRIYDU\LQJJHQUHVRQO\WKH
UK\WKPRJUDP KDV DFFHSWDEOH VLOKRXHWWH YDOXHV
:KHQ DQDO\]LQJ WKH VLOKRXHWWH SHDNHGQHVV WKH
VDPH GHFUHDVLQJ ZLWK DYHUDJH VHJPHQW OHQJWK
SHDNHGQHVVLVREVHUYHGIRUWKH%HDWOHVDOEXPDV
IRUWKHQLQHVRQJVDORQJZLWKVRPHKLJKSHDNHG
QHVVYDOXHVIRUWKHYH\KLJKVHJPHQWOHQJWKV7KH
PHDQSHDNHGQHVVYDOXHVDUHDQG
IRUUK\WKPRJUDPWLPEUHJUDPDQGFKURPDJUDP
UHVSHFWLYHO\7KHWLPEUHJUDPDJDLQKDVWKHEHVW
SHDNHGQHVVDQGWKHFKURPDJUDPWKHZRUVW$OO
LQDOOKRZHYHUWKHUK\WKPRJUDPSHUIRUPVEHVW
ZLWKEHWWHUVLOKRXHWWHYDOXHVDQGDOVRWKHUHLVD
GLVWLQFWLYHJURXSLQJRIWKHUK\WKPRJUDPSHDNVLQ
)LJXUH7KLVLVPRUHYLVLEOHLQWKHSHDNYDOXHV
DQGSHDNHGQHVVVXESORWVWKDQLQWKHKLVWRJUDP
7KHUHLVRQHJURXSFRQVLVWLQJRIREVHUYDWLRQV
EHWZHHQIRXUDQGVL[VHFRQGVDQGRQHJURXSZLWK
ILYHREVHUYDWLRQVEHWZHHQDQGVHFRQGVDQG
DQRWKHUJURXSZLWKILYHREVHUYDWLRQVEHWZHHQ
DQGVHFRQGV$OOLQDOOWKHVHWKUHHJURXSVDF
FRXQWIRURIWKHSHDNVIRUWKHUK\WKPRJUDP
$VIRUWKHFKXQNDQGVXSHUFKXQNLGHQWLILFD
WLRQWKHUHKDVEHHQIRXQGFKXQNV
DQGVXSHUFKXQNIRUWKHUK\WKPRJUDP
FKXQNDQGVXSHUFKXQNIRU
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
)LJXUH+LVWRJUDPRIVLOKRXHWWHSHDNVDVDIXQFWLRQRIDYHUDJHVHJPHQWOHQJWKVIRU7KH%HDWOHV6JW
3HSSHUV /RQHO\ +HDUWV &OXE %DQG WRS DQG VLOKRXHWWH SHDNHGQHVV YDOXHV IRU VDPH ERWWRP 7KH
UK\WKPRJUDPYDOXHVDUHGHSLFWHGZLWKDµ¶WKHWLPEUHJUDPDµ[¶DQGWKHFKURPDJUDPDµR¶LQWKH
PLGGOHDQGORZHUVXESORW
WLPEUHJUDPDQGFKXQNDQG
VXSHUFKXQNIRUWKHFKURPDJUDP
7KHUHKDVEHHQIRXQG
DQGEHORZVHFRQGVJURXSLQJIRU
UK\WKPWLPEUHDQGFKURPDUHVSHFWLYHO\7KHVH
QXPEHUV FRQILUP WKDW WKH UK\WKPRJUDP FRUUH
VSRQGVEHWWHUWRWKHFKXQNDQGJURXSLQJWKHRU\
IRUWKH%HDWOHVVRQJVDVLWGLGIRUWKHQLQHVRQJV
RIYDULHGJHQUHVDERYH
&21&/86,21
5HVHDUFKHUVDQGGHYHORSHUVKDYHIRXQGDQLQFUHDV
LQJQXPEHURIUHDVRQVIRUVHJPHQWLQJPXVLFLQWR
VPDOOHUVHJPHQWVEHLWIRUWKXPEQDLOLQJUHPL[
LQJDUWLVWLFLGHQWLILFDWLRQSOD\OLVWJHQHUDWLRQRU
RWKHUPXVLFLQIRUPDWLRQUHWULHYDOSXUSRVHVFRS\
ULJKWLVVXHVPXVLFDQDO\VLVSXUSRVHVRU\HWRWKHU
LVVXHV+RZHYHUZKLOHVHJPHQWDWLRQFDQHDVLO\EH
GRQHDJURXQGHGWKHRU\RIWKHREWDLQHGRUZLVKHG
IRUVHJPHQWDWLRQVL]HVVKRXOGEHDYDLODEOH7KLV
FDQEHIRXQGLQWKHPXVLFWKHRU\IRULQVWDQFHE\
WKH JURXSLQJ WKHRU\ RI /HUGDKO -DFNHQGRUII
+RZHYHUWKHLUVXEGLYLVLRQLQWRJURXSV
RI QRWHV RIWHQ FRUUHVSRQGLQJ WR PHDVXUHV DUH
EDVHGRQUXOHVRIZKLFKRQHVWDWHVWKDWJURXSVDW
WKHVDPHOHYHOKDYHWKHVDPHGXUDWLRQZKLFKLV
QRWIRXQGLQWKLVZRUN:KLOHWKH\VWDWHWKHUXOHV
DVSUHIHUHQFHVWKDWFDQEHEDVHGRQPHORGLFRU
UK\WKPLF SUR[LPLW\ DQG FRQWLQXLW\ LW GRHV QRW
VHHP FRQVLVWHQW ZLWK WKH UHVXOWV REWDLQHG KHUH
5HVXOWV IURP PHPRU\ UHVHDUFK 6Q\GHU FDQDOVREHXVHGDVWKHJURXQGUHIHUHQFH6Q\GHU
UHIHUV WR HFKRLF PHPRU\ HDUO\ SURFHVVHV IRU
HYHQWIXVLRQZKHUHIXQGDPHQWDOXQLWVDUHIRUPHG
E\FRPSDULVRQZLWKVHFRQGVWKHVKRUWWHUP
PHPRU\IRUPHORGLFDQGUK\WKPLFJURXSLQJE\
FRPSDULVRQ XS WR VHFRQGV DQG ORQJWHUP
PHPRU\ IRU IRUPDO VHFWLRQLQJ E\ FRPSDULVRQ
XSWRRQHKRXU6Q\GHUUHODWHVWKLVWRWKH
*HVWDOWWKHRU\JURXSLQJPHFKDQLVPVRISUR[LP
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
LW\HYHQWVFORVHLQWLPHRUSLWFKZLOOEHJURXSHG
WRJHWKHU3UR[LPLW\LVWKHSULPDU\JURXSLQJIRUFH
DWWKHPHORGLFDQGUK\WKPLFOHYHO6Q\GHU
S7KHVHFRQGIDFWRULQJURXSLQJLVVLPLODULW\
HYHQWVMXGJHGDVVLPLODUPDLQO\ZLWKUHVSHFWWR
WLPEUHZLOOEHJURXSHGWRJHWKHU$WKLUGIDFWRU
LVFRQWLQXLW\HYHQWVFKDQJHLQWKHVDPHGLUHFWLRQ
IRULQVWDQFHSLWFK7KHVHJURXSLQJPHFKDQLVPV
JLYHULVHWRFORVXUHWKDWFDQRSHUDWHDWWKHJURXS
LQJOHYHORUWKHSKUDVHOHYHOZKLFKLVWKHODUJHVW
JURXSWKHVKRUWWHUPPHPRU\FDQKDQGOH:KHQ
VHYHUDOJURXSLQJPHFKDQLVPVRFFXUDWWKHVDPH
WLPHLQWHQVLILFDWLRQRFFXUVZKLFKJLYHVULVHWR
KLJKHUOHYHOJURXSLQJ2WKHUKLJKHUOHYHOJURXS
LQJPHFKDQLVPVDUHSDUDOOHOLVPUHSHDWHGVPDOOHU
JURXSVRUUHFXUUHQFHRISLWFK7KHKLJKHUOHYHO
JURXSLQJGHPDQGVORQJWHUPPHPRU\DQGWKH\
RSHUDWHDWDKLJKHUOHYHOLQWKHEUDLQDVFRPSDUHGWR
WKHVPDOOHUWLPHVFDOHJURXSLQJ7KHKLJKHUOHYHO
JURXSLQJ LV OHDUQHG ZKLOH WKH VKRUWHU JURXSLQJ
LVQRW6Q\GHUIXUWKHUGLYLGHVWKHKLJKHU
OHYHO JURXSLQJ LQWR WKH REMHFWLYH VHW ZKLFK LV
UHODWHGWRDSDUWLFXODUPXVLFDQGWKHVXEMHFWLYH
VHWZKLFKLVUHODWHGWRDVW\OHRIPXVLF%RWKVHWV
DUHOHDUQHGE\OLVWHQLQJWRWKHPXVLFUHSHDWHGO\
6Q\GHUDOVRUHODWHGWKHVKRUWHUJURXSLQJ
WRWKH“WKHRU\0LOOHUWKDWVWDWHVWKDW
WKHVKRUWWHUPPHPRU\FDQUHPHPEHUEHWZHHQ
ILYHWRQLQHHOHPHQWV
:KLOH WKH PXVLF WKHRU\ DQG PHPRU\EDVHG
UHVHDUFKFDQJLYHJURXQGHGUHVXOWVIRUWKHVHJPHQ
WDWLRQWDVNVWKH\DUHVHHPLQJO\QRWJLYLQJWKHIXOO
WUXWK7KHPXVLFWKHRU\RSHUDWHGZLWKDFRQVWDQW
VL]HRIVHJPHQWVZKLFKLVQRWZKDWLVREVHUYHG
E\DXWRPDWLFVHJPHQWDWLRQ2EYLRXVO\ERWKWKH
PXVLFWKHRU\DQGWKHPHPRU\EDVHGJURXSLQJDUH
UHODWHGLQPDQ\VHQVHVZKLFK6Q\GHUDOVR
SRLQWVRXW7KHVHZRUNVILQGVRPHRILWVEDVLVLQ
WUDGLWLRQDOPXVLFWKHRU\DQGVROIqJH7KHPDLQ
SUREOHP ZLWK WKHVH WKHRULHV LV WKH VHHPLQJO\
ODFNRIHPSKDVLVRQWKHDFWXDOVRXQGWKHWLPEUH
DQGWKHSHUIRUPDQFHZLWKUHVSHFWWRWLPLQJDQG
G\QDPLFVLQSDUWLFXODU
,QFRQWUDVWWRWKHVHWKHRULHVWKHZRUNSUHVHQWHG
KHUHRQO\WDNHVLQWRDFFRXQWWKHDFRXVWLFVRIWKH
PXVLF7KHUHLVQRKLJKOHYHOPXVLFWKHRU\DQG
QRSULRUXQGHUVWDQGLQJEDVHGRQWKHPHFKDQLVPV
RIWKHEUDLQ
$XWRPDWLFVHJPHQWDWLRQLVSHUIRUPHGKHUHE\
FDOFXODWLQJWKHVKRUWHVWSDWKWKURXJKWKHVHOIVLPL
ODULW\RI GLIIHUHQWDXGLRIHDWXUHV ZKLFKFDQEH
UHODWHGWRUK\WKPWLPEUHDQGFKURPD%\YDU\LQJ
WKHFRVWRILQVHUWLQJDQHZVHJPHQWGLIIHUHQWWLPH
VFDOHVDUHFUHDWHGJRLQJIURPWKHVKRUWVHFRQGV
WRWKHORQJXSWRVHFRQGV7KHTXHVWLRQWKDW
LVLQYHVWLJDWHGKHUHLVZKHWKHUPXVLFKDVDQLQKHU
HQWVHJPHQWOHQJWK,QGHHGERWKPXVLFWKHRU\DQG
EUDLQUHVHDUFKKDYHWKHRULHVDERXWGLIIHUHQWWLPH
VFDOHZKLFKLVYLVLEOHLQWKHPXVLFVFRUHVDQG
LQGLIIHUHQWSV\FKRSK\VLFDOH[SHULPHQWUHJDUG
LQJPHPRU\,QRUGHUWRLQYHVWLJDWHWKHLQKHUHQW
WLPHVFDOHLQWKHPXVLFWKHVLOKRXHWWHYDOXHVDUH
FDOFXODWHGIRUDOOREVHUYDWLRQVEORFNVIRUHDFK
VHJPHQWDWLRQVFDOH7KHPHDQRIWKHVLOKRXHWWH
YDOXHV LV D JRRG PHDVXUH RI WKH TXDOLW\ RI WKH
VHJPHQWDWLRQ%\PDWFKLQJWKHSHDNVRIWKHVLO
KRXHWWHYDOXHVWRWKHFKXQNWKHRU\RIVHFRQGV
DQGWKHVXSHUFKXQNWKHRU\RIVHFRQGVD
PHDVXUH RI WKH LQKHUHQW VHJPHQWDWLRQ VL]H KDV
EHHQIRXQGWRJHWKHUZLWKLQGLFDWLRQVRIZKLFK
IHDWXUHWKDWSHUPLWVDEHWWHUDQDO\VLVRIWKLV7KH
UK\WKPRJUDPKDVWKHEHVWPDWFKIRUWKHFKXQN
DQGVXSHUFKXQNOHYHOVUHVSHFWLYHO\
IRUQLQHVRQJVRIYDU\LQJJHQUHVZKLOHD%HDWOHV
DOEXPJLYHVDQGIRUUK\WKPRJUDP,Q
WKLVFDVHWKHFKURPDJUDPKDVEHWWHUVXSHUFKXQN
UHVXOW 9LVXDOO\ LQVSHFWLQJ WKH PHDQ VLO
KRXHWWHYDOXHVRIQLQHVRQJVRIYDU\LQJJHQUHV
IXUWKHUUHYHDOVWKDWRQO\WKHUK\WKPRJUDPKDVD
SHDNDWWKHFKXQNOHYHOZKLOHDOOWKUHHIHDWXUHVKDV
SHDNVDWWKHYLFLQLW\RIWKHVXSHUFKXQNVL]HRI
VHFRQGV0RVWSHDNVDUHVLWXDWHGDERYHWKHDYHUDJH
OHQJWKRIHLJKWVHFRQGVZKLFKJLYHVLQGLFDWLRQ
WKDWIRUPLVPRUHSURPLQHQWWKDQJURXSLQJLQWKH
VRQJVLQYHVWLJDWHGKHUH,QGLFDWLRQVWKDWIRUPLV
PRUH SURPLQHQW WKDQ JURXSLQJ 6Q\GHU LVJLYHQDORQJZLWKLQGLFDWLRQVWKDWJURXSLQJLV
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
PRUHSURPLQHQWLQWKHUK\WKPLFIHDWXUHVWKDQLQ
WKHWLPEUDORUFKURPDIHDWXUHV)XUWKHUDQDO\VLV
RI WKH VLOKRXHWWH SHDNV UHYHDOV WKH V\VWHPDWLF
RFFXUUHQFHVRISHDNVLQVHYHUDODYHUDJHVHJPHQW
OHQJWKSRVLWLRQVLQFOXGLQJVKRUWVHJPHQWVDURXQG
VHFRQGVPHGLXPOHQJWKVHJPHQWVDWDURXQG
VHFRQGVDQGORQJHUVHJPHQWV7KHVHILQGLQJVDUH
VLPLODUIRUDFROOHFWLRQRIQLQHVRQJVRIYDU\LQJ
JHQUHVDQGWKH6JW3HSSHUVDOEXPRIWKH%HDWOHV
7KHUK\WKPRJUDPKDVV\VWHPDWLFDOO\ODUJHUVLO
KRXHWWHYDOXHVDWWKHSHDNVZLWKDQDYHUDJHRI
DSSUR[LPDWHO\ ZKLOH WKH WLPEUHJUDP DQG
FKURPDJUDP KDYH PHDQ VLOKRXHWWH SHDN YDOXHV
RIDQGZKLFKLVDQLQGLFDWLRQWKDWDOORE
VHUYDWLRQVFRXOGMXVWDVZHOOEHORQJWRDQRWKHU
VHJPHQWWKDQWKHRQHWKH\EHORQJWR$QDQDO\VLV
RIWKHSHDNHGQHVVRIWKHVLOKRXHWWHSHDNVUHYHDOV
WKDWWKHWLPEUHJUDPSURGXFHVVWURQJHUSHDNVDQG
FKURPDJUDP WKH ZHDNHU SHDNV 6HHPLQJO\ WKH
ORZ OHQJWK SHDNV KDYH KLJKHU SHDNHGQHVV WKDQ
WKHSHDNVIRXQGIRUORQJHUVHJPHQWV
:KLOH PRUH ZRUN LV QHFHVVDU\ LQ RUGHU WR
FRQILUPWKHILQGLQJVKHUHVHYHUDOLQGLFDWLYHFRQ
FOXVLRQVFDQQRQHWKHOHVVEHGUDZQ7KHPXVLF
LQYHVWLJDWHGKHUHZKLFKLVRIYDU\LQJJHQUHVKDV
LQKHUHQWVHJPHQWVL]HVRIGLIIHUHQWOHQJWK7KHVH
LQKHUHQWVHJPHQWOHQJWKVDUHIRXQGIRUDOOVRQJV
ZLWKUHODWLYHVPDOOYDULDWLRQV7KHUK\WKPRJUDP
SHUIRUPVEHVWZKHQWKHIRXQGLQKHUHQWVHJPHQW
OHQJWKV DUH FRPSDUHG WR WKHRU\ DQG LW LV DOVR
WKHRQO\IHDWXUHWKDWKDVDQDFFHSWDEOHDYHUDJH
VLOKRXHWWHSHDNYDOXH
&KDL:9HUFRH%0XVLFWKXPEQDLO
LQJYLDVWUXFWXUDODQDO\VLV3URFHHGLQJVRI$&0
0XOWLPHGLD&RQIHUHQFH1RYHPEHU
5()(5(1&(6
+XURQ'7KH0HORGLF$UFKLQ:HVWHUQ
)RONVRQJV&RPSXWLQJLQ0XVLFRORJ\
%DUWVFK0$:DNHILHOG*+7R&DWFK
D&KRUXV8VLQJ&KURPD%DVHG5HSUHVHQWDWLRQV
)RU $XGLR 7KXPEQDLOLQJ 3URFHHGLQJV RI WKH
:RUNVKRSRQ$SSOLFDWLRQVRI6LJQDO3URFHVVLQJ
WR$XGLRDQG$FRXVWLFV&'1HZ<RUN,(((
&ROOLQV1$FRPSDULVRQRIVRXQGRQVHW
GHWHFWLRQDOJRULWKPVZLWKHPSKDVLVRQSV\FKR
DFRXVWLFDOO\PRWLYDWHGGHWHFWLRQIXQFWLRQV3UR
FHHGLQJV RI $(6 WK &RQYHQWLRQ %DUFHORQD
6SDLQ0D\
&RUPHQ7+6WHLQ&5LYHVW5//HLVHUVRQ
&(,QWURGXFWLRQWR$OJRULWKPVQG(G
%RVWRQ0,73UHVVDQG1HZ<RUN0F*UDZ+LOO
'HOLHJH,0HOHQ3&XHDEVWUDFWLRQ
LQWKHUHSUHVHQWDWLRQRIPXVLFDOIRUP,Q'HOLqJH
- 6ORERGD (GV 3HUFHSWLRQ DQG FRJQLWLRQ RI
PXVLF(DVW6XVVH[(QJODQG3V\FKRO
RJ\3UHVV
'HVDLQ 3 $ GHFRPSRVDEOH WKHRU\ RI
UK\WKP0XVLF3HUFHSWLRQ±
)RRWH - $XWRPDWLF $XGLR 6HJPHQWD
WLRQXVLQJD0HDVXUHRI$XGLR1RYHOW\>-XO\@
3URFHHGLQJV RI ,((( ,QWHUQDWLRQDO &RQIHUHQFH
RQ0XOWLPHGLDDQG([SR±
*RWR 0 $ FKRUXVVHFWLRQ GHWHFWLQJ
PHWKRGIRUPXVLFDODXGLRVLJQDOV3URFHHGLQJVRI
WKH,(((,QWHUQDWLRQDO&RQIHUHQFHRQ$FRXVWLFV
6SHHFKDQG6LJQDO3URFHVVLQJ$SULO
+HUPDQVN\+3HUFHSWXDOOLQHDUSUHGLF
WLYH3/3DQDO\VLVRIVSHHFK7KH-RXUQDORIWKH
$FRXVWLFDO6RFLHW\RI$PHULFD±
GRL
-HQVHQ . $ FDXVDO UK\WKP JURXSLQJ
3URFHHGLQJVRIQG,QWHUQDWLRQDO6\PSRVLXPRQ
&RPSXWHU0XVLF0RGHOLQJDQG5HWULHYDO&005
¶'HQPDUN/1&6YROSS
2QWKH,QKHUHQW6HJPHQW/HQJWKLQ0XVLF
-HQVHQ.0XOWLSOHVFDOHPXVLFVHJPHQWD
WLRQXVLQJUK\WKPWLPEUHDQGKDUPRQ\(85$6,3
-RXUQDO RQ $SSOLHG 6LJQDO 3URFHVVLQJ 6SHFLDO
LVVXHRQ0XVLF,QIRUPDWLRQ5HWULHYDO%DVHGRQ
6LJQDO3URFHVVLQJ
-HQVHQ . ;X - =DFKDULDVHQ 0 5K\WKPEDVHGVHJPHQWDWLRQRI3RSXODU&KLQHVH
0XVLF3URFHHGLQJRIWKH,60,5/RQGRQ8.
SS
.DXIPDQ/5RXVVHHXZ3-)LQG
LQJ*URXSVLQ'DWD$Q,QWURGXFWLRQWR&OXVWHU
$QDO\VLV1HZ<RUN:LOH\
.KO20XVLFDO6HPDQWLFV%HUQ3HWHU
/DQJ
.XKO 2 -HQVHQ . 5HWULHYLQJ DQG
UHFUHDWLQJ 0XVLFDO )RUP /HFWXUHV 1RWHV LQ
&RPSXWHU6FLHQFH1HZ<RUN6SULQJHU9HUODJ
/HUGDKO)-DFNHQGRII-$*HQHUDWLYH
7KHRU\ RI 7RQDO 0XVLF &DPEULGJH 0$ 0,7
3UHVV
0F$GDPV60XVLFDOVLPLODULW\DQGG\
QDPLFSURFHVVLQJLQPXVLFDOFRQWH[W3URFHHGLQJV
RIWKH,60$&'0H[LFR&LW\0H[LFR
0F$XOH\-'$\DOD&7KHHIIHFW
RIWLPEUHRQPHORG\UHFRJQLWLRQE\IDPLOLDULW\
0HHWLQJRIWKH$6$&DQFXQ0H[LFRDEVWUDFW
0LOOHU*7KH0DJLFDO1XPEHU6HYHQ
3OXVRU0LQXV7ZR3V\FKRORJLFDO5HYLHZ
±GRLK
3DXOXV - .ODSXUL$ /DEHOOLQJWKH
6WUXFWXUDO3DUWVRID0XVLF3LHFHZLWK0DUNRY
0RGHOV3URFHHGLQJVRIWKH&RPSXWHUVLQ
0XVLF 0RGHOLQJ DQG 5HWULHYDO SS
&RSHQKDJHQ'HQPDUN
6FKHLUHU ( 7HPSR DQG %HDW $QDO\VLV
RI$FRXVWLF0XVLFDO6LJQDOV7KH-RXUQDORIWKH
$FRXVWLFDO6RFLHW\RI$PHULFD±
GRL
6HNH\$ +DQVRQ %$ ,PSURYHG
EDUNEDQGZLGWKDXGLWRU\ILOWHU7KH-RXUQDORIWKH
$FRXVWLFDO6RFLHW\RI$PHULFD±
GRL
6Q\GHU % 0XVLF DQG 0HPRU\ $Q ,Q
WURGXFWLRQ&DPEULGJH0DVV7KH0,73UHVV