&KDSWHU
F 'XVW LV UHPRYHG IURP D KDQJLQJ
FDUSHWE\EHDWLQJLWZLWKDVWLFN
G :KHQZHVKDNHWKHEUDQFKRIDWUHH
LWVIUXLWVDQGGU\OHDYHVIDOOGRZQ
LL,QHUWLDRIPRWLRQ
7KHWHQGHQF\RIDERG\WRUHPDLQLQLWV
VWDWH RI XQLIRUP PRWLRQ LQ D VWUDLJKW
OLQHLVFDOOHGLQHUWLDRIPRWLRQ
/DZVRI0RWLRQ
:KDWLV$ULVWRWOH¶V)DOODF\"
$QV $FFRUGLQJ WR WKH *UHHN WKLQNHU
$ULVWRWOH %& ± %& DQ
H[WHUQDO IRUFH LV UHTXLUHG WR NHHS D
ERG\LQXQLIRUPPRWLRQ
(J
:KDWLVWKH0RGHUQFRQFHSWDERXW
XQLIRUPPRWLRQ"
D :KHQDPRYLQJEXVVXGGHQO\VWRSV
D SHUVRQ VWDQGLQJ LQ LW WHQGV WR IDOO
IRUZDUG
E :KHQDKRUVHUXQQLQJIDVWVXGGHQO\
VWRSVWKHULGHULVWKURZQIRUZDUG
F $ SHUVRQ JHWWLQJ RXW RI D PRYLQJ
EXV RU WUDLQ IDOOV LQ WKH IRUZDUG
GLUHFWLRQ
G $Q DWKOHWH UXQV IRU D FHUWDLQ
GLVWDQFHEHIRUHWDNLQJDORQJMXPS
H $ EDOO WKURZQXSZDUG LQ DPRYLQJ
WUDLQ FRPHV EDFN LQWR WKH WKURZHU¶V
KDQGV
LLL,QHUWLDRI'LUHFWLRQ
7KHWHQGHQF\RIDERG\WRFRQWLQXHLWV
GLUHFWLRQRIPRWLRQLVFDOOHGLQHUWLDRI
GLUHFWLRQ
(J
D :KHQ D EXV WDNHV D VKDUS WXUQ D
SHUVRQVLWWLQJLQWKHEXVH[SHULHQFHVD
IRUFH DFWLQJ DZD\ IURP WKH FHQWUH RI
WKHFXUYHGSDWK
E :KHQ D VWRQH H[HFXWLQJ FLUFXODU
PRWLRQ LV UHOHDVHG LW IOLHV RII
WDQJHQWLDOO\
F 'XULQJWKHVKDUSHQLQJRIDNQLIHWKH
VSDUNVFRPLQJIURPWKHJULQGVWRQHIO\
RII WDQJHQWLDOO\ WR WKH ULP RI WKH
URWDWLQJVWRQH
G :KHQ D YHKLFOH PRYHV WKH PXG
VWLFNLQJ WR LWV ZKHHOV IOLHV RII
WDQJHQWLDOO\
/DWHU*DOLOHR SURYHGWKDW
WKH DERYH FRQFHSW ZDV ZURQJ
$FFRUGLQJ WR *DOLOHR ³QR H[WHUQDO
IRUFH LV UHTXLUHG WR NHHS D ERG\ LQ
XQLIRUPPRWLRQ´
6WDWHRIUHVWDQGVWDWHRIXQLIRUPOLQHDU
PRWLRQ DUH HTXLYDOHQW ,Q ERWK FDVHV
WKHUHLVQRH[WHUQDOIRUFHDFWLQJRQWKH
ERG\
'HILQH,QHUWLD:KLFKDUHWKHWKUHH
W\SHVRILQHUWLD"*LYHH[DPSOHV
$QV,QHUWLDLVWKHWHQGHQF\RIDERG\
WRFRQWLQXHLQLWVVWDWHRIUHVWRUVWDWHRI
XQLIRUPPRWLRQDORQJDVWUDLJKWOLQH
7KHZRUGLQHUWLDPHDQVUHVLVWDQFHWR
FKDQJH
'LIIHUHQWW\SHVRILQHUWLD
L,QHUWLDRIUHVW
7KHWHQGHQF\RIDERG\WRUHPDLQLQLWV
VWDWHRIUHVWLVFDOOHGLQHUWLDRIUHVW
(J
D $SHUVRQVWDQGLQJLQDEXVWHQGVWR
IDOOEDFNZDUGVZKHQWKHEXVVXGGHQO\
VWDUWVPRYLQJIRUZDUG
E :KHQ D KRUVH VXGGHQO\ VWDUWV
UXQQLQJWKHULGHUIDOOVEDFNZDUG
ϭ
([SODLQ WKH UHODWLRQ EHWZHHQ PDVV
DQGLQHUWLD*LYHDQH[DPSOH
$QV0DVVRIDERG\LVWKHPHDVXUHRI
LWVLQHUWLD,IDERG\KDVPRUHPDVVLW
KDVPRUHLQHUWLD
RURIXQLIRUPPRWLRQLQDVWUDLJKWOLQH
XQOHVV FRPSHOOHG E\ VRPH H[WHUQDO
XQEDODQFHGIRUFHWRFKDQJHWKDWVWDWH´
'HILQH OLQHDU PRPHQWXP S RI D
ERG\
$QV0RPHQWXPRIDERG\LVGHILQHG
DV WKH SURGXFW RI LWV PDVV P DQG
YHORFLW\ Y (J:KHQDGRJ FKDVHV DKDUH WKH
KDUHUXQVDORQJD]LJ]DJSDWK
G
G
3 PY 0RPHQWXPLVDYHFWRUTXDQWLW\
6,XQLWRIPRPHQWXPLVNJPV
6WDWH 1HZWRQ¶V VHFRQG ODZ RI
PRWLRQ /DZRIIRUFH $QV 1HZWRQ¶V VHFRQG ODZ RI VWDWHV
WKDW³WKHUDWHRIFKDQJHRIPRPHQWXP
RIDERG\LVGLUHFWO\SURSRUWLRQDOWRWKH
DSSOLHG IRUFH DQG WKH FKDQJH LQ
PRPHQWXPWDNHVSODFHLQWKHGLUHFWLRQ
RIIRUFH´
5HDVRQ :KHQ WKH KDUH UXQV LQ D
]LJ]DJSDWKLWEHFRPHVGLIILFXOWIRUWKH
GRJWRFDWFKWKHKDUH7KLVLVEHFDXVH
WKHGRJKDVPRUHPDVVDQGKHQFHKDV
PRUHLQHUWLDRIGLUHFWLRQWKDQWKHKDUH
$EORFNRIPDVV LVVXVSHQGHGE\ D
OLJKW FRUG & IURP WKH FHLOLQJ DQG
DQRWKHUVWURQJFRUG'LVDWWDFKHGWRWKH
ERWWRPRIWKHEORFNDVVKRZQ
G
G
GS
)D GW
2EWDLQ WKH H[SUHVVLRQ IRU IRUFH
G
G
) PD IURPVHFRQGODZ
$QV$FFRUGLQJWRVHFRQGODZ
G GSG
)D
GW
G
G
GS
) N
ZKHUHNLVWKH
GW
SURSRUWLRQDOLW\FRQVWDQW
7KH FRUG ' LV SXOOHG E\ D IRUFH )
:KLFKRIWKHVHFRUGVZLOOEUHDNLI
D WKHIRUFHLVLQFUHDVHGVWHDGLO\"
E 7KH IRUFH LV LQFUHDVHG
VXGGHQO\"
$QV
6WDWH 1HZWRQ¶V VW /DZ RI PRWLRQ
/DZRI,QHUWLD $QV 1HZWRQ¶V ILUVW ODZ VWDWHV WKDW
³HYHU\ERG\FRQWLQXHVLQLWVVWDWHRIUHVW
%XWN G
G
G
? ) PY
GW
G
G
GY
) P
> ' PLVDFRQVWDQW@
GW
G
G
) PD
3 $ PDFKLQH JXQ ILUHV EXOOHWV RI
PDVVJHDFKZLWKDVSHHGPV
7KH SHUVRQ FDQ KROG WKH JXQ ZLWK D
PD[LPXP IRUFHRI1:KDW LV WKH
Ϯ
PD[LPXP QXPEHU RI EXOOHWV WKDW FDQ
EHILUHGSHUVHFRQGIURPWKHJXQ"
$QV
3 7KH GULYHU RI D WKUHH ZKHHOHU
PRYLQJZLWKDVSHHGRINPKUVHHVD
FKLOGVWDQGLQJDWWKHPLGGOHRIWKHURDG
DQG EULQJV KLV YHKLFOH WR UHVW LQ VHFRQGV MXVW LQ WLPH WR VDYH WKH FKLOG
3$FRQVWDQWUHWDUGLQJIRUFHRI1
:KDW LV WKH DYHUDJH UHWDUGLQJ IRUFH RQ
LV DSSOLHG WR D ERG\ RI PDVV NJ
WKH YHKLFOH" 7KH PDVV RI WKH WKUHH
PRYLQJLQLWLDOO\ZLWKDVSHHGRIPV
ZKHHOHU LV NJ DQG WKH PDVV RI WKH
+RZORQJGRHVWKHERG\WDNHWRVWRS"
GULYHULVNJ
$QV
$QV
3 $ EXOOHW RI PDVV NJ PRYLQJ
ZLWK D VSHHG RI PV HQWHUV D KHDY\
ZRRGHQ EORFN DQG LV VWRSSHG DIWHU D
GLVWDQFH RI FP :KDW LV WKH DYHUDJH
UHVLVWLYH IRUFH H[HUWHG E\ WKH EORFN RQ
WKHEXOOHW"
$QV
3 $ KRUL]RQWDO IRUFH RI 1 SXOOV
WZRPDVVHV NJ DQGNJ O\LQJ RQ D
IULFWLRQ OHVV WDEOH FRQQHFWHG E\ D OLJKW
VWULQJ:KDWLVWKHWHQVLRQLQWKHVWULQJ"
'RHVWKHDQVZHUGHSHQGRQZKLFKPDVV
WKHSXOOLVDSSOLHG"
$QV
ϯ
3 $ EDWVPDQ KLWV EDFN D EDOO
VWUDLJKW LQ WKHGLUHFWLRQRI WKHERZOHU
ZLWKRXW FKDQJLQJ LWV LQLWLDO VSHHG RI
PV,IWKHPDVVRIWKHEDOOLVNJ
GHWHUPLQHWKHLPSXOVHLPSDUWHGWRWKH
EDOO
$QV
*LYH VRPH DSSOLFDWLRQV RI WKH
FRQFHSWRILPSXOVH
$QV
L :KLOH FDWFKLQJ D EDOO D
FULFNHWHUORZHUVKLVKDQGV
5HDVRQ %\ PRYLQJ WKH KDQGV
EDFNZDUGV WKH FULFNHWHU LQFUHDVHV WKH
WLPH RI FDWFK 7KHQ WKH IRUFH
:KDW LV LPSXOVLYH IRUFH" 'HILQH
LPSXOVH
$QV /DUJH IRUFH DFWLQJ IRU D VKRUW
WLPHLVFDOOHGLPSXOVLYHIRUFH
(J L +LWWLQJDQDLOZLWKDKDPPHU
LL +LWWLQJ D FULFNHW EDOO ZLWK D
EDW
LLL .LFNLQJDIRRWEDOO
, ·
§
¨ p ) ¸ H[HUWHGE\WKHEDOORQKLV
'W n ¹
©
,PSXOVH RI D IRUFH LV WKH SURGXFW RI
IRUFHDQGWLPH
, ) u ' W 6, XQLW RI LPSXOVH LV 16 1HZWRQ
VHFRQG ,PSXOVHLVDYHFWRUTXDQWLW\
6WDWH DQG SURYH LPSXOVH
PRPHQWXPWKHRU\
$QV$FFRUGLQJWRLPSXOVHPRPHQWXP
WKHRU\ LPSXOVH LV HTXDO WR FKDQJH LQ
PRPHQWXP
3URRI
$FFRUGLQJWR1HZWRQ¶VVHFRQGODZ
KDQGV EHFRPHV PXFK VPDOOHU DQG LW
GRHVQRWKXUWKLP
LL $ SHUVRQ IDOOLQJ IURP D FHUWDLQ
KHLJKWUHFHLYHVPRUHLQMXULHVZKHQKH
IDOOVRQDFHPHQWHGIORRUWKDQZKHQKH
IDOOVRQDKHDSRIVDQG
5HDVRQ :KHQ WKH SHUVRQ IDOOV RQ D
KHDS RI VDQG VDQG JHWV GHSUHVVHG
XQGHU KLV ZHLJKW 7KH SHUVRQ WDNHV
ORQJHUWLPHWRVWRS7KLVGHFUHDVHVWKH
IRUFH §¨ p ) GS
GW
Ÿ )GW GS ©
) RQWKHSHUVRQ
LLL $XWRPRELOHV DUH SURYLGHG ZLWK
VKRFNHUV
5HDVRQ:KHQDYHKLFOHPRYHVRQDQ
XQHYHQ URDG LW UHFHLYHV D MHUN 7KH
LH , GS
LH,PSXOVH FKDQJHLQPRPHQWXP
, ·
¸ H[HUWHGE\ WKHIORRU
'W n ¹
ϰ
$QV$FWLRQDQGUHDFWLRQDUHDFWLQJRQ
GLIIHUHQWERGLHV6RWKH\GRQRWFDQFHO
HDFKRWKHU
$KRUVHFDQQRWSXOODFDUWDQGUXQ
LQHPSW\VSDFH:K\"
VKRFN DEVRUEHUV LQFUHDVHV WKH WLPHRI
MHUNDQGKHQFHUHGXFHVLWVIRUFH
LY %XIIHUV DUH SURYLGHG EHWZHHQ
WKHERJLHVRIWUDLQ
5HDVRQ %XIIHUV LQFUHDVH WKH WLPH RI
MHUN7KLVGHFUHDVHVWKHIRUFHRILPSDFW
EHWZHHQ WKH ERJLHV 7KH ERJLHV DUH
WKXV SUHYHQWHG IURP UHFHLYLQJ VHYHUH
MHUNV
Y &KLQDZDUHVDUHSDFNHGLQVWUDZ
SDSHUEHIRUHSDFNLQJ
5HDVRQ7KHVWUDZSDSHUEHWZHHQWKH
FKLQD ZDUHV LQFUHDVHV WKH WLPH RI
H[SHULHQFLQJ WKH MHUN GXULQJ WKH
WUDQVSRUWDWLRQ
6WDWH1HZWRQ¶VWKLUGODZRIPRWLRQ
/DZRI$FWLRQDQG5HDFWLRQ $QV 7KH ODZ VWDWH WKDW ³7R HYHU\
DFWLRQWKHUHLVDQHTXDODQGRSSRVLWH
UHDFWLRQ´
([DPSOHV
L 'XULQJ ZDONLQJ D PDQ SXVKHV WKH
JURXQG DFWLRQ $V D UHDFWLRQ WKH
JURXQG H[HUWV DQ HTXDO EXW RSSRVLWH
UHDFWLRQIRUFHWRWKHSHUVRQ
LL :KLOH VZLPPLQJ D SHUVRQ
SXVKHV ZDWHU EDFNZDUG 7KH ZDWHU
WKHQ H[HUWV DQ HTXDO DQG RSSRVLWH
UHDFWLRQ WR WKH SHUVRQ LQ WKH IRUZDUG
GLUHFWLRQ
LLL :KHQ D SHUVRQ MXPSVRXW RI D
ERDW KH SXVKHV WKH ERDW LQ WKH
EDFNZDUG GLUHFWLRQ 7KH IRUZDUG
UHDFWLRQ IRUFH H[HUWHG E\ WKH ERDW RQ
WKHSHUVRQKHOSVKLPWRMXPSRXWRIWKH
ERDW
$QV ,Q HPSW\ VSDFH KRUVH FDQQRW
DSSO\ DFWLRQ 6R LW ZLOO QRW JHW DQ\
UHDFWLRQWRUXQ
6WDWH WKH ODZ RI FRQVHUYDWLRQ RI
OLQHDUPRPHQWXP
$QV7KHODZVWDWHVWKDW³,IQRH[WHUQDO
IRUFH DFWV RQ D V\VWHP RI VHYHUDO
SDUWLFOHVWKHWRWDOOLQHDUPRPHQWXPRI
WKHV\VWHPUHPDLQVFRQVWDQW´
3URYH WKH ODZ RI FRQVHUYDWLRQ RI
OLQHDU PRPHQWXP IURP 1HZWRQ¶V
VHFRQGODZ
$QV$FFRUGLQJWRVHFRQGODZ ) ,IWKHUHLVQRH[WHUQDOIRUFH
) Ÿ
GS
GW
Ÿ S FRQVW DQ W
7KXV WRWDO OLQHDU PRPHQWXP RI D
V\VWHPUHPDLQVFRQVWDQWLQWKHDEVHQFH
RIH[WHUQDOIRUFH
3URYH WKH ODZ RI FRQVHUYDWLRQ RI
OLQHDUPRPHQWXPIURP1HZWRQ¶VWKLUG
ODZ
$QV&RQVLGHUWZRERGLHV$DQG%RI
PDVVHV P DQG P PRYLQJ ZLWK
YHORFLWLHV X DQG X FROOLGH ZLWK HDFK
RWKHU/HWYDQGYEHWKHLUYHORFLWLHV
DIWHUFROOLVLRQ
(YHQ WKRXJK DFWLRQ DQG UHDFWLRQ
DUH HTXDO DQG RSSRVLWH WKH\ GR QRW
FDQFHOHDFKRWKHU:K\"
GS
GW
ϱ
7KHIRUFHH[HUWHGE\$RQ% DFWLRQ ,WLVIRXQGWKDWWKHWZRSODWHVLQLWLDOO\
DWUHVWQRZPRYHZLWKHTXDOYHORFLW\
)LQG WKH SHUFHQWDJH ORVV RI WKH LQLWLDO
YHORFLW\ RI WKH EXOOHW ZKHQ LW LV
EHWZHHQWKHSODWHV
) PD ) P § Y X · ¨
¸
©
¹
W
6LPLODUO\WKHIRUFHH[HUWHGE\
$QV
%RQ$ UHDFWLRQ ) PD
) P § Y X · ¨
¸
©
W
¹
%\1HZWRQ¶VWKLUGODZ
) ) § Y X ·
§ Y X ·
Ÿ P ¨ ¸ P ¨ ¸ © W ¹
© W ¹
Ÿ PYPX PYP X
Ÿ PX PX PYP Y
Ÿ PYPY PXPX
LH WRWDO OLQHDU PRPHQWXP EHIRUH
FROOLVLRQ LV HTXDO WR WRWDO PRPHQWXP
DIWHUFROOLVLRQ
3 $ EXOOHW RI PDVV J SLHUFHV
WKURXJK DSODWHRIPDVVNJ DQG WKHQ
FRPHVWRUHVWLQVLGHDVHFRQGSODWHRI
PDVVNJDVVKRZQLQILJXUH
ϲ
1RWH 7R UHGXFH UHFRLO YHORFLW\ WKH
PDVV RI WKH JXQ LV WR EH LQFUHDVHG
1HJDWLYHVLJQLQGLFDWHVWKDWWKHUHFRLO
YHORFLW\ LV RSSRVLWH WR WKH PX]]OH
YHORFLW\
*LYH DQ DSSOLFDWLRQ RI ODZ RI
FRQVHUYDWLRQRIPRPHQWXP
'LVWLQJXLVK EHWZHHQ PDVV DQG
ZHLJKW
$QV5HFRLORIJXQLVDQDSSOLFDWLRQRI
ODZ RI FRQVHUYDWLRQ RI DQJXODU
PRPHQWXP
$QV0DVVLVWKHDPRXQWRIVXEVWDQFH
FRQWDLQHG LQ D ERG\ ,W LV D VFDODU
TXDQWLW\LWV6,XQLWLVNJ
:KHQ WKH JXQ SRZGHU H[SORGHV WKH
VKRW PRYHV ZLWK D ODUJH IRUZDUG
PRPHQWXP7KHJXQPRYHVEDFNZDUG
ZLWK WKH VDPH PRPHQWXP 7KLV LV
FDOOHG UHFRLO RI JXQ 7KH YHORFLW\ RI
JXQ MXVW DIWHU ILULQJ LV FDOOHG UHFRLO
YHORFLW\7KHYHORFLW\RIWKHEXOOHWMXVW
DIWHUILULQJLVFDOOHGPX]]OHYHORFLW\
0DVVLVDVFDODUTXDQWLW\
:HLJKWLVWKHJUDYLWDWLRQDOIRUFHDFWLQJ
RQDERG\6,XQLWLV1HZWRQ 1 : PJ
:HLJKWLVDYHFWRUTXDQWLW\
%HIRUH ILULQJ ERWK WKH JXQ DQG EXOOHW
DUH DW UHVW 7KHUH WRWDO OLQHDU
PRPHQWXPLV]HUREHIRUHFROOLVLRQ
'HILQH LQHUWLDO PDVV DQG
*UDYLWDWLRQDO0DVV
/HW0ĺPDVVRIJXQ
$QV)URP1HZWRQ¶V6HFRQGODZ
9ĺYHORFLW\RIJXQ
D PĺPDVVRIEXOOHW
7KDWLVWKHDFFHOHUDWLRQRIDQREMHFW
LV LQYHUVHO\ SURSRUWLRQDO WR LWV PDVV
7KXV WKHPDVV LV DPHDVXUHRI LQHUWLD
RIDERG\6RLWLVFDOOHGLQHUWLDOPDVV
YĺYHORFLW\RIEXOOHW
:HNQRZE\WKHODZRIFRQVHUYDWLRQ
RIOLQHDUPRPHQWXP
7RWDOPRPHQWXPEHIRUHILULQJ 7RWDO
PRPHQWXPDIWHUILULQJ
P 2 09PY
PY
0 :HNQRZ: PJ
?P 7KLV LV WKH H[SUHVVLRQ IRU UHFRLO
YHORFLW\
)
D
³,QHUWLDO PDVV LV WKH UDWLR RI IRUFH
DSSOLHGRQDQREMHFWWRWKHDFFHOHUDWLRQ
SURGXFHG´
Ÿ 09 PY
Ÿ 9 )
P
ϳ
:
J
$SSDUHQW ZHLJKW RI WKH ERG\ LV HTXDO
WRDFWXDOZHLJKW
&DVH± 7KH OLIW LV PRYLQJ XSZDUGV
ZLWKXQLIRUPDFFHOHUDWLRQµD¶
+HUH
) PD
5±PJ PD
Ÿ 5 PDPJ
Ÿ 5 P DJ $SSDUHQWZHLJKWRIWKHERG\LVJUHDWHU
WKDQWKHDFWXDOZHLJKW
&DVH±7KHOLIWLVPRYLQJGRZQZLWK
XQLIRUPDFFHOHUDWLRQµD¶
) PD
PJ±5 PD
PJ±PD 5
5 P J±D $SSDUHQWZHLJKWRIWKH
ERG\GHFUHDVHV
&DVH± 7KH OLIW LV LQ IUHH IDOO
6XSSRVHWKHOLIWFDEOHEUHDNV +HUHD J
5 P J±D P J±J P 7KHDSSDUHQWZHLJKWLV]HUR7KHERG\
IHHOVZHLJKWOHVVQHVV
*UDYLWDWLRQDO PDVV LV WKH UDWLR RI
ZHLJKWRIDQREMHFWWRWKHDFFHOHUDWLRQ
GXHWRJUDYLW\$VWKHPDVVRIDQREMHFW
LQFUHDVHV WKH JUDYLWDWLRQDO IRUFHRQ LW
LQFUHDVHV
*UDYLWDWLRQDO PDVV FDQ EH PHDVXUHG
XVLQJFRPPRQEDODQFH
([SODLQ WKH GLIIHUHQW FDVHV RI
DSSDUHQWZHLJKWRIDERG\LQDOLIW
$QV
&RQVLGHUDERG\RIPDVVPSODFHGLQ
D OLIW DW UHVW 7KH IRUFHV DFWLQJRQ WKH
ERG\DUH
L 7KH ZHLJKW RI WKH ERG\ DFWLQJ
YHUWLFDOO\GRZQZDUGV : PJ LL 7KHQRUPDOUHDFWLRQ 5 DFWLQJ
YHUWLFDOO\XSZDUGV
&DVH± 7KH OLIW LV VWDWLRQDU\ RU
PRYLQJ XS RU GRZQ ZLWK XQLIRUP
YHORFLW\
D 7KHQ WKH UHVXOWDQW IRUFHDFWLQJRQ WKH
ERG\
) PD
5±PJ Pî
?5 PJ
3$FKLOGZHLJKLQJNJLVLQDOLIW
WKDW LV PRYLQJ GRZQ ZLWK DQ
DFFHOHUDWLRQRIPVZKDWZLOOEHWKH
DSSDUHQW
ZHLJKW
RI
WKH
FKLOG" J PV $QV
ϴ
:KDWLVWKHFDXVHRIIULFWLRQ"
$QV )ULFWLRQ LV GXH WR WKH IRUFH RI
DWWUDFWLRQEHWZHHQWKHPROHFXOHVRIWKH
WZRVXUIDFHVLQFRQWDFW
*LYHWKHFODVVLILFDWLRQRIIULFWLRQ
$QV7KHUHDUHWZRW\SHVRIIULFWLRQ L 6WDWLF IULFWLRQ DQG LL .LQHWLF
IULFWLRQ
.LQHWLF IULFWLRQ LV DJDLQ GLYLGHG LQ WR
D 6OLGLQJ IULFWLRQ DQG 5ROOLQJ
IULFWLRQ
'HILQH6WDWLF)ULFWLRQ IV $QV,WLVWKHIULFWLRQDOIRUFHEHWZHHQ
WZRVXUIDFHVLQFRQWDFWEHIRUHWKHUHLV
UHODWLYHPRWLRQEHWZHHQWKHVXUIDFHV
3ORW WKH YDULDWLRQ LQ WKH YDOXH RI
VWDWLFIULFWLRQZLWKWKHDSSOLHGIRUFH
$QV
3 $ PRQNH\ RI PDVV NJ FOLPEV
RQ URSH ZKLFK FDQ ZLWKVWDQG D
PD[LPXP WHQVLRQ RI 1 ,Q ZKLFK
RI WKH IROORZLQJ FDVHV ZLOO WKH URSH
EUHDN"7KHPRQNH\
D &OLPEVXSZLWKDQDFFHOHUDWLRQ
RIPV
E &OLPEV GRZQ ZLWK DQ
DFFHOHUDWLRQRIPV
$QV
:KHQ ZH SXVK RU SXOO D ERG\ WKH
VWDWLFIULFWLRQGHYHORSVLQWKHRSSRVLWH
GLUHFWLRQ ,I ZH LQFUHDVH WKH H[WHUQDO
IRUFHPRUHDQGPRUHVWDWLFIULFWLRQLV
GHYHORSHG%XWWKHVWDWLFIULFWLRQKDVD
PD[LPXP YDOXH FDOOHG WKH OLPLWLQJ
IULFWLRQ ,I ZH DSSO\ PRUH IRUFH WKDQ
WKH OLPLWLQJ IULFWLRQ WKH ERG\ ZLOO
PRYH :KHQ WKH ERG\ RQFH VWDUWV
PRWLRQ WKH IULFWLRQ VOLJKWO\ GHFUHDVHV
DQG WKHUHDIWHU LW KDV D FRQVWDQW YDOXH
FDOOHGNLQHWLFIULFWLRQ
'HILQHOLPLWLQJIULFWLRQ IVPD[ $QV 7KH PD[LPXP YDOXH RI VWDWLF
IULFWLRQLVFDOOHGOLPLWLQJIULFWLRQ
)ULFWLRQ
'HILQHIULFWLRQ
$QV )ULFWLRQ LV WKH IRUFH ZKLFK
RSSRVHV WKH UHODWLYH PRWLRQ EHWZHHQ
WZRVXUIDFHVLQFRQWDFW
ϵ
6WDWHWKHODZVRIVWDWLFIULFWLRQ
$QV7KHODZVRIVWDWLFIULFWLRQDUH
L 7KH PDJQLWXGH RI WKH OLPLWLQJ
IULFWLRQ LV LQGHSHQGHQW RI WKH
DUHDRIFRQWDFW
LL 7KH OLPLWLQJ IULFWLRQ LV GLUHFWO\
SURSRUWLRQDOWRQRUPDOUHDFWLRQ
INĮ5
Ÿ IN ȝNî5
ȝN LV FDOOHG WKH FRHIILFLHQW RI NLQHWLF
IULFWLRQ
'HILQHWKHDQJOHRIIULFWLRQ
$QV
IVPD[Į5
IVPD[ ȝVî5
ȝVLVFDOOHGWKHFRHIILFLHQWRIWKHVWDWLF
IULFWLRQ
'HILQHNLQHWLFIULFWLRQ
$QV,WLVWKHIRUFHRIIULFWLRQEHWZHHQ
WZR VXUIDFHV LQ FRQWDFW ZKHQ WKHUH LV
UHODWLYHPRWLRQEHWZHHQWKHVXUIDFHV
IDĺ$SSOLHGIRUFH
.LQHWLF IULFWLRQ LV DOZD\V OHVV WKDQ
OLPLWLQJIULFWLRQ
5ĺ1RUPDOUHDFWLRQ
IVPD[ĺ/LPLWLQJIULFWLRQ
PJĺZHLJKWRIWKHERG\
:KDW DUH WKH WZR W\SHV RI NLQHWLF
IULFWLRQ"
³7KHDQJOHZKLFKWKHUHVXOWDQW I5 RI
WKH OLPLWLQJ IULFWLRQ DQG QRUPDO
UHDFWLRQ PDNHV ZLWK WKH QRUPDO
UHDFWLRQ 5 LV FDOOHG WKH DQJOH RI
IULFWLRQ Ȝ ´
$QV.LQHWLFIULFWLRQLVRIWZRW\SHV
D
E
6OLGLQJIULFWLRQ
5ROOLQJIULFWLRQ
WDQ O 1RWH 5ROOLQJ IULFWLRQ LV OHVV WKDQ
6OLGLQJIULFWLRQ
W DQ O PV
O W DQ PV
6WDWHWKHODZVRINLQHWLFIULFWLRQ
$QV
L
LL IV
P 5
V PV
5
5
'HILQHDQJOHRIUHSRVH
7KH NLQHWLF IULFWLRQ KDV D
FRQVWDQW YDOXH GHSHQGLQJ RQ
WKHQDWXUHRIWKHWZRVXUIDFHVLQ
FRQWDFW
7KH NLQHWLF IULFWLRQ IN LV
GLUHFWO\ SURSRUWLRQDO WR WKH
QRUPDOUHDFWLRQ5
$QV ³7KH DQJOH RI LQFOLQDWLRQ RI WKH
LQFOLQHG SODQH ZKHQ WKH ERG\ MXVW
VOLGHVGRZQLVFDOOHGDQJOHRIUHSRVH´
ϭϬ
$GYDQWDJHVRIIULFWLRQ
L:H DUH DEOH WR ZDON RQ WKH JURXQG
GXHWRIULFWLRQ
LL:HFDQKROGDQREMHFWLQKDQGGXHWR
IULFWLRQ
LLL0HWHRUV EXUQ LQ DLU GXH WR
DWPRVSKHULFIULFWLRQ
'LVDGYDQWDJHVRIIULFWLRQ
L:KHQDYHKLFOHPRYHVDORWRIHQHUJ\
LVORVWWRRYHUFRPHWKHIULFWLRQ
LL)ULFWLRQFDXVHVWKHZHDUDQGWHDURI
PRYLQJSDUWVRIPDFKLQHV
LLL)ULFWLRQRIIHUHGE\ DWPRVSKHULF DLU
LV GLVDGYDQWDJHRXV WR URFNHWV DQG
VDWHOOLWHV
*LYH VRPH PHWKRGV WR UHGXFH
IULFWLRQ
$QV
L 8VHEDOOEHDULQJVEHWZHHQWZR
PRYLQJSDUWVRIDPDFKLQH
LL 8VH OXEULFDQWV /XEULFDQWV
IRUP D OD\HU EHWZHHQ WKH WZR
VROLG VXUIDFHV DQG WKXVSUHYHQW
WKHP FRPLQJ LQWR GLUHFW
FRQWDFW *UHDVH RLO ZD[ HWF
DUHXVHGDVOXEULFDQWV
&LUFXODU0RWLRQDQG)ULFWLRQ
'HILQH FHQWULSHWDO IRUFH *LYH
H[DPSOHV
$QV &HQWULSHWDO IRUFH LV WKDW IRUFH
H[SHULHQFHGE\DERG\ZKHQLWPRYHV
DORQJ D FXUYHG SDWK 7KH GLUHFWLRQRI
WKH IRUFH LV WRZDUGV WKH FHQWUH RI WKH
FXUYHGSDWK
+HUH
PJ VLQ T IV PD[ """""" PJ FRV T 5 """""" P 5
IV PD[
o WDQT V PV
5
5
WDQT PV
? T WDQ PV """"" $OVRZHKDYHWKHDQJOHRIIULFWLRQ
O WDQ PV """"""" ?)URP DQG T O
$QJOHRI5HSRVH $QJOHRIIULFWLRQ
:KDWLVWKHSULQFLSOHEHKLQGWKHXVH
RIEDOOEHDULQJV"
$QV 5ROOLQJ IULFWLRQ LV OHVV WKDQ
VOLGLQJ IULFWLRQ 7KLV LV WKH SULQFLSOH
EHKLQGWKHXVHRIEDOOEHDULQJV
)ULFWLRQ LV D QHFHVVDU\ HYLO
([SODLQ
$QV )ULFWLRQ KDV PDQ\ DGYDQWDJHV
DQGVRPHGLVDGYDQWDJHV6RIULFWLRQLV
FDOOHGDQHFHVVDU\HYLO
&HQWULSHWDOIRUFH ϭϭ
PY
U
(JL :KHQDVWRQHWLHGWRDVWULQJLV
ZKLUOHG WKH FHQWULSHWDO IRUFH LV
SURYLGHGE\WKHWHQVLRQLQWKHVWULQJ
ȝVPJ>6LQFH5 PJ@
7KH FRQGLWLRQ IRU WKH VDIH WXUQLQJ RI
WKHFDULV
PY d P V PJ
U
PY P D[ P V PJ
U
P PJU
Y PD[ d V
P V JU
P
Y PD[ P V UJ
LL :KHQ D VDWHOOLWHPRYHV DURXQG
WKHHDUWKFHQWULSHWDOIRUFHLVSURYLGHG
E\WKHJUDYLWDWLRQDODWWUDFWLRQRIHDUWK
RQWKHVDWHOOLWH
LLL )RUDFDUWDNLQJDFLUFXODUWXUQRQ
DKRUL]RQWDOURDGWKHFHQWULSHWDOIRUFH
LVWKHIRUFHRIIULFWLRQ
Y PD[ P V UJ
$FDULVPRYLQJRQDFLUFXODUOHYHO
URDG 'HULYH WKH H[SUHVVLRQ IRU
PD[LPXP VSHHGIRU VDIHWXUQLQJ RI
WKHFDU
7KLV LV WKH PD[LPXP VSHHG IRU WKH
YHKLFOHWRDYRLGVNLGGLQJ
$QV
3$F\FOLVWVSHHGLQJDWNPKURQ
DOHYHOURDGWDNHVDVKDUSFLUFXODUWXUQ
RI UDGLXV P ZLWKRXW UHGXFLQJ WKH
VSHHG7KHFRHIILFLHQWRIVWDWLFIULFWLRQ
EHWZHHQ WKHW\UHV DQG WKH URDG LV
:LOO WKH F\FOLVW VOLS ZKLOH WDNLQJ WKH
WXUQ"
$QV
7KHIRUFHVDFWLQJRQWKHFDUDUH
L WKHZHLJKWRIWKHFDUPJ
LL 1RUPDOUHDFWLRQ5
LLL )ULFWLRQDOIRUFHI
7KH FHQWULSHWDO IRUFH UHTXLUHG
PY
IRU WKH PRWLRQ RI WKH FDU U
ZKHUHULVWKHUDGLXVRIFXUYDWXUHRIWKH
URDG 7KLV LV SURYLGHGE\ WKH IRUFHRI
IULFWLRQEHWZHHQWKHW\UHVDQGWKHURDG
7KHPD[LPXPIULFWLRQDOIRUFH
IV PD[ PV 5 ϭϮ
:KDW LV WKH DGYDQWDJH RI EDQNHG
URDG"
$QV2QDEDQNHGURDGDYHKLFOHJHWV
PRUHFHQWULSHWDOIRUFH
([SODQDWLRQ
2QDOHYHOURDGIULFWLRQLVWKHRQO\
DYDLODEOHFHQWULSHWDOIRUFH
2Q D EDQNHG URDG ERWK IULFWLRQ
DQG D FRPSRQHQW RI QRUPDO UHDFWLRQ
DUHDYDLODEOHDVFHQWULSHWDOIRUFH
'HULYH DQ H[SUHVVLRQ IRU WKH
PD[LPXP VSHHG IRU VDIH WXUQLQJRQ D
EDQNHGURDG
$QV
%DQNLQJRI5RDG
:KDWLVPHDQWE\EDQNLQJRIURDG"
$QV $W D FXUYH WKH URDG LV PDGH LQ
VXFK DZD\ WKDW WKHRXWHU HGJHRI WKH
URDG LV UDLVHG DERYH WKH LQQHU HGJH
7KLVLVFDOOHGEDQNLQJRIURDGV
ϭϯ
$WHTXLOLEULXPZHKDYH
5 FRVT PJIV
PD[
VLQT"" ˜˜˜ PY PD[ IV PD[ FRVT5VLQT" U
(TQ o
PY PD[ PV 5FRVT5VLQT
U
PY PD[ Ÿ 5 PV FRVTVLQT " U
(TQ o 5FRVT PJPV 5VLQT
Ÿ 5FRVTPV 5VLQT PJ
Ÿ 5 FRVTPVVLQT PJ
Ÿ 5 PJ
"""""" FRVTPV VLQT
6XEVWLWXWLQJHTQ LQHTQ ZHJHW
PYPD[ PJ
PV FRVTVLQT
U
FRVTPV VLQT
YPD[
UJ PV FRVTVLQT
FRVTPV VLQT
'LYLGLQJ ERWK 1U
3 $ FLUFXODU UDFHWUDFN RI UDGLXV
P LVEDQNHG DW DQDQJOHRI ,I
WKH FRHIILFLHQW RI VWDWLF IULFWLRQ
EHWZHHQWKHZKHHORIDUDFHFDUDQGWKH
URDG LV ZKDW LV WKH D RSWLPXP
VSHHGRIWKHUDFHFDUWRDYRLGZHDUDQG
WHDU RI LWV W\UHV DQG E PD[LPXP
SHUPLVVLEOHVSHHGWRDYRLGVOLSSLQJ"
$QV
'U RI 5+6 E\ FRV T
ª UJ PV FRVTVLQT º
«
»
FRVT
¼
YPD[ ¬
ª FRVTPV VLQT º
«¬
»¼ FRVT
UJ PV WDQT
YPD[ """ PV WDQT
7KLVLVWKHPD[LPXPVSHHGWRDYRLG
VNLGGLQJRIWKHYHKLFOH
:LWKRXWFRQVLGHULQJIULFWLRQ
SXWȝV LQHTQ ? YcPD[ UJWDQ T
7KLV LV WKH PD[LPXP VSHHG WR DYRLG
ZHDUDQGWHDURIW\UHV
ϭϰ