0HWKRG RI RSHUDWLRQ6$
9
&*&
'HWHUPLQDWL RQ RI WKH IDXOW GLVWDQFH
,PSHGDQFH FDOFXODWLRQ
7KHFDOFXODWLRQLVDQLQWHJUDWLRQRIWKHOLQHLGHQWLW\
/ô
GL
GW
5 ô L X
ZLWK L X WKH LQVWDQWDQHRXV YDOXHV DW WKH LQVWDQW W
DQG DOORZV ZLWK LWV LGHDO ILOWHU FKDUDFWHULVWLFV GHWHU
PLQDWLRQ RI WKH 5 DQG ; W
/ FRPSRQHQWV IRU WKH
VKRUW FLUFXLW ORRS LQGHSHQGHQW RI WKH VHWWLQJ RI WKH
WULSSLQJ FKDUDFWHULVWLFV
(DFK HTXDWLRQ LV VROYHG E\ WZR GLIIHUHQW FDOFXODWLRQ
PHWKRGV ZKLFK FRPSOHPHQW HDFK RWKHU ZLWK UHJDUG
WR DFFXUDF\ DQG VSHHG $GGLWLRQDOO\ DGDSWLYH DOJR
ULWKPV DUH XVHG ZKLFK DXWRPDWLFDOO\ PDWFK WR WKH
PHDVXUHG YDOXH FRQGLWLRQV DIWHU IDXOW LQFHSWLRQ
PHDVXUHG YDOXH VKDSH IDXOW W\SH IDXOW GLVWDQFH
HWF UHIHU DOVR WR 6HFWLRQ
)RU FDOFXODWLRQ RI D SKDVHWRSKDVH ORRS YDOXHV FRQ
IRUPLQJ WR )LJXUH JLYHQ LQ IRU X WKH LQVWDQ
WDQHRXV YDOXHV RI SKDVHWRSKDVH YROWDJH DQG IRU L
WKH GLIIHUHQFH RI WKH SKDVH FXUUHQWV DUH XVHG HJ
)LJXUH
/ ô
Æ
GL
/
GW
GL
/
GW
É
5 ô
L
/
L
/
X
/
(
X
/
(
)RU FDOFXODWLRQ RI D SKDVHWRHDUWK ORRS DFFRUGLQJ
)LJXUH
/ ô
Æ
GL
/
GW
;
(
;
/
ô
GL
(
GW
É
5 ô
Æ
L
/
5
(
5
/
L
/
É
X
/
(
5 DQG / DUH WKH UHTXLUHG LPSHGDQFH FRPSRQHQWV
7KH FDOFXODWHG UHDFWDQFH ; W k / LV WKH OLQH UHDF
WDQFH ;
/
XS WR WKH SRLQW RI IDXOW 7KLV GHWHUPLQHV WKH
GLVWDQFH WR IDXOW 7KH UHVLVWDQFH YDOXH RQ WKH RWKHU
KDQG FRQWDLQV LQ DGGLWLRQ WR WKH FRQGXFWRU UHVLV
WDQFH 5
/
WKH IDXOW UHVLVWDQFH 5
)
UHIHU WR )LJXUHV
DQG
1RWH 7KH IDFWRUV 5
(
5
/
DQG ;
(
;
/
DUH SXUHO\ PDWKH
PDWLFDO YDOXHV DQG KDYH QR SK\VLFDO PHDQLQJ 7KH\
FDQ EH UHODWLYHO\ HDVLO\ FDOFXODWHG IURP WKH OLQH GDWD
ZLWKRXW XVLQJ FRPSOH[ IRUPV IURP WKH IRUPXODH
5
(
5
/
ô
Æ
5
5
É
DQG
;
(
;
/
ô
Æ
;
;
É
UHIHU WR 6HFWLRQ
7KH VHSDUDWH VHWWLQJ IDFLOLWLHV IRU WKH IDFWRUV DOORZ
WKH SRVVLEOH SKDVH GLIIHUHQFH EHWZHHQ HDUWK DQG
FRQGXFWRU LPSHGDQFH WR EH WDNHQ LQWR DFFRXQW LQ
DGGLWLRQ WR WKH UHODWLRQVKLS =
(
=
/
7KLV GLIIHUHQFH
FDQ EH RI VLJQLILFDQW YDOXH LQ FDEOH QHWZRUNV
/
/
/
,
/
(
,
/
;
/
;
/
8
/ (
8
/ (
5
)
5
/
5
/
)LJXUH 3KDVHSKDVH VKRUW FLUFXLW ORRS
/
(
/
/
,
/
,
(
;
/
;
(
8
/ (
5
)
5
/
5
(
)LJXUH 3KDVHHDUWK VKRUW FLUFXLW ORRS