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FRQMXJDGRGRELQiULRGRHL[R
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SRWrQFLDUHDOWRWDO
URWDomRVtQFURQD
GHVOL]DPHQWR
UHQGLPHQWR
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)DoDRJUiILFRGRUHQGLPHQWRHPIXQomRGDSRWrQFLDPHFkQLFD
)DoDRJUiILFRGRIDWRUGHSRWrQFLDHPIXQomRGDSRWrQFLDPHFkQLFD
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&iOFXORV
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2YDORUGRUDLRQRIUHLRGH3URQ\pGHP
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• $PSHUtPHWUR
$
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1
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USP
• 9ROWtPHWUR
9
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YDORUHVPHGLGRV
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9DPRVUHVROYHUHVWHH[HPSORFDOFXODQGRDSRWrQFLDHPFY
3FY =
πU Q)
3FY =
(IHWXDQGRWRGRVRVFiOFXORVREWHPRV3FY≅FY
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&RQMXJDGRGRELQiULRGRHL[R
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SRWrQFLDDSDUHQWH WHQVmRGDOLQKDFRUUHQWHGDOLQKD 9DPRVDSOLFDUDVHJXQGDIyUPXODHVFULWDGHIRUPDDEUHYLDGD
3D = (/ Ι  3D = 3D ≅ 9$
3RWrQFLDUHDODEVRUYLGDSHORPRWRU
9DPRVXWLOL]DURVtPEROR: SDUDDOHLWXUDGRZDWWtPHWURH: SDUDDOHLWXUDGR
ZDWWtPHWUR
3DUDDSRWrQFLDUHDOXVDUHPRVRVtPEROR : / $VIyUPXODVVmRDVVHJXLQWHV
: / : : VHRIDWRUGHSRWrQFLDIRUPDLRUTXHRX : / : : VHR
IDWRUGHSRWrQFLDIRUPHQRUTXH
1RSUHVHQWHFDVRYDPRVXWLOL]DUDIyUPXOD
: / : : : / : / :
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SRWrQFLD UHDO
: /
RXGHIRUPDDEUHYLDGD FRV ϕ =
SRWrQFLDDS DUHQWH
3D
$SOLFDQGRRVYDORUHVWHPRV
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FRVϕ 6(1$,63,175$1(7
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*HUDOPHQWHXWLOL]DPRVRIDWRUGHSRWrQFLDHPSRUFHQWDJHP1HVWHFDVRRVtPERORVHUi
FRVϕHRYDORUGHYHUiVHUPXOWLSOLFDGRSRU
FRVϕ FRVϕ 5RWDomRGRFDPSRPDJQpWLFR
(VWDURWDomRGHYHVHUFRQVLGHUDGDjYHORFLGDGHGHVLQFURQLVPR1HVWHFDVRUHFHEHR
QRPHGHURWDomRVtQFURQD
$IyUPXODp URWDomR VtQFURQD =
IUHTrQFLD
SDUHV GH SyOR
2EVHUYHDJRUDDIyUPXODHVFULWDGHIRUPDDEUHYLDGD
1V =
I
S
$SOLFDQGRRVYDORUHVWHPRV
1V =
1V USP
'HVOL]DPHQWR
2GHVOL]DPHQWRpWDPEpPFKDPDGRGHHVFRUUHJDPHQWR6HXYDORUpGDGRHP
SRUFHQWDJHP$IyUPXODp
URWDomR VtQFURQD − URWDomR PHGLGD
RXGHIRUPDDEUHYLDGD
URWDomR VtQFURQD
1V − 1 PHGLGD
6=
1V
GHVOL]DPHQ WR =
6(1$,63,175$1(7
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$SOLFDQGRRVYDORUHVWHPRV
6 =
− 6 2EVHUYDomR
2YDORUGRGHVOL]DPHQWRGHYHVHUPHQRURXLJXDOD(QWUHWDQWRDSHQDVQRV
PRWRUHVDVVtQFURQRVHVWHYDORUFKHJDD
5HQGLPHQWR
2UHQGLPHQWRpGDGRHPSRUFHQWDJHP
$IyUPXODp UHQ GLP HQWR =
µ =
SRWrQFLD PHFkQLFD
RXGHIRUPDDEUHYLDGD
SRWrQFLD UHDO WRWDO
3 : /
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3FY : /
6XEVWLWXLQGRRVYDORUHVWHPRV
µ=
µ &iOFXORVGRVRXWURVYDORUHVGHFDUJDVSDUDHQVDLDU
2YDORU1PHGLGRQRGLQDP{PHWURHTXLYDOHD'HYHPRVUHSHWLUDH[SHULrQFLD
FRPRXWUDVSRUFHQWDJHQVGHVWHYDORU9HMDDVHJXLURFiOFXORGHVWDVSRUFHQWDJHQV
GH 1 =
= 1
6(1$,63,175$1(7
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GH 1 =
= 1
GH 1 =
= 1
GH 1 =
= 1
7DEHOD
9DPRVDJRUDFRQVWUXLUXPDWDEHODFRPRVYDORUHVPHGLGRVHRVYDORUHVFDOFXODGRV2V
YDORUHVPHGLGRVHRVYDORUHVFDOFXODGRVSDUDRYDORUGDIRUoD1IRUDPH[SOLFDGRV
DQWHULRUPHQWH2VYDORUHVPHGLGRVHRVYDORUHVFDOFXODGRVSDUDRVYDORUHVGDVIRUoDV
111H1HVWmRPRVWUDGRVQDWDEHODSDUDRH[HPSORILFDU
FRPSOHWR4XDQGRYRFrHQVDLDURPRWRUGHYHUiHIHWXDUWRGRVRVFiOFXORVQHFHVViULRV
9HMDDWDEHODDVHJXLU
9DORUHVPHGLGRV
&DUJD
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*UiILFRGDURWDomRVtQFURQDHPIXQomRGDSRWrQFLDPHFkQLFD
*UiILFRGHUHQGLPHQWRHPIXQomRGDSRWrQFLDPHFkQLFD
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2EVHUYDomR
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WUrVLQFRQYHQLHQWHV
• $OWRFXVWRGRPRWRU
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$SDUHOKRV
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3P
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