8QLYHUVLGDG1DFLRQDOGH5RVDULR )DFXOWDGGH&LHQFLDV([DFWDV,QJHQLHUtD\$JULPHQVXUD (VFXHODGH,QJHQLHUtD(OHFWUyQLFD 'HSDUWDPHQWRGH(OHFWUyQLFD (/(&75Ï1,&$,,, )8(17(65(*8/$'$6 )HGHULFR0L\DUD $f2 B06.01 5LREDPEDELV 5RVDULR $UJHQWLQD KWWSZZZIFHLDXQUHGXDUHQLFD 7(/ )$; &yGLJRLQWHUQRGHSXEOLFDFLyQ% 3ULPHUDHGLFLyQ 3XEOLFDGRHQ,QWHUQHW 5RVDULR$UJHQWLQD $xR KWWSZZZIFHLDXQUHGXDUHQLFDIXHQWHVWSGI )8(17(65(*8/$'$6 ,QWURGXFFLyQ (QODDFWXDOLGDGODHQHUJtDGLVWULEXLGDSRUODUHGHOpFWULFDVHJHQHUDWUDQVPLWH\ VXPLQLVWUDH[FOXVLYDPHQWHHQIRUPDGHFRUULHQWHDOWHUQDGDGRTXHHVPiVVLPSOH\HIL FLHQWH6LQHPEDUJRODPD\RUtDGHORVVLVWHPDVHOHFWUyQLFRVUHTXLHUHXQDDOLPHQWDFLyQ GHFRUULHQWHFRQWLQXDTXHDGHPiVVHDFDSD]GHPDQWHQHUODWHQVLyQRODFRUULHQWHUHOD WLYDPHQWH FRQVWDQWH LQGHSHQGLHQWHPHQWH GH ODV IOXFWXDFLRQHV TXHSXGLHUHQSURGXFLUVH HQODWHQVLyQGHODOtQHDGHDOLPHQWDFLyQRHQODFDUJD 8Q UHFWLILFDGRU FRQ ILOWUR SHUPLWH REWHQHU FRUULHQWH FRQWLQXD D SDUWLU GH XQD DOL PHQWDFLyQDOWHUQDSHURFRPRYHUHPRVODWHQVLyQGHVDOLGDGHSHQGHPXFKRGHODWHQ VLyQ GH DOLPHQWDFLyQ \ GH OD FDUJD $GHPiV DO DXPHQWDU HO FRQVXPR OD FDOLGDG GH OD WHQVLyQGHVDOLGDHPSHRUD\DTXHVXULSSOHDXPHQWD (VWDVIDOHQFLDVSXHGHQVXEVDQDUVHFRQXQDIXHQWHUHJXODGDHVGHFLUXQGLVSRVLWL YRTXHWRPDHQHUJtDHOpFWULFDGHXQJHQHUDGRURIXHQWHSULPDULD\ODVXPLQLVWUDDXQD FDUJDHQIRUPDHVWDELOL]DGDIUHQWHDYDULDFLRQHVGHGLYHUVRVSDUiPHWURVWtSLFDPHQWHOD WHQVLyQGHDOLPHQWDFLyQODFRUULHQWHGHFDUJD\ODWHPSHUDWXUD &ODVLILFDFLyQ\GHILQLFLRQHV &ODVLILFDFLyQGHODVIXHQWHVUHJXODGDV /DVIXHQWHVUHJXODGDVWDPELpQGHQRPLQDGDVUHJXODGRUHVSXHGHQFODVLILFDUVHVH J~QODYDULDEOHGHVDOLGDTXHHVWDELOL]DQ7HQHPRVDVtIXHQWHVUHJXODGDVGHWHQVLyQ\GH FRUULHQWH/DVGHWHQVLyQHQWUHJDQXQDWHQVLyQFRQVWDQWHDODFDUJDFRQ LQGHSHQGHQFLD GHODFRUULHQWHTXHpVWDGHPDQGH/DVGHFRUULHQWHSRUHOFRQWUDULRDGDSWDQODWHQVLyQ DSOLFDGDDODFDUJDVHJ~QVHDQHFHVDULRSDUDHQWUHJDUXQDFRUULHQWHFRQVWDQWH$XQTXH QRWDQFRPXQHVH[LVWHQWDPELpQIXHQWHVUHJXODGDVGHSRWHQFLDTXHHQWUHJDQXQDSRWHQ FLDFRQVWDQWHDODFDUJDDGDSWDQGRSDUDHOORODWHQVLyQTXHHQWUHJDQDODFDUJD6RQGH XWLOLGDGSRUHMHPSORHQDOJXQRVVLVWHPDVWpUPLFRV1RVHWUDWDUiQHQHVWHWH[WR 2WUDFODVLILFDFLyQHVVHJ~QVLHOIXQFLRQDPLHQWRHVOLQHDORQROLQHDO(QODVIXHQ WHV UHJXODGDV OLQHDOHV ORV GLVSRVLWLYRVGHSRWHQFLDRSHUDQHQVX]RQDOLQHDO(QODV QR OLQHDOHVHQFDPELRpVWRVIXQFLRQDQHQFRUWH\VDWXUDFLyQGHDOOtHOQRPEUHGHIXHQWHV FRQPXWDGDVFRQTXHJHQHUDOPHQWHVHODVFRQRFH/DVIXHQWHVOLQHDOHVWLHQHQSHRUUHQ GLPLHQWRSHURDOFDQ]DQYDORUHVPiVHVWDEOHV/DVIXHQWHVQROLQHDOHVDOXWLOL]DUWUDQVLV WRUHVHQFRUWH\VDWXUDFLyQORFXDOLPSOLFDEDMDGLVLSDFLyQSUHVHQWDQPHMRUUHQGLPLHQ WR SHUR HQ FDPELR WLHQHQ PD\RUHV YDULDFLRQHV D OD VDOLGD 3XHGHQ LQFOXVR JHQHUDU \ HPLWLUDOWDVIUHFXHQFLDVHVSXULDV(QDOJXQRVFDVRVVHXWLOL]DXQSUHUUHJXODGRUFRQPXWD GRVHJXLGRSRUXQUHJXODGRUOLQHDOORFXDOSHUPLWHDSURYHFKDU HODOWRUHQGLPLHQWRGHO SULPHUR\ODHVWDELOLGDGGHORVSDUiPHWURVGHVDOLGDGHOVHJXQGR(QORTXHVLJXHFRQVL GHUDUHPRV~QLFDPHQWHIXHQWHVOLQHDOHV 8QDWHUFHUDFODVLILFDFLyQHVDWHQGLHQGRODWRSRORJtDFLUFXLWDO6HGLVWLQJXHQORVUH JXODGRUHVVHULH\SDUDOHORVHJ~QTXHHOHOHPHQWRGHSRWHQFLDHVWpHQVHULHRHQSDUDOHOR FRQODFDUJD/RVUHJXODGRUHVVHULHWLHQHQHQJHQHUDOPD\RUUHQGLPLHQWR\VHORVSUHILH UHSHURSDUDDOJXQDVDSOLFDFLRQHVVRQPiVLQGLFDGRVORVUHJXODGRUHVHQSDUDOHOR % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV 3DUiPHWURV\HVSHFLILFDFLRQHVGHOUHJXODGRUGHWHQVLyQ /DVSUHVWDFLRQHVGHXQDIXHQWHUHJXODGD\SRUORWDQWRODDGHFXDFLyQDXQGHWHU PLQDGRXVRVHSXHGHQHYDOXDUDWUDYpVGHDOJXQRVSDUiPHWURV(VFRQYHQLHQWHFODVLILFDU ORVSDUiPHWURVHQORVTXHFRUUHVSRQGHQDXQGLVSRVLWLYRHVSHFtILFR\ORVTXHFRUUHVSRQ GHQDWRGDXQDSREODFLyQ/RVSDUiPHWURVFRUUHVSRQGLHQWHVDXQGLVSRVLWLYRHVSHFtILFR VHSXHGHQPHGLUFRQODVLQFHUWLGXPEUHVSURSLDVGHWRGDPHGLFLyQREWHQLpQGRVHYDOR UHVTXHYDULDUiQGHGLVSRVLWLYRHQGLVSRVLWLYR/RVSDUiPHWURVSREODFLRQDOHVFRQVWLWX\HQ OtPLWHVTXHFXPSOHQWRGRVORVGLVSRVLWLYRVGHODSREODFLyQRELHQPHGLGDVHVWDGtVWLFDV FRPRODPHGLD 3DUiPHWURVEiVLFRV 7HQVLyQQRPLQDOGHVDOLGD(VHOYDORUGHWHQVLyQDVRFLDGRDXQPRGHORGHIXHQ WH1RQHFHVDULDPHQWHFRLQFLGHFRQHOYDORUGHWHQVLyQUHDOPHQWHREWHQLGRHQXQDGDGD FRQGLFLyQQLVLTXLHUDHQODFRQGLFLyQQRUPDOL]DGDDXQTXHGHEHUtDVHUSUy[LPRDDTXpO (VHOSDUiPHWURIXQGDPHQWDOGHVHOHFFLyQGHODIXHQWHSDUDXQXVRGDGR 5DQJRGHWHQVLyQGHVDOLGD3DUDXQPRGHORGHUHJXODGRUGHWHQVLyQDMXVWDEOHHV HOUDQJRGHYDORUHVDOFDQ]DEOHVGHWHQVLyQQRPLQDOGHVDOLGD 7HQVLyQGHVDOLGD3DUDXQGHWHUPLQDGRGLVSRVLWLYRHVHOYDORUGHWHQVLyQGHVD OLGDHQXQDFRQGLFLyQHVSHFtILFDGHRSHUDFLyQSRUHMHPSORXQDGHWHUPLQDGDWHPSHUDWX UDWHQVLyQGHHQWUDGD\FRUULHQWHGHFDUJD&XDQGRVHGHVFULEHXQDSREODFLyQGHGLVSR VLWLYRV VH SXHGHQ VXPLQLVWUDU ORV YDORUHV PtQLPR WtSLFR \ Pi[LPR(QDOJXQRVFDVRV ORVYDORUHVPtQLPR\Pi[LPRVHGDQHQIRUPDGHWROHUDQFLDSRUFHQWXDOFRQUHVSHFWRDO YDORUQRPLQDO(OYDORUWtSLFRHVQRUPDOPHQWHHOYDORUPHGLRGHODSREODFLyQ\DXQTXH HVSUy[LPRDOYDORUQRPLQDOQRQHFHVDULDPHQWHFRLQFLGHFRQpVWH 5DQJRGHWHQVLyQGHHQWUDGD9DORUHVPtQLPR\Pi[LPRGHWHQVLyQGHHQWUDGD SDUDORVTXHVHFXPSOHQODVHVSHFLILFDFLRQHV1RUPDOPHQWHHVEDVWDQWHDPSOLR 5DQJR GH WHQVLyQ GLIHUHQFLDO HQWUDGDVDOLGD9DORUHVPtQLPR\Pi[LPRGHOD GLIHUHQFLDGHSRWHQFLDOHQWUHODHQWUDGD\ODVDOLGDSDUDTXHVHFXPSODQODVHVSHFLILFD FLRQHV 5DQJRGHFRUULHQWHGHFDUJD9DORUHVPtQLPR\Pi[LPRGHFRUULHQWHGHFDUJD SDUDORVFXDOHVVHFXPSOHQODVHVSHFLILFDFLRQHV(OYDORUPtQLPRFRUUHVSRQGHQRUPDO PHQWHDODFRUULHQWHQHFHVDULDSDUDPDQWHQHUORVWUDQVLVWRUHVHQVX]RQDOLQHDO$YHFHV VHHVSHFLILFDQSRUVHSDUDGRORVYDORUHVPtQLPR\Pi[LPRGHODFRUULHQWHGHFDUJD 3DUiPHWURVGHHVWDELOLGDG /DWHQVLyQGHVDOLGDRGHFDUJDY/HVXQDIXQFLyQGHODWHQVLyQGHDOLPHQWDFLyQ Y*ODFRUULHQWHGHFDUJDL/\ODWHPSHUDWXUD7 3REODFLyQ HQ HO VHQWLGR HVWDGtVWLFR HV GHFLU HO FRQMXQWR GH WRGDV ODV IXHQWHV UHDO R SRWHQFLDOPHQWH FRQVWUXLGDVEDMRXQPLVPRGLVHxR % )HGHULFR0L\DUD $xR Y / = I Y* L/ 7 3DUDSHTXHxDVGHVYLDFLRQHVGHXQSXQWRGHWUDEDMR9*,/7RHVWDIXQFLyQSXHGHDSUR[L PDUVHOLQHDOPHQWH ∂Y / ∂Y / ∂Y / ∆Y* + ∆L/ + ∆7 Y / ≅ 9/ + ∂L/ ∂7 ∂Y* /DVGHULYDGDVSDUFLDOHV69 ∂Y/∂Y*6, ∂Y/∂L/67 ∂Y/∂7VHGHQRPLQDQIDFWRUHVGH HVWDELOLGDG GH OtQHD GH FDUJD \ GH WHPSHUDWXUD UHVSHFWLYDPHQWH (O IDFWRU ∂Y/∂L/ SXHGHLQWHUSUHWDUVHFRPRODUHVLVWHQFLDGHVDOLGDFDPELDGDGHVLJQR−5R 'HELGRDTXHHVWRVIDFWRUHVGHSHQGHQHQJHQHUDOGHOSXQWRGHRSHUDFLyQHQOX JDUGHHOORVVHVXHOHQHVSHFLILFDUSDUiPHWURVJOREDOHVTXHGHVFULEHQODYDULDFLyQPi[L PDHVSHUDEOHGHQWURGHGHWHUPLQDGRUDQJRGHRSHUDFLyQ7HQHPRVDVtORVSDUiPHWURV VLJXLHQWHV 5HJXODFLyQGHOtQHD3DUDXQGHWHUPLQDGRGLVSRVLWLYRODPi[LPDYDULDFLyQGHOD WHQVLyQGHVDOLGDDQWHYDULDFLRQHVGHODWHQVLyQGHHQWUDGDGHQWURGHXQUDQJRHVSHFLILFD GRPDQWHQLHQGRFRQVWDQWHODFRUULHQWHGHFDUJD\ODWHPSHUDWXUD3XHGHHVSHFLILFDUVHHQ IRUPDDEVROXWDHQ9RP9UHODWLYDDOYDORUQRPLQDOGHVDOLGDHQRUHODWLYDDOYDORU QRPLQDO\DODWHQVLyQGHHQWUDGDHQ9(VWD~OWLPDYHUVLyQHVGHKHFKRXQDIRUPD GHH[SUHVDUODFRWDVXSHULRUGHOIDFWRUGHHVWDELOLGDGGHOtQHDSDUDHOGLVSRVLWLYR&XDQGR VH GHVFULEH XQD SREODFLyQ GH GLVSRVLWLYRV VH VXPLQLVWUDQ ORV YDORUHV PtQLPR WtSLFR \ Pi[LPR(MHPSORV 3DUiPHWUR &RQGLFLRQHV 0tQ 7tS 0i[ 8QLGDG & 7 5HJXODFLyQGHOtQHD ,/ P$ P9 99*9 3DUiPHWUR &RQGLFLRQHV 0tQ 7tS 0i[ 8QLGDG 7 & 5HJXODFLyQGHOtQHD ,/ P$ 99*9 3DUiPHWUR &RQGLFLRQHV 0tQ 7tS 0i[ 8QLGDG 7 & 5HJXODFLyQGHOtQHD ,/ P$ 9 99*9 127$ 8QD YDULDFLyQ GH WHQVLyQ D FRUULHQWH FRQVWDQWH LPSOLFD XQD YDULDFLyQ GH OD SRWHQFLD ∆3 ,∆9 OR FXDO D VXYH]LPSOLFDXQDSRVLEOHYDULDFLyQGHODWHPSHUDWXUD 3DUDHYLWDUORVHXWLOL]DQWpFQLFDVGHSXOVRVFRQVLVWHQWHVHQODDSOLFDFLyQGHOFDPELRGX UDQWHXQWLHPSREUHYHGHORUGHQGHPVGHPRGRGHJDUDQWL]DUTXHSRULQHUFLDWpU PLFDODWHPSHUDWXUDQRYDUtHDSUHFLDEOHPHQWH 7DPELpQVHGHQRPLQDQFRHILFLHQWHVGHUHJXODFLyQGHODWHQVLyQGHVDOLGDFRQUHVSHFWRDODWHQVLyQGH HQWUDGDODFRUULHQWHGHFDUJD\ODWHPSHUDWXUDUHVSHFWLYDPHQWH % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV 127$&XDQGRODUHJXODFLyQGHOtQHDVHH[SUHVDHQP9SRGUtDHVWLPDUVHHOIDFWRUGH HVWDELOLGDGGLYLGLHQGRSRUODYDULDFLyQWRWDOGHODWHQVLyQGHHQWUDGD$VtHQHOHMHPSOR SUHFHGHQWH SRGUtD REWHQHUVH 69≅P99−9 P99 6LQ HPEDUJR HVWHYDORUHVVyORXQSURPHGLR\QRKD\QLQJXQDJDUDQWtDGHTXHODYDULDFLyQVHDOLQHDO 3RGUtD RFXUULU TXH SDUD GHWHUPLQDGRV SXQWRV GH RSHUDFLyQ HO IDFWRU GH HVWDELOLGDG VHD PD\RUSRUORFXDOGHEHREUDUVHFRQSUHFDXFLyQ3RGUtDWRPDUVHXQFRHILFLHQWHGHVHJX ULGDGGH 127$$XQTXHSDUDXQGLVSRVLWLYRHVWHSDUiPHWURGHEHPHGLUVHDWHPSHUDWXUDFRQV WDQWH\DFRUULHQWHFRQVWDQWHDYHFHVVHGDXQDFRWDSDUDWRGRHOUDQJRGHWHPSHUDWXUD \RGHFRUULHQWHGHFDUJD6LQHPEDUJRQRGHEHFRQIXQGLUVHHVWHYDORUFRQODYDULDFLyQ WRWDOLQFOXLGRVORVHIHFWRVGHODWHPSHUDWXUD\GHODFRUULHQWHGHFDUJD6LJQLILFDODYD ULDFLyQPi[LPDGHELGDDODWHQVLyQGHHQWUDGDSDUDFXDOTXLHUWHPSHUDWXUD\RFXDOTXLHU FRUULHQWHGHFDUJDILMDHQHOUDQJRGHRSHUDFLyQDGPLVLEOH1DWXUDOPHQWHHVWHYDORUHV SRWHQFLDOPHQWHPD\RUTXHHOTXHFRUUHVSRQGHDXQDWHPSHUDWXUD\XQDFRUULHQWHGHFDU JDHVSHFLILFDGDV 5HJXODFLyQGHFDUJD3DUDXQGHWHUPLQDGRGLVSRVLWLYRODPi[LPDYDULDFLyQGHOD WHQVLyQGHVDOLGDDQWHYDULDFLRQHVGHODFRUULHQWHGHFDUJDGHQWURGHXQUDQJRHVSHFLIL FDGRPDQWHQLHQGRFRQVWDQWHODWHQVLyQGHHQWUDGD\ODWHPSHUDWXUD3XHGHHVSHFLILFDUVH HQIRUPDDEVROXWDHQ9RP9RUHODWLYDHQ&XDQGRVHGHVFULEHXQDSREODFLyQGH GLVSRVLWLYRVVHVXPLQLVWUDQORVYDORUHVPtQLPRWtSLFR\Pi[LPR3RUHMHPSOR 3DUiPHWUR &RQGLFLRQHV 0tQ 7tS 0i[ 8QLGDG 7 & 5HJXODFLyQGHFDUJD 9* 9 P9 P$,/$ 3DUiPHWUR &RQGLFLRQHV 0tQ 7tS 0i[ 8QLGDG 7 & 5HJXODFLyQGHFDUJD 9* 9 P$,/$ 127$(QIRUPDDQiORJDDOFDVRGHODUHJXODFLyQGHOtQHDVHXWLOL]DQDTXtWpFQLFDVGH SXOVRVEUHYHVGHFRUULHQWHSDUDPHGLUODUHJXODFLyQGHFDUJD 127$6HSXHGHDSUR[LPDUHOIDFWRUGHHVWDELOLGDGGHFDUJDGLYLGLHQGRODUHJXODFLyQ GHFDUJDHQP9SRUODYDULDFLyQWRWDOGHFRUULHQWH6,≅P9$ P9$(O YDORUREWHQLGRHVXQSURPHGLRTXHSRGUtDVXEHVWLPDUHOYHUGDGHURYDORUSDUDGHWHUPL QDGDVFRQGLFLRQHVGHFDUJD 127$7DPELpQDTXtVXHOHQGDUVHFRWDVSDUDWHPSHUDWXUDV\RWHQVLRQHVGHHQWUDGD GHQWUR GHO UDQJR DGPLVLEOH GH IXQFLRQDPLHQWR VLQ TXH UHSUHVHQWHQ OD YDULDFLyQ WRWDO VLQRVyORODGHELGDDYDULDFLRQHVGHODFRUULHQWHGHFDUJD 127$ /D YHUVLyQ UHODWLYD SRUFHQWXDO VH XWLOL]D HQ JHQHUDO HQ ORV UHJXODGRUHV GH WHQVLyQGHVDOLGDDMXVWDEOH % )HGHULFR0L\DUD $xR 5HJXODFLyQWpUPLFD(VODYDULDFLyQSRUFHQWXDOGHODWHQVLyQGHVDOLGDDQWHXQLQ FUHPHQWRGH:GHSRWHQFLDGXUDQWHXQWLHPSRHVWDEOHFLGRHQJHQHUDOSHTXHxRSRU HMHPSORPV6HH[SUHVDHQ: (VWDELOLGDG WpUPLFD (V OD Pi[LPDYDULDFLyQSRUFHQWXDOGHODWHQVLyQGHVDOLGD FRQUHVSHFWRDODWHQVLyQTXHVHWLHQHDWHPSHUDWXUDDPELHQWH&FXDQGRODWHPSH UDWXUDYDUtDHQWRGRHOUDQJRRSHUDWLYR 3DUiPHWURVGHVHJXULGDG 7HQVLyQ GH HQWUDGD Pi[LPD DEVROXWD 0i[LPR YDORU GH OD WHQVLyQ GH HQWUDGD EDMRFXDOTXLHUFRQGLFLyQPiVDOOiGHOFXDOHOUHJXODGRUSXHGHGDxDUVHRGHVWUXLUVH$XQ TXHSXHGHFRLQFLGLUFRQHOYDORUPi[LPRGHOUDQJRGHHQWUDGDHQDOJXQRVFDVRVHVPD \RUTXHpVWH1RREVWDQWHSRVLEOHPHQWHDOJXQDVHVSHFLILFDFLRQHVGHMHQGHFXPSOLUVH 7HQVLyQGLIHUHQFLDOPi[LPDDEVROXWD0i[LPRYDORUGHODGLIHUHQFLDGHSRWHQ FLDOHQWUHODHQWUDGD\ODVDOLGDPiVDOOiGHOFXDOHOUHJXODGRUSXHGHGDxDUVHRGHVWUXLUVH /tPLWHGHFRUULHQWH3DUDXQGHWHUPLQDGRGLVSRVLWLYRHVODPi[LPDFRUULHQWHTXH HOPLVPRHQWUHJDUiDODFDUJDEDMRFRQGLFLRQHVHVSHFtILFDVSRUHMHPSORWHPSHUDWXUDR UDQJRGHWHPSHUDWXUDVWHQVLyQGLIHUHQFLDOHQWUDGDVDOLGD(VWHSDUiPHWURFRUUHVSRQGHD ORV UHJXODGRUHV TXH SRVHHQ SURWHFFLyQ FRQWUD VREUHFRUULHQWH \R VREUHWHPSHUDWXUD 1RUPDOPHQWHH[FHGHHOUDQJRGHFRUULHQWHGHFDUJDSRUORFXDOGHMDQGHFXPSOLUVHODV HVSHFLILFDFLRQHV3DUWLFXODUPHQWHODIXHQWHSDVDDFRPSRUWDUVH FRPRXQDIXHQWHGHFR UULHQWHSRUORFXDOODWHQVLyQGHVDOLGDGHMDGHHVWDUUHJXODGD 127$(QORVUHJXODGRUHVFRQSURWHFFLyQWpUPLFDHOOtPLWHGHFRUULHQWHGHSHQGHIXHU WHPHQWHGHODWHQVLyQGLIHUHQFLDOHQWUDGDVDOLGD &RUULHQWHPi[LPDGHFDUJD3DUDXQUHJXODGRUVLQSURWHFFLyQSRUVREUHFRUULHQ WHHVODPi[LPDFRUULHQWHTXHVHOHSXHGHH[LJLUVLQULHVJRGHGDxDURGHVWUXLUHOUHJXOD GRU /tPLWHGHSRWHQFLD3DUDXQGHWHUPLQDGRGLVSRVLWLYRHVODPi[LPDSRWHQFLDTXH HOPLVPRGLVLSDUiEDMRFRQGLFLRQHVHVSHFtILFDVSRUHMHPSORWHPSHUDWXUDDPELHQWHWHQ VLyQGLIHUHQFLDOHWF(VWHSDUiPHWURFRUUHVSRQGHDUHJXODGRUHVTXHSRVHHQSURWHFFLyQ WpUPLFDRGHiUHDGHRSHUDFLyQVHJXUD 3RWHQFLD Pi[LPD 0i[LPD SRWHQFLD TXH HV SRVLEOH KDFHU GLVLSDU DO GLVSRVLWLYR VLQ TXH HO PLVPR VH GHWHULRUH R GHVWUX\D 6H DSOLFD D UHJXODGRUHV VLQ XQD SURWHFFLyQ WpUPLFDLQWUtQVHFD 5DQJRGHWHPSHUDWXUD/tPLWHVLQIHULRU\VXSHULRUGHWHPSHUDWXUD6HVXHOHQHV SHFLILFDU GRV UDQJRV HO RSHUDWLYR SDUD HO FXDO YDOHQ ODV HVSHFLILFDFLRQHV TXH FRUUHV SRQGDQODVTXHVHGDQSDUDHOUDQJRFRPSOHWR\HOGHDOPDFHQDPLHQWRGHQWURGHOFXDO HOGLVSRVLWLYRQRFRUUHULHVJRGHGHJUDGDFLyQRGHVWUXFFLyQSHURHQHOFXDOQRHVSRVLEOH JDUDQWL]DUHOIXQFLRQDPLHQWRFRUUHFWR % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV 5HVLVWHQFLDWpUPLFD'LIHUHQFLDWpUPLFRHQWUHHOVHPLFRQGXFWRUGHVFULSWRFRPR MXQWXUD \ XQ SXQWR H[WHULRU HVSHFLILFDGR HQ JHQHUDO OD VXSHUILFLH GH OD FiSVXOD R HO DPELHQWH GLYLGLGD SRU OD SRWHQFLD GLVLSDGD /D UHVLVWHQFLD WpUPLFD MXQWXUDDPELHQWH VyOR HV ~WLOFXDQGRVHWUDEDMDVLQGLVLSDGRU3DUDWUDEDMDUFRQXQGLVLSDGRUVHUHTXLHUH FRQRFHUODUHVLVWHQFLDWpUPLFDMXQWXUDFiSVXOD 3DUiPHWURVGHYDULDFLyQSHULyGLFD\DOHDWRULD /DHFXDFLyQSXHGHDPSOLDUVHSDUDLQFOXLUYDULDFLRQHVSHULyGLFDV\DOHDWRULDVGH ODWHQVLyQGHVDOLGDHIHFWRVTXHVHVXSHUSRQHQDODVYDULDFLRQHVSRUFRQGLFLRQHVRSHUD WLYDV Y / = I Y* L/ 7 + Y S + YD + YG /DFRPSRQHQWHSHULyGLFDYSFRUUHVSRQGHDOULSSOHUL]DGR\HQJHQHUDOVHGHEHDOILOWUD GR LQVXILFLHQWH GHO SURFHVR GH UHFWLILFDFLyQ DXQTXH HQ ODV IXHQWHV FRQPXWDGDV SXHGH GHEHUVHWDPELpQDUHVLGXRVGHODSURSLDFRQPXWDFLyQ/DWHQVLyQDOHDWRULDYDSURYLHQH GHODVIXHQWHVGHUXLGRLQWHUQDVGHORVFRPSRQHQWHVGHODIXHQWH/DWHQVLyQYGFRUUHV SRQGHDGHULYDVDODUJRSOD]R )DFWRUGHUHFKD]RDULSSOH(VHOFRFLHQWHHQWUHORVYDORUHVHILFDFHVGHODWHQVLyQ GH ULSSOH D OD HQWUDGD \ D OD VDOLGD D SDUWLU GH XQD IUHFXHQFLD HVSHFLILFDGD H[SUHVDGR ORJDUtWPLFDPHQWHHQG%1RUPDOPHQWHODIUHFXHQFLDVHHVSHFLILFDFRPRHOGREOHGHOD IUHFXHQFLD GH OD OtQHD GH GLVWULEXFLyQ GH HQHUJtD HOpFWULFD +] y +] FRUUHV SRQGLHQGRDXQDUHFWLILFDFLyQGHRQGDFRPSOHWD 127$(OUHFKD]RDULSSOHSXHGHPHMRUDUVHFRQXQFDSDFLWRUGHE\SDVVXELFDGRHQWUH GRVSXQWRVHVSHFLILFDGRVSRUORTXHODHVSHFLILFDFLyQGHEHLQGLFDUVLVHXVDRQRGLFKR FDSDFLWRU\HQWDOFDVRVXYDORU (VWDELOLGDGDODUJRSOD]R0i[LPDYDULDFLyQGHODWHQVLyQGHVDOLGDOXHJRGHXQ WLHPSRHVSHFLILFDGRGHIXQFLRQDPLHQWRFRQWLQXRHQJHQHUDOKDXQDWHPSHUDWXUD HVSHFLILFDGD HQ JHQHUDO & 3XHGHH[SUHVDUVHHQIRUPDDEVROXWDHQ9RP9R UHODWLYDDODWHQVLyQQRPLQDOGHVDOLGDHQ 127$(QDOJXQRVFDVRVVHODHVSHFLILFDHQNKRP9NK6LQHPEDUJRHVWDIRUPDGH H[SUHVDUOD HV LQFRUUHFWD GDGR TXH HO HIHFWR QR HV SURSRUFLRQDO DO WLHPSR VLQR TXH HV PiVELHQXQDYDULDFLyQDOHDWRULDPX\OHQWD(OHQVD\RVHUHDOL]DGXUDQWHXQWLHPSRSUR ORQJDGR\DTXHDODXPHQWDUODPXHVWUDDXPHQWDODSUREDELOLGDGGHHQFRQWUDUYDULDFLRQHV PD\RUHV 7HQVLyQGHUXLGRDODVDOLGD9DORUHILFD]GHOUXLGRDODVDOLGDHQXQDEDQGDGH IUHFXHQFLDVHVSHFLILFDGDFRQXQDFDUJDFRQVWDQWH\HQDXVHQFLDGHULSSOH3XHGHH[SUH VDUVHHQIRUPDDEVROXWDHQ9RP9RUHODWLYDDODWHQVLyQQRPLQDOGHVDOLGDHQ 127$ (Q DOJXQRV FDVRV YHU SRU HMHPSOR HO UHJXODGRU /0 VH VXPLQLVWUD XQD JUiILFDFRQODGHQVLGDGHVSHFWUDOGHODWHQVLyQGHUXLGRH[SUHVDGDFRPRVXUDt]FXDGUD GDORFXDOSHUPLWHREWHQHUHOUXLGRHQRWUDVEDQGDVGLIHUHQWHVGHODHVSHFLILFDGD % )HGHULFR0L\DUD $xR 3DUiPHWURVWUDQVLWRULRV 7LHPSR GH FDOHQWDPLHQWR 7LHPSR UHTXHULGR GHVSXpV GHO HQFHQGLGR HQHUJL]D FLyQSDUDDOFDQ]DUWRGDVODVHVSHFLILFDFLRQHV 7LHPSRGHUHFXSHUDFLyQ7LHPSRUHTXHULGRGHVSXpVGHXQFDPELREUXVFRGHFR UULHQWH GH FDUJD SDUD TXH OD VDOLGD UHWRUQH GHILQLWLYDPHQWH D VXYDORURULJLQDOFRQXQD GDGDWROHUDQFLDTXHSRGUiH[SUHVDUVHHQP9RHQ 127$/DWROHUDQFLDGHEHVHUPD\RUTXHHOFDPELRHVSHUDEOHGHELGRDODUHJX ODFLyQGHFDUJDGHORFRQWUDULRHOWLHPSRGHUHFXSHUDFLyQVHUtDLQILQLWR 127$(OWLHPSRGHFUHFLPLHQWRRGHFUHFLPLHQWRGHOFDPELRGHFRUULHQWHGHEH VHUPiVFRUWRTXHHOYDORUHVSHUDEOHGHOWLHPSRGHUHFXSHUDFLyQ 3DUiPHWURV\HVSHFLILFDFLRQHVGHOUHJXODGRUGHFRUULHQWH 3DUDORVUHJXODGRUHVGHFRUULHQWHVHDSOLFDQFRQVLGHUDFLRQHVVLPLODUHVDODVGHORV UHJXODGRUHVGHWHQVLyQ6yORGHVFULELUHPRVDOJXQRVSDUiPHWURVHVSHFtILFRVSDUDORVUH JXODGRUHVGHFRUULHQWH\DTXHPXFKRVRWURVSDUiPHWURVSRUHMHPSORODWHQVLyQGHHQ WUDGDVRQVLPLODUHVDORV\DYLVWRV 3DUiPHWURVEiVLFRV &RUULHQWHQRPLQDOGHVDOLGD(VHOYDORUGHFRUULHQWHDVRFLDGRDXQPRGHORGH IXHQWH1RQHFHVDULDPHQWHFRLQFLGHFRQHOYDORUGHFRUULHQWHUHDOPHQWHREWHQLGRHQXQD GHWHUPLQDGDFRQGLFLyQDXQTXHGHEHUtDVHUSUy[LPRDDTXpO(VHOSDUiPHWURIXQGDPHQ WDOGHVHOHFFLyQGHXQDIXHQWHGHFRUULHQWHSDUDXQDGDGDDSOLFDFLyQ 5DQJRGHFRUULHQWHGHVDOLGD3DUDXQUHJXODGRUGHFRUULHQWHDMXVWDEOHHVHOUDQ JRGHYDORUHVDOFDQ]DEOHVGHFRUULHQWHQRPLQDOGHVDOLGD &RUULHQWHGHVDOLGD3DUDXQGHWHUPLQDGRGLVSRVLWLYRHVHOYDORUGHFRUULHQWHGH VDOLGDHQXQDFRQGLFLyQHVSHFtILFDGHRSHUDFLyQSRUHMHPSORXQDGHWHUPLQDGDWHPSHUD WXUD WHQVLyQ GH HQWUDGD \ WHQVLyQ HQ OD FDUJD 3DUD XQD SREODFLyQ GH GLVSRVLWLYRV VH SXHGHQGDUORVYDORUHVPtQLPRWtSLFR\Pi[LPR(QDOJXQRVFDVRVORVYDORUHVPtQLPR \ Pi[LPR VH GDQ HQ IRUPD GH WROHUDQFLD SRUFHQWXDO FRQ UHVSHFWR DO YDORU QRPLQDO (O YDORU WtSLFR HV QRUPDOPHQWH HO YDORU PHGLR GH OD SREODFLyQ \ DXQTXH HV SUy[LPR DO YDORUQRPLQDOQRQHFHVDULDPHQWHFRLQFLGHFRQpVWH &RPSOLDQFLD R UDQJR GH WHQVLRQHV HQ OD FDUJD 9DORUHV PtQLPR \ Pi[LPR GH WHQVLyQ HQ OD FDUJD SDUD ORV FXDOHV VH FXPSOHQ ODV HVSHFLILFDFLRQHV (O YDORU PtQLPR FRUUHVSRQGHQRUPDOPHQWHDODFRQGLFLyQGHFRUWRFLUFXLWR(OYDORUPi[LPRVXHOHHVWDU FRQGLFLRQDGRSRUODWHQVLyQGHHQWUDGD$YHFHVVHHVSHFLILFDQSRUVHSDUDGRORVYDORUHV PtQLPR\Pi[LPR % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV 3DUiPHWURVGHHVWDELOLGDG /DFRUULHQWHGHVDOLGDRGHFDUJDL/HVXQDIXQFLyQGHODWHQVLyQGHDOLPHQWDFLyQ Y*ODWHQVLyQHQODFDUJDY/\ODWHPSHUDWXUD7 L/ = I Y* Y / 7 3DUD SHTXHxDV GHVYLDFLRQHV GH XQ SXQWR GH WUDEDMR 9* 9/ 7R HVWD IXQFLyQ SXHGH DSUR[LPDUVHOLQHDOPHQWH L/ ≅ ,/ + ∂L/ ∂L/ ∂L ∆Y* + ∆Y / + / ∆7 ∂Y* ∂Y / ∂7 /DVGHULYDGDVSDUFLDOHV∂L/∂Y*∂L/∂Y/∂L/∂7VHGHQRPLQDQIDFWRUHVGHHVWDELOLGDGGH OtQHDGHFDUJD\GHWHPSHUDWXUDUHVSHFWLYDPHQWH(OIDFWRU∂L/∂Y/SXHGHLQWHUSUHWDUVH FRPRODFRQGXFWDQFLDGHVDOLGDFDPELDGDGHVLJQR−*R ,JXDOTXHHQHOFDVRGHORVUHJXODGRUHVGHWHQVLyQHVWRVIDFWRUHVVXHOHQGHSHQGHU GHOSXQWRGHRSHUDFLyQ(QOXJDUGHHOORVVHSXHGHQHVSHFLILFDUSDUiPHWURVJOREDOHVTXH GHVFULEHQODYDULDFLyQPi[LPDHVSHUDEOHGHQWURGHGHWHUPLQDGRUDQJRGHRSHUDFLyQ3RU HMHPSOR VH SXHGHQ GDU ODV FRWDV GHO IDFWRU GH HVWDELOLGDG GH OtQHD SDUD WRGR HO UDQJR DGPLVLEOHGHWHPSHUDWXUD(OORQRVLJQLILFDTXHDGHPiVGHODWHQVLyQGHHQWUDGDVHKDJD YDULDUODWHPSHUDWXUDVLQRTXHVHPLGHHOIDFWRUGHHVWDELOLGDGGHOtQHDSDUDYDULDVWHP SHUDWXUDVILMDV\OXHJRVHGHWHUPLQDQORVYDORUHVH[WUHPRV 'DGRTXHORVUHJXODGRUHVGHFRUULHQWHVRQPHQRVIUHFXHQWHVTXHORVGHWHQVLyQQR HQWUDUHPRVHQPiVGHWDOOHV /LPLWDFLRQHVGHOUHFWLILFDGRUFRPRUHJXODGRUGH WHQVLyQ $QWHVGHHVWXGLDUGLYHUVRVHVTXHPDV GH UHJXODGRUHV LQYHVWLJDUHPRVEUHYHPHQWH ODVOLPLWDFLRQHVTXHH[KLEHQORVUHFWLILFDGRUHVHQVXIXQFLRQDOLGDGFRPRUHJXODGRUHVGH WHQVLyQ&RQVLGHUHPRVXQUHFWLILFDGRUGHRQGDFRPSOHWDFRQILOWURFDSDFLWLYR\XQDFDU JDUHVLVWLYDYDULDEOH(QODILJXUDVHPXHVWUDODIRUPDGHRQGDGHODVHQRLGDOUHFWLILFD GD\GHODVDOLGDFRQGLYHUVDVUHVLVWHQFLDV 5SHTXHxD 5PHGLD Y 5JUDQGH W )LJXUD)RUPDGHRQGDGHODVDOLGDGHXQUHFWLILFDGRUGHRQGDFRP SOHWDFRQILOWURFDSDFLWLYRSDUDGLYHUVDVUHVLVWHQFLDVGHFDUJD 3DUDEDMDVFRUULHQWHVGHFDUJDVHSXHGHDSUR[LPDUHOYDORUPHGLRGHODWHQVLyQSRU 7DPELpQVHGHQRPLQDQFRHILFLHQWHVGHUHJXODFLyQGHODFRUULHQWHGHVDOLGDFRQUHVSHFWRDODWHQVLyQ GHHQWUDGDODWHQVLyQHQODFDUJD\ODWHPSHUDWXUDUHVSHFWLYDPHQWH % )HGHULFR0L\DUD $xR 9PHG 7 ≅ 9S − 5& GRQGH9SHVODWHQVLyQGHSLFR7HVHOSHULRGR&HOFDSDFLWRUGHOILOWUR\5ODUHVLVWHQFLD GHFDUJD3RGHPRVH[SUHVDUHVWD~OWLPDHQWpUPLQRVGHODFRUULHQWHPHGLDFRPR 9PHG , PHG 5 = 6XVWLWX\HQGRHQODDQWHULRUSRGHPRVGHVSHMDU9PHGHQIXQFLyQGH,PHGUHVXOWDQGR , 9S + 9S − PHG 79S & 9PHG ≅ $VXYH]SRGHPRVDSUR[LPDUGDGRTXHVXSRQHPRV,PHGSHTXHxDSRU 9PHG ≅ 9S − , PHG 7 & &RQ VLPLODUHVUD]RQDPLHQWRVVHREWLHQHODVLJXLHQWHDSUR[LPDFLyQGHOIDFWRUGHULSSOH SDUDSHTXHxDVFRUULHQWHVGHFDUJD )5 ≅ 9S − , PHG 1RHVSRVLEOHREWHQHUUHODFLRQHVH[SOtFLWDVSDUDWRGRVORVYDORUHVSRVLEOHVGH,PHGSHUR VHSXHGHDSUR[LPDUQXPpULFDPHQWHREWHQLpQGRVHODVJUiILFDVGHODILJXUDSDUDHOYD ORUPHGLRHOYDORUHILFD]GHOULSSOH\HOIDFWRUGHULSSOH 9PHG9S π )5 π − 9ULSSOH9S − π ,PHG )LJXUD'HSHQGHQFLDGHODWHQVLyQPHGLDGHVDOLGDGHOULSSOH\GHO IDFWRUGHULSSOHGHXQUHFWLILFDGRUGHRQGDFRPSOHWDFRQILOWURHQIXQ FLyQ GH OD FRUULHQWH GH FDUJD /D WHQVLyQ HILFD] GHO ULSSOH \ HO YDORU PHGLRVHQRUPDOL]DURQFRQUHVSHFWRDODWHQVLyQGHSLFR % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV 9HPRVTXHHOUHFWLILFDGRUGHRQGDFRPSOHWDGLVWDGHFRPSRUWDUVHFRPRXQUHJX ODGRUGHWHQVLyQ\DTXHQRVyORVXWHQVLyQPHGLDGHSHQGHGLUHFWDPHQWHGHODDOLPHQWD FLyQVLQRTXHDGHPiVGHSHQGHGHODFRUULHQWHGHFDUJD6yORSDUDFRQVXPRVPX\EDMRV HOIDFWRUGHULSSOHOOHJDDVHUDFHSWDEOHPHQWHEDMR 1RREVWDQWHORVUHFWLILFDGRUHVFRQILOWURVRQPX\XWLOL]DGRVFRPRIXHQWHVGHDOL PHQWDFLyQGHUHJXODGRUHVFRQPHMRUHVSUHVWDFLRQHV\DTXHSHUPLWHQXQDDFHSWDEOHFRQ YHUVLyQ GH OD FRUULHQWH DOWHUQD SURYHQLHQWH GH XQ WUDQVIRUPDGRU HQ FRUULHQWH FRQWLQXD /DVYDULDFLRQHVGHODWHQVLyQPHGLDDVtFRPRHOIDFWRUGHULSSOHVHUiQPX\DWHQXDGRV SRUHOUHJXODGRUGHWHQVLyQ 5HJXODGRUHVGHWHQVLyQ &RPRVHYLRH[LVWHQGRVWLSRVGHUHJXODGRUHVOLQHDOHVGHWHQVLyQUHJXODGRUHVVH ULH\SDUDOHOR/RVUHJXODGRUHVVHULHVHFDUDFWHUL]DQSRUWHQHUHOGLVSRVLWLYRGHSRWHQFLD HQJHQHUDOXQWUDQVLVWRUHQVHULHFRQODFDUJDPLHQWUDVTXHHQORVUHJXODGRUHVSDUDOHOR GLFKRGLVSRVLWLYRHVWiHQSDUDOHORFRQODFDUJD 5HJXODGRUHVGHWHQVLyQVHULH (QODILJXUDVHPXHVWUDHVTXHPiWLFDPHQWHODHVWUXFWXUDGHXQUHJXODGRUVHULH(O HOHPHQWRGHSRWHQFLDWDPELpQOODPDGRHOHPHQWRGHSDVRQRUPDOPHQWHHVXQWUDQVLVWRU RXQSDU'DUOLQJWRQ/DUHIHUHQFLDHVXQDIXHQWHGHWHQVLyQSUHIHUHQWHPHQWHHVWDELOL]D GDHQWHPSHUDWXUD\HOEORTXHGHFRQWUROHVWiIRUPDGRSRUXQDUHGGHVHQVDGRXQFRP SDUDGRU\XQH[FLWDGRUSDUDHOHOHPHQWRGHSRWHQFLD(VHQFLDOPHQWHVHWUDWDGHXQVLVWH PDUHDOLPHQWDGRFX\DHQWUDGDHVODWHQVLyQGHUHIHUHQFLD L* (OHPHQWR GHSRWHQFLD Y* 5HIHUHQFLD &RQWURO − L/ &DUJD Y/ − )LJXUD'LDJUDPDGHEORTXHVGHXQUHJXODGRUVHULHGHWHQVLyQ 5HQGLPLHQWRGHXQUHJXODGRUVHULH 7HQLHQGRHQFXHQWDTXHODFRUULHQWHDEVRUELGDSRUODIXHQWHGHUHIHUHQFLD\SRUHO EORTXHGHFRQWUROHVPXFKRPHQRUTXHODFRUULHQWHGHFDUJDUHVXOWD L* ≅ L / % )HGHULFR0L\DUD $xR GHGRQGHSRGHPRVDSUR[LPDUHOUHQGLPLHQWRGHOUHJXODGRUVHULHSRU 3 L Y Y/ ηVHULH = / = / / ≅ 3/ L* Y * Y* 'HHVWDHFXDFLyQVHGHVSUHQGHTXHORVPD\RUHVUHQGLPLHQWRVVHORJUDUiQFXDQGRY/VHD FHUFDQRDY*6LQHPEDUJRHQJHQHUDOH[LVWHQGRVLPSHGLPHQWRVSDUDHOOR(OSULPHUR HVTXHHOHOHPHQWRGHSDVRUHTXLHUHFLHUWDWHQVLyQPtQLPDSDUD IXQFLRQDUOLQHDOPHQWH (OVHJXQGRTXHODWHQVLyQGHHQWUDGDYDUtDSRUWROHUDQFLD\GHULYDVSRUORFXDOHOUHQ GLPLHQWRHPSHRUDFXDQGRpVWDDXPHQWD9HUHPRVOXHJRFULWHULRVGHVHOHFFLyQGHODWHQ VLyQGHHQWUDGDTXHSHUPLWHQRSWLPL]DUHOUHQGLPLHQWR 5HJXODGRUHVVHULHGLVFUHWRV (QODILJXUDVHPXHVWUDODIRUPDPiVVLPSOHGHXQUHJXODGRUGHWHQVLyQHQVHULH FRQGLVSRVLWLYRVGLVFUHWRV(QpO7HVHOHOHPHQWRGHSDVR9]ODWHQVLyQGHUHIHUHQFLD\ 5EHVHOHOHPHQWRGHFRQWURO(QHVWHFDVRHOVHQVDGR\ODFRPSDUDFLyQWDPELpQHVWiQD FDUJR GHO WUDQVLVWRU GH SDVR (O FLUFXLWR SXHGH SHQVDUVH FRPR XQ VHJXLGRU SRU HPLVRU DSOLFDGRDODWHQVLyQGHXQ]HQHU L* L/ 7 5E Y* 5/ Y/ 9] − − )LJXUD8QUHJXODGRUVHULHVHQFLOOR /DWHQVLyQGHVDOLGDSXHGHFDOFXODUVHFRPR Y / = 9] − Y %( 'HVSUHFLDQGRODSRWHQFLDHQHOFLUFXLWRGHEDVHODSRWHQFLDGLVLSDGDHQHOWUDQVLVWRUHV 37 = Y* − Y / L/ FX\RYDORUPi[LPRUHVXOWD 37 Pi[ = Y* Pi[ − Y / PtQ L/ Pi[ 3DUDXQUHJXODGRUGHWHQVLyQFRQVWDQWHQRDMXVWDEOHODWHQVLyQGHFDUJDPtQLPDSXHGH HQJHQHUDOFRQVLGHUDUVHLJXDODODWHQVLyQQRPLQDOGHVDOLGD % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV Y /PtQ =9/ 127$(VWHFLUFXLWRQRSRVHHSURWHFFLyQQLQJXQDSRUORFXDODQWHXQFRUWRFLUFXLWRDOD VDOLGDODFRUULHQWHSXHGHFUHFHUFRQVLGHUDEOHPHQWH /D UHVLVWHQFLD 5E GHEH VHU FDSD] GH SURYHHU FRPR PtQLPR OD FRUULHQWH GH EDVH GHOWUDQVLVWRUDSOHQDFDUJDHVGHFLUL/Pi[K)(PiVODPtQLPDFRUULHQWHUHTXHULGD SRUHO]HQHUSDUDUHJXODU(OORGHEHVXFHGHULQFOXVRFXDQGRODWHQVLyQGHHQWUDGDHVPt QLPDGHGRQGH 5E Y* PtQ − 9] < L/ Pi[ K)( PtQ + + L] PtQ 6HKDVXSXHVWRDVLPLVPRHOPtQLPRYDORUGHK)(\DTXHHVHOFDVRHQTXH5EGH EH VXPLQLVWUDUPD\RUFRUULHQWH'HELGR D TXH SDUD XQ WUDQVLVWRUGHSRWHQFLD K)(QRHV PX\HOHYDGRODUHVLVWHQFLD5EUHVXOWDUHODWLYDPHQWHEDMD&XDQGRODWHQVLyQGHHQWUDGD DXPHQWDODFRUULHQWHSRU5EDXPHQWDUi6LODFRUULHQWHGHFDUJDQRFDPELDWDPSRFROR KDUiODFRUULHQWHGHEDVHSRUORFXDOODFRUULHQWHH[WUDFLUFXODUiSRUHO]HQHU'HKHFKR ODFRUULHQWHSRUHO]HQHUHVWiGDGDSRU L] = Y * − 9] 5E − L/ K)( + (OSHRUFDVRVHGDFXDQGRODWHQVLyQGHHQWUDGDHVPi[LPD\ODFRUULHQWHGHFDUJDQXOD RGHVSUHFLDEOH L] Pi[ = Y*Pi[ − 9] 5E 7HQLHQGRHQFXHQWDODGHVLJXDOGDGVHREWLHQHODFRWD L] Pi[ ≥ Y*Pi[ − 9] L/ Pi[ + L] PtQ Y*PtQ − 9] K)( PtQ + (VWDFRUULHQWHSXHGHVHUFRQVLGHUDEOHREOLJDQGRDVREUHGLPHQVLRQDUHOGLRGR]HQHUWDQ WRHQFRUULHQWHFRPRHQSRWHQFLD $GHPiVGHORDQWHULRUHOFLUFXLWRDQDOL]DGRSUHVHQWDRWURVLQFRQYHQLHQWHV(OSUL PHURHVTXHODWHQVLyQGHVDOLGDQRSXHGHHOHJLUVHDUELWUDULDPHQWHVLQRTXHTXHGDFRQ GLFLRQDGDSRUORVYDORUHVGHWHQVLyQGH]HQHUGLVSRQLEOHVFRPHUFLDOPHQWH(OVHJXQGR HVTXHODUHJXODFLyQGHFDUJDHVSRFRVDWLVIDFWRULD\DTXHDOYDULDUODFRUULHQWHGHFDUJD YDUtD OD WHQVLyQ EDVHHPLVRU TXH DIHFWD GLUHFWDPHQWH D OD WHQVLyQ GH VDOLGD 8Q WHUFHU SUREOHPDHVTXHHO]HQHUSRVHHXQFRHILFLHQWHGHWHPSHUDWXUDQRQXORH[FHSWRSDUDWHQ VLRQHVFHUFDQDVD9YHUILJXUDSRUORFXDOVyORSDUDXQDWHQVLyQHVSHFtILFDVHOR JUDUtDXQDDFHSWDEOHHVWDELOLGDGWpUPLFD3RU~OWLPRODUHJXODFLyQGHOtQHDWDPELpQHV SREUH GDGR TXH ODV YDULDFLRQHV GH WHQVLyQ GH HQWUDGD SURYRFDQ YDULDFLRQHV HQ OD FR /RVYDORUHVWtSLFRVVRQGHORUGHQGH 6L ELHQ H[LVWHQ GLRGRV ]HQHU GH SRWHQFLD ORV PLVPRV VRQ PiV FRVWRVRV TXH XQ WUDQVLVWRU GH VLPLODU GLVLSDFLyQ % )HGHULFR0L\DUD $xR ∆9]9]∆7>&@ UULHQWHSRUHO]HQHUFRPRVHGHVSUHQGHGHODHFXDFLyQ\pVWDVVHWUDGXFHQHQYDULD FLRQHVGHY] − − 9]>9@ )LJXUD&RHILFLHQWHGHWHPSHUDWXUDGHXQGLRGR]HQHUHQIXQFLyQGH ODWHQVLyQGHUXSWXUD(OYDORUGH9]VHPLGHDP$0LOOPDQ\+DO NLDV 8QVHJXQGRFLUFXLWRGHUHJXODGRUVHULHHVHOTXHVHLOXVWUDHQODILJXUD(QpOVH KDDJUHJDGRXQVHJXQGRWUDQVLVWRU\VHKDGHVSOD]DGRHO]HQHUKDFLDHOFLUFXLWRGHEDVH GHpVWH L* L/ 7 5 E 9] Y* 5/ Y/ 7 5] − − )LJXUD8QUHJXODGRUVHULHFRQXQDHWDSDDGLFLRQDOGHJDQDQFLD (QHVWHFDVRODWHQVLyQGHVDOLGDHVWiGDGDSRU Y / = 9] + Y %( (VWRVXSRQHDOJXQDVYHQWDMDVFRQUHVSHFWRDOFLUFXLWRDQWHULRU(QHIHFWRODWHQVLyQGH VDOLGD\DQRGHSHQGHGLUHFWDPHQWHGHODWHQVLyQEDVHHPLVRUGHXQWUDQVLVWRUGHSRWHQFLD VLQRGHODGHXQWUDQVLVWRUPiVSHTXHxRHYLWDQGRODVJUDQGHVYDULDFLRQHVTXHVHREVHU YDQHQORVWUDQVLVWRUHVGHSRWHQFLD3RURWUDSDUWHHO]HQHUHVWiVRPHWLGRDPHQRUHVYD ULDFLRQHVGHFRUULHQWH\DTXHDKRUDGHEHPDQHMDUXQDFRUULHQWHK)(YHFHVPHQRUTXH DQWHV 7DPELpQ HV YHQWDMRVR TXH HO ]HQHU HVWp SRODUL]DGR GHVGH OD VDOLGD HVWDELOL]DGD HYLWDQGRDVtODVJUDQGHVYDULDFLRQHVGHODVFRQGLFLRQHVGHSRODUL]DFLyQ/DUHVLVWHQFLD 5] VH KD FRORFDGR SDUD JDUDQWL]DU OD FRUULHQWH PtQLPD SRU HO ]HQHU \D TXH D Pi[LPD FRUULHQWHGHFDUJDODFRUULHQWHSRUODEDVHGH7SXHGHOOHJDUDVHUPX\EDMD % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV $XQTXHHOFLUFXLWRQRSHUPLWHWRGDYtDXQDJUDQIOH[LELOLGDGHQ ORFRQFHUQLHQWHD WHQVLRQHVGHVDOLGDDOPHQRVSHUPLWHDSURYHFKDUXQDVXHUWHGH FRPSHQVDFLyQWpUPLFD HQWUH ORV FRHILFLHQWHV GH WHPSHUDWXUD GHO ]HQHU \ GHO WUDQVLVWRU TXH VH GD D WHQVLRQHV PD\RUHVGH9 (QODILJXUDVHPXHVWUDXQDQXHYDYDULDQWHTXHSHUPLWHYDORUHVDUELWUDULRVGHOD WHQVLyQGHVDOLGD L* L/ 7 5E 5 Y* 5/ 7 Y/ 5 9] − − )LJXUD8QUHJXODGRUVHULHFRQSRVLELOLGDGGHREWHQHUYDORUHVDUEL WUDULRVGHODWHQVLyQGHVDOLGD 'HVSUHFLDQGRODFRUULHQWHSRUODEDVHGH7ODWHQVLyQGHVDOLGDYDOHDKRUD Y/ ≅ (9] 5 + Y %( ) + 5 9HPRVTXHYDULDQGR5\R5HVSRVLEOHREWHQHUFXDOTXLHUWHQVLyQGHVDOLGDVLHPSUHTXH VHDPD\RUTXH9]Y%(0iVD~QSRGUtDVHOHFFLRQDUVH9]SDUDXQDSUHFLVDFRPSHQVDFLyQ WpUPLFDFRQODMXQWXUD%(GH7(QDOJXQRVFDVRVVHSXHGHFRORFDUXQSUHVHWHQWUH5\ 5FRQHFWDQGRODEDVHDOSXQWRPHGLRSDUDXQDMXVWHILQRGHODWHQVLyQGHVDOLGD (VWHFLUFXLWRUHSLWHDOJXQDVGHODVGHVYHQWDMDVGHOSULPHURTXHVHDQDOL]yGHELGRD ODVFRUULHQWHVFRQVLGHUDEOHVSRUHO]HQHUSRUORFXDOSXHGHVXVWLWXLUVHSRUHOFLUFXLWRGH ODILJXUD L* L/ 7 5 E 5 9] Y* 5/ Y/ 7 5] 5 − − % )LJXUD8QUHJXODGRUVHULHFRQSRVLELOLGDGGHREWHQHUYDORUHVDUEL WUDULRVGHODWHQVLyQGHVDOLGD\HO]HQHUHQHOFLUFXLWRGHEDVHGH7 )HGHULFR0L\DUD $xR /DWHQVLyQGHVDOLGDVHREWLHQHFRQODPLVPDHFXDFLyQ8QDSHTXHxDGHVYHQ WDMD HV TXH OD UHG GH PXHVWUHR IRUPDGD SRU 5 \ 5 UHTXLHUH XQD FRUULHQWH LPSRUWDQWH SDUDSHUPLWLUODDGHFXDGDSRODUL]DFLyQGHO]HQHU (QHOFLUFXLWRGHODILJXUDVHDSUHFLDTXHHOWUDQVLVWRU7FXPSOHUXGLPHQWDULD PHQWHODIXQFLyQGHDPSOLILFDGRUGLIHUHQFLDOUHDOLPHQWDGR3XHGHVXVWLWXtUVHORFRQYHQ WDMDSRUXQDPSOLILFDGRURSHUDFLRQDOFRPRVHPXHVWUDHQODILJXUD L* L/ 7 5 5 Y* 5/ − Y/ 9] 5 − − )LJXUD8QUHJXODGRUVHULHFRQXQDPSOLILFDGRURSHUDFLRQDO /DWHQVLyQGHVDOLGDHVHQHVWHFDVR Y/ 5 = 9] + 5 2EVHUYHPRVTXHGHVDSDUHFLyODGHSHQGHQFLDGHWHQVLRQHVEDVHHPLVRUSRUORFXDOWRGD ODUHVSRQVDELOLGDGSRUHOYDORUGHODWHQVLyQGHVDOLGDUHFDHHQHO]HQHU(QOXJDUGHXQ ]HQHU FRQYHQFLRQDO HV SRVLEOH XWLOL]DU XQD IXHQWH GH UHIHUHQFLD LQWHJUDGD WDO FRPR HO /0 R HO /0 TXH VL ELHQ H[WHUQDPHQWH VH SDUHFHQ D XQ ]HQHU LQWHUQDPHQWH FRQWLHQHQHOHPHQWRVSDUDVXHVWDELOL]DFLyQWpUPLFD'HKHFKRHOFLUFXLWRGHODILJXUD HVODEDVHGHOUHJXODGRULQWHJUDGR/0 )DFWRUHVGHHVWDELOLGDGGHXQUHJXODGRUVHULH (OFiOFXORGHORVIDFWRUHVGHHVWDELOLGDGSXHGHHIHFWXDUVHHQIRUPDVLPSOLILFDGD FRQVLGHUDQGR VyOR HIHFWRV GH SULPHU RUGHQ R HQ IRUPD H[DFWD UHVROYLHQGR HO FLUFXLWR PHGLDQWHWpFQLFDVGHDQiOLVLVGHUHGHV(MHPSOLILFDUHPRVDPEDVWpFQLFDVVREUHHOFLUFXL WRGHODILJXUD )DFWRUGHHVWDELOLGDGGHOtQHDFiOFXORVLPSOLILFDGR (QHVWHFDVRODFRUULHQWHGHFDUJDVHPDQWLHQHFRQVWDQWHHVGHFLUVHVXVWLWX\HOD UHVLVWHQFLDGHFDUJD5/SRUXQDIXHQWHGHFRUULHQWH\VHKDFHYDULDUODWHQVLyQGHHQWUD GDY*(OPpWRGRVLPSOLILFDGRVXSRQHTXHODWHQVLyQGHVDOLGDVHPDQWLHQHSUiFWLFDPHQ WHFRQVWDQWH3RUVHUL/FRQVWDQWHWDPELpQORHVODFRUULHQWHGHEDVHGHOWUDQVLVWRU7\ FRQVHFXHQWHPHQWHODWHQVLyQEDVHHPLVRU'DGRTXHY% Y/Y%(ODWHQVLyQHQODEDVH % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV WDPELpQ HV FRQVWDQWH SRU OR FXDO XQ LQFUHPHQWR ∆Y* GH OD WHQVLyQ GH HQWUDGD DSDUHFH tQWHJUDPHQWHHQ 5E7HQHPRVSRUORWDQWRXQLQFUHPHQWRGHFRUULHQWHHQGLFKDUHVLV WHQFLDGDGRSRU ∆L 5 E ≅ ∆Y* 5E &RPRODFRUULHQWHGHEDVHGH7HVFRQVWDQWHGLFKRLQFUHPHQWRGHFRUULHQWHFLUFXODUi H[FOXVLYDPHQWHSRUHOFROHFWRUGH7\WHQLHQGRHQFXHQWDODVLPLOLWXGHQWUHODVFRUULHQ WHVGHFROHFWRU\GHHPLVRUWDPELpQFLUFXODUiSRUHO]HQHU ∆L] ∆Y* 5E ≅ (VWHLQFUHPHQWRGHFRUULHQWHWUDHDSDUHMDGDXQDYDULDFLyQGHODWHQVLyQGH]HQHUDFDXVD GHODUHVLVWHQFLDGLQiPLFDU]GDGDSRU ∆Y ] ∆Y* U] 5E ≅ 7DPELpQVHSURGXFHXQLQFUHPHQWRHQODWHQVLyQEDVHHPLVRUGH7 ∆Y %( ∆Y* KLH 5E KIH ≅ SRUORFXDOODWHQVLyQHQODEDVHGH7H[SHULPHQWDXQLQFUHPHQWRWRWDO ∆Y % = ∆Y ] + ∆Y %( ≅ ∆Y* 5E K U + LH ] KIH (O LQFUHPHQWR HQ OD WHQVLyQ GH VDOLGD ∆Y/ SXHGH REWHQHUVH WHQLHQGR HQ FXHQWD TXHODWHQVLyQHQODEDVHGH7HVODWHQVLyQGHVDOLGDDWHQXDGDSRUHOGLYLVRUGHWHQVLyQ 55FDUJDGRSRUODUHVLVWHQFLDYLVWDHQODEDVHHVGHFLU 5 KLH + KIH + U] Y% = Y/ 5 + 5 KLH + KIH + U] ( ( ( ( ) ) ) ) 6XVWLWX\HQGR\RSHUDQGRUHVXOWDHOIDFWRUGHHVWDELOLGDGGHOtQHD KLH 5 + 69 ≅ U] + 5E KIH 5 K K U + + LH IH ] 9HPRVTXHHOIDFWRUGHHVWDELOLGDGPHMRUDVHUHGXFHFXDQGR5EHVJUDQGHU]SH TXHxR\KIHHOHYDGR (QHOFiOFXORDQWHULRUVXSXVLPRVTXHODFRUULHQWHGHEDVHGH7QRYDULDEDSHURHQ UHDOLGDGYDUtD(QHIHFWRDOLQFUHPHQWDUVHODWHQVLyQFROHFWRUHPLVRUGH7VHLQFUHPHQ ( % ( ) ) )HGHULFR0L\DUD $xR WDODFRUULHQWHSRUODDGPLWDQFLDGHVDOLGDKRHSRUORTXHODFRUULHQWHSRUODIXHQWHGH SHQGLHQWHGHEHUHGXFLUVHSDUDPDQWHQHUFRQVWDQWHODFRUULHQWHGHVDOLGD ∆Y* KRH + KIH + ∆L% = GHGRQGH ∆L% = − KRH KIH + ∆Y* 5HVXOWDDVtTXHQRVyORODFRUULHQWHSRU5EFLUFXODUiVyORSRUHO]HQHUGHPRGRTXHOD HFXDFLyQVHPRGLILFDDVt ∆L] KRH ≅ ∆Y* + 5E + K IH 6L5EHVJUDQGHHVWHHIHFWRGHEHVHUWHQLGRHQFXHQWD5HVXOWDILQDOPHQWH KRH K U + LH ≅ + ] 5E KIH + KIH 69 5 + 5 KLH + KIH + U] ( ( ) ) 8QLQFRQYHQLHQWHGHHVWHFLUFXLWRHVTXHSRUORJHQHUDO5EQRSXHGHHOHJLUVHJUDQ GH VLQ FRPSURPHWHU HO UHQGLPLHQWR (OOR VH GHEH D TXH XQUHQGLPLHQWR DOWR H[LJH XQD WHQVLyQGHHQWUDGDORPiVEDMDSRVLEOHSHURDOPLVPRWLHPSRVHUHTXLHUHXQDFRUULHQWH FRQVLGHUDEOHSDUDVXUWLUODEDVHGH7/RJUDUHVWRFRQXQDUHVLVWHQFLDH[LJHTXHVXYDORU VHDEDMR (MHPSOR 6XSRQJDPRV XQD IXHQWH FRQ 5E Ω 5 NΩ 5 NΩ 9] 9U] ΩKLH ΩKIH ΩKRH P66XVWLWX\HQGRYDORUHVVHRE WLHQH 69≅ (VWHYDORUHVEDVWDQWHDOWRORFXDOVLJQLILFDTXHHOUHJXODGRUVyORUHGXFHHQDOUHGHGRUGH XQODVYDULDFLRQHVGHODWHQVLyQGHHQWUDGD 8QDSRVLEOHVROXFLyQHVUHHPSOD]DUODUHVLVWHQFLDSRUXQDIXHQWHGHFRUULHQWH/D UHVLVWHQFLDHTXLYDOHQWHVHUiHOHYDGDDXQFXDQGRODIXHQWHGHFRUULHQWHFRQSRFDWHQVLyQ HVFDSD]GHHQWUHJDUODFRUULHQWHQHFHVDULD(QHOFLUFXLWRGHODILJXUDVHPXHVWUDXQ HMHPSOR/DFRUULHQWHHQWUHJDGDSRUHOFROHFWRUGH7HVDSUR[LPDGDPHQWH , & ≅ 9] − 9 %( 5 PLHQWUDVTXHVXUHVLVWHQFLDHTXLYDOHQWHGHVSXpVGHDOJXQRVFiOFXORVVHDSUR[LPDSRU KIH 5E ≅ + 5 KLH + KRH K K LH RH % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV L* 9] L/ 7 5 5 7 Y* 5/ Y/ 7 5 5 9] − − )LJXUD(OUHJXODGRUVHULHGHODILJXUDPHMRUDGRFRQXQSUHUUHJX ODGRUGHFRUULHQWH (MHPSOR6L5 ΩKRH P6FRUUHVSRQGLHQWHDXQDFRUULHQWHGHFR OHFWRUGHP$\XQDWHQVLyQGH(DUO\GH9KIH KLH ΩUHVXOWDGHOD HFXDFLyQ XQD UHVLVWHQFLD GH VDOLGD 5E NΩ (Q HVWH FDVR DSOLFDQGR QXHYD PHQWHODHFXDFLyQUHVXOWD 69≅ TXHFRUUHVSRQGHDXQDUHJXODFLyQPXFKRPHMRU )DFWRUGHHVWDELOLGDGGHOtQHDFiOFXORH[DFWR (OFiOFXORH[DFWRGHORVIDFWRUHVGHHVWDELOLGDGSURFHGHSODQWHDQGRODVHFXDFLRQHV GH SRWHQFLDOHV GH QXGR GHO PRGHOR HQ SHTXHxD VHxDO FRUUHVSRQGLHQWH DO FLUFXLWR GH OD ILJXUDPRVWUDGRHQODILJXUD KRH ∆L* KLHL% ϕ KLH 5E 5 ϕ ∆Y* ∆L/ ϕ KLHL% KRH ϕ U] ∆Y/ ∆L/ KLH 5 − )LJXUD0RGHORHQSHTXHxDVHxDOGHOUHJXODGRUGHODILJXUDSDUD HODQiOLVLVSRUHOPpWRGRGHSRWHQFLDOHVGHQXGR % )HGHULFR0L\DUD $xR /DVHFXDFLRQHVGHQXGRVVRQ ϕ KRH + + − ϕ − ϕ KLH 5 5 KLH = ∆Y* KRH + KIH KLH (ϕ − ϕ ) − ∆L/ − ϕ − ϕ + ϕ + + 5 5 KLH 5 KLH − ϕ KLH − ϕ KLH + ϕ + KRH + 5E KLH = KIH − ϕ K ( = − ϕ − ϕ ) + ∆Y* RH K 5 LH E − ϕ KRH + ϕ KRH + + U] KLH K = IH (ϕ − ϕ ) KLH 5HRUGHQDQGR\DJUXSDQGRVHWLHQH KIH + K + − ϕ − ϕ IH ϕ KRH + + = ∆Y* KRH − ∆L/ KLH 5 5 KLH − ϕ − ϕ + ϕ + + 5 5 5 KLH KLH − ϕ KLH + − ϕ KLH ϕ + ϕ + KRH + KLH KLH 5E KIH − ϕ KRH + ϕ KRH + + U] KLH = K − ϕ IH + K = ∆Y RH * KLH 5E K = IH (ϕ − ϕ ) KLH (VWHVLVWHPDSXHGHH[SUHVDUVHHQODIRUPDPDWULFLDO $ Φ = & GRQGH$HVODPDWUL]GHFRHILFLHQWHVΦHOYHFWRUFROXPQDIRUPDGRSRUORVSRWHQFLDOHV GHQXGRVϕN\&HVHOYHFWRUFROXPQDGHORVWpUPLQRVLQGHSHQGLHQWHV0XOWLSOLFDQGRSRU ODPDWUL]LQYHUVDVHREWLHQHHOYHFWRUΦ Φ = $ −& $XQTXHHVSRVLEOHQRLQWHQWDUHPRVREWHQHUODVROXFLyQH[SOtFLWD/DVROXFLyQVHLPSOH PHQWDPiVIiFLOPHQWHHQIRUPDQXPpULFDFRQVRIWZDUHPDWULFLDOWDOFRPR2FWDYH6FL ODER0DWODE6LELHQSDUDPD\RUJHQHUDOLGDGVHFRQVLGHUyXQDIXHQWHGHFRUULHQWH∆L/ FRPRFDUJDDORVHIHFWRVGHOFiOFXORGHOIDFWRUGHHVWDELOLGDGGHOtQHDFRQYLHQHWRPDU ∆L/ /DWHQVLyQGHVDOLGDHV∆Y/ Φ ϕSRUORFXDO % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV 69 Φ ∆Y* = (MHPSOR 6XSRQJDPRV OD IXHQWH GHO HMHPSOR FRQ 5E Ω 5 NΩ 5 NΩ 9] 9 U] Ω KLH Ω KIH Ω KLH Ω KIH KRH P66XVWLWX\HQGRYDORUHVVHREWLHQH 69 (VWHUHVXOWDGRGLILHUHFRQVLGHUDEOHPHQWHGHOYDORUDSUR[LPDGRREWHQLGRDQWHULRUPHQWH 6LVHFDPELDODUHVLVWHQFLD5ESRUODUHVLVWHQFLDGLQiPLFDGHODIXHQWHGHFRUULHQWHFRPR HQHOHMHPSOR5E NΩHOUHVXOWDGRHV 69 YDORUPiVFHUFDQRDOUHVXOWDGRDSUR[LPDGR )DFWRUGHHVWDELOLGDGGHFDUJDFiOFXORVLPSOLILFDGR (QHVWHFDVRVHPDQWLHQHFRQVWDQWHODWHQVLyQGHHQWUDGD\VHSHUPLWHYDULDUODFR UULHQWHGHFDUJDL/,JXDOTXHHQDOFDVRDQWHULRUHOPpWRGRVLPSOLILFDGRVXSRQHTXHOD WHQVLyQGHVDOLGDSUiFWLFDPHQWHQRYDUtD(QHVWHFDVR Y*WDPELpQHVFRQVWDQWHSRUOR TXHODFRUULHQWHSRUKRHHVDSUR[LPDGDPHQWHFRQVWDQWH/DVYDULDFLRQHVGHFRUULHQWHGH VDOLGDFLUFXODQH[FOXVLYDPHQWHSRUODIXHQWHGHSHQGLHQWHGHDOOtTXH ∆L% ∆L/ KIH + ≅ (VWRLPSOLFDXQLQFUHPHQWRHQODWHQVLyQEDVHHPLVRUGH7 ∆Y%( ∆L/ KLH KIH + ≅ 'DGRTXHY/\Y*VRQFRQVWDQWHVHOLQFUHPHQWR∆Y%(LPSOLFDXQGHFUHPHQWRGHODWHQ VLyQHQ5E(OLQFUHPHQWRGHODFRUULHQWHSRUHO]HQHUVHUiHQWRQFHV ∆L] ≅ − ∆L/ KLH + KIH + 5E (VWDFRUULHQWHSURYRFDXQDXPHQWRHQODWHQVLyQGHO]HQHU\HQ ODWHQVLyQEDVHHPLVRU GH7SRUORFXDOODWHQVLyQGHEDVHGH7VHLQFUHPHQWDHQ ∆Y % ≅ − K ∆L/ KLH U] + LH + KIH + 5E KIH $SOLFDQGRODHFXDFLyQ\UHRUGHQDQGRVHREWLHQH % )HGHULFR0L\DUD $xR KLH 6, + K 5E U + LH ≅ − ] KIH + KIH 5 + 5 KLH + KIH + U] ( ( ) ) (OVLJQR−VHGHEHDTXHXQDXPHQWRGHODFRUULHQWHGHFDUJDSURYRFDXQDGLVPLQXFLyQ GHODWHQVLyQGHVDOLGD1XHYDPHQWHYHPRVTXHHVLPSRUWDQWHTXHODUHVLVWHQFLD5EVHD HOHYDGD SHUR WDPELpQ VH DSUHFLD OD QHFHVLGDG GH TXH OD JDQDQFLD GH FRUULHQWH GH 7 K)(VHDDOWD(OIDFWRUGHHVWDELOLGDGGHFDUJDPHMRUDFXDQGRVH UHHPSOD]D7SRUXQ SDU'DUOLQJWRQ (MHPSOR&RQORVGDWRVGHOHMHPSORVHREWLHQH 6,≅−Ω 6LVHXWLOL]DXQDIXHQWHGHFRUULHQWHFRQXQDUHVLVWHQFLD5E NΩUHVXOWD 6,≅−Ω 6LHQFDPELRVHXWLOL]DXQ'DUOLQJWRQGHJDQDQFLDFRQVHUYDQGR5E ΩUHVXOWD 6,≅−Ω PLHQWUDVTXHVLVHFRPELQDQDPEDVPHMRUDVVHREWLHQH 6,≅−Ω )DFWRUGHHVWDELOLGDGGHFDUJDFiOFXORH[DFWR 3DUDFDOFXODUHOIDFWRUGHHVWDELOLGDGGHFDUJDHQIRUPDH[DFWDOD~QLFDPRGLILFD FLyQTXHGHEHKDFHUVHFRQUHVSHFWRDOFDVRGHOIDFWRUGHHVWDELOLGDGGHOtQHDHVTXHDKR UD∆Y* \∆L/≠3XHGHXWLOL]DUVHHOVLVWHPDGHHFXDFLRQHV\DSOLFDUVHODVROX FLyQPDWULFLDO(QHVWHFDVRUHVXOWD 6, Φ ∆L/ = (MHPSOR&RQORVGDWRVGHOHMHPSORVHREWLHQH 6, −Ω YDORUXQPHQRUTXHSDUDHOFiOFXORDSUR[LPDGR6L5E NΩUHVXOWD 6, Ω YDORUPiVFHUFDQRDOYDORUDSUR[LPDGRREWHQLGRDQWHULRUPHQWH 127$&DPELDQGRHOVLJQRDOIDFWRUGHHVWDELOLGDGGHFDUJDVHREWLHQHODUHVLVWHQFLDGH VDOLGDGHOUHJXODGRU % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV )DFWRUHVGHHVWDELOLGDGGHOUHJXODGRUFRQDPSOLILFDGRU RSHUDFLRQDO 3RUHVWDUHQSUHVHQFLDGHXQDPSOLILFDGRURSHUDFLRQDOILJXUDHOPpWRGRVLP SOLILFDGRRIUHFHXQUHVXOWDGRPX\FHUFDQRDOH[DFWR3DUDODHVWDELOLGDGGHOtQHDVXSR QHPRVXQDFRUULHQWHGHFDUJDFRQVWDQWH+D\GRVPHFDQLVPRVTXHYLQFXODQHOLQFUHPHQ WRGHY*FRQHOGHY/(OSULPHURHVODYDULDFLyQGHFRUULHQWHSRUHO]HQHUTXHSURYRFD XQDYDULDFLyQGHVXWHQVLyQGHUXSWXUDGDGDSRU ∆Y ] = ∆Y* U] 5 + U] (OVHJXQGRPHFDQLVPRHVODYDULDFLyQGHWHQVLyQHQODEDVHGH7TXHLPSOLFDXQDYD ULDFLyQHQODWHQVLyQGLIHUHQFLDOGHODPSOLILFDGRU$SOLFDQGRODHFXDFLyQTXHWLHQH HQFXHQWDODVYDULDFLRQHVGHL% DXQPDQWHQLpQGRVHFRQVWDQWHL/GHELGDVDODYDULDFLyQ GHFRUULHQWHHQODUHVLVWHQFLDGHVDOLGDSRGHPRVREWHQHU ∆Y %( KRH KLH = − KIH + ∆Y* (VWDYDULDFLyQGLYLGLGDSRUODJDQDQFLDGHODPSOLILFDGRUSURSRUFLRQDHOLQFUHPHQWRHQ ODWHQVLyQGLIHUHQFLDOTXHGHEHUHVWDUVHDOLQFUHPHQWRGHODWHQVLyQGH]HQHUSDUDREWH QHUHOLQFUHPHQWRWRWDOGHODWHQVLyQY− ∆Y − KRH KLH U] = ∆Y* + 5 + U] KIH + DY )LQDOPHQWHWHQLHQGRHQFXHQWDTXHHOGLYLVRU55QRHVFDUJDGRSRUHOWHUPLQDO LQYHUVRUGHODPSOLILFDGRU 69 KRH KLH U] ≅ + 5 + U] KIH + D Y + 5 5 1RUPDOPHQWH DY HV VXILFLHQWHPHQWH HOHYDGR WtSLFDPHQWH PD\RU GH FRPR SDUD TXHSXHGDGHVSUHFLDUVHHOVHJXQGRWpUPLQRGHQWURGHOSDUpQWHVLV 69 ≅ U] 5 + 5 + U] 5 (QHVWHFDVRGDGRTXH5QRWLHQHRWURUHTXLVLWRGHFRUULHQWHTXHODSRODUL]DFLyQ GHO ]HQHU HQ JHQHUDO VH OD SXHGH HOHJLU UHODWLYDPHQWH DOWD REWHQLpQGRVH FRQ IDFLOLGDG YDORUHVGH69PHQRUHVDO (QFXDQWRDODHVWDELOLGDGGHFDUJDXQLQFUHPHQWRGH L/VyORUHSHUFXWHHQODFR UULHQWHGHEDVHGH7RFDVLRQDQGRXQLQFUHPHQWR∆Y%(GDGRSRU ∆Y%( KLH = KIH + ∆L/ 8QUD]RQDPLHQWRDQiORJRDODQWHULRUOOHYDD % )HGHULFR0L\DUD $xR 6, = − KLH 5 + KIH + D Y 5 (VWHYDORUHVVXPDPHQWHEDMR(VHQFLDOPHQWHHOORVHGHEHDTXH HVWDPRVHQSUHVHQFLD GHXQFLUFXLWRUHDOLPHQWDGRFRQVHQVDGRHQSDUDOHOR\DOWDJDQDQFLDGHOD]RSRUORTXH ODLPSHGDQFLDGHVDOLGDVHUHGXFHSRUXQIDFWRUPX\JUDQGH /DVH[SUHVLRQHV\PXHVWUDQODVXSHULRULGDGGHHVWHFLUFXLWRFRQUHVSHFWR DORVDQWHULRUHVGDGRTXHODHVWDELOLGDGGHOtQHD\GHFDUJDHVPX\EXHQD )DFWRUGHHVWDELOLGDGGHWHPSHUDWXUD $XQTXHQRDEXQGDUHPRVHQGHWDOOHVDQDOtWLFRVTXHTXHGDQFRPRHMHUFLFLRHOIDF WRUGHHVWDELOLGDGGHWHPSHUDWXUDSXHGHHVWLPDUVHDSDUWLUGHORVFRHILFLHQWHVGHWHPSH UDWXUDGHORVHOHPHQWRVLQYROXFUDGRV$VtHQHOHMHPSORGHODILJXUDHOFRHILFLHQWHGH WHPSHUDWXUDGHO]HQHUVXPDGRDOGHODMXQWXUDEDVHHPLVRUGH7VRQORVSDUiPHWURVPiV UHOHYDQWHV\DTXHODHVWDELOLGDGGHWHPSHUDWXUDGHSHQGHGLUHFWDPHQWHGHHOORV/RVFR HILFLHQWHVGHWHPSHUDWXUDGHODVUHVLVWHQFLDV5\5WLHQHQSRFDLQFLGHQFLDGDGRTXHDO VHUGHODPLVPDWHFQRORJtDODVGHULYDVSRUFHQWXDOHVVRQLJXDOHVPDQWHQLpQGRVHFRQVWDQ WHHOIDFWRUGHDWHQXDFLyQ(OFRHILFLHQWHGHWHPSHUDWXUDGHODWHQVLyQEDVHHPLVRUGH7 SXHGHLQFLGLULQGLUHFWDPHQWHDOLPSOLFDUXQDOHYHUHGXFFLyQGHODFRUULHQWHSRU5ESHUR HQ JHQHUDO WDPSRFR LQFLGH QRWDEOHPHQWH (Q OD PD\RUtD GH ORV FDVRV ODHVWDELOLGDGGH WHPSHUDWXUDGHODWHQVLyQGHUHIHUHQFLDHVHOIDFWRUSUHGRPLQDQWHUD]yQSRUODFXDOVH VXHOHQXWLOL]DUUHIHUHQFLDVLQWHJUDGDVFRPSHQVDGDVHQWHPSHUDWXUD 3URWHFFLRQHV $XQTXHHQDOJXQRVFDVRVODVFRQGLFLRQHVGHDOLPHQWDFLyQ\GHFDUJDGHXQUHJX ODGRU VH PDQWLHQHQ GHQWUR GH OR SUHYLVWR PXFKRV UHJXODGRUHV SXHGHQ HVWDU VXMHWRV D FRQGLFLRQHV PX\ YDULDEOHV DOJXQDV GH ODV FXDOHV FDHQ IXHUD GH ORV OtPLWHV DGPLVLEOHV SDUDDOJXQDRDOJXQDVGHODVYDULDEOHVHQJHQHUDOFRUULHQWHSRWHQFLDRWHPSHUDWXUD /DVLWXDFLyQGHVFULSWDSXHGHSRQHUHQULHVJRODIXQFLRQDOLGDGRLQFOXVRODVHJXUL GDGGHOUHJXODGRUORFXDOOOHYDDODQHFHVLGDGGHGRWDUDOFLUFXLWRGHXQDRPiVSURWHF FLRQHV/DILQDOLGDGGHODVPLVPDVHVGHWHQHUHOIXQFLRQDPLHQWRRDOWHUDUORGHPRGRGH HYLWDUULHVJRV /DVSURWHFFLRQHVSXHGHQFODVLILFDUVHHQSURWHFFLRQHVGHUHSRVLFLyQPDQXDORDX WRPiWLFD'HQWURGHODVSULPHUDVVHHQFXHQWUDQSRUHMHPSORORVIXVLEOHVHVGHFLUGLV SRVLWLYRVIRUPDGRVSRUXQDODPEUHUHODWLYDPHQWHGHOJDGRTXHDQWHXQLQFUHPHQWRGHOD FRUULHQWHSRUHQFLPDGHFLHUWRYDORUHVSHFLILFDGRVHIXQGHFRUWDQGRHOVXPLQLVWURHOpF WULFR 2WUR HMHPSOR VRQ ORV GLVSRVLWLYRV GH FRQWURO ELHVWDEOH SRUHMHPSORXQUHOpTXH LQWHUUXPSHHOVXPLQLVWURHQIRUPDQRDXWRGHVWUXFWLYDSHURUHTXLHUHLQWHUYHQFLyQKXPD QDSDUDUHWRPDUODRSHUDFLyQ 'HQWURGHODVSURWHFFLRQHVDXWRPiWLFDVWHQHPRVODVSURWHFFLRQHVFRQWUDVREUHFR UULHQWHFRQWUDFRUWRFLUFXLWRFRQWUDVREUHWHPSHUDWXUDGHiUHDVHJXUD\FRQWUDVREUHWHQ 8QD SURWHFFLyQ FRQWUD VREUHFRUULHQWH QR QHFHVDULDPHQWH SURWHJH FRQWUD FRUWRFLUFXLWR \D TXH SRGUtD OLPLWDUVHODFRUULHQWHSHURGHELGRDODWHQVLyQTXHFDHHQHOWUDQVLVWRUGHSDVRUHVXOWDUH[FHVLYDODSR WHQFLDGLVLSDGD % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV VLyQ/DV~OWLPDVVRQSRFRIUHFXHQWHVDXQTXHXQHMHPSORVRQODVSURWHFFLRQHVYDOYXOD UHVGHGHVFDUJDJDVHRVDFRQWUDSLFRVPX\DOWRVGHWHQVLyQSRUHMHPSORORVGHULYDGRVGH ODFDtGDGHXQUHOiPSDJRHQSUR[LPLGDGHVGHXQDLQVWDODFLyQHOpFWULFD )XVLEOHV /RVIXVLEOHVVHXWLOL]DQHQODPD\RUtDGHORVFDVRVFRPRSURWHFFLyQH[WUHPDLQ FOXVRDQWHODHYHQWXDOIDOODGHRWUDVSURWHFFLRQHV(VEXHQDGHSUiFWLFDLQFOXLUIXVLEOHV HQFXDOTXLHUHTXLSRTXHVHFRQHFWHDODOtQHDGHGLVWULEXFLyQHOpFWULFDRTXHSXHGDPD QHMDUFRUULHQWHVLPSRUWDQWHV /RVIXVLEOHVVHHVSHFLILFDQSRUPHGLRGHVXFRUULHQWHQRPLQDOHVGHFLUODFRUULHQWH TXHSXHGHQFRQGXFLUHQIRUPDSHUPDQHQWHVLQTXHVHIXQGDQDXQTXHHVUHFRPHQGDEOH QRH[FHGHUHQIXQFLRQDPLHQWRQRUPDOHOGHODFRUULHQWHQRPLQDO'LFKRPDUJHQ GHVHJXULGDGGHEHDXPHQWDUVHHQFDVRGHTXHHOIXVLEOHGHEDIXQFLRQDUHQXQDPELHQWH JDELQHWHHWFDWHPSHUDWXUDVHOHYDGDV 3DUDFRUULHQWHVWUDQVLWRULDVGHFRUWDGXUDFLyQHOIXVLEOHWROHUDUiSLFRVRFDVLRQDOHV WDOHVTXHQRVHDOFDQFHXQYDORU,WPi[XQDPHGLGDGHODHQHUJtDQHFHVDULDSDUDIXQGLUOR HQXQWLHPSRPHQRURLJXDOTXHPVRPHQRURLJXDOTXHPVSDUDHOFDVRGHIXVLEOHV UiSLGRVGHSHOtFXODGHOJDGD3RUHMHPSORXQIXVLEOHTXHWHQJD,WPi[ $VVRSRU WDUiXQSLFRGH $ VV $GXUDQWHPVRELHQXQRGH$GX UDQWHPV'HWRGDVPDQHUDVVHUHFRPLHQGDQRH[SRQHUDOIXVLEOHDSXOVRVFRQ,WPD \RU GHO GH ,WPi[ (V PiV DQWH SXOVRV FtFOLFRV VXSRQLHQGR XQ LQWHUYDOR HQWUH SXOVRVWDOTXHHOIXVLEOHDOFDQFHDHQIULDUVHH[LVWHXQPi[LPRQ~PHURDGPLVLEOH1GH FLFORV GHQWUR GH OD YLGD ~WLO GHO GLVSRVLWLYR HQ IXQFLyQ GHO SRUFHQWDMH 3 GHO ,WPi[H[SUHVDGRHQJHQHUDOHQODIRUPDHPStULFD 3 1 = 1 R 3R α 3RUHMHPSORSDUDIXVLEOHV/LWWHOIXVH1R 3R α −$VtHOIX VLEOHDQWHULRUWROHUDUiXQDFDQWLGDG $ V$ V 1 = − = SXOVRVGH$V /DUHVLVWHQFLDHOpFWULFDGHOIXVLEOHHVWiHQSURSRUFLyQLQYHUVDFRQVXFRUULHQWHQR PLQDO3DUDIXVLEOHVGHEDMDFRUULHQWHSXHGHQVHUGHDOJXQRVRKPVORFXDOGHEHWHQHUVH HQFXHQWDHQHOGLVHxRGHOFLUFXLWRVLODUHVLVWHQFLDWRWDOHVXQSDUiPHWURFUtWLFR /DWHQVLyQPi[LPDDGPLVLEOHHVXQSDUiPHWURGHXWLOLGDGHQFDVRVGHDOWDVWHQVLR QHV\DTXHHOIXVLEOHSRGUtDIXQGLUVH\VLQHPEDUJRQRLQWHUUXPSLUODFRUULHQWHGHELGRD ODIRUPDFLyQGHXQDUFRYROWDLFR 3URWHFFLyQFURVVRYHU /D SURWHFFLyQ FURVVRYHU HV XQD SURWHFFLyQ FRQWUD VREUHFRUULHQWH (Q HO FDVR GH IXHQWHVGHEDMDSRWHQFLDSRGUtDLQFOXVRIXQFLRQDUFRPRSURWHFFLyQFRQWUDFRUWRFLUFXLWR % )HGHULFR0L\DUD $xR (VWiIRUPDGDFRPRVHPXHVWUDHQODILJXUDSRUXQWUDQVLVWRUFX\DEDVHHPLVRU VHSRODUL]DDWUDYpVGHODFDtGDHQODUHVLVWHQFLDGHVHQVDGRGHFRUULHQWH5V L* L/ 5V 7 5 5 7 Y* Y/ 5/ − 9] 5 − − )LJXUD3URWHFFLyQFURVVRYHUSDUDHOUHJXODGRUVHULHFRQXQDPSOL ILFDGRURSHUDFLRQDO 3DUDEDMDVFRUULHQWHVGHFDUJDHOWUDQVLVWRU7SHUPDQHFHFRUWDGR&XDQGRODFR UULHQWHGHFDUJDDXPHQWDVXILFLHQWHPHQWHODFDtGDHQ5VDOFDQ]DHOYDORU9γGHFRQGXF FLyQGH7\pVWHFRPLHQ]DDGHULYDUFRUULHQWH(OORVXFHGHFXDQGR L/ 9γ = 5V 5 0LHQWUDV HO DPSOLILFDGRU RSHUDFLRQDO QR DOFDQFH VX SURSLR OtPLWH GH FRUULHQWH OD FR UULHQWHGHFDUJDSRGUiFRQWLQXDUDXPHQWDQGROLJHUDPHQWHORFXDOSRODUL]DUiD~QPiVDO WUDQVLVWRU7KDVWDTXHpVWHDEVRUEDWRGDODFRUULHQWHGHODPSOLILFDGRUPHQRVODTXHYD KDFLDODEDVHGH7$SDUWLUGHHVHPRPHQWRHODPSOLILFDGRUVHVDWXUDHQFRUULHQWHSRU ORFXDOGHMDGHIXQFLRQDUOLQHDOPHQWH/DUHDOLPHQWDFLyQVHLQWHUUXPSH\FXDOTXLHULQ WHQWRSRUDXPHQWDUODFRUULHQWHGHFDUJDUHGXQGDUiHQXQDGLVPLQXFLyQGHODWHQVLyQGH VDOLGD(OUHJXODGRUSDVDDRSHUDUFRPRIXHQWHGHFRUULHQWH(QODILJXUDVHPXHVWUD ODUHODFLyQHQWUHODWHQVLyQGHVDOLGD\ODFRUULHQWHGHFDUJD Y/ 9/ L/ ,/Pi[ )LJXUD7HQVLyQGHVDOLGDHQIXQFLyQGHODFRUULHQWHGHFDUJDSDUD XQUHJXODGRUFRQSURWHFFLyQFURVVRYHU 2EVpUYHVHTXH7QROOHJDDFRUWDUVHVLQRTXHVLJXHFRQGXFLHQGR\DTXHGHRWURPRGRODFDtGDHQ5V VHDQXODUtDSRUORTXH7YROYHUtDDHVWDUFRUWDGR % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV (VWDSURWHFFLyQDXPHQWDODWHQVLyQPtQLPDQHFHVDULDSDUDHOIXQFLRQDPLHQWRGHO FLUFXLWR SRU OR TXH WDPELpQ UHGXFH HO UHQGLPLHQWR 3RU RWUD SDUWH HQ OD VLWXDFLyQ GH FRUWRFLUFXLWR9/ ODFRUULHQWHHVPi[LPD'DGRTXHWDPELpQHVPi[LPDODWHQVLyQ TXHFDHHQHOWUDQVLVWRU7ODSRWHQFLDGLVLSDGDHVPX\DOWDREOLJDQGRDVREUHGLPHQVLR QDUHOWUDQVLVWRU 3URWHFFLyQIROGEDFN /D SURWHFFLyQ IROGEDFN ILJXUD HV WDPELpQ XQD SURWHFFLyQ FRQWUD VREUHFR UULHQWHSHURFRQODSURSLHGDGGHUHGXFLUODFRUULHQWHUHVLGXDOHQVLWXDFLyQGHFRUWRFLUFXL WRSRUORWDQWRHVPiVDSURSLDGDFRPRSURWHFFLyQFRQWUDFRUWRFLUFXLWR L* L/ 5V 7 5 5 5 − 7 5/ Y/ Y* 9] 5 5 − − )LJXUD3URWHFFLyQIROGEDFNSDUDHOUHJXODGRUVHULHFRQXQDPSOL ILFDGRURSHUDFLRQDO (VVLPLODUDODSURWHFFLyQFURVVRYHUVyORTXHODEDVHGHOWUDQVLVWRUGHSURWHFFLyQ 7HVWiWRPDGDGHXQGLYLVRUHQWUHHOHPLVRUGH7\PDVD/DWHQVLyQY%(DKRUDQRVyOR GHSHQGHGHODFRUULHQWHGHFDUJDVLQRWDPELpQGHODWHQVLyQGHVDOLGD 5 Y %( = (Y / + L/ 5V ) − Y / 5 + 5 HVGHFLU 5 5 Y %( = L/ 5V − Y/ 5 + 5 5 + 5 1RUPDOPHQWHVHHOLJH55&XDQGRODSURWHFFLyQWRGDYtDQRKDDFWXDGRY/HVDOWD FHUFDQD D VX YDORU QRPLQDO $ GLIHUHQFLD GH OD SURWHFFLyQ FURVVRYHU OD FDtGD HQ 5V QHFHVDULD SDUD TXH 7 FRPLHQFH D FRQGXFLU HV PD\RU TXH 9γ \ OR HVSRUGRVUD]RQHV HVWiOLJHUDPHQWHDWHQXDGDSRU555\HVWiDFRPSDxDGDSRUXQWpUPLQRQHJDWLYR /DFRUULHQWHLQLFLDOGHOSURFHVRGHSURWHFFLyQHV % )HGHULFR0L\DUD $xR L/ Pi[ 9γ 5 Y 5 + + / 5V 5 5V 5 = $SDUWLUGHHVWHPRPHQWRFXDOTXLHULQWHQWRSRUDXPHQWDUODFRUULHQWHGHFDUJDVDWXUDHQ FRUULHQWHUiSLGDPHQWHDODPSOLILFDGRUSRUORFXDOODWHQVLyQGHVDOLGDHPSLH]DDEDMDU$ PHGLGDTXHY/GLVPLQX\HWDPELpQORKDUiODFRUULHQWHGHFDUJDQHFHVDULDSDUDPDQWHQHU 7HQFRQGXFFLyQ)LQDOPHQWHHQODVLWXDFLyQGHFRUWRFLUFXLWRVHWLHQH L/ FF = 9γ 5 + 5V 5 (QODILJXUDVHPXHVWUDODUHODFLyQHQWUHODWHQVLyQGHVDOLGD\ODFRUULHQWHGHFDUJD Y/ 9/ L/FF L/Pi[ L/ )LJXUD7HQVLyQGHVDOLGDHQIXQFLyQGHODFRUULHQWHGHFDUJDSDUD XQUHJXODGRUFRQSURWHFFLyQIROGEDFN &RPRVHDSUHFLDHVWDSURWHFFLyQHVVXSHULRUIUHQWHDODFURVVRYHUHQORTXHDFR UULHQWHGHFRUWRFLUFXLWRVHUHILHUH6LQHPEDUJRFXDQWRPHQRU VHSUHWHQGDTXHVHDL/FF FRQUHVSHFWRDL/Pi[WDQWRPD\RUGHEHUiVHUODFDtGDGHWHQVLyQHQ5VSDUDTXHDFW~HSRU SULPHUDYH]ODSURWHFFLyQORFXDOVHWUDGXFHHQXQSHRUUHQGLPLHQWR'HEHUiEXVFDUVH XQDVROXFLyQGHFRPSURPLVRHQWUHHOUHQGLPLHQWRFHUFDGHODFRUULHQWHPi[LPD\ODFR UULHQWHUHVLGXDOHQFRUWRFLUFXLWR(QDOJXQRVFDVRVSXHGHFRQYHQLUXQDQiOLVLVHVWDGtVWLFR GHODIUHFXHQFLDFRQTXHVHGDUiFDGDXQDGHHVWDVVLWXDFLRQHV3RUHMHPSORVLORVFRUWR FLUFXLWRVSXHGHQVHUIUHFXHQWHV\ODIXHQWHIXQFLRQDGHVDWHQGLGDWDOYH]FRQYHQJDXQD PHQRUL/FF6LVyORUDUDYH]VHGDUiXQFRUWRFLUFXLWRHQWRQFHVFRQYLHQHXQDPHQRUFDtGD LQLFLDOHQ5V % (OHFWUyQLFD,,, )XHQWHVUHJXODGDV $JUDGHFLPLHQWR (ODXWRUDJUDGHFHDO3URI,QJ$OEHUWR*DOLDQRODLQIRUPDFLyQREWHQLGDGHODSX EOLFDFLyQFLWDGDHQODVUHIHUHQFLDV3DUWLFXODUPHQWHODRUJDQL]DFLyQJHQHUDOGHOPDWHULDO HVWiLQVSLUDGDHQDTXHOWUDEDMR 5HIHUHQFLDV *DOLDQR$OEHUWR³)XHQWHVUHJXODGDVFRQVDOLGDGHFRUULHQWHFRQWLQXD´3XEOLFDFLyQLQWHUQDGHODFiWHGUD GH(OHFWUyQLFD/LQHDO,,FD ³1DWLRQDO3RZHU,&V'DWDERRN´1DWLRQDO6HPLFRQGXFWRU6DQWD&ODUD&$86$ 0LOOPDQ-DFRE+DONLDV&KULVWRV³'LVSRVLWLYRV\FLUFXLWRVHOHFWUyQLFRV´(GLFLRQHV3LUiPLGH0DGULG %