Buscar

APOSTILA DE ESTATISTICA

Prévia do material em texto

$$33226677,,//$$
((6677$$77ËË6677,,&&$$
/XLV�)HOLSH�'LDV�/RSHV��'U�
OIORSHV#VPDLO�XIVP�EU��SKLO�]D]#]D]�FRP�EU
'�(�� 8)60
�������
66XXPPiiUULLRR
���&RQFHLWRV�EiVLFRV
�����3RSXODomR�[�$PRVWUD
�����&HQVR�[�$PRVWUDJHP
�����'DGR�[�9DULiYHO
�����3DUkPHWURV�[�HVWDWtVWLFDV
�����$UUHGRQGDPHQWR�GH�GDGRV
�����)DVHV�GR�PpWRGR�HVWDWtVWLFR
���5HSUHVHQWDomR�WDEXODU
�����5HSUHVHQWDomR�HVTXHPiWLFD
�����(OHPHQWRV�GH�XPD�WDEHOD
�����6pULHV�HVWDWtVWLFDV
�����'LVWULEXLomR�GH�IUHT�rQFLD
���5HSUHVHQWDomR�JUiILFD
�����*UiILFRV�GH�/LQKDV
�����*UiILFRV�GH�FROXQDV�RX�EDUUDV
�����*UiILFRV�FLUFXODUHV�RX�GH�6HWRUHV��3LH�&KDUWV�
�����*UiILFR�3LFWRULDO���3LFWRJUDPD
�����*UiILFR�3RODU
�����&DUWRJUDPD
�����*UiILFRV�XWLOL]DGRV�SDUD�D�DQiOLVH�GH�XPD�GLVWULEXLomR�GH�IUHT�rQFLD
���0HGLGDV�GHVFULWLYDV
�����0HGLGDV�GH�SRVLomR
�����0HGLGDV�GH�YDULDELOLGDGH�RX�GLVSHUVmR
�����0HGLGDV�GH�GLVSHUVmR�UHODWLYDV
�����0RPHQWRV��DVVLPHWULD�H�FXUWRVH
�����([HUFtFLRV
���3UREDELOLGDGH�H�YDULiYHLV�DOHDWyULDV
�����0RGHORV�PDWHPiWLFRV
�����&RQFHLWRV�HP�SUREDELOLGDGH
�����&RQFHLWRV�GH�SUREDELOLGDGH
�����([HUFtFLRV
�����7HRUHPD�GH�%D\HV
�����9DULiYHLV�DOHDWyULDV
�����)XQomR�GH�SUREDELOLGDGH
�����([HPSORV
�����([HUFtFLRV
���'LVWULEXLo}HV�GH�3UREDELOLGDGH
�����'LVWULEXLo}HV�GLVFUHWDV�GH�SUREDELOLGDGH
�����([HUFtFLRV
�����'LVWULEXLo}HV�FRQWtQXDV�GH�SUREDELOLGDGH
�����([HUFtFLRV
���$PRVWUDJHP
�����&RQFHLWRV�HP�DPRVWUDJHP
�����3ODQRV�GH�DPRVWUDJHP
�����7LSRV�GH�DPRVWUDJHP
�����$PRVWUDJHP�FRP�H�VHP�UHSRVLomR
�����5HSUHVHQWDomR�GH�XPD�GLVWULEXLomR�DPRVWUDO
�����'LVWULEXLo}HV�DPRVWUDLV�GH�SUREDELOLGDGH
�����([HUFtFLRV
�����(VWDWtVWLFDV�DPRVWUDLV
�����7DPDQKR�GD�DPRVWUD
���(VWLPDomR�GH�SDUkPHWURV
�����(VWLPDomR�SRQWXDO
�����(VWLPDomR�LQWHUYDODU
�����([HUFtFLRV
���7HVWHV�GH�KLSyWHVHV
�����3ULQFLSDLV�FRQFHLWRV
�����7HVWH�GH�VLJQLILFkQFLD
�����([HUFtFLRV
�����7HVWHV�GR�4XL�TXDGUDGR
�����([HUFtFLRV
�� 5HJUHVVmR H�&RUUHODomR
���� �,QWURGXomR
���� 'HILQLomR
���� 0RGHOR �GH�5HJUHVVmR
���� �0pWRGR�SDUD�HVWLPDomR�GRV�SDUkPHWURV�Ⴂ�H�Ⴃ
���� �'HFRPSRVLomR�GD�YDULkQFLD�7RWDO
���� $QiOLVH�GH�9DULkQFLD�GD�5HJUHVVmR
���� �&RHILFLHQWH�GH�'HWHUPLQDomR��Uð�
���� �&RHILFLHQWH�GH�&RUUHODomR��U�
���� ([HUFtFLRV
����5HIHUrQFLDV�ELEOLRJUiILFDV
�
�� &&RRQQFFHHLLWWRRVV %%iiVVLLFFRRVV
����3RSXODomR�[�$PRVWUD
� 3RSXODomR��1���&RQMXQWR�GH�WRGRV�RV�HOHPHQWRV�UHODWLYRV�D�XP�GHWHUPLQDGR�IHQ{PHQR�
TXH� SRVVXHP� SHOR� PHQRV� XPD� FDUDFWHUtVWLFD� HP� FRPXP�� D� SRSXODomR� p� R� FRQMXQWR
8QLYHUVR��SRGHQGR�VHU�ILQLWD�RX�LQILQLWD�
� )LQLWD ��DSUHVHQWD�XP�Q~PHUR�OLPLWDGR�GH�REVHUYDo}HV��TXH�p�SDVVtYHO�GH�FRQWDJHP�
� ,QILQLWD �� DSUHVHQWD� XP� Q~PHUR� LOLPLWDGR� GH� REVHUYDo}HV� TXH� p� LPSRVVtYHO� GH� FRQWDU� H� JHUDOPHQWH� HVWD�
DVVRFLDGD�D�SURFHVVRV�
� $PRVWUD��Q���e�XP�VXEFRQMXQWR�GD�SRSXODomR�H�GHYHUi�VHU�FRQVLGHUDGD�ILQLWD��D�DPRVWUD�
GHYH� VHU� VHOHFLRQDGD� VHJXLQGR� FHUWDV� UHJUDV� H� GHYH� VHU� UHSUHVHQWDWLYD�� GH�PRGR� TXH� HOD�
UHSUHVHQWH�WRGDV�DV�FDUDFWHUtVWLFDV�GD�SRSXODomR�FRPR�VH�IRVVH�XPD�IRWRJUDILD�GHVWD�
�8PD�SRSXODomR�SRGH��PHGLDQWH�SURFHVVRV�RSHUDFLRQDLV��VHU�FRQVLGHUDGD�LQILQLWD��SRLV�D�PHVPD�LUi�GHSHQGHU�
GR� WDPDQKR� GD� DPRVWUD�� 6H� D� IUHT�rQFLD� UHODWLYD� HQWUH� DPRVWUD� H� SRSXODomR� IRU� PHQRU� GR� TXH� ��� HOD� p�
FRQVLGHUDGD�LQILQLWD��VH�D�IUHT�rQFLD�UHODWLYD�IRU�PDLRU�GR����HOD�p�FRQVLGHUDGD�ILQLWD�
��� &HQVR�[�$PRVWUDJHP
� 3HVTXLVD�(VWDWtVWLFD�� e� TXDOTXHU� LQIRUPDomR� UHWLUDGD� GH� XPD� SRSXODomR� RX� DPRVWUD��
SRGHQGR�VHU�DWUDYpV�GH�&HQVR�RX�$PRVWUDJHP�
� &HQVR��e�D�FROHWD�H[DXVWLYD�GH�LQIRUPDo}HV�GDV��1��XQLGDGHV�SRSXODFLRQDLV�
� $PRVWUDJHP��e�R�SURFHVVR�GH�UHWLUDGD�GH�LQIRUPDo}HV�GRV��Q��HOHPHQWRV�DPRVWUDLV��QR�
TXDO�GHYH�VHJXLU�XP�PpWRGR�FULWHULRVR�H�DGHTXDGR��WLSRV�GH�DPRVWUDJHP��
����'DGR�[�9DULiYHO
� 'DGRV�HVWDWtVWLFRV��p�TXDOTXHU�FDUDFWHUtVWLFD�TXH�SRVVD�VHU�REVHUYDGD�RX�PHGLGD�GH�
DOJXPD�PDQHLUD��$V�PDWpULDV�SULPDV�GD�HVWDWtVWLFD�VmR�RV�GDGRV�REVHUYiYHLV�
� 9DULiYHO��e�DTXLOR�TXH�VH�GHVHMD�REVHUYDU�SDUD�VH�WLUDU�DOJXP�WLSR�GH�FRQFOXVmR��JHUDOPHQWH�
DV� YDULiYHLV� SDUD� HVWXGR� VmR� VHOHFLRQDGDV� SRU� SURFHVVRV� GH� DPRVWUDJHP�� 2V� VtPERORV
XWLOL]DGRV�SDUD�UHSUHVHQWDU�DV�YDULiYHLV�VmR�DV�OHWUDV�PDL~VFXODV�GR�DOIDEHWR��WDLV�FRPR�;��<��
=������TXH�SRGH�DVVXPLU�TXDOTXHU�YDORU�GH�XP�FRQMXQWR�GH�GDGRV��$V�YDULiYHLV�SRGHP�VHU�
FODVVLILFDGDV�GRV�VHJXLQWHV�PRGRV�
�
�� 4XDOLWDWLYDV� �RX� DWULEXWRV��� 6mR� FDUDFWHUtVWLFDV� GH� XPD� SRSXODomR� TXH� QmR� SRGH� VHU
PHGLGDV�
1RPLQDO���VmR�XWLOL]DGRV�VtPERORV��RX�Q~PHURV��SDUD�UHSUHVHQWDU�GHWHUPLQDGR�WLSR�GH�
GDGRV��PRVWUDQGR��DVVLP��D�TXDO�JUXSR�RX�FDWHJRULD�HOHV�SHUWHQFHP�
2UGLQDO� RX� SRU� SRVWRV�� TXDQGR� XPD� FODVVLILFDomR IRU� GLYLGLGD� HP� FDWHJRULDV
RUGHQDGDV�HP�JUDXV�FRQYHQFLRQDGRV��KDYHQGR�XPD�UHODomR�HQWUH�DV�FDWHJRULDV�GR�WLSR�
´PDLRU�GR�TXHµ��´PHQRU�GR�TXHµ��´LJXDO�Dµ��RV�GDGRV�SRU�SRVWRV�FRQVLVWHP�GH�YDORUHV�
UHODWLYRV� DWULEXtGRV� SDUD� GHQRWDU� D� RUGHP� GH� SULPHLUR�� VHJXQGR�� WHUFHLUR� H�� DVVLP�
VXFHVVLYDPHQWH�
�� 4XDQWLWDWLYDV�� 6mR� FDUDFWHUtVWLFDV� SRSXODFLRQDLV� TXH� SRGHP� VHU� TXDQWLILFDGDV�� VHQGR
FODVVLILFDGDV�HP�GLVFUHWDV�H�FRQWtQXDV�
'LVFUHWDV�� VmR� DTXHODV� YDULiYHLV� TXH� SRGH� DVVXPLU� VRPHQWH� YDORUHV� LQWHLURV� QXP�
FRQMXQWR� GH� YDORUHV�� e� JHUDGD� SHOR� SURFHVVR� GH� FRQWDJHP�� FRPR� R� Q~PHUR� GH�
YHtFXORV�TXH�SDVVD�HP�XP�SRVWR�GH�JDVROLQD��R�Q~PHUR�GH�HVWXGDQWHV�QHVWD�VDOD�GH�DXOD�
&RQWtQXDV��VmR�DTXHODV�YDULiYHLV�TXH�SRGHP�DVVXPLU�XP�YDORU�GHQWUR�GH�XP�LQWHUYDOR�
GH�YDORUHV��e�JHUDGD�SHOR�SURFHVVR�GH�PHGLomR��1HVWH�FDVR�VHUYH�FRPR�H[HPSOR�R�
YROXPH�GH�iJXD�HP�XP�UHVHUYDWyULR�RX�R�SHVR�GH�XP�SDFRWH�GH�FHUHDO�
����3DUkPHWURV�[�(VWDWtVWLFDV
� 3DUkPHWURV�� VmR� PHGLGDV� SRSXODFLRQDLV� TXDQGR� VH� LQYHVWLJD� D� SRSXODomR� HP� VXD
WRWDOLGDGH��QHVWH�FDVR�p�LPSRVVtYHO�ID]HU�LQIHUrQFLDV��SRLV�WRGD�D�SRSXODomR�IRL�LQYHVWLJDGD�
� (VWDWtVWLFDV� RX�(VWLPDGRUHV�� VmR�PHGLGDV�REWLGDV�GD� DPRVWUD�� WRUQD�VH�SRVVtYHO�QHVWH�
FDVR� XWLOL]DUPRV� DV� WHRULDV� LQIHUrQFLDV� SDUD� TXH� SRVVDPRV� ID]HU� FRQFOXV}HV� VREUH� D
SRSXODomR�
�
����$UUHGRQGDPHQWR�GH�'DGRV
5HJUDV�� 3RUWDULD� ��� GH� ����������� �� ,130 ɝ � ,QVWLWXWR� 1DFLRQDO� GH� 3HVRV� H
0HGLGDV�
�D�� 6H� R� SULPHLUR� DOJDULVPR� DSyV� DTXHOH� TXH� IRUPRV� DUUHGRQGDU� IRU� GH� �� D� ��
FRQVHUYDPRV�R�DOJDULVPR�D�VHU�DUUHGRQGDGR�H�GHVSUH]DPRV�RV�VHJXLQWHV�
([������������SDUD�GpFLPRV��ȝ ����
�D�� 6H� R� SULPHLUR� DOJDULVPR� DSyV� DTXHOH� TXH� IRUPRV� DUUHGRQGDU� IRU� GH� �� D� ��
DFUHVFHQWD�VH� XPD� XQLGDGH� QR� DOJDULVPR� D� VHU� DUUHGRQGDGR� H� GHVSUH]DPRV� RV�
VHJXLQWHV�
([�����������SDUD�GpFLPRV��ȝ ����
�D��6H�R�SULPHLUR�DOJDULVPR�DSyV�DTXHOH�TXH�IRUPRV�DUUHGRQGDU�IRU����VHJXLGR�DSHQDV�
GH�]HURV��FRQVHUYDPRV�R�DOJDULVPR�VH�HOH�IRU�SDU�RX�DXPHQWDPRV�XPD�XQLGDGH�VH�
HOH�IRU�tPSDU��GHVSUH]DQGR�RV�VHJXLQWHV�
([�����������SDUD�GpFLPRV��ȝ ����
��������SDUD�GpFLPRV��ȝ �����
�6H�R� �� IRU� VHJXLGR�GH�RXWURV� DOJDULVPRV�GRV� TXDLV�� SHOR�PHQRV�XP�p�GLIHUHQWH�GH�]HUR��DXPHQWDPRV�XPD�
XQLGDGH�QR�DOJDULVPR�H�GHVSUH]DPRV�RV�VHJXLQWHV�
([�����������SDUD�GpFLPRV��ȝ ����
��������SDUD�GpFLPRV��ȝ ����
�D��4XDQGR��DUUHGRQGDUPRV�XPD�VpULH�GH�SDUFHODV��H�D�VRPD�ILFDU�DOWHUDGD��GHYHPRV�
ID]HU�XP�QRYR�DUUHGRQGDPHQWR��SRU�IDOWD�RX�SRU�H[FHVVR���QD�PDLRU�SDUFHOD�GR�
FRQMXQWR��GH�PRGR�TXH�D�VRPD�ILTXH�LQDOWHUDGD�
([�� ����� � ����� � ����� � ����� � ����� ����
DUUHGRQGDQGR�SDUD�LQWHLUR�
��� � ��� � ��� � ��� � ��� ���
��� � ��� � ��� � ��� � ��� ����
�
����)DVHV�GR�PpWRGR�HVWDWtVWLFR
2�PpWRGR�HVWDWtVWLFR�DEUDQJH�DV�VHJXLQWHV�IDVHV�
D��'HILQLomR�GR�3UREOHPD
&RQVLVWH�QD�
��IRUPXODomR�FRUUHWD�GR�SUREOHPD�
��H[DPLQDU�RXWURV�OHYDQWDPHQWRV�UHDOL]DGRV�QR�PHVPR�FDPSR��UHYLVmR�GD�OLWHUDWXUD��
��VDEHU�H[DWDPHQWH�R�TXH�VH�SUHWHQGH�SHVTXLVDU�GHILQLQGR�R�SUREOHPD�FRUUHWDPHQWH�
�YDULiYHLV��SRSXODomR��KLSyWHVHV��HWF��
E��3ODQHMDPHQWR
'HWHUPLQDU�R�SURFHGLPHQWR�QHFHVViULR�SDUD�UHVROYHU�R�SUREOHPD�
��&RPR�OHYDQWDU�LQIRUPDo}HV�
��7LSRV�GH�OHYDQWDPHQWRV��3RU�&HQVR��FRPSOHWR��
�3RU�$PRVWUDJHP��SDUFLDO��
��&URQRJUDPD��&XVWRV��HWF�
F��&ROHWD�RX�OHYDQWDPHQWR�GRV�GDGRV
&RQVLVWH�QD�REWHQomR�GRV�GDGRV�UHIHUHQWHV�DR�WUDEDOKR�TXH�GHVHMDPRV�ID]HU�$�FROHWD�SRGH�VHU��'LUHWD ��GLUHWDPHQWH�GD�IRQWH�
�,QGLUHWD ��IHLWD�DWUDYpV�GH�RXWUDV�IRQWHV�
2V�GDGRV�SRGHP�VHU�REWLGRV�SHOD�SUySULD�SHVVRD��SULPiULRV��RX�VH�EDVHLD�QR�UHJLVWUR�
GH�WHUFHLURV��VHFXQGiULRV��
G��$SXUDomR�GRV�'DGRV�RX�VXPDUL]DomR
&RQVLVWH� HP� UHVXPLU� RV� GDGRV�� DWUDYpV� GH� XPD� FRQWDJHP� H� DJUXSDPHQWR��e�XP�
WUDEDOKR�GH�FRRUGHQDomR�H�GH�WDEXODomR�
$SXUDomR��PDQXDO��PHFkQLFD��HOHWU{QLFD�H�HOHWURPHFkQLFD�
H��$SUHVHQWDomR�GRV�GDGRV
e�D�IDVH�HP�TXH�YDPRV�PRVWUDU�RV�UHVXOWDGRV�REWLGRV�QD�FROHWD�H�QD�RUJDQL]DomR�
(VWD�DSUHVHQWDomR�SRGH�VHU� 7DEXODU��DSUHVHQWDomR�QXPpULFD�
*UiILFD��DSUHVHQWDomR�JHRPpWULFD�
I��$QiOLVH�H�LQWHUSUHWDomR�GRV�GDGRV
e�D�IDVH�PDLV�LPSRUWDQWH�H�WDPEpP�D�PDLV�GHOLFDGD��7LUD�FRQFOXV}HV�TXH�DX[LOLDP�R�
SHVTXLVDGRU�D�UHVROYHU�VHX�SUREOHPD�
�
�� 55HHSSUUHHVVHHQQWWDDoommRR WWDDEEXXOODDUU
&RQVLVWH� HP�GLVSRU�RV�GDGRV�HP� OLQKDV�H�FROXQDV�GLVWULEXtGDV�GH�PRGR�RUGHQDGR��$�
HODERUDomR�GH� WDEHODV�REHGHFH�j�5HVROXomR�QR������GH����GH�RXWXEUR�GH�������GR�&RQVHOKR�
1DFLRQDO�GH�(VWDWtVWLFD��$V�QRUPDV�GH�DSUHVHQWDomR�VmR�HGLWDGDV�SHOD�)XQGDomR�%UDVLOHLUD�GH�
*HRJUDILD�H�(VWDWtVWLFD��,%*(��
����5HSUHVHQWDomR�HVTXHPiWLFD
7tWXOR
&DEHoDOKR
&RUSR
5RGDSp
����(OHPHQWRV�GH�XPD�WDEHOD
� 7tWXOR��2�WtWXOR�GHYH�UHVSRQGHU�DV�VHJXLQWHV�TXHVW}HV�
��2�TXH"��$VVXQWR�D�VHU�UHSUHVHQWDGR��)DWR���
��2QGH"��2�OXJDU�RQGH�RFRUUHX�R�IHQ{PHQR��ORFDO���
��4XDQGR"��$�pSRFD�HP�TXH�VH�YHULILFRX�R�IHQ{PHQR��WHPSR���
� &DEHoDOKR��SDUWH�GD�WDEHOD�QD�TXDO�p�GHVLJQDGD�D�QDWXUH]D�GR�FRQWH~GR�GH�FDGD�FROXQD�
� &RUSR��SDUWH�GD�WDEHOD�FRPSRVWD�SRU�OLQKDV�H�FROXQDV�
� /LQKDV��SDUWH�GR�FRUSR�TXH�FRQWpP�XPD�VHT�rQFLD�KRUL]RQWDO�GH�LQIRUPDo}HV�
� &ROXQDV��SDUWH�GR�FRUSR�TXH�FRQWpP�XPD�VHT�rQFLD�YHUWLFDO�GH�LQIRUPDo}HV�
� &ROXQD� ,QGLFDGRUD�� FROXQD�TXH�FRQWpP�DV�GLVFULPLQDo}HV�FRUUHVSRQGHQWHV� DRV�YDORUHV�
GLVWULEXtGRV�SHODV�FROXQDV�QXPpULFDV�
� &DVD�RX�FpOXOD��SDUWH�GD�WDEHOD�IRUPDGD�SHOR�FUX]DPHQWR�GH�XPD�OLQKD�FRP�XPD�FROXQD�
� 5RGDSp��e�R�HVSDoR�DSURYHLWDGR�HP�VHJXLGD� DR� IHFKR�GD� WDEHOD��RQGH� VmR�FRORFDGDV� DV�
QRWDV�GH�QDWXUH]D�LQIRUPDWLYD��IRQWH��QRWDV�H�FKDPDGDV��
� )RQWH��UHIHUH�VH�j�HQWLGDGH�TXH�RUJDQL]RX�RX�IRUQHFHX�RV�GDGRV�H[SRVWRV�
� 1RWDV�H�&KDPDGDV��VmR�HVFODUHFLPHQWRV�FRQWLGRV�QD�WDEHOD��QRWD ��FRQFHLWXDomR�JHUDO��
FKDPDGD ��HVFODUHFHU�PLQ~FLDV�HP�UHODomR�D�XPD�FpOXOD��
�
��� 6pULHV�(VWDWtVWLFDV
8PD� VpULH� HVWDWtVWLFD� p� XP� FRQMXQWR� GH� GDGRV� RUGHQDGRV� VHJXQGR� XPD�FDUDFWHUtVWLFD�
FRPXP��DV�TXDLV�VHUYLUmR�SRVWHULRUPHQWH�SDUD�VH�ID]HU�DQiOLVHV�H�LQIHUrQFLDV�
� 6pULH� 7HPSRUDO� RX� &URQROyJLFD� e� D� VpULH� FXMRV� GDGRV� HVWmR� GLVSRVWRV� HP
FRUUHVSRQGrQFLD�FRP�R�WHPSR��RX�VHMD��YDULD�R� WHPSR�H�SHUPDQHFH�FRQVWDQWH�R�IDWR�H�R�
ORFDO�
3URGXomR�GH�3HWUyOHR�%UXWR�QR�%UDVLO�GH������D�������[������Pò�
$QRV 3URGXomR
���� �����
���� �����
���� �����
���� �����
���� ������
)RQWH��&RQMXQWXUD�(FRQ{PLFD��IHY�������
� 6pULH� *HRJUiILFD� RX� 7HUULWRULDO� e� D� VpULH� FXMRV� GDGRV� HVWmR� GLVSRVWRV� HP
FRUUHVSRQGrQFLD�FRP�R�ORFDO��RX�VHMD��YDULD�R�ORFDO�H�SHUPDQHFH�FRQVWDQWH�D�pSRFD�H�R�IDWR�
3RSXODomR�8UEDQD�GR�%UDVLO�HP�������[������
5HJLmR 3RSXODomR
1RUWH ������
1RUGHVWH ������
6XGHVWH ������
6XO ������
&HQWUR�2HVWH ������
7RWDO ������
)RQWH��$QXiULR�(VWDWtVWLFR�������
� 6pULH� (VSHFtILFD� RX� 4XDOLWDWLYD� e� D� VpULH� FXMRV� GDGRV� HVWmR� GLVSRVWRV� HP
FRUUHVSRQGrQFLD�FRP�D�HVSpFLH�RX�TXDOLGDGH��RX�VHMD��YDULD�R�IDWR�H�SHUPDQHFH�FRQVWDQWH�D�
pSRFD�H�R�ORFDO�
3RSXODomR�8UEDQD�H�5XUDO�GR�%UDVLO�HP�������[������
/RFDOL]DomR 3RSXODomR
8UEDQD �������
5XUDO �������
7RWDO �������
)RQWH��$QXiULR�(VWDWtVWLFR�������
�
� 6pULH�0LVWD�RX�&RPSRVWD�� $�FRPELQDomR�HQWUH�GXDV�RX�PDLV�VpULHV�FRQVWLWXHP�QRYDV�
VpULHV�GHQRPLQDGDV�FRPSRVWDV�H�DSUHVHQWDGDV�HP�WDEHODV�GH� GXSOD� HQWUDGD��2�QRPH�GD�
VpULH�PLVWD�VXUJH�GH�DFRUGR�FRP�D�FRPELQDomR�GH�SHOR�PHQRV�GRLV�HOHPHQWRV�
/RFDO���eSRFD� �6pULH�*HRJUiILFD�7HPSRUDO
3RSXODomR�8UEDQD�GR�%UDVLO�SRU�5HJLmR�GH������D�������[������
5�(�*�,�¯�(�6
$QRV 1 1( 6( 6 &2
���� ���� ������ ������ ������ �����
���� ���� ������ ������ ������ �����
���� ���� ������ ������ ������ �����
���� ����� ������ ������ ������ �����
���� ����� ������ ������ ������ �����
)RQWH��$QXiULR�(VWDWtVWLFR�������
����'LVWULEXLomR�GH�)UHT�rQFLD
e�R�WLSR�GH�VpULH�HVWDWtVWLFD�QD�TXDO�SHUPDQHFH�FRQVWDQWH�R�IDWR��R�ORFDO�H�D�pSRFD��2V�
GDGRV�VmR�FRORFDGRV�HP�FODVVHV�SUHHVWDEHOHFLGDV��UHJLVWUDQGR�D�IUHT�rQFLD�GH�RFRUUrQFLD��8PD�
GLVWULEXLomR�GH�IUHT�rQFLD�SRGH�VHU�FODVVLILFDGD�HP�GLVFUHWD�H�LQWHUYDODU�
D��'LVWULEXLomR�GH�)UHT�rQFLD�'LVFUHWD�RX�3RQWXDO��e�XPD�VpULH�GH�GDGRV�DJUXSDGRV�QD�
TXDO�R�Q~PHUR�GH�REVHUYDo}HV�HVWi�UHODFLRQDGR�FRP�XP�SRQWR�UHDO�
1RWDV�GR�$OXQR��;��QD�'LVFLSOLQD�GH�(VWDWtVWLFD�VHJXQGR
FULWpULRV�GH�DYDOLDomR�GR�'(�GD�8)60�²�����
;L IL
��� �
��� �
��� �
��� �
��� �
ႛ ��
)RQWH��'HSDUWDPHQWR�GH�(VWDWtVWLFD�������
�
E��'LVWULEXLomR� GH� )UHT�rQFLDV� ,QWHUYDODU�� 1D�GLVWULEXLomR� GH� IUHT�rQFLD�� RV� LQWHUYDORV�
SDUFLDLV�GHYHUmR�VHU�DSUHVHQWDGRV�GH�PDQHLUD�D�HYLWDU�G~YLGDV�TXDQWR�j�FODVVH�D�TXH�SHUPDQHFH�
GHWHUPLQDGR�HOHPHQWR�
2� WLSR� GH� LQWHUYDOR� PDLV� XVDGR� p� GR� WLSR� IHFKDGR� D� HVTXHUGD� H� DEHUWR� D� GLUHLWD�
UHSUHVHQWDGR�SHOR�VtPEROR��_����
$OWXUD�HP�FHQWtPHWURV�GH�����DOXQRV�GR�&XUVR�GH�$GPLQLVWUDomR�GD�8)60�������
$OWXUD��FP� ;L IL
��� _��� ��� ��� ��
��� _��� ��� ��� ��
��� _��� ��� ��� ��
��� _��� ��� ��� ��
��� _��� ��� ��� ��
��� _��� ��� ��� ��
ႛ ���� ���
)RQWH��'HSDUWDPHQWR�GH�(VWDWtVWLFD�������
(OHPHQWRV�GH�XPD�'LVWULEXLomR�GH�)UHT�rQFLDV�
¾ &ODVVH�RX�&ODVVH�GH�)UHT�rQFLD� �.���e�FDGD� VXELQWHUYDOR� �OLQKD��QD�TXDO�GLYLGLPRV�R�
IHQ{PHQR�
3DUD�GHWHUPLQDU�R�Q~PHUR�GH�FODVVHV�D�SDUWLU�GRV�GDGRV�QmR�WDEHODGRV��SRGHPRV�XVDU�D�
)yUPXOD� GH� 6WXUJHV�� PDV� GHYH�VH� VDEHU� TXH� H[LVWHP� RXWURV� PpWRGRV� GH� GHWHUPLQDomR�GR�
Q~PHUR�GH�FODVVHV�HP�XPD�WDEHOD�GH�IUHT�rQFLD��2�TXH�VH�GHVHMD�ID]HU�p�DSHQDV�FRPSULPLU�XP�
FRQMXQWR�GH�GDGRV�HP�XPD�WDEHOD��SDUD�IDFLOLWDU�D�YLVXDOL]DomR�H�LQWHUSUHWDomR�GRV�PHVPRV�
QORJ����Q�.� � ��RQGH�´Qµ�p�QR�GH�LQIRUPDo}HV�
�$OpP�GD�5HJUD�GH�6WXUJHV��H[LVWHP�RXWUDV�IyUPXODV�HPStULFDV�SDUD�UHVROYHU�R�SUREOHPD�SDUD�GHWHUPLQDomR�
GR�Q~PHUR�GH�FODVVHV�>Q�N�@��Ki�TXHP�SUHILUD� Q�N�Q ː ��(QWUHWDQWR��D�YHUGDGH�p�TXH�HVVDV�IyUPXODV�QmR�
QRV�OHYDP�D�XPD�GHFLVmR�ILQDO��HVWD�YDL�GHSHQGHU� QD�UHDOLGDGH�GH�XP�MXOJDPHQWR�SHVVRDO��TXH�GHYHUi�HVWDU�
OLJDGR� D� QDWXUH]D� GRV� GDGRV�� SURFXUDQGR�� VHPSUH� TXH� SRVVtYHO�� HYLWDU� FODVVHV� FRP� IUHT�rQFLDV� QXODV� RX�
IUHT�rQFLDV�UHODWLYDV�H[DJHUDGDPHQWH�JUDQGHV�
¾ /LPLWH�GH�&ODVVH��OL�RX�/L���6mR�RV�YDORUHV�H[WUHPRV�GH�FDGD�FODVVH�
OL� �OLPLWH�LQIHULRU�GD�L�pVLPD�FODVVH��
/L� �OLPLWH�VXSHULRU�GD�L�pVLPD�FODVVH��
�
¾ $PSOLWXGH� GR� LQWHUYDOR� GH� FODVVH� �K��� e� D� GLIHUHQoD� HQWUH� GRLV� OLPLWHV� LQIHULRUHV� RX�
VXSHULRUHV�FRQVHFXWLYRV���
OOK �QQ ʝʝ �RX� �QQ // K ʝʝ
�$�DPSOLWXGH�GR�LQWHUYDOR�GH�FODVVH�GHYH�VHU�FRQVWDQWH�HP�WRGR�D�GLVWULEXLomR�GH�IUHT�rQFLDV�LQWHUYDODU�
¾ $PSOLWXGH�WRWDO��+��� e�D�GLIHUHQoD� HQWUH�R� OLPLWH� VXSHULRU�GD�~OWLPD� FODVVH� H�R� OLPLWH�
LQIHULRU�GD����FODVVH��RX�D�GLIHUHQoD�HQWUH�~OWLPR�H�R�SULPHLUR�HOHPHQWR�GH�XP�FRQMXQWR�GH�
GDGRV�SRVWRV�HP�RUGHP�FUHVFHQWH�
�Q O/+ ʝ 
¾ 3RQWR�PpGLR�GH�FODVVH��;L���e�D�PpGLD�DULWPpWLFD�VLPSOHV�GR�OLPLWH�LQIHULRU�FRP�R�OLPLWH�
VXSHULRU�GH�XPD�PHVPD�FODVVH�
�
/O
; LLL
�
 
RX�D�SDUWLU�GR�;��RV�GHPDLV�SRQWRV�PpGLRV�SRGH�VHU�GHWHUPLQDGR�SRU�
K;; �QQ � ʝ
�4XDQGR� VXEVWLWXLUPRV� RV� LQWHUYDORV� GH� FODVVHV� SHORV� SRQWRV�PpGLRV� �;L��� WHU�VH��i�XPD� GLVWULEXLomR�GH�
IUHT�rQFLD�SRQWXDO �
¾ )UHT�rQFLD�DEVROXWD��IL���e�D�TXDQWLGDGH�GH�YDORUHV�HP�FDGD�FODVVH
Q��
Q
�L
L I���IIIQ ��� ʜ
 
¾ )UHT�rQFLD�$FXPXODGD��)L���e�R�VRPDWyULR�GD�IUHT�rQFLD�DEVROXWD�GD�L�pVLPD�FODVVH�FRP�
D�IUHT�rQFLD�DEVROXWD�GDV�FODVVHV�DQWHULRUHV��RX�D�IUHT�rQFLD�DFXPXODGD�GD�FODVVH�DQWHULRU�
QI)
Q
�L
LQ ʜ
 
¾ )UHT�rQFLD�5HODWLYD� �IUL���e�R�TXRFLHQWH� HQWUH� D� IUHT�rQFLD� DEVROXWD� GD� L�pVLPD�FODVVH�
FRP�R�VRPDWyULR�GDV�IUHT�rQFLDV�
ʜ
 
 
Q
�L
L
L
L
I
I
IU 2EV��� �IU
Q
�L
L ʜ
 
¾ )UHT�rQFLD�5HODWLYD�$FXPXODGD��)UL���e�R�VRPDWyULR�GD�IUHT�rQFLD�UHODWLYD�GD�L�pVLPD�FODVVH�FRP�DV�IUHT�rQFLDV�UHODWLYDV�GDV�FODVVHV�DQWHULRUHV�
�IU)U
Q
�L
LQ ʜ
 
��
�� 55HHSSUUHHVVHHQQWWDDoommRR JJUUiiIILLFFDD
2V�JUiILFRV�VmR�XPD�IRUPD�GH�DSUHVHQWDomR�YLVXDO�GRV�GDGRV��1RUPDOPHQWH��FRQWpP�
PHQRV�LQIRUPDo}HV�TXH�DV�WDEHODV��PDV�VmR�GH�PDLV�IiFLO�OHLWXUD��2�WLSR�GH�JUiILFR�GHSHQGH�GD�
YDULiYHO�HP�TXHVWmR
����*UiILFRV�GH�/LQKDV
8VDGR�SDUD�LOXVWUDU�XPD�VpULH�WHPSRUDO�
3URGXomR�GH�3HWUyOHR�%UXWR�QR�%UDVLO�GH������D�������[������Pò�
$QRV
3URGXomR
����
����
����
�����
�����
�����
���� ���� ���� ���� ����
)RQWH��&RQMXQWXUD�(FRQ{PLFD��)HY�������
������*UiILFR�GH�OLQKDV�FRPSDUDWLYDV
3RSXODomR�8UEDQD�GR�%UDVLO�SRU�5HJLmR�GH������D�������[������
�
����
�����
�����
�����
�����
�����
�����
�����
�����
���� ���� ���� ���� ����
1(
1
6(
6
&2
)RQWH��$QXiULR�(VWDWtVWLFR�������
��
����*UiILFRV�GH�FROXQDV�RX�EDUUDV
5HSUHVHQWDomR� JUiILFD� GD� GLVWULEXLomR� GH� IUHT�rQFLDV�� (VWH� JUiILFR� p� XWLOL]DGR� SDUD�
YDULiYHLV�QRPLQDLV�H�RUGLQDLV��
&DUDFWHUtVWLFDV�
��WRGDV�DV�EDUUDV�GHYHP�WHU�D�PHVPD�ODUJXUD�
��GHYHP�H[LVWLU�HVSDoRV�HQWUH�DV�EDUUDV�
������*UiILFR�GH�&ROXQDV
8VDGR�SDUD�LOXVWUDU�TXDOTXHU�WLSR�GH�VpULH�
3RSXODomR�8UEDQD�GR�%UDVLO�HP�������[������
1 1( 6( 6 &2
5HJL}HV
����
�����
�����
�����
����
�
�����
�����
�����
�����
�����
3RS�
1 1( 6( 6 &2
5HJL}HV
)RQWH��$QXiULR�(VWDWtVWLFR�������
�$V�ODUJXUDV�GDV�EDUUDV�TXH�GHYHUmR�VHU�WRGDV�LJXDLV�SRGHQGR�VHU�DGRWDGR�TXDOTXHU�GLPHQVmR��GHVGH�TXH�VHMD�
FRQYHQLHQWH� H� GHVGH�TXH�QmR� VH� VXSHUSRQKDP��2�Q~PHUR�QR� WRSR�GH� FDGD�EDUUD�SRGH�RX�QmR�RPLWLGR�� VH�
IRUHP�FRQVHUYDGRV��D�HVFDOD�YHUWLFDO�SRGH�VHU�RPLWLGD�
��������*UiILFR�GH�FROXQDV�FRPSDUDWLYDV
D��&ROXQDV�-XVWDSRVWDV��JUiILFR�FRPSDUDWLYR�
3RSXODomR�8UEDQD�GR�%UDVLO�SRU�5HJLmR�GH������D�������[������
�
����
�����
�����
�����
�����
�����
�����
�����
�����
���� ���� ���� ���� ����
1
1(
6(
6
&2
)RQWH��$QXiULR�(VWDWtVWLFR�������
��
E��&ROXQDV�6REUHSRVWDV��JUiILFR�FRPSDUDWLYR�
3RSXODomR�8UEDQD�GR�%UDVLO�SRU�5HJLmR�GH������D�������[������
�
�����
�����
�����
�����
������
���� ���� ���� ���� ����
&2
6
6(
1
1(
)RQWH��$QXiULR�(VWDWtVWLFR�������
������*UiILFR�GH�%DUUDV
$V�UHJUDV�XVDGDV�SDUD�R�JUiILFR�GH�EDUUDV�VmR�LJXD LV�DV�XVDGDV�SDUD�R�JUiILFR�GH�FROXQDV�
3RSXODomR�8UEDQD�GR�%UDVLO�HP�������[������
5HJL}HV
3RSXODomR
� ����� ����� ����� ����� �����
1
1(
6(
6
&2
����
�����
�����
�����
����
)RQWH��$QXiULR�(VWDWtVWLFR�������
��$VVLP�FRPR�RV�JUiILFRV�GH�&ROXQDV�SRGHP�VHU�FRQVWUXtGRV�JUiILFRV�GH�EDUUDV�FRPSDUDWLYDV�
����*UiILFRV�FLUFXODUHV�RX�GH�6HWRUHV��3LH�&KDUWV�
5HSUHVHQWDomR� JUiILFD� GD� IUHT�rQFLD� UHODWLYD� �SHUFHQWDJHP�� GH� FDGD� FDWHJRULD� GD�
YDULiYHO��(VWH�JUiILFR�p�XWLOL]DGR�SDUD�YDULiYHLV�QRPLQDLV�H�RUGLQDLV��e�XPD�RSomR�DR�JUiILFR�GH�
EDUUDV� TXDQGR� VH� SUHWHQGH� GDU� rQIDVH� j� FRPSDUDomR� GDV� SHUFHQWDJHQV� GH� FDGD� FDWHJRULD�� $�
FRQVWUXomR�GR�JUiILFR�GH� VHWRUHV� VHJXH�XPD� UHJUD�GH��� VLPSOHV��RQGH�DV� IUHT�rQFLDV�GH�FDGD�
FODVVH� FRUUHVSRQGHP�DR�kQJXOR�TXH� VH�GHVHMD� UHSUHVHQWDU� HP� UHODomR� D� IUHT�rQFLD� WRWDO�TXH�
UHSUHVHQWD�R�WRWDO�GH����� �
��
&DUDFWHUtVWLFDV�
��$�iUHD�GR�JUiILFR�HTXLYDOH�j�WRWDOLGDGH�GH�FDVRV�����R� �������
��&DGD�´IDWLDµ�UHSUHVHQWD�D�SHUFHQWDJHP�GH�FDGD�FDWHJRULD
3RSXODomR�8UEDQD�H�5XUDO�GR�%UDVLO�HP�������[������
���
���
8UEDQD
5XUDO
)RQWH��$QXiULR�(VWDWtVWLFR�������
����*UiILFR�3LFWRULDO���3LFWRJUDPD
7HP� SRU� REMHWLYR� GHVSHUWDU� D� DWHQomR� GR� S~EOLFR� HP� JHUDO�� PXLWR� GHVVHV� JUiILFRV
DSUHVHQWDP�JUDQGH�GRVH�GH�RULJLQDOLGDGH�H�GH�KDELOLGDGH�QD�DUWH�GH�DSUHVHQWDomR�GRV�GDGRV�
(YROXomR�GD�PDWULFXOD�QR�(QVLQR�6XSHULRU�QR�%UDVLO�GH������D�������[������
���� ���� ���� ���� ���� ����
�
���
���
���
����
����
����
)RQWH��*UDQGHV�Q~PHURV�GD�HGXFDomR�EUDVLOHLUD�PDUoR�GH�����
��
������([HPSORV�GH�SLFWRJUDPDV
(YROXomR�GD�IURWD�QDFLRQDO�GH�FDUURV�j�iOFRRO�GH������j�����
�����
����
���������
����
���������
����
���������
����
2V�PpWRGRV�PDLV�HILFLHQWHV�SDUD�GHL[DU�GH�IXPDU�VHJXQGR��������IXPDQWHV
HQWUHYLVWDGRV�QR�&DQDGi
���
���
���
�����
�����
*RPD�GH�PDVFDU�FRP�QLFRWLQD
PDLV�VHVV}HV�GH�DSRLR�SVLFROyJLFR
,QWHUQDPHQWR�HP�KRVSLWDO
�H�XVR�GH�GURJDV�UHOD[DQWHV�
$FXPSXQWXUD
+LSQRVH
,QMHomR�GH�&ORQLGLQD��GURJD�TXH
UHGX]�RV�HIHLWRV�GD�DEVWLQrQFLD
'HYDVWDomR�6HOYDJHP��H[WUDomR�GH�PDGHLUDV�QR�%UDVLO
(XFDOLSWR
0DGHLUD
�QDWLYD
3LQXV
�����
�����
����
��
����*UiILFR�3RODU
e�R�WLSR�GH�JUiILFR�LGHDO�SDUD�UHSUHVHQWDU�VpULHV�WHPSRUDLV�FtFOLFDV��RX�VHMD��WRGD�D�VpULH�
TXH�DSUHVHQWD�XPD�GHWHUPLQDGD�SHULRGLFLGDGH�
������&RPR�FRQVWUXLU�XP�JUiILFR�SRODU
��� 7UDoD�VH� XPD� FLUFXQIHUrQFLD� GH� UDLR� DUELWUiULR� �SUHIHUHQFLDOPHQWH�� D� XP� UDLR� GH
FRPSULPHQWR�SURSRUFLRQDO�D�PpGLD�GRV�YDORUHV�GD�VpULH��
���&RQVWUyL�VH�XPD�VHPL�UHWD��GH�SUHIHUrQFLD�KRUL]RQWDO��SDUWLQGR�GR�SRQWR����SyOR��H�
FRP�XPD�HVFDOD��HL[R�SRODU��
���'LYLGH�VH�D�FLUFXQIHUrQFLD�HP�WDQWRV�DUFRV�IRUHP�DV�XQLGDGHV�WHPSRUDLV�
���7UDoD �VH�VHPL�UHWDV�D�SDUWLU�GR�SRQWR����SyOR��SDVVDQGR�SHORV�SRQWRV�GH�GLYLVmR�
���0DUFD�VH�RV�YDORUHV�FRUUHVSRQGHQWHV�GD�YDULiYHO��LQLFLDQGR�SHOD�VHPL�UHWD�KRUL]RQWDO�
�HL[R�SRODU��
���/LJDP�VH�RV�SRQWRV�HQFRQWUDGRV�FRP�VHJPHQWRV�GH�UHWD�
���3DUD�IHFKDU�R�SROtJRQR�REWLGR��HPSUHJD�VH�XPD�OLQKD�LQWHUURPSLGD�
3UHFLSLWDomR�SOXYLRPpWULFD�GR�PXQLFtSLR�GH�6DQWD�
0DULD�±�56������
0HVHV 3UHFLSLWDomR��PP�
-DQHLUR �����
)HYHUHLUR ����
0DUoR ����
$EULO �����
0DLR �����
-XQKR �����
-XOKR �����
$JRVWR �����
6HWHPEUR ����
2XWXEUR ����
1RYHPEUR ����
'H]HPEUR �����
)RQWH��%DVH�$pUHD�GH�6DQWD�0DULD
0pGLD� ��������PP
3UHFLSLWDomR�SOXYLRPpWULFD�GR�PXQLFtSLR�GH�6DQWD�
0DULD�±�56������
)RQWH��%DVH�$pUHD�GH�6DQWD�0DULD
��
����&DUWRJUDPD
e�D�UHSUHVHQWDomR�GH�XPD�FDUWD�JHRJUiILFD��(VWH�WLSR�GH�JUiILFR�p�HPSUHJDGR�TXDQGR�R�
REMHWLYR�p�R�GH�ILJXUDU� RV�GDGRV�HVWDWtVWLFRV�GLUHWDPHQWH�UHODFLRQDGRV�FRP�DV�iUHDV�JHRJUiILFDV�
RX�SROtWLFDV
'DGRV�DEVROXWRV��SRSXODomR��²�XVD�VH�SRQWRV�SURSRUFLRQDLV�DRV�GDGRV�
'DGRV�UHODWLYRV��GHQVLGDGH��²�XVD�VH�KDFKDGXUDV�
([HPSOR�
3RSXODomR�GD�5HJLmR�6XO�GR�%UDVLO�������
(VWDGR 3RSXODomR��KDE�� ÉUHD��P �� 'HQVLGDGH
3DUDQi ��������� ������� ����
6DQWD�&DWDULQD ��������� ������ ����
5LR�*UDQGH�GR�6XO ��������� ������� ����
)RQWH��,%*(
3RSXODomR�GD�5HJLmR�6XO�GR�%UDVLO�±�����
)RQWH��,%*(
'HQVLGDGH�SRSXODFLRQDO�GD�5HJLmR�6XO�GR�%UDVLO�±�����
)RQWH��,%*(
��
����*UiILFRV�XWLOL]DGRV�SDUD�D�DQiOLVH�GH�XPD�GLVWULEXLomR�GH�IUHT�rQFLD
������+LVWRJUDPD
$OWXUD�HP�FHQWtPHWURV�GH�����DOXQRV�GR�&XUVR�GH�$GPLQLVWUDomR�GD�8)60�������
)RQWH��'HSDUWDPHQWR�GH�(VWDWtVWLFD�������
������3ROtJRQR�GH�)UHT�rQFLDV
$OWXUD�HP�FHQWtPHWURV�GH�����DOXQRV�GR�&XUVR�GH�$GPLQLVWUDomR�GD�8)60�������
)RQWH��'HSDUWDPHQWR�GH�(VWDWtVWLFD�������
��
������2JLYDV
$OWXUD�HP�FHQWtPHWURV�GH�����DOXQRV�GR�&XUVR�GH�$GPLQLVWUDomR�GD�8)60�²�����
2JLYD�&UHVFHQWH 2JLYD�'HFUHVFHQWH
������*UiILFR�HP�VHJPHQWRV�GH�UHWD�YHUWLFDO
e� XWLOL]DGR� SDUD� UHSUHVHQWDU� XPD� GLVWULEXLomR� GH� IUHT�rQFLD� SRQWXDO�� RQGH� RV
VHJPHQWRV�GH�UHWD�VmR�SURSRUFLRQDLV�jV�UHVSHFWLYDV�IUHT�rQFLDV�DEVROXWDV�
$OWXUD�HP�FHQWtPHWURV�GH�����DOXQRV�GR�&XUVR�GH�$GPLQLVWUDomR�GD�8)60�������
)RQWH��'HSDUWDPHQWR�GH�(VWDWtVWLFD�������
������&RPR�VH�LQWHUSUHWD�XP�KLVWRJUDPD"
$� UHSUHVHQWDomR� JUiILFD� GD� GLVWULEXLomR� GD� YDULiYHO�� SRU� KLVWRJUDPDV�� (VWH� JUiILFR� p
XWLOL]DGR�SDUD�YDULiYHLV�FRQWtQXDV�
&DUDFWHUtVWLFDV�
��&DGD�EDUUD�UHSUHVHQWD�D�IUHT�rQFLD�GR�LQWHUYDOR�UHVSHFWLYR�
��2V�LQWHUYDORV�GHYHP�WHU�D�PHVPD�DPSOLWXGH�
��$V�EDUUDV�GHYHP�HVWDU�WRGDV�MXQWDV�
��
$�VLPSOHV�REVHUYDomR�GD� IRUPD�GR�
KLVWRJUDPD� SHUPLWH� DOJXPDV� FRQFOXV}HV�
9HMD�D�ILJXUD������$�PHGLGD�GRV�GDGRV�HVWi�
QR�FHQWUR�GR�GHVHQKR��$V�IUHT�rQFLDV�PDLV�
DOWDV� WDPEpP� HVWmR� QR� FHQWUR� GD� ILJXUD�
1RV� SURFHVVRV� LQGXVWULDLV�� HVWD� p� D� IRUPD�
GHVHMiYHO��
)LJXUD�����+LVWRJUDPD
��
��
��
��
��
��
�
$� ILJXUD� ���� DSUHVHQWD� XP
KLVWRJUDPD� FRP� DVVLPHWULD� SRVLWLYD�� $
PpGLD�GRV�GDGRV�HVWi�ORFDOL]DGD�j�HVTXHUGD�
GR� FHQWUR� GD� ILJXUD� H� D� FDXGD�j�GLUHLWD�p�
DORQJDGD�� (VWD� RFRUUH� TXDQGR� R�OLPLWH
LQIHULRU� p� FRQWURODGR� RX� TXDQGR� QmR
SRGHP� RFRUUHU� YDORUHV� DEDL[R� GH
GHWHUPLQDGR�OLPLWH�
)LJXUD� ���� +LVWRJUDPD� FRP� DVVLPHWULD
SRVLWLYD
��
��
��
��
��
��
�
$� ILJXUD� ���� DSUHVHQWD� XP
KLVWRJUDPD� FRP� DVVLPHWULD� QHJDWLYD�� $
PpGLD�GRV�GDGRV�HVWi�ORFDOL]DGD�j�GLUHLWD�GR�
FHQWUR� GD� ILJXUD� H� D� FDXGD� j� HVTXHUGD� p
DORQJDGD�� (VWD� IRUPD� RFRUUH� TXDQGR� R
OLPLWH�VXSHULRU�p�FRQWURODGR�RX�TXDQGR�QmR�
SRGHP� RFRUUHU� YDORUHV� DFLPD� GH� FHUWR
OLPLWH
)LJXUD� ���� +LVWRJUDPD� FRP� DVVLPHWULD
QHJDWLYD
��
��
��
��
��
��
�
��
$�ILJXUD�����PRVWUD�XP�KLVWRJUDPD�
HP� SODWHDX�� ,VWR� p�� FRP� H[FHomR� GDV
SULPHLUDV� H� GDV� ~OWLPDV� FODVVHV�� WRGDV� DV
RXWUDV� WrP� IUHT�rQFLDV� TXDVH� LJXDLV�� (VVD�
IRUPD� RFRUUH� TXDQGR� VH� PLVWXUDP� YiULDV
GLVWULEXLo}HV�FRP�GLIHUHQWHV�PpGLDV�
)LJXUD�����+LVWRJUDPD�HP�SODWHDX
��
��
��
��
��
��
�
$�ILJXUD�����PRVWUD�XP�KLVWRJUDPD�
FRP� GRLV� SLFRV �� RX� GXDV� PRGDV�� $V
IUHT�rQFLDV�VmR�EDL[DV�QR�FHQWUR�GD�ILJXUD��
PDV�H[LVWHP�GRLV�SLFRV�IRUD�GR�FHQWUR��(VWD�
IRUPD� RFRUUH� TXDQGR� GXDV� GLVWULEXLo}HV
FRP� PpGLDV� EHP� GLIHUHQWHV� VH� PLVWXUDP�
3RGHP� HVWDU�PLVWXUDGRV�� SRU� H[HPSOR�� RV�
SURGXWRV�GH�GRLV�WXUQRV�GH�WUDEDOKR�
)LJXUD� ���� +LVWRJUDPD� FRP� GRLV
SLFRV
��
��
��
��
��
��
�
2V�KLVWRJUDPDV�WDPEpP�PRVWUDP�R�JUDX�GH�GLVSHUVmR�GD�YDULiYHO��9HMD�D�ILJXUD������2�
KLVWRJUDPD� j� HVTXHUGD�PRVWUD� SRXFD� GLVSHUVmR�� PDV� R� KLVWRJUDPD� j� GLUHLWD� PRVWUD� JUDQGH�
GLVSHUVmR�
)LJXUD�����+LVWRJUDPDV�FRP�GLVSHUV}HV�GLIHUHQWHV
)UHT�rQFLD��������������������������������������������������������������)UHT�rQFLD�������������
��
��
��
��
��
��
�
��
��
��
��
��
��
�
��
������&XUYD�GH�IUHT�rQFLD�²�FXUYD�SROLGD
&RPR�� HP� JHUDO�� RV� GDGRV� FROHWDGRV� SHUWHQFHP� D� XPD� DPRVWUD� H[WUDtGD� GH� XPD�
SRSXODomR��SRGH�VH�LPDJLQDU�DV�DPRVWUDV�WRUQDQGR�VH�FDGD�YH]�PDLV�DPSODV�H�D�DPSOLWXGH�GDV�
FODVVHV� ILFDQGR�FDGD�YH]�PHQRU��R�TXH�QRV�SHUPLWH�FRQFOXLU�TXH�R�FRQWRUQR�GR�SROtJRQR�GH�
IUHT�rQFLDV� WHQGH� D� VH� WUDQVIRUPDU� QXPD� FXUYD� �FXUYD� GH� IUHT�rQFLD���PRVWUDQGR��GH�PRGR�
PDLV�HYLGHQWH��D�YHUGDGHLUD�QDWXUH]D�GD�GLVWULEXLomR�GD�SRSXODomR�
3RGH�VH�GL]HU�� HQWmR��TXH�� HQTXDQWR�TXH�R�SROtJRQR�GH� IUHT�rQFLD�QRV�Gi�D� LPDJHP�
UHDO�GR�IHQ{PHQR�HVWXGDGR��D�FXUYD�GH�IUHT�rQFLD�QRV�Gi�D�LPDJHP�WHQGHQFLRVD�
$VVLP��DSyV�R�WUDoDGR�GH�XP�SROtJRQR�GH�IUHT�rQFLD��p�GHVHMiYHO��PXLWDV�YH]HV��TXH�VH�
IDoD�XP�SROLPHQWR�� GH�PRGR�D�PRVWUDU�R�TXH� VHULD� WDO�SROtJRQR�FRP�XP�Q~PHUR�PDLRU�GH�
GDGRV�
(VVH�SURFHGLPHQWR�p�FODUR��QmR�QRV�GDUi�FHUWH]D�DEVROXWD�TXH�D�FXUYD�SROLGD�VHMD�WDO�
TXDO� D� FXUYD� UHVXOWDQWH� GH� XP� JUDQGH� Q~PHUR� GH� GDGRV�� 3RUpP�� SRGH�VH� DILUPDU� TXH� HOD�
DVVHPHOKD�VH�PDLV�D�FXUYD�GH�IUHT�rQFLD�TXH�R�SROtJRQR�GH�IUHT�rQFLD�REWLGR�GH�XPD�DPRVWUD�
OLPLWDGD�
2� SROLPHQWR�� JHRPHWULFDPHQWH�� FRUUHVSRQGH� j� HOLPLQDomR� GRV� YpUWLFHV� GD� OLQKD
SROLJRQDO��&RQVHJXH�VH�LVVR�FRP�D�VHJXLQWH�IyUPXOD�
�
II�I
IF �SRVWL�DQWL
��
 
RQGH�
IFL� �IUHT�rQFLD�FDOFXODGD�GD�FODVVH�FRQVLGHUDGD�
IL� �IUHT�rQFLD�DEVROXWD�GD�FODVVH�L�
IDQW�� �IUHT�rQFLD�DEVROXWD�GD�FODVVH�DQWHULRU�D�L�
ISRVW�� �IUHT�rQFLD�DEVROXWD�GD�FODVVH�SRVWHULRU�D�L�
��4XDQGR�IRU�HP�ID]HU�R�XVR�GD�FXUYD�SROLGD�FRQYpP�PRVWUDU�DV�IUHT�rQFLDV�DEVROXWDV��SRU�PHLR�GH�
XP�SHTXHQR�FLUFXOR��GH�PRGR�TXH�TXDOTXHU�LQWHUHVVDGR�SRVVD�MXOJDU�VH�HVVH�SRQWR�VH�R�SRQWR�p�
XP�GDGR�RULJLQDO�RX�XP�GDGR�SROLGR�
$OWXUD�HP�FHQWtPHWURV�GH����DOXQDV�GR�&XUVR�GH�(QIHUPDJHP�GD�8)60�������
$OWXUD��FP� ;L IL IFL
��� _��� ��� ��� � ������[���������� �����
��� _��� ��� ��� � �������[����������� �����
��� _��� ��� ��� �� �������[����������� �����
��� _��� ��� ��� � ��������[���������� �����
��� _��� ��� ��� � �������[���������� �����
��� _��� ��� ��� � �������[���������� �����
ႛ ���� �� ���
)RQWH��'HSDUWDPHQWR�GH�(VWDWtVWLFD�������
��
$OWXUD�HP�FHQWtPHWURV�GH����DOXQDV�GR�&XUVR�GH�(QIHUPDJHP�GD�8)60�������
)RQWH��'HSDUWDPHQWR�GH�(VWDWtVWLFD�������
������&XUYDV�HP�IRUPD�GH�VLQR
$V� FXUYDV� HP� IRUPD� GH� VLQR� FDUDFWHUL]DP�VH� SHOR� IDWR� GH� DSUHVHQWDUHP� XP� YDORU
Pi[LPR�QD�UHJLmR�FHQWUDO�
'LVWLQJXHP�VH�DV�FXUYDV�HP�IRUPD�GH�VLQR�HP��VLPpWULFD H�DVVLPpWULFD
D��&XUYD�VLPpWULFD
(VWD�FXUYD�FDUDFWHUL]D�VH�SRU�DSUHVHQWDU�R�YDORU�Pi[LPR�QR�SRQWR�FHQWUDO�H�RV�SRQWRV�
HT�LGLVWDQWHV�GHVVH�SRQWR�WHUHP�D�PHVPD�IUHT�rQFLD�
��
E��&XUYDV�DVVLPpWULFDV
1D�SUiWLFD��QmR� VH� HQFRQWUDP�GLVWULEXLo}HV�SHUIHLWDPHQWH�VLPpWULFDV��$V�GLVWULEXLo}HV�
REWLGDV�GH�PHGLGDV� UHDLV� VmR�PDLV�RX�PHQRV�DVVLPpWULFDV�� HP�UHODomR�j� IUHT�rQFLD�Pi[LPD��
$VVLP�� DV� FXUYDV� FRUUHVSRQGHQWHV� D� WDLV� GLVWULEXLo}HV� DSUHVHQWDP� D� FDXGD� GH� XP� ODGR� GD�
RUGHQDGD�Pi[LPD�PDLV�ORQJD�GR�TXH�R�RXWUR��6H�D�FDXGD�PDLV�ORQJD�ILFD�D�GLUHLWD�p�FKDPDGD�
DVVLPpWULFD� SRVLWLYD �RX� HQYLHVDGD� j� GLUHLWD�� VH� D� FDXGD� VH� DORQJD� D� HVTXHUGD�� D� FXUYD� p�
FKDPDGD�DVVLPpWULFD�QHJDWLYD �RX�HQYLHVDGD�j�HVTXHUGD�
$VVLPpWULFD�3RVLWLYD $VVLPpWULFD�1HJDWLYD
��
���0HGLGDV�'HVFULWLYDV
7HP�SRU�REMHWLYR�GHVFUHYHU�XP�FRQMXQWR�GH�GDGRV�GH� IRUPD�RUJDQL]DGD�H� FRPSDFWD�
TXH�SRVVLELOLWD�D�YLVXDOL]DomR�GR�FRQMXQWR�HVWXGDGR�SRU�PHLR�GH�VXDV�HVWDWtVWLFDV��R�TXH�QmR�
VLJQLILFD�TXH�HVWHV�FiOFXORV�H�FRQFOXV}HV�SRVVDP�VHU�OHYDGRV�SDUD�D�SRSXODomR�
3RGHPRV�FODVVLILFDU�DV�PHGLGDV�GH�SRVLomR�FRQIRUPH�R�HVTXHPD�DEDL[R�
����0HGLGDV�GH�3RVLomR
0pGLD�$ULWPpWLFD
5HSUHVHQWDWLYDV � 0pGLDV 0pGLD�*HRPpWULFD
0pGLD�+DUP{QLFD
0HGLDQD
6HSDUDWUL]HV 4XDUWLV
'HFLV
&HQWLV�RX�3HUFHQWLV
'RPLQDQWHV 0RGD�GH�&]XEHU
0RGD�GH�.LQJ
0RGD�GH�3HDUVRQ
������5HSUHVHQWDWLYDV��0pGLDV�
6mR�PHGLGDV�GHVFULWLYDV�TXH�WHP�SRU�ILQDOLGDGH�UHSUHVHQWDU�XP�FRQMXQWR�GH�GDGRV�
D��0pGLD�$ULWPpWLFD� $PRVWUDO��; ���3RSXODFLRQDO����
'DGRV�1mR�7DEHODGRV
;
;
Q
��RX�� 
;
1
L
L �
Q
L
L �
1
 
ʜ ʜ
P
��
'DGRV�7DEHODGRV�FRP�9DORUHV�3RQGHUDGRV
0pGLD�$ULWPpWLFD�3RQGHUDGD��;Z ����RQGH�:L�p�R�SHVR�
1RWD�GR�DOXQR��;�
�� �VHPHVWUH�GH��������8)60
1RWDV��;L� 3HVRV��:L�
��� �
��� �
��� �
��� �
ႛ ��
)RQWH��'DGRV�+LSRWpWLFRV
;
; �:
:
Z
L L
L �
Q
L
L �
Q 
 
ʜ
ʜ
'LVWULEXLomR�GH�IUHT�rQFLDV
��0pGLD�$ULWPpWLFD��; �
$OWXUD�HP�FHQWtPHWURV�GH�����DOXQRV�GR
&XUVR�GH�$GPLQLVWUDomR�GD�8)60�������
$OWXUD��FP� ;L IL ;L���IL
��� _��� ��� ��� �� ������
��� _��� ��� ��� �� ������
��� _��� ��� ��� �� ������
��� _��� ��� ��� �� ������
��� _��� ��� ��� �� ������
��� _��� ��� ��� �� �������
ႛ ���� ��� �����
)RQWH��'HSDUWDPHQWR�GH�(VWDWtVWLFD�������
;
; �I
I
L L
L �
Q
L
L �
Q 
ʜ
ʜ
� &DUDFWHUtVWLFDV�GD�0pGLD�$ULWPpWLFD�6LPSOHV
�D��$�0pGLD�$ULWPpWLFD�6LPSOHV�GHYHUi�HVWDU�HQWUH�R�PHQRU�H�R�PDLRU�YDORU�REVHUYDGR��
PD[�PLQ� ;;; ˯˯
�D�� $� VRPD� DOJpEULFD� GRV� GHVYLRV� FDOFXODGRV� HQWUH� RV� YDORUHV� REVHUYDGRV� H� D�PpGLD�
DULWPpWLFD�p�LJXDO�D�]HUR��GHVYLRV G [ L ʝP
G �[ ]HUR
L �
Q
L
L �
Q
 
ʜ ʜ ʝ P�
��
�D��6RPDQGR�VH�RX�VXEWUDLQGR�VH�WRGRV�RV�YDORUHV��;L��GD�VpULH�SRU�XPD�FRQVWDQWH��N��
�N� �˫����D�QRYD�PpGLD�DULWPpWLFD�VHUi�LJXDO�D�PpGLD�RULJLQDO�VRPDGD�RX�VXEWUDtGD�SRU�
HVWD�FRQVWDQWH��N��
N;<;
N[\[ LLL
� 
ɞɞ
� 
�D��0XOWLSOLFDQGR�VH�RX�GLYLGLQGR�VH�WRGRV�RV�YDORUHV��;L��GD�VpULH�SRU�XPD�FRQVWDQWH�
�N�� �N� �˫ ���� D� QRYD�PpGLD� DULWPpWLFD� VHUi� LJXDO� D�PpGLD� RULJLQDO�PXOWLSOLFDGD� RX�
GLYLGLGD�SRU�HVWD�FRQVWDQWH��N��
N;<N;<;
N[\N[\[ LLLLL
¬ Ø 
ɞɞɞ
¬ Ø 
E��0pGLD�*HRPpWULFD���;J��
$�DSOLFDomR�GD�PpGLD�JHRPpWULFD�GHYH�VHU�IHLWD��TXDQGR�RV�YDORUHV�GR�FRQMXQWR�GH�GDGRV�
FRQVLGHUDGR�VH�FRPSRUWDP�VHJXQGR�XPD�SURJUHVVmR�JHRPpWULFD��3�*��RX�GHOD�VH�DSUR[LPDP�
'DGRV�1mR�7DEHODGRV
Q
Q��Q
Q
�L
LJ �;�����;;;; ʚ
 
'DGRV�7DEHODGRV
ʜʜ ʚ 
 
Q
� L
L
Q��
Q
� L
L
L
I
I
Q
I
�
I
�
I Q
�L
I
LJ �;�����;;;;
8VDQGR� XP� DUWLItFLR� PDWHPiWLFR�� SRGH�VH� XVDU� SDUD� FDOFXODU� D� PpGLD� JHRPpWULFD� D
VHJXLQWH�IyUPXOD�
� � ʜ
ʜ
 
ʜ
 
 
 
���
Q
�L
LLQ
�L
L
QQ����Q
�L
L
;ORJ�I
I
�
;ORJ�I���;ORJ�I;ORJ�I
I
�
J ����;
��
F��0pGLD�+DUP{QLFD��;K�
e�XVDGD�SDUD�GDGRV�LQYHUVDPHQWH�SURSRUFLRQDLV�
([���9HORFLGDGH�0pGLD��3UHoR�GH�&XVWR�0pGLR
������(PSUHJR�GD�PpGLD
���'HVHMD�VH�REWHU�D�PHGLGD�GH�SRVLomR�TXH�SRVVXL�D�PDLRU�HVWDELOLGDGH�
���+RXYHU�QHFHVVLGDGH�GH�XP�WUDWDPHQWR�DOJpEULFR�XOWHULRU�'DGRV�1mR�7DEHODGRV
Q��
Q
�L L
K
;
�
���
;
�
;
�
;
�
;
���
 
ʜ
 
QQ
'DGRV�7DEHODGRV
;
I
I
;
I I �� � I
I
;
I
;
� ��
I
;
K
L
L �
Q
L
LL �
Q
� � Q
�
�
�
�
Q
Q
 � � �
� � �
 
 
ʜ
ʜ
�'HYH�VH�REVHUYDU�HVWD�SURSULHGDGH�HQWUH�DV�PpGLDV KJ ;;; ˰˰
������6HSDUDWUL]HV��0HGLDQD��4XDUWLV��'HFLV�H�&HQWLV�RX�3HUFHQWLV�
6mR� PHGLGDV� GH� SRVLomR� TXH� GLYLGH� R� FRQMXQWR� GH� GDGRV� HP� SDUWHV� SURSRUFLRQDLV��
TXDQGR�RV�PHVPRV�VmR�RUGHQDGRV�
D��'DGRV�QmR�WDEHODGRV
$QWHV�GH�GHWHUPLQDUPRV�DV�VHSDUDWUL]HV�GHYHPRV�HP�SULPHLUR�OXJDU�HQFRQWUDU�D�SRVLomR�
GD�PHVPD�
��6H�R�Q~PHUR�GH�HOHPHQWRV�IRU�SDU�RX�tPSDU��DV�VHSDUDWUL]HV�VHJXHP�D�VHJXLQWH�RUGHP�
6
���L�Q
3RVLomR 
VH�IRU�PHGLDQD
д
г
в
 
 
�6
�L
VH�IRU�TXDUWLV
д
г
в
 
˯˯
�6
�L�
��
VH�IRU�GHFLV
д
г
в
 
˯˯
��6
�L�
VH�IRU�FHQWLV
д
г
в
 
˯˯
���6
��L�
'DGRV�7DEHODGRV
E��'LVWULEXLomR�GH�IUHT�rQFLDV�SRQWXDO��VHJXH�D�PHVPD�UHJUD�XVDGD�SDUD�GDGRV�
QmR�WDEHODGRV
F��'LVWULEXLomR�GH�IUHT�rQFLDV�LQWHUYDODU
L
L
6
DQW
6L I
�K)
6
L�Q
O6
Ъ
Ы
ЩЧ
Ш
Ц ʝ
� 
RQGH�
6 0G �L �L ɝ �
6 4 �� L �L L ɝ ˯ ˯ �
6 ' �� LL L ɝ ˯ ˯��
6 & �RX�3 �� LL L L ɝ ˯ ˯��
O6L ɝ �OLPLWH�LQIHULRU�GD�FODVVH�TXH�FRQWpP�D�VHSDUDWUL]�
L�Q
6
ɝ �SRVLomR�GD�VHSDUDWUL]�
)DQW ɝ �IUHT�rQFLD�DFXPXODGD�GD�FODVVH�DQWHULRU�D�TXH�FRQWpP�D�VHSDUDWUL]�
K� ɝ �DPSOLWXGH�GR�LQWHUYDOR�GH�FODVVH�
I6L ɝ �IUHT�rQFLD�DEVROXWD�GD�FODVVH�TXH�FRQWpP�D�VHSDUDWUL]�
������(PSUHJR�GD�PHGLDQD
���4XDQGR�VH�GHVHMD�REWHU�XP�SRQWR�TXH�GLYLGH�D�GLVWULEXLomR�HP�SDUWHV�LJXDLV�
���+i�YDORUHV�H[WUHPRV�TXH�DIHWDP�GH�XPD�PDQHLUD�DFHQWXDGD�D�PpGLD�
���$�YDULiYHO�HP�HVWXGR�p�VDOiULR�
������'RPLQDQWHV���0RGD��0R�
e�GHILQLGD�FRPR�VHQGR�D�REVHUYDomR�GH�PDLRU�IUHT�rQFLD�
��
D��'DGRV�QmR�WDEHODGRV
([���������������������������������� ɝ �0R� ����XQLPRGDO�
����������������������������� ɝ �0R� ��ʎ��DPRGDO�
������������������������������� ɝ �0R�� ���0R�� ����ELPRGDO�
���������������������� ɝ �0R� ��ʎ ��DPRGDO�
������������������� ɝ �0R�� �����0R�� ������0R�� ����PXOWLPRGDO�
�$FLPD�GH���PRGDV�XVDPRV�R�WHUPR�PXOWLPRGDO�
'DGRV�7DEHODGRV
D��'LVWULEXLomR�GH�IUHT�rQFLDV�SRQWXDO
��0RGD�%UXWD��0RE���p�R�SRQWR�PpGLR�GD�FODVVH�GH�PDLRU�IUHT�rQFLD
LE ;0R 
E��'LVWULEXLomR�GH�IUHT�rQFLDV�LQWHUYDODU
��0RGD�GH�&]XEHU��0RF���2�SURFHVVR�SDUD�GHWHUPLQDU�D�PRGD�XVDGR�SRU�&]XEHU�OHYD�
HP�FRQVLGHUDomR�DV�IUHT�rQFLDV�DQWHULRUHV�H�SRVWHULRUHV�j�FODVVH�PRGDO�
д
г
в
ʝ ʑ
ʝ ʑ
ɝЪЪ
Ы
Щ
ЧЧ
Ш
Ц
ʑ�ʑ
ʑ� 
SRV0R�
DQW0R�
��
�
0RF II
II
�KO0R
RQGH�
O0R ɝ �OLPLWH�LQIHULRU�GD�FODVVH�PRGDO�
I0R ɝ �IUHT�rQFLD�DEVROXWD�GD�FODVVH�PRGDO�
K� ɝ �DPSOLWXGH�GR�LQWHUYDOR�GH�FODVVH�
IDQW ɝ �IUHT�rQFLD�DEVROXWD�GD�FODVVH�DQWHULRU�D�FODVVH�PRGDO�
ISRV ɝ �IUHT�rQFLD�DEVROXWD�GD�FODVVH�SRVWHULRU�D�FODVVH�PRGDO�
�� 0RGD� GH� .LQJ �0RN��� 2� SURFHVVR� SURSRVWR� SRU� .LQJ� FRQVLGHUD� D� LQIOXrQFLD
H[LVWHQWH�GDV�FODVVHV�DQWHULRU�H�SRVWHULRU�VREUH�D�FODVVH�PRGDO��$�LQFRQYHQLrQFLD�GHVWH�SURFHVVR�
p�MXVWDPHQWH�QmR�OHYDU�HP�FRQVLGHUDomR�D�IUHT�rQFLD�Pi[LPD�
�K
II
I
O0R
DQWSRV
SRV
0RN Ъ
Ъ
Ы
Щ
Ч
Ч
Ш
Ц
�
� 
��
�� 0RGD� GH� 3HDUVRQ �0RS��� 2� SURFHVVR� XVDGR� SRU� 3HDUVRQ� SUHVVXS}H� TXH� D
GLVWULEXLomR� VHMD� DSUR[LPDGDPHQWH� VLPpWULFD�� QD� TXDO� D� PpGLD� DULWPpWLFD� H� D� PHGLDQD� VmR
OHYDGDV�HP�FRQVLGHUDomR�
0R �0G�� � ;S �
�8P�GLVWULEXLomR�p�FRQVLGHUDGD�VLPpWULFD�TXDQGR ; 0G 0Rˬ ˬ �
������(PSUHJR�GD�PRGD
���4XDQGR�VH�GHVHMD�REWHU�XPD�PHGLGD�UiSLGD�H�DSUR[LPDGD�GH�SRVLomR�
���4XDQGR�D�PHGLGD�GH�SRVLomR�GHYH�VHU�R�YDORU�PDLV�WtSLFR�GD�GLVWULEXLomR�
������3RVLomR�UHODWLYD�GD�PpGLD��PHGLDQD�H�PRGD
4XDQGR�XPD�GLVWULEXLomR�p�VLPpWULFD��DV�WUrV�PHGLGDV�FRLQFLGHP��3RUpP��D�DVVLPHWULD�
WRUQD�DV�GLIHUHQWHV�H�HVVD�GLIHUHQoD�p�WDQWR�PDLRU�TXDQWR�PDLRU�p�D�DVVLPHWULD��$VVLP��HP�XPD�
GLVWULEXLomR�WHPRV�
0R0G[ ȝ �FXUYD�VLPpWULFD
0R0G[ �� ȝ �FXUYD�DVVLPpWULFD�QHJDWLYD
[0G0R �� ȝ �FXUYD�DVVLPpWULFD�SRVLWLYD
0R0G[ 
0G0G0R [ 0R[
0 RGD
G LDQ DH0
GL Dp0
��
������([HUFtFLRV
3DUD�RV�GDGRV�DEDL[R�FDOFXOH��0G��4���4���'���&��
��
� � � �� �� �� �� �� �� ��
� � � �� �� �� �� �� �� �� ��
��
$OWXUDV�GRV�DOXQRV�GD�7XUPD�´;µ
QR��R�VHP��GH��������8)60
$OWXUDV IL
�� ��
�� ��
�� ��
�� ��
ႛ ��
)RQWH��'DGRV�+LSRWpWLFRV
��
$OWXUDV�GRV�DOXQRV�GD�7XUPD�´<µ
QR��R�VHP��GH������²�8)60
$OWXUDV IL )L
�� _��� �� �� ��
�� _��� �� �� ��
�� _��� �� �� ��
�� _��� �� �� ��
�� _��� �� �� ���
ႛ ��� ���
)RQWH��'DGRV�+LSRWpWLFRV
����0HGLGDV�GH�9DULDELOLGDGH�RX�'LVSHUVmR
9LVDP�GHVFUHYHU�RV�GDGRV�QR�VHQWLGR�GH�LQIRUPDU�R�JUDX�GH�GLVSHUVmR�RX�DIDVWDPHQWR�
GRV�YDORUHV�REVHUYDGRV�HP�WRUQR�GH�XP�YDORU�FHQWUDO�UHSUHVHQWDWLYR�FKDPDGR�PpGLD��,QIRUPD�
VH� XP� FRQMXQWR� GH� GDGRV� p� KRPRJrQHR� �SRXFD� YDULDELOLGDGH�� RX� KHWHURJrQHR� �PXLWD
YDULDELOLGDGH��
$V�PHGLGDV�GH�GLVSHUVmR�SRGHP�VHU�
� 'HVYLR�H[WUHPR���DPSOLWXGH
$EVROXWD � 'HVYLR�0pGLR
� 'HVYLR�3DGUmR
� 'HVYLR�TXDGUiWLFR���9DULkQFLD
��
3DUD�HVWXGDUPRV�DV�PHGLGDV�GH�YDULDELOLGDGH�SDUD�GDGRV�QmR�WDEHODGRV�XVDUHPRV�XP�
H[HPSOR�SUiWLFR��6XSRPRV�TXH�XPD�HPSUHVD�HVWHMD�TXHUHQGR�FRQWUDWDU�XP�IXQFLRQiULR��H�QR�
ILQDO�GD�FRQFRUUrQFLD�VREUDUDP�GRLV�FDQGLGDWRV�SDUD�XPD�~QLFD�YDJD��(QWmR�IRL�GDGR���WDUHIDV�
SDUD�FDGD�XP��RQGH�DV�PHVPDV�WLYHUDP�FRPR�UHJLVWUR�R�WHPSR��HP�PLQXWRV��GH�H[HFXomR�
7$5()$6 � � � �
23(5É5,2����7(032� �� �� �� ��
23(5É5,2����7(032 �� �� �� ��
��$QiOLVH�*UiILFD
��0HGLGDV�GH�GLVSHUVmR�$EVROXWD�
��'HVYLR�([WUHPR�RX�$PSOLWXGH�GH�9DULDomR��+���e�D�GLIHUHQoD�HQWUH�R�PDLRU�H�R�
PHQRU�YDORU�GH�XP�FRQMXQWR�GH�GDGRV
+ ; ;PD[ PLQ ʝ
� 'HVYLR�0pGLR��G ���(P�YLUWXGH�GR � �ʜ
 
 ʝ
Q
L
L ;;
�
� ��XVDPRV�SDUD�FDOFXODU�R�GHVYLR�
PpGLR ; ;L
L
Q
ʝ 
 
ʜ �
�
��DVVLP�ILFDQGR�
3DUD�GDGRV�QmR�WDEHODGRV
G
; ;
Q
; ; ; ; ; ;
Q
L
L
Q
Q 
ʝ
 
ʝ � ʝ � � ʝ
 
ʜ
� � �
���
3DUD�GDGRV�WDEHODGRV
��
� �
ʜʜ
ʜ
 
 
ʝ��ʝ�ʝ
 
ʝ
 
Q
L
L
QQ
Q
L
L
Q
L
LL
I
;;I;;I;;I
I
;;I
G
�
����
�
�
���
��'HVYLR�4XDGUiWLFR�RX�9DULkQFLD���6���DPRVWUD��RX�Ⴔ���SRSXODomR�
3DUD�GDGRV�QmR�WDEHODGRV�
� � � � � � � �
Q
;;;;;;
Q
;;
Q
Q
L
L ��
�
�
��
�
� ��� ʝ��ʝ�ʝ 
ʝ
 
ʜ
 V
� � � � � � � �
�
���
�
��
�
�
��
�
�
ʝ
ʝ��ʝ�ʝ
 
ʝ
ʝ
 
ʜ
 
Q
;;;;;;
Q
;;
6 Q
Q
L
L
3DUD�GDGRV�WDEHODGRV
� � � � � � � �
ʜʜ
ʜ
 
 ʝ��ʝ�ʝ 
ʝ
 
Q
L
L
QQ
Q
L
L
Q
L
LL
I
;;I;;I;;I
I
;;I
�
��
��
�
��
�
�
�
� ���V
� � � � � � � �
�
���
�
�
��
��
�
��
�
�
�
�
ʝ
ʝ��ʝ�ʝ 
ʝ
ʝ
 
ʜʜ
ʜ
 
 
Q
L
L
QQ
Q
L
L
Q
L
LL
I
;;I;;I;;I
I
;;I
6
��
��'HVYLR�3DGUmR��6��DPRVWUD��RX�Ⴔ��SRSXODomR�
3DUD�GDGRV�QmR�WDEHODGRV�
� � � � � � � �
Q
;;;;;;
Q
;;
Q
Q
L
L ��
�
�
��
�
��� ʝ��ʝ�ʝ 
ʝ
 
ʜ
 V
� � � � � � � �
�
���
�
��
�
�
��
�
ʝ
ʝ��ʝ�ʝ 
ʝ
ʝ
 
ʜ
 
Q
;;;;;;
Q
;;
6 Q
Q
L
L
3DUD�GDGRV�WDEHODGRV
� � � � � � � �
ʜʜ
ʜ
 
 ʝ��ʝ�ʝ 
ʝ
 Q
L
L
QQ
Q
L
L
Q
L
LL
I
;;I;;I;;I
I
;;I
�
��
��
�
��
�
�
�
���V
� � � � � � � �
�
���
�
�
��
��
�
��
�
�
�
ʝ
ʝ��ʝ�ʝ
 
ʝ
ʝ
 
ʜʜ
ʜ
 
 
Q
L
L
QQ
Q
L
L
Q
L
LL
I
;;I;;I;;I
I
;;I
6
��Q� ����� p� XVDGR� FRPR� XP� IDWRU� GH� FRUUHomR�� RQGH� GHYHPRV� FRQVLGHUDU� D� YDULkQFLD� DPRVWUDO� FRPR� XPD�
HVWLPDWLYD�GD�YDULkQFLD�SRSXODFLRQDO�
� 3URSULHGDGHV�GD�9DULkQFLD
����6RPDQGR�VH�RX�VXEWUDLQGR�VH�XPD�FRQVWDQWH�N�D�FDGD�YDORU�REVHUYDGR�D�YDULkQFLD�QmR�VHUi�DOWHUDGD�
���� 0XOWLSOLFDQGR�VH� RX� GLYLGLQGR�VH� SRU� XPD� FRQVWDQWH� N� FDGD� YDORU� REVHUYDGR� D� YDULkQFLD� ILFDUi�
PXOWLSOLFDGD�RX�GLYLGLGD�SHOR�TXDGUDGR�GHVVD�FRQVWDQWH�
2XWUD�IRUPD�GH�FDOFXODU�R�GHVYLR�SDGUmR
2�GHVYLR�SDGUmR�PHGH�EHP�D�GLVSHUVmR�GH�XP�FRQMXQWR�GH�GDGRV��PDV� p�GLItFLO� GH�
FDOFXODU��(QWmR��YRFr�SRGH�REWHU�R�GHVYLR�SDGUmR�DWUDYpV�GD�VHJXLQWH�UHODomR�
�G
5× Ⴔ
RQGH�5�p�D�DPSOLWXGH�H�R�YDORU�GH�G����TXH�GHSHQGH�GR�WDPDQKR�GD�DPRVWUD��p�HQFRQWUDGR�QD�
WDEHOD� D� VHJXLU�� (VWH� PpWRGR� GH� FDOFXODU� R� GHVYLR� SDGUmR� IRUQHFH� ERDV� HVWLPDWLYDV� SDUD�
DPRVWUDV�GH�SHTXHQR� WDPDQKR� �Q ��� ��RX�����PDV�SHUGH� D� HILFLrQFLD� VH�Q!����'H�TXDOTXHU�
��
IRUPD��p�HVVD�UHODomR�HQWUH�D�DPSOLWXGH�H�R�GHVYLR�SDGUmR�GH�XPD�DPRVWUD�TXH�SHUPLWH�ID]HU�
JUiILFRV�GH�FRQWUROH� 5; ʝ �
7$%(/$������)DWRUHV�SDUD�FRQVWUXLU�XP�JUiILFR�GH�FRQWUROHQ � � � � � � � � �� �� �� �� ��
G� ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� �����
Q �� �� �� �� �� �� �� �� ��� �� �� ��� ���
G� ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� ����� ��� ���
)RQWH��0RQWJRPHU\��'�&��6WDWLFDO�4XDOLW\�&RQWURO��1RYD�<RUN��:\OH\�������
����0HGLGDV�GH�'LVSHUVmR�5HODWLYD
� 9DULkQFLD�UHODWLYD
5HODWLYD
� &RHILFLHQWH�GH�9DULDomR��3HDUVRQ�
e�D�PHGLGD�GH�YDULDELOLGDGH�TXH�HP�JHUDO�p�H[SUHVVD�HP�SRUFHQWDJHP��H�WHP�SRU�IXQomR�
GHWHUPLQDU�R�JUDX�GH�FRQFHQWUDomR�GRV�GDGRV�HP�WRUQR�GD�PpGLD��JHUDOPHQWH�XWLOL]DGD�SDUD�VH�
ID]HU� D� FRPSDUDomR� HQWUH�GRLV�FRQMXQWRV�GH�GDGRV�HP�WHUPRV�SHUFHQWXDLV��HVWD�FRPSDUDomR�
UHYHODUi�R�TXDQWR�RV�GDGRV�HVWmR�SUy[LPRV�RX�GLVWDQWHV�GD�PpGLD�GR�FRQMXQWR�GH�GDGRV�
��9DULkQFLD�5HODWLYD
9 5
;
� � Ⴔ
�
�
� �
�RX�
6�
��&RHILFLHQWH�GH�9DULDomR�GH�3HDUVRQ
���[
;
6
RX��9�&
�
Ⴔ
 
�&�9��˯ �����ɝ D�PpGLD�p�UHSUHVHQWDWLYD
&�9��ː ���ɝ p�D�PDLRU�UHSUHVHQWDWLYLGDGH�GD�PpGLD��6� ���
����0RPHQWRV��DVVLPHWULD�H�FXUWRVH
$V� PHGLGDV� GH� DVVLPHWULD� H� FXUWRVH� FRPSOHPHQWDP� DV� PHGLGDV� GH� SRVLomR� H� GH
GLVSHUVmR� QR� VHQWLGR� GH� SURSRUFLRQDU� XPD� GHVFULomR� H� FRPSUHHQVmR� PDLV� FRPSOHWD� GDV
GLVWULEXLo}HV�GH�IUHT�rQFLDV��(VWDV�GLVWULEXLo}HV�QmR�GLIHUHP�DSHQDV�TXDQWR�DR�YDORU�PpGLR�H�j�
YDULDELOLGDGH��PDV�WDPEpP�TXDQWR�D�VXD�IRUPD��DVVLPHWULD�H�FXUWRVH��
��
3DUD�HVWXGDU�DV�PHGLGDV�GH�DVVLPHWULD�H�FXUWRVH��p�QHFHVViULR�R�FRQKHFLPHQWR�GH�FHUWDV�
TXDQWLGDGHV��FRQKHFLGDV�FRPR�PRPHQWRV�
������0RPHQWRV
6mR� PHGLGDV� GHVFULWLYDV� GH� FDUiWHU� PDLV� JHUDO� H� GmR� RULJHP� jV� GHPDLV� PHGLGDV
GHVFULWLYDV��FRPR�DV�GH�WHQGrQFLD�FHQWUDO��GLVSHUVmR��DVVLPHWULD�H�FXUWRVH��&RQIRUPH�D�SRWrQFLD�
FRQVLGHUDGD�WHP�VH�D�RUGHP�RX�R�JUDX�GR�PRPHQWR�FDOFXODGR�
��0RPHQWRV�VLPSOHV�RX�FHQWUDGRV�QD�RULJHP��PU�
2�PRPHQWR�VLPSOHV�GH�RUGHP�´Uµ�p�GHILQLGR�FRPR�
Q
;
P
U
L
U
ʜ � SDUD�GDGRV�QmR�WDEHODGRV�
ʜ
ʜ 
L
L
U
L
U I
I;
P � SDUD�GDGRV�WDEHODGRV�
RQGH�
U�p�XP�Q~PHUR�LQWHLUR�SRVLWLYR�
P�� ���
P�� �PpGLD�DULWPpWLFD�
��0RPHQWRV�FHQWUDGRV�QD�PpGLD��0U�
2�PRPHQWR�GH�RUGHP�´Uµ�FHQWUDGR�QD�PpGLD��p�GHILQLGR�FRPR�
� �
Q
G
Q
;;
0
U
L
U
L
U
ʜʜ ʝ ��SDUD�GDGRV�QmR�WDEHODGRV
� �
Q
IG
I
I;;
0 L
U
L
L
L
U
L
U
ʜ
ʜ
ʜ ʝ ��SDUD�GDGRV�WDEHODGRV
RQGH� 0�� ���
0�� ���
0�� �YDULkQFLD��V
���
��
��0RPHQWRV�DEVWUDWRV��ႢU�
6mR�GHILQLGRV�GD�VHJXLQWH�IRUPD�
U
U
U
V
0 Ⴂ
RQGH��V� �GHVYLR�SDGUmR�
������$VVLPHWULD
8PD�GLVWULEXLomR�GH�YDORUHV�VHPSUH�SRGHUi�VHU�UHSUHVHQWDGD�SRU�XPD�FXUYD��JUiILFR���
(VVD�FXUYD��FRQIRUPH�D�GLVWULEXLomR��SRGH�DSUHVHQWDU�YiULDV�IRUPDV��6H�FRQVLGHUDUPRV�R�YDORU�
GD�PRGD�GD�GLVWULEXLomR�FRPR�SRQWR�GH�UHIHUrQFLD��YHPRV�TXH�HVVH�SRQWR�VHPSUH�FRUUHVSRQGH�
DR� YDORU� GH� RUGHQDGD� Pi[LPD�� GDQGR�QRV� R� SRQWR� PDLV� DOWR� GD� FXUYD� UHSUHVHQWDWLYD� GD�
GLVWULEXLomR�FRQVLGHUDGD��ORJR�D�FXUYD�VHUi�DQDOLVDGD�TXDQWR�j�VXD�DVVLPHWULD�
��'LVWULEXLomR�6LPpWULFD�� e�DTXHOD�TXH�DSUHVHQWD� D�; �ˬ0R� �ˬ0G� H� RV� TXDUWLV�4��H�4�
HT�LGLVWDQWHV�GR�4��
; �ˬ0R� �ˬ0G
��'LVWULEXLomR�$VVLPpWULFD
$VVLPpWULFD�3RVLWLYD
0R���0G���;
$VVLPpWULFD�1HJDWLYD
; ���0G���0R
3RGHPRV� PHGLU� D� DVVLPHWULD� GH� XPD� GLVWULEXLomR�� FDOFXODQGR� RV� FRHILFLHQWHV� GH
DVVLPHWULD��6HQGR�R�PDLV�XWLOL]DGR�R�&RHILFLHQWH�GH�$VVLPHWULD�GH�3HDUVRQ�
$V
; 0R
6
 ʝ
��6H�$V�����ɝ �D�GLVWULEXLomR�VHUi�$VVLPpWULFD�1HJDWLYD �
��6H�$V�!���ɝ �D�GLVWULEXLomR�VHUi�$VVLPpWULFD�3RVLWLYD�
��6H�$V� ���ɝ �D�GLVWULEXLomR�VHUi�6LPpWULFD�
��
4XDQGR� QmR� WLYHUPRV� FRQGLo}HV� GH� FDOFXODUPRV� R� GHVYLR� SDGUmR� SRGHPRV� XVDU� D�
VHJXLQWH�IyUPXOD�
$V
4 4 0G
4 4
 � ʝ
ʝ
� �
� �
�
��&RHILFLHQWH�PRPHQWR�GH�DVVLPHWULD���Ⴂ ����e�R�WHUFHLUR�PRPHQWR�DEVWUDWR�
�
�
�
V
0 Ⴂ
2�FDPSR�GH�YDULDomR�GR�FRHILFLHQWH�GH�DVVLPHWULD�p�����˯ Ⴂ � �˯��
��,QWHQVLGDGH�GD�DVVLPHWULD�
_Ⴂ��_������� ɝ VLPHWULD�
�������_Ⴂ �_������ ɝ DVVLPHWULD�IUDFD�
_Ⴂ�_�!���� ɝ DVVLPHWULD�IRUWH�
������&XUWRVH
-i� DSUHFLDPRV� DV� PHGLGDV� GH� WHQGrQFLD� FHQWUDO�� GH� GLVSHUVmR� H� GH� DVVLPHWULD�� )DOWD�
VRPHQWH� H[DPLQDUPRV� PDLV� XPD� GDV� PHGLGDV� GH� XVR� FRPXP� HP� (VWDWtVWLFD�� SDUD� VH
SRVLWLYDUHP� DV� FDUDFWHUtVW LFDV� GH� XPD� GLVWULEXLomR� GH� YDORUHV�� VmR� DV� FKDPDGDV�0HGLGDV� GH�
&XUWRVH�RX�GH�$FKDWDPHQWR�� TXH�QRV�PRVWUD� DWp�TXH�SRQWR� D� FXUYD� UHSUHVHQWDWLYD�GH�XPD�
GLVWULEXLomR�p�D�PDLV�DJXGD�RX�D�PDLV�DFKDWDGD�GR�TXH�XPD�FXUYD�QRUPDO��GH�DOWXUD�PpGLD�
��&XUYD�0HVRF~UWLFD��1RUPDO���e�FRQVLGHUDGD�D�FXUYD�SDGUmR�
��&XUYD�/HSWRF~UWLFD�� e� XPD� FXUYD�PDLV� DOWD� GR� TXH� D� QRUPDO�� $SUHVHQWD� R� WRSR�
UHODWLYDPHQWH�DOWR��VLJQLILFDQGR�TXH�RV�YDORUHV�VH�DFKDP�PDLV�DJUXSDGRV�HP�WRUQR�GD�PRGD�
��&XUYD�3ODWLF~UWLFD�� e�XPD� FXUYD�PDLV�EDL[D�GR�TXH�D�QRUPDO��$SUHVHQWD�R� WRSR�
DFKDWDGR��VLJQLILFDQGR�TXH�YiULDV�FODVVHV�DSUHVHQWDP�IUHT�rQFLDV�TXDVH�LJXDLV�
��
��&RHILFLHQWH�GH�&XUWRVH
.
4 4
3 3
 ʝ
ʝ
� �
�� ���� �
��6H�.�!�������ɝ �D�GLVWULEXLomR�VHUi�3ODWLF~UWLFD�
��6H�.� �������ɝ �D�GLVWULEXLomR�VHUi�0HVRF~UWLFD�
��6H�.���������ɝ �D�GLVWULEXLomR�VHUi�/HSWRF~UWLFD�
&RHILFLHQWH�PRPHQWR�GH�FXUWRVH��Ⴂ � ���&RUUHVSRQGH�DR�PRPHQWR�DEVWUDWR�GH�TXDUWD�RUGHP�
�
�
�
V
0 Ⴂ
RQGH���0�� �PRPHQWR�FHQWUDGR�GH�TXDUWD�RUGHP�
,QWHUSUHWDomR�
��6H�Ⴂ ������ɝ �FXUYD�3ODWLF~UWLFD�
��6H�Ⴂ �� ���ɝ �FXUYD�0HVRF~UWLFD�
��6H�Ⴂ ��!���ɝ �FXUYD�/HSWRF~UWLFD�
����([HUFtFLRV
3DUD�RV�H[HUFtFLRV�DEDL[R�FRQVWUXD�XPD�WDEHOD�GH�GLVSHUVmR�R�VXILFLHQWH�SDUD�GHWHUPLQDU�
DV�PHGLGDV�GH�SRVLomR��PpGLD�DULWPpWLFD��PHGLDQD�H�PRGD�GH�F]XEHU���GLVSHUVmR��GHVYLR�SDGUmR�
H� YDULkQFLD�� FRHILFLHQWH� GH� YDULDomR� GH� 3HDUVRQ��� DVVLPHWULD� �FRHILFLHQWH� GH� DVVLPHWULD�� H
FRHILFLHQWH�GH�FXUWRVH���)DoD�XP�UHODWyULR�UHIHUHQWH�DR�FRPSRUWDPHQWR�GRV�GDGRV�HP�IXQomR�
GRV�UHVXOWDGRV�REWLGRV�
��� 'H� XP� H[DPH� ILQDO� GH� (VWDWtVWLFD�� DSOLFDGR� D� ��� DOXQRV� GD� 8QLYHUVLGDGH
/XWHUDQD�$QR������UHVXOWDUDP�DV�VHJXLQWHV�QRWDV�
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
��� ��� ��� ��� ��� ��� ��� ��� ��� ����
��
���2V�GDGRV�D�VHJXLU�UHIHUH�VH�D�DOWXUD�HP�FHQWtPHWURV�GH����DOXQRV�GD�38&&��WXUPD����
DQR������
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
��� ��� ��� ��� ��� ��� ��� ��� ��� ���
���2V�GDGRV�D�VHJXLU�UHIHUHP�VH�DRV�VDOiULRV�DQXDLV�SDJRV�HP�GyODUHV�D����IXQFLRQiULRV�
GD�(PSUHVD�´3(7$�6�$�µ�HP������
����� ����� ����� ����� ����� ����� ����� ����� ����� �����
����� ����� ����� ����� ����� ����� ����� ����� ����� �����
����� ����� ����� ����� ����� ����� ����� ����� ����� �����
����� ����� ����� ����� ����� ����� ����� ����� ����� �����
����� ����� ����� ����� ����� ����� ����� ����� ����� �����
������ ������ ������ ������ ������ ������ ������ ������ ������ ������
��
�� 33UURREEDDEELLOOLLGGDDGGHH HH 99DDUULLiiYYHHLLVV $$OOHHDDWWyyUULLDDVV
����0RGHORV�0DWHPiWLFRV
3RGHP�VH�GHVWLQJXLU�GRLV�WLSRV�GH�PRGHORV�PDWHPiWLFRV�
������0RGHORV�'HWHUPLQtVWLFRV
5HIHUH �VH�D�XP�PRGHOR�TXH�HVWLSXOH�TXH�DV�FRQGLo}HV�VRE�DV�TXDLV�XP�H[SHULPHQWR�
VHMD�H[HFXWDGR�GHWHUPLQHP�R�UHVXOWDGR�GR�H[SHULPHQWR� 2�PRGHOR GHWHUPLQtVWLFR�UHTXHU�R�XVR�
GH�SDUkPHWURV�SUp�GHWHUPLQDGRV HP�HTXDo}HV�TXH�GHILQHP�SURFHVVRV�SUHFLVRV�
(P�RXWUDV�SDODYUDV��XP�PRGHOR�GHWHUPLQtVWLFR�HPSUHJD��&RQVLGHUDo}HV�)tVLFDV��SDUD�
SUHYHU�UHVXOWDGRV�
������0RGHORV�1mR�'HWHUPLQtVWLFRV�RX�3UREDELOtVWLFRV
6mR� DTXHOHV� TXH� LQIRUPDP� FRP� TXH� FKDQFH� RX� SUREDELOLGDGH� RV� DFRQWHFLPHQWRV
SRGHP� RFRUUHU�� 'HWHUPLQD� R� �JUDX� GH� FUHGLELOLGDGH�� GRV� DFRQWHFLPHQWRV�� �0RGHORV�
(VWRFiVWLFRV��
(P� RXWUDV� SDODYUDV�� XP� PRGHOR� SUREDELOtVWLFR� HPSUHJD� XPD� PHVPD� HVSpFLH� GH
FRQVLGHUDo}HV�SDUD�HVSHFLILFDU�XPD�GLVWULEXLomR�GH�SUREDELOLGDGH�
����&RQFHLWRV�HP�3UREDELOLGDGH
2V� FRQFHLWRV� IXQGDPHQWDLV� HP� SUREDELOLGDGH� VmR� H[SHULPHQWRV� DOHDWyULRV��HVSDoR�
DPRVWUDO�H�HYHQWRV�
������([SHULPHQWR�DOHDWyULR��: �
4XDOTXHU�SURFHVVR�DOHDWyULR��FDSD]�GH�SURGX]LU�REVHUYDo}HV��RV�UHVXOWDGRV�VXUJHP�DR�DFDVR��SRGHQGR�DGPLWLU�UHSHWLo}HV�QR�IXWXUR��8P�H[SHULPHQWR�DOHDWyULR�DSUHVHQWD�DV�VHJXLQWHV�
FDUDFWHUtVWLFDV�
D���RV�UHVXOWDGRV�SRGHP�UHSHWLU�VH�Q�YH]HV � ʩȝQ � �
��
E� �� HPERUD� QmR� VH� SRVVD� SUHYHU� TXH� UHVXOWDGRV� RFRUUHUmR�� SRGH�VH� GHVFUHYHU� R
FRQMXQWR�GH�UHVXOWDGRV�SRVVtYHLV�
F���D�PHGLGD�TXH�VH�DXPHQWD�R�Q~PHUR�GH�UHSHWLo}HV��DSDUHFH�XPD�FHUWD�UHJXODULGDGH�
QRV�UHVXOWDGRV�
������(VSDoR�$PRVWUDO��6�
e� R� FRQMXQWR� GH� UHVXOWDGRV� SRVVtYHLV�� GH� XP� H[SHULPHQWR� DOHDWyULR�� 4XDQWR� DR
Q~PHUR�GH�HOHPHQWRV�SRGH�VHU�
��������)LQLWR
1~PHUR�OLPLWDGR�GH�HOHPHQWRV�
([���6� �^����������������`
��������,QILQLWR
1~PHUR�LOLPLWDGR�GH�HOHPHQWRV��SRGH�VHU�VXE�GLYLGLGR�HP�
D���(QXPHUiYHO
4XDQGR�RV�SRVVtYHLV�UHVXOWDGRV�SXGHUHP�VHU�SRVWRV�HP�FRQFRUGkQFLD�ELXQtYRFD�FRP�
R�FRQMXQWR�GRV�Q~PHURV�QDWXUDLV��1���FDVR�GDV�YDULiYHLV�DOHDWyULDV�GLVFUHWDV��
([���1
E���1mR�(QXPHUiYHO
4XDQGR�RV�SRVVtYHLV�UHVXOWDGRV�QmR�SXGHUHP�VHU�SRVWRV�HP�FRQFRUGkQFLD�ELXQtYRFD�
FRP�R�FRQMXQWR�GRV�Q~PHURV�QDWXUDLV��FDVR�GDV�YDULiYHLV�DOHDWyULDV�FRQWtQXDV��
([���5
������(YHQWR��(�
8P�HYHQWR��(��p�TXDOTXHU�VXEFRQMXQWR�GH�XP�HVSDoR�DPRVWUDO��6��
3RGH�VH� WHU� RSHUDo}HV� HQWUH� HYHQWRV� GD� PHVPD� IRUPD� � TXH� FRP� FRQMXQWRV�� FRPR�
PRVWUD�D�VHJXLU�
������2SHUDo}HV�FRP�(YHQWRV
��������$�XQLmR�%
6tPEROR�XWLOL]DGR������p�R�HYHQWR�TXH�RFRUUHUi�VH��H�VRPHQWH�VH��$�RX�%�RX�DPERV�
RFRUUHUHP�
��
%$
6
),*85$�������(YHQWR�$�XQLmR�%
��������$�LQWHUVHomR�%
6tPEROR� XWLOL]DGR� ����� p�R�HYHQWR�TXH�RFRUUHUi� VH�� H� VRPHQWH� VH��$�H�%�RFRUUHP�
VLPXOWDQHDPHQWH�
%$
6
$�����%
8
),*85$�������(YHQWR�$�LQWHUVHomR�%
��������&RPSOHPHQWDU�GH�$
6LPERORJLD���$
B
���p�R�HYHQWR�TXH�RFRUUHUi�VH��H�VRPHQWH�VH�$�QmR�RFRUUHU�
$
6
),*85$��������(YHQWR�FRPSOHPHQWDU�GH�$��$
B
�
��
������7LSRV�GH�HYHQWRV
��������(YHQWRV�0XWXDPHQWH�([FOXGHQWHV
6mR�GLWRV�HYHQWRV�PXWXDPHQWH�H[FOXGHQWHV��TXDQGR�D�RFRUUrQFLD�GH�XP�LPSOLFD�RX�
QmR�RFRUUrQFLD�GH�RXWUR�� LVWR� p��QmR�SRGH�RFRUUHU� MXQWRV�� H� FRQVHT�HQWHPHQWH��$� � �%�p�R�
FRQMXQWR�YD]LR��ʐ��
),*85$�������(YHQWRV�PXWXDPHQWH�H[FOXGHQWHV
��������(YHQWRV�1mR�([FOXGHQWHV�RX�4XDLVTXHU
6mR�GLWRV�HYHQWRV�QmR�H[FOXGHQWHV�TXDQGR�D�RFRUUrQFLD�GH�XP�LPSOLFD�QD�RFRUUrQFLD�
GR�RXWUR��LVWR�p��VmR�DTXHOHV�TXH�RFRUUHP�DR�PHVPR�WHPSR��$ %� ˫ʐ�
),*85$�������(YHQWR�QmR�H[FOXGHQWHV
��������(YHQWRV�,QGHSHQGHQWHV
6mR�DTXHOHV�FXMD�RFRUUrQFLD�GH�XP�HYHQWR��QmR�SRVVXL�HIHLWR�DOJXP�QD�SUREDELOLGDGH�
GH�RFRUUrQFLD�GR�RXWUR�
��
$ %� ˫ʐ��VH�$�H�%�IRUHP�4XDLVTXHU�
$ %� ʐ��VH�$�H�%�IRUHP�0XWXDPHQWH�([FOXGHQWHV�
ORJR�
� � 3�%���$�3%$3 �
([���$�H�%�HYHQWRV�4XDLVTXHU
6� �^������������`� $� �^�����` %� �^������` `�^%$ �
� � 3�%���$�3%$3 �
3 $� � �
�
3 %� � �
�
� �
�
�
%$3 �
��������(YHQWRV�'HSHQGHQWHV�RX�&RQGLFLRQDGRV
([LVWHP�YDULDV�VLWXDo}HV�RQGH�D�RFRUUrQFLD�GH�XP�HYHQWR�SRGH�LQIOXHQFLDU�IRUWHPHQWH�
QD�RFRUUrQFLD�GH�RXWUR�
$VVLP�� VH� �$�� H� �%�� VmR� HYHQWRV�� GHVHMD�VH� GHILQLU� XPD� TXDQWLGDGH� GHQRPLQDGD
SUREDELOLGDGH� FRQGLFLRQDO� GR� HYHQWR� �$�� GDGR� TXH� R� HYHQWR� �%�� RFRUUH�� RX� VRE� D� IRUPD
VLPEyOLFD� � �%$3 �
$VVLP��Gi�VH�D�VHJXLQWH�GHILQLomR�
� �
3�%�
%�3�$
%
$3
� 
RQGH�3�%��!����6H�3�%�� ����WHP�VH�TXH� � �%$3 �QmR�p�GHILQLGD�
��������(YHQWRV�&ROHWLYDPHQWH�([DXVWLYRV
6mR�DTXHOHV�TXH�RFRUUHP�VH�QHQKXP�RXWUR�RFRUUHU�
��
$ % & '� � � ʐ
),*85$�������(YHQWR�FROHWLYDPHQWH�H[DXVWLYRV
����&RQFHLWRV�GH�3UREDELOLGDGH
������&RQFHLWR�(PStULFR�GH�3UREDELOLGDGH
2�SUREOHPD� � IXQGDPHQWDO�GD�SUREDELOLGDGH�FRQVLVWH�HP�DWULEXLU�XP�Q~PHUR�D�FDGD�
HYHQWR��(���R�TXDO�DYDOLDUi�TXmR�SRVVtYHO�VHUi�D�RFRUUrQFLD�GH��(���TXDQGR�R�H[SHULPHQWR�IRU�
UHDOL]DGR�
8PD�SRVVtYHO�PDQHLUD�GH� WUDWDU� D�TXHVWmR� VHULD�GHWHUPLQDU� D� IUHT�rQFLD� UHODWLYD�GR�
HYHQWR�(��IU�(���
I (�
Q~PHUR�GH�RFRUUrQFLDV�GR�HYHQWR� �(�
Q~PHUR�GH�UHSHWLo}HV�GR�H[SHULPHQWR� � �U
� 
Ƕ
�
6XUJHP��QR�HQWDQWR��GRLV�SUREOHPDV�
D���4XDO�GHYH�VHU�R�Q~PHUR�GH�UHSHWLo}HV�GR�H[SHULPHQWR��Ƕ��
E���$�VRUWH�RX�KDELOLGDGH�GR�H[SHULPHQWDGRU�SRGHUi�LQIOXLU�QRV�UHVXOWDGRV��GH�IRUPD�
WDO�TXH�D�SUREDELOLGDGH�p�GHILQLGD�FRPR�VHQGR�
3�(� �OLP I �(�Q Uȝʩ �
RQGH��Q��p�R�Q~PHUR�GH�UHSHWLo}HV�GR�H[SHULPHQWR�Ƕ �
������'HILQLomR�&OiVVLFD�RX�(QIRTXH��$�SULRUL��GH�3UREDELOLGDGH
6H�H[LVWH� �D�� UHVXOWDGRV�SRVVtYHLV� IDYRUiYHLV� D�RFRUUrQFLD�GH�XP�HYHQWR��(��H� �E��
UHVXOWDGRV�SRVVtYHLV�QmR�IDYRUiYHLV��VHQGR�RV�PHVPRV�PXWXDPHQWH�H[FOXGHQWHV��HQWmR�
��
3�(� 
D
D � E
�
RQGH�RV�UHVXOWDGRV�GHYHP�VHU�YHURVVtPHLV��SRVVtYHO�H�YHUGDGHLUR��H�SHUPLWH�D�REVHUYDomR�GRV�
YDORUHV�GD�SUREDELOLGDGH�DQWHV�GH�VHU�REVHUYDGR�TXDOTXHU�DPRVWUD�GR�HYHQWR��(��
������'HILQLomR�$[LRPiWLFD
6HMD��Ƕ��XP�H[SHULPHQWR��VHMD��6��XP�HVSDoR�DPRVWUDO�DVVRFLDGR�D��Ƕ���$�FDGD�HYHQWR�
�(��DVVRFLD�VH�XP�Q~PHUR�UHDO�UHSUHVHQWDGR�SRU�3�(��H�GHQRPLQDUHPRV�GH�SUREDELOLGDGH�GH�(��
VDWLVID]HQGR�DV�VHJXLQWHV�SURSULHGDGHV�
D�����˯ �3�(��˯ ���
E���3�6�� ���
F���6H�$�H�%�VmR�HYHQWRV�PXWXDPHQWH�H[FOXGHQWHV��HQWmR�
3�$�� �%�� �3�$����3�%��
G���6H�$���$��������$Q��VmR�HYHQWRV�PXWXDPHQWH�H[FOXGHQWHV�GRLV�D�GRLV��HQWmR�
3�$� � �$� � ������ �$Q��� �3�$�����3�$����������3�$Q�
RX
3� $ 3�$
L �
Q
L L
L �
Q
� � � ʜ �
$V�SURSULHGDGHV�DQWHULRUHV�VmR�FRQKHFLGDV�FRPR�D[LRPDV�GD�WHRULD�GD�SUREDELOLGDGH��
2V�D[LRPDV��PXLWDV�YH]HV�� VH� LQVSLUDP�HP�UHVXOWDGRV�H[SHULPHQWDLV� H�TXH�� DVVLP��GHILQHP�D�
SUREDELOLGDGH�GH�IRUPD�TXH�SRVVD�VHU�FRQILUPDGD�H[SHULPHQWDOPHQWH�
������7HRUHPDV�)XQGDPHQWDLV
7HRUHPD�����6H�ʐ�IRU�HYHQWR�YD]LR��HQWmR�3�ʐ�� ���
3URYD��6HMD�XP�HYHQWR�$� �ʐ��$VVLP��$� �$�� ʐ��FRPR�$�� ʐ� �ʐ��GH�DFRUGR�FRP�R�LWHP�
�����������$�H�ʐ�VmR�PXWXDPHQWH�H[FOXGHQWHV��HQWmR�
3�$�� �3�$�� ʐ�
3�$�� �3�$����3�ʐ�
��
3�ʐ�� �3�$����3�$�
3�ʐ�� ���
7HRUHPD�����6H�R�HYHQWR�$
B
�IRU�R�HYHQWR�FRPSOHPHQWDU�GH�$��HQWmR�3�$
B
� ��3�$��
3URYD��$�� $
B
� �6��PDV�$�H�$
B
�VmR�PXWXDPHQWH�H[FOXGHQWHV��HQWmR�
3�$�� $
B
�� �3�6�
3�$�� $
B
�� �3�$����3�$
B
�
3�$����3�$
B
�� ��
ORJR�
3�$
B
�� �����3�$��
7HRUHPD�����6H�$�H�%�VmR�HYHQWRV�TXDLVTXHU��HQWmR�
3�$�� �%�� �3�$����3�%����3�$�� �%�
3URYD�� 3DUD� SURYDU� R� 7HRUHPD� �� GHYHPRV� WUDQVIRUPDU� $ � � %� HP� HYHQWRV� PXWXDPHQWH
H[FOXGHQWHV��FRQIRUPH�D�),*85$���
),*85$������'HFRPSRVLomR�GH�HYHQWRV�TXDLVTXHU�HP�PXWXDPHQWH�H[FOXGHQWHV
7HP�VH�HQWmR�TXH�
�$���%�� �$����%�� $
B
�
��
H
%� ��$�� �%��� ��%�� $
B
�
ORJR�SHOD�SURSULHGDGH��F��WHPRV�
3�$�� �%�� �3>$�� ��%�� $
B
�@
3�$�� �%�� �3�$����3�%�� $
B
� ���
H
3�%�� �3>�$���%�����%�� $
B
�@
3�%�� �3�$�� �%����3�%�� $
B
�
RX
3�%�� $
B
�� �3�%����3�$�� �%� ����
VXEVWLWXLQGR�VH�D�HTXDomR�����QD�HTXDomR������WHP�VH�
3�$�� �%�� �3�$����3�%����3�$�� �%��
'HFRUUrQFLDV�GR�7HRUHPD���
6HMDP�$��%�H�&�HYHQWRV�TXDLVTXHU�
3�$�� �%�� �&�� �3>�$���%����&@
3�$�� �%�� �&�� �3�$�� �%����3�&����3>�$�� �%��� �&@
3�$�� �%�� �&�� �3�$����3�%����3�&����3�$���%����3>�$�&��� ��%�&�@
3�$�� �%�� �&�� �3�$����3�%����3�&����3�$�%����>3�$�&����3�%�&����3�$�%�&�@
3�$�� �%�� �&�� �3�$����3�%����3�&����3�$�%����3�$�&����3�%�&����3�$�%�&�
6HMDP�$���$��������$Q�HYHQWRV�TXDLVTXHU�
��
3�$ $ ��� $ 3�$ � 3�$ $ � 3�$ $ $ �
3�$ $ $ $ � 3�$ $ $ ��
� � Q L L M
L M �
Q
L �
Q
L M N
L M N �
Q
L M N
Q �
L M N �
Q
� � Q
� � � � � �
� � � � � �"
"
�
��� � � ���
 ʝ � �
ʝ � � ʝ
� � � 
ʝ
� � � 
ʜʜ ʜ
ʜ �
5(6802
е
е
д
ее
г
в
ʐ˫
ɝ
ʐ 
ɝ
�
%$
%�3�$�3�%��3�$� %�3�$4XDLVTXHU
%$
3�%��3�$� %�3�$V([FOXGHQWH0XWXDPHQWH
�28�
�
��
�
�
�
е
е
д
ее
г
в
ɝ
ʐ˫
ɝ
3�%�$��[�3�$� %�3�$V'HSHQGHQWH
%$
3�%��[�3�$� %�3�$WHV,QGHSHQGHQ
�(�[ �
�
�
�
��
����([HUFtFLRV
���$�SUREDELOLGDGH�GH��� MRJDGRUHV�PDUFDUHP�XP�SHQDOWL� p� UHVSHFWLYDPHQWH�� ����� �����
�����FREUDQGR�XPD�~QLFD�YH]�
D��WRGRV�DFHUWDUHP���������
E��DSHQDV�XP�DFHUWDU�������
F��WRGRV�HUUDUHP��������
���1XPD�EROVD�FRP���PRHGDV� GH������H����PRHGDV�GH�������4XDO�D�SUREDELOLGDGH�GH�DR�
UHWLUDUPRV���PRHGDV�REWHU�D�VRPD��������������
���8PD�XUQD�FRQWpP���ERODV�SUHWDV����YHUPHOKDV�H���EUDQFDV��7UrV�ERODV�VmR�UHWLUDGDV��
4XDO�D�SUREDELOLGDGH�GH�UHWLUDU���SUHWDV�H���YHUPHOKD�"D��VHP�UHSRVLomR������
E��FRP�UHSRVLomR�������
�� �� 1XPD� FODVVH� Ki� ��� KRPHQV� H� ��� PXOKHUHV�� PHWDGH� GRV� KRPHQV� H� PHWDGH� GDV
PXOKHUHV�SRVVXHP�ROKRV�FDVWDQKRV��$FKH�D�SUREDELOLGDGH�GH�XPD�SHVVRD�HVFROKLGD�DR�
DFDVR�VHU�KRPHP�RX�WHU�ROKRV�FDVWDQKRV�������
���$�SUREDELOLGDGH�GH�XP�KRPHP�HVWDU�YLYR�GDTXL�D����DQRV�p�GH�����H�GH�VXD�PXOKHU�p�
GH�������4XDO�D�SUREDELOLGDGH�GH�TXH�
D��DPERV�HVWHMDP�YLYRV�QR�SHUtRGR�"��������
E��VRPHQWH�R�KRPHP�HVWDU�YLYR�"��������
F��DR�PHQRV�D�PXOKHU�HVWDU�YLYD�"�������
G��VRPHQWH�D�PXOKHU�HVWDU�YLYD"��������
���)DoD�R�H[HUFtFLR�DQWHULRU�FRQVLGHUDQGR�����D�FKDQFH�GR�KRPHP�HVWDU�YLYR�H�����D�
FKDQFH�GD�PXOKHU�HVWDU�YLYD�H�FRPSDUD�RV�UHVXOWDGRV�
���8PD�XUQD�FRQWpP��� ILFKDV�YHUPHOKDV�H���EUDQFDV��([WUDHP�VH�VXFHVVLYDPHQWH�GXDV�
ILFKD��VHP�UHSRVLomR�H�FRQVWDWRX�VH�TXH�D����p�EUDQFD�
D��TXDO�D�SUREDELOLGDGH�GD�VHJXQGD�WDPEpP�VHU�EUDQFD�"�������
E��TXDO�D�SUREDELOLGDGH�GD����VHU�YHUPHOKD�"�������
���1XPD�FLGDGH������GD�SRSXODomR�SRVVXL�FDEHORV�FDVWDQKRV������ROKRV�FDVWDQKRV�H�
�����ROKRV�H�FDEHORV�FDVWDQKRV��8PD�SHVVRD�p�VHOHFLRQDGD�DOHDWRULDPHQWH�
D��VH�HOD�WLYHU�ROKRV�FDVWDQKRV��TXDO�D�SUREDELOLGDGH�GH�WDPEpP�WHU�FDEHORV�FDVWDQKRV"�
E�� VH�HOD� WLYHU�FDEHORV�FDVWDQKRV��TXDO� D�SUREDELOLGDGH�GH� WHU�ROKRV�FDVWDQKRV� "� ������
�����
��
���8P�FRQMXQWR�GH����SHVVRDV�WHP�DV�FDUDFWHUtVWLFDV�DEDL[R�
%5$6,/(,52 $5*(17,12 858*8$,2 727$/
0$6&8/,12 �� �� �� ��
)(0,1,12 �� �� �� ��
727$/ �� �� �� ��
6H�UHWLUDUPRV�XPD�SHVVRD�DR�DFDVR��TXDO�D�SUREDELOLGDGH�GH�TXH�HOD�VHMD�
D��EUDVLOHLUD�RX�XUXJXDLD����������
E��GR�VH[R�PDVFXOLQR�RX�WHQKD�QDVFLGR�QD�DUJHQWLQD��������
F��EUDVLOHLUR�GR�VH[R�PDVFXOLQR����������
G��XUXJXDLR�GR�VH[R�IHPLQLQR����������
H��VHU�PXOKHU�VH�IRU�DUJHQWLQR����������
����8P�JUXSR�GH�SHVVRDV�HVWi�DVVLP�IRUPDGR�
0pGLFR (QJHQKHLUR 9HWHULQiULR
0DVF� �� �� ��
)HPLQ� �� �� ��
(VFROKHQGR�VH��DR�DFDVR��XPD�SHVVRD�GR�JUXSR��TXDO�D�SUREDELOLGDGH�GH�TXH�VHMD�
D��8PD�PXOKHU�TXH�IH]�R�FXUVR�GH�PHGLFLQD�"
E��8PD�SHVVRD�TXH�IH]�R�FXUVR�GH�PHGLFLQD�"
F��8P�HQJHQKHLUR�GDGR�TXH�VHMD�KRPHP�"
G��1mR�VHU�PpGLFR�GDGR�TXH�QmR�VHMD�KRPHP�"
����1XP�JLQiVLR�GH�HVSRUWHV������GRV�IUHTXHQWDGRUHV�MRJDP��Y{OHL������MRJDP�EDVTXHWH�
H�����SUDWLFDP�RV�GRLV�HVSRUWHV��8P�GRV�IUHTXHQWDGRUHV�p�VRUWHDGR�SDUD�JDQKDU�XPD�
PHGDOKD�� 6DEHQGR�VH� TXH� HOH� MRJD� EDVTXHWH�� TXDO� D� SUREDELOLGDGH�GH�TXH� WDPEpP�
MRJXH�Y{OHL�"
���� $� SUREDELOLGDGH� GH� XP� DOXQR� UHVROYHU� XP� GHWHUPLQDGR� SUREOHPD� p� GH� ���� H� D�
SUREDELOLGDGH� GH� RXWUR� p� GH� ����� 6DEHQGR� TXH� RV� DOXQRV� WHQWDP� VROXFLRQDU� R
SUREOHPD�LQGHSHQGHQWHPHQWH��4XDO�D�SUREDELOLGDGH�GR�SUREOHPD�VHU�UHVROYLGR��
D��VRPHQWH�SHOR�SULPHLUR�"
E��DR�PHQRV�SRU�XP�GRV�DOXQRV�"
F��SRU�QHQKXP�"
��
����7HRUHPD�GH�%D\HV
'HILQLomR�� 6HMD� 6� XP� HVSDoR� DPRVWUDO� H $ � �$ � ���� �$ �� � N � N� HYHQWRV�� 'L]�VH�TXH�
$ � �$ � ���� �$ �� � N �IRUPDP�XPD�SDUWLomR�GH�6�VH�
$ � �L �� �� ���� �NL ˫ʐ 
$ 6�L
L �
N
 
 
�
$ $ ��L ML M� ʐ ˫
$ � �$ � �$ � �$ ��$ � ���� �$� � � � � N �IRUPDP�XPD�SDUWLomR�GH�6�
),*85$�������'LDJUDPD�UHSUHVHQWDWLYR�GR�7HRUHPD�GH�%D\HV
6HMD�%�XP�HYHQWR�TXDOTXHU�GH�6��RQGH��
% �%� �$ � �%� �$ � ��� �%� �$� � N � � � � � � �
� �ʜ
 
Ъ
Ы
ЩЧ
Ш
Ц 
N
�M M
M $
%�3$33�%� ���M� ������������N ���
ЪЫ
ЩЧШ
Ц 
L
LL $
%��33�$�$3�%� � ����
FRPR
��
3�%�
�$3�%
%
$3 LL
� ЪЫ
ЩЧШ
Ц � �����
VXEVWLWXLQGR�DV�HTXDo}HV�����H������QD�HTXDomR�������WHPRV�
� �
� �ʜ
 
Ъ
Ы
ЩЧ
Ш
Ц
ЪЫ
ЩЧШ
Ц
 ЪЫ
ЩЧШ
Ц
N
�M M
M
L
L
L
$
%�3$3
$
%�3$3
%
$3 ��M� ������������N��
([HPSOR�
8UQD 8� 8� 8�
$]XO � � �
%UDQFD � � �
&
RU
HV
3UHWD � � �
(VFROKH�VH�XPD�XUQD�DR�DFDVR�H�GHOD�H[WUDL�VH�XPD�EROD�DR�DFDVR��YHULILFDQGR�VH�TXH�
HOD�p�EUDQFD��4XDO�D�SUREDELOLGDGH�GHOD�WHU�VDtGR�GD�XUQD�
8��" 8��" �8��"
���7HPRV���FDL[DV��QD�SULPHLUD�Ki���ERODV�EUDQFDV�H���SUHWDV�H�QD�VHJXQGD����EUDQFD�
H���SUHWDV��'H�XPD�FDL[D�HVFROKLGD�DOHDWRULDPHQWH��VHOHFLRQRX�VH�XPD�EROD�H�YHULILFRX�VH�TXH�
p�SUHWD��4XDO�D�SUREDELOLGDGH�GH�TXH�WHQKD�VDtGR�GD�SULPHLUD�FDL[D�"�VHJXQGD�FDL[D�"
����9DULiYHLV�DOHDWyULDV
$R�GHVFUHYHU�XP�HVSDoR�DPRVWUDO��6��DVVRFLDGR��D�XP��H[SHULPHQWR��Ƕ��HVSHFLILFD�VH�
TXH�XP�UHVXOWDGR�LQGLYLGXDO�QHFHVVDULDPHQWH��VHMD�XP�Q~PHUR��&RQWXGR��HP�PXLWDV�VLWXDo}HV�
H[SHULPHQWDLV��HVWDUHPRV�LQWHUHVVDGR�QD�PHQVXUDomR�GH�DOJXPD�FRLVD�H�QR�VHX�UHJLVWUR�FRPR�
XP�Q~PHUR�
'HILQLomR�� 6HMD � �Ƕ�� XP� H[SHULPHQWR� DOHDWyULR� H� VHMD� �6�� XP� HVSDoR� DPRVWUDO� DVVRFLDGR� DR�
H[SHULPHQWR��8PD�IXQomR�GH�;��TXH�DVVRFLH�D�FDGD�HOHPHQWR�V�ʓ�6�XP�Q~PHUR�
UHDO�[�V���p�GHQRPLQDGD�YDULiYHO�DOHDWyULD�
��
),*85$������5HSUHVHQWDomR�GH�XPD�YDULiYHO�DOHDWyULD
8PD�YDULiYHO�;� VHUi�GLVFUHWD� �9�$�'��� VH�R�Q~PHUR�GH�YDORUHV�GH�[�V�� IRU� ILQLWR�RX�
LQILQLWR� QXPHUiYHO�� &DVR� HQFRQWUDUPRV� [�V�� HP� IRUPD� GH� LQWHUYDOR� RX� XP� FRQMXQWR� GH
LQWHUYDORV��WHUHPRV�XPD�YDULiYHO�DOHDWyULD�FRQWtQXD��9�$�&���
����)XQomR�GH�3UREDELOLGDGH
$�SUREDELOLGDGH�GH�TXH�XPD�YDULiYHO�DOHDWyULD��;��DVVXPD�R�YDORU��[��p�XPD�IXQomR�
GH�SUREDELOLGDGH��UHSUHVHQWDGD�SRU�3�;� �[��RX�3�[��
������)XQomR�GH�3UREDELOLGDGH�GH�XPD�9�$�'�
$�IXQomR�GH�SUREDELOLGDGH�SDUD�XPD�YDULiYHO�DOHDWyULD�GLVFUHWD�p�FKDPDGD�GH�IXQomR�
GH�SUREDELOLGDGH�QR�SRQWR��RX�VHMD��p�R�FRQMXQWR�GH�SDUHV��[L�3�[L����L� ������������Q�������FRQIRUPH�
PRVWUD�D�),*85$���
),*85$��������'LVWULEXLomR�GH�SUREDELOLGDGH�GH�XPD�9�$�'�
��
3DUD�FDGD�SRVVtYHO�UHVXOWDGR�GH�[�WHUHPRV�
� 3�;� �˯ ˯ �
3�; � �L
L �
 
 
ʩ
ʜ
������)XQomR�GH�5HSDUWLomR�SDUD�9�$�'�
6HMD�;�XPD�YDULiYHO�DOHDWyULD�GLVFUHWD�
'HILQH�VH�)XQomR�GH�5HSDUWLomR�GD�9DULiYHO�DOHDWyULD�;��QR�SRQWR�[L��FRPR�VHQGR�D�
SUREDELOLGDGH�GH�TXH�;�DVVXPD�XP�YDORU�PHQRU�RX�LJXDO�D�[L��LVWR�p�
� �)�; 3 ; [L� ˯
3URSULHGDGHV�
�D�� � �)�; 3 [L
[ [L
� ʜ˯
�D�� )�ʝʩ � �
�D�� )��ʩ � �
�D�� � �3 D [ E )�E )�D� ˯ ʝ� �
�D�� � �3 D [ E )�E )�D 3 ; D˯ ˯ ʝ � � � � �
�D�� � �3 D [ E )�E )�D 3 ; E� � ʝ ʝ � � � �
�D��)�;��p�FRQWtQXD�j�GLUHLWD�ɝ � �OLP �[ [ R)�; ) ;ȝ �
�D��)�;��p�GHVFRQWtQXD�j�HVTXHUGD��QRV�SRQWRV�HP�TXH�D�SUREDELOLGDGH�p�GLIHUHQWH�GH�
]HUR�
� �OLP � � �
[ [
R)�; ) ;
ȝ
˫ ˫
�
��SDUD�3�; [R
�D��$�IXQomR�QmR�p�GHFUHVFHQWH��LVWR�p��)�E��˰ �)�D��SDUD�E�!�D�
������(VSHUDQoD�0DWHPiWLFD�GH�9�$�'�
'HILQLomR��6HMD�;�XPD�9�$�'���FRP�YDORUHV��SRVVtYHLV�[���[��������[Q�������6HMD�3�[L�� �
3�;� �[L���L� ������������Q��������(QWmR��R�YDORU�HVSHUDGR�GH�;��RX�(VSHUDQoD�
0DWHPiWLFD�GH�;���GHQRWDGR�SRU�(�;��p�GHILQLGR�FRPR
��
(�;� [ �3�[ �L L
L �
 
 
ʩ
ʜ
VH� D� VpULH (�;� [ �3�[ �L L
L �
 
 
ʩ
ʜ � FRQYHUJLU� � DEVROXWDPHQWH�� LVWR� p�� VH� _[ _�3�[ �L L
L � 
ʩ
ʜ �ʩ�� HVWH
Q~PHUR�p�WDPEpP�GHQRPLQDGR�R�YDORU�PpGLR�GH�;��RX�H[SHFWkQFLD�GH�;�
������9DULkQFLD�GH�XPD�9�$�'�
'HILQLomR��6HMD�;�XPD�9�$�'����'HILQH�VH�D�YDULkQFLD�GH�;��GHQRWDGD�SRU�9�;��RX�Ⴔ�[��
GD�VHJXLQWH�PDQHLUD�
� �9�;� [ (�;� �3�[ �L � L
L �
 ʝ
 
ʩ
ʜ �RX�9�;� (�; � (�;�� � ʝ
RQGH�(�; � [ �3�[ �� L
�
L
L �
 
 
ʩ
ʜ �H�D�UDL]�TXDGUDGD�SRVLWLYD�GH�9�;��p�GHQRPLQDGD�R�GHVYLR�SDGUmR�
GH�;��H�GHQRWDGR�SRU�Ⴔ[�
������)XQomR�GH�3UREDELOLGDGH�GH�XPD�9�$�&�
1R� LQVWDQWH� HP�TXH�;�p�GHILQLGD� VREUH�XP�HVSDoR�DPRVWUDO� FRQWtQXR�� D� IXQomR�GH�
SUREDELOLGDGH� VHUi� FRQWtQXD��RQGH� D� FXUYD� OLPLWDGD�SHOD� iUHD� HP� UHODomR� DR�YDORUHV�GH�[� VHUi�
LJXDO�D���
),*85$�������'LVWULEXLomR�GH�SUREDELOLGDGH�GH�XPD�9�$�&�
6H� TXLVHUPRV� FDOFXODU� D� SUREDELOLGDGH� GH� ;� DVVXPLU� XP� YDORU� [� HQWUH� �D�� H� �E��
GHYHPRV�FDOFXODU�
3�D [ E� I�[��G[
D
E
˯ ˯ ʶ
��
3HOR�IDWR�GH�TXH�D�iUHD��UHSUHVHQWD�SUREDELOLGDGH��H�D�PHVPD�WHP�YDORUHV�QXPpULFRV�
SRVLWLYRV��ORJR�D�IXQomR�SUHFLVD�HVWDU�LQWHLUDPHQWH�DFLPD�GR�HL[R�GDV�DEVFLVVDV��[��
'HILQLomR��$��IXQomR�I�[��p�XPD�)XQomR�'HQVLGDGH�GH�3UREDELOLGDGH��I�G�S���SDUD�XPD�
9�$�&��;��GHILQLGD�QRV�UHDLV�TXDQGR
I �[� �˰ �
I�[��G[� ��
ʝʩ
�ʩ
ʶ �
3�D [ E� I�[��G[
D
E
˯ ˯ ʶ �
������)XQomR�GH�5HSDUWLomR�SDUD�9�$�&�
6HMD�;�XPD�YDULiYHO�DOHDWyULD�FRQWtQXD�
'HILQH�VH�)XQomR�GH�5HSDUWLomR�GD�9DULiYHO�DOHDWyULD�;��QR�SRQWR�[L��FRPR�VHQGR�
)�; I [ G[
[
� � � 
ʝʩʁ
� � � � � � � � �3 D [ E 3 D [ E 3 D [ E 3 D[ E˯ ˯ � � � ˯ ˯ �
������(VSHUDQoD�0DWHPiWLFD�GH�XPD�9�$�&�
'HILQLomR��6HMD�;�XPD�9�$�&��FRP�I�G�S��I�[���2�YDORU�HVSHUDGR�GH�;�p�GHILQLGR�FRPR
ʶ
ʩ
ʩ
 
�
�
G[[�I�[�(�;�
SRGH�DFRQWHFHU�TXH�HVWD�LQWHJUDO�LPSUySULD�QmR�FRQYLUMD�
&RQVHT�HQWHPHQWH�� GLUHPRV� TXH� (�;�� H[LVWLUi� VH�� H� VRPHQWH� VH�� ʶ
�ʩ
ʩʝ
I�[�_[_ � IRU�
ILQLWD�
��
������9DULkQFLD�GH�XPD�9�$�&�
'HILQLomR��6HMD�;�XPD�9�$�&��GH�XPD�IXQomR�GLVWULEXLomR�GH�SUREDELOLGDGH��I�G�S����$
YDULkQFLD�GH�;�p�
� �9�;� [ (�;� I�[��G[� ʝ
ʝʩ
�ʩ
ʶ �RX�9�;� (�; � (�;�� � ʝ
RQGH
(�; � [ �I�[��G[� � 
ʝʩ
�ʩ
ʶ
����([HPSORV
��9DULiYHO�$OHDWyULD�'LVFUHWD
6HMD� ;� R� ODQoDPHQWR� GH� GXDV� PRHGDV� H� GHVFUHYHU� R� H[SHULPHQWR� HP� IXQomR� GD�
REWHQomR�GR�Q~PHUR�GH�FDUDV�
L��GHWHUPLQDU�D�IXQomR�GH�SUREDELOLGDGH�H�UHSUHVHQWH�JUDILFDPHQWH�
LL��FRQVWUXLU�D�IXQomR�GH�UHSDUWLomR�H�UHSUHVHQWH�JUDILFDPHQWH�
LLL��8VH�DV�SURSULHGDGHV�SDUD�GHWHUPLQDU�
D��3�����[�������E��3���˯ �[� �˯����F��3�����[�˯ �����G��)�����H��)���
LY��(�;��H�9�;�
L� 5HSUHVHQWDomR�JUiILFD
� � �
�
���
���
���
���
���
���
��
LL� 5HSUHVHQWDomR�JUiILFD
)�[�� ���VH�[��
)�;�� �����VH���˯ �[����
)�;�� �����VH���˯ �[����
)�;�� ���VH�[� �˰�
LLL�
D�� � �
�
�
�
�
�
�
���;�3���)���)�[�3 ʝʝ ʝʝ ��
E�� � �3 [ )� )� 3 ;� � � � �
�
�
�
�
�
�
�
�
˯ ˯ ʝ � ʝ � � � � �
F�� � �3 [ )� )�� � � � � ��
�
�
� ˯ ʝ ʝ � �
G��)���� ���� H��)���� ��
LY��(VSHUDQoD�0DWHPiWLFD
(�;� [ �3�[ �L L
L �
 
 
ʩ
ʜ � �� � � ��� �� ��
�
�
��
�
�
� � 
9DULkQFLD
(�; � [ �3�[ �� L
�
L
L �
 
 
ʩ
ʜ � � � � ��
� � ���
�
�
��
�
�
��
�
�
� � 
9�;� (�; � (�;��
� ʝ � �
�
�
�
�
�
�
��ʝ �
��
��9DULiYHO�$OHDWyULD�&RQWtQXD
6HMD�;�XPD�YDULiYHO�DOHDWyULD�FRQWtQXD�
д
г
в �� 
�YDORURXWURTXDOTXHU�SDUD��
�[�SDUD�[�
�[�I
L���UHSUHVHQWH�JUDILFDPHQWH�IXQomR�GHQVLGDGH�GH�SUREDELOLGDGH�
LL��GHWHUPLQDU�D�IXQomR�GH�UHSDUWLomR�H�UHSUHVHQWH�JUDILFDPHQWH�
LLL��'HWHUPLQH� Ъ
Ы
ЩЧ
Ш
Ц ˯˯
�
�
[
�
�
3 �H Ъ
Ы
ЩЧ
Ш
Ц �˯ �[
�
�
3
LY��(�;��H�9�;�
L�
LL�
SDUD�[��� ɝ
ʩʁʝ
 
[
�G[��;�)
SDUD���˯ �[���� ɝ > @ʶ ʶʩʝ � � 
[ �[
�
�[
�
[[�G[[�G[��;�)
SDUD�[� �˰�� ɝ > @ʶ ʶ ʶʩʝ
�ʩ
 �� �� 
[ �
�
�
�
� �
��[�G[�G[[�G[��;�)
��
5HSUHVHQWDomR�JUiILFD
LLL�� > @3 [ [�� �� � �� �� ��� � ��
�
�
�
�
�
�
�
� �
˯ ˯Ц
ШЧ
Щ
ЫЪ
 Ц
ШЧ
Щ
ЫЪ
ʝЦ
ШЧ
Щ
ЫЪ
 ʶ �G[ [� �
LY�� > @(�;� �I�[��G[ ��[�G[ �I�[��G[ �� ʶ ʶ ʶ[ [ [ [�
�
�
�
�
�
�
�
�
�
�
�
�
> @(�; � �I�[��G[ ��[�G[ �I�[��G[ ��� ʶ ʶ ʶ[ [ [ [��
�
�
�
�
�
�
�
�
�
�
�
�
�
ORJR��
> @9�;� (�; � (�;�� � ʝ ʝЦШЧ
Щ
ЫЪ
 ʝ �
�
�
�
� �
��
�
��
�
����([HUFtFLRV
���$GPLWD�TXH�D�YDULiYHO�;�WRPH�YDORUH������H���FRP�SUREDELOLGDGHV����������H�����
UHVSHFWLYDPHQWH�
D��'HWHUPLQH�VXD�IXQomR�GH�UHSDUWLomR�H�UHSUHVHQWH�JUDILFDPHQWH�
E��&DOFXOH�XVDQGR�DV�SURSULHGDGHV�
E����D��3�����[�������E��3���˯ �[� �˯����F��3�����[�˯ �����G��)�����H��)���
F��(�;��H�9�;�
��� 1R� ODQoDPHQWR� VLPXOWkQHR� GH� GRLV� GDGRV�� FRQVLGHUH� DV� VHJXLQWHV� YDULiYHLV
DOHDWyULDV�
��
;� �Q~PHUR�GH�SRQWRV�REWLGRV�QR��R�GDGR�
<� �Q~PHUR�GH�SRQWRV�REWLGRV�QR��R�GDGR�
D�� &RQVWUXLU� D� GLVWULEXLomR� GH� SUREDELOLGDGH� DWUDYpV� GH� XPD� WDEHOD� H� JUiILFR� GDV
VHJXLQWH�YDULiYHLV�
L��:� �;���<
LL��$� ���<
LLL��=� �;���<
E��&RQVWUXLU�D�IXQomR�GH�UHSDUWLomR�GDV�9DULiYHLV�:��$�H�=
F��$SOLFDU�DV�SURSULHGDGHV�H�GHWHUPLQDU�
L��3�������:� �˯�� Y��3��=� ���
LL��3����˯ �:� �˯�� YL��3��$� �˰���
LLL��3��$�!��� YLL��3�����˯ �=� �˯���
LY��3��=�˯ ����� YLLL��3�������=������
G��'HWHUPLQH�(�:���(�$���(�=���9�:���9�$��H�9�=�
���8PD�YDULiYHO�DOHDWyULD�GLVFUHWD�WHP�D�GLVWULEXLomR�GH�SUREDELOLGDGH�GDGD�SRU�
� �3 ; .
[
 �SDUD�[� ���������H��
D��FDOFXOH�R�YDORU�GH�N E��&DOFXODU�3�; ��
F��(�;� G��9�;�
���6HMD�=�D�YDULiYHO�DOHDWyULD�FRUUHVSRQGHQWH�DR�Q~PHUR�GH�SRQWRV�GH�XPD�SHoD�GH�
GRPLQy�
D��&RQVWUXLU�D�WDEHOD�H�WUDoDU�R�JUiILFR�3�=��
E��'HWHUPLQDU�)�=��H�WUDoDU�R�JUiILFR�
F��&DOFXODU�3�� �˯=������
G��&DOFXODU�)����
H��(�=��H�9�=��
��
���6HMD � �
ед
е
г
в ��ʝ 
FRQWUiULRFDVR��
�[��[�
�
�
�[�I
�
�
L��$FKH�D�IXQomR�GH�UHSDUWLomR�H�HVERFH�R�JUiILFR�
LL��'HWHUPLQH�(�;��H�9�;��
���6HMD
ед
е
г
в ˯˯ 
FRQWUiULRFDVR��
�[��[
�
�
�[�I �
L��$FKH�D�IXQomR�GH�UHSDUWLomR�H�HVERFH�R�JUiILFR�
LL��3����[��������
LLL��(�;��H�9�;��
���8PD�YDULiYHO�DOHDWyULD�;�WHP�D�VHJXLQWH�I�G�S��
[���� I�[�� ��
�� �˯[����� I�[�� �N
�� �˯[����� I�[�� �N�[�����
[� �˰� I�[�� ��
D��5HSUHVHQWH�JUDILFDPHQWH�I�[��
E��'HWHUPLQH�N�
F��'HWHUPLQH�)�;��H�IDoD�R�JUiILFR
G��(�;��H�9�;�
���$�IXQomR�GH�SUREDELOLGDGH�GH�XPD�9�$�&��;�p�
� �
д
г
в ��ʝ 
FRQWUiULRFDVR��
�[��[�[�
�[�I
D��'HWHUPLQH�)�;��H�UHSUHVHQWH�JUDILFDPHQWH�
E��&DOFXOH�3 [ ˯
Ц
ШЧ
Щ
ЫЪ
�
�
F��(�;��H�9�;�
��
���8PD�YDULiYHO�DOHDWyULD�;�WHP�D�VHJXLQWH�I�G�S��
I�[�� �� [����
I�[�� �$[ �� �˯[������
I�[�� �$�������[� ����˯ �[�������
I�[�� �� [� �˰����
D��'HWHUPLQH�R�YDORU�GH�$�
E��3������˯ �[� �˯�����
����'DGD�D�IXQomR�GH�UHSDUWLomR�
)�;�� �� SDUD�[�����
)�;�� �
[ ��
� SDUD����˯ �[����
)�;�� �� SDUD [� �˰�
D��&DOFXOH�� 3 [ʝ ˯ ˯
Ц
ШЧ
Щ
ЫЪ
�
�
�
� ��E��3�;� ���
��
�� ''LLVVWWUULLEEXXLLoo}}HHVV GGHH 33UURREEDDEELLOOLLGGDDGGHH
$SyV� WHUPRV� YLVWR� DV� GHILQLo}HV� GH� 9�$�'�� H� 9�$�&��� FLWDUHPRV� DV� SULQFLSDLV
GLVWULEXLo}HV�GH�SUREDELOLGDGH�UHODFLRQDGDV�D�HVWDV�YDULiYHLV�
����'LVWULEXLo}HV�'LVFUHWDV�GH�3UREDELOLGDGH
������'LVWULEXLomR�GH�%HUQRXOOL
&RQVLGHUDPRV�XPD�~QLFD�WHQWDWLYD�GH�XP�H[SHULPHQWR�DOHDWyULR�SRGHPRV�WHU�VXFHVVR�
RX� IUDFDVVR� QHVVD� WHQWDWLYD�� 6HMD� �S�� D� SUREDELOLGDGH� GH� VXFHVVR� H� �T�� D� SUREDELOLGDGH� GH�
IUDFDVVR��RQGH�S���T� ���
6HMD�;�R�Q~PHUR�GH�VXFHVVR�HP�XPD�~QLFD�WHQWDWLYD��ORJR�;�SRGH�DVVXPLU�
;� ���VH�RFRUUHU�IUDFDVVR�H�;� ���VH�RFRUUHU�VXFHVVR�
RX�DLQGD�
д
г
в 
�S �� 3�;FRPVXFHVVR�IRU�VH��
T �� 3�;FRPIUDFDVVR�IRU�VH��
;
6XSRQGR�TXH�HP�XPD�~QLFD�WHQWDWLYDV�R�Q~PHUR�GH�FDVRV�SRVVtYHLV�VHMDP�
$� �$� ���� �$ $� $� ���� $
[�VXFHVVRV Q�[�IUDFDVVRV
	 
�� ��� 	 
�� ���
�
VHQGR�RV�UHVXOWDGRV�LQGHSHQGHQWHV��WHPRV�
3�$ $ ��� $ $ $ ��� $� 3�$��3�$�� ��� � �3�$��3�$��3�$�� ��� ��3�$�� � � � � � � 
3�$��3�$�� ��� �3�$� � 3�$�� 3�$�� ��� �3�$�
[�VXFHVVRV Q�[�IUDFDVVRV
	 
���� ����� 	 
���� ����� ��RQGH�3�$� �S�H�3�$
B
�� �T�
��
QHVVD� FRQGLomR� D� YDULiYHO� DOHDWyULD� ;� WHP� GLVWULEXLomR� GH� %HUQRXOOL�� H� VXD� IXQomR� GH
SUREDELOLGDGH��I��S����IXQomR�GH�SUREDELOLGDGH��p�GDGD�SRU�
3�; [� S �T[ Q [ ʝ �
��������(VSHUDQoD�0DWHPiWLFD�GD�'LVWULEXLomR�GH�%HUQRXOOL
(�;� [ �3�[ �L L
L �
 
 
ʩ
ʜ
(�;� [ 3�[ � [ 3�[ �� � � � �
(�;� 3��� 3��� �� �� �
(�;� ��T� ���S �
(�;� S� 
��������9DULkQFLD�GD�'LVWULEXLomR�GH�%HUQRXOOL
9�;� (�; � (�;��
� ʝ
RQGH
(�; � [ �3�[ �� L
�
L
L �
 
 
ʩ
ʜ
(�; � [ 3�[ � [ 3�[ �� �
�
� �
�
� �
(�; � ���S� �S� ���T
ORJR
9�;� S S� ʝ
� �S��S�9�;� 
9�;� S�� �T 
������'LVWULEXLomR�%LQRPLDO
2�WHUPR��%LQRPLDO��p�XWLOL]DGR�TXDQGR�XPD�YDULiYHO�DOHDWyULD�HVWD�DJUXSDGD�HP�GXDV�
FODVVHV�RX�FDWHJRULDV��$V�FDWHJRULDV�GHYHP�VHU�PXWXDPHQWH�H[FOXGHQWHV��GH�PRGR�D�GHL[DU�EHP�
FODUR�D�TXDO�FDWHJRULD�SHUWHQFH�GHWHUPLQDGD�REVHUYDomR��H�DV�FODVVHV�GHYHP�VHU�FROHWLYDPHQWH�
H[DXVWLYDV��GH�IRUPD�TXH�QHQKXP�RXWUR�UHVXOWDGR�IRUD�GHODV�p�SRVVtYHO
��
6HMDP���S��SUREDELOLGDGHV�GH��VXFHVVR��H���T���SUREDELOLGDGHV�GH ��IDOKD���RX��VHMD�S���T�
 ���
$�SUREDELOLGDGH�GH�[�VXFHVVRV�HP�[�WHQWDWLYDV�p�GDGR��SRU��S[��H��GH��Q���[��IDOKDV�HP�
�Q���[��WHQWDWLYDV�p�GDGR�SRU�TQ�[��RQGH�R�Q~PHUR�GH�YH]HV�HP�TXH�SRGH�RFRUUHU�[�VXFHVVRV�H�
�Q�[��IDOKDV�p�GDGR�SRU�
[���Q[�
Q�
[
Q
& [Q� ʝ
 ЪЪЫ
Щ
ЧЧШ
Ц 
ORJR��D�SUREDELOLGDGH�GH�RFRUUHU�[�VXFHVVRV�FRP�Q�WHQWDWLYDV�VHUi
[Q[ TS
[
Q
[�3�; ʝЪЪЫ
Щ
ЧЧШ
Ц 
3URSULHGDGHV�QHFHVViULDV�SDUD�KDYHU�XPD�XWLOL]DomR�GD�'LVWULEXLomR�%LQRPLDO�
�D��1~PHUR�GH�WHQWDWLYDV�IL[DV�
�D��&DGD�WHQWDWLYD�GHYH�UHVXOWDU�QXPD�IDOKD�RX�VXFHVVR�
�D��$V�SUREDELOLGDGHV�GH�VXFHVVR�GHYHP�VHU�LJXDLV�SDUD�WRGDV�DV�WHQWDWLYDV�
�D��7RGDV�DV�WHQWDWLYDV�GHYHP�VHU�LQGHSHQGHQWHV�
��������(VSHUDQoD�0DWHPiWLFD�GH�'LVWULEXLomR�%LQRPLDO
(�;� [ �3�[ �L L
L �
 
 
ʩ
ʜ
[Q[ TS[
Q
[�(�;� ʝЪЪЫ
Щ
ЧЧШ
Ц 
FRPR�3�;��VHJXH�XPD�'LVWULEXLomR�GH�3UREDELOLGDGH��WHPRV�
ʜʜ
ʩ
ʝ
ʩ
 
 ЪЪЫ
Щ
ЧЧШ
Ц 
�
� [
[Q[
�L
L �TS[
Q
RX���[ 3�;
ORJR�
(�;� [�
Q�
[�[ �����Q �[��
S �T[ Q [
[
 ʝ
 
ʩ
ʜ
�
(�;� �
�Q ����
�[ �����Q � [��
S �T[ Q [
[
 ʝ
 
ʩ
ʜQ
�
��RX�VHMD�SDUD�V� �[�����H�[� �V������WHPRV
���VQ�V
� [
TS
V
��Q
Q�(�;� �ʝ�
ʩ
ʜ ЪЪЫ
Щ
ЧЧШ
Ц 
��
V���QV
� [
T�SS
V
��Q
Q�(�;� ʝʝ
ʩ
ʜ ЪЪЫ
Щ
ЧЧШ
Ц 
��� ���� 
	
�
V���QV
� [
T�S
V
��Q
Q�S(�;� ʝʝ
ʩ
ʜ ЪЪЫ
Щ
ЧЧШ
Ц 
S�Q�(�;� 
��������9DULkQFLD�GH�XPD�'LVWULEXLomR�%LQRPLDO
9�;� (�; � (�;��
� ʝ
RQGH
(�; � [ �3�[ �� L
�
L
L �
 
 
ʩ
ʜ
(�; � [�[
Q�
[��[ ����Q [��
S T �SDUD�V [ ���H�[ V��� �WHPRV�� [ Q [
[
 
ʝ ʝ
ʝ
 
ʩ
ʜ
�
�
(�; �
Q�
V��Q ��
S T� V�� Q
[
 �
ʝ �
ʝ �
 
ʩ
ʜ� � � �
� �V
V
V�
�
�
�
(�; � V�Q
�Q ����
V��Q ��� V��
S �S�T Q
�Q ����
V��Q ���V��
S � S�T� V Q � V V Q � V
[[
 �ʝ ʝ ʝ ʝ
 
ʩ
 
ʩ
ʜʜ
��
а
а
а
а
б
Я
Э
Э
Э
Э
Ю
Ь
ЪЪЫ
Щ
ЧЧШ
Ц�ЪЪЫ
Щ
ЧЧШ
Ц ʝ ʜʜ
ʩ
 
ʝʝ
ʝ
ʩ
 
ʝʝ
��� ���� 
	��� ���� 
	
�
�[
V�QV
��S�Q
�[
V�QV� TS
V
��Q
T�SS
V
�Q
VQ�S�(�;
(�; �� ʝ �Q S Q S� � �� �
(�; �� ʝ �Q S QS S� � �
(�; � Q S QS QS� � � � ʝ �
9�;� S QS QS� � �QS�� � � ʝ �Q�
9�;� Q� S���� S� 
9�;� Q� S�T 
��
��������(VSHUDQoD�0DWHPiWLFD�H�9DULkQFLD�SDUD�D�3UREDELOLGDGH�GH�6XFHVVR��S��
GH�XPD�'LVWULEXLomR�%LQRPLDO
S(�S� �H�9�S� S�T
Q
 
������'LVWULEXLomR�GH�3RLVVRQ
4XDQGR� QXPD� GLVWULEXLomR� ELQRPLDO� R� WDPDQKR� �Q�� GDV� REVHUYDo}HV� IRU� PXLWR
JUDQGH�H�D�SUREDELOLGDGH��S��GH�VXFHVVR�IRU�PXLWR�SHTXHQD��D�SUREDELOLGDGH�[�GH�RFRUUrQFLD�GH�
XP�GHWHUPLQDGR�Q~PHUR�GH�REVHUYDo}HV�VHJXH�XPD�'LVWULEXLomR�GH�3RLVVRQ�
$�DSOLFDomR�GD�GLVWULEXLomR�VHJXH�DOJXPDV�UHVWULo}HV�
��6RPHQWH�D�FKDQFH�DIHWD�R�DSDUHFLPHQWR�GR�HYHQWR��FRQWDQGR�VH�DSHQDV�FRP�D�VXD�
RFRUUrQFLD��RX�VHMD��D�SUREDELOLGDGH�GH�VXFHVVR��S��
��8PD�YH]�QmR�FRQKHFLGR�R�Q~PHUR� WRWDO�GH�HYHQWRV�� D�GLVWULEXLomR�QmR�SRGH� VHU�
DSOLFDGD�
6H�Q�ȝ ʩ�HP�FRQVHT�rQFLD�Q�!!�[�DVVLP�
Q�
�Q [��
Q��Q ����Q ��� ��� ��Q � [��� Q[
ʝ
 ʝ ʝ ˓
ORJR�
3�[�
Q
[�
S T
[
[ Q [ ʝ �
6H�S�ȝ ���H�Q�!!�[�ORJR�� � � QQ[Q S�TT ʝ ˓ʝ
DVVLP�
3�[�
�Q� S� �� S�
[�
[ Q
 ʝ
аб
Я
ЭЮ
Ь �ʝʝ�ʝ ����S�
���
��Q�Q
S�Q�
[�
�Q�S�
3�[� �
[
а
б
Я
Э
Ю
Ь ��ʝː ���
��
�S�Q�
S�Q�
[�
�Q�S�
3�[�
�[
��
3�[�
�Q� S� H
[�
[ �Q�S
 
6XEVWLWXLQGR�R�YDORU�HVSHUDGR�Q�S�SRU� Ⴌ� H� FRQVLGHUDQGR�R�FRPR�VHQGR�R�Q~PHUR�
PpGLR�GH�RFRUUrQFLD�H[SUHVVR�HP�XQLGDGHV�GH�WHPSR��SRGH�VH�GL]HU�TXH�Ⴌ�p�D�WD[D�PpGLD�GH�
IDOKDV��IDOKD���XQLG��WHPSR��H�W�R�WHPSR��ORJR�R�Q~PHUR�PpGLR�GH�IDOKDV�VHUi�ႬW��DVVLP�
3�[�
��H
[�
�
 Ⴌ
Ⴌ
W
[
IRUQHFH�D�SUREDELOLGDGH�GH�[�IDOKDV�QR�SHUtRGR�GH�WHPSR�W�
$� SUREDELOLGDGH� GH� ]HUR� IDOKDV� QR� WHPSR� W� p� D� FRQILDELOLGDGH� GR� FRPSRQHQWH� HP�
IXQomR�GR�WHPSR�
3��� 5�W� H W ʝႬ
��������(VSHUDQoD�0DWHPiWLFD�GD�'LVWULEXLomR�GH�3RLVVRQ
(�;� [ �3�[ �L L
L �
 
 
ʩ
ʜ
(�;� [�
H
[�
� [
[ �
 
 
ʩ
ʜ
ႬႬ
(�;�
H
�[ ����
� [
[ �
 
 
ʩ
ʜ
ႬႬ
��VXEVWLWXLQGR�V� �[����H�[� �V�����WHPRV�
(�;�
H
V�
� V��
[ �
 
 
ʩ
ʜ
ႬႬ
(�;�
H
V�
� V
[ �
 
 
ʩ
ʜႬ Ⴌ
Ⴌ
�
	
� ��
(�[�� �Ⴌ
��������9DULkQFLD�GD�'LVWULEXLomR�GH�3RLVVRQ
9�;� (�; � (�;��
� ʝ
RQGH
(�; � [ �3�[ �� L
�
L
L �
 
 
ʩ
ʜ
(�; � [� [�
H
[�[ ����
�
� [
[ �
 
 
ʩ
ʜ
ႬႬ
��VXEVWLWXLQGR�V� �[�����H�[� �V�����WHPRV�
��
(�; � �V� ��
H
V�
�
� V��
[ �
 
 
ʩ
ʜ
ႬႬ
(�; � �V���
H
V�
�
� V
[ �
 
 
ʩ
ʜႬ Ⴌ
Ⴌ
а
а
а
а
б
Я
Э
Э
Э
Э
Ю
Ь
Ⴌ�ႬႬ ʜʜ
ʩ
 
Ⴌʩ
 
Ⴌ
���
	���
	
�
�[
V�
(�;�
�[
V�
�
V�
H
V�
H
V�(�;
(�;�� �Ⴌ Ⴌ�
9�;� � ʝႬ Ⴌ Ⴌ� �� �
9�;� Ⴌ
����([HUFtFLRV
��� $GPLWLQGR�VH� R� QDVFLPHQWR� GH� PHQLQRV� H� PHQLQDV� VHMDP� LJXDLV�� FDOFXODU� D
SUREDELOLGDGH�GH�XP�FDVDO�FRP���ILOKRV�WHU�
D����ILOKRV�H���ILOKDV E����ILOKRV�H���ILOKDV
���(P�����IDPtOLDV�FRP���FULDQoDV�FDGD�XPD��TXDQWDV�VH�HVSHUDULD�TXH�WLYHVVHP�
D��QHQKXPD�PHQLQD� E����PHQLQRV F����PHQLQRV
���8P�WLPH�;� WHP�����GH�SUREDELOLGDGH�GH�YLWyULD� VHPSUH�TXH� MRJD��6H�;� MRJDU���
SDUWLGDV��FDOFXOH�D�SUREDELOLGDGH�GH�
D��;�YHQFHU�H[DWDPHQWH���SDUWLGDV�
E��;�YHQFHU�DR�PHQRV�XPD�SDUWLGD�
F��;�YHQFHU�PDLV�GD�PHWDGH�GDV�SDUWLGDV�
G��;�SHUGHU�WRGDV�DV�SDUWLGDV�
���$�SUREDELOLGDGH�GH�XP�DWLUDGRU�DFHUWDU�XP�DOYR�p������6H�HOH�DWLUDU���YH]HV��TXDO�D�
SUREDELOLGDGH�GH�
D��DFHUWDU�H[DWDPHQWH���WLURV� E��QmR�DFHUWDU�QHQKXP�WLUR�
���1XP�WHVWH�GH�FHUWR�HUUDGR��FRP�����SHUJXQWDV��TXDO�D�SUREDELOLGDGH�GH�XP�DOXQR��
UHVSRQGHQGR�DV�TXHVW}HV�DR�DFDVR��DFHUWDU�����GDV�SHUJXQWDV�"
��
���6H����GDV�OkPSDGDV�GH�FHUWD�PDUFD�VmR�GHIHLWXRVDV��DFKDU�D�SUREDELOLGDGH�GH�TXH��
QXPD�DPRVWUD�GH�����OkPSDGDV��HVFROKLGDV�DR�DFDVR��WHQKDPRV�
D��QHQKXPD�GHIHLWXRVD��XVH�ELQRPLDO�H�SRLVVRQ�
E����GHIHLWXRVDV�
F��PDLV�GR�TXH�XPD�ERD�
���8PD�IDEULFD�GH�SQHXV�YHULILFRX�TXH�DR�WHVWDU�VHXV�SQHXV�QDV�SLVWDV��KDYLD�HP�PpGLD�
XP�HVWRXUR�GH�SQHX�D�FDGD�������NP�
D�� TXDO� D� SUREDELOLGDGH� TXH� QXP� WHVWH� GH� ������ NP� KDMD� QR� Pi[LPR� XP� SQHX�
HVWRXUDGR�"
E��4XDO�D�SUREDELOLGDGH�GH�XP�FDUUR�DQGDU�������NP�VHP�HVWRXUDU�QHQKXP�SQHX�"
��� &HUWR� SRVWR� GH� ERPEHLURV� UHFHEH� HP� PpGLD� �� FKDPDGDV� SRU� GLD�� &DOFXODU�D�
SUREDELOLGDGH�GH�
D��UHFHEHU���FKDPDGDV�QXP�GLD�
E��UHFHEHU���RX�PDLV�FKDPDGDV�QXP�GLD�
F�����FKDPDGDV�QXPD�VHPDQD�
���$�PpGLD�GH�FKDPDGDV�WHOHI{QLFDV�HP�XPD�KRUD�p����4XDO�D�SUREDELOLGDGH�
D��UHFHEHU�H[DWDPHQWH���FKDPDGDV�QXPD�KRUD�
E��UHFHEHU���RX�PDLV�FKDPDGDV�HP����PLQXWRV�
F�����FKDPDV�QXP�GLD�
����1D�SLQWXUD�GH�SDUHGHV�DSDUHFHP�GHIHLWRV�HP�PpGLD�QD�SURSRUomR�GH���GHIHLWR�SRU�
PHWUR�TXDGUDGR��4XDO�D�SUREDELOLGDGH�GH�DSDUHFHUHP���GHIHLWRV�QXPD�SDUHGH���[���
P�"
����6XSRQKD�TXH�KDMD�HP�PpGLD���VXLFtGLRV�SRU�DQR�QXPD�SRSXODomR�GH��������KDE��
(P�XPD�FLGDGH�GH���������KDELWDQWHV��HQFRQWUH�D�SUREDELOLGDGH�GH�TXH�XP�GDGR�
DQR�WHQKD�KDYLGR��D��QHQKXP�VXLFtGLR��E����VXLFtGLR��F����RX�PDLV�VXLFtGLRV�
����6XSRQKD�����HUURV�GH�LPSUHVVmR�GLVWULEXtGRV�DOHDWRULDPHQWH�HP�XP�OLYUR�GH�����
SiJLQDV��(QFRQWUH�D�SUREDELOLGDGH�GH�TXH�XPD�GDGD�SiJLQD�FRQWHQKD�
D��QHQKXP�HUUR�
E������HUURV�HP�����SiJLQDV�
��
����'LVWULEXLo}HV�&RQWtQXDV�GH�3UREDELOLGDGH
������'LVWULEXLomR�8QLIRUPH
e� XPD� GLVWULEXLomR� GH� SUREDELOLGDGH� XVDGD� SDUD� YDULiYHLV� DOHDWyULDV� FRQWtQXDV�
GHILQLGD�QXP�LQWHUYDOR� D� E ��H�VXD�IXQomR�GHQVLGDGH�GH�SUREDELOLGDGH�p�GDGD�SRU�
ед
е
г
в ˯˯
ʝ 
E!RX�[D��[VH�
E[DVH
DE
�
I�[� �
),*85$���� ��5HSUHVHQWDomR�GH�XPD�'LVWULEXLomR�8QLIRUPH
��������(VSHUDQoD�0DWHPiWLFD�GD�'LVWULEXLomR�8QLIRUPH
ʶ
�ʩ
ʩʝ
 G[I�[�[�(�;�
ʶ 
E
D
G[
D�E
�
[�(�;�
E
D
�
�
[
D�E
�
(�;� а
б
Я 
(�;�
E D
��E D�
� �
 ʝ
ʝ
(�;�
�E �D� �E � D�
��E D�
 
ʝ
(�;�
�E �D�
�
 
��
��������9DULkQFLD�GD�'LVWULEXLomR�8QLIRUPH
9�;� (�; � (�;��
� ʝ
ʶ
�ʩ
ʩʝ
 G[I�[�[�(�; ��
ʶ 
E
D
�� G[
D�E
�
[�(�;
ʶ 
E
D
�� G[[
D�E
�
�(�;
E
D
�
�
�
[
D�E
�
�(�; а
б
Я
 
(�; �
E D
��E D�
�
� �
 ʝ
ʝ
(�; �
�E � D��E DE D �
��E D�
�
� �
 � �
ʝ
(�; �
E DE D
�
�
� �
 � �
���
�
DE
�
DDEE
9�;� Ъ
Ы
ЩЧ
Ш
Ц �ʝ�� 
9�;�
E DE D
�
E DE D
�
� � � �
 � � ʝ ʝ �
9�;�
�E �DE �D �E �DE �D
��
� � � �
 � � ʝ ʝ ʝ
9�;�
E DE D
��
� �
 ʝ ��
9�;�
�E D�
��
�
 ʝ
������'LVWULEXLomR�1RUPDO�RX�*DXVVLDQD
e�XP�PRGHOR�GH�GLVWULEXLomR�FRQWtQXD�GH�SUREDELOLGDGH��XVDGR� WDQWR�SDUD�YDULiYHLV�
DOHDWyULDV�GLVFUHWDV�FRPR�FRQWtQXDV�
8PD� YDULiYHO� DOHDWyULD� ;�� TXH� WRPH� WRGRV� RV� YDORUHV� UHDLV �ʩ� �� [� � �� �ʩ� WHP
GLVWULEXLomR�QRUPDO�TXDQGR�VXD�IXQomR�GHQVLGDGH�GH�SUREDELOLGDGH��I�G�S���IRU�GD�IRUPD�
ʩ�ʝʩ
ႴႱ
 
Ъ
Ы
Щ
Ч
Ш
Ц
Ⴔ
�ʝʝ
��[�H
�
�
I�[�
�
[
�
�
��
2V�SDUkPHWURV���H�Ⴔ�VHJXHP�DV�VHJXLQWHV�FRQGLo}HV�
ʝʩ ʩ� � � ��H�� ! �� Ⴔ �
��������3URSULHGDGHV�GD�'LVWULEXLomR�1RUPDO
D��I�p�XPD�I�G�S��OHJtWLPD�SDUD�I�[� �˰��ORJR
�G�[�I�[� ʶ
�ʩ
ʩʝ
ID]HQGR�W
[ ʝ�
Ⴔ
�WHPRV�
, GWH
�
�
G�[�I�[� �
W
ʝʩ�
ʩʝ
ʩ�
ʩʝ ʶʶ ႴႱ �
3DUD�FDOFXODU�HVWD�LQWHJUDO�XVDUHPRV�XP�DUWLItFLR��RX�VHMD��QR�OXJDU�GH�,�XVDUHPRV�,ñ�
ʶʶ
ʩ�
ʩʝ
ʝʩ�
ʩʝ
ʝ
Ⴑ
 GVH�GW�H
�
�
, �
V
�
W
�
GVGWH
�
�
,
�
�
�
�V�W
�
�
�
��
ʶʶ
ʩ
ʩ
�
ʝʩ
ʩႱ
 
LQWURGX]LQGR�FRRUGHQDGDV�SRODUHV�SDUD�UHDOL]DU�R�FiOFXOR�GHVVD�LQWHJUDO�GXSOD��WHPRV�

Continue navegando

Outros materiais