$16:(56727(67<2856(/)48(67,216 &KDSWHU KDV XQLWV 7KHTXDQWLW\ IURP ZKLFK WKH UHVXOW IROORZV 6ROYLQJ IRU WKH HQHUJ\ ZH JHW 7KHXQFHUWDLQW\VKRXOGEHJLYHQWRVI7KHSHUFHQWDJHXQFHUWDLQW\LQWKHUHVLVWDQFHLV q͘ࡁq͘ 6LQFH9 DWKHIUDFWLRQDOXQFHUWDLQW\LV VRWKHSHUFHQWDJHXQFHUWDLQW\LV 7KHSHUFHQWDJHXQFHUWDLQW\LV (TXDWLRQ DQGVR̈́5 q &RQVWDQWV 9DULDEOHVWREHSORWWHGWRJLYHVWUDLJKWOLQH *UDGLHQW 9HUWLFDOLQWHUFHSW 3 N7 N 3YHUVXV7 N ]HUR Y XDW Y DV XD D YYHUVXVW YYHUVXVV D D X ]HUR NTT )YHUVXV N ]HUR DYHUVXV[ ࠺ ]HUR NT 9YHUVXV N ]HUR *0 7YHUVXV5 ,D ,Q,YHUVXV7 KPT ͪYHUVXV D ࠺[ , ,H࠺D7 ]HUR ࠺D ]HUR ]HUR RU ͪYHUVXV ) DYEY DE YHUVXVE P$ I ,Q, E D (YHUVXV[ YHUVXV ࠺ 3ORW,QGYHUVXV,QKWRJHWDVWUDLJKWOLQHZLWKVORSHDQGYHUWLFDOLQWHUFHSW,QF$OWHUQDWLYHO\GYHUVXVKRUGYHUVXVKJLYHVWUDLJKW OLQHVWKURXJKWKHRULJLQ D q J E q P/ D 6LQFHULVSURSRUWLRQDOWR9WKHJUDSKZLOOEHDVWUDLJKWOLQHWKURXJKWKHRULJLQ E 7KHVORSHLV F )RUWKHYDOXHU ZHWKXVKDYHU ࡁFPWRVḮU :HKDYHWKDW FPWRVI7KHOHDVWXQFHUWDLQGLJLWLQWKHYDOXHRIULVLQWKHXQLWVGLJLWDQGVRWKHXQFHUWDLQW\PXVWH[SUHVVWKLVIDFW+HQFHWKH XQFHUWDLQW\PXVWEHURXQGHGWRWKHXQLWVGLJLWVR̈́U ࡁFP+HQFHU qFP,QWKHVDPHZD\ZHFDQILOOWKHUHVWRIWKH WDEOH 1RWHWKDWWKHDEVROXWHXQFHUWDLQWLHVLQDOOWKHYDOXHVRIUDUHWKHVDPH7KLVLVQRWJHQHUDOO\WKHFDVH 5DGLXVUFPqFP 3RWHQWLDOGLIIHUHQFH99 UFP q q q q q G DQGH7KHHUURUEDUVEHVWILWOLQHDQGPLQLPXPDQGPD[LPXPVORSHOLQHVDUHVKRZQKHUH I 7KHVORSHRIWKHEHVWILWOLQHLV 7KHVORSHRIWKHPD[LPXPVORSHOLQHLV 7KHVORSHRIWKHPLQLPXPVORSHOLQHLV 7KHXQFHUWDLQW\LQWKHVORSHLVWKHUHIRUH WRVI:HWKHUHIRUHTXRWHWKHVORSHDV q ࠺P9࠺ J 7KHVORSHLVHTXDOWR DQGVR /HW8EHWKHXQFHUWDLQW\LQWKHPHDVXUHGYDOXHRI 7KHXQFHUWDLQW\LVLQWKHILUVWGHFLPDOSODFHDQGVRWKH 7KHQ PHDVXUHGYDOXHRI VKRXOGEHURXQGHGWRWKHILUVWGHFLPDOSODFHKHQFH 7KHVSHHGRIWKHERDWZLWKUHVSHFWWRWKHVKRUHLV 7KHPDVVRIDQDSSOHLVDERXWJVRLWVZHLJKWLVDERXWࡁ1 7KH QXPEHU RI VHFRQGV DQGWKHWLPHWDNHQWRJHWDFURVVLV LQ D \HDU LV RI RUGHU 7KH GLDPHWHU RI D QXFOHXV LV RI RUGHU ࠺ P 7KHQ WKH WLPH WDNHQ E\ OLJKW WR FURVV WKH GLDPHWHU RI D QXFOHXV LV RI RUGHU <RXVKRXOGNQRZWKDWWKHKHDUWEHDWVDWDUDWHRIDERXWSHUPLQXWH7KHQWKHLQWHUYDOEHWZHHQEHDWVLV 7KHUDGLXVRIWKH(DUWKLVNPDQGVRWKHYROXPHRIWKH(DUWKLVDERXW 7KH YROXPH RI D JUDLQ RI VDQG LV DERXW PP DQG VR WKH QXPEHU RI JUDLQV RI VDQG WKDW FDQ ILW LQWR D VSDFH WKH VL]H RI WKH (DUWK LV $JODVVFRQWDLQVDERXWJRIZDWHU7KHPRODUPDVVRIZDWHULVJSHUPROHDQGVRJFRUUHVSRQGVWR PROHV(DFK PROHFRQWDLQVPROHFXOHVVRWKHJODVVFRQWDLQVࡁPROHFXOHVRIZDWHU :HNQRZWKDW DQGVRWKHSHUFHQWDJHLQFUHDVHLQWKHLQWHQVLW\UHFHLYHGZRXOGEHDERXW &KDSWHU 7KHGLVSODFHPHQWLVWKHYHFWRUVKRZQLQWKHILJXUH ,WKDVPDJQLWXGHPDQGVRWKHDYHUDJHYHORFLW\LV 7KHGLVWDQFHWUDYHOOHGLV 8VH D LQWKHGLUHFWLRQRIWKHDUURZ DQGVRWKHDYHUDJHVSHHGLV WRJHW 'UDZLQJDWDQJHQWDQGILQGLQJLWVVORSHJLYHVDSSUR[LPDWHO\PV࠺ E F 7KHDUHDXQGHUWKHFXUYHIURPVWRVLQ)LJXUHFDQEHREWDLQHGE\FRXQWLQJVTXDUHVDQGLVDSSUR[LPDWHO\P7KLVLVWKH GLVSODFHPHQW 7KHDUHDXQGHUWKHFXUYHEHWZHHQVDQGVFDQEHREWDLQHGE\FRXQWLQJVTXDUHVDQGLVPV࠺6LQFHWKHLQLWLDOVSHHGLV]HURWKHILQDO VSHHGLVWKHQPV࠺ D 7KHERG\ZLOOIDOODYHUWLFDOGLVWDQFHRIP6RIURP JLYLQJW V E 7KHKRUL]RQWDOGLVWDQFHWUDYHOOHGLQWKLVWLPHLVWKHQ[ YW P F 7KHKRUL]RQWDOFRPSRQHQWRIYHORFLW\VWD\VFRQVWDQWDWY[ PV࠺7KHYHUWLFDOFRPSRQHQWDWLPSDFWZLWKWKHIORRULVY\ X\࠺JW ࠺ ࠺PV࠺7KHDQJOHWRWKHKRUL]RQWDOLVWKHQ KRUL]RQWDO RUpEHORZWKH 7KHDQVZHUPXVWEHWKDWHLWKHUSRLQWRIYLHZJLYHVWKHVDPHWLPH([SOLFLWO\OHWKEHWKHKHLJKWIURPWKHIORRUDQGOHWWEHWKHWLPHWRKLWWKH IORRU/HWXEHWKHGRZQZDUGVSHHGRIWKHHOHYDWRU7KHQIRUDQREVHUYHURXWVLGHWKHEDOOZLOOFRYHUDGLVWDQFHKXW WKHIORRUZLOOPRYH GRZQDGLVWDQFHXW DQGVR WKHEDOOKDVDQLQLWLDOVSHHGHTXDOWRWKDWRIWKHHOHYDWRU DQGVR WKHUHVXOWZH ZRXOGJHWIRUDQHOHYDWRUDWUHVW /RRNDWWKHWZRPDVVHVVHSDUDWHO\DVLQWKHGLDJUDP 7KHQHWIRUFHRQPLVPJ࠺7DQGVRPJ࠺7 PD7KHQHWIRUFHRQ0LV7DQGVR7 0D7KXV +HQFHE\DGGLQJWKHVHHTXDWLRQVPJ 0P DDQGVR DQG $OWHUQDWLYHO\ \RX FRXOG FRQVLGHU WKH WZR PDVVHV DV D VLQJOH ERG\ ,Q WKLV FDVH WKH QHW IRUFH LV PJ DQG VR WKH DFFHOHUDWLRQ LV 7KHQWUHDWWKHERGLHVDVVHSDUDWHDJDLQWRILQGWKHWHQVLRQ7 7KHWHQVLRQLQ'SXOOVDELJJHUPDVVWKDQWKHWHQVLRQVLQWKHRWKHUVWULQJVDQGVLQFHDOOVWULQJVXQGHUJRWKHVDPHPRWLRQ'KDVWKHJUHDWHVW WHQVLRQ D 7UHDWLQJWKHWZRERGLHVDVRQHZHVHHWKDWWKHWRWDOPDVVLVNJDQGWKHQHWIRUFH1VRWKDWWKHDFFHOHUDWLRQLVPV࠺ E 7KHQHWIRUFHRQWKHNJERG\LVWKHWHQVLRQLQWKHVWULQJDQGVR7 PD 1 F ,IWKHERGLHVDUHUHYHUVHGWKHDFFHOHUDWLRQZLOOVWD\WKHVDPHEXWWKHWHQVLRQZLOOQRZEH7 PD 1 G 7KHIRUFHVDUHQRZDVVKRZQEHORZDQGZHKDYHHTXLOLEULXP 7KHPD[LPXPIULFWLRQDOIRUFHRQWKHODUJHUEORFNLV 1+HQFHWKHWHQVLRQLV࠺ 17KHIULFWLRQDOIRUFHRQWKH NJEORFNLV1 7KHVFDOHH[HUWVDIRUFH5RQWKHJLUO+HQFHE\1HZWRQߞVWKLUGODZWKHJLUOH[HUWVDIRUFH5RQWKHVFDOHZKLFKLVZKDWWKHVFDOHUHDGV7KH DQVZHULVF 7KHIRUFHVRQWKHEORFNDUHDVVKRZQEHORZ :HPXVWWDNHFRPSRQHQWVDORQJWKHKRUL]RQWDODQGYHUWLFDOD[HV EHFDXVHPRWLRQWDNHVSODFHKRUL]RQWDOO\ 7KHYHUWLFDOFRPSRQHQWRI1LV1 FRVͧDQGWKLVPXVWHTXDOWKHZHLJKWRIWKHEORFNPJ7KHKRUL]RQWDOFRPSRQHQWLV1VLQͧDQGWKLVPXVWHTXDOPD6R 7KLVJLYHV 7UHDWLQJWKHWZRERGLHVDVRQHZHVHHWKDWWKHQHWIRUFHLVMXVW)DQGVRWKHDFFHOHUDWLRQLV DVUHTXLUHG 7KHERG\LVDFFHOHUDWLQJXSZDUGVVR5LVELJJHUWKDQPJ ZKHUHPLVWKHFRPELQHGPDVV+HQFH 7KHQHWIRUFHLVWKXV5࠺PJDQGVR5࠺PJ PDRU5࠺PDPJ D WRWKHULJKW E F ,IWKHV\VWHPLVWDNHQWREHMXVWWKHEDOOFRQVHUYDWLRQRIPRPHQWXPGRHVQRWDSSO\VLQFHWKHUHLVDIRUFHRQWKHEORFNIURPWKHZDOO,IWKH V\VWHPLVWDNHQWREHWKHEDOODQGWKHZDOOWKHQLWGRHVDSSO\7KHZDOOPXVWKDYHDFTXLUHGDPRPHQWXPRI1VWRWKHOHIW G 7KHQHWIRUFHRQWKHEDOOLVQRZ) 5࠺PJDQGVR JLYLQJ5 ࡁ1 D ,QWLPH࠷WDPDVVͫ࠷WRIJDVZLOOEHHMHFWHGIURPWKHURFNHW7KHPRPHQWXPRIWKLVPDVVLV ͫ࠷W X6LQFHHYHU\WKLQJZDVDVVXPHGWREH LQLWLDOO\DWUHVW ͫ࠷W XLVDOVRWKHFKDQJHLQPRPHQWXP࠷SDQGVRWKHIRUFHRQWKHJDVHVLV E 7KHIRUFHH[HUWHGRQWKHJDVHVLV 1 F %\1HZWRQߞVWKLUGODZWKLVIRUFHLVDOVRWKHIRUFHDFWLQJRQWKHURFNHWLQWKHRSSRVLWHGLUHFWLRQDQGVRLWDFFHOHUDWHVWKHURFNHW G 7KHLQLWLDOPDVVRIWKHURFNHWLVNJVRWKHLQLWLDODFFHOHUDWLRQLV D $ERXWPV E 7KHDUHDLV E\FRXQWLQJVTXDUHV DERXW࠺1V F 7KHDYHUDJHIRUFHLVJLYHQE\)࠷W LPSXOVH ࠺1VRU) 1 G 7KHLPSXOVHLVDOVR࠷S PY࠺P ࠺Y PYDQGVRP ࠺NJ 7KHFKDQJHLQWKHNLQHWLFHQHUJ\RIWKHERG\LV࠷(. ࠺ ࠺-7KHRQO\IRUFHGRLQJZRUNRQWKHERG\LVWKHIULFWLRQDOIRUFHDQG:QHW IGFRVp ࠺G+HQFH࠺G ࠺⇒G P 7KHZRUNLV: )GFRVͧZLWKͧ pDQGVRHTXDOV: ͯࡁ- 6LQFHHODVWLFSRWHQWLDOHQHUJ\ H[WHQGLQJWKHVSULQJIURPLWVQDWXUDOOHQJWKWRDQH[WHQVLRQHZRXOGUHTXLUHZRUNHTXDOWR: 6RWRH[WHQGLWIURPHWRHUHTXLUHV:࠺: :KHQFHWKHDQVZHULVF D 7KHWRWDOPRPHQWXPEHIRUHWKHFROOLVLRQLV 1V$IWHUWKHFROOLVLRQLWLV Y7KXVY 1V⇒Y PV࠺ E 7KH WRWDO NLQHWLF HQHUJ\ EHIRUH WKH FROOLVLRQ LV $IWHU WKH FROOLVLRQ LW LV 7KHFROOLVLRQLVLQHODVWLFVLQFHNLQHWLFHQHUJ\KDVQRWEHHQFRQVHUYHG D 7KHIULFWLRQDOIRUFHLV1DQGWKHSRZHULWGLVVLSDWHVLV3 : E 7KHUDWHRILQFUHDVHRIWKHJUDYLWDWLRQDOSRWHQWLDOHQHUJ\LV3* PJYVLQͧ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࠺7 7KHWKHUPDOHQHUJ\JDLQHGE\WKHZDWHUDQGFDORULPHWHULV 7࠺ 7࠺ )URPFRQVHUYDWLRQRIHQHUJ\ZHKDYH ࠺7 7࠺ 7࠺ 6ROYLQJIRU7ZHILQGWKDW7 p& D ,WWDNHVVWRZDUPWKHSDUDIILQIURPp&WRp&VR : E 7KHFRQVWDQWWHPSHUDWXUHDWZKLFKSDUDIILQPHOWVLVp& F ,WWDNHVWKHSDUDIILQ࠺ VWRPHOW7KHHQHUJ\SURYLGHGLV4 3W -DQGVRWKHVSHFLILFODWHQWKHDWRI IXVLRQLV G ,W WDNHV DQ DGGLWLRQDO ࠺ H V WR ZDUP OLTXLG SDUDIILQ DW p& WR D WHPSHUDWXUH RI p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∝ 17 7KHUHIRUH WKH LQWHUQDO HQHUJ\ LV 7KH SLVWRQ PRYLQJ UDSLGO\ LQZDUGV FROOLGHV ZLWK PROHFXOHV VR WKH PROHFXOHV UHERXQG ZLWK VSHHGV JUHDWHU WKDQ EHIRUH WKH FROOLVLRQ 7KH DYHUDJHNLQHWLFHQHUJ\RIWKHPROHFXOHVߙDQGKHQFHWKHWHPSHUDWXUHߙLQFUHDVHV 8VH 6LQFHNLVDFRQVWDQWDQG7LVKHOGFRQVWDQW 6R DQG VRWKHDQVZHULVE &KDSWHU D <HVVLQFHDFFHOHUDWLRQLVRSSRVLWHWRDQGSURSRUWLRQDOWRGLVSODFHPHQW E 1RVLQFHDFFHOHUDWLRQLVQRWRSSRVLWHWRGLVSODFHPHQW F 1RVLQFHDFFHOHUDWLRQLVQRWSURSRUWLRQDOWRGLVSODFHPHQW D 7KHJUDSKLVDVWUDLJKWOLQHWKURXJKWKHRULJLQZLWKQHJDWLYHVORSHDQGVRWKHPRWLRQVDWLVILHVWKHGHILQLQJHTXDWLRQIRU6+0 E FP D V E $WDQ\PD[LPXPRUPLQLPXPIRUH[DPSOHV F $WDQ\WLPHZKHQWKHVSHHGLV]HURIRUH[DPSOHV +HQFH G 6HHWKHJUDSKEHORZ D PV࠺ E 6HHWKHEOXHFXUYHEHORZ F P D E 7KHIUHTXHQF\RIOLJKWPXVWVWD\WKHVDPHDQGVR F 7KHDQJOHVLQWKHUHIUDFWLRQIRUPXODDUHPHDVXUHGUHODWLYHWRWKHQRUPDOWRWKHVXUIDFH)URPQVLQͧ QVLQͧZHKDYHVLQp VLQͧ⇒VLQͧ ⇒ͧ 7RWDOLQWHUQDOUHIOHFWLRQFDQRFFXUZKHQOLJKWSDVVHVIURPJODVVLQWRZDWHUVLQͧ VLQp⇒VLQͧF ⇒ͧF p ZHZLOOKDYHFRQVWUXFWLYHLQWHUIHUHQFHDW3 $WDQ\SRLQW 7KHSDWKGLIIHUHQFHDW3LV63࠺63 PDQG WKDWLVHTXLGLVWDQWIURPWKHVRXUFHVWKHSDWKGLIIHUHQFHLV]HURDQGVRZHKDYHFRQVWUXFWLYHLQWHUIHUHQFH $W464࠺64 PDQG ZHZLOOKDYHGHVWUXFWLYHLQWHUIHUHQFHDW4 7KHHQHUJ\JHWVUHGLVWULEXWHGLQWKHLQWHUIHUHQFHSDWWHUQ7KHHQHUJ\WKDWZRXOGDSSHDUDWWKHPLQLPDDSSHDUVDWWKHPD[LPD 7KHLQWHQVLW\LVUHGXFHGE\DIDFWRURIDIWHUJRLQJWKURXJKWKHILUVWSRODULVHU7KHUHLVDIXUWKHUUHGXFWLRQE\FRVpDIWHUWUDQVPLVVLRQ WKURXJK WKH VHFRQG SRODULVHU DQG WKHQ DQRWKHU FRV p DIWHU WUDQVPLVVLRQ WKURXJK WKH WKLUG 2YHUDOO WKH LQWHQVLW\ LV UHGXFHG E\ 7KHZDYHOHQJWKRIWKHILUVWKDUPRQLFLVͪ /DQGWKDWRIWKHVHFRQGLVͪ /,IFLVWKHVSHHGRIDZDYHRQWKHVWULQJWKHQ +HQFH 7KHZDYHOHQJWKLQWXEHLVͪ; /DQGWKDWLQWXEH<LVͪ< /+HQFH ,QWKHILUVWFDVHZHKDYHWKHILUVWKDUPRQLFVRͪ /,QWKHVHFRQGFDVH ͪ P7KXVY ͪI VRͪ /6XEWUDFWLQJͪ /࠺/ [ ⇒ ࡁPV࠺ &KDSWHU $FFRUGLQJWR&RXORPEߞVODZLIWKHFKDUJHGRXEOHVVRGRHVWKHIRUFH%XWWKHPDJQLWXGHRIWKHIRUFHLVWKHVDPHRQERWKFKDUJHVKHQFHELV FRUUHFW ,I4LVSRVLWLYHDQHJDWLYHFKDUJHLVLQGXFHGRQWKHQHDUVLGHRIWKHVSKHUHOHDYLQJDSRVLWLYHFKDUJHRQWKHIDUVLGHIURP&RXORPEߞ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࠺ ࠺9JLYLQJ9 97KHSRWHQWLDO GLIIHUHQFHDFURVVWKHLQWHUQDOUHVLVWRULV 9DQGVRWKH(0)LV 9 D :HKDYHWKHWRSWZRUHVLVWRUVLQVHULHVIRUDWRWDORIDQGWKLVLVLQSDUDOOHOZLWKWKHERWWRP͘UHVLVWRUIRUDJUDQGWRWDOUHVLVWDQFH EHWZHHQSRLQWV$DQG%RI E 7KHERWWRPUHVLVWRUPXVWKDYHEXUQWRXWߙWKDWLVWKHFLUFXLWWKHUHLVEURNHQ D 7KH SRWHQWLDO GLIIHUHQFH DFURVV WKH ͘ UHVLVWRU LV 9 DQG WKLV LV DOVR WKH SRWHQWLDO GLIIHUHQFH DFURVV 5 +HQFH E 7KHFXUUHQWWKURXJK5LV$DQGWKHSRWHQWLDOGLIIHUHQFHDFURVVLWLV࠺ 9+HQFH D :H KDYH UHVLVWRUV LQ VHULHV IRU D WRWDO RI ͘ DQG WKLV LV LQ SDUDOOHO ZLWK WKH ERWWRP UHVLVWRU IRU D WRWDO RI ,QWXUQWKLVLVLQVHULHVZLWKWKHLQWHUQDOUHVLVWRUIRUDJUDQGWRWDORI ͘7KHFXUUHQWLV WKHUHIRUHLV E ,IWKHERWWRPUHVLVWRUEXUQVRXWWKHWRWDOEHFRPHV ͘ D 7KHODPSVDUHLQVHULHVVRWKH\WDNHWKHVDPHFXUUHQW6LQFH3 5,LWIROORZVWKDWODPS$KDVWKHJUHDWHUUHVLVWDQFH E 7KHODPSVDUHLQSDUDOOHOVRWKH\KDYHWKHVDPHSRWHQWLDOGLIIHUHQFHDFURVVWKHP+HQFHWKHFRQYHQLHQWSRZHUIRUPXODLV %KDVWKHVPDOOHUUHVLVWDQFHDQGVRWKHJUHDWHUSRZHU 7KHWRWDOUHVLVWDQFHRI55 ͘DQG5 ͘LV 7KLVLVLQVHULHVZLWKWKHLQWHUQDOUHVLVWDQFH DQGVRWKHRYHUDOOWRWDOUHVLVWDQFHRIWKHFLUFXLWLV57 ͘7KHFXUUHQWLVWKHQ YROWPHWHULV9 ࠺ 9 D )URP ZHILQG E )URP3 9,ZHJHW /DPS DQGVRWKHUHDGLQJRIWKH F 7KH SRWHQWLDO GLIIHUHQFH DFURVV ZLUH $% LV 9 DQG VR WKH SRWHQWLDO GLIIHUHQFH DFURVV %& LV DOVR 9 6LQFH WKH UHVLVWDQFH RI $% LV GRXEOHWKDWRI%&WKHFXUUHQWLQ%&LVGRXEOHWKDWLQ$%/HW[VWDQGIRUWKHFXUUHQWLQ$%7KHQ+HQFH[ [DQGVR[ $ 7KHUHVLVWDQFHRI$%LVWKHQ DQGVR5$& ͘ D :KHQWKHWHPSHUDWXUHLVLQFUHDVHGWKHUHVLVWDQFHRI7ZLOOGHFUHDVH7KHUHIRUHWKHSRWHQWLDOGLIIHUHQFHDFURVV7ZLOOGHFUHDVHDVZHOO:H FDQVHHWKLVDVIROORZVWKLQNRIWKHFLUFXLWDVDSRWHQWLDOGLYLGHU6LQFHWKHUHVLVWDQFHRI7LVOHVVWKDQ5DQGWKHFXUUHQWVLQ7DQG5DUHWKH VDPHWKHSRWHQWLDOGLIIHUHQFHGURSV E 7KH/'5ZLOOGHFUHDVHLQUHVLVWDQFHDVWKHOLJKWJHWVEULJKWHUDQGVRWKHDQVZHULVWKHVDPHDVLQD :HGHILQHFXUUHQWV[DQG\WKURXJKWKHWZRFHOOVDVVKRZQ7KHFXUUHQWLQWKH9FHOOLV\࠺[E\DSSO\LQJWKHFXUUHQWODZWRMXQFWLRQ% 7KHOHIWKDQGORRSJLYHV [࠺ \࠺[ VR[࠺\ 7KHULJKWKDQGORRSJLYHV [\VR[\ 6ROYLQJJLYHV[ $DQG\ $ D 7KHFXUUHQWWKURXJKWKH9FHOOLV$LQWKHGLUHFWLRQRIWKHDUURZ,QWKH9FHOOLWLV$LQWKHGLUHFWLRQRIWKHDUURZ,QWKH9 FHOOLWLV$LQWKHGLUHFWLRQRIWKHDUURZ E 7KHFXUUHQWLQWKH9FHOOJRHVߝEDFNZDUGVߞߙWKDWLVIURPWKHSRVLWLYHWRWKHQHJDWLYHWHUPLQDOߙZKLFKPHDQVWKDWWKHFHOOLVEHLQJ FKDUJHG F :HPD\WDNHWKHSRWHQWLDODW%WREHDQ\WKLQJZHOLNHVD\97KHSRWHQWLDODW$LV9$ ࠺ 97KHSRWHQWLDOGLIIHUHQFH LVWKHQ9ZLWK%DWWKHKLJKHUSRWHQWLDO G 3RZHULVJHQHUDWHGE\WKH9DQG9FHOOV7KLVSRZHULV 3 ࠹ͤ, :7KHSRZHUGLVVLSDWHGLQWKHUHVLVWRUVLV 3 ࠹5, :DQGLQWKH9FHOOLWLV 3 ͤ, :7KHWRWDOGLVVLSDWHGSRZHULV:DQGHQHUJ\LVFRQVHUYHG $SSO\LQJWKHULJKWKDQGUXOHWRILQGWKHPDJQHWLFILHOGVDW=IURPHDFKFXUUHQWDQGDGGLQJDVYHFWRUVJLYHVGDOHIWZDUGQHWILHOG &KDSWHU %RWKSRLQWVFRPSOHWHRQHUHYROXWLRQLQWKHVDPHWLPHDQGVRKDYHHTXDODQJXODUVSHHGV7KHOLQHDUVSHHGLVJLYHQE\Y UDQGVR<KDV GRXEOHWKHOLQHDUVSHHGVRWKHDQVZHULVE D )RUPD[LPXPVSHHGZHZLOOQHHGWKHPD[LPXPIULFWLRQDOIRUFHIPD[ ͫ61ZKHUH1 PJ7KLVSURYLGHVWKHFHQWULSHWDOIRUFHVR E ,IWKHURDGZHUHEDQNHGWKHQRUPDOIRUFHZRXOGEHDWDQDJOHWRWKHYHUWLFDODVVKRZQ :HVHHWKDWWKHUH LVQRZDQDGGLWLRQDOIRUFHWRZDUGVWKHFHQWUHRIWKHFLUFOHQDPHO\WKHKRUL]RQWDOFRPSRQHQWRIWKHQRUPDOUHDFWLRQ IRUFH17KLVSURYLGHVDGGLWLRQDOFHQWULSHWDOIRUFHZLWKJUHDWHUFHQWULSHWDOIRUFHWKHFHQWULSHWDODFFHOHUDWLRQLVJUHDWHUDQGIURP WKHVSHHGFDQEHJUHDWHUDVZHOO 7KHFDUHIXOUHDGHUZLOOKDYHQRWLFHGWKDWDWWKHVDPHWLPHWKHIULFWLRQDOIRUFHWRZDUGVWKHFHQWUHLV UHGXFHGVLQFHRQO\LWVFRPSRQHQWIFRVͧSRLQWVWRZDUGVWKHFHQWUHRIWKHFXUYH7KHUHIRUHVWULFWO\VSHDNLQJDPRUHGHWDLOHGDQDO\VLVLV QHHGHG7KHFRUUHFWDQDO\VLVGRHVLQIDFWVXSSRUWWKLVFRQFOXVLRQ 5HIHUULQJWR)LJXUHWKHQHWFHQWULIXJDOIRUFHRQWKHFDULVPJ࠺1DQGWKLVHTXDOV 7KHFDUZRXOGORVHFRQWDFWZLWKWKHURDGLI1࠱ZKLFKFRUUHVSRQGVWR 7KH EORFN LV PRYLQJ LQ D FLUFOH RI UDGLXV / 7KLV UHTXLUHV D QHW IRUFH VR LW LV QRW LQ HTXLOLEULXP $V WKH VWULQJ PRYHV SDVW WKH YHUWLFDO SRVLWLRQWKHQHWIRUFHRQWKHEORFNSRLQWVWRZDUGVWKHRWKHUHQGRIWKHVWULQJߙWKDWLVXSZDUGV$QHWXSZDUGVIRUFHPHDQVWKDWWKHWHQVLRQLQ WKH VWULQJ LV ODUJHU WKDQ WKH ZHLJKW RI WKH EORFN $SSO\LQJ 1HZWRQߞV VHFRQG ODZ ) PD ZLWK ) 7 ࠺ PJ DQG ZH KDYH 7R ILQG WKH WHQVLRQ ZH WKHUHIRUH QHHG WR NQRZ WKH VSHHG RI WKH EORFN )RU WKLV ZH FDQ DSSO\ FRQVHUYDWLRQ RI HQHUJ\ VR OHDGLQJILQDOO\WR7 PJ 1RWHWKDWWKHUHVXOWGRHVQߞWGHSHQGRQWKHOHQJWKRIWKHVWULQJ 7KH ERG\ߞD ZHLJKW LV WKH JUDYLWDWLRQDO IRUFH DFWLQJ RQ LW $W WKH SODQHWߞV VXUIDFH 1HZWRQߞV ODZ RI JUDYLWDWLRQ JLYHV $WDKHLJKW5DERYHWKHVXUIDFHWKHERG\LV5IURPWKHFHQWUHRIWKHSODQHWDQG1HZWRQߞVODZJLYHV :ULWHWKHHTXDWLRQIRUWKHJUDYLWDWLRQDOILHOGVWUHQJWKRIWKH(DUWK WKHRWKHUSODQHW ZKHUH0LVWKH(DUWKߞVPDVVDQG5LVLWVUDGLXV'RWKHVDPHIRU 'LYLGHVLGHE\VLGH 7KHQ $OWHUQDWLYHO\ZULWH )RUVPDOOYDOXHVRIU LHFORVHWRWKHODUJHUPDVV WKHILHOGPXVWEHGLUHFWHGWRWKHOHIWWKXVLWPXVWEHQHJDWLYH7KLVHOLPLQDWHV%DQG& 7KHILHOGPXVWEH]HURFORVHUWRWKHVPDOOHUPDVVDQGVRWKHDQVZHULV$ &KDSWHU 7KHORQJHVWZDYHOHQJWKPHDQVWKHVPDOOHVWHQHUJ\ VLQFH 8VLQJ࠷( KIZHILQG +HQFHLWLVWKHWUDQVLWLRQIURP1 WR1 DQGVRͪ ࠺P VLQFHWKHPRPHQWDDUHHTXDODQGRSSRVLWH GD\VFRUUHVSRQGVWRKDOIOLYHVDQGVRWKHDFWLYLW\LV 7KHWDEOHVKRZVWKHIUDFWLRQRIHDFKLVRWRSHSUHVHQWLQLWLDOO\DQGDIWHUDQGPLQXWHV RIWKHRULJLQDO 7LPHPLQ ; < 6RPLQXWHVPXVWJRE\ F 7KHUHLVDFKDQFHRIGHFD\LQJLQDQ\KDOIOLIHLQWHUYDO D 7KHHQHUJ\UHOHDVHGLVJLYHQE\4 03R࠺ 03E0+H F1RZ%(3R PSPQ࠺03R F⇒03RF PSPQ F࠺%(3R %(3E PSPQ࠺03E F⇒03EF PSPQ F࠺%(3E %(+H PSPQ࠺0+H F⇒0+HF PSPQ F࠺%(+H +HQFH4 %(3E%(+H࠺%(3R 7KLVVKRZVWKDWWKHHQHUJ\UHOHDVHGLVWKHGLIIHUHQFHEHWZHHQWKHWRWDOELQGLQJHQHUJ\RIWKHSURGXFWVPLQXVWKHELQGLQJHQHUJ\RIWKH GHFD\LQJQXFOHXV E 7KHELQGLQJHQHUJ\RISRORQLXP 3R LVࡁ0H9WKDWRIKHOLXP +H ࡁ0H9DQGWKDWRIOHDG 3E ࡁ 0H97KHHQHUJ\UHOHDVHGLVWKHQDERXW࠺ 0H9 7KHUHDUHQXFOHRQVLQ 7KHWRWDOPDVVRQWKHOHIWLVXDQGLVVPDOOHUWKDQWKHWRWDORQWKHULJKWRIXE\X5RXJKO\VSHDNLQJWKHPLVVLQJ HQHUJ\ RI 0H9 PXVW EH SURYLGHG E\ WKH DOSKD SDUWLFOHߞV NLQHWLF HQHUJ\ ,Q IDFW EHFDXVH PRPHQWXP PXVW EH FRQVHUYHGWKHDOSKDߞVNLQHWLFHQHUJ\PXVWEHVRPHZKDWODUJHUWKDQWKLV D DQGVRWKHHQHUJ\LV 0H9 7KHEHDPPXVWEHYHU\QDUURZLQRUGHUWKDWWKHVFDWWHULQJDQJOHFDQEHPHDVXUHGDFFFXUDWHO\ E 7KHIRLOPXVWEHYHU\WKLQLQRUGHUWRDYRLGDEVRUSWLRQRIWKHDOSKDSDUWLFOHVE\WKHIRLODQGDOVRLQRUGHUWRDYRLGPXOWLSOHVFDWWHULQJV 1REHFDXVHWKH.PHVRQKDVQRQ]HURVWUDQJHQHVVTXDQWXPQXPEHU D S࠱H࠺͢EDU\RQQXPEHUHOHFWULFFKDUJHOHSWRQQXPEHU E S࠺ͯ࠺ͯHOHFWULFFKDUJHEDU\RQQXPEHU F Q࠱SH࠺OHSWRQQXPEHU G H࠺H࠱͢PRPHQWXP H H࠱ͫͬͫHQHUJ\OHSWRQQXPEHU I S࠱QHͬHHQHUJ\ EXWWKLVFDQRFFXUZLWKLQDQXFOHXVZKHUHWKHUHTXLUHGHQHUJ\LVSURYLGHGE\WKHELQGLQJHQHUJ\RIWKHQXFOHXV D 6WUDQJHQHVVLVYLRODWHGVLQFH6 ࠺RQWKHOHIWKDQGVLGHRIWKHUHDFWLRQHTXDWLRQEXW6 RQWKHULJKWKDQGVLGH+HQFHWKHGHFD\PXVW EHDZHDNLQWHUDFWLRQSURFHVV E $SRVVLEOHGLDJUDPLVWKHIROORZLQJ &KDSWHU D 7KHHQHUJ\SHUVHFRQGߙWKDWLVWKHSRZHUߙH[WUDFWHGIURPEXUQLQJ0NJSHUVHFRQGLV0(7KHHIILFLHQF\LVHDQGVRWKHSRZHUSURGXFHG LVH0( 7KHXVHIXOHQHUJ\LVDQGWKHHIILFLHQF\LV 7KHSRZHUWREHSURYLGHGE\QXFOHDUILVVLRQLV ,IWKHQXPEHURIUHDFWLRQVSHUVHFRQGLV1WKHQ1 ࠺ DQGVR ,QDVLQJOHUHDFWLRQDPDVVRIXRU࠺ ࠺NJLVXVHG+HQFHWKHPDVVXVHGDWDUDWHRI࠺ ࠺NJV࠺,QRQH\HDUZHQHHG࠺ ࡁNJ :LWKRXWDPRGHUDWRUWKHQHXWURQVZRXOGEHWRRIDVWWRFDXVHDQ\UHDFWLRQVVRYHU\OLWWOHHQHUJ\ZRXOGEHSURGXFHG 7KHPDVVLQWKHEDVLQLV NJ7KHDYHUDJHSRWHQWLDOHQHUJ\ORVWDVWKHZDWHUGHVFHQGVLV - XVLQJWKHDYHUDJHGHSWKP 7KHEDVLQHPSWLHVLQPLQXWHVDQGVRWKHSRZHULV D )URPWKHIRUPXODZHKDYHVLPSO\ LVWKHUHIRUH 7KHQXPEHURIZLQGWXUELQHVQHHGHG E ,QSUDFWLFHHDFKZLQGWXUELQHZLOOJHQHUDWHOHVVWKDQN:EHFDXVHRIIULFWLRQDQGRWKHUORVVHVVXFKDVWXUEXOHQFHDQGEHFDXVHWKHZLQG WXUELQHGRHVQRWH[WUDFWDOORIWKHZLQGߞVNLQHWLFHQHUJ\7KHFDOFXODWLRQDOVRDVVXPHVWKDWWKHZLQGEORZVDWULJKWDQJOHVWRWKHEODGHV ZKLFKLVQRWDOZD\VWKHFDVHXQOHVVWKHZLQGWXUELQHFDQEHWXUQHGLQWRWKHZLQG :HZDQWWKHODUJHVWUDWLRRIWHPSHUDWXUHGLIIHUHQFHWRZLGWKDQGWKDWLVF 7KHSRZHULVSURSRUWLRQDOWRWKHWKSRZHURIWKH.HOYLQWHPSHUDWXUHVRGRXEOLQJ7PDNHVWKHSRZHU WLPHVODUJHU D 7KHSRZHUUHFHLYHGE\PRIWKH(DUWKߞVVXUIDFH DSRZHU 7KHVHFRQGWHUPDULVHVEHFDXVH LVUHIOHFWHGEDFNLQWRVSDFH7KH(DUWKUDGLDWHVSRZHUIURPWKHHQWLUHVXUIDFHDUHDRILWVVSKHULFDOVKDSHDQGVRWKHSRZHU UDGLDWHGIURPPLV E\WKH6WHIDQߙ%ROW]PDQQODZ 3RXW Ͳ7 :HDUHDVVXPLQJWKDWWKHHPLVVLYLW\RIWKH(DUWKߞVVXUIDFHLV 2I WKH RI UHIOHFWHG UDGLDWLRQ RQO\ DERXW WR LV UHIOHFWHG IURP WKH VXUIDFH LWVHOI DQG VR WKH HPLVVLYLW\ LV DFWXDOO\ DERXW ࠺ (TXDWLQJWKHWZR E F :HILQG LV 7KLVWHPSHUDWXUHLV࠺p& $WHPSHUDWXUHRI.LV.ORZHUWKDQWKH(DUWKߞVDFWXDODYHUDJHWHPSHUDWXUHRI.VRREYLRXVO\WKHPRGHOLVZURQJ2QHUHDVRQ WKLVPRGHOLVWRRVLPSOHLVSUHFLVHO\EHFDXVHZHKDYHQRWWDNHQDFFRXQWRIWKHIDFWWKDWQRWDOOWKHSRZHUUDGLDWHGE\WKH(DUWKDFWXDOO\ HVFDSHV 6RPH LV DEVRUEHG E\ JDVHV LQ WKH DWPRVSKHUH DQG UHUDGLDWHG GRZQ WR WKH (DUWKߞV VXUIDFH FDXVLQJ IXUWKHU ZDUPLQJ ,Q RWKHU ZRUGVWKLVPRGHOQHJOHFWVWKHJUHHQKRXVHHIIHFW$QRWKHUGUDZEDFNRIWKLVVLPSOHPRGHOLVWKDWLWLVHVVHQWLDOO\D]HURGLPHQVLRQDOPRGHO ߙWKH(DUWKLVWUHDWHGDVDSRLQWZLWKRXWLQWHUDFWLRQVEHWZHHQWKHVXUIDFHDQGWKHDWPRVSKHUH ODWHQWKHDWIORZVWKHUPDOHQHUJ\IORZLQ RFHDQVWKURXJKFXUUHQWVWKHUPDOHQHUJ\WUDQVIHUEHWZHHQWKHVXUIDFHDQGWKHDWPRVSKHUHGXHWRWHPSHUDWXUHGLIIHUHQFHVEHWZHHQWKHWZR DUHDOOLJQRUHG 5HDOLVWLFPRGHOVPXVWWDNHDOOWKHVHIDFWRUV DQGPDQ\RWKHUV LQWRDFFRXQWDQGVRDUHYHU\FRPSOH[ &KDSWHU D 7KHJUDSKLVDVWUDLJKWOLQHWKURXJKWKHRULJLQZLWKQHJDWLYHVORSHVRLWVDWLVILHVWKHGHILQLQJHTXDWLRQIRU6+0D ࠺[ E )URP WKH JUDSK WKH VORSH LV 7KLV HTXDOV ࠺ DQG VR ࡁ V࠺ +HQFH F G D 7KHPD[LPXPVSHHGLVY [ࡁ PV࠺ )URP ZHILQG 7KH PD[LPXP NLQHWLF HQHUJ\ LV - DQG VR E 7KHPD[LPXPVSHHGLVYPD[ [ PV࠺7KHPD[LPXPDFFHOHUDWLRQLVDPD[ [ ࡁPV࠺ F 6HHWKHUHGOLQHLQWKHJUDSK +HQFH G 7KHWZRFXUYHVLQWHUVHFWDW[ࡁqFP 8VH 7KHDQJXODUVHSDUDWLRQRIWZRSRLQWVDWWKHHQGVRIWKHGLDPHWHURI0DUVLV )URP)LJXUHͧ' UDGDQGVR 7KHDQJOHRIWKHILUVWGLIIUDFWLRQ 7KH DQJXODU VHSDUDWLRQ LV OHVV WKDQ WKLV ͧ$ ͧ' DQG VR WKH SRLQWV DUH QRW PLQLPXP DW WKH H\H LV UHVROYHG0DUVDSSHDUVDVDSRLQWVRXUFH +HQFH 7KH Q SULPDU\ 7KH QXPEHU Q RI OLQHV SHU PP JLYHV G DV ࠺ ࠺ PD[LPXPLVREVHUYHGDWͧ pDQGVRIURPGVLQͧ QͪZHILQG VLQp ͪJLYLQJͪ P 7KHVPDOOHVWGLIIHUHQFHLQZDYHOHQJWKWKDWFDQEHUHVROYHGLV ZDYHOHQJWKRIWKHWZROLQHV QP DQGVRWKHOLQHVFDQEHUHVROYHG :HKDYHDSKDVHFKDQJHDWRQO\RQHERXQGDU\7KHFRQGLWLRQRIFRQVWUXFWLYHLQWHUIHUHQFHLVWKHUHIRUH 7KHFDULVDSSURDFKLQJWKHHPLWWHUVRWKHIUHTXHQF\LWUHFHLYHVLV ZKHUHXLVWKHXQNQRZQFDUVSHHG7KHFDUQRZ DFWVDVDQHPLWWHURIDZDYHRIWKLVVDPHIUHTXHQF\ I DQGWKHRULJLQDOHPLWWHUQRZDFWVDVWKHQHZUHFHLYHU7KHIUHTXHQF\UHFHLYHGDWWKLV IURPZKLFKZHILQGX PV࠺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q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ߞV ODZ WKLV LQGXFHG (0) KDV RSSRVLWHVLJQWRWKHEDWWHU\ߞV(0)VRWKHFXUUHQWULVHVRQO\JUDGXDOO\WRDILQDOFRQVWDQWYDOXH6LQFHWKHFRQVWDQWILQDOFXUUHQWLV$WKH UHVLVWDQFHRI'PXVWEH D L LL E L 7KHUHVLVWDQFHLV LL 7KHDYHUDJHSRZHULV LLL 7KHSHDNSRZHULV F DQGVR JLYLQJ RU DQGKHQFH DQVZHUF &KDSWHU D ȸ $WWKHWKUHVKROGIUHTXHQF\(N DQGVR E 7KHNLQHWLFHQHUJ\RIWKHHPLWWHGHOHFWURQVLV ȸ +HQFH IURP ZH ILQG ȸ ȸ ȸDQG(N T9ZHILQG )URP +HQFHWKHYHUWLFDOLQWHUFHSWLV ȸ DQGVR ȸ JLYLQJȸ H9 ࠺- ࠺- 7KHVORSHRIWKHJUDSKHTXDOV DQGLVPHDVXUHGWREH࠺-V&࠺+HQFHK ࠺࠺ ࠺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ߙWKDWLV̈́Wࡁ࠺V7KHQ E 7KHDQVZHUWRDPHDQVWKDWWKHHQHUJ\GLIIHUHQFHEHWZHHQOHYHOVLVQRWSUHFLVHO\NQRZQ+HQFHWKHUHZLOOEHDUDQJHRIZDYHOHQJWKVIRUD JLYHQWUDQVLWLRQUDWKHUWKDQDVWULFWO\PRQRFKURPDWLFSKRWRQ $IWHUDFFHOHUDWLRQWKHNLQHWLFHQHUJ\RIWKHSURWRQLVH9DQGWKLVLVDOOFRQYHUWHGWRHOHFWULFDOSRWHQWLDOHQHUJ\ZKHQLWMXVWVWRSVDWWKHQXFOHDU VXUIDFH+HQFH ZKHUH5LVWKHUDGLXVRIWKHQXFOHXV7KHUDGLXVLV5ࡁ࠺ ࠺P+HQFH 7KXV$ $H࠺ͪW $H࠺ $RUDERXWRIWKHRULJLQDODFWLYLW\ 7KHGHFD\FRQVWDQWLV +HQFH )RU;ZHJRWRKDOIWKHLQLWLDODFWLYLW\DQGILQGDWLPHRIPLQ)RU<ZHPXVWZDLWXQWLOPRVWRI;KDVGHFD\HGDZD\VRWKDWQRQHZ< QXFOHLDUHSURGXFHG/RRNLQJDWKRZORQJLWWDNHVIRUWKHDFWLYLW\WRKDOYH DIWHUPLQ ZHILQGD<KDOIOLIHRIDERXWPLQ 2SWLRQ$ $ /LJKWZLOOFRYHUWKHGLVWDQFḦ́[ ࠺ PLQDWLPHRI 7KH HYHQW ߝOLJKWQLQJ VWULNHVߞ WKXV RFFXUUHG DW W ࠺ V DW SRVLWLRQ [ P$OO REVHUYHUV LQ IUDPH 6 DJUHH WKDW WKHVH DUH WKH FRRUGLQDWHVRIWKHHYHQWߝOLJKWQLQJVWULNHVߞ $ 7DNHWKHJURXQGDVIUDPH6DQG$DVIUDPH6߯7KHQY FDQGX ࠺FDQGZHQHHGWRILQGX߯ 7KHVSHHGRI%UHODWLYHWR$LVF $ 7KH WZR VWULNHV DUH VLPXOWDQHRXV LQ IUDPH 6 LH ̈́W DQG ̈́[ P 7KH WLPH VHSDUDWLQJ WKHVH HYHQWV LQ IUDPH 6߯ LV $ 7KHWRWDOHQHUJ\LV +HQFHWKHJDPPDIDFWRULV 6R $ DQG 7KHJDPPDIDFWRULV DQGVRWKHWRWDOHQHUJ\DIWHUDFFHOHUDWLRQLV ( ͢PF 0H97KHNLQHWLFHQHUJ\WKHUHIRUHLV (N ࠺ 0H9DQGWKXVWKHYROWDJHLV9 ࡁ09 $ 7KHWRWDOHQHUJ\LVWKXV 7KHJDPPDIDFWRULV ( ͢PF 0H9DQGVRWKHNLQHWLFHQHUJ\LV (N ࠺ 0H9 $ $ 8VH( PF SFWRJHW SF⇒S ࡁ0H9F࠺ 6LQFH ( ͢PF WKH JDPPD IDFWRU LV +HQFH VR $ D &RPELQLQJ( ͢PFDQGS ͢PYZHILQG E )RUDPDVVOHVVSDUWLFOH( SFDQGVR VRP 0H9F࠺ F $ %HIRUHDFFHOHUDWLRQ( PF$IWHUDFFHOHUDWLRQ( ͢PF+HQFHWKHFKDQJHLV̈́( ͢PF࠺PF ͢࠺ PFDQGWKLVHTXDOVT9 H9 0H96R +HQFH DQGS ͢PY 0H9F࠺7KLVFDQDOVREHH[SUHVVHGDVS *H9F࠺ $ 7KHEHVWZD\WRSURFHHGLVWRILQGWKHWRWDOHQHUJ\RIWKHSURWRQWKURXJK( PF SFWKXV 7KHQXVH( $ $ ͢PFWRILQG DQGILQDOO\ %\WKHHTXLYDOHQFHSULQFLSOHWKHVLWXDWLRQLVHTXLYDOHQWWRDURFNHWDWUHVWRQWKHVXUIDFHRIDPDVVLYHERG\,QWKLVFDVHZHNQRZWKDWWKHUD\ RIOLJKWZLOOEHQGWRZDUGVWKHPDVVLYHERG\DQGVRWKHUD\ZLOOIROORZDFXUYHGGRZQZDUGSDWK,WZLOOWKHUHIRUHKLWWKHRSSRVLWHVLGHRIWKH URFNHWDWDKHLJKWOHVVWKDQK :RUNLQJEDFNZDUGVIURPWKHSUHYLRXVH[DPSOHWKHVLWXDWLRQLVHTXLYDOHQWWRDURFNHWDFFHOHUDWLQJLQRXWHUVSDFHZLWKDQDFFHOHUDWLRQPV ,Q WKLV WLPH WKH URFNHW KDV PRYHG XS D GLVWDQFH ࠺ 7KH WLPH IRU OLJKW WR FURVV WKH GLVWDQFH RI P LV $ 1HZWRQZRXOGFODLPWKDWWKHSDWKRIWKHSODQHWLVWKHUHVXOWRIWKHJUDYLWDWLRQDOIRUFHEHWZHHQWKH6XQDQGWKHSODQHW(LQVWHLQZRXOGFODLP WKDWWKHSDWKLVGXHWRWKHFXUYDWXUHRIVSDFHWLPHWKHSODQHWIROORZVDJHRGHVLFߙWKDWLVDSDWKRIOHDVWOHQJWKߙLQWKHFXUYHGVSDFHWLPH DURXQGWKHPDVVLYH6XQ $ :H KDYH WKDW DQG VR +HQFH WKH GLVWDQFH K IURP WKH HYHQW KRUL]RQ LV 2SWLRQ% % 8VLQJ ͧ͠ZHILQG ࠺ͧDQGVRͧ UDGRU % 7KHQHWIRUFHLV]HURDQGWKHQHWWRUTXHLV)5)5 )5 % 7KHQHWIRUFHRQWKHF\OLQGHULQWKHGLUHFWLRQRIWKHSODQHLV0JVLQͧ࠺IDQGVR IXOOUHYROXWLRQV )QHW 0D 0JVLQͧ࠺I 0D 7KHQHWWRUTXHDERXWDKRUL]RQWDOD[LVWKURXJKWKHFHQWUHRIPDVVLVI5 1DQG0JKDYH]HURWRUTXHVDERXWWKLVSRLQW DQGVREHFDXVHWKH PRPHQWRILQHUWLDRIDF\OLQGHUDERXWLWVD[LVLV :HDVVXPHUROOLQJZLWKRXWVOLSSLQJDQGVR 6RRXUWZRHTXDWLRQVEHFRPH JLYLQJ DQGVR0J % $SSO\LQJDQJXODUPRPHQWXPFRQVHUYDWLRQ % 8VH % D ZKHUH߯LVWKHDQJXODUYHORFLW\DIWHUWKHH[SORVLRQ+HQFH߯ ߯7KHQXPEHURIUHYROXWLRQVSHUVHFRQGLVWKHQ )URP WRILQG ZHVHHWKDW DQGVRWKHQHZWHPSHUDWXUHLV 7KHSUHVVXUHLV FRQVWDQWVRZHPD\FDOFXODWHWKHZRUNGRQHIURP: S̈́9 ࠺ - E 6LQFHWKHWHPSHUDWXUHKDVLQFUHDVHG̈́8!DQGWKHJDVKDVH[SDQGHG6RIURP4 ̈́8:ZHVHHWKDW:!VR4! 7KHUPDO HQHUJ\KDVEHHQVXSSOLHGWRWKHJDV % D 7KHLQWHUQDOHQHUJ\RIDQLGHDOJDVLVWKHWRWDOUDQGRPNLQHWLFHQHUJ\(NRIWKHPROHFXOHVRIWKHJDV E 7KHDEVROXWHWHPSHUDWXUHLVSURSRUWLRQDOWRWKHDYHUDJHNLQHWLFHQHUJ\RIWKHPROHFXOHV 7KHUHIRUHWKHLQWHUQDOHQHUJ\LVSURSRUWLRQDOWRWKHDEVROXWHWHPSHUDWXUH DQGWKHQXPEHURIPROHFXOHV 8 (N∝ 17 % 7KHSLVWRQPRYLQJUDSLGO\LQZDUGVFROOLGHVZLWKPROHFXOHVDQGWKHPROHFXOHVUHERXQGZLWKDVSHHGJUHDWHUWKDQEHIRUH7KHDYHUDJHNLQHWLF HQHUJ\RIWKHPROHFXOHVLQFUHDVHVDQGKHQFHVRGRHVWKHWHPSHUDWXUH % $WFRQVWDQWYROXPHZHKDYH4 ̈́8VLQFHQRZRUNLVEHLQJGRQH$WFRQVWDQWSUHVVXUH4 ̈́8߯:ZLWK:!+HQFHWKHFKDQJHLQ LQWHUQDOHQHUJ\LVODUJHULQWKHFRQVWDQWYROXPHFDVHDQGWKHUHZHKDYHWKHODUJHUWHPSHUDWXUHLQFUHDVH % D $%LVWKHLVRWKHUPDOVLQFHLWLVOHVVVWHHSWKDQWKHDGLDEDWLF&$ E %&EHFDXVHWKHZRUNGRQHLVQHJDWLYH RQWKHJDV DQGWKHWHPSHUDWXUHGURSVVRWKDẄ́86LQFH4 ̈́8:ZHKDYH4 F :RUNLVWKHDUHDXQGHUWKHFXUYHLQDSUHVVXUHߙYROXPHGLDJUDP7KLVLVODUJHVWIRUWKHLVRWKHUPDOH[SDQVLRQ % $SSO\LQJ4 ̈́8:WRWKHHQWLUHF\FOHZHVHHWKDẄ́8 7KHWRWDOZRUNGRQHLVWKHDUHDZLWKLQWKHORRSDQGWKLVLVSRVLWLYH7KHWRWDO WKHUPDOHQHUJ\WUDQVIHUUHGLV4࠺4+HQFH4࠺4 :DQGVR4LVODUJHU % 7KHWHPSHUDWXUHDW%LVKLJKHUWKDQWKDWDW$VR̈́8!:RUNLVGRQHE\WKHJDVVLQFHLWLVH[SDQGLQJDQGVR:!+HQFH4! 7KHWHPSHUDWXUHDW'LVORZHUWKDQWKDWDW&DQGVR̈́87KHYROXPHVWD\VFRQVWDQWDQGVR: +HQFH4 % 7KHHIILFLHQF\LV +HQFHWKHZRUNGRQHLV % :HKDYHHTXLOLEULXPDQGVRPJ ͰIOXLGJ9LPPRUͰERG\J9 ͰIOXLGJ9LPPVR % $SSO\LQJ %HUQRXOOLߞ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࠺ ࠺G%7KHQHWJDLQRIWKHDPSOLILHUVPXVWWKHQEHG%DQGVR ZHQHHG DPSOLILHUV & D 7KH DWWHQXDWLRQ DIWHU D GLVWDQFH RI NP LV ; G% 7KH SRZHU LV WKHQ IRXQG IURP E $WWHQXDWLRQLQFRD[LDOFDEOHVLVYHU\IUHTXHQF\GHSHQGHQW7KHUHLVPXFKPRUHDWWHQXDWLRQDWKLJKHUIUHTXHQFLHV & , ,H࠺u[ ,H࠺ , & 7KH SKRWRHOHFWULF HIIHFW LV PRUH XVHIXO VLQFH ZH QHHG WR KDYH FRQWUDVW EHWZHHQ IRU H[DPSOH WLVVXH DQG ERQH WKDW KDYH GLIIHUHQW DWRPLF QXPEHUV & 7KHWUDQVGXFHUDFWVDVERWKHPLWWHUDQGUHFHLYHU7KHHPLVVLRQVPXVWVWRSVRWKDWWKHUHIOHFWHGXOWUDVRXQGPD\EHGHWHFWHG 2SWLRQ' ' 7KLV LV D UDWLR SUREOHP :ULWH /$ Ͳ$$ DQG /% Ͳ$% 7DNH UDWLRV VLGH E\ VLGH WR JHW 6LQFH DUHD LV UHODWHG WR UDGLXV E\ $ ͯ5 LW IROORZV WKDW ' 7KH ZDYHOHQJWK LV IRXQG IURP DQG VR WKH VWDU ZLOO DSSHDU UHGGLVK 7KH SHDN ZDYHOHQJWK LV LQ WKH LQIUDUHGEXWWKHOHIWHQGRIWKHEODFNERG\FXUYHLVPDLQO\RYHUUHGZDYHOHQJWKV ' $FKHUQDUDQG(*KDYHWKHVDPHWHPSHUDWXUHEXW$FKHUQDUKDVDPXFKKLJKHUOXPLQRVLW\VRLWPXVWKDYHDYHU\ODUJHDUHDDSSUR[LPDWHO\ $FKHUQDULVDEOXHJLDQWDQG(*DZKLWHGZDUIVR$FKHUQDULVPXFKODUJHU ' )URPWKH+5GLDJUDPLWVOXPLQRVLW\LVDERXW࠺;/4 ;:+HQFH ' ,ILWZHUHDPDLQVHTXHQFHVWDULWVOXPLQRVLW\ZRXOGKDYHWREHࡁWLPHVODUJHUWKDQWKHOXPLQRVLW\RIWKH6XQ6RLWQRWDPDLQ VHTXHQFHVWDU ' 2QHSLHFHRIHYLGHQFHLVWKHH[LVWHQFHRIWKHFRVPLFPLFURZDYHEDFNJURXQG &0% UDGLDWLRQ7KLVLVUDGLDWLRQWKDWH[LVWHGZKHQWKHXQLYHUVH ZDVYHU\\RXQJ$VWKHXQLYHUVHKDVH[SDQGHGLWVRULJLQDOKLJKWHPSHUDWXUHKDVIDOOHQWRDERXW.VKLILWQJWKHSHDNZDYHOHQJWKRIWKLV UDGLDWLRQWRLWVSUHVHQWYDOXH$VHFRQGSLHFHRIHYLGHQFHLVWKHH[SDQVLRQRIWKHXQLYHUVHDFFRUGLQJWR+XEEOHߞVODZ,IWKHGLVWDQFHEHWZHHQ JDOD[LHVLVJHWWLQJODUJHUWKHQLQWKHSDVWWKHGLVWDQFHPXVWKDYHEHHQVPDOOHULQGLFDWLQJDYLROHQWVWDUWRIWKHXQLYHUVHIURPDVPDOOUHJLRQ ' )URP WKHVSHHGRIWKHUHFHGLQJJDOD[\LV )URPY +G G⇒Gࡁ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Ͱ ͰFFXUYHGOLNHDVSKHUHLIͰ! ͰFDQGFXUYHGOLNHDVDGGOHLIͰͰF