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Lu |üi €h4<t Lê?ihtc êüðUü êi _i?L|i üS ë `üi? @** 4@UhLií UL?L4ðU ñ@hð@M*it @hi t|LUü@t|ðUc LT|ð4@* ThðUit @hiG R' > .EüS Sç*@ä > ý • .EüS Sä Eeä RW ' > .EüS SW ç*@ä > ý • .EüS 7SW ä EDä èhðUit @hi t|ð** i^ý@* |L @ t|@?_@h_ 4@h!ýT Lñih ý?ð| ULt|ë•D Aüi *@||ih ðt ?Lê 44 Krrshu dqg Nrkokdjhq +4<:;, frqvlghu d vrphzkdw glòhuhqw vhwxs/ zlwk erwk lpsruwhuv dqg h{sruwhuv ehdulqj sduw ri wkh h{fkdqjh udwh ulvn1 Zkhq h{sruwhuv ehdu prvw ri wkh ulvn/ h{fkdqjh udwh xqfhuwdlqw| udlvhv wkh h{sruw sulfh dqg uhgxfhv wudgh1 Zkhq lpsruwhuv ehdu prvw ri wkh ulvn/ h{fkdqjh udwh xqfhuwdlqw| uhgxfhv lpsruw ghpdqg +dqg wkhuhiruh wudgh,/ dqg orzhuv wkh lpsruw sulfh1 Lq jhqhudo wkh sulfh hòhfw lv wkhuhiruh dpeljxrxv/ exw wkh wudgh hòhfw lv xqdpeljxrxvo| qhjdwlyh1 45 Vhh Hwklhu +4<:6,/ Edurq +4<:9,/ Yldhqh dqg gh Yulhv +4<<5, dqg Ihhqvwud dqg Nhqgdoo +4<<4,1 46 Dgdp0Pxhoohu +4<<:, lqfoxghv erwk uhyhqxh dqg h{fkdqjh udwh xqfhuwdlqw|1 47 Wkh sulflqj0nhuqho fruuhvsrqgv wr wkh sulfh ri vwdwh0frqwlqjhqw fodlpv li wkh| duh wudghg +zklfk lv qrw uhtxluhg iru wkh sulflqj0nhuqho wr h{lvw,1 48 Qrwlfh wkdw wkhvh htxdwlrqv duh vlplodu wr wkrvh irxqg lq g|qdplf jhqhudo htxloleulxp prg0 hov zlwk SWP/ vxfk dv Ehwwv dqg Ghyhuhx{ +4<<:,/ Fkdul/ Nhkrh dqg PfJudwwdq +4<<:, dqg Nroopdqq +4<<:,1 S êhð||i? @t |üi Uih|@ð?|) i^ýðñ@*i?| Lu |L|@* *@MLh ULt|c _ðñð_i_ M) |üi Uih|@ð?|) i^ýðñ@*i?| Lu t@*itë ,^ý@|ðL?t Eeä @?_ EDä tüLê |ü@| i í@?|i ThðUi _ðtUhð4ð?@|ðL? 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Lu }LL_ ð @?_ > ðt |üi i*@t|ðUð|) Lu týMt|ð|ý|ðL? Mi|êii? @?) |êL }LL_tc êüðUü 4ýt| Mi *@h}ih |ü@? L?ië > ðt @*tL |üi ThðUiíi*@t|ðUð|) Lu _i4@?_c @t ð? 5iU|ðL? 2ë `ð|ü @ ê@}i h@|i Lu çc @?_ @ |ð4i i?_Lê4i?| Lu •c *@MLh ð?UL4i ðt çE• ý ,äë 6ðh4 ThL€|t i@h?i_ M) |üi üLýtiüL*_ @hi _i?L|i_ áë W? i@Uü t|@|i Lu |üi êLh*_c |üi üLýtiüL*_ Mý_}i| UL?t|h@ð?| ðt Eêi L4ð| |üi t|@|i Lu |üi êLh*_ ð?_i uLh UL?ñi?ði?UiäG ] f • RM EðäSEðä_ð n ] 2 • R8 EðäSEðä_ð ' çE• ý ,ä n á ì t EHä `i hiuih |L |üi hð}ü| ü@?_ tð_i Lu EHä @t |L|@* ?L4ð?@* ð?UL4i t Lu |üi üLýtiüL*_ë W? i^ýð*ðMhðý4c @** €h4t< ð?UL4i ðt _ðt|hðMý|i_ |L üLýtiüL*_tc tL |ü@| t @*tL _i?L|it ?L4ð?@* Lý|Tý|ë Aüi €ht| Lh_ih UL?_ð|ðL?t uLh UL?tý4T|ðL? @?_ *iðtýhi U@? Mi êhð||i? @t ç üS ' ü, Ebä å # $3> • RM Eðä t SEðä ' Eð é •ä E•fä 2 å å Oihi üS @?_ ü, @hi |üi 4@h}ð?@* ý|ð*ð|ðit Lu UL?tý4T|ðL? @?_ *iðtýhië ,^ý@|ðL? Ebä hiThiti?|t |üi t|@?_@h_ |h@_iíLg Mi|êii? UL?tý4T|ðL? @?_ *iðtýhië ,^ý@|ðL? 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Lu • @t hiThiti?|ð?} ML|ü 4L?i) týTT*) @?_ 4L?i) _i4@?_ tüLU!të 6Lh Lýh TýhTLtit |üiti @hi ð?_ðt|ð?}ýðtü@M*ië•H ôë•ëô 6ðh4t Aüi Miü@ñðLh Lu €h4t ðt tð4ð*@h |L |ü@| _itUhðMi_ ð? 5iU|ðL? 2ë `i @ttý4i @| |üðt t|@}i |ü@| |üi) @hi Lê?i_ M) _L4it|ðU UL?tý4ihtë 5ð?Ui |üihi @hi ?L ThL_ýU|ðñð|) tüLU!t ð? |üi Mi?Uü4@h! 4L_i*c êi ti| @ ' •ë Ntð?} |üi ?L|@|ðL? ð?|hL_ýUi_ ð? |üðt tiU|ðL?c ThL€|t Lu @ OL4i €h4 ð Eð? i@Uü t|@|i Lu |üi êLh*_ä @hi }ðñi? M) á ' RM EðäSEðä n 7RWM EðäSW Eðä ý çESEðä n SW Eðää E•ôä OL4i _i4@?_ ðt }ðñi? M) E•fäc ýtð?} E•2äë 6Lhið}? _i4@?_ ðt }ðñi? @?@*L}Lýt*) M)G # $3> • RWM Eðä •W W S Eðä ' E•eä 2 åW åW êð|ü |üi uLhið}? 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Lu _L4it|ðU }LL_t @t SM ' SEðä @?_ SWM ' SW Eðä uLh f ÷ ð ÷ •ë `i €?@**) ?ii_ |L tL*ñi uLh |üi i^ýð*ðMhðý4 i Uü@?}i h@|ië Aüðt uL**Lêt uhL4 |üi 4L?i) 4@h!i| i^ýð*ðMhðý4 UL?_ð|ðL? • ' t ' RM SM n 7RWM SWM ë úu|ih týMt|ð|ý|ð?} |üi _i4@?_ uý?U|ðL?t uLh _L4it|ðU }LL_tc êi U@? tL*ñi•b • E•.ä •W Aüi t)44i|hðU t|hýU|ýhi Lu |üi 4L_i* ð4T*ðit |ü@| |üi ?L4ð?@* i Uü@?}i h@|i ðt i^ý@* |L |üi h@|ðL Lu 4L?i) týTT*ðitë Aüðt ðt U*i@h*) @ ñih) tð4T*ðt|ðU i Uü@?}i h@|i i^ý@|ðL?c iñi? ðu L?i |@!it @UULý?| Lu |üi u@U| |ü@| • U@? @*tL hiThiti?| 4L?i) _i4@?_ tüLU!të `ü@| 4@||iht |üLý}ü ðt |ü@| ð| U@T|ýhit ð? @ tð4T*i ê@) |üi M@tðU ð_i@ |ü@| |üi i Uü@?}i h@|i ðt UL??iU|i_ |L ý?_ih*)ð?} uý?_@4i?|@*tc êüðUü ð4T*ðit |üi ð4TLh|@?Ui Lu }i?ih@* i^ýð*ðMhðý4 @?@*)tðtë N?Uih|@ð?|) @MLý| |üi uý?_@4i?|@*t E|üi 4L?i) týTT*ðitä ?L| L?*) *i@_t |L ý?Uih|@ð?|) @MLý| i Uü@?}i h@|it €h4t u@Uic Mý| @*tL @MLý| ê@}it |üi) T@) @?_ _i4@?_ uLh |üiðh }LL_të 7' ôë2 W4T*ðU@|ðL?t uLh ïT|ð4@* èhðUit @?_ Ah@_i `i @hi ?Lê hi@_) |L @?@*)3i |üi ð4T@U| Lu |üi i Uü@?}i h@|i hi}ð4i L? 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E•b.Häc RAüi ,giU| Lu , Uü@?}i +@|i N?Uihí |@ð?|) L? |üi èhðUit @?_ VL*ý4i Lu W?|ih?@|ðL?@* Ah@_iâc aLýh?@* Lu W?|ih?@í |ðL?@* ,UL?L4ðUt Hc eHôíD••ë dôôo Wê@4L|Lc vë @?_ ,ë ñ@? `ð?ULLT E•bbHäc R#L îLh_iht •@||ihq ,ñð_i?Ui uhL4 a@T@?iti W?|h@?@|ðL?@* ç@Tð|@* ãLêtâc W?|ih?@|ðL?@* ,UL?L4ðUt +iñðiêc uLh|üUL4ð?}ë dôeo k@t@c kë E•bb2äc Rú_éýt|4i?| çLt|t @?_ èhðUð?} |L •@h!i|ë AüiLh) @?_ ,ñí ð_i?Uiâc aLýh?@* Lu W?|ih?@|ðL?@* ,UL?L4ðUt ô2c •íôfë ô. dôDo kð4c 5ë @?_ ûë +LýMð?ð E•bb.äc Rwð^ýð_ð|) @?_ , Uü@?}i +@|it ð? |üi Bí. çLý?|hðitG ,ñð_i?Ui uhL4 W_i?|ð€i_ Vú+tâc êLh!ð?} T@Tihc ûiê vLh! N?ðí ñihtð|)ë dôSo kð?_*iMih}ihc çëèë E•bSbäc RAüi ç@ti uLh 6ð i_ , Uü@?}i +@|itâc ð? Aüi W?í |ih?@|ðL?@* ú_éýt|4i?| •iUü@?ðt4c çL?uihi?Ui 5ihðit ?Lë 2c 6i_ih@* +itihñi î@?! Lu îLt|L?c bôí•fHë ú*tL ð? çëèë kð?_*iMih}ihc W?|ih?@|ðL?@* •L?i)c ú çL**iU|ðL? Lu ,tt@)tc BiLh}i ú**i? : N?êð?c •bH•ë dô.o kL**4@??c Aë E•bbDäc RçL?tý4T|ðL?c +i@* , Uü@?}i +@|it @?_ |üi 5|hýU|ýhi Lu W?|ih?@|ðL?@* útti| •@h!i|tâc aLýh?@* Lu W?|ih?@|ðL?@* •L?i) @?_ 6ð?@?Uic •eG2c •b•í2••ë dôHo kL**4@??c +ë E•bb.äc RAüi , Uü@?}i +@|i ð? @ #)?@4ðUíïT|ð4ð3ð?} çýhhi?| úUULý?| •L_i* êð|ü ûL4ð?@* +ð}ð_ð|ðitG ú "ý@?|ð|@|ðñi W?ñit|ð}@|ðL?âc W•6 `Lh!ð?} è@Tih b.%.ë dôbo •@U#L?@*_c +ë @?_ •ëèë A@)*Lh E•bbeäc RAüi •L?i|@h) •L_i* Lu |üi , í Uü@?}i +@|iG wL?} +ý? +i*@|ðL?tüðTtc 5üLh|í+ý? #)?@4ðUt @?_ OLê |L îi@| @ +@?_L4 `@*!âc aLýh?@* Lu W?|ih?@|ðL?@* •L?i) @?_ 6ð?@?Ui •ôEôäc 2.Sí2bfë defo •@}ð**c •ë @?_ •ë "ýð?3ðð E•bbSäc AüiLh) Lu W?UL4T*i|i •@h!i|tc •WA èhittë de•o •@h!c ûëçë E•bbDäc R, Uü@?}i +@|it @?_ 6ý?_@4i?|@*tG ,ñð_i?Ui L? wL?} OLhð3L? èhi_ðU|@Mð*ð|)âc ú4ihðU@? ,UL?L4ðU +iñðiê HDc ?Lë •c 2f•í2•Hë de2o •@h!c ûëçë @?_ #ë çüLð E•bb.äc R+i@* , Uü@?}i +@|i èhi_ðU|ðL?t Lñih wL?} OLhð3L?tâc aLýh?@* Lu W?|ih?@|ðL?@* ,UL?L4ðUt eôc 2bíSfë deôo •Uç@**ý4c aë E•bbDäc Rû@|ðL?@* îLh_iht •@||ihâc ú4ihðU@? ,UL?L4ðU +iñðiê HDc S•DíS2ôë deeo •ý?_i**c +ëúë E•bS•äc Rú AüiLh) Lu ïT|ð4ý4 çýhhi?U) úhi@tâc ú4ihðU@? ,UL?L4ðU +iñðiê D•c SD.íSDë deDo ûiý4i)ihc èë úë E•bbHäc Rçýhhi?Uðit @?_ |üi ú**LU@|ðL? Lu +ðt!G Aüi `i*u@hi ,giU|t Lu @ •L?i|@h) N?ðL?âc ú4ihðU@? ,UL?L4ðU +iñðiê HHc 2eSí2Dbë ôH deSo ïMt|ui*_c •ë @?_ kë +L}Lg E•bbDäc R, Uü@?}i +@|i #)?@4ðUt +i_ý âc aLýhí ?@* Lu èL*ð|ðU@* ,UL?L4) •fôc S2eíSfë de.o ïMt|ui*_c •ë @?_ kë +L}Lg E•bbHäc R+ðt! @?_ , Uü@?}i +@|itâc êLh!ð?} T@Tihc N?ðñihtð|) Lu ç@*ðuLh?ð@c îih!i*i)ë deHo +@?!ð?c ûë E•bbHäc RûL4ð?@* +ð}ð_ð|) @?_ •L?i|@h) N?Uih|@ð?|) ð? @ 54@** ïTi? ,UL?L4)âc aLýh?@* Lu ,UL?L4ðU #)?@4ðUt @?_ çL?|hL* 22c S.bí.f2ë debo +L}ihtc aë E•bbHäc R•L?i|@h) 5üLU!t @?_ +i@* , Uü@?}i +@|itâc W?|ih?@|ðL?@* 6ð?@?Ui #ðtUýttðL? è@Tihtc ?Lë S•2c îL@h_ Lu BLñih?Lht Lu |üi 6i_ih@* +itihñi 5)t|i4ë dDfo 5ñi?ttL?c wë,ëïë @?_ 5ë ñ@? `ðé?Mih}i? E•bHbäc R, Uitt ç@T@Uð|)c •L?LTL*ðtí |ðU çL4Ti|ð|ðL?c @?_ W?|ih?@|ðL?@* Ah@?t4ðttðL? Lu •L?i|@h) #ðt|ýhM@?Uitâc ,UL?L4ðU aLýh?@* bbc .HDíHfDë dD•o Að**ic çë E•bbHäc RAüi W?|ih?@|ðL?@* @?_ #L4it|ðU `i*u@hi ,giU|t Lu •L?i|@h) èL*ðU) ý?_ih èhðUð?}í|Lí•@h!i|âc êLh!ð?} T@Tihc èhð?Ui|L? N?ðñihtð|)ë dD2o Vð@i?ic aë @?_ çëBë _i Vhðit E•bb2äc RW?|ih?@|ðL?@* Ah@_i @?_ , Uü@?}i +@|i VL*@|ð*ð|)âc ,ýhLTi@? ,UL?L4ðU +iñðiê ôSc •ô••í2•ë dDôo VLttc Bë•ë E•bbHäc R•L?i|@h) W?|i}h@|ðL?c N?Uih|@ð?|) @?_ |üi +L*i Lu •L?i) 6ð?@?Uiâc ,UL?L4ðU@ SDc 2ô•íeDë dDeo `iðc 5ëE•bbSäc RW?|h@í?@|ðL?@* ñihtýt W?|ih?@|ðL?@* Ah@_iG OLê 5|ýMMLh? @hi û@|ðL?t ð? B*LM@* W?|i}h@|ðL?qâc ûî,+ êLh!ð?} T@Tih DDô•ë ôb dKA .,, ,.,."'"',.,.,."'"',. intertemporal allocation (eqn. 40) .,, .,, "'(KA 1 A~.,"' .,, .,, .,, dr-dr* portfolio allocation (eqn. 41) Figure 1