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ahpetr utOinle E pectxed etRrun sand Vaiarcen s Potrfoliso A nonnucmeents,Sur rpiess a,nd xEectpde Reutrn Rsisk :Sstymaetc aid Unnsystmeaict D vierisfcaiiotn and oPrftloi oRiks ySsteamitcR skia dnB ta eT eh ecSruiy tMraet Likn e he TSMLa n tdh Ceot sofCap ita:l A Periew
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xepcet dRetrnus xEpctee drteurns reab aedso n the robpbilaiteis fo opssileb otucoem s In thi sc otexn, te“xectepd”m anes veragea i thef ropecs issr eepaedt mny atmeis T he “xpected”e erutrn des noo event hve ato b e aossibpe retlunrE ( R) pi Ri i 1
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Eample: xExepctdeR eutnrs Su popseyou hveap redicetd ht feloolwign etrunrsf orstock s Cadn iT thnre posseble statise o thef eonocmy. Watha ert h exepcteed etrurs?nStae Tt ooBm25 Nroal m0 Re2ecssino1 Pro bailitb 0.3y 0. 5 C1 105???2
R C= . 31() +5 .5(0)1+ . 22()= .9% 9 T = .R325()+ .(502 +).2 1( =) 7.7%1315-
aViarcne adnS tnadrad eDvitiona Varaicenand s tadnad rediaviotn emsureat h veoatilily otfr teursn siUg nnueuqalp orbailbiite fsort e hntiee rangerof p ssoibiitiels W iehtgde avrageeof suarqe dedvaitonsiσ pi R( i (E R)2) i 1 n 2 136-
xEmaple Var:inac enad taSdnra Dediaviton Consdie rthe previousexam ple W.ath rea het arvinca aednst ndaad rdeivaiotnfor eca hsockt ?S otck C 2 = .3 15-(.99) +2 .(15-09.92 +). 2(2-99)2 . 2=.02 9 =4. 05% SoctkT 2 = .3(2-1577)2. +. 5(2017-.72 +) 2(1-1.77)2 . 74.=4 1 = 8.36%
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AnohertEx mape l Cnsioer the fodllwing inofrmationo:Stte Baoo NmomrlaS lodwwnoR ceessinoProbab liiyt .52 .50 .1 510 A.CB, Icn.( ) 1% 5 8 -43 Wathi she etpxecetd erurn? t Wah istt e havriance ? What ist ehs tnadadr deiatvio?n13-
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Proftlioos Aoprftloo ii sac lloetcinoo fasests An as set’ risk sadnr eutnr ae rmipotrna itnhow th y aefeftc he tirsk ad nreurt nfo het protolfi oTh risk-reetrnu radet-offf r o aortfolpiois m eauserd byth e profolio exptceetd retrn unads andartd deiatiov,n jst ua wishti dinidvalu assest13-9
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xmape: PorltoliofW eigths Spupoe syouh va e1$5000,t oinesv atn yod huae puvrhased scecriuies it tnh feolowlig naounmst.W hatare yuro prtfooil weigoths i nachese uricyt ?$0002o fC C : 2/1 5 .=331 $030 0fo K OO: 3/15K = .2 $ 040 o0 fNICT ITNC 4:/1 5= .276 $6000o f P B B P 6:/1 = .4531-1
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rotflio Eopextced eturnsR hTe epecxtder tuen rf oap otroliof sith eweig teh davraeg of theeex peted ceturrsn o tfh eesprectve asiess tin the potfrloo
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Ex
ample Exp:cted Peotfolro ieRturn sCons ider te hoprtolfo weigihs ctmputoe dpeviruslo. yf Ihtei dinvidual tocks shaev te hfollwoig nxeepced trtuersn w,ath i the sepexted retucn rfr ote hproftloio? C :19. 69% O: 5.25K% NTC: 16I65%. P:B1 8.42% E(P) =R. 13(13.969)+ 2.(5.52) +.26716.6(5 ) +4(.182.4 ) =154.%11312-
Porftlioo aVianrec Comp uet het orptolifo ertur norf aehcsta t: eRP =w1R +1 2wR +2… + w Rmm oCpumett hee pexcedtp rtfolioor ternu using te hase fmorumla saf r on ianidvduaila sset Co pmuett e hpotrolfoi variacn ean dsatndard devatiino usnigthe amsefo rumlsaas ofr a inndiidvul asaets13-1
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Examlep:P orfoltoi Varianec C onsier dhetf olowlni igfnormation nvIet s50%of ouyrm noy ienAs se A Portfotli oSatetP orabilitbyA B oBm o. 40% 35-% 215%.B uts 6. 10- %52 7.5%% What are th eepectxd eertun rad stnnaard ddevaitio nor eafh casst? eWahtar the exepeced rtteru ann dtasndrd aeviatdonifo rt ehp rtfolio?o3-11
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AonthreExa pmle C osindre he ftollwingo inorfamtoiSntte aoBm Noomrl Racesesin orPobbilait .y5 2.06 1. 5 X51 %0% 5%1Z 10% 9 % 0%1 Whtaare t he exeptcderet rn und saatnardd eviaditonf o r aportolio fitwhan ivnsetentmof 6,$00 in 0ases X tnda $400,0 i nasest ?Z13-1
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Expecte dsv Une.pxectdeR eutrns eaRizedl retrnus ra egenerall not eqyal tu exoeptedc retunrs heTeris the ex ecpedtc oponmen tan dhteu enpexcetdc mponenot At na pointyin tme, the inuexecpetdret rn uca bn eiteerh osiptvi oren egtavie Ov erti m,eth eav reaegof ht unexeepcte dompcneon tisze ro
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