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1、CHAPTERR 9: TTHE CAAPITALL ASSEET PRIICING MODELL1.c.2.d.FFrom CCAPM, the ffair eexpectted reeturn = 8 + 1.255(15 - 8) = 16.755%Actuallly exppectedd retuurn = 17%a = 17 - 16.755 = 0.25%3.Sincce thee stoccks bbeta iis equual too 1.2, its expeccted rrate oof retturn iis:6 + 1.2 (116 66) = 18%4.The ser
2、iees of $1,0000 payymentss is aa perppetuitty. IIf betta is 0.5, the ccash fflow sshouldd be ddiscouunted at thhe ratte:6 + 0.5 (116 66) = 11%PV = $11,000/0.11 = $9,090.991If, howwever, betaa is eequal to 1, thenn the invesstmentt shouuld yiield 116%, aand thhe priice paaid foor thee firmm shouuld b
3、ee:PV = $11,000/0.16 = $6,250The diffferennce, $2,8400.91, is thhe amoount yyou wiill ovverpayy if yyou errroneoously assumme thaat betta is 0.5 rratherr thann 1.5.Usinng thee SML: 4 = 6 + b(16 6) b = 22/10 = 0.226.a.7.E(rPP) = rf + b P E(rM ) rrf 18 = 6 + b P(14 6) b P = 112/8 = 1.58.a.FFalse. b =
4、0 impplies E(r) = rf , nott zeroo.b. False. Inveestorss requuire aa riskk premmium oonly ffor beearingg systtematiic (unndiverrsifiaable oor marrket) risk. Tottal voolatillity iincluddes diiversiifiablle rissk.c. False. Yourr porttfolioo shouuld bee inveested 75% iin thee markket poortfollio annd 25
5、% in TT-billls. TThen:bP = (0.75 1) + (0.255 0) = 0.759.Not possiible. Porttfolioo A haas a hhigherr betaa thann Porttfolioo B, bbut thhe exppectedd retuurn foor Porrtfoliio A iis lowwer thhan thhe exppectedd retuurn foor Porrtfoliio B. Thuss, theese twwo porrtfoliios caannot existt in eequiliibrium
6、m.10.Posssiblee. Iff the CAPM is vaalid, the eexpectted raate off retuurn coompenssates only for ssystemmatic (markket) rrisk, repreesenteed by beta, rathher thhan foor thee stanndard deviaation, whicch inccludess nonssystemmatic risk. Thuus, Poortfollio As lowwer raate off retuurn caan be paireed w
7、itth a hhigherr stanndard deviaation, as llong aas Ass betaa is lless tthan BBs.11.Nott posssible. Thee rewaard-too-variiabiliity raatio ffor Poortfollio A is beetter than that of thhe marrket. Thiss scennario is immpossiible aaccordding tto thee CAPMM becaause tthe CAAPM prredictts thaat thee markk
8、et iss the most efficcient portffolio. Usiing thhe nummbers suppllied:Portfollio A proviides aa bettter riisk-reeward tradeeoff tthan tthe maarket portffolio.12.Nott posssible. Porrtfoliio A cclearlly domminatees thee markket poortfollio. Portffolio A hass bothh a loower sstandaard deeviatiion annd
9、a hhigherr expeected returrn.13.Nott posssible. Thee SML for tthis sscenarrio iss: E(rr) = 110 + b(18 10)Portfollios wwith bbeta eequal to 1.5 havve an expeccted rreturnn equaal to:E(r) = 10 + 1.5 (18 10) = 222%The exppectedd retuurn foor Porrtfoliio A iis 16%; thaat is, Porttfolioo A pllots bbelow
10、the SSML (a A = 6%), and hhence, is aan oveerpricced poortfollio. This is innconsiistentt withh the CAPM.14.Nott posssible. Thee SML is thhe samme as in Prroblemm 13. Heere, PPortfoolio AAs reequireed retturn iis: 100 + (00.9 8) = 17.2%This iss greaater tthan 116%. Portffolio A is overppricedd withh
11、 a neegativve alppha:a A = 11.2%15.Posssiblee. Thhe CMLL is tthe saame ass in PProbleem 11. PPortfoolio AA plotts bellow thhe CMLL, as any aasset is exxpecteed to. Thiis sceenarioo is nnot innconsiistentt withh the CAPM.16.If the ssecuriitys correelatioon coeefficiient wwith tthe maarket portffolio
12、doublles (wwith aall otther vvariabbles ssuch aas varriancees uncchangeed), tthen bbeta, and tthereffore tthe riisk prremiumm, willl alsso douuble. The curreent riisk prremiumm is: 14 6 = 88%The neww riskk premmium wwould be 166%, annd thee new discoount rrate ffor thhe seccurityy woulld be: 16 + 6
13、= 22%If the stockk payss a coonstannt perrpetuaal divvidendd, theen we know from the ooriginnal daata thhat thhe divvidendd (D) must satissfy thhe equuationn for the ppresennt vallue off a peerpetuuity:Price = Diviidend/Discoount rrate50 = D/0.14 D = 50 00.14 = $7.000At the new ddiscouunt raate off
14、22%, the stockk woulld be worthh: $7/0.22 = $311.82The inccreasee in sstock risk has llowereed itss valuue by 36.366%.17.d.18.a.Sincee the markeet porrtfoliio, byy defiinitioon, haas a bbeta oof 1, its eexpectted raate off retuurn iss 12%.b. b = 0 meaans noo systtematiic rissk. HHence, the stockks e
15、xxpecteed ratte of returrn in markeet equuilibrrium iis thee riskk-freee ratee, 5%.c. Using tthe SMML, thhe faiir exppectedd ratee of rreturnn for a stoock wiith b = 0.5 is:E(r) = 5 + (0.55)(12 5) = 1.5%The acttuallyy expeected rate of reeturn, usinng thee expeected pricee and dividdend ffor neext yeear iss:E(r)
