博迪投資學答案chap009-7thed

1、9CHAPTERR 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% = 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 seriees

2、 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 bee:P

3、V = $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 + (16 6) = 22/10 = 0.226.a.7.E(rPP) = rf + P E(rM ) rrf 18 = 6 + P(14 6) P = 112/8 = 1.58.a.FFalse. = 0 impplies E(r)

4、 = rf , nott zeroo.False. Inveestorss requuire aa riskk premmium oonly ffor beearingg systtematiic (unndiverrsifiaable oor marrket) risk. Tottal voolatillity iincluddes diiversiifiablle rissk.False. Yourr porttfolioo shouuld bee inveested 75% iin thee markket poortfollio annd 25% in TT-billls. TThen

5、:P = (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 eequiliibriumm.10.Posssiblee. Iff t

6、he 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 witth a hhigherr stannd

7、ard 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 markket iss the most efficc

8、ient 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 a hhigherr expeected r

9、eturrn.13.Nott posssible. Thee SML for tthis sscenarrio iss: E(rr) = 110 + (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 the SSML ( A = 6%), and

10、 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 a neegativve alppha: A

11、= 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 doublles (wwith aall otth

12、er 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 = 22%If the stockk payss

13、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 22%, the stockk woulld be

14、 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%.= 0 meaans noo systtematiic rissk. HHence, the stockks exxpecteed ratte of returrn in

15、markeet equuilibrrium iis thee riskk-freee ratee, 5%.Using tthe SMML, thhe faiir exppectedd ratee of rreturnn for a stoock wiith = 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) = ($411 + $11)/40 1 =

16、 0.110 = 110%Becausee the actuaally eexpectted reeturn exceeeds thhe faiir retturn, the sstock is unnderprriced.19.a.E(rP) = rf + P E(rM ) rrf = 5% + 0.8 (15% 5%) = 13% = 14% 13% = 1%You shoould iinvestt in tthis ffund bbecausse alppha iss posiitive.b.The passiive poortfollio wiith thhe samme betta

17、as the ffund sshouldd be iinvestted 800% in the mmarkett-indeex porrtfoliio andd 20% in thhe monney maarket accouunt. For tthis pportfoolio:E(rP) = (0.88 155%) + (0.2 5%) = 133%14% 113% = 1% = 20.d.You need to knnow thhe rissk-freee ratte21.d.You need to knnow thhe rissk-freee ratte22.a.Expecteed Re

18、tturnAlphaStock XX5% + 0.8(14% 5%) = 122.2%14.0% 12.2% = 1.8%Stock YY5% + 1.5(14% 5%) = 188.5%17.0% 18.5% = 1.5%i. Kay shoulld reccommennd Stoock X becauuse off its posittive aalpha, comppared to Sttock YY, whiich haas a nnegatiive allpha. In ggraphiical tterms, the expeccted rreturnn/riskk proffile

19、 ffor Sttock XX plotts aboove thhe seccurityy markket liine (SSML), whilee the profiile foor Stoock Y plotss beloow thee SML. Alsso, deependiing onn the indivviduall riskk prefferencces off Kays cliients, the lowerr betaa for Stockk X maay havve a bbenefiicial effecct on overaall poortfollio riisk.i

20、i. Kayy shouuld reecommeend Sttock YY becaause iit hass highher foorecassted rreturnn and lowerr stanndard deviaation than Stockk X. The rrespecctive Sharppe rattios ffor Sttocks X andd Y annd thee markket inndex aare:Stock XX:(14% 5%)/36% = 0.255Stock YY:(17% 5%)/25% = 0.488Market indexx:(14% 5%)/1

21、5% = 0.600The marrket iindex has aan eveen morre atttractiive Shharpe ratioo thann eithher off the indivviduall stoccks, bbut, ggiven the cchoicee betwween SStock X andd Stocck Y, Stockk Y iss the superrior aalternnativee.When a stockk is hheld aas a ssinglee stocck porrtfoliio, sttandarrd devviatio

22、on is the rrelevaant riisk meeasuree. Foor succh a pportfoolio, beta as a risk measuure iss irreelevannt. AAlthouugh hooldingg a siingle assett is nnot a typiccally recommmendeed invvestmeent sttrateggy, soome innvestoors maay holld whaat is essenntiallly a ssinglee-asseet porrtfoliio wheen theey ho

23、lld thee stocck of theirr emplloyer compaany. For ssuch iinvesttors, the rrelevaance oof staandardd deviiationn verssus beeta iss an iimporttant iissue.23.Thee apprropriaate diiscounnt ratte forr the projeect iss:rf + EE(rM ) rf = 8 + 1.8 (16 8) = 22.4%Using tthis ddiscouunt raate: = 4000 pesoos + 1

24、50 ppesos Annnuity factoor (222.4%, 10 yeears) = 1800.92 ppesosThe intternall ratee of rreturnn (IRRR) forr the projeect iss 35.773%. Recalll froom youur inttroducctory finannce cllass tthat NNPV iss posiitive if IRRR ddiscouunt raate (oor, eqquivallentlyy, hurrdle rrate). Thee highhest vvalue that

25、beta can ttake bbeforee the hurdlle ratte excceeds the IIRR iss deteermineed by:35.73 = 8 + (16 8) = 277.73/88 = 3.4724.a.McKayy shouuld boorrow fundss and invesst thoose fuunds pproporrtionaately in Muurrays exiistingg porttfolioo (i.ee., buuy morre rissky asssets on maargin). Inn addiition to innc

26、reassed exxpecteed retturn, the aalternnativee porttfolioo on tthe caapitall markket liine wiill allso haave inncreassed riisk, wwhich is caaused by thhe higgher pproporrtion of riisky aassetss in tthe tootal pportfoolio.b.McKaay shoould ssubstiitute low bbeta sstockss for high beta stockks in order

27、r to rreducee the overaall beeta off Yorkks poortfollio. By reeducinng thee overrall pportfoolio bbeta, McKayy willl reduuce thhe sysstemattic riisk off the portffolio, and thereefore reducce itss volaatilitty rellativee to tthe maarket. Thee secuurity markeet linne (SMML) suuggestts succh acttion (

28、i.e., moviing doown thhe SMLL), evven thhough reduccing bbeta mmay reesult in a slighht losss of portffolio efficciencyy unleess fuull diiversiificattion iis maiintainned. Yorkss primmary oobjecttive, howevver, iis nott to mmaintaain effficieency, but tto redduce rrisk eexposuure; rreduciing poortfo

29、llio beeta meeets tthat oobjecttive. Becaause YYork ddoes nnot waant too engaage inn borrrowingg or llendinng, MccKay ccannott reduuce riisk byy sellling eequitiies annd usiing thhe prooceedss to bbuy riisk-frree asssets (i.e., lennding part of thhe porrtfoliio).25.d.26.r1 = 19%; r2 = 166%; 1 = 1.5;

30、 2 = 1a.To ddetermmine wwhich invesstor wwas a betteer sellectorr of iindiviidual stockks we look at abbnormaal retturn, whichh is tthe exx-postt alphha; thhat iss, thee abnoormal returrn is the ddifferrence betweeen thhe acttual rreturnn and that prediicted by thhe SMLL. Wiithoutt infoormatiion abb

31、out tthe paarametters oof thiis equuationn (rissk-freee ratte andd markket raate off retuurn) wwe cannnot ddetermmine wwhich invesstor wwas moore acccuratte.b.If rrf = 6% and rM = 144%, thhen (uusing the nnotatiion allpha ffor thhe abnnormall retuurn): 1 = 199 66 + 1.5(14 6) = 199 188 = 1% 2 = 166 6

32、6 + 1(14 6) =16 14 = 2%Here, tthe seecond invesstor hhas thhe larrger aabnormmal reeturn and tthus aappearrs to be thhe supperiorr stocck sellectorr. Byy makiing beetter prediictionns, thhe seccond iinvesttor apppearss to hhave ttiltedd his portffolio towarrd undderpriiced sstockss.c.If rrf = 3% and

33、 rM = 155%, thhen: 1 =19 3 + 1.55(15 3) = 19 21 = 2% 2 = 166 33+ 1(115 33) = 16 15 = 1%Here, nnot onnly dooes thhe seccond iinvesttor apppear to bee the superrior sstock selecctor, but tthe fiirst iinvesttors prediictionns apppear vvaluelless (or woorse).27.In the zzero-bbeta CCAPM tthe zeero-beeta

34、poortfollio reeplacees thee riskk-freee ratee, andd thuss:E(r) = 8 + 00.6(177 8) = 133.4%28.a.Call the aaggresssive stockk A annd thee defeensivee stocck D. Betaa is tthe seensitiivity of thhe stoocks returrn to the mmarkett retuurn, ii.e., the cchangee in tthe sttock rreturnn per unit changge in th

35、e mmarkett retuurn. Thereefore, we ccomputte eacch stoocks beta by caalculaating the ddifferrence in itts retturn aacrosss the two sscenarrios ddivideed by the ddifferrence in thhe marrket rreturnn:With thhe twoo scennarioss equaally llikelyy, thee expeected returrn is an avveragee of tthe twwo poss

36、siblee outccomes:E(rA ) = 0.55 (22 + 388) = 118%E(rD ) = 0.55 (6 + 12) = 9%The SMLL is ddetermmined by thhe marrket eexpectted reeturn of 00.5(255 + 5) = 115%, wwith aa betaa of 11, andd the T-billl retturn oof 6% with a betta of zero. Seee the folloowing graphh.The equuationn for the ssecuriity maa

37、rket line is:E(r) = 6 + (15 6)Based oon itss riskk, thee aggrressivve stoock haas a rrequirred exxpecteed retturn oof:E(rA ) = 6 + 2.0(15 6) = 24%The anaalysts forrecastt of eexpectted reeturn is onnly 188%. TThus tthe sttockss alphha is: A = acctuallly exppectedd retuurn requiired rreturnn (givven

38、riisk)= 18% 24% = 6%Similarrly, tthe reequireed retturn ffor thhe deffensivve stoock iss:E(rD) = 6 + 0.3(115 66) = 88.7%The anaalysts forrecastt of eexpectted reeturn for DD is 99%, annd hennce, tthe sttock hhas a posittive aalpha: D = acctuallly exppectedd retuurn requiired rreturnn (givven riisk)=

39、 9 88.7 = +0.3%The poiints ffor eaach sttock pplot oon thee grapph as indiccated abovee.e.The hurdlle ratte is deterrminedd by tthe prrojectt betaa (0.33), noot thee firmms beeta. The ccorrecct disscountt ratee is 88.7%, the ffair rrate oof retturn ffor sttock DD.29.a.Agreee; Reggans concllusionn is

40、 ccorrecct. BBy deffinitiion, tthe maarket portffolio lies on thhe cappital markeet linne (CMML). Underr the assummptionns of capittal maarket theorry, alll porrtfoliios onn the CML ddominaate, iin a rrisk-rreturnn sensse, poortfollios tthat llie onn the Markoowitz efficcient fronttier bbecausse, gi

41、iven tthat lleveraage iss alloowed, the CCML crreatess a poortfollio poossibiility line that is hiigher than all ppointss on tthe effficieent frrontieer exccept ffor thhe marrket pportfoolio, whichh is RRainboows pportfoolio. Becaause EEagles porrtfoliio liees on the MMarkowwitz eefficiient ffrontii

42、er att a pooint oother than the mmarkett porttfolioo, Raiinbows porrtfoliio domminatees Eaggles portffolio.b.Unsyystemaatic rrisk iis thee uniqque riisk off indiividuaal stoocks iin a pportfoolio tthat iis divversiffied aaway bby hollding a welll-divversiffied pportfoolio. Totaal rissk is compoosed

43、oof sysstemattic (mmarkett) rissk andd unsyystemaatic (firm-speciific) risk.Disagreee; Wiilsons remmark iis inccorrecct. BBecausse botth porrtfoliios liie on the MMarkowwitz eefficiient ffrontiier, nneitheer Eaggle noor Raiinbow has aany unnsysteematicc riskk. Thherefoore, uunsysttematiic rissk doee

44、s nott expllain tthe diiffereent exxpecteed retturns. Thee deteerminiing faactor is thhat Raainboww liess on tthe (sstraigght) lline (the CCML) cconneccting the rrisk-ffree aasset and tthe maarket portffolio (Rainnbow), at tthe pooint oof tanngencyy to tthe Maarkowiitz effficieent frrontieer havving tthe hiighestt retuurn peer uniit of risk. Willsonss remaark iss alsoo counnteredd by tthe faact thhat, ssin