博迪投资学答案chap009-7thed

1、9-PAGE14般CHAPTER半 9: THE把 CAPITA袄L ASSET癌 PRICIN霸G MODEL1.c.鞍2.暗隘d.唉袄From CA板PM, the鞍 fair e扮xpected癌 return哎 = 8 + 翱1.25(15坝 蔼 8) = 1捌6.75%坝Actuall袄y expec颁ted ret般urn = 1爸7%按 = 17 凹 16.75 巴= 0.25%拌3.岸哎Since t啊he stoc傲ks bet肮a is eq盎ual to 矮1.2, it哀s expec扳ted rat柏e of re矮turn is鞍:白6 + 1.斑2 伴 (16 笆

2、6) = 1霸8%吧4.伴俺The ser叭ies of 翱$1,000 绊payment背s is a 暗perpetu搬ity. I暗f beta 盎is 0.5,稗 the ca胺sh flow碍 should拜 be dis板counted百 at the唉 rate:板6 + 0.败5 埃 (16 俺6) = 1白1%蔼PV = $1哎,000/0.背11 = $9疤,090.91笆If, how板ever, b佰eta is 挨equal t傲o 1, th绊en the 懊investm翱ent sho耙uld yie扒ld 16%,办 and th把e price瓣 paid

3、f昂or the 埃firm sh胺ould be邦:爸PV = $1挨,000/0.奥16 = $6哎,250扒The dif俺ference挨, $2,84斑0.91, i爱s the a皑mount y稗ou will昂 overpa般y if yo肮u erro霸neously巴 assume俺 that b啊eta is 摆0.5 rat爸her tha稗n 1.扮5.胺隘Using t岸he SML:八 4 = 6 扒+ 般(16 6板) 扮 啊 = 2/1熬0 = 0.盎26.a.哎7斑.爱肮E(r哎P白)肮 = r肮f靶 + 氨 P 懊E(r阿M 巴) r叭f 凹挨18 = 6

4、 百+ 埃 P坝(14 6柏) 暗 按 P板 = 12/8霸 = 1.5搬8.扒奥a.敖熬False. 办 捌 = 0 im俺plies E扳(r) = r拌f 斑, not z埃ero.笆False. 稗 Inves昂tors re暗quire a跋 risk p瓣remium 埃only fo爸r beari般ng syst稗ematic 哀(undive百rsifiab柏le or m昂arket) 坝risk. 隘Total v伴olatili懊ty incl跋udes di摆versifi哀able ri氨sk.稗False. 澳 Your p俺ortfoli案o shoul败d b

5、e in办vested 爸75% in 佰the mar般ket por哀tfolio 拜and 25%案 in T-b坝ills. 背Then:搬P哀 = (0.7盎5 百 哀1) + (0般.百25 暗 爸0) = 0.吧75罢9.搬柏Not pos扒sible. 八 Portfo盎lio A h暗as a hi吧gher be扮ta than翱 Portfo疤lio B, 斑but the绊 expect败ed retu坝rn for 拌Portfol凹io A is般 lower 爸than th胺e expec哀ted ret哀urn for爸 Portfo挨lio B. 爱 Thu

6、s, 爱these t拜wo port懊folios 瓣cannot 斑exist i翱n equil挨ibrium.拜10.板哀Possibl鞍e. If 耙the C凹APM is 霸valid, 翱the exp巴ected r袄ate of 皑return 案compens艾ates on办ly for 班systema吧tic (ma奥rket) r板isk, re凹present爸ed by b耙eta, ra奥ther th隘an for 傲the sta扮ndard d啊eviatio叭n, whic埃h inclu癌des non跋systema唉tic ris爱k. Thu

7、叭s, Port版folio A拔s lowe袄r rate 懊of retu白rn can 拜be pair鞍ed with矮 a high跋er stan隘dard de按viation班, as lo挨ng as A白s beta百 is les捌s than 巴Bs.矮11.扳白Not pos办sible. 罢 The re昂ward-to盎-variab白ility r熬atio fo碍r Portf熬olio A 摆is bett阿er than爸 that o哀f the m鞍arket. 摆 This s耙cenario跋 is imp伴ossible岸 accord扮ing

8、to 颁the CAP澳M becau办se the 拜CAPM pr唉edicts 翱that th碍e marke白t is th氨e most 澳efficie芭nt port唉folio. 佰 Using 笆the num背bers su罢pplied:氨Portfol奥io A pr斑ovides 盎a bette百r risk-艾reward 澳tradeof佰f than 敖the mar哎ket por凹tfolio.拜12.埃拜Not pos啊sible. 癌 Portfo败lio A c挨learly 芭dominat肮es the 哎market 唉portfol摆io.

9、 Po挨rtfolio唉 A has 澳both a 斑lower s瓣tandard矮 deviat岸ion and碍 a high瓣er expe摆cted re叭turn.坝13.霸爱Not pos肮sible. 俺 The SM盎L for t敖his sce哎nario i岸s: E(r)扮 = 10 +俺 板(18 1伴0)昂Portfol案ios wit哎h beta 熬equal t扮o 1.5 h阿ave an 八expecte挨d retur隘n equal拜 to:白E(r) = 跋10 + 1罢.5 爸 艾(18 1爸0) = 2胺2%八The exp把ected r柏

10、eturn f霸or Port板folio A邦 is 16%拔; that 柏is, Por板tfolio 柏A plots爸 below 袄the SML扮 (奥 A搬 = 6%)摆, and h哀ence, i佰s an ov霸erprice俺d portf埃olio. 案Thi阿s is in绊consist捌ent wit澳h the C奥APM.翱14.拌扒Not pos盎sible. 案 The SM碍L is th熬e same 案as in P啊roblem 版1佰3爸. Here隘, Portf摆olio A版s requi八red ret败urn is:柏 10 + (熬

11、0.9 矮 氨8) = 17办.2%傲This is暗 greate扳r than 跋16%. P澳ortfoli蔼o A is 版overpri斑ced wit绊h a neg捌ative a胺lpha:阿 A哀 = 1.2拜%懊15.奥板Possi拌ble. T袄he CML 罢is the 瓣same as巴 in Pro坝blem 矮11熬. Port凹folio A柏 plots 把below t岸he CML,白 as any邦 asset 绊is expe背cted to氨. This爱 scenar八io is n岸ot inco邦nsisten熬t with 敖the CAP

12、笆M.颁16.埃癌If the颁 securi蔼tys co芭rrelati办on coef颁ficient皑 with t笆he mark蔼et port胺folio d扮oubles 捌(with a版ll othe般r varia般bles su鞍ch as v班ariance啊s uncha捌nged), 唉then be安ta, and敖 theref氨ore the凹 risk p伴remium,班 will a般lso dou岸ble. T瓣he curr蔼ent ris盎k premi傲um is: 敖14 6 艾= 8%袄The new鞍 risk p板remium 盎wou

13、ld b胺e 16%, 伴and the埃 new di奥scount 拌rate fo拜r the s啊ecurity拜 would 颁be: 16 耙+ 6 = 2拔2%哀If the 般stock p奥ays a c办onstant熬 perpet拌ual div氨idend, 鞍then we暗 know f凹rom the俺 origin芭al data般 that t背he divi隘dend (D袄) must 背satisfy挨 the eq笆uation 版for the暗 presen靶t value拔 of a p罢erpetui皑ty:般Price =敖 Divide板

14、nd/Disc挨ount ra邦te澳50 = D/敖0.14 巴 D = 50罢 安 0.14 =隘 $7.00哎At the 拜new dis扳count r熬ate of 颁22%, th跋e stock挨 would 绊be wort拜h: $7/0叭.22 = $胺31.82艾The inc阿rease i胺n stock罢 risk h艾as lowe埃red its拔 value 斑by 36.3绊6%.17.d.俺18.奥败a.唉稗Since t皑he mark胺et port盎folio, 办by defi氨nition,碍 has a 白beta of罢 1, its般 e

15、xpect岸ed rate笆 of ret佰urn is 按12%.八= 0 mea氨ns no s氨ystemat疤ic risk熬. Henc巴e, the 挨stocks搬 expect斑ed rate唉 of ret哀urn in 瓣market 肮equilib啊rium is哎 the ri皑sk-free斑 rate, 颁5%.啊Using t板he SML,拜 the 懊fair板 expect碍ed rate柏 of ret扮urn for翱 a stoc矮k with 扒= 0.5 邦is:懊E(r) = 奥5 + (百0.5)(12岸 5) 叭= 1.5%版The 佰ac

16、tuall办y袄 expe碍cted ra盎te of r拌eturn, 靶using t拜he expe凹cted pr氨ice and摆 divide隘nd for 哎next ye安ar is:芭E(r) = 癌($41 +半 $1)/40稗 1 =八 0.10 =拔 10%瓣Because艾 the ac昂tually 疤expecte胺d retur哎n excee氨ds the 爱fair re版turn, t艾he stoc扮k is un翱derpric拌ed.肮19.稗叭a.绊懊E(r背P阿)捌 = r捌f背 + 熬 P 背E(r斑M 熬) r艾f 拜 = 5% 班+ 0.8

17、 (阿15% 5艾%) = 13昂%爸 = 14% 昂 13% = 邦1%扳You sho斑uld inv把est in 八this fu疤nd beca隘use alp盎ha is p跋ositive胺.摆b.捌啊The pas办sive po扳rtfolio疤 with t挨he same昂 beta a耙s the f安und sho艾uld be 袄investe爸d 80% i扮n the m啊arket-i拌ndex po爸rtfolio佰 and 20斑% in th啊e money摆 market巴 accoun佰t. For傲 this p阿ort暗folio:拔E(r熬P按

18、) = (0.搬8 15%办) + (0.奥2 5%)安 = 13%把14% 1澳3% = 1%氨 = 爱 袄20.罢傲d.案拔You ne邦ed to k扒now the按 risk-f板ree rat按e唉21.奥胺d.佰案You ne伴ed to k盎now the挨 risk-f半ree rat伴e22.a.版Expecte板d Retur班n跋Alpha半Stock X扳5% + 0.拌8(14% 拜 5%) = 埃12.2%俺14.0% 柏 12.2% 挨= 1.8%熬Stock 坝Y拔5% + 1.哎5(14% 拔 5%) = 埃18.5%耙17.0% 佰 18.5% 蔼= 熬1

19、.5%伴i. Kay 癌should 鞍recomme扒nd Stoc芭k X bec搬ause of奥 its po爱sitive 百alpha, 鞍compare安d to St爱ock Y, 熬which h吧as a ne啊gative 澳alpha. 罢 In gra俺phical 版terms, 板the exp霸ected r艾eturn/r拌isk pro佰file fo挨r Stock邦 X plot鞍s above翱 the se稗curity 版market 般line (S哀ML), wh昂ile the扒 profil伴e for S捌tock Y 肮plots b盎

20、elow th班e SML. 跋 Also, 霸dependi暗ng on t巴he indi疤vidual 唉risk pr败eferenc绊es of K八ays cl半ients, 芭the low摆er beta奥 for St八ock X m奥ay have伴 a bene扳ficial 跋effect 叭on over扳all por岸tfolio 傲risk.绊ii. Kay靶 should爱 recomm坝end Sto板ck Y be艾cause i蔼t has h傲igher f捌orecast颁ed retu爸rn and 巴lower s百tandard稗 deviat

21、靶ion tha傲n Stock霸 X. Th盎e respe柏ctive S邦harpe r盎atios f疤or Stoc爸ks X an般d Y and跋 the ma澳rket in癌dex are懊:安Stock X俺:斑八(14% 疤 5%)/36笆% = 0.2熬5爱Stock Y澳:稗搬(17% 坝 5%)/25奥% = 0.4拜8坝Market 拔index:案八(14% 版 5%)/15捌% = 0.6翱0按The mar阿ket ind唉ex has 颁an even伴 more a胺ttracti啊ve Shar翱pe rati隘o than 颁either 班of t

22、he 碍individ芭ual sto绊cks, bu跋t, give唉n the c爸hoice b办etween 跋Stock X办 and St昂ock Y, 叭Stock Y坝 is the凹 superi搬or alte拌rnative癌.拌When a 稗stock i坝s held 澳as a si柏ngle st般ock por败tfolio,傲 standa扮rd devi敖ation i班s the r埃elevant爱 risk m熬easure.摆 For s安uch a p澳ortfoli氨o, beta扒 as a r澳isk mea柏sure is把 irrele

23、傲vant. 般Althoug白h holdi暗ng a si挨ngle as班set is 颁not a t把ypicall胺y recom跋mended 暗investm把ent str岸ategy, 办some in邦vestors搬 may ho耙ld what隘 is ess蔼entiall白y a sin哀gle-ass昂et port瓣folio w氨hen the颁y hold 柏the sto矮ck of t白heir em般ployer 班company扮. For 佰such in碍vestors隘, the r佰elevanc把e of st岸andard 昂devia

24、ti埃on vers板us beta癌 is an 邦importa爸nt issu摆e.吧2靶3.罢昂The app般ropriat俺e disco笆unt rat肮e for t捌he proj八ect is:澳r拌f俺 + 败E(r熬M 奥) r柏f 爸 = 8 +邦 1.8 捌 (16 拌8) = 2哀2.4%百Using t伴his dis稗count r安ate:隘 = 400绊 pesos 碍+ 150 柏pesos 坝 Annuit氨y facto俺r (22.4巴%, 10 y鞍ears) =哎 180.92懊 pesos版The int鞍ernal r般ate of 熬re

25、turn 碍(IRR) f败or the 笆project百 is 35.扳73%. R拜ecall f暗rom you板r int岸roducto埃ry fina捌nce cla岸ss that傲 NPV is笆 positi把ve if I笆RR di暗scount 皑rate (o啊r, equi八valentl版y, hurd哀le rate岸). The艾 highes哀t value懊 that b奥eta can芭 take b摆efore t吧he hurd巴le rate百 exceed袄s the I翱RR is d氨etermin爸ed by:案35.73 =挨 8 +

26、邦(16 8背) 胺 芭 = 27.7哎3/8 = 3柏.47拜24.傲把a.翱耙McKay s暗h鞍ould bo芭rrow fu盎nds and办 invest百 those 袄funds p捌roporti白onately板 in 背Murray拜s exis唉ting po碍rtfolio八 (i.e.,癌 buy mo佰re risk奥y asset胺s on ma傲rgin). 俺 In add艾ition t捌o incre疤ased ex安pected 搬return,柏 the al叭ternati伴ve port笆folio o耙n the c敖apital 把market

27、 罢line wi鞍ll also颁 have i俺ncrease八d risk,俺 which 蔼is caus绊ed by t白he high唉er prop霸ortion 百of risk唉y asset白s in th皑e total盎 portfo碍lio.奥b.败埃McKay s暗hould s熬ubstitu八te low 盎beta st耙ocks fo案r high 肮beta st芭ocks in袄 order 颁to redu拔ce the 百overall跋 beta o坝f 办York胺s port唉folio. 柏 By red敖ucing t柏he over肮al

28、l por隘tfolio 佰beta, M拜cKay wi败ll redu半ce the 隘systema凹tic ris背k of th挨e portf挨olio, a敖nd ther奥efore r叭educe i拔ts vola霸tility 翱relativ佰e to th盎e marke百t. The癌 securi暗ty mark傲et line唉 (SML) 哀suggest笆s such 半action 袄(i.e., 岸moving 靶down th暗e SML),扳 even t斑hough r爱educing笆 beta m般ay resu埃lt in a伴 slight

29、哀 loss o绊f portf阿olio ef傲ficienc摆y unles搬s full 瓣diversi霸ficatio按n is ma笆intaine埃d. 俺York扮s prim盎ary obj八ective,艾 howeve版r, is n般ot to m阿aintain拜 effici白ency, b般ut to r伴educe r鞍isk exp拜osure; 百reducin板g portf绊olio be阿ta meet罢s that 埃objecti把ve. Be版cause 岸York哀 does n版ot want板 to eng邦age in 癌borrowi懊

30、ng or l般ending,拜 熬McKay c颁annot r跋educe r埃isk by 肮selling矮 equiti班es and 班using t般he proc巴eeds to澳 buy ri伴sk-free隘 assets碍 (i.e.,般 lendin版g part 袄of the 扳portfol按io).25.d.坝26.敖傲r半1安 = 19%;盎 r肮2稗 = 16%;背 安1伴 = 1.5;把 安2斑 = 1霸a.傲搬To dete百rmine w懊hich in澳vestor 罢was a b案etter s绊elector唉 of ind敖ividual爸

31、stocks盎 版we look哀 at abn巴ormal r靶eturn, 耙which i挨s the e蔼x-post 肮alpha; 爸that is懊, the a罢bnormal背 return半 is the拌 differ吧ence be爱tween t笆he actu暗al retu半rn and 靶that pr奥edicted挨 by the爸 SML. 颁Without伴 inform瓣ation a办bout th胺e param瓣eters o敖f this 俺equatio奥n (risk昂-free r版ate and挨 market笆 rate o霸f re

32、tur隘n) we c斑annot d柏etermin拌e which半 invest白or was 皑more ac罢curate.案b.拌碍If r耙f爸 = 6% a斑nd r败M昂 = 14%,瓣 then (艾using t阿he nota捌tion al霸pha for笆 the ab拜normal 肮return)笆:跋 1伴 = 19 哀 6 + 1碍.5(14 靶 6) = 胺19 18肮 = 1%岸 2吧 = 16 澳 6 + 1颁(14 6版) =16 巴 14 = 鞍2%奥Here, t柏he seco爱nd inve跋stor ha皑s the l盎arger a爱b

33、normal翱 return懊 and th扒us appe班ars to 笆be the 傲superio矮r stock疤 select叭or. By爸 making胺 better胺 predic把tions, 凹the sec傲ond inv佰estor a哎ppears 皑to 办have ti癌lted hi胺s portf搬olio to斑ward un埃derpric埃ed stoc颁ks.敖c.鞍把If r凹f扳 = 3% a霸nd r拜M扮 = 15%,哎 then:拌 1邦 =19 巴3 + 1.爸5(15 奥3) = 1疤9 21 鞍= 2%盎 2板 = 16 熬 3+

34、 1(扮15 3)敖 = 16 氨 15 = 岸1%暗Here, n昂ot only哎 does t半he seco半nd inve艾stor ap般pear to坝 be the笆 superi百or stoc案k selec邦tor, b埃ut the 扮first i叭nvestor板s pred拜ictions癌 appear奥 valuel凹ess (or八 worse)俺.癌27.笆疤In the 隘zero-be挨ta CAPM班 the ze搬ro-beta翱 portfo搬lio rep懊laces t鞍he risk扳-free r拜ate, an哎d thus:叭E(r)

35、 = 懊8 + 0.6叭(17 8瓣) = 13.捌4%拔28拔.澳癌a.跋盎Call th扮e aggre坝ssive s巴tock A 疤and the熬 defens把ive sto颁ck D. 靶Beta is阿 the se隘nsitivi挨ty of t半he stoc巴ks ret哀urn to 爸the mar靶ket ret坝urn, i.疤e., the叭 cha懊nge in 氨the sto敖ck retu笆rn per 背unit ch爱ange in蔼 the ma半rket re俺turn. 哀Therefo蔼re, we 挨compute盎 each s伴toc

36、ks 靶beta by跋 calcul捌ating t绊he diff啊erence 搬in its 懊return 办across 氨the two熬 scenar耙ios div翱ided by暗 the di暗fferenc白e in th翱e marke霸t retur白n:叭With th班e two s熬cenario熬s equal暗ly like瓣ly, the吧 expect背ed retu啊rn is a癌n avera袄ge of t哀he two 艾possibl佰e outco碍mes:翱E(r捌A 癌) = 0.5颁 胺 (2 + 绊38) = 1挨8%捌E(r扮D

37、 奥) = 0.5耙 败 (6 + 1盎2) = 9%靶The SML搬 is det把ermined案 by the翱 market扳 expect隘ed retu爱rn of 癌0.5(25 爸+ 5) =盎 15%, w靶it啊h a bet哀a of 1,坝 and th颁e T-bil傲l retur盎n of 6%吧 with a阿 beta o哎f zero.皑 See t袄he foll颁owing g版raph.绊The equ芭ation f袄or the 傲securit稗y marke皑t line 捌is:笆E罢(r)癌 = 6 + 八(15 6氨)版Based o皑

38、n its r拜isk, th坝e aggre蔼ssive s耙tock ha爱s a req案uired e凹xpected肮 return碍 of:哎E(r按A 澳) = 6 +坝 2.0(15霸 6) =挨 24%爸The ana翱lysts 阿forecas瓣t of ex摆pected 伴return 跋is only叭 18%. 跋Thus th俺e stock跋s alph哀a is:安 A八 = actu般ally ex板pected 办return 艾 requi罢red ret扒urn (gi捌ven ris版k)爱= 18% 叭 24% = 罢6%芭Similar艾ly,

39、 the摆 requir阿ed retu拜rn for 败the def摆ensive 安stock i熬s般:奥E(r百D罢) = 6 +半 0.3(15懊 6) =笆 8.7%笆The ana袄lysts 跋forecas爸t of ex吧pected 熬return 翱for D i耙s 9%, a扮nd henc绊e, the 摆stock h把as a po按sitive 巴alpha:按 D爱 = actu背ally ex柏pected 安return 罢 requi傲red ret摆urn (gi伴ven ris颁k)摆= 9 8半.7 = +0熬.3%哎The poi邦nts

40、for邦 each s傲tock pl艾ot on t案he grap氨h a俺s indic绊ated ab阿ove.爱e.埃凹The hur敖dle rat唉e is de巴termine摆d by th叭e proje啊ct beta笆 (0.3),柏 not th靶e firm把s beta.耙 The c昂orrect 奥discoun哀t rate 按is 8.7%敖, the f般air rat败e of re半turn fo鞍r stock稗 D.斑29半.阿隘a.跋昂Agree; 耙Regans敖 conclu半sion is百 correc拜t. By 埃definit吧i

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