罗斯公司理财第九版第十一章课后答案对应版

第十一章：收益和风险：资本资产定价模型1.系统性风险通常是不可分散的，而非系统性风险是可分散的。但是，系统风险是可以控制的，这需要很大的降低投资者的期望收益。2.（1）系统性风险（2）非系统性风险（3）都有，但大多数是系统性风险（4）非系统性风险（5）非系统性风险（6）系统性风险3.否，应在两者之间4.错误，单个资产的方差是对总风险的衡量。5.是的，组合标准差会比组合中各种资产的标准差小，但是投资组合的贝塔系数不会小于最小的贝塔值。6.可能为0，因为当贝塔值为0时，贝塔值为0的风险资产收益=无风险资产的收益，也可能存在负的贝塔值，此时风险资产收益小于无风险资产收益。7.因为协方差可以衡量一种证券与组合中其他证券方差之间的关系。8.如果我们假设，在过去3年市场并没有停留不变，那么南方公司的股价价格缺乏变化表明该股票要么有一个标准差或贝塔值非常接近零。德州仪器的股票价格变动大并不意味着该公司的贝塔值高，只能说德州仪器总风险很高。9.石油股票价格的大幅度波动并不表明这些股票是一个很差的投资。如果购买的石油股票是作为一个充分多元化的产品组合的一部分，它仅仅对整个投资组合做出了贡献。这种贡献是系统风险或β来衡量的。所以，是不恰当的。10.Thestatementisfalse.Ifasecurityhasanegativebeta,investorswouldwanttoholdtheassettoreducethevariabilityoftheirportfolios.Thoseassetswillhaveexpectedreturnsthatarelowerthantherisk-freerate.Toseethis,examinetheCapitalAssetPricingModel:E(RS)=Rf+S[E(RM)–Rf]IfS<0,thentheE(RS)<Rf11.Totalvalue=95($53)+120($29)=$8,515Theportfolioweightforeachstockis:WeightA=95($53)/$8,515=.5913WeightB=120($29)/$8,515=.408712.Totalvalue=$1,900+2,300=$4,200So,theexpectedreturnofthisportfoliois:E(Rp)=($1,900/$4,200)(0.10)+($2,300/$4,200)(0.15)=.1274or12.74%13.E(Rp)=.40(.11)+.35(.17)+.25(.14)=.1385or13.85%14.Herewearegiventheexpectedreturnoftheportfolioandtheexpectedreturnofeachassetintheportfolioandareaskedtofindtheweightofeachasset.Wecanusetheequationfortheexpectedreturnofaportfoliotosolvethisproblem.Sincethetotalweightofaportfoliomustequal1(100%),theweightofStockYmustbeoneminustheweightofStockX.Mathematicallyspeaking,thismeans:E(Rp)=.129=.16wX+.10(1–wX)WecannowsolvethisequationfortheweightofStockXas:.129=.16wX+.10–.10wXwX=0.4833So,thedollaramountinvestedinStockXistheweightofStockXtimesthetotalportfoliovalue,or:InvestmentinX=0.4833($10,000)=$4,833.33AndthedollaramountinvestedinStockYis:InvestmentinY=(1–0.4833)($10,000)=$5,166.6715.E(R)=.2(–.09)+.5(.11)+.3(.23)=.1060or10.60%16.E(RA)=.15(.06)+.65(.07)+.20(.11)=.0765or7.65%E(RB)=.15(–.2)+.65(.13)+.20(.33)=.1205or12.05%17.E(RA)=.10(–.045)+.25(.044)+.45(.12)+.20(.207)=.1019or10.19%方差=.10(–.045–.1019)⌒2+.25(.044–.1019)⌒2+.45(.12–.1019)⌒2+.20(.207–.1019)⌒2=.00535标准差=(.00535)1/2=.0732or7.32%18.E(Rp)=.15(.08)+.65(.15)+.20(.24)=.1575or15.75%Ifweownthisportfolio,wewouldexpecttogetareturnof15.75percent.19.a.Boom:E(Rp)=(.07+.15+.33)/3=.1833or18.33%Bust:E(Rp)=(.13+.03.06)/3=.0333or3.33%E(Rp)=.80(.1833)+.20(.0333)=.1533or15.33%b.Boom:E(Rp)=.20(.07)+.20(.15)+.60(.33)=.2420or24.20%Bust:E(Rp)=.20(.13)+.20(.03)+.60(.06)=–.0040or–0.40%E(Rp)=.80(.2420)+.20(.004)=.1928or19.28%P的方差=.80(.2420–.1928)⌒2+.20(.0040–.1928)⌒2=.0096820.a．Boom:E(Rp)=.30(.3)+.40(.45)+.30(.33)=.3690or36.90%Good:E(Rp)=.30(.12)+.40(.10)+.30(.15)=.1210or12.10%Poor:E(Rp)=.30(.01)+.40(–.15)+.30(–.05)=–.0720or–7.20%Bust:E(Rp)=.30(–.06)+.40(–.30)+.30(–.09)=–.1650or–16.50%E(Rp)=.20(.3690)+.35(.1210)+.30(–.0720)+.15(–.1650)=.0698or6.98%b．σp⌒2=.20(.3690–.0698)⌒2+.35(.1210–.0698)⌒2+.30(–.0720–.0698)⌒2+.15(–.1650–.0698)⌒2=.03312p的标准差=(.03312)⌒1/2=.1820or18.20%21.β=.25(.75)+.20(1.90)+.15(1.38)+.40(1.16)=1.2422.βp=1.0=1/3(0)+1/3(1.85)+1/3(βX)βX=1.1523.E(Ri)=Rf+[E(RM)–Rf]×βiE(Ri)=.05+(.12–.05)(1.25)=.1375or13.75%24.WearegiventhevaluesfortheCAPMexceptfortheofthestock.WeneedtosubstitutethesevaluesintotheCAPM,andsolvefortheofthestock.Oneimportantthingweneedtorealizeisthatwearegiventhemarketriskpremium.Themarketriskpremiumistheexpectedreturnofthemarketminustherisk-freerate.Wemustbecarefulnottousethisvalueastheexpectedreturnofthemarket.UsingtheCAPM,wefind:E(Ri)=.142=.04+.07βi则βi=1.4625.E(Ri)=.105=.055+[E(RM)–.055](.73)则E(RM)=.1235or12.35%26.E(Ri)=.162=Rf+(.11–Rf)(1.75).162=Rf+.1925–1.75Rf则Rf=.0407or4.07%27.a.E(Rp)=(.103+.05)/2=.0765or7.65%b.Weneedtofindtheportfolioweightsthatresultinaportfoliowithaof0.50.Weknowthe贝塔oftherisk-freeassetiszero.Wealsoknowtheweightoftherisk-freeassetisoneminustheweightofthestocksincetheportfolioweightsmustsumtoone,or100percent.So:c.Weneedtofindtheportfolioweightsthatresultinaportfoliowithanexpectedreturnof9percent.Wealsoknowtheweightoftherisk-freeassetisoneminustheweightofthestocksincetheportfolioweightsmustsumtoone,or100percent.So:d.Solvingfortheoftheportfolioaswedidinparta,wefind:18.ßp=wW(1.3)+(1–wW)(0)=1.3wWSo,tofindtheβoftheportfolioforanyweightofthestock,wesimplymultiplytheweightofthestocktimesitsβ.Eventhoughwearesolvingfortheandexpectedreturnofaportfolioofonestockandtherisk-freeassetfordifferentportfolioweights,wearereallysolvingfortheSML.Anycombinationofthisstockandtherisk-freeassetwillfallontheSML.Forthatmatter,aportfolioofanystockandtherisk-freeasset,oranyportfolioofstocks,willfallontheSML.WeknowtheslopeoftheSMLlineisthemarketriskpremium,sousingtheCAPMandtheinformationconcerningthisstock,themarketriskpremiumis:E(RW)=.138=.05+MRP(1.30)MRP=.088/1.3=.0677or6.77%So,nowweknowtheCAPMequationforanystockis:E(Rp)=.05+.0677*贝塔p29.E(RY)=.055+.068(1.35)=.1468or14.68%E(RZ)=.055+.068(0.85)=.1128or11.28%Reward-to-riskratioY=(.14–.055)/1.35=.0630Reward-to-riskratioZ=(.115–.055)/.85=.070630.(.14–Rf)/1.35=(.115–Rf)/0.85Wecancrossmultiplytoget:0.85(.14–Rf)=1.35(.115–Rf)Solvingfortherisk-freerate,wefind:0.119–0.85Rf=0.15525–1.35RfRf=.0725or7.25%31.32.[E(RA)–Rf]/A=[E(RB)–Rf]/ßBRPA/βA=RPB/βBβB/βA=RPB/RPA33.Boom:E(Rp)=.4(.20)+.4(.35)+.2(.60)=.3400or34.00%Normal:E(Rp)=.4(.15)+.4(.12)+.2(.05)=.1180or11.80%Bust:E(Rp)=.4(.01)+.4(–.25)+.2(–.50)=–.1960or–19.60%E(Rp)=.35(.34)+.40(.118)+.25(–.196)=.1172or11.72%σp⌒2=.35(.34–.1172)2+.40(.118–.1172)2+.25(–.196–.1172)2=.04190σp=(.04190)1/2=.2047or20.47%b.RPi=E(Rp)–Rf=.1172–.038=.0792or7.92%c．Approximateexpectedrealreturn=.1172–.035=.0822or8.22%1+E(Ri)=(1+h)[1+e(ri)]1.1172=(1.0350)[1+e(ri)]e(ri)=(1.1172/1.035)–1=.0794or7.94%Approximateexpectedrealriskpremium=.0792–.035=.0442or4.42%Exactexpectedrealriskpremium=(1.0792/1.035)–1=.0427or4.27%34.wA=$180,000/$1,000,000=.18wB=$290,000/$1,000,000=.29βp=1.0=wA(.75)+wB(1.30)+wC(1.45)+wRf(0)wC=.33655172InvestinStockC=.33655172($1,000,000)=$336,551.721=wA+wB+wC+wRf1=.18+.29+.33655172+wRfwRf=.19344828Investinrisk-freeasset=.19344828($1,000,000)=$193,448.2835.E(Rp)=.1070=wX(.172)+wY(.0875)+(1–wX–wY)(.055)βp=.8=wX(1.8)+wY(0.50)+(1–wX–wY)(0)wX=–0.11111wY=2.00000wRf=–0.88889InvestmentinstockX=–0.11111($100,000)=–$11,111.1136.E(RA)=.33(.082)+.33(.095)+.33(.063)=.0800or8.00%E(RB)=.33(–.065)+.33(.124)+.33(.185)=.0813or8.13%股票A：方差=.33(.082–.0800)⌒2+.33(.095–.0800)⌒2+.33(.063–.0800)⌒2=.00017标准差=(.00017)⌒1/2=.0131or1.31%股票B：方差=.33(–.065–.0813)⌒2+.33(.124–.0813)⌒2+.33(.185–.0813)⌒2=.01133标准差=(.01133)1/2=.1064or1064%Cov(A,B)=.33(.092–.0800)(–.065–.0813)+.33(.095–.0800)(.124–.0813)+.33(.063–.0800)(.185–.0813)=–.000472ρA,B=Cov(A,B)/（标准差A标准差B）=–.000472/(.0131)(.1064)=–.337337.E(RA)=.30(–.020)+.50(.138)+.20(.218)=.1066or10.66%E(RB)=.30(.034)+.50(.062)+.20(.092)=.0596or5.96%A的方差=.30(–.020–.1066)⌒2+.50(.138–.1066)⌒2+.20(.218–.1066)⌒2=.007782A的标准差=(.00778)⌒1/2=.0882or8.82%B的方差=.30(.034–.0596)⌒2+.50(.062–.0596)⌒2+.20(.092–.0596)⌒2=.00041B的标准差=(.00041)⌒1/2=.0202or2.02%Cov(A,B)=.30(–.020–.1066)(.034–.0596)+.50(.138–.1066)(.062–.0596)+.20(.218–.1066)(.092–.0596)=.001732ρA,B=Cov(A,B)/A的标准差*B的标准差=.001732/(.0882)(.0202)=.970138.a.E(RP)=wFE(RF)+wGE(RG)E(RP)=.30(.10)+.70(.17)=.1490or14.90%b.Thevarianceofaportfoliooftwoassetscanbeexpressedas:标准差=(.18675)⌒1/2=.4322or43.22%39.a.Theexpectedreturnoftheportfolioisthesumoftheweightofeachassettimestheexpectedreturnofeachasset,so:E(RP)=wAE(RA)+wBE(RB)=.45(.13)+.55(.19)=.1630or16.30%c.AsStockAandStockBbecomelesscorrelated,ormorenegativelycorrelated,thestandarddeviationoftheportfoliodecreases.40.(iv)Themarkethasacorrelationof1withitself.(v)Thebetaofthemarketis1.(vi)Therisk-freeassethaszerostandarddeviation.(vii)Therisk-freeassethaszerocorrelatio