投资学第10版课后习题答案Chap007

Chapter7-OptimalRiskyPortfolios7-1Copyright©2014McGraw-HillEducation.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGraw-HillEducation.CHAPTER7:OPTIMALRISKYPORTFOLIOSPROBLEMSETS1.(a)and(e).Short-termratesandlaborissuesarefactorsthatarecommontoallfirmsandthereforemustbeconsideredasmarketriskfactors.Theremainingthreefactorsareuniquetothiscorporationandarenotapartofmarketrisk.2.(a)and(c).Afterrealestateisaddedtotheportfolio,therearefourassetclassesintheportfolio:stocks,bonds,cash,andrealestate.Portfoliovariancenowincludesavariancetermforrealestatereturnsandacovariancetermforrealestatereturnswithreturnsforeachoftheotherthreeassetclasses.Therefore,portfolioriskisaffectedbythevariance(orstandarddeviation)ofrealestatereturnsandthecorrelationbetweenrealestatereturnsandreturnsforeachoftheotherassetclasses.(Notethatthecorrelationbetweenrealestatereturnsandreturnsforcashismostlikelyzero.)3.(a)Answer(a)isvalidbecauseitprovidesthedefinitionoftheminimumvarianceportfolio.4.Theparametersoftheopportunitysetare:E(rS)=20%,E(rB)=12%,σS=30%,σB=15%,ρ=0.10Fromthestandarddeviationsandthecorrelationcoefficientwegeneratethecovariancematrix[notethat(,)SBSBCovrr]:BondsStocksBonds22545Stocks45900Theminimum-varianceportfolioiscomputedasfollows:wMin(S)=1739.0)452(22590045225)(Cov2)(Cov222BSBSBSB,rr,rrwMin(B)=10.1739=0.8261Theminimumvarianceportfoliomeanandstandarddeviationare:E(rMin)=(0.1739×.20)+(0.8261×.12)=.1339=13.39%σMin=2/12222)],(Cov2[BSBSBBSSrr=[(0.17392900)+(0.82612225)+(20.17390.826145)]1/2=13.92%Chapter7-OptimalRiskyPortfolios7-2Copyright©2014McGraw-HillEducation.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGraw-HillEducation.5.ProportioninStockFundProportioninBondFundExpectedReturnStandardDeviation0.00%100.00%12.00%15.00%17.3982.6113.3913.92minimumvariance20.0080.0013.6013.9440.0060.0015.2015.7045.1654.8415.6116.54tangencyportfolio60.0040.0016.8019.5380.0020.0018.4024.48100.000.0020.0030.00Graphshownbelow.0.005.0010.0015.0020.0025.000.005.0010.0015.0020.0025.0030.00TangencyPortfolioMinimumVariancePortfolioEfficientfrontierofriskyassetsCMLINVESTMENTOPPORTUNITYSETrf=8.006.Theabovegraphindicatesthattheoptimalportfolioisthetangencyportfoliowithexpectedreturnapproximately15.6%andstandarddeviationapproximately16.5%.Chapter7-OptimalRiskyPortfolios7-3Copyright©2014McGraw-HillEducation.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGraw-HillEducation.7.Theproportionoftheoptimalriskyportfolioinvestedinthestockfundisgivenby:222[()][()](,)[()][()][()()](,)SfBBfSBSSfBBfSSfBfSBErrErrCovrrwErrErrErrErrCovrr[(.20.08)225][(.12.08)45]0.4516[(.20.08)225][(.12.08)900][(.20.08.12.08)45]10.45160.5484BwThemeanandstandarddeviationoftheoptimalriskyportfolioare:E(rP)=(0.4516×.20)+(0.5484×.12)=.1561=15.61%σp=[(0.45162900)+(0.54842225)+(20.45160.5484×45)]1/2=16.54%8.Thereward-to-volatilityratiooftheoptimalCALis:().1561.080.4601.1654pfpErr9.a.Ifyourequirethatyourportfolioyieldanexpectedreturnof14%,thenyoucanfindthecorrespondingstandarddeviationfromtheoptimalCAL.TheequationforthisCALis:()().080.4601pfCfCCPErrErrIfE(rC)isequalto14%,thenthestandarddeviationoftheportfoliois13.04%.b.TofindtheproportioninvestedintheT-billfund,rememberthatthemeanofthecompleteportfolio(i.e.,14%)isanaverageoftheT-billrateandtheoptimalcombinationofstocksandbonds(P).LetybetheproportioninvestedintheportfolioP.ThemeanofanyportfolioalongtheoptimalCALis:()(1)()[()].08(.1561.08)CfPfPfEryryErryErrySettingE(rC)=14%wefind:y=0.7884and(1−y)=0.2119(theproportioninvestedintheT-billfund).Tofindtheproportionsinvestedineachofthefunds,multiply0.7884timestherespectiveproportionsofstocksandbondsintheoptimalriskyportfolio:Proportionofstocksincompleteportfolio=0.78840.4516=0.3560Chapter7-OptimalRiskyPortfolios7-4Copyright©2014McGraw-HillEducation.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGraw-HillEducation.Proportionofbondsincompleteportfolio=0.78840.5484=0.432310.Usingonlythestockandbondfundstoachieveaportfolioexpectedreturnof14%,wemustfindtheappropriateproportioninthestockfund(wS)andtheappropriateproportioninthebondfund(wB=1−wS)asfollows:0.14=0.20×wS+0.12×(1−wS)=0.12+0.08×wSwS=0.25Sotheproportionsare25%investedinthestockfundand75%inthebondfund.Thestandarddeviationofthisportfoliowillbe:σP=[(0.252900)+(0.752225)+(20.250.7545)]1/2=14.13%Thisisconsiderablygreaterthanthestandarddeviationof13.04%achievedusingT-billsandtheoptimalportfolio.11.a.Eventhoughitseemsthatgoldisdominatedbystocks,goldmightstillbeanattractiveassettoholdasapartofaportfolio.Ifthecorrelationbetweengoldandstocksissufficientlylow,goldwillbeheldasacomponentinaportfolio,specifically,theoptimaltangencyportfolio.Chapter7-OptimalRiskyPortfolios7-5Copyright©2014McGraw-HillEducation.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGraw-HillEducation.b.Ifthecorrelationbetweeng