金融学 博迪 第二版 课后答案(英文+中文翻译)\金融学 博迪 第二版 课后答案(英文PDF)\Bodie2_IM_Ch12

CHAPTER12-PortfolioOpportunitiesandChoiceEnd-of-ChapterProblems1.Analyzetheexpert’sanswerstothefollowingquestions:a.Question:Ihaveapproximatelyone-thirdofmyinvestmentsinstocks,andtherestinamoneymarket.Whatdoyousuggestasasomewhat“safer”placetoinvestanotherone-third?Iliketokeepone-thirdaccessibleforemergencies.Expert’sanswer:Well,youcouldtry1or2yearTreasurybonds.You’dgetalittlebitmoreyieldwithnorisk.b.Question:Wherewouldyouinvestifyouweretostarttoday?Expert’sanswer:Thatdependsonyourageandshort-termgoals.Ifyouareveryyoung–sayunder40–anddon’tneedthemoneyyou’reinvestingforahomeorcollegetuitionorsuch,youwouldputitinastockfund.Evenifthemarkettanks,youhavetimetorecoup.And,sofar,nothinghasbeatenstocksoveraperiodof10yearsormore.Butifyouaregoingtoneedmoneyfairlysoon,forahomeorforyourretirement,youneedtoplayitsafer.Solution:a.Youarenotgettingalittlebitmoreyieldwithnorisk.Therealvalueofthebondpayoffissubjecttoinflationrisk.Inaddition,ifyoueverneedtoselltheTreasurybondsbeforeexpiration,youaresubjecttothefluctuationofsellingpricecausedbyinterestrisk.b.Theexpertisrightinpointingoutthatyourinvestmentdecisiondependsonyourageandshort-termgoals.Inaddition,theinvestmentdecisionalsodependsonothercharacteristicsoftheinvestor,suchasthespecialcharacterofthelaborincome(whetheritishighlycorrelatedwiththestockmarketornot),andrisktolerance.Also,thefactthatoveranyperiodof10yearsormorethestockbeatseverythingelsecannotbeusedtopredictthefuture.2.Supposethatyour58-year-oldfatherworksfortheRuffyStuffedToyCompanyandhascontributedregularlytohiscompany-matchedsavingsplanforthepast15years.Ruffycontributes$0.50forevery$1.00yourfatherputsintothesavingsplan,uptothefirst6%ofhissalary.Participantsinthesavingsplancanallocatetheircontributionsamongfourdifferentinvestmentchoices:afixed-incomebondfund,a“blend”optionthatinvestsinlargecompanies,smallcompanies,andthefixed-incomebondfund,agrowth-incomemutualfundwhoseinvestmentsdonotincludeothertoycompanies,andafundwhosesoleinvestmentisstockintheRuffyStuffedToyCompany.OverThanksgivingvacation,Dadrealizesthatyouhavebeenmajoringinfinanceanddecidestoreapsomeearlyreturnsonthattuitionmoneyhe’sbeeninvestinginyoureducation.Heshowsyouthemostrecentquarterlystatementforhissavingsplan,andyouseethat98%ofitscurrentvalueisinthefourthinvestmentoption,thatoftheRuffyCompanystock.a.AssumethatyourDadisatypicalrisk-aversepersonwhoisconsideringretirementinfiveyears.Whenyouaskhimwhyhehasmadetheallocationinthisway,herespondsthatthecompanystockhascontinuallyperformedquitewell,exceptforafewdeclinesthatwerecausedbyproblemsinadivisionthatthecompanyhaslongsincesoldoff.Inaddition,hesays,manyofhisfriendsatworkhavedonethesame.Whatadvicewouldyougiveyourdadaboutadjustmentstohisplanallocations?Why?b.IfyouconsiderthefactthatyourdadworksforRuffyinadditiontohis98%allocationtotheRuffystockfund,doesthismakehissituationmorerisky,lessrisky,ordoesitmakenodifference?Why?Solution:a.DadhasexposedhimselftoriskbyconcentratingalmostallofhisplanmoneyintheRuffyStockfund.Thisisanalogoustotaking100%ofthemoneyafamilyhasputasideforinvestmentandinvestingitinasinglestock.First,Dadneedstobeshownthatjustbecausethecompanystockhascontinuallyperformedquitewellisnoguaranteethatitwilldosoindefinitely.Thecompanymayhavesoldoffthedivisionswhichproducedpricedeclinesinthepast,butfutureproblemsareunpredictable,andsoisthemovementofthestockprice.“Pastperformanceisnoguaranteeoffutureresults”isthelesson.Chapter12-1Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManualSecond,Dadneedstohearaboutdiversification.Heneedstobecounseledthathecanreducehisriskbyallocatinghismoneyamongseveraloftheoptionsavailabletohim.Indeed,hecanreducehisriskconsiderablymerelybymovingallofhismoneyintothe“blend”fundbecauseitisdiversifiedbydesign:ithasafixed-incomecomponent,alargecompaniescomponent,andasmallcompaniescomponent.Diversificationisachievednotonlyviathethreedifferingobjectivesofthesecomponents,butalsoviathenumerousstocksthatcompriseeachofthethreecomponents.Finally,Dad’sageandhisretirementplansneedtobeconsidered.Peoplenearingretirementagetypicallybegintoshiftthevalueoftheirportfoliosintosaferinvestments.“Safer”normallyconnoteslessvariability,sothattheriskofalargedeclineinthevalueofaportfolioisreduced.Thisdeclinecouldcomeatanytime,anditwouldbeveryunfortunateifitweretohappenthedaybeforeDadretires.Inthisexample,thesafestoptionwouldbethefixed-incomebondfundbecauseofitsdiversifiedcompositionandinterest-bearingdesign,butthereisstillriskexposuretoinflationandthelevelofinterestrates.Notethatthetax-deferrednatureofthesavingsplanencouragesallocationtosomethingthatproducesinterestordividends.Asitstandsnow,Dadisveryexposedtoalargedeclineinthevalueofhissavingsplanbecauseitisdependentonthevalueofonestock.Individualequitiesovertimehaveproventoproducethemostvariableofreturns,soDadshoulddefinitelymovesome,probablyatleasthalf,ofhismoneyoutoftheRuffystockfund.Infact,agoodrecommendationgivenhisretirementhorizonoffiveyearswouldbetore-aligntheportfoliosothatithas50%inthefixed-incomefundandtheremaining50%splitbetweentheRuffystockfund(sinceDadinsists)andthe“blend”fund.Or,maybe40%fixed-income,25%Ruffy,15%growth-incomefund,and20%“blend”fund.Thislatterallocationhastheadvantageofintroducinganotherincome-producingcomponentthatcanbeshieldedbythetax-deferredstatusoftheplan.b.ThefactthatDadisemployedbytheRuffyCompanymakeshissituationmorerisky.Let’ssaythatthecompanyhitsaperiodofslowedbusinessactivities.Ifthestockpricedeclines,sowillthevalueofDad’ssavingsplan.Ifthecompanyencountersenoughtrouble,itmayconsiderlayoffs.Dad’sjobmaybeinjeopardy.Atthesametimethathissavingsplanmaybedeclininginvalue,Dadmayalsoneedtolookforajoborgoonunemployment.Thus,Dadisexposedontwofrontstothesamerisk.Hehasinvestedbothhishumancapitalandhiswealthalmostexclusivelyinonecompany.3.SupposewedefineadatasetfromtheoutcomesoffootballgamesbetweenOhioStateandMichiganoverthepasthundredyears.Eachgamerepresentsanobservationandthewinnerofthegameisgivenavalueofonewiththelosergivenazerovalue.Assumingnoties,howdoyouinterprettheexpectedvaluescalculatedfromthedataseries?Whatwillthecorrelationbebetweenthetwoseries?Solution:Foreitherteamtheexpectedvaluefromthedataissimplytheteam'swinningpercentageintheseries,thatistheratioofthenumberoftheteam'stotalvictoriestothetotalnumberofgamesplayed.Thecorrelationwillbeperfectlynegative.Thecorrelationcoefficientwillbe-1.0asonlytwopossibledatapointsexist(0,1)and(1,0)andtheseplotexactlyonadownwardslopingline.4.DeterminethecorrelationbetweenpricemovementsofstockAandBusingtheforecastsoftheirrateofreturnandtheassessmentsofthepossiblestatesoftheworldinthefollowingtable.Beforedoingthecalculation,formanexpectationofwhetherthatcorrelationwillbecloserto1or-1bymerelyinspectingthenumbers.StateoftheStockA:StockB:EconomyProbabilityRateofReturnRateofReturnModeraterecession.05-.02-.20Slightrecession.15-.01-.102%growth.60.15.153%growth.20.15.30Chapter12-2Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManualSolution:Firstcalculatetheexpectedreturnsonthetwostocks:Pr:=Ra:=Rb:=4i12:=,..4iiiEr:=Pr⋅RaEr=0.11750a∑()iia5%−2%−20%i=115%−1%−10%460%15%15%Er:=Pr⋅RbEr=0.1250020%15%30%b∑()iibi=1Nextcalculatethestandarddeviations:4422σ:=⎡Pr⋅Ra−Er⎤σ=0.06503σ:=⎡Pr⋅Rb−Er⎤σ=0.13919a∑⎣i()ia⎦ab∑⎣i()ib⎦bi=1i=14σ:=Pr⋅Ra−Er⋅Rb−Erσ=0.00816ab∑⎣⎡i()ia()ib⎦⎤abi=1σabFinallythecorrelationcoefficientisgivenby:ρ:=ρ=0.9018σa⋅σb5.Giventheinformationbelowabouttherisksandreturnsoffivealternativeportfolios.Plottherisksandreturns.Whichdonotrepresentefficientportfolios?PortfolioExpectedReturnRiskI0.050II0.0750.12III0.0750.05IV0.0750.04V0.05.05Solution:ER:=Risk:=tt507.547.51267.55ERt4552OnlyportfoliosIandIVareefficient.0510RisktChapter12-3Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManual6.Iftherisk-rewardtrade-offlineforarisklessassetandariskyassetresultsinanegativeslope,whatdoesthatimplyabouttheriskyassetvis-a-vistherisklessasset?Solution:Atrade-offlinewithanegativeslopeindicatesthattheinvestoris“rewarded”withlessexpectedreturnfortakingonadditionalriskviaallocationtotheriskyasset.Ifthisweretrue,allriskaverseinvestorswouldinvestinonlytherisklessasset.7.Considertwoassetswithexpectedreturnsandriskgiveninthetablebelow.BlauZwartzMean.15.12StandardDeviation.10.08Iftheseassetreturnshaveacorrelationcoefficientof+0.5,whatistheriskandreturnofaportfolioequallydividedbetweenthetwosecurities?Whatmixofthetwosecuritiesproducestheportfoliohavingthelowestrisk?Whatlevelofriskisthis?Solution:LetBlauberepresentedasAsset1andZwartzasAsset2.Whenthecorrelationis+0.5wehavethefollowinginformation;Εr1:=15⋅%Εr2:=12⋅%σ1:=10⋅%σ2:=8%⋅ρ12:=0.5Aportfoliowith50%investedineachassetwillhaveexpectedreturnandriskof;Εr()w,Εr1,Εr2:=w⋅Εr1+()1w−⋅Εr2Εr50%(),Εr1,Εr2=0.135013.5%expectedreturn2222σ()w,σ1,σ2,ρ12:=w⋅σ1+()1w−⋅σ2+2w⋅⋅()1w−⋅ρ12⋅σ1⋅σ2σ()50%,σ1,σ2,ρ12=0.07817.81%riskTheminimumriskportfolioisfoundas:2σ2−σ1⋅σ2⋅ρ12wmin()σ1,σ2,ρ12:=22wmin()σ1,σ2,ρ12=0.2857Invest28.57%σ1+σ2−2⋅()σ1⋅σ2⋅ρ12inBlauand71.43%in1−28.57%=0.7143Zwartz.σ().2857,σ1,σ2,ρ12=0.07567.56%istheminimumlevelofriskChapter12-4Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManual8.Repeatthepreviousproblemwhenthetwoassetsareuncorrelated.Solution:Εr1:=15⋅%Εr2:=12⋅%σ1:=10⋅%σ2:=8%⋅ρ12:=0Aportfoliowith50%investedineachassetwillhaveexpectedreturnandriskof;Εr()w,Εr1,Εr2:=w⋅Εr1+()1w−⋅Εr2Εr50%(),Εr1,Εr2=0.135013.5%expectedreturn(sameasinthepreviousproblem2222σ()w,σ1,σ2,ρ12:=w⋅σ1+()1w−⋅σ2+2w⋅⋅()1w−⋅ρ12⋅σ1⋅σ2σ()50%,σ1,σ2,ρ12=0.06406.4%risk(lowerthaninthepreviousproblem)Theminimumriskportfolioisfoundas:2σ2−σ1⋅σ2⋅ρ12wσ,σ,ρ:=Invest39.02%min()121222wσ,σ,ρ=0.3902σ+σ−2⋅σ⋅σ⋅ρmin()1212inBlau(more12()1212thaninprevious1−39.02%=0.6098problem)and60.98%inZwartz(lessthaninpreviousσ().3902,σ1,σ2,ρ12=0.06256.25%istheminimumlevelofrisk(lessthaninthepreviousproblem)problem)9.ChallengeProblem:Supposewehavetworiskyassetswithuncorrelatedreturns[!=0].Supposethefirstassethaslevelsofexpectedreturnandriskequaltotwicetheleveloftheexpectedreturnandriskofthesecondassetorinotherwordsitofferstwicethelevelofexpectedreturnforbearingtwicethelevelofrisk[E(r1)=2$E(r2)"1=2$"2].InparticularassumeE(r2)=6%and"2=2%.Supposeyouwishtobearthesamelevelofriskasthatofferedbythesecondasset.Canyouconstructaportfoliocomprisedofbothassetswiththesameriskasthesecondassetbutahigherexpectedrateofreturn?Whatisthecompositionofthisportfolio?Howmuchofanexpectedreturnpremiumdoesthisportfolioofferoverthatofthesecondasset?Solution:Simplysettheportfoliorisklevelattheriskofthesecondassetandsolvefortheportfolioweight:root(σ()2%w4%,,2%,0−,w)=0.4000Thusinvest40percentinAsset1and(140%−=0.6000)=60%inAsset2.Thisproducesaportfoliowiththeriskof:σ(40%,4%,2%,0)=0.020SameriskasAsset2Andaexpectedreturnpremiumof:Εr()6%40%,12%,6%−=0.02402.4%overthereturnonAsset2.Chapter12-5Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManual10.Considertwouncorrelatedassetswithexpectedreturnsandriskgiveninthetablebelow.BlancRougeExpectedReturn.075.125StandardDeviation.05.075Amongtheportfoliosmadeupofpositiveinvestmentsinbothassetswhichareinefficienct?Solution:LetBlancbeAsset1andRougeAsset2.Findtheportfoliowiththeminimumrisk:Εr1:=7.5⋅%Εr2:=12.5⋅%σ1:=5%⋅σ2:=7.5⋅%ρ12:=0Theminimumriskportfolioisfoundas:2σ2−σ1⋅σ2⋅ρ12wmin()σ1,σ2,ρ12:=22wmin()σ1,σ2,ρ12=0.6923Theminimumriskσ1+σ2−2⋅()σ1⋅σ2⋅ρ12portfoliocontainsa69.23%investmentinBlancanda1−69.23%=0.3077=Theriskandexpectedreturnfromtheminimumriskportfolio30.77%investmentinRougeσ()wmin()σ1,σ2,ρ12,σ1,σ2,ρ12=0.0416Εr()69.23%,Εr1,Εr2=0.0904PortfolioRisk&Return4.16%σ10.19.04%Εrw(),Εr1,Εr2Εr1Return(Expected)0.0500.020.040.06σ()w,σ1,σ2,ρ12Risk(Std.Dev.)Soallportfolioswithmorethan69.23%investedinBlancwillbeinefficientsinceitwouldbepossibletoshiftfundsfromBlancintoRougeandincreaseexpectedreturnwhileloweringrisk.Chapter12-6Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManual11.Whentherisklessrateis0.04,assumetheoptimalcombinationofriskyassetsproducesaportfoliowithanexpectedrateofreturnequalto0.13andastandarddeviationof0.10.Alongtheefficienttradeoffline,thereward-to-riskratiowithhavewhatvalue?Supposeyouwishtotolerateonly¾oftheriskpresentintheoptimalriskyportfolio.Howmustyoudivideyouinvestmentbetweentheriskfreeassetandtheoptimalriskyportfolio?Whatexpectedrateofreturndoyouachieve?13%−4%Solution:Thereward-to-riskratioisequalto:=0.9000Soeachunitofriskborne(eachpercentof10%standarddeviation)increasesexpectedreturnby9/10thofonepercent.Thelevelofriskyoucantolerateis:75%⋅10%=0.07507.5%Lettingwbetheproportioninvestedintheriskfreeassetwecansolveforw:root[[(1−w)10%]−7.5%,w]=0.2500Letuschecktheresult.With25%intheriskfreeassettheriskoftheportfolioisgivenby:σ(25%,0,10%,0)=0.07507.5%Andtheexpectedreturnwillbe:25%⋅4%75%13+⋅%=0.107510.75%12.Referringtothepreviousquestion,supposeyourmotherpreferstotolerateagooddealofrisk.Infactshewishestobeartwicetheriskasofferedbytheoptimalriskyportfolio.Howcanshebuildaportfoliofromtheriskfreeassetandtheoptimalriskyportfoliowiththerisklevelshedesires?Whenshesatisfiesherappetiteforriskwhatwillbelevelofexpectedreturnonherportfolio?Solution:Thelevelofriskyourmothercantolerateis:200%⋅10%=0.200020%Lettingwbetheproportioninvestedintheriskfreeassetwecansolveforw:root[[(1−w)10%]−20%,w]=−1.0000Letuschecktheresult.With-100%intheriskfreeassettheriskoftheportfolioisgivenby:σ(−100%0,,10%,0)=0.200020%Andtheexpectedreturnwillbe:−100%4⋅%+200%⋅13%=0.220022%SotellMumtoborrowadollarforeachdollarshehastoinvestandputbothintotheriskyportfolio.Bydoingsosheshouldexpecta22%return.13.RefertoTable12.1inthetext.a.Performthecalculationstoverifythattheexpectedreturnsofeachoftheportfolios(F,G,H,J,S)inthetable(column4)arecorrect.b.Dothesameforthestandarddeviationsincolumn5ofthetable.Chapter12-7Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManualSolution:Table12.1fromthetextcontainsthefollowinginformation(wecalculatethefinaltwocolumnstoconfirm):Εr1:=14⋅%Εr2:=6%⋅σ1:=20⋅%σ2:=0%⋅ρ12:=0ProportionProportionExpectedRiskInvestedinInvestedinRateofReturn(StandardDeviation)PRiskyAssetRisklessAssetonPortfolioofPortfolioorw=1w−=Εrw(),Εr1,Εr2=σ()w,σ1,σ2,ρ12=t0.00001.00000.06000.0000f0.25000.75000.08000.0500ol0.50000.50000.10000.1000i0.75000.25000.12000.1500o1.00000.00000.14000.2000s14.Referingtothepreviousproblem,assumethatyouhave$1milliontoinvest.AllocatethemoneyasindicatedintheTable12.1foreachofthefiveportfoliosandcalculatetheexpecteddollarreturnofeachoftheportfolios.Whichoftheportfolioswouldsomeonewhoisextremelyrisktolerantbemostlikelytoselect?Solution:Thedollarreturnwouldbedefinedby:Dollar_return(w):=1000000⋅Εrw(),Εr1,Εr2Pow=Dollar_return()w=r0.000060000.0000Anextremelyrisk-tolerantpersonwouldt0.250080000.0000fselecttheportfoliowhichhasthelargesto0.5000100000.0000standarddeviationbutalsothelargestl0.7500120000.0000expectedreturn.InthisexamplethatisPortfolioS.i1.0000140000.0000osChapter12-8Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManualUsethefollowinginformationtoanswerQuestions15-19.SupposethatyouhavetheopportunitytobuystockinAT&TandMicrosoft.AT&TMicrosoftExpectedReturn.10.21StandardDeviation.15.2515.Whatistheminimum-risk(standarddeviation)portfolioofAT&TandMicrosoftifthecorrelationbetweenthetwostocksis0?0.5?1?-1?WhatdoyounoticeaboutthechangeintheallocationsbetweenAT&TandMicrosoftasthecorrelationcoefficientmovesfrom-1to0?to0.5?to+1?Whymightthisbe?Whatisthestandarddeviationofeachoftheseminimum-riskportfolios?Solution:Εr1:=10⋅%Εr2:=21⋅%σ1:=15⋅%σ2:=25⋅%ρ12:=−1wmin()σ1,σ2,ρ12=0.6250σ()wmin()σ1,σ2,ρ12,σ1,σ2,ρ12=0.0000PortfolioRisk&Returnσ1σ2Εr20.2Εrw(),Εr1,Εr2Return(Expected)0.1Εr100.10.2σ()w,σ1,σ2,ρ12Risk(Std.Dev.)ρ12:=0wmin()σ1,σ2,ρ12=0.7353σ()wmin()σ1,σ2,ρ12,σ1,σ2,ρ12=0.1286Chapter12-9Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManualPortfolioRisk&Returnσ1σ2Εr20.2Εrw(),Εr1,Εr2Return(Expected)0.1Εr100.10.2σ()w,σ1,σ2,ρ12Risk(Std.Dev.)ρ12:=.5wmin()σ1,σ2,ρ12=0.9211σ()wmin()σ1,σ2,ρ12,σ1,σ2,ρ12=0.1490PortfolioRisk&Returnσ1σ2Εr20.2Εrw(),Εr1,Εr2Return(Expected)0.1Εr100.10.2σ()w,σ1,σ2,ρ12Risk(Std.Dev.)ρ12:=1wmin()σ1,σ2,ρ12=2.5000σ()wmin()σ1,σ2,ρ12,σ1,σ2,ρ12=0.0000Chapter12-10Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManualPortfolioRisk&Returnσ1σ2Εr20.2Εrw(),Εr1,Εr2Return(Expected)0.1Εr100.10.2σ()w,σ1,σ2,ρ12Risk(Std.Dev.)Answer:Asthecorrelationmovesfrom-1to+1,theallocationtoAT&Tincrease.When2stockshavenegativecorrelation,standarddeviationcanbereduceddramaticallybymixingtheminaportfolio.Itistotheinvestor'sbenefittoweightmoreheavilythestockwithhehigherexpectedreturnsincethiswillproduceahigherportfolioexpectedreturnwhilethestandarddeviationoftheportfolioisdecreased.ThisiswhythehighestallocationtoMicrosoftisobservedforacorrelationof-1,anddecreasesasthecorrelationbecomespositiveandmovesto+1.Withcorrelationcloseto+1,thereturnsofthetwostockswillmovecloselytogether,soyouwanttoweightmostheavilythestockwiththelowerindividualstandarddeviation.16.Whatistheoptimalcombinationofthesetwosecuritiesinaportfolioforeachofthefourgivenvaluesofthecorrelationcoefficient,assumingtheexistenceofamoneymarketfundthatcurrentlypaysariskfree0.045?Doyounoticeanyrelationbetweentheseweightsandtheweightsfortheminimumvarianceportfolios?Whatisthestandarddeviationofeachoftheoptimalportfolios?Whatistheexpectedreturnofeachoftheoptimalportfolios?Solution:Letw1betheoptimalweightforAT&Tandw2theoptimalweightforMicrosoft.2()Er1−rf⋅σ2−()Er2−rf⋅ρ12⋅σ1⋅σ2w1()rf,Er1,Er2,σ1,σ2,ρ12:=⎡22⎤⎣()Er1−rf⋅σ2+()Er2−rf⋅σ1⎦−⎣⎡()Er1−rf+()Er2−rf⎦⎤⋅()ρ12⋅σ1⋅σ2w2()rf,Er1,Er2,σ1,σ2,ρ12:=1w−1()rf,Er1,Er2,σ1,σ2,ρ12Given:Er1:=10⋅%Er2:=21⋅%σ1:=15⋅%σ2:=25⋅%rf:=4.5⋅%ρ12:=−1w1()rf,Er1,Er2,σ1,σ2,ρ12=0.6250w2()rf,Er1,Er2,σ1,σ2,ρ12=0.3750Chapter12-11Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManualρ12:=0w1()rf,Er1,Er2,σ1,σ2,ρ12=0.4808w2(rf,Er1,Er2,σ1,σ2,ρ12)=0.5192ρ12:=0.5w1()rf,Er1,Er2,σ1,σ2,ρ12=0.1136w2()rf,Er1,Er2,σ1,σ2,ρ12=0.8864ρ12:=1w1()rf,Er1,Er2,σ1,σ2,ρ12=2.5000w2()rf,Er1,Er2,σ1,σ2,ρ12=−1.5000Thestandarddeviationsoftheseoptimalportfolioare:ρ12:=−1w1:=62.5⋅%σ()w1,σ1,σ2,ρ12=0.0000ρ12:=0w1:=48.08⋅%σ()w1,σ1,σ2,ρ12=0.1485ρ12:=0.5w1:=11.36⋅%σ()w1,σ1,σ2,ρ12=0.2306ρ12:=1w1:=250⋅%σ()w1,σ1,σ2,ρ12=0.0000Theexpectedreturnsoftheseoptimalportfolioare:ρ12:=−1w1:=62.5⋅%Εrw()1,Εr1,Εr2=0.1412ρ12:=0w1:=48.08⋅%Εrw()1,Εr1,Εr2=0.1571ρ12:=0.5w1:=11.36⋅%Εrw()1,Εr1,Εr2=0.1975ρ12:=1w1:=250⋅%Εrw()1,Εr1,Εr2=−0.065017.Derivetherisk-rewardtrade-offlinefortheoptimalportfoliowhenthecorrelationis0.5.Howmuchextraexpectedreturncanyouanticipateifyoutakeonanextraunitofrisk?Solution:Twopointsaretheriskfreerateof4.5%andtheoptimalportfoliowithriskof23.06%andexpectedreturnof19.75%.Sotherisk-rewardtrade-offlineisgivenby:19.75⋅%−4.5⋅%ER=4.5⋅%+⋅σER=0.045+.6613⋅σ23.06⋅%Chapter12-12Copyright©2009PearsonEducation,Inc.PublishingasPrenticeHall.FinancialEconomicsSolutionsManualPortfolioRisk&Returnσ1σ2Εr20.2Εrw(),Εr1,Εr24.5%+66.13%⋅σ()w,σ1,σ2,0.5Return(Expected)0.1Εr100.10.2σ()w,σ1,σ2,0.5Risk(Std.Dev.)18.UsingtheoptimalportfolioofAT&TandMicrosoftstockwhenthecorrelationoftheirpricemovementsis0.5,alongwiththeresultsofproblem17,determine:a.theexpectedreturnandstandarddeviationofaportfoliowhichinvests100%inamoneymarketfundreturningacurrentrateof4.5%.Whereisthispointontherisk-rewardtrade-offline?b.theexpectedreturnandstandarddeviationofaportfoliowhichinvests90%inthemoneymarketfundand10%intheportfolioofAT&TandMicrosoftstock.c.theexpectedreturnandstandarddeviationofaportfoliowhichinvests25%inthemoneymarketfundand75%intheportfolioofAT&TandMicrosoftstock.d.theexpectedreturnandstandarddeviationofaportfoliowhichinvests0%inthemoneymarketfundand100%intheportfolioofAT&TandMicrosoftstock.Whatpointisthis?Solution:a.Thisistheriskfreeinvestmentwitha4.5%returnandnorisk(zerostandarddeviation)anditistheverticalinterceptontherisk-rewardtrade-offline.b.With90%inthemoneymarketfund(w)and10%intheriskyportfolio(1-w)ofAT&Tstocktheexpectedreturnandriskaregivenby:rf:=4.5%Erp:=19.75%σp:=23.