投资学concept-check

CHAPTER51、a.Supposetherealinterestrateis3%peryearandtheexpectedinflationrateis8%.Whatisthenominalinterestrate?b.Supposetheexpectedinflationraterisesto10%,buttherealrateisunchanged.Whathappenstothenominalinterestrate?Solution:a.1+R=(1+i)(1+r)=(1.03)(1.08)=1.1124R=11.24%b.1+R=(1.03)(1.10)=1.133R=13.3%2、Abankoffersyoutwoalternativeinterestschedulesforasavingsaccountof$100,000lockedinfor3years:(a)amonthlyrateof1%;(b)anannually,continuouslycompoundedrate(rcc)of12%.Whichalternativeshouldyouchoose?Solution:a.EAR=(1+0.01)epx12-1=12.68%b.EAR=e12-1=12.75%ChoosethecontinuouslycompoundedrateforitshigherEAR.3、Youinvest$27000inacorporationbondsellingfor$900per$1000parvalue.Overthecomingyear,thebondwillpayinterestof$75per$1000ofparvalue.Thepriceofthebondatyear’sendwilldependonthelevelofinterestratesthatwillprevailatthattime.Youconstructthefollowingscenarioanalysis:InterestratesprobabilityYear-EndbondpriceHigh0.2$850Unchanged0.5$915low0.3$985YouralternativeinvestmentisaT-billthatyieldsasurerateofreturnof5%.CalculatetheHPRforeachscenario,theexpectedrateofreturn,andtheriskpremiumonyourinvestment.Whatistheexpectedend-of-yeardollarvalueofyourinvestment.Solution:Numberofbondsboughtis27,000/900=30InterestratesprobabilityYear-EndbondpriceHPREnd-of-YearValueHigh0.2$850（75+850）/900-1=0.0278(75+850)*30=$27750Unchanged0.5$9150.1$29700low0.3$9850.1778$31800Expectedrateofreturn0.1089Expectedend-of-yeardollarvalue$29940Riskpremium0.05894、Usingtheannualreturnsforyear2003-2005inSpreadsheet5.2,a.Computethearithmeticaveragereturn.b.Computethegeometricaveragereturn.c.Computethestandarddeviationofreturns.d.computetheSharperatioassumingtherisk-freeratewas6%peryear.Solution:a.Arithmeticreturn=(1/3)(0.2869)+(1/3)(0.1088)+(1/3)(0.0491)=14.83%;b.Geometricreturn=30.2869*0.1088*0.0491-1=14.39%;c.Standarddeviation=12.37%;d.Sharperatio=(14.83-6.0)/12.37=0.71;5、WhatistheprobabilitythatthereturnontheindexinExample5.10willbebelow-15%?Solution:Theprobabilityofamoreextremebadmonth,withreturnbelow-15%,ismuchlower:NORMDIST(-15,1,6,TRUE)=0.00383.Alternatively,wecannotethat-15%is16/6standarddeviationsbelowthemeanreturn,andthestandardnormalfunctiontocomputeNORMSDIST(-16/6)=0.003836、EstimatetheskewandkurtosisofthefiveratesinSpreadsheet5.2.Solution:IftheprobabilityinSpreadsheet5.2representedthetruereturndistribution,wewouldobtain:Skew=E[r(s)-E(r)]3/σ3=0.0931,Kurtosis=E[r(s)-E(r)]4/σ4-3=-1.2081Chapter61Assumethatdollar-denominatedT-billsintheUnitedStatesandpound-denominatedbillsintheUnitedKingdomofferequalyieldstomaturity.Bothareshort-termassets,andbotharefreeofdefaultrisk.Neitheroffersinvestorsariskpremium.However,aU.S.investorwhoholdsU.K.billsissubjecttoexchangeraterisk,becausethepoundsearnedontheU.K.billseventuallywillbeexchangedfordollarsatthefutureexchangerate.IstheU.S.investorengaginginspeculationorgambling?Theinvestoristakingonexchangerateriskbyinvestinginapound-denominatedasset.Iftheexchangeratemovesintheinvestor’sfavor,theinvestorwillbenefitandwillearnmorefromtheU.K.billthantheU.S.bill.Forexample,ifboththeU.S.andU.K.interestratesare5%,andthecurrentexchangerateis$2perpound,a$2investmenttodaycanbuy1pound,whichcanbeinvestedinEnglandatacertainrateof5%,forayear-endvalueof1.05pounds.Iftheyear-endexchangerateis$2.10perpound,the1.05poundscanbeexchangedfor1.05×$2.10＝$2.205forarateofreturnindollarsof1＋r=$2.205/$2=1.1025,orr=10.25%,morethanisavailablefromU.S.bills.Therefore,iftheinvestorexpectsfavorableexchangeratemovements,theU.K.billisaspeculativeinvestment.Otherwise,itisagamble.2Aportfoliohasanexpectedrateofreturnof20%andstandarddeviationof30%.T-billsofferasaferateofreturnof7%.Wouldaninvestorwithrisk-aversionparameterA=4prefertoinvestinT-billsortheriskyportfolio?WhatifA=2?FortheA=4investortheutilityoftheriskyportfolioisU=.20-(½×4×.32)=.02whiletheutilityofbillsisU=.07-(½×4×0)=.07Theinvestorwillpreferbillstotheriskyportfolio.(Ofcourse,amixtureofbillsandtheportfoliomightbeevenbetter,butthatisnotachoicehere.)EvenfortheA=2investor,theutilityoftheriskyportfolioisU=.20-(½×2×.32)=.11whiletheutilityofbillsisagain.07.Thelessrisk-averseinvestorpreferstheriskyportfolio.3.a.HowwilltheindifferencecurveofalessriskaverseinvestorcomparetotheindifferencecurvedrawninFigure6.2?b.DrawbothindifferencecurvespassingthroughpointP.Thelessrisk-averseinvestorhasashallowerindifferencecurve.Anincreaseinriskrequireslessincreaseinexpectedreturntorestoreutilitytotheoriginallevel.4Whatwillbethedollarvalueofyourpositioninequities(E),anditsproportioninyouroverallportfolio,ifyoudecidetohold50%ofyourinvestmentbudgetinReadyAsset?Holding50%ofyourinvestedcapitalinReadyAssetsmeansthatyourinvestmentproportionintheriskyportfolioisreducedfrom70%to50%.Yourriskyportfolioisconstructedtoinvest54%inEand46%inB.ThustheproportionofEinyouroverallportfoliois.5×54%=27%,andthedollarvalueofyourpositioninEis$300,000×.27=$81,000.5.Canthereward-to-volatility(Sharpe)ratio,S=[E(rC)_rf]/δC,ofanycombinationoftheriskyassetandtherisk-freeassetbedifferentfromtheratiofortheriskyassettakenalone,[E(rP)-rf]/δP,whichinthiscaseis.36?In