投资学 第8版 英文 (博迪 凯恩 马库斯 著) 机械工业出版社 课后答案 309页

'课后答案网：www.hackshp.cn课后答案网您最真诚的朋友www.hackshp.cn网团队竭诚为学生服务，免费提供各门课后答案，不用积分，甚至不用注册，旨在为广大学生提供自主学习的平台！课后答案网：www.hackshp.cn视频教程网：www.efanjy.comPPT课件网：www.ppthouse.com课后答案网www.hackshp.cn若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter01-TheInvestmentEnvironmentCHAPTER1:THETHEINVESTMENTINVESTMENTINVESTMENTENVIRONMENTENVIRONMENTPROBLEMPROBLEMSETSSETS1.Ultimately,itistruethatrealassetsdeterminethematerialwellbeingofaneconomy.Nevertheless,individualscanbenefitwhenfinancialengineeringcreatesnewproductsthatallowthemtomanagetheirportfoliosoffinancialassetsmoreefficiently.Becausebundlingandunbundlingcreatesfinancialproductswithnewpropertiesandsensitivitiestovarioussourcesofrisk,itallowsinvestorstohedgeparticularsourcesofriskmoreefficiently.2.Securitizationrequiresaccesstoalargenumberofpotentialinvestors.Toattracttheseinvestors,thecapitalmarketneeds:(1)asafesystemofbusinesslawsandlowprobabilityofconfiscatorytaxation/regulation;(2)awell-developedinvestmentbankingindustry;(3)awell-developedsystemofbrokerageandfinancialtransactions,and;(4)well-developedmedia,particularlyfinancialreporting.Thesecharacteristicsarefoundin(indeedmakefor)awell-developedfinancialmarket.3.Securitizationleadstodisintermediation;thatis,securitizationprovidesameansformarketparticipantstobypassintermediaries.Forexample,mortgage-backedsecuritieschannelfundstothehousingmarketwithoutrequiringthatbanksorthriftinstitutionsmakeloansfromtheirownportfolios.Assecuritizationprogresses,financial课后答案网intermediariesmustincreaseotheractivitiessuchasprovidingshort-termliquiditytoconsumersandsmallbusiness,andfinancialservices.4.Financialassetsmakewww.hackshp.cniteasyforlargefirmstoraisethecapitalneededtofinancetheirinvestmentsinrealassets.IfGeneralMotors,forexample,couldnotissuestocksorbondstothegeneralpublic,itwouldhaveafarmoredifficulttimeraisingcapital.Contractionofthesupplyoffinancialassetswouldmakefinancingmoredifficult,therebyincreasingthecostofcapital.Ahighercostofcapitalresultsinlessinvestmentandlowerrealgrowth.1-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter01-TheInvestmentEnvironment5.Evenifthefirmdoesnotneedtoissuestockinanyparticularyear,thestockmarketisstillimportanttothefinancialmanager.Thestockpriceprovidesimportantinformationabouthowthemarketvaluesthefirm"sinvestmentprojects.Forexample,ifthestockpricerisesconsiderably,managersmightconcludethatthemarketbelievesthefirm"sfutureprospectsarebright.Thismightbeausefulsignaltothefirmtoproceedwithaninvestmentsuchasanexpansionofthefirm"sbusiness.Inaddition,thefactthatsharescanbetradedinthesecondarymarketmakesthesharesmoreattractivetoinvestorssinceinvestorsknowthat,whentheywishto,theywillbeabletoselltheirshares.Thisinturnmakesinvestorsmorewillingtobuysharesinaprimaryoffering,andthusimprovesthetermsonwhichfirmscanraisemoneyintheequitymarket.6.a.Cashisafinancialassetbecauseitistheliabilityofthefederalgovernment.b.No.Thecashdoesnotdirectlyaddtotheproductivecapacityoftheeconomy.c.Yes.d.Societyasawholeisworseoff,sincetaxpayers,asagroupwillmakeupfortheliability.7.a.ThebankloanisafinancialliabilityforLanni.(Lanni"sIOUisthebank"sfinancialasset.)ThecashLannireceivesisafinancialasset.ThenewfinancialassetcreatedisLanni"spromissorynote(thatis,Lanni’sIOUtothebank).b.Lannitransfersfinancialassets(cash)tothesoftwaredevelopers.Inreturn,Lannigetsarealasset,thecompletedsoftware.Nofinancialassetsarecreatedor课后答案网destroyed;cashissimplytransferredfromonepartytoanother.c.Lannigivestherealasset(thesoftware)toMicrosoftinexchangeforafinancialasset,1,500sharesofMicrosoftstock.IfMicrosoftissuesnewsharesinordertopayLanni,thenthiswouldrepresentthecreationofnewfinancialassets.www.hackshp.cnd.Lanniexchangesonefinancialasset(1,500sharesofstock)foranother($120,000).Lannigivesafinancialasset($50,000cash)tothebankandgetsbackanotherfinancialasset(itsIOU).Theloanis"destroyed"inthetransaction,sinceitisretiredwhenpaidoffandnolongerexists.1-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter01-TheInvestmentEnvironment8.a.Liabilities&AssetsShareholders’equityCash$70,000Bankloan$50,000Computers30,000Shareholders’equity50,000Total$100,000Total$100,000Ratioofrealassetstototalassets=$30,000/$100,000=0.30b.Liabilities&AssetsShareholders’equitySoftwareproduct*$70,000Bankloan$50,000Computers30,000Shareholders’equity50,000Total$100,000Total$100,000*ValuedatcostRatioofrealassetstototalassets=$100,000/$100,000=1.0c.Liabilities&AssetsShareholders’equityMicrosoftshares$120,000Bankloan$50,000Computers30,000Shareholders’equity100,000Total$150,000Total$150,000Ratioofrealassetstototalassets=$30,000/$150,000=0.20Conclusion:whenthefirmstartsupandraisesworkingcapital,itischaracterizedbyalowratioofrealassetstototalassets.Whenitisinfullproduction,ithasahighratioofrealassetsto课后答案网totalassets.Whentheproject"shutsdown"andthefirmsellsitoffforcash,financialassetsonceagainreplacerealassets.9.Forcommercialbanks,theratiois:$107.5/$10,410.9=0.010Fornon-financialfirms,theratiowww.hackshp.cnis:$13,295/$25,164=0.528Thedifferenceshouldbeexpectedprimarilybecausethebulkofthebusinessoffinancialinstitutionsistomakeloans;whicharefinancialassetsforfinancialinstitutions.10.a.Primary-markettransactionb.Derivativeassetsc.Investorswhowishtoholdgoldwithoutthecomplicationandcostofphysicalstorage.1-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter01-TheInvestmentEnvironment11.a.Afixedsalarymeansthatcompensationis(atleastintheshortrun)independentofthefirm"ssuccess.Thissalarystructuredoesnottiethemanager’simmediatecompensationtothesuccessofthefirm.However,themanagermightviewthisasthesafestcompensationstructureandthereforevalueitmorehighly.b.Asalarythatispaidintheformofstockinthefirmmeansthatthemanagerearnsthemostwhentheshareholders’wealthismaximized.Thisstructureisthereforemostlikelytoaligntheinterestsofmanagersandshareholders.Ifstockcompensationisoverdone,however,themanagermightviewitasoverlyriskysincethemanager’scareerisalreadylinkedtothefirm,andthisundiversifiedexposurewouldbeexacerbatedwithalargestockpositioninthefirm.c.Calloptionsonsharesofthefirmcreategreatincentivesformanagerstocontributetothefirm’ssuccess.Insomecases,however,stockoptionscanleadtootheragencyproblems.Forexample,amanagerwithnumerouscalloptionsmightbetemptedtotakeonaveryriskyinvestmentproject,reasoningthatiftheprojectsucceedsthepayoffwillbehuge,whileifitfails,thelossesarelimitedtothelostvalueoftheoptions.Shareholders,incontrast,bearthelossesaswellasthegainsontheproject,andmightbelesswillingtoassumethatrisk.12.Evenifanindividualshareholdercouldmonitorandimprovemanagers’performance,andtherebyincreasethevalueofthefirm,thepayoffwouldbesmall,sincetheownershipshareinalargecorporationwouldbeverysmall.Forexample,ifyouown$10,000ofGMstockandcanincreasethevalueofthefirmby5%,averyambitiousgoal,youbenefitbyonly:0.05×$10,000=$500Incontrast,abankthathasamultimillion-dollarloanoutstandingtothefirmhasabigstakeinmakingsurethatthe课后答案网firmcanrepaytheloan.Itisclearlyworthwhileforthebanktospendconsiderableresourcestomonitorthefirm.13.Mutualfundsacceptfundsfromsmallinvestorsandinvest,onbehalfoftheseinvestors,inthenationalandinternationalsecuritiesmarkets.Pensionfundsacceptfundsandtheninvest,www.hackshp.cnonbehalfofcurrentandfutureretirees,therebychannelingfundsfromonesectoroftheeconomytoanother.Venturecapitalfirmspoolthefundsofprivateinvestorsandinvestinstart-upfirms.Banksacceptdepositsfromcustomersandloanthosefundstobusinesses,orusethefundstobuysecuritiesoflargecorporations.14.Treasurybillsserveapurposeforinvestorswhopreferalow-riskinvestment.Theloweraveragerateofreturncomparedtostocksisthepriceinvestorspayforpredictabilityofinvestmentperformanceandportfoliovalue.1-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter01-TheInvestmentEnvironment15.Witha“top-down”investingstyle,youfocusonassetallocationorthebroadcompositionoftheentireportfolio,whichisthemajordeterminantofoverallperformance.Moreover,top-downmanagementisthenaturalwaytoestablishaportfoliowithalevelofriskconsistentwithyourrisktolerance.Thedisadvantageofanexclusiveemphasisontop-downissuesisthatyoumayforfeitthepotentialhighreturnsthatcouldresultfromidentifyingandconcentratinginundervaluedsecuritiesorsectorsofthemarket.Witha“bottom-up”investingstyle,youtrytobenefitfromidentifyingundervaluedsecurities.Thedisadvantageisthatyoutendtooverlooktheoverallcompositionofyourportfolio,whichmayresultinanon-diversifiedportfoliooraportfoliowitharisklevelinconsistentwithyourlevelofrisktolerance.Inaddition,thistechniquetendstorequiremoreactivemanagement,thusgeneratingmoretransactioncosts.Finally,youranalysismaybeincorrect,inwhichcaseyouwillhavefruitlesslyexpendedeffortandmoneyattemptingtobeatasimplebuy-and-holdstrategy.16.Youshouldbeskeptical.Iftheauthoractuallyknowshowtoachievesuchreturns,onemustquestionwhytheauthorwouldthenbesoreadytosellthesecrettoothers.Financialmarketsareverycompetitive;oneoftheimplicationsofthisfactisthatrichesdonotcomeeasily.Highexpectedreturnsrequirebearingsomerisk,andobviousbargainsarefewandfarbetween.Oddsarethattheonlyonegettingrichfromthebookisitsauthor.17.a.TheSECwebsitedefinesthedifferencebetweensavingandinvestingintermsoftheinvestmentalternativesorthefinancialassetstheindividualchoosestoacquire.AccordingtotheSECwebsite,savingistheprocessofacquiringa“safe”financialassetandinvestingistheprocessofacquiring“risky”financialassets.b.Theeconomist’sdefinitionofsavingsisthedifferencebetweenincomeandconsumption.Investing课后答案网istheprocessofallocatingone’ssavingsamongavailableassets,bothrealassetsandfinancialassets.TheSECdefinitionsactuallyrepresent(accordingtheeconomist’sdefinition)twokindsofinvestmentalternatives.18.AsisthecasefortheSECdefinitions(seeProblem17),theSIAdefinessavingandinvestingasacquisitionofalternativekindsoffinancialassets.AccordingtotheSIA,www.hackshp.cnsavingistheprocessofacquiringsafeassets,generallyfromabank,whileinvestingistheacquisitionofotherfinancialassets,suchasstocksandbonds.Ontheotherhand,thedefinitionsinthechapterindicatethatsavingmeansspendinglessthanone’sincome.Investingistheprocessofallocatingone’ssavingsamongfinancialassets,includingsavingsaccountdepositsandmoneymarketaccounts(“saving”accordingtotheSIA),otherfinancialassetssuchasstocksandbonds(“investing”accordingtotheSIA),aswellasrealassets.1-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter02-AssetClassesandFinancialInstrumentsCHAPTER2:ASSETASSETCLASSESCLASSESCLASSESANDANDFINANCIALFINANCIALINSTRUMENTSINSTRUMENTSPROBLEMPROBLEMSETSSETS1.Preferredstockislikelong-termdebtinthatittypicallypromisesafixedpaymenteachyear.Inthisway,itisaperpetuity.Preferredstockisalsolikelong-termdebtinthatitdoesnotgivetheholdervotingrightsinthefirm.Preferredstockislikeequityinthatthefirmisundernocontractualobligationtomakethepreferredstockdividendpayments.Failuretomakepaymentsdoesnotsetoffcorporatebankruptcy.Withrespecttothepriorityofclaimstotheassetsofthefirmintheeventofcorporatebankruptcy,preferredstockhasahigherprioritythancommonequitybutalowerprioritythanbonds.2.Moneymarketsecuritiesarecalled“cashequivalents”becauseoftheirgreatliquidity.Thepricesofmoneymarketsecuritiesareverystable,andtheycanbeconvertedtocash(i.e.,sold)onveryshortnoticeandwithverylowtransactioncosts.3.Thespreadwillwiden.Deteriorationoftheeconomyincreasescreditrisk,thatis,thelikelihoodofdefault.Investorswilldemandagreaterpremiumondebtsecuritiessubjecttodefaultrisk.4.Onthedaywetriedthisexperiment,36ofthe50stocksmetthiscriterion,leading课后答案网ustoconcludethatreturnsonstockinvestmentscanbequitevolatile.5.a.Youwouldhavetopaytheaskedpriceof:www.hackshp.cn118:31=118.96875%ofpar=$1,189.6875b.Thecouponrateis11.750%implyingcouponpaymentsof$117.50annuallyor,moreprecisely,$58.75semiannually.c.Currentyield=Annualcouponincome/price=$117.50/$1,189.6875=0.0988=9.88%6.P=$10,000/1.02=$9,803.922-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter02-AssetClassesandFinancialInstruments7.Thetotalbefore-taxincomeis$4.Afterthe70%exclusionforpreferredstockdividends,thetaxableincomeis:0.30×$4=$1.20Therefore,taxesare:0.30×$1.20=$0.36After-taxincomeis:$4.00–$0.36=$3.64Rateofreturnis:$3.64/$40.00=9.10%8.a.GeneralDynamicsclosedtodayat$74.59,whichwas$0.17higherthanyesterday’sprice.Yesterday’sclosingpricewas:$74.42b.Youcouldbuy:$5,000/$74.59=67.03sharesc.Yourannualdividendincomewouldbe:67.03×$0.92=$61.67d.Theprice-to-earningsratiois16andthepriceis$74.59.Therefore:$74.59/Earningspershare=16⇒Earningspershare=$4.669.a.Att=0,thevalueoftheindexis:(90+50+100)/3=80Att=1,thevalueoftheindexis:(95+45+110)/3=83.333Therateofreturnis:(83.333/80)−1=4.17%b.Intheabsenceofasplit,StockCwouldsellfor110,sothevalueoftheindexwouldbe:250/3=83.333Afterthesplit,StockCsellsfor55.Therefore,weneedtofindthedivisor(d)suchthat:83.333=(95+45+55)/d课后答案网⇒d=2.340c.Thereturniszero.Theindexremainsunchangedbecausethereturnforeachstockseparatelyequalszero.10.a.Totalmarketvalueatwww.hackshp.cnt=0is:($9,000+$10,000+$20,000)=$39,000Totalmarketvalueatt=1is:($9,500+$9,000+$22,000)=$40,500Rateofreturn=($40,500/$39,000)–1=3.85%b.Thereturnoneachstockisasfollows:rA=(95/90)–1=0.0556rB=(45/50)–1=–0.10rC=(110/100)–1=0.10Theequally-weightedaverageis:[0.0556+(-0.10)+0.10]/3=0.0185=1.85%2-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter02-AssetClassesandFinancialInstruments11.Theafter-taxyieldonthecorporatebondsis:0.09×(1–0.30)=0.0630=6.30%Therefore,municipalsmustofferatleast6.30%yields.12.Equation(2.2)showsthattheequivalenttaxableyieldis:r=rm/(1–t)a.4.00%b.4.44%c.5.00%d.5.71%13.a.Thehighercouponbond.b.Thecallwiththelowerexerciseprice.c.Theputonthelowerpricedstock.14.a.Youboughtthecontractwhenthefuturespricewas1427.50(seeFigure2.12).Thecontractclosesatapriceof1300,whichis127.50lessthantheoriginalfuturesprice.Thecontractmultiplieris$250.Therefore,thelosswillbe:127.50×$250=$31,875b.Openinterestis601,655contracts.课后答案网15.a.Sincethestockpriceexceedstheexerciseprice,youwillexercisethecall.Thepayoffontheoptionwillbe:$42−$40=$2Theoptionoriginallycost$2.14,sotheprofitis:$2.00−$2.14=−$0.14Rateofreturn=www.hackshp.cn−$0.14/$2.14=−0.0654=−6.54%b.Ifthecallhasanexercisepriceof$42.50,youwouldnotexerciseforanystockpriceof$42.50orless.Thelossonthecallwouldbetheinitialcost:$0.72c.Sincethestockpriceislessthantheexerciseprice,youwillexercisetheput.Thepayoffontheoptionwillbe:$42.50−$42.00=$0.50Theoptionoriginallycost$1.83sotheprofitis:$0.50−$1.83=−$1.33Rateofreturn=−$1.33/$1.83=−0.7268=−72.68%2-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter02-AssetClassesandFinancialInstruments16.Thereisalwaysapossibilitythattheoptionwillbein-the-moneyatsometimepriortoexpiration.Investorswillpaysomethingforthispossibilityofapositivepayoff.17.ValueofcallatexpirationInitialCostProfita.04-4b.04-4c.04-4d.541e.1046ValueofputatexpirationInitialCostProfita.1064b.56-1c.06-6d.06-6e.06-618.Aputoptionconveystherighttoselltheunderlyingassetattheexerciseprice.Ashortpositioninafuturescontractcarriesanobligationtoselltheunderlyingassetatthefuturesprice.19.Acalloptionconveystherighttobuytheunderlyingassetattheexerciseprice.Alongpositioninafuturescontractcarriesanobligationtobuytheunderlyingassetatthefuturesprice.课后答案网CFACFAPROBLEMSPROBLEMS1.(d)www.hackshp.cn2.Theequivalenttaxableyieldis:6.75%/(1−0.34)=10.23%3.(a)Writingacallentailsunlimitedpotentiallossesasthestockpricerises.2-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter02-AssetClassesandFinancialInstruments4.a.Thetaxablebond.Withazerotaxbracket,theafter-taxyieldforthetaxablebondisthesameasthebefore-taxyield(5%),whichisgreaterthantheyieldonthemunicipalbond.b.Thetaxablebond.Theafter-taxyieldforthetaxablebondis:0.05×(1–0.10)=4.5%c.Youareindifferent.Theafter-taxyieldforthetaxablebondis:0.05×(1–0.20)=4.0%Theafter-taxyieldisthesameasthatofthemunicipalbond.d.Themunicipalbondoffersthehigherafter-taxyieldforinvestorsintaxbracketsabove20%.5.Iftheafter-taxyieldsareequal,then:0.056=0.08×(1–t)Thisimpliesthatt=0.30=30%.课后答案网www.hackshp.cn2-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter03-HowSecuritiesareTradedCHAPTER3:HOWHOWSECURITIESSECURITIESSECURITIESAREAREARETRADEDTRADEDPROBLEMPROBLEMSETSSETS1.Answerstothisproblemwillvary.2.TheSuperDotsystemexpeditestheflowofordersfromexchangememberstothespecialists.Itallowsmemberstosendcomputerizedordersdirectlytotheflooroftheexchange,whichallowsthenearlysimultaneoussaleofeachstockinalargeportfolio.Thiscapabilityisnecessaryforprogramtrading.3.Thedealersetsthebidandaskedprice.Spreadsshouldbehigheroninactivelytradedstocksandloweronactivelytradedstocks.4.a.Inprinciple,potentiallossesareunbounded,growingdirectlywithincreasesinthepriceofIBM.b.Ifthestop-buyordercanbefilledat$128,themaximumpossiblelosspershareis$8.IfthepriceofIBMsharesgoesabove$128,thenthestop-buyorderwouldbeexecuted,limitingthelossesfromtheshortsale.5.a.Thestockispurchasedfor:300×$40=$12,000Theamountborrowed课后答案网is$4,000.Therefore,theinvestorputupequity,ormargin,of$8,000.b.Ifthesharepricefallsto$30,thenthevalueofthestockfallsto$9,000.Bytheendoftheyear,theamountoftheloanowedtothebrokergrowsto:$4,000×1.08=$4,320www.hackshp.cnTherefore,theremainingmarginintheinvestor’saccountis:$9,000−$4,320=$4,680Thepercentagemarginisnow:$4,680/$9,000=0.52=52%Therefore,theinvestorwillnotreceiveamargincall.c.Therateofreturnontheinvestmentovertheyearis:(Endingequityintheaccount−Initialequity)/Initialequity=($4,680−$8,000)/$8,000=−0.415=−41.5%3-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter03-HowSecuritiesareTraded6.a.Theinitialmarginwas:0.50×1,000×$40=$20,000AsaresultoftheincreaseinthestockpriceOldEconomyTradersloses:$10×1,000=$10,000Therefore,margindecreasesby$10,000.Moreover,OldEconomyTradersmustpaythedividendof$2persharetothelenderoftheshares,sothatthemarginintheaccountdecreasesbyanadditional$2,000.Therefore,theremainingmarginis:$20,000–$10,000–$2,000=$8,000b.Thepercentagemarginis:$8,000/$50,000=0.16=16%Sotherewillbeamargincall.c.Theequityintheaccountdecreasedfrom$20,000to$8,000inoneyear,forarateofreturnof:(−$12,000/$20,000)=−0.60=−60%7.Muchofwhatthespecialistdoes(e.g.,crossingordersandmaintainingthelimitorderbook)canbeaccomplishedbyacomputerizedsystem.Infact,someexchangesuseanautomatedsystemfornighttrading.Amoredifficultissuetoresolveiswhetherthemorediscretionaryactivitiesofspecialistsinvolvingtradingfortheirownaccounts(e.g.,maintaininganorderlymarket)canbereplicatedbyacomputersystem.8.a.Thebuyorderwillbefilledatthebestlimit-sellorderprice:$50.25b.Thenextmarketbuyorderwillbefilledatthenext-bestlimit-sellorderprice:$51.50课后答案网c.Youwouldwanttoincreaseyourinventory.Thereisconsiderablebuyingdemandatpricesjustbelow$50,indicatingthatdownsideriskislimited.Incontrast,limitsellordersaresparse,indicatingthatamoderatebuyordercouldresultinasubstantialpriceincrease.www.hackshp.cn9.a.Youbuy200sharesofTelecomfor$10,000.Thesesharesincreaseinvalueby10%,or$1,000.Youpayinterestof:0.08×$5,000=$400Therateofreturnwillbe:,1$000−$400=0.12=12%,5$0003-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter03-HowSecuritiesareTradedb.Thevalueofthe200sharesis200P.Equityis(200P–$5,000).Youwillreceiveamargincallwhen:200P−,5$000=0.30⇒whenP=$35.71orlower200P10.a.Initialmarginis50%of$5,000or$2,500.b.Totalassetsare$7,500($5,000fromthesaleofthestockand$2,500putupformargin).Liabilitiesare100P.Therefore,equityis($7,500–100P).Amargincallwillbeissuedwhen:,7$500−100P=0.30⇒whenP=$57.69orhigher100P11.Thetotalcostofthepurchaseis:$40×500=$20,000Youborrow$5,000fromyourbroker,andinvest$15,000ofyourownfunds.Yourmarginaccountstartsoutwithequityof$15,000.a.(i)Equityincreasesto:($44×500)–$5,000=$17,000Percentagegain=$2,000/$15,000=0.1333=13.33%(ii)Withpriceunchanged,equityisunchanged.Percentagegain=zero(iii)Equityfallsto($36×500)–$5,000=$13,000Percentagegain=课后答案网(–$2,000/$15,000)=–0.1333=–13.33%Therelationshipbetweenthepercentagereturnandthepercentagechangeinthepriceofthestockisgivenby:Totalinvestment%return=%changeinprice×=%changeinprice×1.333www.hackshp.cnInvestor"sinitialequityForexample,whenthestockpricerisesfrom$40to$44,thepercentagechangeinpriceis10%,whilethepercentagegainfortheinvestoris:$20,000%return=10%×=13.33%$15,000b.Thevalueofthe500sharesis500P.Equityis(500P–$5,000).Youwillreceiveamargincallwhen:500P−,5$000=0.25⇒whenP=$13.33orlower500P3-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter03-HowSecuritiesareTradedc.Thevalueofthe500sharesis500P.Butnowyouhaveborrowed$10,000insteadof$5,000.Therefore,equityis(500P–$10,000).Youwillreceiveamargincallwhen:500P−$10,000=0.25⇒whenP=$26.67500PWithlessequityintheaccount,youarefarmorevulnerabletoamargincall.d.Bytheendoftheyear,theamountoftheloanowedtothebrokergrowsto:$5,000×1.08=$5,400Theequityinyouraccountis(500P–$5,400).Initialequitywas$15,000.Therefore,yourrateofreturnafteroneyearisasfollows:(500×$44)−,5$400−$15,000(i)=0.1067=10.67%$15,000(500×$40)−,5$400−$15,000(ii)=–0.0267=–2.67%$15,000(500×$36)−,5$400−$15,000(iii)=–0.1600=–16.00%$15,000TherelationshipbetweenthepercentagereturnandthepercentagechangeinthepriceofIntelisgivenby:⎛Totalinvestment⎞⎛Fundsborrowed⎞%return=⎜%changeinprice×⎟−⎜8%×⎟⎜⎟⎜⎟⎝Investor"sinitialequity⎠⎝Investor"sinitialequity⎠Forexample,whenthestockpricerisesfrom$40to$44,thepercentagechange课后答案网inpriceis10%,whilethepercentagegainfortheinvestoris:⎛$20,000⎞⎛,5$000⎞⎜10%×⎟−⎜8%×⎟=10.67%⎝$15,000⎠⎝$15,000⎠e.Thevalueofthe500shareswww.hackshp.cnis500P.Equityis(500P–$5,400).Youwillreceiveamargincallwhen:500P−,5$400=0.25⇒whenP=$14.40orlower500P3-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter03-HowSecuritiesareTraded12.a.Thegainorlossontheshortpositionis:(–500×∆P)Investedfunds=$15,000Therefore:rateofreturn=(–500×∆P)/15,000Therateofreturnineachofthethreescenariosis:(i)rateofreturn=(–500×$4)/$15,000=–0.1333=–13.33%(ii)rateofreturn=(–500×$0)/$15,000=0%(iii)rateofreturn=[–500×(–$4)]/$15,000=+0.1333=+13.33%b.Totalassetsinthemarginaccountequal:$20,000(fromthesaleofthestock)+$15,000(theinitialmargin)=$35,000Liabilitiesare500P.Youwillreceiveamargincallwhen:$35,000−500P=0.25⇒whenP=$56orhigher500Pc.Witha$1dividend,theshortpositionmustnowpayontheborrowedshares:($1/share×500shares)=$500.Rateofreturnisnow:[(–500×∆P)–500]/15,000(i)rateofreturn=[(–500×$4)–$500]/$15,000=–0.1667=–16.67%(ii)rateofreturn=[(–500×$0)–$500]/$15,000=–0.0333=–3.33%(iii)rateofreturn=[(–500)×(–$4)–$500]/$15,000=+0.1000=+10.00%Totalassetsare$35,000,andliabilitiesare(500P+500).Amargincallwillbeissuedwhen:课后答案网35,000−500P−500=0.25⇒whenP=$55.20orhigher500P13.Thebrokerisinstructedtoattempttowww.hackshp.cnsellyourMarriottstockassoonastheMarriottstocktradesatabidpriceof$38orless.Here,thebrokerwillattempttoexecute,butmaynotbeabletosellat$38,sincethebidpriceisnow$37.95.Thepriceatwhichyousellmaybemoreorlessthan$38becausethestop-lossbecomesamarketordertosellatcurrentmarketprices.3-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter03-HowSecuritiesareTraded14.a.$55.50b.$55.25c.Thetradewillnotbeexecutedbecausethebidpriceislowerthanthepricespecifiedinthelimitsellorder.d.Thetradewillnotbeexecutedbecausetheaskedpriceisgreaterthanthepricespecifiedinthelimitbuyorder.15.a.Inanexchangemarket,therecanbepriceimprovementinthetwomarketorders.Brokersforeachofthemarketorders(i.e.,thebuyorderandthesellorder)canagreetoexecuteatradeinsidethequotedspread.Forexample,theycantradeat$55.37,thusimprovingthepriceforbothcustomersby$0.12or$0.13relativetothequotedbidandaskedprices.Thebuyergetsthestockfor$0.13lessthanthequotedaskedprice,andthesellerreceives$0.12moreforthestockthanthequotedbidprice.b.Whereasthelimitordertobuyat$55.37wouldnotbeexecutedinadealermarket(sincetheaskedpriceis$55.50),itcouldbeexecutedinanexchangemarket.Abrokerforanothercustomerwithanordertosellatmarketwouldviewthelimitbuyorderasthebestbidprice;thetwobrokerscouldagreetothetradeandbringittothespecialist,whowouldthenexecutethetrade.16.a.Youwillnotreceiveamargincall.Youborrowed$20,000andwithanother$20,000ofyourownequityyoubought1,000sharesofDisneyat$40pershare.At$35pershare,themarketvalueofthestockis$35,000,yourequityis$15,000,andthepercentagemargin课后答案网is:$15,000/$35,000=42.9%Yourpercentagemarginexceedstherequiredmaintenancemargin.b.Youwillreceiveamargincallwhen:,1000P−$20,000=0.35⇒whenP=$30.77orlower,1000www.hackshp.cnP3-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter03-HowSecuritiesareTraded17.Theproceedsfromtheshortsale(netofcommission)were:($14×100)–$50=$1,350Adividendpaymentof$200waswithdrawnfromtheaccount.Coveringtheshortsaleat$9persharecostyou(includingcommission):$900+$50=$950Therefore,thevalueofyouraccountisequaltothenetprofitonthetransaction:$1350–$200–$950=$200Notethatyourprofit($200)equals(100shares×profitpershareof$2).Yournetproceedspersharewas:$14sellingpriceofstock–$9repurchasepriceofstock–$2dividendpershare–$12trades×$0.50commissionpershare$2CFACFAPROBLEMSPROBLEMS1.a.Inadditiontotheexplicitfeesof$70,000,FBNappearstohavepaidanimplicitpriceinunderpricingoftheIPO.Theunderpricingis$3pershare,oratotalof$300,000,implyingtotalcostsof$370,000.b.No.Theunderwritersdonotcapturethepartofthecostscorrespondingtotheunderpricing.Theunderpricingmaybearationalmarketingstrategy.Withoutit,theunderwriterswouldneedtospendmoreresourcesinordertoplacetheissuewiththepublic.Theunderwriterswouldthenneedtochargehigherexplicitfeestotheissuingfirm.Theissuingfirmmaybejustas课后答案网welloffpayingtheimplicitissuancecostrepresentedbytheunderpricing.2.(d)Thebrokerwillsell,atcurrentmarketprice,afterthefirsttransactionat$55orless.www.hackshp.cn3.(d)3-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter04-MutualFundsandOtherInvestmentCompaniesCHAPTER4:MUTUALMUTUALFUNDSFUNDSFUNDSANDANDOTHEROTHERINVESTMENTINVESTMENTINVESTMENTCOMPANIESCOMPANIESPROBLEMPROBLEMSETSSETS1.Theunitinvestmenttrustshouldhaveloweroperatingexpenses.Becausetheinvestmenttrustportfolioisfixedoncethetrustisestablished,itdoesnothavetopayportfoliomanagerstoconstantlymonitorandrebalancetheportfolioasperceivedneedsoropportunitieschange.Becausetheportfolioisfixed,theunitinvestmenttrustalsoincursvirtuallynotradingcosts.2.a.Unitinvestmenttrusts:diversificationfromlarge-scaleinvesting,lowertransactioncostsassociatedwithlarge-scaletrading,lowmanagementfees,predictableportfoliocomposition,guaranteedlowportfolioturnoverrate.b.Open-endmutualfunds:diversificationfromlarge-scaleinvesting,lowertransactioncostsassociatedwithlarge-scaletrading,professionalmanagementthatmaybeabletotakeadvantageofbuyorsellopportunitiesastheyarise,recordkeeping.c.Individualstocksandbonds:Nomanagementfee,realizationofcapitalgainsorlossescanbecoordinatedwithinvestors’personaltaxsituations,portfoliocanbedesignedtoinvestor’sspecificriskprofile.3.Open-endfundsareobligatedtoredeeminvestor"ssharesatnetassetvalue,andthus课后答案网mustkeepcashorcash-equivalentsecuritiesonhandinordertomeetpotentialredemptions.Closed-endfundsdonotneedthecashreservesbecausetherearenoredemptionsforclosed-endfunds.Investorsinclosed-endfundsselltheirshareswhentheywishtocashout.www.hackshp.cn4.Balancedfundskeeprelativelystableproportionsoffundsinvestedineachassetclass.Theyaremeantasconvenientinstrumentstoprovideparticipationinarangeofassetclasses.Life-cyclefundsarebalancedfundswhoseassetmixgenerallydependsontheageoftheinvestor.Aggressivelife-cyclefunds,withlargerinvestmentsinequities,aremarketedtoyoungerinvestors,whileconservativelife-cyclefunds,withlargerinvestmentsinfixed-incomesecurities,aredesignedforolderinvestors.Assetallocationfunds,incontrast,mayvarytheproportionsinvestedineachassetclassbylargeamountsaspredictionsofrelativeperformanceacrossclassesvary.Assetallocationfundsthereforeengageinmoreaggressivemarkettiming.4-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter04-MutualFundsandOtherInvestmentCompanies5.Theofferingpriceincludesa6%front-endload,orsalescommission,meaningthateverydollarpaidresultsinonly$0.94goingtowardpurchaseofshares.Therefore:NAV$10.70Offeringprice===$11.381−load1−.0066.NAV=offeringprice×(1–load)=$12.30×0.95=$11.697.StockValueheldbyfundA$7,000,000B12,000,000C8,000,000D15,000,000Total$42,000,000$42,000,000−$30,000Netassetvalue==$10.49,4000,0008.Valueofstockssoldandreplaced=$15,000,000$15,000,000Turnoverrate==0.357=35.7%$42,000,000$200,000,000−,3$000,0009.a.NAV==$39.40课后答案网,5000,000Price−NAV$36−$39.40b.Premium(ordiscount)===–0.086=-8.6%NAV$39.40Thefundsellsatan8.6%discountfromNAV.www.hackshp.cn10.Rateofreturn=NAV1−NAV0+distributions$12.10−$12.50+.1$50==.0088=8.8%NAV$12.5004-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter04-MutualFundsandOtherInvestmentCompanies11.a.Start-of-yearprice:P0=$12.00×1.02=$12.24End-of-yearprice:P1=$12.10×0.93=$11.25AlthoughNAVincreasedby$0.10,thepriceofthefunddecreasedby:$0.99P1−P0+Distributions$11.25−$12.24+.1$50Rateofreturn===.0042=2.4%P$12.240b.AninvestorholdingthesamesecuritiesasthefundmanagerwouldhaveearnedarateofreturnbasedontheincreaseintheNAVoftheportfolio:Rateofreturn=NAV−NAV+distributions$12.10−$12.00+.1$5010==.0133=133.%NAV$12.00012.a.Empiricalresearchindicatesthatpastperformanceofmutualfundsisnothighlypredictiveoffutureperformance,especiallyforbetter-performingfunds.Whiletheremaybesometendencyforthefundtobeanaboveaverageperformernextyear,itisunlikelytoonceagainbeatop10%performer.b.Ontheotherhand,theevidenceismoresuggestiveofatendencyforpoorperformancetopersist.Thistendencyisprobablyrelatedtofundcostsandturnoverrates.Thusifthefundisamongthepoorestperformers,investorswouldbeconcernedthatthepoorperformancewillpersist.13.NAV0=$200,000,000/10,000,000=$20Dividendspershare=$2,000,000/10,000,000=$0.20课后答案网NAV1isbasedonthe8%pricegain,lessthe1%12b-1fee:NAV1=$20×1.08×(1–0.01)=$21.384$21.384−$20+.0$20Rateofreturn==0.0792=7.92%www.hackshp.cn$2014.Theexcessofpurchasesoversalesmustbeduetonewinflowsintothefund.Therefore,$400millionofstockpreviouslyheldbythefundwasreplacedbynewholdings.Soturnoveris:$400/$2,200=0.182=18.2%15.Feespaidtoinvestmentmanagerswere:0.007×$2.2billion=$15.4millionSincethetotalexpenseratiowas1.1%andthemanagementfeewas0.7%,weconcludethat0.4%mustbeforotherexpenses.Therefore,otheradministrativeexpenseswere:0.004×$2.2billion=$8.8million4-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter04-MutualFundsandOtherInvestmentCompanies16.Asaninitialapproximation,yourreturnequalsthereturnonthesharesminusthetotaloftheexpenseratioandpurchasecosts:12%−1.2%−4%=6.8%Buttheprecisereturnislessthanthisbecausethe4%loadispaidupfront,notattheendoftheyear.Topurchasetheshares,youwouldhavehadtoinvest:$20,000/(1−0.04)=$20,833Thesharesincreaseinvaluefrom$20,000to:$20,000×(1.12−0.012)=$22,160Therateofreturnis:($22,160−$20,833)/$20,833=6.37%17.Supposeyouhave$1,000toinvest.TheinitialinvestmentinClassAsharesis$940netofthefront-endload.Afterfouryears,yourportfoliowillbeworth:$940×(1.10)4=$1,376.25ClassBsharesallowyoutoinvestthefull$1,000,butyourinvestmentperformancenetof12b-1feeswillbeonly9.5%,andyouwillpaya1%back-endloadfeeifyousellafterfouryears.Yourportfoliovalueafterfouryearswillbe:$1,000×(1.095)4=$1,437.66Afterpayingtheback-endloadfee,yourportfoliovaluewillbe:$1,437.66×0.99=$1,423.28ClassBsharesarethebetterchoiceifyourhorizonisfouryears.Withafifteen-yearhorizon,theClassAshareswillbeworth:$940×(1.10)15=$3,926.61FortheClassBshares,thereisnoback-endloadinthiscasesincethehorizonisgreaterthanfiveyears.Therefore,thevalueoftheClassBshareswillbe:$1,000×(1.095)15=$3,901.32Atthislongerhorizon,Class课后答案网Bsharesarenolongerthebetterchoice.TheeffectofClassB"s0.5%12b-1feesaccumulatesovertimeandfinallyoverwhelmsthe6%loadchargedtoClassAinvestors.18.a.Aftertwoyears,eachdollarinvestedinafundwitha4%loadandaportfolioreturnequaltorwww.hackshp.cnwillgrowto:$0.96×(1+r–0.005)2EachdollarinvestedinthebankCDwillgrowto:$1×1.062Ifthemutualfundistobethebetterinvestment,thentheportfolioreturn(r)mustsatisfy:0.96×(1+r–0.005)2>1.0620.96×(1+r–0.005)2>1.1236(1+r–0.005)2>1.17041+r–0.005>1.08191+r>1.0869Therefore:r>0.0869=8.69%4-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter04-MutualFundsandOtherInvestmentCompaniesb.Ifyouinvestforsixyears,thentheportfolioreturnmustsatisfy:0.96×(1+r–0.005)6>1.066=1.4185(1+r–0.005)6>1.47761+r–0.005>1.06721+r>1.0722r>7.22%Thecutoffrateofreturnislowerforthesix-yearinvestmentbecausethe“fixedcost”(i.e.,theone-timefront-endload)isspreadoutoveragreaternumberofyears.c.Witha12b-1feeinsteadofafront-endload,theportfoliomustearnarateofreturn(r)thatsatisfies:1+r–0.005–0.0075>1.06Inthiscase,rmustexceed7.25%regardlessoftheinvestmenthorizon.19.Theturnoverrateis50%.Thismeansthat,onaverage,50%oftheportfolioissoldandreplacedwithothersecuritieseachyear.Tradingcostsonthesellordersare0.4%andthebuyorderstoreplacethosesecuritiesentailanother0.4%intradingcosts.Totaltradingcostswillreduceportfolioreturnsby:2×0.4%×0.50=0.4%20.Forthebondfund,thefractionofportfolioincomegivenuptofeesis:6.0%=0.150=15.0%0.4%课后答案网Fortheequityfund,thefractionofinvestmentearningsgivenuptofeesis:6.0%=0.050=5.0%120.%Feesareamuchhigherfractionofexpectedearningsforthebondfund,andthereforewww.hackshp.cnmaybeamoreimportantfactorinselectingthebondfund.Thismayhelptoexplainwhyunmanagedunitinvestmenttrustsareconcentratedinthefixedincomemarket.Theadvantagesofunitinvestmenttrustsarelowturnover,lowtradingcostsandlowmanagementfees.Thisisamoreimportantconcerntobond-marketinvestors.4-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter04-MutualFundsandOtherInvestmentCompanies21.Supposethatfinishinginthetophalfofallportfoliomanagersispurelyluck,andthattheprobabilityofdoingsoinanyyearisexactly½.Thentheprobabilitythatanyparticularmanagerwouldfinishinthetophalfofthesamplefiveyearsinarowis(½)5=1/32.Wewouldthenexpecttofindthat[350×(1/32)]=11managersfinishinthetophalfforeachofthefiveconsecutiveyears.Thisispreciselywhatwefound.Thus,weshouldnotconcludethattheconsistentperformanceafterfiveyearsisproofofskill.Wewouldexpecttofindelevenmanagersexhibitingpreciselythislevelof"consistency"evenifperformanceisduesolelytoluck.课后答案网www.hackshp.cn4-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter05-LearningAboutReturnandRiskfromtheHistoricalRecordCHAPTER5:LEARNINGLEARNINGABOUTABOUTABOUTRETURNRETURNRETURNANDANDANDRISKRISKFROMFROMTHETHETHEHISTORICALHISTORICALHISTORICALRECORDRECORDPROBLEMPROBLEMSETSSETS1.TheFisherequationpredictsthatthenominalratewillequaltheequilibriumrealrateplustheexpectedinflationrate.Hence,iftheinflationrateincreasesfrom3%to5%whilethereisnochangeintherealrate,thenthenominalratewillincreaseby2%.Ontheotherhand,itispossiblethatanincreaseintheexpectedinflationratewouldbeaccompaniedbyachangeintherealrateofinterest.Whileitisconceivablethatthenominalinterestratecouldremainconstantastheinflationrateincreased,implyingthattherealratedecreasedasinflationincreased,thisisnotalikelyscenario.2.Ifweassumethatthedistributionofreturnsremainsreasonablystableovertheentirehistory,thenalongersampleperiod(i.e.,alargersample)increasestheprecisionoftheestimateoftheexpectedrateofreturn;thisisaconsequenceofthefactthatthestandarderrordecreasesasthesamplesizeincreases.However,ifweassumethatthemeanofthedistributionofreturnsischangingovertimebutwearenotinapositiontodeterminethenatureofthischange,thentheexpectedreturnmustbeestimatedfromamorerecentpartofthehistoricalperiod.Inthisscenario,wemustdeterminehowfarback,historically,togoinselectingtherelevantsample.Here,itislikelytobedisadvantageoustousetheentiredatasetbackto1880.3.Thetruestatementsare(c)and(e).Theexplanationsfollow.课后答案网Statement(c):Letσ=theannualstandarddeviationoftheriskyinvestmentsandσ1=thestandarddeviationofthefirstinvestmentalternativeoverthetwo-yearperiod.Then:σ=2×σ1Therefore,theannualizedstandarddeviationforthefirstinvestmentalternativewww.hackshp.cnisequalto:σσ1=<σ225-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter05-LearningAboutReturnandRiskfromtheHistoricalRecordStatement(e):Thefirstinvestmentalternativeismoreattractivetoinvestorswithlowerdegreesofriskaversion.Thefirstalternative(entailingasequenceoftwoidenticallydistributedanduncorrelatedriskyinvestments)isriskierthanthesecondalternative(theriskyinvestmentfollowedbyarisk-freeinvestment).Therefore,thefirstalternativeismoreattractivetoinvestorswithlowerdegreesofriskaversion.Notice,however,thatifyoumistakenlybelievedthat‘timediversification’canreducethetotalriskofasequenceofriskyinvestments,youwouldhavebeentemptedtoconcludethatthefirstalternativeislessriskyandthereforemoreattractivetomorerisk-averseinvestors.Thisisclearlynotthecase;thetwo-yearstandarddeviationofthefirstalternativeisgreaterthanthetwo-yearstandarddeviationofthesecondalternative.4.Forthemoneymarketfund,yourholdingperiodreturnforthenextyeardependsonthelevelof30-dayinterestrateseachmonthwhenthefundrollsovermaturingsecurities.Theone-yearsavingsdepositoffersa7.5%holdingperiodreturnfortheyear.Ifyouforecastthattherateonmoneymarketinstrumentswillincreasesignificantlyabovethecurrent6%yield,thenthemoneymarketfundmightresultinahigherHPRthanthesavingsdeposit.The20-yearTreasurybondoffersayieldtomaturityof9%peryear,whichis150basispointshigherthantherateontheone-yearsavingsdeposit;however,youcouldearnaone-yearHPRmuchlessthan7.5%onthebondiflong-terminterestratesincreaseduringtheyear.IfTreasurybondyieldsriseabove9%,thenthepriceofthebondwillfall,andtheresultingcapitallosswillwipeoutsomeorallofthe9%returnyouwouldhaveearnedifbondyieldshadremainedunchangedoverthecourseoftheyear.5.a.Ifbusinessesreducetheircapitalspending,thentheyarelikelytodecreasetheirdemandforfunds.This课后答案网willshiftthedemandcurveinFigure5.1totheleftandreducetheequilibriumrealrateofinterest.b.Increasedhouseholdsavingwillshiftthesupplyoffundscurvetotherightandcauserealinterestratestofall.c.OpenmarketpurchasesofU.S.TreasurysecuritiesbytheFederalReserveBoardwww.hackshp.cnisequivalenttoanincreaseinthesupplyoffunds(ashiftofthesupplycurvetotheright).Theequilibriumrealrateofinterestwillfall.5-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter05-LearningAboutReturnandRiskfromtheHistoricalRecord6.a.The“Inflation-Plus”CDisthesaferinvestmentbecauseitguaranteesthepurchasingpoweroftheinvestment.Usingtheapproximationthattherealrateequalsthenominalrateminustheinflationrate,theCDprovidesarealrateof1.5%regardlessoftheinflationrate.b.Theexpectedreturndependsontheexpectedrateofinflationoverthenextyear.Iftheexpectedrateofinflationislessthan3.5%thentheconventionalCDoffersahigherrealreturnthantheInflation-PlusCD;iftheexpectedrateofinflationisgreaterthan3.5%,thentheoppositeistrue.c.Ifyouexpecttherateofinflationtobe3%overthenextyear,thentheconventionalCDoffersyouanexpectedrealrateofreturnof2%,whichis0.5%higherthantherealrateontheinflation-protectedCD.Butunlessyouknowthatinflationwillbe3%withcertainty,theconventionalCDisalsoriskier.Thequestionofwhichisthebetterinvestmentthendependsonyourattitudetowardsriskversusreturn.Youmightchoosetodiversifyandinvestpartofyourfundsineach.d.No.Wecannotassumethattheentiredifferencebetweentherisk-freenominalrate(onconventionalCDs)of5%andtherealrisk-freerate(oninflation-protectedCDs)of1.5%istheexpectedrateofinflation.PartofthedifferenceisprobablyariskpremiumassociatedwiththeuncertaintysurroundingtherealrateofreturnontheconventionalCDs.Thisimpliesthattheexpectedrateofinflationislessthan3.5%peryear.7.E(r)=[0.35×44.5%]+[0.30×14.0%]+[0.35×(–16.5%)]=14%σ2=[0.35×(44.5–14)2]+[0.30×(14–14)2]+[0.35×(–16.5–14)2]=651.175σ=25.52%课后答案网Themeanisunchanged,butthestandarddeviationhasincreased,astheprobabilitiesofthehighandlowreturnshaveincreased.8.Probabilitydistributionofpriceandone-yearholdingperiodreturnfora30-yearU.S.Treasurybond(whichwww.hackshp.cnwillhave29yearstomaturityatyear’send):CapitalCouponEconomyProbabilityYTMPriceHPRGainInterestBoom0.2011.0%$74.05−$25.95$8.00−17.95%NormalGrowth0.508.0%$100.00$0.00$8.008.00%Recession0.307.0%$112.28$12.28$8.0020.28%5-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter05-LearningAboutReturnandRiskfromtheHistoricalRecord9.E(q)=(0×0.25)+(1×0.25)+(2×0.50)=1.25σq=[0.25×(0–1.25)2+0.25×(1–1.25)2+0.50×(2–1.25)2]1/2=0.829210.(a)Withprobability0.9544,thevalueofanormallydistributedvariablewillfallwithintwostandarddeviationsofthemean;thatis,between–40%and80%.11.FromTable5.3,theaverageriskpremiumforlarge-capitalizationU.S.stocksfortheperiod1926-2005was:(12.15%−3.75%)=8.40%peryearAdding8.40%tothe6%risk-freeinterestrate,theexpectedannualHPRfortheS&P500stockportfoliois:6.00%+8.40%=14.40%12.Theaverageratesofreturnandstandarddeviationsarequitedifferentinthesubperiods:STOCKSStandardMeanSkewnessKurtosisDeviation1926–200512.15%20.26%-0.3605-0.06731976–200513.85%15.68%-0.4575-0.64891926–19416.39%30.33%-0.0022-1.0716BONDSStandardMeanSkewnessKurtosisDeviation1926–20055.68%8.09%0.99031.63141976–20059.57%10.32%0.3772-0.03291926–19414.42%4.32%-0.50360.5034Themostrelevantstatisticstouseforprojectingintothefuturewouldseemtobethestatisticsestimatedovertheperiod1976-2005,becausethislaterperiodseemstohave课后答案网beenadifferenteconomicregime.After1955,theU.S.economyenteredtheKeynesianera,whentheFederalgovernmentactivelyattemptedtostabilizetheeconomyandtopreventextremesinboomandbustcycles.Notethatthestandarddeviationofstockreturnshasdecreasedsubstantiallyinthelaterperiodwhilethestandarddeviationofbondreturnshasincreased.www.hackshp.cn1+RR−i.080−.07013.ar=−1===.00588=.588%1+i1+i.170b.r≈R−i=80%−70%=10%Clearly,theapproximationgivesarealHPRthatistoohigh.5-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter05-LearningAboutReturnandRiskfromtheHistoricalRecord14.FromTable5.2,theaveragerealrateonT-billshasbeen:0.72%a.T-bills:0.72%realrate+3%inflation=3.72%b.Expectedreturnonlargestocks:3.72%T-billrate+8.40%historicalriskpremium=12.12%c.Theriskpremiumonstocksremainsunchanged.Apremium,thedifferencebetweentworates,isarealvalue,unaffectedbyinflation.15.Realinterestratesareexpectedtorise.Theinvestmentactivitywillshiftthedemandforfundscurve(inFigure5.1)totheright.Thereforetheequilibriumrealinterestratewillincrease.16.a.ProbabilityDistributionoftheHPRontheStockMarketandPut:STOCKPUTStateoftheEndingPriceProbabilityHPREndingValueHPREconomy+DividendBoom0.30$13434%$0.00−100%NormalGrowth0.50$11414%$0.00−100%Recession0.20$84−16%$29.50146%Rememberthatthecostoftheindexfundis$100pershare,andthecostoftheputoptionis$12.b.Thecostofoneshareoftheindexfundplusaputoptionis$112.TheprobabilitydistributionoftheHPR课后答案网ontheportfoliois:EndingPriceStateoftheProbability+Put+HPREconomy$4DividendBoom0.30$134.0019.6%=(134−112)/112NormalGrowth0.50$114.001.8%=(114−112)/112Recessionwww.hackshp.cn0.20$113.501.3%=(113.50−112)/112c.BuyingtheputoptionguaranteestheinvestoraminimumHPRof1.3%regardlessofwhathappenstothestock"sprice.Thus,itoffersinsuranceagainstapricedecline.5-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter05-LearningAboutReturnandRiskfromtheHistoricalRecord17.TheprobabilitydistributionofthedollarreturnonCDpluscalloptionis:StateoftheEndingValueEndingValueCombinedProbabilityEconomyofCDofCallValueBoom0.30$114.00$19.50$133.50NormalGrowth0.50$114.00$0.00$114.00Recession0.20$114.00$0.00$114.00CFACFAPROBLEMSPROBLEMS1.Theexpecteddollarreturnontheinvestmentinequitiesis$18,000comparedtothe$5,000expectedreturnforT-bills.Therefore,theexpectedriskpremiumis$13,000.2.E(r)=[0.2×(−25%)]+[0.3×10%]+[0.5×24%]=10%3.E(rX)=[0.2×(−20%)]+[0.5×18%]+[0.3×50%]=20%E(rY)=[0.2×(−15%)]+[0.5×20%]+[0.3×10%]=10%4.σ2=[0.2×(–20–20)2]+[0.5×(18–20)2]+[0.3×(50–20)2]=592XσX=24.33%σ2=[0.2×(–15–10)2]+[0.5×(20–10)2]+[0.3×(10–10)2]=175YσX=13.23%课后答案网5.E(r)=(0.9×20%)+(0.1×10%)=19%6.Theprobabilitythattheeconomywillbeneutralis0.50,or50%.Givenaneutraleconomy,thestockwillwww.hackshp.cnexperiencepoorperformance30%ofthetime.Theprobabilityofbothpoorstockperformanceandaneutraleconomyistherefore:0.30×0.50=0.15=15%7.E(r)=(0.1×15%)+(0.6×13%)+(0.3×7%)=11.4%5-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssetsCHAPTER6:RISKRISKAVERSIONAVERSIONAVERSIONANDANDCAPITALCAPITALALLOCATIONALLOCATIONALLOCATIONTOTOTORISKYRISKYRISKYASSETSASSETSPROBLEMPROBLEMSETSSETS1.(e)2.(b)Ahigherborrowingisaconsequenceoftheriskoftheborrowers’default.Inperfectmarketswithnoadditionalcostofdefault,thisincrementwouldequalthevalueoftheborrower’soptiontodefault,andtheSharpemeasure,withappropriatetreatmentofthedefaultoption,wouldbethesame.However,inrealitytherearecoststodefaultsothatthispartoftheincrementlowerstheSharperatio.Also,noticethatanswer(c)isnotcorrectbecausedoublingtheexpectedreturnwithafixedrisk-freeratewillmorethandoubletheriskpremiumandtheSharperatio.3.Assumingnochangeinrisktolerance,thatis,anunchangedriskaversioncoefficient(A),thenhigherperceivedvolatilityincreasesthedenominatoroftheequationfortheoptimalinvestmentintheriskyportfolio(Equation6.12).Theproportioninvestedintheriskyportfoliowillthereforedecrease.4.a.Theexpectedcashflowis:(0.5×$70,000)+(0.5×200,000)=$135,000Withariskpremiumof8%overtherisk-freerateof6%,therequiredrateofreturnis14%.Therefore,thepresentvalueoftheportfoliois:$135,000/1.14=$118,421课后答案网b.Iftheportfolioispurchasedfor$118,421,andprovidesanexpectedcashinflowof$135,000,thentheexpectedrateofreturn[E(r)]isderivedasfollows:$118,421×www.hackshp.cn[1+E(r)]=$135,000Therefore,E(r)=14%.Theportfoliopriceissettoequatetheexpectedrateorreturnwiththerequiredrateofreturn.c.IftheriskpremiumoverT-billsisnow12%,thentherequiredreturnis:6%+12%=18%Thepresentvalueoftheportfolioisnow:$135,000/1.18=$114,4076-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssetsd.Foragivenexpectedcashflow,portfoliosthatcommandgreaterriskpremiamustsellatlowerprices.Theextradiscountfromexpectedvalueisapenaltyforrisk.5.WhenwespecifyutilitybyU=E(r)–0.5Aσ2,theutilitylevelforT-billsis:0.07Theutilitylevelfortheriskyportfoliois:U=0.12–0.5A(0.18)2=0.12–0.0162AInorderfortheriskyportfoliotobepreferredtobills,thefollowinginequalitymusthold:0.12–0.0162A>0.07⇒A<0.05/0.0162=3.09Amustbelessthan3.09fortheriskyportfoliotobepreferredtobills.6.PointsonthecurvearederivedbysolvingforE(r)inthefollowingequation:U=0.05=E(r)–0.5Aσ2=E(r)–1.5σ2ThevaluesofE(r),giventhevaluesofσ2,aretherefore:σσ2E(r)0.000.00000.050000.050.00250.053750.100.01000.065000.150.02250.083750.200.04000.110000.250.06250.14375Theboldlineinthefollowinggraph(labeledQ6,forQuestion6)depictstheindifferencecurve.课后答案网www.hackshp.cn6-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssetsE(r)U(Q7,A=4)U(Q6,A=3)5U(Q8,A=0)4U(Q9,A<0)σ7.RepeatingtheanalysisinProblem6,utilityisnow:U=E(r)–0.5Aσ2=E(r)–2.0σ2=0.04Theequal-utilitycombinationsofexpectedreturnandstandarddeviationarepresentedinthetablebelow.Theindifferencecurveistheupwardslopinglineinthegraphabove,labeledQ7(forQuestion7).σσ2E(r)0.000.0000课后答案网0.04000.050.00250.04500.100.01000.06000.150.02250.08500.200.04000.12000.250.0625www.hackshp.cn0.1650TheindifferencecurveinProblem7differsfromthatinProblem6inbothslopeandintercept.WhenAincreasesfrom3to4,theincreasedriskaversionresultsinagreaterslopefortheindifferencecurvesincemoreexpectedreturnisneededinordertocompensateforadditionalσ.ThelowerlevelofutilityassumedforProblem7(0.04ratherthan0.05)shiftstheverticalinterceptdownby1%.8.Thecoefficientofriskaversionforariskneutralinvestoriszero.Therefore,thecorrespondingutilityisequaltotheportfolio’sexpectedreturn.Thecorrespondingindifferencecurveintheexpectedreturn-standarddeviationplaneisahorizontalline,labeledQ8inthegraphabove(seeProblem6).6-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssets9.Arisklover,ratherthanpenalizingportfolioutilitytoaccountforrisk,derivesgreaterutilityasvarianceincreases.Thisamountstoanegativecoefficientofriskaversion.Thecorrespondingindifferencecurveisdownwardslopinginthegraphabove(seeProblem6),andislabeledQ9.10.Theportfolioexpectedreturnandvariancearecomputedasfollows:(1)(2)(3)(4)rPortfolioσPortfolioσ2PortfolioWBillsrBillsWIndexrIndex(1)×(2)+(3)×(4)(3)×20%0.05%1.013.5%13.5%=0.13520%=0.200.04000.25%0.813.5%11.8%=0.11816%=0.160.02560.45%0.613.5%10.1%=0.10112%=0.120.01440.65%0.413.5%8.4%=0.0848%=0.080.00640.85%0.213.5%6.7%=0.0674%=0.040.00161.05%0.013.5%5.0%=0.0500%=0.000.000011.ComputingutilityfromU=E(r)–0.522×Aσ=E(r)–1.5σ,wearriveatthevaluesinthecolumnlabeledU(A=3)inthefollowingtable:W2BillsWIndexrPortfolioσPortfolioσPortfolioU(A=3)U(A=5)0.01.00.1350.200.04000.07500.03500.20.80.1180.160.02560.07960.05400.40.60.1010.120.01440.07940.06500.60.40.0840.080.00640.07440.06800.80.20.0670.040.00160.06460.06301.00.00.0500.000.00000.05000.0500ThecolumnlabeledU(A=3)impliesthatinvestorswithA=3preferaportfoliothatisinvested80%inthemarketindexand20%inT-billstoanyoftheotherportfoliosinthe课后答案网table.12.ThecolumnlabeledU(A=5)inthetableaboveiscomputedfrom:U=E(r)–0.5Aσwww.hackshp.cn2=E(r)–2.5σ2Themoreriskaverseinvestorsprefertheportfoliothatisinvested40%inthemarketindex,ratherthanthe80%marketweightpreferredbyinvestorswithA=3.13.Expectedreturn=(0.7×18%)+(0.3×8%)=15%Standarddeviation=0.7×28%=19.6%6-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssets14.Investmentproportions:30.0%inT-bills0.7×25%=17.5%inStockA0.7×32%=22.4%inStockB0.7×43%=30.1%inStockC18−815.Yourreward-to-volatilityratio:S==.035712815−8Client"sreward-to-volatilityratio:S==.03571196.16.3025CAL(Slope=0.3571)20E(r)P15%Client1050课后答案网010203040σ(%)17.a.E(rC)=rf+y[E(rwww.hackshp.cnP)–rf]=8+y(18−8)Iftheexpectedreturnfortheportfoliois16%,then:16−816=8+10y⇒y==8.010Therefore,inordertohaveaportfoliowithexpectedrateofreturnequalto16%,theclientmustinvest80%oftotalfundsintheriskyportfolioand20%inT-bills.6-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssetsb.Client’sinvestmentproportions:20.0%inT-bills0.8×25%=20.0%inStockA0.8×32%=25.6%inStockB0.8×43%=34.4%inStockCc.σC=0.8×σP=0.8×28%=22.4%18.a.σC=y×28%Ifyourclientprefersastandarddeviationofatmost18%,then:y=18/28=0.6429=64.29%investedintheriskyportfoliob.E(rC)=8+10y=8+(0.6429×10)=8+6.429=14.429%E(rP)−rf0.18−0.080.1019.a.y*====0.364422Aσ3.5×0.280.2744PTherefore,theclient’soptimalproportionsare:36.44%investedintheriskyportfolioand63.56%investedinT-bills.b.E(rC)=8+10y*=8+(0.3644×10)=11.644%σC=0.3644×28=10.203%20.a.Iftheperiod1926-2005isassumedtoberepresentativeoffutureexpectedperformance,thenweusethefollowingdatatocomputethefractionallocatedtoequity:A=4,E(rM)−rf=8.39%,σM=20.54%(weusethestandarddeviationoftheriskpremiumfromTable6.8).Theny课后答案网*isgivenby:E(rM)−rf0.0839y*===0.497222Aσ4×0.2054MThatis,49.72%oftheportfolioshouldbeallocatedtoequityand50.28%shouldbeallocatedtoT-bills.www.hackshp.cnb.Iftheperiod1986-2005isassumedtoberepresentativeoffutureexpectedperformance,thenweusethefollowingdatatocomputethefractionallocatedtoequity:A=4,E(rM)−rf=8.60%,σM=16.24%andy*isgivenby:E(r)−r0.0860Mfy*===0.815222Aσ4×0.1624MTherefore,81.52%ofthecompleteportfolioshouldbeallocatedtoequityand18.48%shouldbeallocatedtoT-bills.6-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssetsc.Inpart(b),themarketriskpremiumisexpectedtobehigherthaninpart(a)andmarketriskislower.Therefore,thereward-to-volatilityratioisexpectedtobehigherinpart(b),whichexplainsthegreaterproportioninvestedinequity.8−521.a.E(rC)=8%=5%+y(11%–5%)⇒y==5.011−5b.σC=yσ=0.50×15%=7.5%Pc.Thefirstclientismoreriskaverse,allowingasmallerstandarddeviation.B22.Data:rf=5%,E(rM)=13%,σM=25%,andr=9%fTheCMLandindifferencecurvesareasfollows:E(r)borrowlendCALCMLP139课后答案网5σwww.hackshp.cn256-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssets23.Forytobelessthan1.0(sothattheinvestorisalender),riskaversion(A)mustbelargeenoughsuchthat:E(rM)−rf0.13−0.05y=<1⇒A>=1.2822Aσ0.25MForytobegreaterthan1.0(sothattheinvestorisaborrower),riskaversionmustbesmallenoughsuchthat:E(r)−r0.13−0.09Mfy=>1⇒A<=0.6422Aσ0.25MForvaluesofriskaversionwithinthisrange,theclientwillneitherborrownorlend,butinsteadwillholdacompleteportfoliocomprisedonlyoftheoptimalriskyportfolio:y=1for0.64≤Α≤1.2824.a.ThegraphforProblem22hastoberedrawnhere,with:E(rP)=11%andσP=15%0.11−0.05b.Foralendingposition:A>=2.6720.150.11−0.09Foraborrowingposition:A<=0.8920.15Therefore,y=1for0.89≤A≤2.67课后答案网www.hackshp.cn6-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssetsE(r)CMLM13FCAL1195σ152525.Themaximumfeasiblefee,denotedf,dependsonthereward-to-variabilityratio.Fory<1,thelendingrate,5%,isviewedastherelevantrisk-freerate,andwesolveforfasfollows:11−5−f13−515×8=⇒f=6−=2.1%1525课后答案网25Fory>1,theborrowingrate,9%,istherelevantrisk-freerate.Thenwenoticethat,evenwithoutafee,theactivefundisinferiortothepassivefundbecause:11−913−9=.013<=.01615www.hackshp.cn25Morerisktolerantinvestors(whoaremoreinclinedtoborrow)willnotbeclientsofthefundevenwithoutafee.(Ifyousolvedforthefeethatwouldmakeinvestorswhoborrowindifferentbetweentheactiveandpassiveportfolio,aswedidaboveforlendinginvestors,youwouldfindthatfisnegative:thatis,youwouldneedtopayinvestorstochooseyouractivefund.)Theseinvestorsdesirehigherrisk-higherreturncompleteportfoliosandthusareintheborrowingrangeoftherelevantCAL.Inthisrange,thereward-to-variabilityratiooftheindex(thepassivefund)isbetterthanthatofthemanagedfund.6-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssets13−826.a.SlopeoftheCML==.02025Thediagramfollows.b.Myfundallowsaninvestortoachieveahighermeanforanygivenstandarddeviationthanwouldapassivestrategy,i.e.,ahigherexpectedreturnforanygivenlevelofrisk.CMLandCAL1816CAL:Slope=0.357114ExpectedRetrunExpected1210CML:Slope=0.20Retrun864200102030StandardDeviation27.a.With70%ofhismoneyinvestedinmyfund’sportfolio,theclient’sexpectedreturnis15%peryearandstandarddeviation课后答案网is19.6%peryear.Ifheshiftsthatmoneytothepassiveportfolio(whichhasanexpectedreturnof13%andstandarddeviationof25%),hisoverallexpectedreturnbecomes:E(rC)=rf+0.7[E(rM)−rf]=8+[0.7×(13–8)]=11.5%Thestandarddeviationofthecompleteportfoliousingthepassiveportfoliowouldbe:www.hackshp.cnσC=0.7×σM=0.7×25%=17.5%Therefore,theshiftentailsadecreaseinmeanfrom14%to11.5%andadecreaseinstandarddeviationfrom19.6%to17.5%.Sincebothmeanreturnandstandarddeviationdecrease,itisnotyetclearwhetherthemoveisbeneficial.Thedisadvantageoftheshiftisthat,iftheclientiswillingtoacceptameanreturnonhistotalportfolioof11.5%,hecanachieveitwithalowerstandarddeviationusingmyfundratherthanthepassiveportfolio.6-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssetsToachieveatargetmeanof11.5%,wefirstwritethemeanofthecompleteportfolioasafunctionoftheproportioninvestedinmyfund(y):E(rC)=8+y(18−8)=8+10yOurtargetis:E(rC)=11.5%.Therefore,theproportionthatmustbeinvestedinmyfundisdeterminedasfollows:115.−811.5=8+10y⇒y==.03510Thestandarddeviationofthisportfoliowouldbe:σC=y×28%=0.35×28%=9.8%Thus,byusingmyportfolio,thesame11.5%expectedreturncanbeachievedwithastandarddeviationofonly9.8%asopposedtothestandarddeviationof17.5%usingthepassiveportfolio.b.Thefeewouldreducethereward-to-volatilityratio,i.e.,theslopeoftheCAL.Theclientwillbeindifferentbetweenmyfundandthepassiveportfolioiftheslopeoftheafter-feeCALandtheCMLareequal.Letfdenotethefee:18−8−f10−fSlopeofCALwithfee==282813−8SlopeofCML(whichrequiresnofee)==.02025Settingtheseslopesequalwehave:10−f=.020⇒10−f=28×0.20=5.6⇒f=10−5.6=4.4%peryear28课后答案网28.a.Theformulafortheoptimalproportiontoinvestinthepassiveportfoliois:E(r)−rMfy*=2Aσwww.hackshp.cnMSubstitutethefollowing:E(rM)=13%;rf=8%;σM=25%;A=3.5:0.13−0.08y*==0.228623.5×0.25b.TheanswerhereisthesameastheanswertoProblem27(b).Thefeethatyoucanchargeaclientisthesameregardlessoftheassetallocationmixoftheclient’sportfolio.Youcanchargeafeethatwillequatethereward-to-volatilityratioofyourportfoliotothatofyourcompetition.6-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssetsCFACFAPROBLEMSPROBLEMS1.Utilityforeachinvestment=E(r)–0.5×4×σ2Wechoosetheinvestmentwiththehighestutilityvalue.ExpectedStandardUtilityInvestmentreturndeviationUE(r)σ10.120.30-0.060020.150.50-0.350030.210.160.158840.240.210.15182.Wheninvestorsareriskneutral,thenA=0;theinvestmentwiththehighestutilityisInvestment4becauseithasthehighestexpectedreturn.3.(b)4.Indifferencecurve25.PointE6.(0.6×$50,000)+[0.4×(−$30,000)]−$5,000=$13,0007.(b)课后答案网8.Expectedreturnforequityfund=T-billrate+riskpremium=6%+10%=16%Expectedreturnofclient’soverallportfolio=(0.6×16%)+(0.4×6%)=12%Standarddeviationofwww.hackshp.cnclient’soverallportfolio=0.6×14%=8.4%109.Reward-to-volatilityratio==.071146-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssetsCHAPTERCHAPTER6:6:6:APPENDIXAPPENDIX1.Byyearend,the$50,000investmentwillgrowto:$50,000×1.06=$53,000Withoutinsurance,theprobabilitydistributionofend-of-yearwealthis:ProbabilityWealthNofire0.999$253,000Fire0.001$53,000Forthisdistribution,expectedutilityiscomputedasfollows:E[U(W)]=[0.999×ln(253,000)]+[0.001×ln(53,000)]=12.439582Thecertaintyequivalentis:W12.439582CE=e=$252,604.85Withfireinsurance,atacostof$P,theinvestmentintherisk-freeassetis:$(50,000–P)Year-endwealthwillbecertain(sinceyouarefullyinsured)andequalto:[$(50,000–P)×1.06]+$200,000SolveforPinthefollowingequation:[$(50,000–P)×1.06]+$200,000=$252,604.85⇒P=$372.78Thisisthemostyouarewillingtopayforinsurance.Notethattheexpectedlossis“only”$200,soyouarewillingtopayasubstantialriskpremiumovertheexpectedvalueoflosses.Theprimaryreasonisthatthevalueofthehouseisalargeproportionofyourwealth.课后答案网2.a.Withinsurancecoverageforone-halfthevalueofthehouse,thepremiumis$100,andtheinvestmentinthesafeassetis$49,900.Byyearend,theinvestmentof$49,900willgrowto:$49,900×1.06=$52,894Ifthereisafire,yourinsuranceproceedswww.hackshp.cnwillbe$100,000,andtheprobabilitydistributionofend-of-yearwealthis:ProbabilityWealthNofire0.999$252,894Fire0.001$152,894Forthisdistribution,expectedutilityiscomputedasfollows:E[U(W)]=[0.999×ln(252,894)]+[0.001×ln(152,894)]=12.4402225Thecertaintyequivalentis:W=e12.4402225=$252,766.77CE6-13若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter06-RiskAversionandCapitalAllocationtoRiskyAssetsb.Withinsurancecoverageforthefullvalueofthehouse,costing$200,end-of-yearwealthiscertain,andequalto:[($50,000–$200)×1.06]+$200,000=$252,788Sincewealthiscertain,thisisalsothecertaintyequivalentwealthofthefullyinsuredposition.c.Withinsurancecoveragefor1½timesthevalueofthehouse,thepremiumis$300,andtheinsurancepaysoff$300,000intheeventofafire.Theinvestmentinthesafeassetis$49,700.Byyearend,theinvestmentof$49,700willgrowto:$49,700×1.06=$52,682Theprobabilitydistributionofend-of-yearwealthis:ProbabilityWealthNofire0.999$252,682Fire0.001$352,682Forthisdistribution,expectedutilityiscomputedasfollows:E[U(W)]=[0.999×ln(252,682)]+[0.001×ln(352,682)]=12.4402205Thecertaintyequivalentis:W12.440222CE=e=$252,766.27Therefore,fullinsurancedominatesbothover-andunder-insurance.Over-insuringcreatesagamble(youactuallygainwhenthehouseburnsdown).Riskisminimizedwhenyouinsureexactlythevalueofthehouse.课后答案网www.hackshp.cn6-14若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfoliosCHAPTER7:OPTIMALOPTIMALRISKYRISKYRISKYPORTFOLIOSPORTFOLIOSPROBLEMPROBLEMSETSSETS1.(a)and(e).2.(a)and(c).Afterrealestateisaddedtotheportfolio,therearefourassetclassesintheportfolio:stocks,bonds,cashandrealestate.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[notethatCov(rS,rB)=ρσSσB]:BondsStocksBonds22545Stocks45课后答案网900Theminimum-varianceportfolioiscomputedasfollows:2σB−Covr(S,rB)225−45wMin(S)===.0173922σ+σ−2Covr(,r)900+225−(2×45)SBSBwMin(B)=1−0.1739=0.8261www.hackshp.cnTheminimumvarianceportfoliomeanandstandarddeviationare:E(rMin)=(0.1739×20)+(0.8261×12)=13.39%22222/1σ=[wσ+wσ+2wwCovr(,r)]MinSSBBSBSB=[(0.17392×900)+(0.82612×225)+(2×0.1739×0.8261×45)]1/2=13.92%7-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfolios5.ProportionProportionExpectedStandardinstockfundinbondfundreturnDeviation0.00%100.00%12.00%15.00%17.39%82.61%13.39%13.92%minimumvariance20.00%80.00%13.60%13.94%40.00%60.00%15.20%15.70%45.16%54.84%15.61%16.54%tangencyportfolio60.00%40.00%16.80%19.53%80.00%20.00%18.40%24.48%100.00%0.00%20.00%30.00%Graphshownbelow.25.00INVESTMENTOPPORTUNITYSETCML20.00TangencyPortfolioEfficientfrontier15.00ofriskyassets10.00MinimumVariancePortfolio5.00课后答案网0.000.005.0010.0015.0020.0025.0030.006.www.hackshp.cnThegraphindicatesthattheoptimalportfolioisthetangencyportfoliowithexpectedreturnapproximately15.6%andstandarddeviationapproximately16.5%.7-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfolios7.Theproportionoftheoptimalriskyportfolioinvestedinthestockfundisgivenby:2[Er()−r]σ−[Er()−r]Covr(,r)SfBBfSBw=S22[Er()−r]σ+[Er()−r]σ−[Er()−r+Er()−r]Covr(,r)SfBBfSSfBfSB[(20−8)×225]−[(12−8)×45]==.04516[(20−8)×225]+[(12−8)×900]−[(20−8+12−8)×45]wB=1−0.4516=0.5484Themeanandstandarddeviationoftheoptimalriskyportfolioare:E(rP)=(0.4516×20)+(0.5484×12)=15.61%σ2×900)+(0.54842×225)+(2×0.4516×0.5484×45)]1/2p=[(0.4516=16.54%8.Thereward-to-volatilityratiooftheoptimalCALis:Er(p)−rf15.61−8==.04601σ16.54p9.a.Ifyourequirethatyourportfolioyieldanexpectedreturnof14%,thenyoucanfindthecorrespondingstandarddeviationfromtheoptimalCAL.TheequationforthisCALis:Er()−rpfEr()=r+σ=8+.04601σCfCCσPSettingE(rC)equalto14%,wefindthatthestandarddeviationoftheoptimal课后答案网portfoliois13.04%.b.TofindtheproportioninvestedintheT-billfund,rememberthatthemeanofthecompleteportfolio(i.e.,14%)isanaverageoftheT-billrateandtheoptimalcombinationofstocksandbonds(P).LetybetheproportioninvestedintheportfolioP.Themeanwww.hackshp.cnofanyportfolioalongtheoptimalCALis:E(rC)=(l−y)rf+yE(rP)=rf+y[E(rP)−rf]=8+y(15.61−8)SettingE(rC)=14%wefind:y=0.7884and(1−y)=0.2116(theproportioninvestedintheT-billfund).Tofindtheproportionsinvestedineachofthefunds,multiply0.7884timestherespectiveproportionsofstocksandbondsintheoptimalriskyportfolio:Proportionofstocksincompleteportfolio=0.7884×0.4516=0.3560Proportionofbondsincompleteportfolio=0.7884×0.5484=0.43247-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfolios10.Usingonlythestockandbondfundstoachieveaportfolioexpectedreturnof14%,wemustfindtheappropriateproportioninthestockfund(wS)andtheappropriateproportioninthebondfund(wB=1−wS)asfollows:14=20wS+12(1−wS)=12+8wS⇒wS=0.25Sotheproportionsare25%investedinthestockfundand75%inthebondfund.Thestandarddeviationofthisportfoliowillbe:σ221/2P=[(0.25×900)+(0.75×225)+(2×0.25×0.75×45)]=14.13%Thisisconsiderablygreaterthanthestandarddeviationof13.04%achievedusingT-billsandtheoptimalportfolio.11.a.25.00OptimalCAL20.00PStocks15.0010.00Gold5.000.00课后答案网010203040StandardDeviation(%)Eventhoughitseemsthatgoldisdominatedbystocks,goldmightstillbeanattractiveassettoholdasawww.hackshp.cnpartofaportfolio.Ifthecorrelationbetweengoldandstocksissufficientlylow,goldwillbeheldasacomponentinaportfolio,specifically,theoptimaltangencyportfolio.b.Ifthecorrelationbetweengoldandstocksequals+1,thennoonewouldholdgold.TheoptimalCALwouldbecomprisedofbillsandstocksonly.Sincethesetofrisk/returncombinationsofstocksandgoldwouldplotasastraightlinewithanegativeslope(seethefollowinggraph),thesecombinationswouldbedominatedbythestockportfolio.Ofcourse,thissituationcouldnotpersist.Ifnoonedesiredgold,itspricewouldfallanditsexpectedrateofreturnwouldincreaseuntilitbecamesufficientlyattractivetoincludeinaportfolio.7-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfolios252018Stocks1510Gold5rf00.0010.0020.0030.0040.00StandardStandardDeviation(%)Deviation(%)12.SinceStockAandStockBareperfectlynegativelycorrelated,arisk-freeportfoliocanbecreatedandtherateofreturnforthisportfolio,inequilibrium,willbetherisk-freerate.Tofindtheproportionsofthisportfolio[withtheproportionwAinvestedinStockAandwB=(1–wA)investedinStockB],setthestandarddeviationequaltozero.Withperfectnegativecorrelation,theportfoliostandarddeviationis:σP=Absolutevalue课后答案网[wAσA−wBσB]0=5wA−[10×(1–wA)]⇒wA=0.6667Theexpectedrateofreturnforthisrisk-freeportfoliois:E(r)=(0.6667×10)+(0.3333×15)=11.667%Therefore,therisk-freeratewww.hackshp.cnis:11.667%13.False.Iftheborrowingandlendingratesarenotidentical,then,dependingonthetastesoftheindividuals(thatis,theshapeoftheirindifferencecurves),borrowersandlenderscouldhavedifferentoptimalriskyportfolios.7-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfolios14.False.Theportfoliostandarddeviationequalstheweightedaverageofthecomponent-assetstandarddeviationsonlyinthespecialcasethatallassetsareperfectlypositivelycorrelated.Otherwise,astheformulaforportfoliostandarddeviationshows,theportfoliostandarddeviationislessthantheweightedaverageofthecomponent-assetstandarddeviations.Theportfoliovarianceisaweightedsumoftheelementsinthecovariancematrix,withtheproductsoftheportfolioproportionsasweights.15.Theprobabilitydistributionis:ProbabilityRateofReturn0.7100%0.3−50%Mean=[0.7×100]+[0.3×(−50)]=55%Variance=[0.7×(100−55)2]+[0.3×(−50−55)2]=4725Standarddeviation=47251/2=68.74%16.σP=30=yσ=40y⇒y=0.75E(rP)=12+0.75(30−12)=25.5%17.Thecorrectchoiceisc.Intuitively,wenotethatsinceallstockshavethesameexpectedrateofreturnandstandarddeviation,wechoosethestockthatwillresultinlowestrisk.ThisisthestockthathasthelowestcorrelationwithStockA.Moreformally,wenotethatwhenallstockshavethesameexpectedrateofreturn,theoptimalportfolioforanyrisk-averseinvestor课后答案网istheglobalminimumvarianceportfolio(G).WhentheportfolioisrestrictedtoStockAandoneadditionalstock,theobjectiveistofindGforanypairthatincludesStockA,andthenselectthecombinationwiththelowestvariance.Withtwostocks,IandJ,theformulafortheweightsinGis:2σ−Covr(,r)JIJw)I(=Min22σI+σwww.hackshp.cnJ−2Covr(I,rJ)w(J)=1−w)I(MinMin7-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfoliosSinceallstandarddeviationsareequalto20%:Cov(rI,rJ)=ρσIσJ=400ρandwMin(I)=wMin(J)=0.5Thisintuitiveresultisanimplicationofapropertyofanyefficientfrontier,namely,thatthecovariancesoftheglobalminimumvarianceportfoliowithallotherassetsonthefrontierareidenticalandequaltoitsownvariance.(Otherwise,additionaldiversificationwouldfurtherreducethevariance.)Inthiscase,thestandarddeviationofG(I,J)reducesto:σ1/2Min(G)=[200(1+ρIJ)]ThisleadstotheintuitiveresultthatthedesiredadditionwouldbethestockwiththelowestcorrelationwithStockA,whichisStockD.TheoptimalportfolioisequallyinvestedinStockAandStockD,andthestandarddeviationis17.03%.18.No,theanswertoProblem17wouldnotchange,atleastaslongasinvestorsarenotrisklovers.Riskneutralinvestorswouldnotcarewhichportfoliotheyheldsinceallportfolioshaveanexpectedreturnof8%.19.No,theanswerstoProblems17and18wouldnotchange.Theefficientfrontierofriskyassetsishorizontalat8%,sotheoptimalCALrunsfromtherisk-freeratethroughG.ThebestPortfolioGis,again,theonewiththelowestvariance.Theoptimalcompleteportfoliodependsonriskaversion.20.Rearrangingthetable(convertingrowstocolumns),andcomputingserialcorrelationresultsinthefollowingtable:NominalRates课后答案网SmallLargeLong-termIntermed-termTreasurycompanycompanygovernmentgovernmentInflationbillsstocksstocksbondsbonds1920s-3.7218.363.983.773.56-1.001930s7.28-1.254.603.910.30-2.041940s20.63www.hackshp.cn9.113.591.700.375.361950s19.0119.410.251.111.872.221960s13.727.841.143.413.892.521970s8.755.906.636.116.297.361980s12.4617.6011.5012.019.005.101990s13.8418.208.607.745.022.93SerialCorrelation0.46-0.220.600.590.630.237-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfoliosForexample:tocomputeserialcorrelationindecadenominalreturnsforlarge-companystocks,wesetupthefollowingtwocolumnsinanExcelspreadsheet.Then,usetheExcelfunction“CORREL”tocalculatethecorrelationforthedata.DecadePrevious1930s-1.25%18.36%1940s9.11%-1.25%1950s19.41%9.11%1960s7.84%19.41%1970s5.90%7.84%1980s17.60%5.90%1990s18.20%17.60%Notethateachcorrelationisbasedononlysevenobservations,sowecannotarriveatanystatisticallysignificantconclusions.Lookingattheresults,however,itappearsthat,withtheexceptionoflarge-companystocks,thereispersistentserialcorrelation.(Thisconclusionchangeswhenweturntorealratesinthenextproblem.)21.Thetableforrealrates(usingtheapproximationofsubtractingadecade’saverageinflationfromthedecade’saveragenominalreturn)is:RealRatesSmallLargeLong-termIntermed-termTreasurycompanycompanygovernmentgovernmentbillsstocksstocksbondsbonds1920s-2.7219.364.984.774.561930s9.320.796.645.952.341940s15.273.75-1.77-3.66-4.991950s16.7917.19-1.97-1.11-0.351960s11.20课后答案网5.32-1.380.891.371970s1.39-1.46-0.73-1.25-1.071980s7.3612.506.406.913.901990s10.9115.275.674.812.09SerialCorrelation0.29-0.270.380.110.00Whiletheserialcorrelationindecadewww.hackshp.cnnominalreturnsseemstobepositive,itappearsthatrealratesareseriallyuncorrelated.Thedecadetimeseries(althoughagaintooshortforanydefinitiveconclusions)suggestthatrealratesofreturnareindependentfromdecadetodecade.7-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfoliosCFACFAPROBLEMSPROBLEMS1.a.Restrictingtheportfolioto20stocks,ratherthan40to50stocks,willincreasetheriskoftheportfolio,butitispossiblethattheincreaseinriskwillbeminimal.Supposethat,forinstance,the50stocksinauniversehavethesamestandarddeviation(σ)andthecorrelationsbetweeneachpairareidentical,withcorrelationcoefficientρ.Then,thecovariancebetweeneachpairofstockswouldbeρσ2,andthevarianceofanequallyweightedportfoliowouldbe:212n−12σ=σ+ρσPnnTheeffectofthereductioninnonthesecondtermontheright-handsidewouldberelativelysmall(since49/50iscloseto19/20andρσ2issmallerthanσ2),butthedenominatorofthefirsttermwouldbe20insteadof50.Forexample,ifσ=45%andρ=0.2,thenthestandarddeviationwith50stockswouldbe20.91%,andwouldriseto22.05%whenonly20stocksareheld.Suchanincreasemightbeacceptableiftheexpectedreturnisincreasedsufficiently.b.Hennessycouldcontaintheincreaseinriskbymakingsurethathemaintainsreasonablediversificationamongthe20stocksthatremaininhisportfolio.Thisentailsmaintainingalowcorrelationamongtheremainingstocks.Forexample,inpart(a),withρ=0.2,theincreaseinportfolioriskwasminimal.Asapracticalmatter,thismeansthatHennessywouldhavetospreadhisportfolioamongmanyindustries;concentratingonjustafewindustrieswouldresultinhighercorrelationsamongtheincludedstocks.2.Riskreductionbenefitsfromdiversificationarenotalinearfunctionofthenumber课后答案网ofissuesintheportfolio.Rather,theincrementalbenefitsfromadditionaldiversificationaremostimportantwhenyouareleastdiversified.RestrictingHenneseyto10insteadof20issueswouldincreasetheriskofhisportfoliobyagreateramountthanwouldareductioninthesizeoftheportfoliofrom30to20stocks.Inourexample,restrictingthenumberofstocksto10willincreasethestandarddeviationto23.81%.The1.76%increaseinstandarddeviationresultingfromgivingwww.hackshp.cnup10of20stocksisgreaterthanthe1.14%increasethatresultsfromgivingup30of50stocks.3.Thepointiswelltakenbecausethecommitteeshouldbeconcernedwiththevolatilityoftheentireportfolio.SinceHennessy’sportfolioisonlyoneofsixwell-diversifiedportfoliosandissmallerthantheaverage,theconcentrationinfewerissuesmighthaveaminimaleffectonthediversificationofthetotalfund.Hence,unleashingHennessytodostockpickingmaybeadvantageous.7-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfolios4.d.PortfolioYcannotbeefficientbecauseitisdominatedbyanotherportfolio.Forexample,PortfolioXhasbothhigherexpectedreturnandlowerstandarddeviation.5.c.6.d.7.b.8.a.9.c.10.Sincewedonothaveanyinformationaboutexpectedreturns,wefocusexclusivelyonreducingvariability.StocksAandChaveequalstandarddeviations,butthecorrelationofStockBwithStockC(0.10)islessthanthatofStockAwithStockB(0.90).Therefore,aportfoliocomprisedofStocksBandCwillhavelowertotalriskthanaportfoliocomprisedofStocksAandB.11.FundDrepresentsthesinglebestadditiontocomplementStephenson"scurrentportfolio,givenhisselectioncriteria.First,FundD’sexpectedreturn(14.0percent)hasthepotentialtoincreasetheportfolio’sreturnsomewhat.Second,FundD’srelativelylowcorrelationwithhiscurrentportfolio(+0.65)indicatesthatFundDwillprovidegreaterdiversificationbenefitsthananyoftheotheralternativesexceptFundB.TheresultofaddingFundDshouldbeaportfolio课后答案网withapproximatelythesameexpectedreturnandsomewhatlowervolatilitycomparedtotheoriginalportfolio.Theotherthreefundshaveshortcomingsintermsofeitherexpectedreturnenhancementorvolatilityreductionthroughdiversificationbenefits.FundAoffersthepotentialforincreasingtheportfolio’sreturn,butistoohighlycorrelatedtoprovidesubstantialvolatilityreductionbenefitsthroughdiversification.Fundwww.hackshp.cnBprovidessubstantialvolatilityreductionthroughdiversificationbenefits,butisexpectedtogenerateareturnwellbelowthecurrentportfolio’sreturn.FundChasthegreatestpotentialtoincreasetheportfolio’sreturn,butistoohighlycorrelatedwiththecurrentportfoliotoprovidesubstantialvolatilityreductionbenefitsthroughdiversification.7-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfolios12.a.SubscriptOPreferstotheoriginalportfolio,ABCtothenewstock,andNPtothenewportfolio.i.E(rNP)=wOPE(rOP)+wABCE(rABC)=(0.9×0.67)+(0.1×1.25)=0.728%ii.Cov=r×σOP×σABC=0.40×2.37×2.95=2.7966≅2.80iii.σ22221/2NP=[wOPσOP+wABCσABC+2wOPwABC(CovOP,ABC)]=[(0.92×2.372)+(0.12×2.952)+(2×0.9×0.1×2.80)]1/2=2.2673%≅2.27%b.SubscriptOPreferstotheoriginalportfolio,GStogovernmentsecurities,andNPtothenewportfolio.i.E(rNP)=wOPE(rOP)+wGSE(rGS)=(0.9×0.67)+(0.1×0.042)=0.645%ii.Cov=r×σOP×σGS=0×2.37×0=0iii.σNP=[wOP2σOP2+wGS2σGS2+2wOPwGS(CovOP,GS)]1/2=[(0.92×2.372)+(0.12×0)+(2×0.9×0.1×0)]1/2=2.133%≅2.13%c.Addingtherisk-freegovernmentsecuritieswouldresultinalowerbetaforthenewportfolio.Thenewportfoliobetawillbeaweightedaverageoftheindividualsecuritybetasintheportfolio;thepresenceoftherisk-freesecuritieswouldlowerthatweightedaverage.d.Thecommentisnotcorrect.Althoughtherespectivestandarddeviationsandexpectedreturnsforthetwosecuritiesunderconsiderationareequal,thecovariancesbetweeneachsecurityandtheoriginalportfolioareunknown,making课后答案网itimpossibletodrawtheconclusionstated.Forinstance,ifthecovariancesaredifferent,selectingonesecurityovertheothermayresultinalowerstandarddeviationfortheportfolioasawhole.Insuchacase,thatsecuritywouldbethepreferredinvestment,assumingallotherfactorsareequal.e.i.Graceclearlyexpressedthesentimentthattheriskwww.hackshp.cnoflosswasmoreimportanttoherthantheopportunityforreturn.Usingvariance(orstandarddeviation)asameasureofriskinhercasehasaseriouslimitationbecausestandarddeviationdoesnotdistinguishbetweenpositiveandnegativepricemovements.7-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter07-OptimalRiskyPortfoliosii.Twoalternativeriskmeasuresthatcouldbeusedinsteadofvarianceare:Rangeofreturns,whichconsidersthehighestandlowestexpectedreturnsinthefutureperiod,withalargerrangebeingasignofgreatervariabilityandthereforeofgreaterrisk.Semivariance,whichcanbeusedtomeasureexpecteddeviationsofreturnsbelowthemean,orsomeotherbenchmark,suchaszero.EitherofthesemeasureswouldpotentiallybesuperiortovarianceforGrace.Rangeofreturnswouldhelptohighlightthefullspectrumofrisksheisassuming,especiallythedownsideportionoftherangeaboutwhichsheissoconcerned.Semivariancewouldalsobeeffective,becauseitimplicitlyassumesthattheinvestorwantstominimizethelikelihoodofreturnsfallingbelowsometargetrate;inGrace’scase,thetargetratewouldbesetatzero(toprotectagainstnegativereturns).13.a.Systematicriskreferstofluctuationsinassetpricescausedbymacroeconomicfactorsthatarecommontoallriskyassets;hencesystematicriskisoftenreferredtoasmarketrisk.Examplesofsystematicriskfactorsincludethebusinesscycle,inflation,monetarypolicyandtechnologicalchanges.Firm-specificriskreferstofluctuationsinassetpricescausedbyfactorsthatareindependentofthemarket,suchasindustrycharacteristicsorfirmcharacteristics.Examplesoffirm-specificriskfactorsincludelitigation,patents,management,andfinancialleverage.b.Trudyshouldexplaintotheclientthatpickingonlythetopfivebestideaswouldmostlikelyresultintheclientholdingamuchmoreriskyportfolio.Thetotalriskofaportfolio,orportfoliovariance,isthecombinationofsystematicriskandfirm-specificrisk.课后答案网Thesystematiccomponentdependsonthesensitivityoftheindividualassetstomarketmovementsasmeasuredbybeta.Assumingtheportfolioiswelldiversified,thenumberofassetswillnotaffectthesystematicriskcomponentofportfoliovariance.Theportfoliobetadependsontheindividualsecuritybetasandtheportfolioweightsofthosesecurities.www.hackshp.cnOntheotherhand,thecomponentsoffirm-specificrisk(sometimescallednonsystematicrisk)arenotperfectlypositivelycorrelatedwitheachotherand,asmoreassetsareaddedtotheportfolio,thoseadditionalassetstendtoreduceportfoliorisk.Hence,increasingthenumberofsecuritiesinaportfolioreducesfirm-specificrisk.Forexample,apatentexpirationforonecompanywouldnotaffecttheothersecuritiesintheportfolio.Anincreaseinoilpricesmighthurtanairlinestockbutaidanenergystock.Asthenumberofrandomlyselectedsecuritiesincreases,thetotalrisk(variance)oftheportfolioapproachesitssystematicvariance.7-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModelsCHAPTER8:INDEXINDEXMODELSMODELSPROBLEMPROBLEMSETSSETS1.Theadvantageoftheindexmodel,comparedtotheMarkowitzprocedure,isthevastlyreducednumberofestimatesrequired.Inaddition,thelargenumberofestimatesrequiredfortheMarkowitzprocedurecanresultinlargeaggregateestimationerrorswhenimplementingtheprocedure.Thedisadvantageoftheindexmodelarisesfromthemodel’sassumptionthatreturnresidualsareuncorrelated.Thisassumptionwillbeincorrectiftheindexusedomitsasignificantriskfactor.2.Thetrade-offentailedindepartingfrompureindexinginfavorofanactivelymanagedportfolioisbetweentheprobability(orpossibility)ofsuperiorperformanceagainstthecertaintyofadditionalmanagementfees.3.Theanswertothisquestioncanbeseenfromtheformulasforw0andw*.Otherthingsheldequal,w0issmallerthegreatertheresidualvarianceofacandidateassetforinclusionintheportfolio.Further,weseethatregardlessofbeta,whenw0decreases,sodoesw*.Therefore,otherthingsequal,thegreatertheresidualvarianceofanasset,thesmalleritspositionintheoptimalriskyportfolio.Thatis,increasedfirm-specificriskreducestheextenttowhichanactiveinvestorwillbewillingtodepartfromanindexedportfolio.4.Thetotalriskpremiumequals:课后答案网α+(β×marketriskpremium).Wecallalphaa“nonmarket”returnpremiumbecauseitistheportionofthereturnpremiumthatisindependentofmarketperformance.TheSharperatioindicatesthatahigheralphamakesasecuritymoredesirable.Alpha,thenumeratoroftheSharperatio,isafixednumberthatisnotaffectedbythestandarddeviationofreturns,thedenominatoroftheSharperatio.Hence,anincreaseinalphawww.hackshp.cnincreasestheSharperatio.Sincetheportfolioalphaistheportfolio-weightedaverageofthesecurities’alphas,then,holdingallotherparametersfixed,anincreaseinasecurity’salpharesultsinanincreaseintheportfolioSharperatio.8-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModels5.a.Tooptimizethisportfolioonewouldneed:n=60estimatesofmeansn=60estimatesofvariances2n−n=,1770estimatesofcovariances22n+3nTherefore,intotal:=,1890estimates2b.Inasingleindexmodel:ri−rf=αi+βi(rM–rf)+eiEquivalently,usingexcessreturns:Ri=αi+βiRM+eiThevarianceoftherateofreturnoneachstockcanbedecomposedintothecomponents:22(l)Thevarianceduetothecommonmarketfactor:βσiM2(2)Thevarianceduetofirmspecificunanticipatedevents:σ(e)iInthismodel:Covr(,r)=ββσijijThenumberofparameterestimatesis:n=60estimatesofthemeanE(r)in=60estimatesofthesensitivitycoefficientβin=60estimatesofthefirm-specificvarianceσ2(ei)1estimateofthemarketmeanE(r课后答案网M)21estimateofthemarketvarianceσMTherefore,intotal,182estimates.Thus,thesingleindexmodelreducesthetotalnumberofrequiredparameterestimatesfrom1,890to182.Ingeneral,thenumberofparameterestimateswww.hackshp.cnisreducedfrom:2⎛n+3n⎞⎜⎟to(3n+2)⎜⎟⎝2⎠8-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModels6.a.Thestandarddeviationofeachindividualstockisgivenby:222/12σ=[βσ+σ(e)]iiMiSinceβA=0.8,βB=1.2,σ(eA)=30%,σ(eB)=40%,andσM=22%,weget:σ2221/2A=(0.8×22+30)=34.78%σ2221/2B=(1.2×22+40)=47.93%b.Theexpectedrateofreturnonaportfolioistheweightedaverageoftheexpectedreturnsoftheindividualsecurities:E(rP)=wAE(rA)+wBE(rB)+wfrfwherewA,wB,andwfaretheportfolioweightsforStockA,StockB,andT-bills,respectively.Substitutingintheformulaweget:E(rP)=(0.30×13)+(0.45×18)+(0.25×8)=14%Thebetaofaportfolioissimilarlyaweightedaverageofthebetasoftheindividualsecurities:βP=wAβA+wBβB+wfβfThebetaforT-bills(βf)iszero.Thebetafortheportfolioistherefore:βP=(0.30×0.8)+(0.45×1.2)+0=0.78Thevarianceofthisportfoliois:2222σ=βσ+σ(e)PPMP222whereβσisthesystematiccomponentandσ(e)isthenonsystematicPM课后答案网Pcomponent.Sincetheresiduals(ei)areuncorrelated,thenon-systematicvarianceis:2222222σ(e)=wσ(e)+wσ(e)+wσ(e)PAABBff=(0.302×30www.hackshp.cn2)+(0.452×402)+(0.252×0)=405whereσ2(e2A)andσ(eB)arethefirm-specific(nonsystematic)variancesofStocksAandB,andσ2(ef),thenonsystematicvarianceofT-bills,iszero.Theresidualstandarddeviationoftheportfolioisthus:σ(e1/2P)=(405)=20.12%Thetotalvarianceoftheportfolioisthen:222σ=(.078×22)+405=699.47PThestandarddeviationis26.45%.8-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModels7.a.Thetwofiguresdepictthestocks’securitycharacteristiclines(SCL).StockAhashigherfirm-specificriskbecausethedeviationsoftheobservationsfromtheSCLarelargerforStockAthanforStockB.DeviationsaremeasuredbytheverticaldistanceofeachobservationfromtheSCL.b.BetaistheslopeoftheSCL,whichisthemeasureofsystematicrisk.TheSCLforStockBissteeper;henceStockB’ssystematicriskisgreater.c.TheR2(orsquaredcorrelationcoefficient)oftheSCListheratiooftheexplainedvarianceofthestock’sreturntototalvariance,andthetotalvarianceisthesumoftheexplainedvarianceplustheunexplainedvariance(thestock’sresidualvariance):22βσ2iMR=222βσ+σ(e)iMiSincetheexplainedvarianceforStockBisgreaterthanforStockA(theexplained22varianceisβσ,whichisgreatersinceitsbetaishigher),anditsresidualBMvarianceσ2(e2B)issmaller,itsRishigherthanStockA’s.d.AlphaistheinterceptoftheSCLwiththeexpectedreturnaxis.StockAhasasmallpositivealphawhereasStockBhasanegativealpha;hence,StockA’salphaislarger.e.ThecorrelationcoefficientissimplythesquarerootofR2,soStockB’scorrelationwiththemarketishigher.8.a.Firm-specificriskismeasuredbytheresidualstandarddeviation.Thus,stockAhasmorefirm-specificrisk:10.3%>9.1%课后答案网b.Marketriskismeasuredbybeta,theslopecoefficientoftheregression.Ahasalargerbetacoefficient:1.2>0.8c.R2measuresthefractionoftotalvarianceofreturnexplainedbythemarketreturn.A’sR2islargerthanwww.hackshp.cnB’s:0.576>0.436d.RewritingtheSCLequationintermsoftotalreturn(r)ratherthanexcessreturn(R):rA–rf=α+β(rM–rf)⇒rA=α+rf(1−β)+βrMTheinterceptisnowequalto:α+rf(1−β)=1+rf(l–1.2)Sincerf=6%,theinterceptwouldbe:1–1.2=–0.2%8-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModels9.ThestandarddeviationofeachstockcanbederivedfromthefollowingequationforR2:22βσExplainedvariance2iMR==i2σTotalvarianceiTherefore:22222βAσM7.0×20σ===980A2R.020Aσ=31.30%AForstockB:2222.1×20σ==,4800B.012σ=69.28%B10.ThesystematicriskforAis:2222βσ=.070×20=196AMThefirm-specificriskofA(theresidualvariance)isthedifferencebetweenA’stotalriskanditssystematicrisk:980–196=784ThesystematicriskforBis:2222βσ=.120×20=576BM课后答案网B’sfirm-specificrisk(residualvariance)is:4800–576=422411.Thecovariancebetweenthereturnswww.hackshp.cnofAandBis(sincetheresidualsareassumedtobeuncorrelated):2Covr(,r)=ββσ=.070×.120×400=336ABABMThecorrelationcoefficientbetweenthereturnsofAandBis:Covr(A,rB)336ρ===.0155ABσσ31.30×69.28AB8-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModels12.NotethatthecorrelationisthesquarerootofR2:2ρ=RCov(r1/2A,rM)=ρσAσM=0.20×31.30×20=280Cov(r1/2B,rM)=ρσBσM=0.12×69.28×20=48013.ForportfolioPwecancompute:σ221/21/2P=[(0.6×980)+(0.4×4800)+(2×0.4×0.6×336]=[1282.08]=35.81%βP=(0.6×0.7)+(0.4×1.2)=0.9022222σ(e)=σ−βσ=1282.08−(0.90×400)=958.08PPPM2Cov(rP,rM)=βPσ=0.90×400=360MThissameresultcanalsobeattainedusingthecovariancesoftheindividualstockswiththemarket:Cov(rP,rM)=Cov(0.6rA+0.4rB,rM)=0.6Cov(rA,rM)+0.4Cov(rB,rM)=(0.6×280)+(0.4×480)=36014.NotethatthevarianceofT-billsiszero,andthecovarianceofT-billswithanyassetiszero.Therefore,forportfolioQ:[2222]/12σ=wσ+wσ+2×w×w×Covr(,r)QPPMMPMPM[22]2/1=(5.0×,1282.08)+(3.0×400)+(2×5.0×3.0×360)=21.55%β=wβ+wβ=(5.0×.090)+(3.0×1)+0=.075QPP课后答案网MM22222σ(e)=σ−βσ=464.52−(.075×400)=239.52QQQM2Covr(,r)=βσ=.075×400=300QMQMwww.hackshp.cn15.a.MerrillLynchadjustsbetabytakingthesampleestimateofbetaandaveragingitwith1.0,usingtheweightsof2/3and1/3,asfollows:adjustedbeta=[(2/3)×1.24]+[(1/3)×1.0]=1.16b.Ifyouuseyourcurrentestimateofbetatobeβt–1=1.24,thenβt=0.3+(0.7×1.24)=1.1688-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModels16.ForStockA:αA=rA−[rf+βA(rM−rf)]=11−[6+0.8(12−6)]=0.2%ForstockB:αB=14−[6+1.5(12−6)]=−1%StockAwouldbeagoodadditiontoawell-diversifiedportfolio.AshortpositioninStockBmaybedesirable.17.a.Alpha(α)Expectedexcessreturnαi=ri–[rf+βi(rM–rf)]E(ri)–rfα=20%–[8%+1.3(16%–8%)]=1.6%20%–8%=12%Aα=18%–[8%+1.8(16%–8%)]=–4.4%18%–8%=10%Bα=17%–[8%+0.7(16%–8%)]=3.4%17%–8%=9%Cα=12%–[8%+1.0(16%–8%)]=–4.0%12%–8%=4%DStocksAandChavepositivealphas,whereasstocksBandDhavenegativealphas.Theresidualvariancesare:σ2(e2A)=58=3,364σ2(e2B)=71=5,041σ2(e2C)=60=3,600σ2(eD)=552=3,025b.Toconstructtheoptimalriskyportfolio,wefirstdeterminetheoptimalactiveportfolio.课后答案网UsingtheTreynor-Blacktechnique,weconstructtheactiveportfolio:αα/σ2(e)σ2(e)ΣαΣα//σ2(e)www.hackshp.cnA0.000476–0.6142B–0.0008731.1265C0.000944–1.2181D–0.0013221.7058Total–0.0007751.0000Donotbeconcernedthatthepositivealphastockshavenegativeweightsandviceversa.Wewillseethattheentirepositionintheactiveportfoliowillbenegative,returningeverythingtogoodorder.8-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModelsWiththeseweights,theforecastfortheactiveportfoliois:α=[–0.6142×1.6]+[1.1265×(–4.4)]–[1.2181×3.4]+[1.7058×(–4.0)]=–16.90%β=[–0.6142×1.3]+[1.1265×1.8]–[1.2181×0.70]+[1.7058×1]=2.08Thehighbeta(higherthananyindividualbeta)resultsfromtheshortpositionsintherelativelylowbetastocksandthelongpositionsintherelativelyhighbetastocks.σ2(e)=[(–0.6142)2×3364]+[1.12652×5041]+[(–1.2181)2×3600]+[1.70582×3025]=21,809.6σ(e)=147.68%Here,again,theleveredpositioninstockB[withhighσ2(e)]overcomesthediversificationeffect,andresultsinahighresidualstandarddeviation.Theoptimalriskyportfoliohasaproportionw*intheactiveportfolio,computedasfollows:2α/σ(e)−16.90/21,8096.w===−.005124022[Er()−r]/σ8/23MfMThenegativepositionisjustifiedforthereasonstatedearlier.Theadjustmentforbetais:w−.0051240w*===−.004861+(1−β)w1+(1−.208)(−.005124)0Sincew*isnegative,theresultisapositivepositioninstockswithpositivealphasandanegativepositioninstockswithnegativealphas.Thepositionintheindexportfoliois:课后答案网1–(–0.0486)=1.0486c.TocalculateSharpe’smeasurefortheoptimalriskyportfolio,wecomputetheinformationratiofortheactiveportfolioandSharpe’smeasureforthemarketportfolio.Theinformationratiofortheactiveportfoliowww.hackshp.cniscomputedasfollows:A=α/σ(e)=–16.90/147.68=–0.1144A2=0.0131Hence,thesquareofSharpe’smeasure(S)oftheoptimizedriskyportfoliois:2222⎛8⎞S=SM+A=⎜⎟+.00131=.01341⎝23⎠S=0.36628-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModelsComparethistothemarket’sSharpemeasure:SM=8/23=0.3478Thedifferenceis:0.0184Notethattheonly-moderateimprovementinperformanceresultsfromthefactthatonlyasmallpositionistakenintheactiveportfolioAbecauseofitslargeresidualvariance.d.Tocalculatetheexactmakeupofthecompleteportfolio,wefirstcompute`themeanexcessreturnoftheoptimalriskyportfolioanditsvariance.Theriskyportfoliobetaisgivenby:βP=wM+(wA×βA)=1.0486+[(–0.0486)×2.08]=0.95E(RP)=αP+βPE(RM)=[(–0.0486)×(–16.90%)]+(0.95×8%)=8.42%22222(2)σ=βσ+σ(e)=(.095×23)+(−.00486)×21,8096.=528.94PPMPσP=23.00%SinceA=2.8,theoptimalpositioninthisportfoliois:.842y==.05685.001×8.2×528.94Incontrast,withapassivestrategy:8y==.054012.001×8.2×23Thisisadifferenceof:0.0284Thefinalpositionsofthecompleteportfolioare:课后答案网Bills1–0.5685=43.15%M0.5685×l.0486=59.61%A0.5685×(–0.0486)×(–0.6142)=1.70%B0.5685×(–0.0486)×1.1265=–3.11%C0.5685www.hackshp.cn×(–0.0486)×(–1.2181)=3.37%D0.5685×(–0.0486)×1.7058=–4.71%100.00%[sumissubjecttoroundingerror]NotethatMmayincludepositiveproportionsofstocksAthroughD.8-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModels18.a.Ifamanagerisnotallowedtosellshorthewillnotincludestockswithnegativealphasinhisportfolio,sohewillconsideronlyAandC:2αα/σ2(e)ασ(e)σ2(e)Σα/σ2(e)A1.63,3640.0004760.3352C3.43,6000.0009440.66480.0014201.0000Theforecastfortheactiveportfoliois:α=(0.3352×1.6)+(0.6648×3.4)=2.80%β=(0.3352×1.3)+(0.6648×0.7)=0.90σ2(e)=(0.33522×3,364)+(0.66482×3,600)=1,969.03σ(e)=44.37%Theweightintheactiveportfoliois:2α/σ(e).280/,1969.03w===.00940022E(R)/σ8/23MMAdjustingforbeta:w.00940w*===.009311+(1−β)w1+[(1−.090)×.0094]0Theinformationratiooftheactiveportfoliois:A=α/σ(e)=2.80/44.37=0.0631课后答案网Hence,thesquareofSharpe’smeasureis:S2=(8/23)2+0.06312=0.1250Therefore:S=0.3535www.hackshp.cnThemarket’sSharpemeasureis:SM=0.3478Whenshortsalesareallowed(Problem18),themanager’sSharpemeasureishigher(0.3662).ThereductionintheSharpemeasureisthecostoftheshortsalerestriction.8-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModelsThecharacteristicsoftheoptimalriskyportfolioare:βP=wM+wA×βA=(1–0.0931)+(0.0931×0.9)=0.99E(RP)=αP+βPE(RM)=(0.0931×2.8%)+(0.99×8%)=8.18%222222σ=βσ+σ(e)=(.099×23)+(.00931×,1969.03)=535.54PPMPσ=23.14%PWithA=2.8,theoptimalpositioninthisportfoliois:.818y==.05455.001×8.2×535.54Thefinalpositionsineachassetare:Bills1–0.5455=45.45%M0.5455×(1−0.0931)=49.47%A0.5455×0.0931×0.3352=1.70%C0.5455×0.0931×0.6648=3.38%100.00%b.Themeanandvarianceoftheoptimizedcompleteportfoliosintheunconstrainedandshort-salesconstrainedcases,andforthepassivestrategyare:2E(RC)σCUnconstrained0.56852×8.42=4.790.5685×528.94=170.95Constrained0.5455×8.18=4.460.54552×535.54=159.36Passive0.5401×8.00=4.320.54012×529.00=154.312Theutilitylevelsbelowarecomputedusingtheformula:Er()−.0005Aσ课后答案网CCUnconstrained8+4.79–(0.005×2.8×170.95)=10.40Constrained8+4.46–(0.005×2.8×159.36)=10.23Passivewww.hackshp.cn8+4.32–(0.005×2.8×154.31)=10.168-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModels19.Allalphasarereducedto0.3timestheirvaluesintheoriginalcase.Therefore,therelativeweightsofeachsecurityintheactiveportfolioareunchanged,butthealphaoftheactiveportfolioisonly0.3timesitspreviousvalue:0.3×−16.90%=−5.07%Theinvestorwilltakeasmallerpositionintheactiveportfolio.Theoptimalriskyportfoliohasaproportionw*intheactiveportfolioasfollows:2α/σ(e)−.507/21,8096.w===−.001537022Er(−r)/σ8/23MfMThenegativepositionisjustifiedforthereasongivenearlier.Theadjustmentforbetais:w−.0015370w*===−.001511+(1−β)w1+[(1−.208)×(−.001537)]0Sincew*isnegative,theresultisapositivepositioninstockswithpositivealphasandanegativepositioninstockswithnegativealphas.Thepositionintheindexportfoliois:1–(–0.0151)=1.0151TocalculateSharpe’smeasurefortheoptimalriskyportfoliowecomputetheinformationratiofortheactiveportfolioandSharpe’smeasureforthemarketportfolio.Theinformationratiooftheactiveportfoliois0.3timesitspreviousvalue:A=α/σ(e)=–5.07/147.68=–0.0343andA2=0.00118Hence,thesquareofSharpe’smeasureoftheoptimizedriskyportfoliois:S2=S2M+A2=(8/23)2+0.00118=0.1222S=0.3495Comparethistothemarket’sSharpemeasure:SM=8/23=0.3478Thedifferenceis:0.0017课后答案网Notethatthereductionoftheforecastalphasbyafactorof0.3reducedthesquaredinformationratioandtheimprovementinthesquaredSharperatiobyafactorof:0.32=0.09www.hackshp.cn20.Ifeachofthealphaforecastsisdoubled,thenthealphaoftheactiveportfoliowillalsodouble.Otherthingsequal,theinformationratio(IR)oftheactiveportfolioalsodoubles.ThesquareoftheSharperatiofortheoptimizedportfolio(S-square)equalsthesquareoftheSharperatioforthemarketindex(SM-square)plusthesquareoftheinformationratio.Sincetheinformationratiohasdoubled,itssquarequadruples.Therefore:S-square=SM-square+(4×IR)ComparedtothepreviousS-square,thedifferenceis:3IRNowyoucanembarkonthecalculationstoverifythisresult.8-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModelsCFACFAPROBLEMSPROBLEMS1.Theregressionresultsprovidequantitativemeasuresofreturnandriskbasedonmonthlyreturnsoverthefive-yearperiod.βforABCwas0.60,considerablylessthantheaveragestock’sβof1.0.Thisindicatesthat,whentheS&P500roseorfellby1percentagepoint,ABC’sreturnonaverageroseorfellbyonly0.60percentagepoint.Therefore,ABC’ssystematicrisk(ormarketrisk)waslowrelativetothetypicalvalueforstocks.ABC’salpha(theinterceptoftheregression)was–3.2%,indicatingthatwhenthemarketreturnwas0%,theaveragereturnonABCwas–3.2%.ABC’sunsystematicrisk(orresidualrisk),asmeasuredbyσ(e),was13.02%.ForABC,R2was0.35,indicatingclosenessoffittothelinearregressiongreaterthanthevalueforatypicalstock.βforXYZwassomewhathigher,at0.97,indicatingXYZ’sreturnpatternwasverysimilartotheβforthemarketindex.Therefore,XYZstockhadaveragesystematicriskfortheperiodexamined.AlphaforXYZwaspositiveandquitelarge,indicatingareturnofalmost7.3%,onaverage,forXYZindependentofmarketreturn.Residualriskwas21.45%,halfagainasmuchasABC’s,indicatingawiderscatterofobservationsaroundtheregressionlineforXYZ.Correspondingly,thefitoftheregressionmodelwasconsiderablylessthanthatofABC,consistentwithanR2ofonly0.17.Theeffectsofincludingoneortheotherofthesestocksinadiversifiedportfoliomaybequitedifferent.Ifitcanbeassumedthatbothstocks’betaswillremainstableovertime,thenthereisalargedifferenceinsystematicrisklevel.Thebetasobtainedfromthetwobrokeragehousesmayhelptheanalystdrawinferencesforthefuture.ThethreeestimatesofABC’sβaresimilar,regardlessofthesampleperiodoftheunderlyingdata.Therangeoftheseestimatesis0.60to0.71,wellbelowthemarketaverageβof1.0.ThethreeestimatesofXYZ课后答案网’sβvarysignificantlyamongthethreesources,rangingashighas1.45fortheweeklydataoverthemostrecenttwoyears.OnecouldinferthatXYZ’sβforthefuturemightbewellabove1.0,meaningitmighthavesomewhatgreatersystematicriskthanwasimpliedbythemonthlyregressionforthefive-yearperiod.Thesestocksappeartohavesignificantlydifferentsystematicriskcharacteristics.www.hackshp.cnIfthesestocksareaddedtoadiversifiedportfolio,XYZwilladdmoretototalvolatility.8-13若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter08-IndexModels2.TheR2oftheregressionis:0.702=0.49Therefore,51%oftotalvarianceisunexplainedbythemarket;thisisnonsystematicrisk.3.9=3+β(11−3)⇒β=0.754.d.5.b.课后答案网www.hackshp.cn8-14若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter09-TheCapitalAssetPricingModelCHAPTER9:THETHECAPITALCAPITALCAPITALASSETASSETASSETPRICINGPRICINGPRICINGMODELMODELPROBLEMPROBLEMSETSSETS1.E(rP)=rf+βP[E(rM)–rf]18=6+βP(14–6)⇒βP=12/8=1.52.Ifthesecurity’scorrelationcoefficientwiththemarketportfoliodoubles(withallothervariablessuchasvariancesunchanged),thenbeta,andthereforetheriskpremium,willalsodouble.Thecurrentriskpremiumis:14–6=8%Thenewriskpremiumwouldbe16%,andthenewdiscountrateforthesecuritywouldbe:16+6=22%Ifthestockpaysaconstantperpetualdividend,thenweknowfromtheoriginaldatathatthedividend(D)mustsatisfytheequationforthepresentvalueofaperpetuity:Price=Dividend/Discountrate50=D/0.14⇒D=50×0.14=$7.00Atthenewdiscountrateof22%,thestockwouldbeworth:$7/0.22=$31.82Theincreaseinstockriskhaslowereditsvalueby36.36%.3.a.False.β=0impliesE(r)=rf,notzero.b.False.Investorsrequireariskpremiumonlyforbearingsystematic(undiversifiableormarket)risk.Totalvolatilityincludesdiversifiablerisk.c.False.Yourportfolioshouldbeinvested75%inthemarketportfolioand25%in课后答案网T-bills.Then:βP=(0.75×1)+(0.25×0)=0.754.Theappropriatediscountratefortheprojectwww.hackshp.cnis:rf+β[E(rM)–rf]=8+[1.8×(16–8)]=22.4%Usingthisdiscountrate:10$15NPV=−$40+∑=−$40+[$15×Annuityfactor(22.4%,10years)]=$18.09tt=1.1224Theinternalrateofreturn(IRR)fortheprojectis35.73%.RecallfromyourintroductoryfinanceclassthatNPVispositiveifIRR>discountrate(or,equivalently,hurdlerate).ThehighestvaluethatbetacantakebeforethehurdlerateexceedstheIRRisdeterminedby:35.73=8+β(16–8)⇒β=27.73/8=3.479-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter09-TheCapitalAssetPricingModel5.a.CalltheaggressivestockAandthedefensivestockD.Betaisthesensitivityofthestock’sreturntothemarketreturn,i.e.,thechangeinthestockreturnperunitchangeinthemarketreturn.Therefore,wecomputeeachstock’sbetabycalculatingthedifferenceinitsreturnacrossthetwoscenariosdividedbythedifferenceinthemarketreturn:−2−38β==.200A5−256−12β==.030D5−25b.Withthetwoscenariosequallylikely,theexpectedreturnisanaverageofthetwopossibleoutcomes:E(rA)=0.5×(–2+38)=18%E(rD)=0.5×(6+12)=9%c.TheSMLisdeterminedbythemarketexpectedreturnof[0.5(25+5)]=15%,withabetaof1,andtheT-billreturnof6%withabetaofzero.Seethefollowinggraph.ExpectedReturn-BetaRelationship4035SML3025课后答案网αA2015ADM10ExpectedReturn5www.hackshp.cn000.511.522.53BetaTheequationforthesecuritymarketlineis:E(r)=6+β(15–6)9-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter09-TheCapitalAssetPricingModeld.Basedonitsrisk,theaggressivestockhasarequiredexpectedreturnof:E(rA)=6+2.0(15–6)=24%Theanalyst’sforecastofexpectedreturnisonly18%.Thusthestock’salphais:αA=actuallyexpectedreturn–requiredreturn(givenrisk)=18%–24%=–6%Similarly,therequiredreturnforthedefensivestockis:E(rD)=6+0.3(15–6)=8.7%Theanalyst’sforecastofexpectedreturnforDis9%,andhence,thestockhasapositivealpha:αD=actuallyexpectedreturn–requiredreturn(givenrisk)=9–8.7=+0.3%Thepointsforeachstockplotonthegraphasindicatedabove.e.Thehurdlerateisdeterminedbytheprojectbeta(0.3),notthefirm’sbeta.Thecorrectdiscountrateis8.7%,thefairrateofreturnforstockD.6.Notpossible.PortfolioAhasahigherbetathanPortfolioB,buttheexpectedreturnforPortfolioAislowerthantheexpectedreturnforPortfolioB.Thus,thesetwoportfolioscannotexistinequilibrium.7.Possible.IftheCAPMisvalid,theexpectedrateofreturncompensatesonlyforsystematic(market)risk,represented课后答案网bybeta,ratherthanforthestandarddeviation,whichincludesnonsystematicrisk.Thus,PortfolioA’slowerrateofreturncanbepairedwithahigherstandarddeviation,aslongasA’sbetaislessthanB’s.8.Notpossible.Thereward-to-variabilityratioforPortfolioAisbetterthanthatofthemarket.Thisscenariowww.hackshp.cnisimpossibleaccordingtotheCAPMbecausetheCAPMpredictsthatthemarketisthemostefficientportfolio.Usingthenumberssupplied:16−10S==5.0A1218−10S==.033M24PortfolioAprovidesabetterrisk-rewardtradeoffthanthemarketportfolio.9.Notpossible.PortfolioAclearlydominatesthemarketportfolio.PortfolioAhasbothalowerstandarddeviationandahigherexpectedreturn.9-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter09-TheCapitalAssetPricingModel10.Notpossible.TheSMLforthisscenariois:E(r)=10+β(18–10)Portfolioswithbetaequalto1.5haveanexpectedreturnequalto:E(r)=10+[1.5×(18–10)]=22%TheexpectedreturnforPortfolioAis16%;thatis,PortfolioAplotsbelowtheSML(αA=–6%),andhence,isanoverpricedportfolio.ThisisinconsistentwiththeCAPM.11.Notpossible.TheSMListhesameasinProblem10.Here,PortfolioA’srequiredreturnis:10+(0.9×8)=17.2%Thisisgreaterthan16%.PortfolioAisoverpricedwithanegativealpha:αA=–1.2%12.Possible.TheCMListhesameasinProblem8.PortfolioAplotsbelowtheCML,asanyassetisexpectedto.ThisscenarioisnotinconsistentwiththeCAPM.13.Sincethestock’sbetaisequalto1.2,itsexpectedrateofreturnis:6+[1.2×(16–6)]=18%D+P−P110E)r(=P06+P−501.018=⇒P=$53150课后答案网14.Theseriesof$1,000paymentsisaperpetuity.Ifbetais0.5,thecashflowshouldbediscountedattherate:6+[0.5×(16–6)]=11%PV=$1,000/0.11=$9,090.91www.hackshp.cnIf,however,betaisequalto1,thentheinvestmentshouldyield16%,andthepricepaidforthefirmshouldbe:PV=$1,000/0.16=$6,250Thedifference,$2,840.91,istheamountyouwilloverpayifyouerroneouslyassumethatbetais0.5ratherthan1.15.UsingtheSML:4=6+β(16–6)⇒β=–2/10=–0.29-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter09-TheCapitalAssetPricingModel16.r1=19%;r2=16%;β1=1.5;β2=1a.Todeterminewhichinvestorwasabetterselectorofindividualstockswelookatabnormalreturn,whichistheex-postalpha;thatis,theabnormalreturnisthedifferencebetweentheactualreturnandthatpredictedbytheSML.Withoutinformationabouttheparametersofthisequation(risk-freerateandmarketrateofreturn)wecannotdeterminewhichinvestorwasmoreaccurate.b.Ifrf=6%andrM=14%,then(usingthenotationalphafortheabnormalreturn):α1=19–[6+1.5(14–6)]=19–18=1%α2=16–[6+1(14–6)]=16–14=2%Here,thesecondinvestorhasthelargerabnormalreturnandthusappearstobethesuperiorstockselector.Bymakingbetterpredictions,thesecondinvestorappearstohavetiltedhisportfoliotowardunderpricedstocks.c.Ifrf=3%andrM=15%,then:α1=19–[3+1.5(15–3)]=19–21=–2%α2=16–[3+1(15–3)]=16–15=1%Here,notonlydoesthesecondinvestorappeartobethesuperiorstockselector,butthefirstinvestor’spredictionsappearvalueless(orworse).17.a.Sincethemarketportfolio,bydefinition,hasabetaof1,itsexpectedrateofreturnis12%.b.β=0meansno课后答案网systematicrisk.Hence,thestock’sexpectedrateofreturninmarketequilibriumistherisk-freerate,5%.c.UsingtheSML,thefairexpectedrateofreturnforastockwithβ=–0.5is:E(r)=5+[(–0.5)(12–5)]=1.5%Theactuallyexpectedrateofreturn,usingtheexpectedpriceanddividendforwww.hackshp.cnnextyearis:E(r)=[($41+$1)/40]–1=0.10=10%Becausetheactuallyexpectedreturnexceedsthefairreturn,thestockisunderpriced.18.Inthezero-betaCAPMthezero-betaportfolioreplacestherisk-freerate,andthus:E(r)=8+0.6(17–8)=13.4%9-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter09-TheCapitalAssetPricingModel19.a.E(rP)=rf+βP[E(rM)–rf]=5%+0.8(15%−5%)=13%α=14%−13%=1%Youshouldinvestinthisfundbecausealphaispositive.b.Thepassiveportfoliowiththesamebetaasthefundshouldbeinvested80%inthemarket-indexportfolioand20%inthemoneymarketaccount.Forthisportfolio:E(rP)=(0.8×15%)+(0.2×5%)=13%14%−13%=1%=α20.a.WewouldincorporateliquidityintotheCCAPMinamanneranalogoustothewayinwhichliquidityisincorporatedintotheconventionalCAPM.Inthelattercase,inadditiontothemarketriskpremium,expectedreturnisalsodependentontheexpectedcostofilliquidityandthreeliquidity-relatedbetaswhichmeasurethesensitivityof:(1)thesecurity’silliquiditytomarketilliquidity;(2)thesecurity’sreturntomarketilliquidity;and,(3)thesecurity’silliquiditytothemarketreturn.AsimilarapproachcanbeusedfortheCCAPM,exceptthattheliquiditybetaswouldbemeasuredrelativetoconsumptiongrowthratherthantheusualmarketindex.b.Asinpart(a),non-tradedassetswouldbeincorporatedintotheCCAPMinafashionsimilartothatdescribedabove,and,asinpart(a),wewouldreplacethemarketportfoliowithconsumptiongrowth.However,theissueofliquidityismoreacutewithnontraded-assetssuchasprivately-heldbusinessesandlaborincome.Whileownershipofaprivately-heldbusinessisanalogoustoownershipofanilliquidstock,weshouldexpectagreaterdegreeofilliquidityforthetypical课后答案网privatebusiness.Aslongastheownerofaprivately-heldbusinessissatisfiedwiththedividendspaidoutfromthebusiness,thenthelackofliquidityisnotanissue.However,iftheownerseekstorealizeincomegreaterthanthebusinesscanpayout,thensellingownership,infullorinpart,typicallyentailsasubstantialliquiditydiscount.Thecorrectionforilliquidityinthiscaseshouldbetreatedassuggestedinpart(a).www.hackshp.cnThesamegeneralconsiderationsapplytolaborincome,althoughitisprobablethatthelackofliquidityforlaborincomehasanevengreaterimpactonsecuritymarketequilibriumvalues.Laborincomehasamajorimpactonportfoliodecisions.Whileitispossibletoborrowagainstlaborincometosomedegree,andsomeoftheriskassociatedwithlaborincomecanbeamelioratedwithinsurance,itisplausiblethattheliquiditybetasofconsumptionstreamsarequitesignificant,astheneedtoborrowagainstlaborincomeislikelycyclical.9-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter09-TheCapitalAssetPricingModelCFACFAPROBLEMSPROBLEMS1.a.Agree;Regan’sconclusioniscorrect.Bydefinition,themarketportfolioliesonthecapitalmarketline(CML).Undertheassumptionsofcapitalmarkettheory,allportfoliosontheCMLdominate,inarisk-returnsense,portfoliosthatlieontheMarkowitzefficientfrontierbecause,giventhatleverageisallowed,theCMLcreatesaportfoliopossibilitylinethatishigherthanallpointsontheefficientfrontierexceptforthemarketportfolio,whichisRainbow’sportfolio.BecauseEagle’sportfolioliesontheMarkowitzefficientfrontieratapointotherthanthemarketportfolio,Rainbow’sportfoliodominatesEagle’sportfolio.b.Nonsystematicriskistheuniqueriskofindividualstocksinaportfoliothatisdiversifiedawaybyholdingawell-diversifiedportfolio.Totalriskiscomposedofsystematic(market)riskandnonsystematic(firm-specific)risk.Disagree;Wilson’sremarkisincorrect.BecausebothportfolioslieontheMarkowitzefficientfrontier,neitherEaglenorRainbowhasanynonsystematicrisk.Therefore,nonsystematicriskdoesnotexplainthedifferentexpectedreturns.ThedeterminingfactoristhatRainbowliesonthe(straight)line(theCML)connectingtherisk-freeassetandthemarketportfolio(Rainbow),atthepointoftangencytotheMarkowitz课后答案网efficientfrontierhavingthehighestreturnperunitofrisk.Wilson’sremarkisalsocounteredbythefactthat,sincenonsystematicriskcanbeeliminatedbydiversification,theexpectedreturnforbearingnonsystematiciszero.Thisisaresultofthefactthatwell-diversifiedinvestorsbidupthepriceofeverywww.hackshp.cnassettothepointwhereonlysystematicriskearnsapositivereturn(nonsystematicriskearnsnoreturn).2.E(r)=rf+β×[E(rM)−rf]FuhrmanLabs:E(r)=5+1.5×[11.5−5.0]=14.75%GartenTesting:E(r)=5+0.8×[11.5−5.0]=10.20%Iftheforecastrateofreturnislessthan(greaterthan)therequiredrateofreturn,thenthesecurityisovervalued(undervalued).FuhrmanLabs:Forecastreturn–Requiredreturn=13.25%−14.75%=−1.50%9-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter09-TheCapitalAssetPricingModelGartenTesting:Forecastreturn–Requiredreturn=11.25%−10.20%=1.05%Therefore,FuhrmanLabsisovervaluedandGartenTestingisundervalued.3.a.4.d.FromCAPM,thefairexpectedreturn=8+1.25(15−8)=16.75%Actuallyexpectedreturn=17%α=17−16.75=0.25%课后答案网www.hackshp.cn9-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter09-TheCapitalAssetPricingModel5.d.6.c.7.d.8.d.[Youneedtoknowtherisk-freerate]9.d.[Youneedtoknowtherisk-freerate]10.UndertheCAPM,theonlyriskthatinvestorsarecompensatedforbearingistheriskthatcannotbediversifiedaway(systematicrisk).Becausesystematicrisk(measuredbybeta)isequalto1.0forbothportfolios,aninvestorwouldexpectthesamerateofreturnfrombothportfoliosAandB.Moreover,sincebothportfoliosarewelldiversified,itdoesn’tmatterifthespecificriskoftheindividualsecuritiesishighorlow.Thefirm-specificriskhasbeendiversifiedawayforbothportfolios.11.a.McKayshouldborrowfundsandinvestthosefundsproportionatelyinMurray’sexistingportfolio(i.e.,buymoreriskyassetsonmargin).Inadditiontoincreasedexpectedreturn,thealternativeportfolioonthecapitalmarketlinewillalsohaveincreasedrisk,whichiscausedbythehigherproportionofriskyassetsinthetotalportfolio.b.McKayshouldsubstitutelowbetastocksforhighbetastocksinordertoreducetheoverallbetaofYork’sportfolio.Byreducingtheoverallportfoliobeta,McKaywillreducethesystematicriskoftheportfolio,andthereforereduceitsvolatility课后答案网relativetothemarket.Thesecuritymarketline(SML)suggestssuchaction(i.e.,movingdowntheSML),eventhoughreducingbetamayresultinaslightlossofportfolioefficiencyunlessfulldiversificationismaintained.York’sprimaryobjective,however,isnottomaintainefficiency,buttoreduceriskexposure;reducingportfoliobetameetsthatobjective.BecauseYorkdoesnotwanttowww.hackshp.cnengageinborrowingorlending,McKaycannotreduceriskbysellingequitiesandusingtheproceedstobuyrisk-freeassets(i.e.,lendingpartoftheportfolio).9-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter09-TheCapitalAssetPricingModel12.a.ExpectedReturnAlphaStockX5%+0.8(14%−5%)=12.2%14.0%−12.2%=1.8%StockY5%+1.5(14%−5%)=18.5%17.0%−18.5%=−1.5%b.i.KayshouldrecommendStockXbecauseofitspositivealpha,comparedtoStockY,whichhasanegativealpha.Ingraphicalterms,theexpectedreturn/riskprofileforStockXplotsabovethesecuritymarketline(SML),whiletheprofileforStockYplotsbelowtheSML.Also,dependingontheindividualriskpreferencesofKay’sclients,thelowerbetaforStockXmayhaveabeneficialeffectonoverallportfoliorisk.ii.KayshouldrecommendStockYbecauseithashigherforecastedreturnandlowerstandarddeviationthanStockX.TherespectiveSharperatiosforStocksXandYandthemarketindexare:StockX:(14%−5%)/36%=0.25StockY:(17%−5%)/25%=0.48Marketindex:(14%−5%)/15%=0.60ThemarketindexhasanevenmoreattractiveSharperatiothaneitheroftheindividualstocks,but,giventhechoicebetweenStockXandStockY,StockYisthesuperioralternative.Whenastockisheldasasinglestockportfolio,standarddeviationistherelevantriskmeasure.Forsuchaportfolio,betaasariskmeasureisirrelevant.Althoughholdingasingleassetisnotatypicallyrecommendedinvestmentstrategy,someinvestorsmayholdwhatisessentiallyasingle-assetportfoliowhentheyholdthestockoftheiremployercompany.Forsuchinvestors,therelevanceofstandard课后答案网deviationversusbetaisanimportantissue.www.hackshp.cn9-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter10-ArbitragePricingTheoryandMultifactorModelsofRiskandReturnCHAPTER10:ARBITRAGEARBITRAGEPRICINGPRICINGPRICINGTHEORYTHEORYANDANDMULTIFACTORMULTIFACTORMULTIFACTORMODELSMODELSMODELSOFOFOFRISKRISKRISKANDANDANDRETURNRETURNPROBLEMPROBLEMSETSSETS1.Therevisedestimateoftheexpectedrateofreturnonthestockwouldbetheoldestimateplusthesumoftheproductsoftheunexpectedchangeineachfactortimestherespectivesensitivitycoefficient:revisedestimate=12%+[(1×2%)+(0.5×3%)]=15.5%2.TheAPTfactorsmustcorrelatewithmajorsourcesofuncertainty,i.e.,sourcesofuncertaintythatareofconcerntomanyinvestors.Researchersshouldinvestigatefactorsthatcorrelatewithuncertaintyinconsumptionandinvestmentopportunities.GDP,theinflationrate,andinterestratesareamongthefactorsthatcanbeexpectedtodetermineriskpremiums.Inparticular,industrialproduction(IP)isagoodindicatorofchangesinthebusinesscycle.Thus,IPisacandidateforafactorthatishighlycorrelatedwithuncertaintiesthathavetodowithinvestmentandconsumptionopportunitiesintheeconomy.3.Anypatternofreturnscanbe“explained”ifwearefreetochooseanindefinitelylargenumberofexplanatoryfactors.Ifatheoryofassetpricingistohavevalue,itmustexplainreturnsusingareasonablylimitednumberofexplanatoryvariables(i.e.,systematicfactors).4.Equation10.9applieshere:课后答案网E(rp)=rf+βP1[E(r1)−rf]+βP2[E(r2)–rf]Weneedtofindtheriskpremium(RP)foreachofthetwofactors:RP1=[E(r1)−rf]andRP2=[E(r2)−rf]Inordertodoso,wesolvethefollowingsystemwww.hackshp.cnoftwoequationswithtwounknowns:31=6+(1.5×RP1)+(2.0×RP2)27=6+(2.2×RP1)+[(–0.2)×RP2]Thesolutiontothissetofequationsis:RP1=10%andRP2=5%Thus,theexpectedreturn-betarelationshipis:E(rP)=6%+(βP1×10%)+(βP2×5%)10-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter10-ArbitragePricingTheoryandMultifactorModelsofRiskandReturn5.TheexpectedreturnforPortfolioFequalstherisk-freeratesinceitsbetaequals0.ForPortfolioA,theratioofriskpremiumtobetais:(12−6)/1.2=5ForPortfolioE,theratioislowerat:(8–6)/0.6=3.33Thisimpliesthatanarbitrageopportunityexists.Forinstance,youcancreateaPortfolioGwithbetaequalto0.6(thesameasE’s)bycombiningPortfolioAandPortfolioFinequalweights.TheexpectedreturnandbetaforPortfolioGarethen:E(rG)=(0.5×12%)+(0.5×6%)=9%βG=(0.5×1.2)+(0.5×0)=0.6ComparingPortfolioGtoPortfolioE,Ghasthesamebetaandhigherreturn.Therefore,anarbitrageopportunityexistsbybuyingPortfolioGandsellinganequalamountofPortfolioE.Theprofitforthisarbitragewillbe:rG–rE=[9%+(0.6×F)]−[8%+(0.6×F)]=1%Thatis,1%ofthefunds(longorshort)ineachportfolio.6.Substitutingtheportfolioreturnsandbetasintheexpectedreturn-betarelationship,weobtaintwoequationswithtwounknowns,therisk-freerate(rf)andthefactorriskpremium(RP):12=rf+(1.2×RP)9=rf+(0.8×RP)Solvingtheseequations,weobtain:rf=3%andRP=7.5%课后答案网7.a.Shortinganequally-weightedportfolioofthetennegative-alphastocksandinvestingtheproceedsinanequally-weightedportfolioofthetenpositive-alphastockseliminatesthemarketexposureandcreatesazero-investmentportfolio.DenotingthesystematicmarketfactorasRM,theexpecteddollarreturnis(notingthattheexpectationofnon-systematicrisk,www.hackshp.cne,iszero):$1,000,000×[0.02+(1.0×RM)]−$1,000,000×[(–0.02)+(1.0×RM)]=$1,000,000×0.04=$40,000Thesensitivityofthepayoffofthisportfoliotothemarketfactoriszerobecausetheexposuresofthepositivealphaandnegativealphastockscancelout.(NoticethatthetermsinvolvingRMsumtozero.)Thus,thesystematiccomponentoftotalriskisalsozero.Thevarianceoftheanalyst’sprofitisnotzero,however,sincethisportfolioisnotwelldiversified.10-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter10-ArbitragePricingTheoryandMultifactorModelsofRiskandReturnForn=20stocks(i.e.,long10stocksandshort10stocks)theinvestorwillhavea$100,000position(eitherlongorshort)ineachstock.Netmarketexposureiszero,butfirm-specificriskhasnotbeenfullydiversified.Thevarianceofdollarreturnsfromthepositionsinthe20stocksis:20×[(100,000×0.30)2]=18,000,000,000Thestandarddeviationofdollarreturnsis$134,164.b.Ifn=50stocks(25stockslongand25stocksshort),theinvestorwillhavea$40,000positionineachstock,andthevarianceofdollarreturnsis:50×[(40,000×0.30)2]=7,200,000,000Thestandarddeviationofdollarreturnsis$84,853.Similarly,ifn=100stocks(50stockslongand50stocksshort),theinvestorwillhavea$20,000positionineachstock,andthevarianceofdollarreturnsis:100×[(20,000×0.30)2]=3,600,000,000Thestandarddeviationofdollarreturnsis$60,000.Noticethat,whenthenumberofstocksincreasesbyafactorof5(i.e.,from20to100),standarddeviationdecreasesbyafactorof5=2.23607(from$134,164to$60,000).22228.a.σ=βσ+σ(e)M2222σ=(8.0×20)+25=881A2222σ=(0.1×20)+10=500B课后答案网2222σ=(2.1×20)+20=976Cb.Ifthereareaninfinitenumberofassetswithidenticalcharacteristics,thenawell-diversifiedportfolioofeachtypewillhaveonlysystematicrisksincethenon-systematicriskwillwww.hackshp.cnapproachzerowithlargen.Themeanwillequalthatoftheindividual(identical)stocks.c.Thereisnoarbitrageopportunitybecausethewell-diversifiedportfoliosallplotonthesecuritymarketline(SML).Becausetheyarefairlypriced,thereisnoarbitrage.10-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter10-ArbitragePricingTheoryandMultifactorModelsofRiskandReturn9.a.Alongpositioninaportfolio(P)comprisedofPortfoliosAandBwillofferanexpectedreturn-betatradeofflyingonastraightlinebetweenpointsAandB.Therefore,wecanchooseweightssuchthatβP=βCbutwithexpectedreturnhigherthanthatofPortfolioC.Hence,combiningPwithashortpositioninCwillcreateanarbitrageportfoliowithzeroinvestment,zerobeta,andpositiverateofreturn.b.Theargumentinpart(a)leadstothepropositionthatthecoefficientofβ2mustbezeroinordertoprecludearbitrageopportunities.10.a.E(r)=6+(1.2×6)+(0.5×8)+(0.3×3)=18.1%b.Surprisesinthemacroeconomicfactorswillresultinsurprisesinthereturnofthestock:Unexpectedreturnfrommacrofactors=[1.2(4–5)]+[0.5(6–3)]+[0.3(0–2)]=–0.3%E(r)=18.1%−0.3%=17.8%11.TheAPTrequired(i.e.,equilibrium)rateofreturnonthestockbasedonrfandthefactorbetasis:requiredE(r)=6+(1×6)+(0.5×2)+(0.75×4)=16%Accordingtotheequationforthereturnonthestock,theactuallyexpectedreturnonthestockis15%(becausetheexpectedsurprisesonallfactorsarezerobydefinition).Becausetheactuallyexpectedreturnbasedonriskislessthantheequilibriumreturn,weconcludethatthestock课后答案网isoverpriced.12.Thefirsttwofactorsseempromisingwithrespecttothelikelyimpactonthefirm’scostofcapital.Botharemacrofactorsthatwouldelicithedgingdemandsacrossbroadsectorsofinvestors.Thethirdfactor,whileimportanttoPorkProducts,www.hackshp.cnisapoorchoiceforamultifactorSMLbecausethepriceofhogsisofminorimportancetomostinvestorsandisthereforehighlyunlikelytobeapricedriskfactor.Betterchoiceswouldfocusonvariablesthatinvestorsinaggregatemightfindmoreimportanttotheirwelfare.Examplesinclude:inflationuncertainty,short-terminterest-raterisk,energypricerisk,orexchangeraterisk.Theimportantpointhereisthat,inspecifyingamultifactorSML,wenotconfuseriskfactorsthatareimportanttoaparticularinvestorwithfactorsthatareimportanttoinvestorsingeneral;onlythelatterarelikelytocommandariskpremiuminthecapitalmarkets.10-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter10-ArbitragePricingTheoryandMultifactorModelsofRiskandReturn13.Themaximumresidualvarianceistiedtothenumberofsecurities(n)intheportfoliobecause,asweincreasethenumberofsecurities,wearemorelikelytoencountersecuritieswithlargerresidualvariances.Thestartingpointistodeterminethepracticallimitontheportfolioresidualstandarddeviation,σ(eP),thatstillqualifiesasa‘well-diversifiedportfolio.’Areasonableapproachistocompareσ2(eP)tothemarketvariance,orequivalently,tocompareσ(eP)tothemarketstandarddeviation.Supposewedonotallowσ(eP)toexceedpσM,wherepisasmalldecimalfraction,forexample,0.05;then,thesmallerthevaluewechooseforp,themorestringentourcriterionfordefininghowdiversifieda‘well-diversified’portfoliomustbe.Nowconstructaportfolioofnsecuritieswithweightsw1,w2,…,wn,sothatΣwi=1.Theportfolioresidualvarianceis:σ2(e22P)=Σw1σ(ei)Tomeetourpracticaldefinitionofsufficientlydiversified,werequirethisresidualvariancetobelessthan(pσM)2.Asureandsimplewaytoproceedistoassumetheworst,thatis,assumethattheresidualvarianceofeachsecurityisthehighestpossiblevalueallowedundertheassumptionsoftheproblem:σ2(ei)=nσ2M222Inthatcase:σ(eP)=ΣwinσMNowapplytheconstraint:Σwi2nσM2≤(pσM)2Thisrequiresthat:nΣw22i≤pOr,equivalently,that:Σwi2≤p2/nArelativelyeasywaytogenerateasetofwell-diversifiedportfoliosistouseportfolioweightsthatfollowageometricprogression,sincethecomputationsthenbecomerelativelystraightforward.Choosew1andacommonfactorqforthegeometricprogressionsuchthatq<1.Therefore,theweightoneachstockisafractionqoftheweightonthepreviousstockintheseries.Thenthesumofntermsis:Σwi=w1(1–qn)/(1–课后答案网q)=1or:w1=(1–q)/(1–qn)Thesumofthensquaredweightsissimilarlyobtainedfromw12andacommongeometricprogressionfactorofq2.Therefore:Σw222n2i=w1(1–qwww.hackshp.cn)/(1–q)Substitutingforw1fromabove,weobtain:Σw22n22n2i=[(1–q)/(1–q)]×[(1–q)/(1–q)]10-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter10-ArbitragePricingTheoryandMultifactorModelsofRiskandReturnForsufficientdiversification,wechooseqsothat:Σwi2≤p2/nForexample,continuetoassumethatp=0.05andn=1,000.Ifwechooseq=0.9973,thenwewillsatisfytherequiredcondition.Atthisvalueforq:w1,0001=0.0029andwn=0.0029×0.9973Inthiscase,w1isabout15timeswn.Despitethissignificantdeparturefromequalweighting,thisportfolioisneverthelesswelldiversified.Anyvalueofqbetween0.9973and1.0resultsinawell-diversifiedportfolio.Asqgetscloserto1,theportfolioapproachesequalweighting.14.a.Assumeasingle-factoreconomy,withafactorriskpremiumEManda(large)setofwell-diversifiedportfolioswithbetaβP.SupposewecreateaportfolioZbyallocatingtheportionwtoportfolioPand(1–w)tothemarketportfolioM.TherateofreturnonportfolioZis:RZ=(w×RP)+[(1–w)×RM]PortfolioZisrisklessifwechoosewsothatβZ=0.Thisrequiresthat:βZ=(w×βP)+[(1–w)×1]=0⇒w=1/(1–βP)and(1–w)=–βP/(1–βP)SubstitutethisvalueforwintheexpressionforRZ:RZ={[1/(1–βP)]×RP}–{[βP/(1–βP)]×RM}SinceβZ=0,then,inordertoavoidarbitrage,RZmustbezero.Thisimpliesthat:RP=βP×RMTakingexpectationswehave:EP=βP×课后答案网EMThisistheSMLforwell-diversifiedportfolios.b.Thesameargumentcanbeusedtoshowthat,inathree-factormodelwithfactorriskpremiumsEM,E1andE2,inordertoavoidarbitrage,wemusthave:EP=(βPM×www.hackshp.cnEM)+(βP1×E1)+(βP2×E2)ThisistheSMLforathree-factoreconomy.10-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter10-ArbitragePricingTheoryandMultifactorModelsofRiskandReturn15.a.TheFama-French(FF)three-factormodelholdsthatoneofthefactorsdrivingreturnsisfirmsize.Anindexwithreturnshighlycorrelatedwithfirmsize(i.e.,firmcapitalization)thatcapturesthisfactorisSMB(SmallMinusBig),thereturnforaportfolioofsmallstocksinexcessofthereturnforaportfoliooflargestocks.ThereturnsforasmallfirmwillbepositivelycorrelatedwithSMB.Moreover,thesmallerthefirm,thegreateritsresidualfromtheothertwofactors,themarketportfolioandtheHMLportfolio,whichisthereturnforaportfolioofhighbook-to-marketstocksinexcessofthereturnforaportfoliooflowbook-to-marketstocks.Hence,theratioofthevarianceofthisresidualtothevarianceofthereturnonSMBwillbelargerand,togetherwiththehighercorrelation,resultsinahighbetaontheSMBfactor.b.ThisquestionappearstopointtoaflawintheFFmodel.Themodelpredictsthatfirmsizeaffectsaveragereturns,sothat,iftwofirmsmergeintoalargerfirm,thentheFFmodelpredictsloweraveragereturnsforthemergedfirm.However,thereseemstobenoreasonforthemergedfirmtounderperformthereturnsofthecomponentcompanies,assumingthatthecomponentfirmswereunrelatedandthattheywillnowbeoperatedindependently.Wemightthereforeexpectthattheperformanceofthemergedfirmwouldbethesameastheperformanceofaportfoliooftheoriginallyindependentfirms,buttheFFmodelpredictsthattheincreasedfirmsizewillresultinloweraveragereturns.Therefore,thequestionrevolvesaroundthebehaviorofreturnsforaportfolioofsmallfirms,comparedtothereturnforlargerfirmsthatresultfrommergingthosesmallfirmsintolargerones.Hadpastmergersofsmallfirmsintolargerfirmsresulted,onaverage,innochangeintheresultantlargerfirms’stockreturncharacteristics(comparedtotheportfolioofstocksofthemergedfirms),thesizefactorintheFFmodelwouldhavefailed.Perhapsthereasonthesizefactorseemstohelpexplainstockreturns课后答案网isthat,whensmallfirmsbecomelarge,thecharacteristicsoftheirfortunes(andhencetheirstockreturns)changeinasignificantway.Putdifferently,stocksoflargefirmsthatresultfromamergerofsmallerfirmsappearempiricallytobehavedifferentlyfromportfoliosofthesmallercomponentfirms.Specifically,theFFmodelpredictsthatthelargefirmwillhaveasmallerriskpremium.Noticethatthisdevelopmentisnotnecessarilyabadthingforthestockholdersofthesmallerfirmswww.hackshp.cnthatmerge.Thelowerriskpremiummaybedue,inpart,totheincreaseinvalueofthelargerfirmrelativetothemergedfirms.10-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter10-ArbitragePricingTheoryandMultifactorModelsofRiskandReturnCFACFAPROBLEMSPROBLEMS1.a.Thisstatementisincorrect.TheCAPMrequiresamean-varianceefficientmarketportfolio,butAPTdoesnot.b.Thisstatementisincorrect.TheCAPMassumesnormallydistributedsecurityreturns,butAPTdoesnot.c.Thisstatementiscorrect.2.b.SincePortfolioXhasβ=1.0,thenXisthemarketportfolioandE(RM)=16%.UsingE(RM)=16%andrf=8%,theexpectedreturnforportfolioYisnotconsistent.3.d.4.c.5.d.6.c.Investorswilltakeonaslargeapositionaspossibleonlyifthemispricingopportunityisanarbitrage.Otherwise,considerationsofriskanddiversificationwilllimitthepositiontheyattempttotakeinthemispricedsecurity.7.d.课后答案网8.d.www.hackshp.cn10-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter11-TheEfficientMarketHypothesisCHAPTER11:THETHEEFFICIENTEFFICIENTEFFICIENTMARKETMARKETMARKETHYPOTHESISHYPOTHESISPROBLEMPROBLEMSETSSETS1.Thecorrelationcoefficientbetweenstockreturnsfortwonon-overlappingperiodsshouldbezero.Ifnot,onecouldusereturnsfromoneperiodtopredictreturnsinlaterperiodsandmakeabnormalprofits.2.No.Microsoft’scontinuingprofitabilitydoesnotimplythatstockmarketinvestorswhopurchasedMicrosoftsharesafteritssuccesswasalreadyevidentwouldhaveearnedanexceptionallyhighreturnontheirinvestments.3.Expectedratesofreturndifferbecauseofdifferentialriskpremiums.4.No.Thevalueofdividendpredictabilitywouldbealreadyreflectedinthestockprice.5.Overthelonghaul,thereisanexpectedupwarddriftinstockpricesbasedontheirfairexpectedratesofreturn.Thefairexpectedreturnoveranysingledayisverysmall(e.g.,12%peryearisonlyabout0.03%perday),sothatonanydaythepriceisvirtuallyequallylikelytoriseorfall.However,overlongerperiods,thesmallexpecteddailyreturnsaccumulate,andupwardmovesareindeedmorelikelythandownwardones.课后答案网6.c.Thisisapredictablepatterninreturnswhichshouldnotoccuriftheweak-formEMHisvalid.www.hackshp.cn7.c.Thisisaclassicfilterrulewhichshouldnotproducesuperiorreturnsinanefficientmarket.8.b.Thisisthedefinitionofanefficientmarket.9.c.TheP/Eratioispublicinformationandshouldnotbepredictiveofabnormalsecurityreturns.11-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter11-TheEfficientMarketHypothesis10.d.Inasemistrong-formefficientmarket,itisnotpossibletoearnabnormallyhighprofitsbytradingonpubliclyavailableinformation.InformationaboutP/Eratiosandrecentpricechangesispubliclyknown.Ontheotherhand,aninvestorwhohasadvanceknowledgeofmanagementimprovementscouldearnabnormallyhightradingprofits(unlessthemarketisalsostrong-formefficient).11.Thequestionregardingmarketefficiencyiswhetherinvestorscanearnabnormalrisk-adjustedprofits.Ifthestockpricerun-upoccurswhenonlyinsidersareawareofthecomingdividendincrease,thenitisaviolationofstrong-form,butnotsemistrong-form,efficiency.Ifthepublicalreadyknowsoftheincrease,thenitisaviolationofsemistrong-formefficiency.12.Whilepositivebetastocksrespondwelltofavorablenewinformationabouttheeconomy’sprogressthroughthebusinesscycle,theyshouldnotshowabnormalreturnsaroundalreadyanticipatedevents.Ifarecovery,forexample,isalreadyanticipated,theactualrecoveryisnotnews.Thestockpriceshouldalreadyreflectthecomingrecovery.13.a.Consistent.Basedonpureluck,halfofallmanagersshouldbeatthemarketinanyyear.b.Inconsistent.Thiswouldbethebasisofan“easymoney”rule:simplyinvestwithlastyear"sbestmanagers.c.Consistent.Incontrasttopredictablereturns,predictablevolatilitydoesnotconveyameanstoearnabnormalreturns.课后答案网d.Inconsistent.TheabnormalperformanceoughttooccurinJanuarywhenearningsareannounced.e.Inconsistent.Reversalsofferameanstoearneasymoney:justbuylastweek’slosers.www.hackshp.cn14.Thereturnonthemarketis8%.Therefore,theforecastmonthlyreturnforGMis:0.10%+(1.1×8%)=8.9%GM’sactualreturnwas7%,sotheabnormalreturnwas–1.9%.11-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter11-TheEfficientMarketHypothesis15.a.Basedonbroadmarkettrends,theCAPMindicatesthatAmbChaserstockshouldhaveincreasedby:1.0%+2.0(1.5%–1.0%)=2.0%Itsfirm-specific(nonsystematic)returnduetothelawsuitis$1millionper$100millioninitialequity,or1%.Therefore,thetotalreturnshouldbe3%.(Itisassumedherethattheoutcomeofthelawsuithadazeroexpectedvalue.)b.Ifthesettlementwasexpectedtobe$2million,thentheactualsettlementwasa“$1milliondisappointment,”andsothefirm-specificreturnwouldbe–1%,foratotalreturnof2%–1%=1%.16.Givenmarketperformance,predictedreturnsonthetwostockswouldbe:Apex:0.2%+(1.4×3%)=4.4%Bpex:–0.1%+(0.6×3%)=1.7%Apexunderperformedthisprediction;Bpexoutperformedtheprediction.WeconcludethatBpexwonthelawsuit.17.a.E(rM)=12%,rf=4%andβ=0.5Therefore,theexpectedrateofreturnis:4%+0.5(12%–4%)=8%Ifthestockisfairlypriced,thenE(r)=8%.b.IfrMfallsshortofyourexpectationby2%(thatis,10%–12%)thenyouwouldexpectthereturnforChangingFortunesIndustriestofallshortofyouroriginalexpectationby:课后答案网β×2%=1%Therefore,youwouldforecasta“revised”expectationforChangingFortunesof:8%–1%=7%c.Givenamarketreturnof10%,youwouldforecastareturnforChangingFortunesof7%.Theactualreturnis10%.Therefore,thesurpriseduetofirm-specificfactorsis10%–7%=3%whichweattributetothesettlement.Becausethefirmwww.hackshp.cnisinitiallyworth$100million,thesurpriseamountofthesettlementis3%of$100million,or$3million,implyingthatthepriorexpectationforthesettlementwasonly$2million.18.Implicitinthedollar-costaveragingstrategyisthenotionthatstockpricesfluctuatearounda“normal”level.Otherwise,thereisnomeaningtostatementssuchas:“whenthepriceishigh.”Howdoweknow,forexample,whetherapriceof$25todaywillturnouttobeviewedashighorlowcomparedtothestockpricesixmonthsfromnow?11-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter11-TheEfficientMarketHypothesis19.Themarketrespondspositivelytonewnews.Iftheeventualrecoveryisanticipated,thentherecoveryisalreadyreflectedinstockprices.Onlyabetter-than-expectedrecoveryshouldaffectstockprices.20.Buy.Inyourview,thefirmisnotasbadaseveryoneelsebelievesittobe.Therefore,youviewthefirmasundervaluedbythemarket.Youarelesspessimisticaboutthefirm’sprospectsthanthebeliefsbuiltintothestockprice.21.Hereweneedatwo-factormodelrelatingFord’sreturntothoseofboththebroadmarketandtheautoindustry.IfwecallrItheindustryreturn,thenwewouldfirstestimateparametersa,b,cinthefollowingregression:rFORD=a+brM+crI+eGiventheseestimateswewouldcalculateFord’sfirm-specificreturnas:rFORD−[a+brM+crI+e]Thisestimateoffirm-specificnewswouldmeasurethemarket’sassessmentofthepotentialprofitabilityofFord’snewmodel.22.Themarketmayhaveanticipatedevengreaterearnings.Comparedtopriorexpectations,theannouncementwasadisappointment.23.Thenegativeabnormalreturns(downwarddriftinCAR)justpriortostockpurchasessuggestthatinsidersdeferredtheirpurchasesuntilafterbadnewswasreleasedtothepublic.Thisisevidenceofvaluableinsideinformation.Thepositiveabnormalreturnsafterpurchasesuggestinsiderpurchasesinanticipationofgoodnews.Theanalysisissymmetricforinsidersales.课后答案网CFACFAPROBLEMSPROBLEMS1.b.Semi-strongformefficiencyimpliesthatmarketpricesreflectwww.hackshp.cnallpubliclyavailableinformationconcerningpasttradinghistoryaswellasfundamentalaspectsofthefirm.2.a.Thefullpriceadjustmentshouldoccurjustasthenewsaboutthedividendbecomespubliclyavailable.3.d.IflowP/Estockstendtohavepositiveabnormalreturns,thiswouldrepresentanunexploitedprofitopportunitythatwouldprovideevidencethatinvestorsarenotusingallavailableinformationtomakeprofitableinvestments.11-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter11-TheEfficientMarketHypothesis4.c.Inanefficientmarket,nosecuritiesareconsistentlyoverpricedorunderpriced.Whilesomesecuritieswillturnoutafteranyinvestmentperiodtohaveprovidedpositivealphas(i.e.,risk-adjustedabnormalreturns)andsomenegativealphas,thesepastreturnsarenotpredictiveoffuturereturns.5.c.Arandomwalkimpliesthatstockpricechangesareunpredictable,usingpastpricechangesoranyotherdata.6.d.Agradualadjustmenttofundamentalvalueswouldallowfortheuseofstrategiesbasedonpastpricemovementsinordertogenerateabnormalprofits.7.a.8.a.SomeempiricalevidencethatsupportstheEMH:(i)professionalmoneymanagersdonottypicallyearnhigherreturnsthancomparablerisk,passiveindexstrategies;(ii)eventstudiestypicallyshowthatstocksrespondimmediatelytothepublicreleaseofrelevantnews;(iii)mosttestsoftechnicalanalysisfindthatitisdifficulttoidentifypricetrendsthatcanbeexploitedtoearnsuperiorrisk-adjustedinvestmentreturns.b.SomeevidencethatisdifficulttoreconcilewiththeEMHconcernssimpleportfoliostrategiesthatapparentlywouldhaveprovidedhighrisk-adjustedreturnsinthepast.Someexamplesofportfolioswithattractivehistoricalreturns:(i)lowP/Estocks;(ii)highbook-to-marketratiostocks;课后答案网(iii)smallfirmsinJanuary;(iv)firmswithverypoorstockpriceperformanceinthelastfewmonths.Otherevidenceconcernspost-earnings-announcementstockpricedriftandintermediate-termpricemomentum.www.hackshp.cnc.Aninvestormightchoosenottoindexevenifmarketsareefficientbecauseheorshemaywanttotailoraportfoliotospecifictaxconsiderationsortospecificriskmanagementissues,forexample,theneedtohedge(oratleastnotaddto)exposuretoaparticularsourceofrisk(e.g.,industryexposure).11-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter11-TheEfficientMarketHypothesis9.a.Theefficientmarkethypothesis(EMH)statesthatamarketisefficientifsecuritypricesimmediatelyandfullyreflectallavailablerelevantinformation.Ifthemarketfullyreflectsinformation,theknowledgeofthatinformationwouldnotallowaninvestortoprofitfromtheinformationbecausestockpricesalreadyincorporatetheinformation.i.TheweakformoftheEMHassertsthatstockpricesreflectalltheinformationthatcanbederivedbyexaminingmarkettradingdatasuchasthehistoryofpastpricesandtradingvolume.Astrongbodyofevidencesupportsweak-formefficiencyinthemajorU.S.securitiesmarkets.Forexample,testresultssuggestthattechnicaltradingrulesdonotproducesuperiorreturnsafteradjustingfortransactioncostsandtaxes.ii.Thesemistrongformstatesthatafirm’sstockpricereflectsallpubliclyavailableinformationaboutafirm’sprospects.Examplesofpubliclyavailableinformationarecompanyannualreportsandinvestmentadvisorydata.Evidencestronglysupportsthenotionofsemistrongefficiency,butoccasionalstudies(e.g.,thoseidentifyingmarketanomaliessuchasthesmall-firm-in-Januaryorbook-to-marketeffects)andevents(suchasthestockmarketcrashofOctober19,1987)areinconsistentwiththisformofmarketefficiency.However,thereisaquestionconcerningtheextenttowhichthese“anomalies”resultfromdatamining.iii.ThestrongformoftheEMHholdsthatcurrentmarketpricesreflectallinformation(whetherpubliclyavailableorprivatelyheld)thatcanberelevanttothevaluationofthefirm.Empiricalevidencesuggeststhatstrong-formefficiencydoesnothold.Ifthisformwerecorrect,priceswouldfullyreflectallinformation.Thereforeeveninsiderscouldnotearnexcessreturns.Buttheevidenceisthatcorporateofficersdohaveaccesstopertinentinformationlongenoughbeforepublicreleasetoenablethemto课后答案网profitfromtradingonthisinformation.b.i.Technicalanalysisinvolvesthesearchforrecurrentandpredictablepatternsinstockpricesinordertoenhancereturns.TheEMHimpliesthattechnicalanalysisiswithoutvalue.Ifpastpricescontainnousefulinformationforpredictingfutureprices,thereisnopointinfollowinganytechnicaltradingrule.www.hackshp.cnii.Fundamentalanalysisusesearningsanddividendprospectsofthefirm,expectationsoffutureinterestrates,andriskevaluationofthefirmtodetermineproperstockprices.TheEMHpredictsthatmostfundamentalanalysisisdoomedtofailure.Accordingtosemistrong-formefficiency,noinvestorcanearnexcessreturnsfromtradingrulesbasedonpubliclyavailableinformation.Onlyanalystswithuniqueinsightachievesuperiorreturns.11-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter11-TheEfficientMarketHypothesisInsummary,theEMHholdsthatthemarketappearstoadjustsoquicklytoinformationaboutbothindividualstocksandtheeconomyasawholethatnotechniqueofselectingaportfoliousingeithertechnicalorfundamentalanalysiscanconsistentlyoutperformastrategyofsimplybuyingandholdingadiversifiedportfolioofsecurities,suchasthosecomprisingthepopularmarketindexes.c.Portfoliomanagershaveseveralrolesandresponsibilitieseveninperfectlyefficientmarkets.Themostimportantresponsibilityistoidentifytherisk/returnobjectivesforaportfoliogiventheinvestor’sconstraints.Inanefficientmarket,portfoliomanagersareresponsiblefortailoringtheportfoliotomeettheinvestor’sneeds,ratherthantobeatthemarket,whichrequiresidentifyingtheclient’sreturnrequirementsandrisktolerance.Rationalportfoliomanagementalsorequiresexaminingtheinvestor’sconstraints,includingliquidity,timehorizon,lawsandregulations,taxes,anduniquepreferencesandcircumstancessuchasageandemployment.10.a.Theearnings(anddividend)growthrateofgrowthstocksmaybeconsistentlyoverestimatedbyinvestors.Investorsmayextrapolaterecentgrowthtoofarintothefutureandtherebydownplaytheinevitableslowdown.Atanygiventime,growthstocksarelikelytorevertto(lower)meanreturnsandvaluestocksarelikelytorevertto(higher)meanreturns,oftenoveranextendedfuturetimehorizon.b.Inefficientmarkets,thecurrentpricesofstocksalreadyreflectallknownrelevantinformation.Inthissituation,growthstocksandvaluestocksprovidethesamerisk-adjustedexpectedreturn.课后答案网www.hackshp.cn11-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter12-BehavioralFinanceandTechnicalAnalysisCHAPTER12:BEHAVIORALBEHAVIORALFINANCEFINANCEANDANDTECHNICALTECHNICALTECHNICALANALYSISANALYSISPROBLEMPROBLEMSETSSETS1.Technicalanalysiscangenerallybeviewedasasearchfortrendsorpatternsinmarketprices.Technicalanalyststendtoviewthesetrendsasmomentum,orgradualadjustmentsto‘correct’prices,or,alternatively,reversalsoftrends.Anumberofthebehavioralbiasesdiscussedinthechaptermightcontributetosuchtrendsandpatterns.Forexample,aconservatismbiasmightcontributetoatrendinpricesasinvestorsgraduallytakenewinformationintoaccount,resultingingradualadjustmentofpricestowardstheirfundamentalvalues.Anotherexamplederivesfromtheconceptofrepresentativeness,whichleadsinvestorstoinappropriatelyconclude,onthebasisofasmallsampleofdata,thatapatternhasbeenestablishedthatwillcontinuewellintothefuture.Wheninvestorssubsequentlybecomeawareofthefactthatpriceshaveoverreacted,correctionsreversetheinitialerroneoustrend.2.Evenifmanyinvestorsexhibitbehavioralbiases,securitypricesmightstillbesetefficientlyiftheactionsofarbitrageursmovepricestotheirintrinsicvalues.Arbitrageurswhoobservemispricinginthesecuritiesmarketswouldbuyunderpricedsecurities(orpossiblysellshortoverpricedsecurities)inordertoprofitfromtheanticipatedsubsequentchangesaspricesmovetotheirintrinsicvalues.Consequently,securitiespriceswouldstillexhibitthecharacteristicsofanefficientmarket.3.Oneofthemajorfactorslimitingtheability课后答案网ofrationalinvestorstotakeadvantageofany‘pricingerrors’thatresultfromtheactionsofbehavioralinvestorsisthefactthatamispricingcangetworseovertime.AnexampleofthisfundamentalriskistheapparentongoingoverpricingoftheNASDAQindexinthelate1990s.Arelatedfactoristheinherentcostsandlimitsrelatedtoshortselling,whichrestricttheextenttowhicharbitragecanforceoverpricedsecurities(orindexes)tomovetowardstheirwww.hackshp.cnfairvalues.Rationalinvestorsmustalsobeawareoftheriskthatanapparentmispricingis,infact,aconsequenceofmodelrisk;thatis,theperceivedmispricingmaynotberealbecausetheinvestorhasusedafaultymodeltovaluethesecurity.12-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter12-BehavioralFinanceandTechnicalAnalysis4.TworeasonswhybehavioralbiasesmightnotaffectequilibriumassetpricesarediscussedinQuizProblems(1)and(2)above:first,behavioralbiasesmightcontributetothesuccessoftechnicaltradingrulesaspricesgraduallyadjusttowardstheirintrinsicvalues,and;second,theactionsofarbitrageursmightmovesecuritypricestowardstheirintrinsicvalues.Itmightbeimportantforinvestorstobeawareofthesebiasesbecauseeitherofthesescenariosmightcreatethepotentialforexcessprofitsevenifbehavioralbiasesdonotaffectequilibriumprices.5.Efficientmarketadvocatesbelievethatpubliclyavailableinformation(and,foradvocatesofstrong-formefficiency,eveninsiderinformation)is,atanypointintime,reflectedinsecuritiesprices,andthatpriceadjustmentstonewinformationoccurveryquickly.Consequently,pricesareatfairlevelssothatactivemanagementisveryunlikelytoimproveperformanceabovethatofabroadlydiversifiedindexportfolio.Incontrast,advocatesofbehavioralfinanceidentifyanumberofinvestorerrorsininformationprocessinganddecisionmakingthatcouldresultinmispricingofsecurities.However,thebehavioralfinanceliteraturegenerallydoesnotprovideguidanceastohowtheseinvestorerrorscanbeexploitedtogenerateexcessprofits.Therefore,intheabsenceofanyprofitablealternatives,evenifsecuritiesmarketsarenotefficient,theoptimalstrategymightstillbeapassiveindexingstrategy.Volumedeclining/Numberdeclining766,901,460/,20686.Trin===.0978Volumeadvancing/Numberadvancing467,560,150/,1233Thistrinratio,whichisbelow1.0,wouldbetakenasabullishsignal.7.Breadth:课后答案网NetAdvancesDeclinesAdvances1,2332,068-835Breadthisnegative.Thisisabearishsignal(althoughnoonewouldactuallyuseaone-daymeasureasinthisexample).www.hackshp.cn8.Thisexerciseislefttothestudent;answerswillvary.9.Theconfidenceindexincreasesfrom(7%/8%)=0.875to(8%/9%)=0.889Thisindicatesslightlyhigherconfidence.Buttherealreasonfortheincreaseintheindexistheexpectationofhigherinflation,nothigherconfidenceabouttheeconomy.12-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter12-BehavioralFinanceandTechnicalAnalysis10.Atthebeginningoftheperiod,thepriceofComputers,Inc.dividedbytheindustryindexwas0.39;bytheendoftheperiod,theratiohadincreasedto0.50.Astheratioincreasedovertheperiod,itappearsthatComputers,Inc.outperformedotherfirmsinitsindustry.Theoveralltrend,therefore,indicatesrelativestrength,althoughsomefluctuationexistedduringtheperiod,withtheratiofallingtoalowpointof0.33onday19.11.Fivedaymovingaverages:Days1–5:(19.63+20+20.5+22+21.13)/5=20.65Days2–6=21.13Days3–7=21.50Days4–8=21.90Days5–9=22.13Days6–10=22.68Days7–11=23.18Days8–12=23.45←Sellsignal(day12pricemovingaverage)Days18–22=19.28Days19–23=19.93课后答案网Days20–24=21.05Days21–25=22.05Days22–26=23.18Days23–27=24.13Days24–28=25.13Days25–29=26.00www.hackshp.cnDays26–30=26.80Days27–31=27.45Days28–32=27.80Days29–33=27.90←Sellsignal(day33price$100.901+Er()2E(HPR)>6%13.a.Weobtainforwardratesfromthefollowingtable:MaturityYTMForwardRatePrice(forpartsc,d)1year10%$1,000/1.10=$909.092years11%(1.112/1.10)–1=12.01%$1,000/1.112=$811.623years12%(1.123/1.112)–1=14.03%$1,000/1.123=$711.78b.Weobtainnextyear’spricesandyieldsbydiscountingeachzero’sfacevalueattheforwardratesfornextyearthatwederivedinpart(a):MaturityPriceYTM1year课后答案网$1,000/1.1201=$892.7812.01%2years$1,000/(1.1201×1.1403)=$782.9313.02%Notethatthisyear’supwardslopingyieldcurveimplies,accordingtotheexpectationshypothesis,ashiftupwardinnextyear’scurve.c.Nextyear,the2-yearzerowillbea1-yearzero,andwillthereforewww.hackshp.cnsellatapriceof:$1,000/1.1201=$892.78Similarly,thecurrent3-yearzerowillbea2-yearzeroandwillsellfor:$782.93Expectedtotalrateofreturn:$892.782-yearbond:−1=.11000−1=10.00%$811.62$782.933-yearbond:−1=.11000−1=10.00%$711.7815-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter15-TheTermStructureofInterestRatesd.Thecurrentpriceofthebondshouldequalthevalueofeachpaymenttimesthepresentvalueof$1tobereceivedatthe“maturity”ofthatpayment.Thepresentvalueschedulecanbetakendirectlyfromthepricesofzero-couponbondscalculatedabove.Currentprice=($120×0.90909)+($120×0.81162)+($1,120×0.71178)=$109.0908+$97.3944+$797.1936=$1,003.68Similarly,theexpectedpricesofzerosoneyearfromnowcanbeusedtocalculatetheexpectedbondvalueatthattime:Expectedprice1yearfromnow=($120×0.89278)+($1,120×0.78293)=$107.1336+$876.8816=$984.02Totalexpectedrateofreturn=$120+($984.02−,1$003.68)=.01000=10.00%,1$003.6814.a.MaturityForwardPriceYTM(years)rate1$925.938.00%2$853.398.25%8.50%3$782.928.50%9.00%4$715.008.75%9.50%5$650.009.00%10.00%b.Foreach3-yearzeroissuedtoday,usetheproceedstobuy:$782.92/$715.00=1.095four-yearzeros课后答案网Yourcashflowsarethusasfollows:TimeCashFlow0$03-$1,000www.hackshp.cnThe3-yearzeroissuedattime0matures;theissuerpaysout$1,000facevalue4+$1,095The4-yearzerospurchasedattime0mature;receivefacevalueThisisasyntheticone-yearloanoriginatingattime3.Therateonthesyntheticloanis0.095=9.5%,preciselytheforwardrateforyear3.15-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter15-TheTermStructureofInterestRatesc.Foreach4-yearzeroissuedtoday,usetheproceedstobuy:$715.00/$650.00=1.100five-yearzerosYourcashflowsarethusasfollows:TimeCashFlow0$04-$1,000The4-yearzeroissuedattime0matures;theissuerpaysout$1,000facevalue5+$1,100The5-yearzerospurchasedattime0mature;receivefacevalueThisisasyntheticone-yearloanoriginatingattime4.Therateonthesyntheticloanis0.100=10.0%,preciselytheforwardrateforyear4.15.a.Foreachthree-yearzeroyoubuytoday,issue:$782.92/$650.00=1.2045five-yearzerosThetime-0cashflowequalszero.b.Yourcashflowsarethusasfollows:TimeCashFlow0$03+$1,000.00The3-yearzeropurchasedattime0matures;receive$1,000facevalue5-$1,204.50The5-yearzerosissuedattime0mature;issuerpaysfacevalueThisisasynthetictwo-yearloanoriginatingattime3.课后答案网c.Theeffectivetwo-yearinterestrateontheforwardloanis:$1,204.50/$1,000−1=0.2045=20.45%d.Theone-yearforwardratesforyears4and5are9.5%and10%,respectively.Noticethat:www.hackshp.cn1.095×1.10=1.2045=1+(two-yearforwardrateonthe3-yearaheadforwardloan)The5-yearYTMis9.0%.The3-yearYTMis8.5%.Therefore,anotherwaytoderivethe2-yearforwardrateforaloanstartingattime3is:55(1+y5).109f(2)=−1=−1=.02046=20.46%333(1+y).10853[Note:thereisaslightdiscrepancyhereduetoroundingerrorintheYTMcalculationsabove.]15-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter15-TheTermStructureofInterestRatesCFACFAPROBLEMSPROBLEMS1.Expectationshypothesis:Theyieldsonlong-termbondsaregeometricaveragesofpresentandexpectedfutureshortrates.Anupwardslopingcurveisexplainedbyexpectedfutureshortratesbeinghigherthanthecurrentshortrate.Adownward-slopingyieldcurveimpliesexpectedfutureshortratesarelowerthanthecurrentshortrate.Thusbondsofdifferentmaturitieshavedifferentyieldsifexpectationsoffutureshortratesaredifferentfromthecurrentshortrate.Liquiditypreferencehypothesis:Yieldsonlong-termbondsaregreaterthantheexpectedreturnfromrolling-overshort-termbondsinordertocompensateinvestorsinlong-termbondsforbearinginterestraterisk.Thusbondsofdifferentmaturitiescanhavedifferentyieldsevenifexpectedfutureshortratesareallequaltothecurrentshortrate.Anupwardslopingyieldcurvecanbeconsistentevenwithexpectationsoffallingshortratesifliquiditypremiumsarehighenough.If,however,theyieldcurveisdownwardslopingandliquiditypremiumsareassumedtobepositive,thenwecanconcludethatfutureshortratesareexpectedtobelowerthanthecurrentshortrate.2.d.3.a.(1+y434)=(1+y3)(1+f4)(1.055)4=(1.05)3(1+f4)1.2388=1.1576(1+f4)⇒f4=0.0701=7.01%b.Theconditionswouldbethosethatunderlietheexpectationstheoryofthetermstructure:riskneutralmarketparticipantswhoarewillingtosubstituteamongmaturitiessolelyonthebasisofyielddifferentials.课后答案网Thisbehaviorwouldruleoutliquidityortermpremiarelatingtorisk.c.Undertheexpectationshypothesis,lowerimpliedforwardrateswouldindicatelowerexpectedfuturespotratesforthecorrespondingperiod.Sincethelowerexpectedfutureratesembodiedinthetermstructurearenominalrates,eitherlowerexpectedfuturerealratesorlowerexpectedfutureinflationrateswouldbewww.hackshp.cnconsistentwiththespecifiedchangeintheobserved(implied)forwardrate.4.Thegivenratesareannualrates,buteachperiodisahalf-year.Therefore,theperperiodspotratesare2.5%onone-yearbondsand2%onsix-monthbonds.Thesemiannualforwardrateisobtainedbysolvingforfinthefollowingequation:2.10251+f==.1030.102Thismeansthattheforwardrateis0.030=3.0%semiannually,or6.0%annually.15-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter15-TheTermStructureofInterestRates5.Thepresentvalueofeachbond’spaymentscanbederivedbydiscountingeachcashflowbytheappropriateratefromthespotinterestrate(i.e.,thepureyield)curve:$10$10$110BondA:PV=++=$98.5323.105.108.1116$6$$106BondB:PV=++=$88.3623.105.108.111BondAsellsfor$0.13(i.e.,0.13%ofparvalue)lessthanthepresentvalueofitsstrippedpayments.BondBsellsfor$0.02lessthanthepresentvalueofitsstrippedpayments.BondAismoreattractivelypriced.6.a.Basedonthepureexpectationstheory,VanHusen’sconclusionisincorrect.Accordingtothistheory,theexpectedreturnoveranytimehorizonwouldbethesame,regardlessofthematuritystrategyemployed.b.Accordingtotheliquiditypreferencetheory,theshapeoftheyieldcurveimpliesthatshort-terminterestratesareexpectedtoriseinthefuture.Thistheoryassertsthatforwardratesreflectexpectationsaboutfutureinterestratesplusaliquiditypremiumthatincreaseswithmaturity.Giventheshapeoftheyieldcurveandtheliquiditypremiumdataprovided,theyieldcurvewouldstillbepositivelysloped(atleastthroughmaturityofeightyears)aftersubtractingtherespectiveliquiditypremiums:2.90%–0.55%=2.35%3.50%–0.55%=2.95%3.80%–0.65%=3.15%4.00%–0.75%=3.25%课后答案网4.15%–0.90%=3.25%4.30%–1.10%=3.20%4.45%–1.20%=3.25%4.60%–1.50%=3.10%4.70%–1.60%=3.10%www.hackshp.cn7.Thecouponbondscanbeviewedasportfoliosofstrippedzeros:eachcouponcanstandaloneasanindependentzero-couponbond.Therefore,yieldsoncouponbondsreflectyieldsonpaymentswithdatescorrespondingtoeachcoupon.Whentheyieldcurveisupwardsloping,couponbondshaveloweryieldsthanzeroswiththesamematuritybecausetheyieldstomaturityoncouponbondsreflecttheyieldsontheearlierinterimcouponpayments.15-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter15-TheTermStructureofInterestRates8.Thefollowingtableshowstheexpectedshort-terminterestratebasedontheprojectionsofFederalReserveratecuts,thetermpremium(whichincreasesatarateof0.10%per12months),theforwardrate(whichisthesumoftheexpectedrateandtermpremium),andtheYTM,whichisthegeometricaverageoftheforwardrates.ExpectedTermForwardForwardrateYTMTimeshortratepremiumrate(annual)(semi-annual)(semi-annual)05.00%0.00%5.00%2.500%2.500%6months4.500.054.552.2752.38712months4.000.104.102.0502.27518months4.000.154.152.0752.22524months5.000.205.202.6002.30030months5.000.255.252.6252.354Thisanalysisispredicatedontheliquiditypreferencetheoryofthetermstructure,whichassertsthattheforwardrateinanyperiodisthesumoftheexpectedshortrateplustheliquiditypremium.9.a.Five-yearSpotRate:$70$70$70$70,1$070,1$000=++++12345(1+y)(1+y)(1+y)(1+y)(1+y)12345$70$70$70$70,1$070,1$000=++++2345(.105)(.10521)(.10605)(.10716)(1+y)5,1$070,1$000=$66.67+$63.24+$58.69+$53.08+5(1+y)5,1$070$758.32=课后答案网5(1+y)55,1$0705(1+y)=⇒y=.1411−1=.713%55$758.32Five-yearForwardRatewww.hackshp.cn:5(.10713)−1=.10701−1=.701%4(.10716)15-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter15-TheTermStructureofInterestRatesb.Theyieldtomaturityisthesinglediscountratethatequatesthepresentvalueofaseriesofcashflowstoacurrentprice.Itistheinternalrateofreturn.Thespotrateforagivenperiodistheyieldtomaturityonazero-couponbondthatmaturesattheendoftheperiod.Aspotrateisthediscountrateforeachperiod.Spotratesareusedtodiscounteachcashflowofacouponbondinordertocalculateacurrentprice.Spotratesaretheratesappropriatefordiscountingfuturecashflowsofdifferentmaturities.Aforwardrateistheimplicitratethatlinksanytwospotrates.Forwardratesaredirectlyrelatedtospotrates,andthereforetoyieldtomaturity.Somewouldargue(asintheexpectationshypothesis)thatforwardratesarethemarketexpectationsoffutureinterestrates.Aforwardraterepresentsabreak-evenratethatlinkstwospotrates.Itisimportanttonotethatforwardrateslinkspotrates,notyieldstomaturity.Yieldtomaturityisnotuniqueforanyparticularmaturity.Inotherwords,twobondswiththesamematuritybutdifferentcouponratesmayhavedifferentyieldstomaturity.Incontrast,spotratesandforwardratesforeachdateareunique.c.The4-yearspotrateis7.16%.Therefore,7.16%isthetheoreticalyieldtomaturityforthezero-couponU.S.Treasurynote.Thepriceofthezero-couponnotediscountedat7.16%isthepresentvalueof$1,000tobereceivedin4years.Usingannualcompounding:,1$000PV==$758.354(.10716)10.a.Thetwo-yearimpliedannuallycompoundedforwardrateforadeferredloanbeginningin3years课后答案网iscalculatedasfollows:2/12/155⎡(1+y5)⎤⎡.109⎤f(2)=⎥−1=⎥−1=.00607=.607%3⎢3⎢3⎣(1+y3)⎦⎣.111⎦b.Assumingaparvalueof$1,000,thebondpricewww.hackshp.cniscalculatedasfollows:$90$90$90$90,1$090P=++++12345(1+y)(1+y)(1+y)(1+y)(1+y)12345$90$90$90$90,1$090=++++=$987.1012345(.113)(.112)(.111)(.110)(.109)15-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfoliosCHAPTER16:MANAGINGMANAGINGBONDBONDBONDPORTFOLIOSPORTFOLIOSPROBLEMPROBLEMSETSSETS1.Whileitistruethatshort-termratesaremorevolatilethanlong-termrates,thelongerdurationofthelonger-termbondsmakestheirpricesandtheirratesofreturnmorevolatile.Thehigherdurationmagnifiesthesensitivitytointerest-ratechanges.2.Durationcanbethoughtofasaweightedaverageofthe‘maturities’ofthecashflowspaidtoholdersoftheperpetuity,wheretheweightforeachcashflowisequaltothepresentvalueofthatcashflowdividedbythetotalpresentvalueofallcashflows.Forcashflowsinthedistantfuture,presentvalueapproacheszero(i.e.,theweightbecomesverysmall)sothatthesedistantcashflowshavelittleimpact,andeventually,virtuallynoimpactontheweightedaverage.3.Thepercentagechangeinthebond’spriceis:Duration.7194−×∆y=−×.0005=−.00327=−.327%ora3.27%decline1+y.1104.a.YTM=6%(1)课后答案网(2)(3)(4)(5)TimeuntilPVofCFColumn(1)×PaymentCashFlow(DiscountWeightColumn(4)(years)rate=6%)1$60.00$56.600.05660.05662$60.00$53.400.05340.10683$1,060.00www.hackshp.cn$890.000.89002.6700ColumnSums$1,000.001.00002.8334Duration=2.833years16-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfoliosb.YTM=10%(1)(2)(3)(4)(5)TimeuntilPVofCFColumn(1)×PaymentCashFlow(DiscountWeightColumn(4)(years)rate=10%)1$60.00$54.550.06060.06062$60.00$49.590.05510.11023$1,060.00$796.390.88442.6532ColumnSums$900.531.00002.8240Duration=2.824years,whichislessthanthedurationattheYTMof6%.5.Forasemiannual6%couponbondsellingatpar,weusethefollowingparameters:coupon=3%perhalf-yearperiod,y=3%,T=6semiannualperiods.(1)(2)(3)(4)(5)TimeuntilPVofCFColumn(1)×PaymentCashFlow(DiscountWeightColumn(4)(years)rate=3%)1$3.00$2.9130.029130.029132$3.00$2.8280.028280.056563$3.00$2.7450.027450.082364$3.00$2.6650.026650.106625$3.00$2.5880.025880.129396$103.00$86.2610.862615.17565ColumnSums$100.0001.000005.57971D=5.5797half-yearperiods=2.7899years课后答案网Ifthebond’syieldis10%,useasemiannualyieldof5%,andsemiannualcouponof3%:(1)(2)(3)(4)(5)TimeuntilPVofCFColumn(1)×PaymentCashFlow(DiscountWeightColumn(4)(years)www.hackshp.cnrate=5%)1$3.00$2.8570.031800.031802$3.00$2.7210.030290.060573$3.00$2.5920.028840.086534$3.00$2.4680.027470.109885$3.00$2.3510.026160.130816$103.00$76.8600.855445.13265ColumnSums$89.8491.000005.55223D=5.5522half-yearperiods=2.7761years16-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfolios6.a.BondBhasahigheryieldtomaturitythanbondAsinceitscouponpaymentsandmaturityareequaltothoseofA,whileitspriceislower.(Perhapstheyieldishigherbecauseofdifferencesincreditrisk.)Therefore,thedurationofBondBmustbeshorter.b.BondAhasaloweryieldandalowercoupon,bothofwhichcauseBondAtohavealongerdurationthanBondB.Moreover,Acannotbecalled,sothatitsmaturityisatleastaslongasthatofB,whichgenerallyincreasesduration.7.a.(1)(2)(3)(4)(5)TimeuntilPVofCFColumn(1)×PaymentCashFlow(Discountrate=WeightColumn(4)(years)10%)1$10million$9.09million0.78570.78575$4million$2.48million0.21431.0715ColumnSums$11.57million1.00001.8572D=1.8572years=requiredmaturityofzerocouponbond.b.Themarketvalueofthezeromustbe$11.57million,thesameasthemarketvalueoftheobligations.Therefore,thefacevaluemustbe:$11.57million×(1.10)1.8572=$13.81million8.Ineachcase,choosethelonger-durationbondinordertobenefitfromaratedecrease.a.TheAaa-ratedbondhastheloweryieldtomaturityandthereforethelonger课后答案网duration.b.Thelower-couponbondhasthelongerdurationandgreaterdefactocallprotection.c.Thelowercouponbondwww.hackshp.cnhasthelongerduration.16-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfolios9.Thetablebelowshowstheholdingperiodreturnsforeachofthethreebonds:Maturity1year2years3yearsYTMatbeginningofyear7.00%8.00%9.00%Beginningofyearprices$1,009.35$1,000.00$974.69Pricesatyearend(at9%YTM)$1,000.00$990.83$982.41Capitalgain–$9.35–$9.17$7.72Coupon$80.00$80.00$80.001-yeartotal$return$70.65$70.83$87.721-yeartotalrateofreturn7.00%7.08%9.00%Youshouldbuythe3-yearbondbecauseitprovidesa9%holding-periodreturnoverthenextyear,whichisgreaterthanthereturnoneitheroftheotherbonds.10.a.PVoftheobligation=$10,000×Annuityfactor(8%,2)=$17,832.65(1)(2)(3)(4)(5)TimeuntilPVofCFColumn(1)×PaymentCashFlow(DiscountWeightColumn(4)(years)rate=8%)1$10,000.00$9,259.2590.519230.519232$10,000.00$8,573.3880.480770.96154ColumnSums$17,832.6471.000001.48077Duration=1.4808yearsb.Azero-couponbondmaturingin1.4808yearswouldimmunizetheobligation.Sincethepresentvalueofthezero-couponbondmustbe$17,832.65,thefacevalue(i.e.,thefutureredemptionvalue)mustbe:$17,832.65课后答案网×1.081.4808=$19,985.26c.Iftheinterestrateincreasesto9%,thezero-couponbondwoulddecreaseinvalueto:$19,985.26=$17,590.921.4808.109Thepresentvalueofthetuitionobligationwoulddecreasewww.hackshp.cnto:$17,591.11Thenetpositiondecreasesinvalueby:$0.19Iftheinterestratedecreasesto7%,thezero-couponbondwouldincreaseinvalueto:$19,985.26=$18,079.991.4808.107Thepresentvalueofthetuitionobligationwouldincreaseto:$18,080.18Thenetpositiondecreasesinvalueby:$0.19Thereasonthenetpositionchangesatallisthat,astheinterestratechanges,sodoesthedurationofthestreamoftuitionpayments.16-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfolios11.a.PVofobligation=$2million/0.16=$12.5millionDurationofobligation=1.16/0.16=7.25yearsCallwtheweightonthe5-yearmaturitybond(whichhasdurationof4years).Then:(w×4)+[(1–w)×11]=7.25⇒w=0.5357Therefore:0.5357×$12.5=$6.7millioninthe5-yearbondand0.4643×$12.5=$5.8millioninthe20-yearbond.b.Thepriceofthe20-yearbondis:[$60×Annuityfactor(16%,20)]+[$1,000×PVfactor(16%,20)]=$407.12Therefore,thebondsellsfor0.4071timesitsparvalue,and:Marketvalue=Parvalue×0.4071$5.8million=Parvalue×0.4071⇒Parvalue=$14.25millionAnotherwaytoseethisistonotethateachbondwithparvalue$1,000sellsfor$407.12.Iftotalmarketvalueis$5.8million,thenyouneedtobuyapproximately14,250bonds,resultingintotalparvalueof$14.25million.12.a.Thedurationoftheperpetuityis:1.05/0.05=21yearsCallwtheweightofthezero-couponbond.Then:(w×5)+[(1–w)×21]=10⇒w=11/16=0.6875Therefore,theportfolioweightswouldbeasfollows:11/16investedinthezeroand5/16intheperpetuity.课后答案网b.Nextyear,thezero-couponbondwillhaveadurationof4yearsandtheperpetuitywillstillhavea21-yearduration.Toobtainthetargetdurationofnineyears,whichisnowthedurationoftheobligation,weagainsolveforw:(w×4)+[(1–www.hackshp.cnw)×21]=9⇒w=12/17=0.7059So,theproportionoftheportfolioinvestedinthezeroincreasesto12/17andtheproportioninvestedintheperpetuityfallsto5/17.16-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfolios13.a.Thedurationoftheannuityifitweretostartin1yearwouldbe:(1)(2)(3)(4)(5)TimeuntilPVofCFColumn(1)×PaymentCashFlow(DiscountWeightColumn(4)(years)rate=10%)1$10,000$9,090.9090.147950.147952$10,000$8,264.4630.134500.269003$10,000$7,513.1480.122270.366824$10,000$6,830.1350.111160.444635$10,000$6,209.2130.101050.505266$10,000$5,644.7390.091870.551197$10,000$5,131.5810.083510.584608$10,000$4,665.0740.075920.607389$10,000$4,240.9760.069020.6211810$10,000$3,855.4330.062750.62745ColumnSums$61,445.6711.000004.72546D=4.7255yearsBecausethepaymentstreamstartsinfiveyears,insteadofoneyear,weaddfouryearstotheduration,sothedurationis8.7255years.b.Thepresentvalueofthedeferredannuityis:10,000×Annuityfactor(10%,10)=$41,9684.110Callwtheweightoftheportfolioinvestedinthe5-yearzero.Then:(w×5)+[(1–课后答案网w)×20]=8.7255⇒w=0.7516Theinvestmentinthe5-yearzeroisequalto:0.7516×$41,968=$31,543Theinvestmentinthe20-yearzerosisequalto:0.2484×$41,968=$10,425www.hackshp.cnThesearethepresentormarketvaluesofeachinvestment.Thefacevaluesareequaltotherespectivefuturevaluesoftheinvestments.Thefacevalueofthe5-yearzerosis:$31,543×(1.10)5=$50,800Therefore,between50and51zero-couponbonds,eachofparvalue$1,000,wouldbepurchased.Similarly,thefacevalueofthe20-yearzerosis:$10,425×(1.10)20=$70,13416-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfolios14.Usingafinancialcalculator,wefindthattheactualpriceofthebondasafunctionofyieldtomaturityis:YieldtomaturityPrice7%$1,620.458%$1,450.319%$1,308.21UsingtheDurationRule,assumingyieldtomaturityfallsto7%:⎛Duration⎞Predictedpricechange=⎜−⎟×∆y×P⎜⎟0⎝1+y⎠⎛11.54⎞=⎜−⎟×(−.001)×,1$450.31=$154.97⎝.108⎠Therefore:predictednewprice=$1,450.31+$154.97=$1,605.28Theactualpriceata7%yieldtomaturityis$1,620.45.Therefore:,1$605.28−,1$620.45%error==−.00094=−.094%(approximationistoolow),1$620.45UsingtheDurationRule,assumingyieldtomaturityincreasesto9%:⎛Duration⎞Predictedpricechange=⎜−⎟×∆y×P⎜⎟0⎝1+y⎠⎛11.54⎞=⎜−⎟×.001×,1$450.31=−$154.97⎝.108⎠Therefore:predictednewprice=$1,450.31–$154.97=$1,295.34Theactualpriceata9%yieldtomaturity课后答案网is$1,308.21.Therefore:,1$295.34−,1$308.21%error==−.00098=−.098%(approximationistoolow),1$308.21UsingDuration-with-ConvexityRule,assumingyieldtomaturityfallsto7%www.hackshp.cn⎧⎪⎡⎛Duration⎞⎤2⎫⎪Predictedpricechange=⎨⎢⎜⎜−⎟⎟×∆y⎥+[5.0×Convexity×(∆y)]⎬×P0⎪⎩⎣⎝1+y⎠⎦⎪⎭⎧⎡⎛11.54⎞⎤[2]⎫=⎨⎢⎜−⎟×(−.001)⎥+5.0×1924.×(−.001)⎬×,1$450.31=$168.92⎩⎣⎝.108⎠⎦⎭Therefore:predictednewprice=$1,450.31+$168.92=$1,619.23Theactualpriceata7%yieldtomaturityis$1,620.45.Therefore:,1$619.23−,1$620.45%error==−.000075=−.0075%(approximationistoolow),1$620.4516-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfoliosUsingDuration-with-ConvexityRule,assumingyieldtomaturityrisesto9%:⎧⎪⎡⎛Duration⎞⎤2⎫⎪Predictedpricechange=⎨⎢⎜⎜−⎟⎟×∆y⎥+[5.0×Convexity×(∆y)]⎬×P0⎪⎩⎣⎝1+y⎠⎦⎪⎭⎧⎡⎛11.54⎞⎤[2]⎫=⎨⎢⎜−⎟×.001⎥+5.0×1924.×(.001)⎬×,1$450.31=−$141.02⎩⎣⎝.108⎠⎦⎭Therefore:predictednewprice=$1,450.31–$141.02=$1,309.29Theactualpriceata9%yieldtomaturityis$1,308.21.Therefore:,1$309.29−,1$308.21%error==.000083=.0083%(approximationistoohigh),1$308.21Conclusion:Theduration-with-convexityruleprovidesmoreaccurateapproximationstothetruechangeinprice.Inthisexample,thepercentageerrorusingconvexitywithdurationislessthanone-tenththeerrorusingonlydurationtoestimatethepricechange.15.Theminimumterminalvaluethatthemanageriswillingtoacceptisdeterminedbytherequirementfora3%annualreturnontheinitialinvestment.Therefore,theflooris:$1million5×(1.03)=$1.16millionThreeyearsaftertheinitialinvestment,onlytwoyearsremainuntilthehorizondate,andtheinterestratehasrisento8%.Therefore,atthistime,inordertobeassuredthatthetargetvaluecanbeattained,themanagerneedsaportfolioworth:$1.16million/(1.08)2=$0.9945millionThisisthetriggerpoint.课后答案网16.Thematurityofthe30-yearbondwillfallto25years,anditsyieldisforecasttobe8%.Therefore,thepriceforecastforthebondis:$893.25[Usingafinancialcalculator,enterthefollowing:n=25;i=8;FV=1000;PMT=70]Ata6%interestrate,thefivecouponpaymentswww.hackshp.cnwillaccumulateto$394.60afterfiveyears.Therefore,totalproceedswillbe:$394.60+$893.25=$1,287.85Therefore,the5-yearreturnis:($1,287.85/$867.42)–1=0.4847Thisisa48.47%5-yearreturn,or8.23%annually.16-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfoliosThematurityofthe20-yearbondwillfallto15years,anditsyieldisforecasttobe7.5%.Therefore,thepriceforecastforthebondis:$911.73[Usingafinancialcalculator,enterthefollowing:n=15;i=7.5;FV=1000;PMT=65]Ata6%interestrate,thefivecouponpaymentswillaccumulateto$366.41afterfiveyears.Therefore,totalproceedswillbe:$366.41+$911.73=$1,278.14Therefore,the5-yearreturnis:($1,278.14/$879.50)–1=0.4533Thisisa45.33%5-yearreturn,or7.76%annually.The30-yearbondoffersthehigherexpectedreturn.17.a.TimePVofCFuntilCashYears×PeriodDiscountrate=WeightPaymentFlowWeight6%perperiod(Years)A.8%couponbond10.5$40$37.7360.04050.020321.04035.6000.03830.038331.54033.5850.03610.054142.01,040823.7770.88511.7702Sum:$930.6981.00001.8829B.Zero-coupon10.5$0$0.0000.00000.000021.000.0000.00000.000031.500.0000.00000.000042.01,000792.0941.00002.0000Sum:$792.0941.00002.0000Forthecouponbond,theweightonthelastpaymentinthetableaboveislessthanitisinSpreadsheet16.1becausethediscountrateishigher;theweightsforthefirstthreepaymentsarelargerthanthoseinSpreadsheet16.1.Consequently,thedurationofthebondfalls.The课后答案网zerocouponbond,bycontrast,hasafixedweightof1.0forthesinglepaymentatmaturity.b.TimePVofCFuntilCashYears×PeriodDiscountrate=WeightPaymentFlowWeight5%perperiodwww.hackshp.cn(Years)A.8%couponbond10.5$60$57.1430.05520.027621.06054.4220.05260.052631.56051.8300.05010.075142.01,060872.0650.84221.6844Sum:$1,035.4601.00001.8396Sincethecouponpaymentsarelargerintheabovetable,theweightsontheearlierpaymentsarehigherthaninSpreadsheet16.1,sodurationdecreases.16-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfolios18.a.TimeCashPV(CF)t+t2(t+t2)×PV(CF)(t)FlowCoupon=$801$80$72.7272145.455YTM=0.1028066.1166396.694Maturity=538060.10512721.262Price=$924.18448054.641201,092.82251,080670.5953020,117.851Price:$924.184Sum:22,474.0832]=20.097Convexity=Sum/[Price×(1+y)b.TimeCashPV(CF)t22+t(t+t)×PV(CF)(t)FlowCoupon=$01$0$0.00020.000YTM=0.10200.00060.000Maturity=5300.000120.000Price=$924.184400.000200.00051,000620.9213018,627.640Price:$620.921Sum:18,627.6402]=24.793Convexity=Sum/[Price×(1+y)19.a.Thepriceofthezerocouponbond($1,000facevalue)sellingatayieldtomaturityof8%is$374.84andthepriceofthecouponbondis$774.84AtaYTMof9%theactualpriceofthezerocouponbondis$333.28andtheactualpriceofthecouponbond课后答案网is$691.79Zerocouponbond:$333.28−$374.84Actual%loss==−.01109=11.09%loss$374.84Thepercentagelosspredictedwww.hackshp.cnbytheduration-with-convexityruleis:2Predicted%loss=[(−11.81)×.001]+[5.0×1503.×.001]=−.01106=11.06%lossCouponbond:$691.79−$774.84Actual%loss==−.01072=10.72%loss$774.84Thepercentagelosspredictedbytheduration-with-convexityruleis:2Predicted%loss=[(−11.79)×.001]+[5.0×2312.×.001]=−.01063=10.63%loss16-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfoliosb.Nowassumeyieldtomaturityfallsto7%.Thepriceofthezeroincreasesto$422.04,andthepriceofthecouponbondincreasesto$875.91Zerocouponbond:$422.04−$374.84Actual%gain==.01259=12.59%gain$374.84Thepercentagegainpredictedbytheduration-with-convexityruleis:2Predicted%gain=[(−11.81)×(−.001)]+[5.0×1503.×.001]=.01256=12.56%gainCouponbond$875.91−$774.84Actual%gain==.01304=13.04%gain$774.84Thepercentagegainpredictedbytheduration-with-convexityruleis:2Predicted%gain=[(−11.79)×(−.001)]+[5.0×2312.×.001]=.01295=12.95%gainc.The6%couponbond,whichhashigherconvexity,outperformsthezeroregardlessofwhetherratesriseorfall.Thiscanbeseentobeageneralpropertyusingtheduration-with-convexityformula:thedurationeffectsonthetwobondsduetoanychangeinratesareequal(sincetherespectivedurationsarevirtuallyequal),buttheconvexityeffect,whichisalwayspositive,alwaysfavorsthehigherconvexitybond.Thus,iftheyieldsonthebondschangebyequalamounts,asweassumedinthisexample,thehigherconvexitybondoutperformsalowerconvexitybondwiththesamedurationandinitialyieldtomaturity.d.Thissituationcannotpersist.Noonewouldbewillingtobuythelowerconvexitybondifitalwaysunderperformstheotherbond.Thepriceofthelowerconvexity课后答案网bondwillfallanditsyieldtomaturitywillrise.Thus,thelowerconvexitybondwillsellatahigherinitialyieldtomaturity.Thathigheryieldiscompensationforlowerconvexity.Ifrateschangeonlyslightly,thehigheryield-lowerconvexitybondwillperformbetter;ifrateschangebyasubstantialamount,theloweryield-higherconvexitybondwww.hackshp.cnwillperformbetter.16-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfolios20.a.Thefollowingspreadsheetshowsthattheconvexityofthebondis64.933.Thepresentvalueofeachcashflowisobtainedbydiscountingat7%.(Sincethebondhasa7%couponandsellsatpar,itsYTMis7%.)Convexityequals:thesumofthelastcolumn(7,434.175)dividedby:[P×(1+y)2]=100×(1.07)2=114.49TimeCashflow22PV(CF)t+t(t+t)×PV(CF)(t)(CF)176.542213.084276.114636.684375.7141268.569475.34020106.805574.99130149.727674.66442195.905774.35956244.118874.07472293.333973.80890342.6781010754.3931105,983.271Sum:100.0007,434.175Convexity:64.933Thedurationofthebondis:(1)(2)(3)(4)(5)TimeuntilPVofCFColumn(1)×PaymentCashFlow(DiscountWeightColumn(4)(years)rate=7%)1$7$6.5420.065420.065422$7$6.1140.061140.122283$7$5.7140.057140.171424课后答案网$7$5.3400.053400.213615$7$4.9910.049910.249556$7$4.6640.046640.279867$7$4.3590.043590.305158$7$4.0740.040740.325939www.hackshp.cn$7$3.8080.038080.3426810$107$54.3930.543935.43934ColumnSums$100.0001.000007.51523D=7.515yearsb.Iftheyieldtomaturityincreasesto8%,thebondpricewillfallto93.29%ofparvalue,apercentagedecreaseof6.71%.16-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfoliosc.Thedurationrulepredictsapercentagepricechangeof:⎛D⎞⎛.7515⎞⎜−⎟×.001=⎜−⎟×.001=−.00702=−.702%⎝.107⎠⎝.107⎠Thisoverstatestheactualpercentagedecreaseinpriceby0.31%.Thepricepredictedbythedurationruleis7.02%lessthanfacevalue,or92.98%offacevalue.d.Theduration-with-convexityrulepredictsapercentagepricechangeof:⎡⎛.7515⎞⎤[2]⎢⎜−⎟×.001⎥+5.0×64.933×.001=−.00670=−.670%⎣⎝.107⎠⎦Thepercentageerroris0.01%,whichissubstantiallylessthantheerrorusingthedurationrule.Thepricepredictedbythedurationruleis6.70%lessthanfacevalue,or93.30%offacevalue.CFACFAPROBLEMSPROBLEMS1.a.Thecallfeatureprovidesavaluableoptiontotheissuer,sinceitcanbuybackthebondataspecifiedcallpriceevenifthepresentvalueofthescheduledremainingpaymentsisgreaterthanthecallprice.Theinvestorwilldemand,andtheissuerwillbewillingtopay,ahigheryieldontheissueascompensationforthisfeature.b.Thecallfeaturereducesboththeduration(interestratesensitivity)andthe课后答案网convexityofthebond.Ifinterestratesfall,theincreaseinthepriceofthecallablebondwillnotbeaslargeasitwouldbeifthebondwerenoncallable.Moreover,theusualcurvaturethatcharacterizespricechangesforastraightbondisreducedbyacallfeature.Theprice-yieldcurve(seeFigure16.6)flattensoutastheinterestratefallsandtheoptiontocallthebondbecomesmoreattractive.Infact,atverylowinterestrates,thebondexhibitsnegativeconvexity.www.hackshp.cn16-13若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfolios2.a.Bondpricedecreasesby$80.00,calculatedasfollows:10×0.01×800=80.00b.½×120×(0.015)2=0.0135=1.35%c.9/1.10=8.18d.(i)e.(i)f.(iii)Macaulayduration103.a.Modifiedduration===.926years1+YTM.108b.Foroption-freecouponbonds,modifieddurationisabettermeasureofthebond’ssensitivitytochangesininterestrates.Maturityconsidersonlythefinalcashflow,whilemodifieddurationincludesotherfactors,suchasthesizeandtimingofcouponpayments,andthelevelofinterestrates(yieldtomaturity).Modifiedduration,unlikematurity,indicatestheapproximatepercentagechangeinthebondpriceforagivenchangeinyieldtomaturity.c.i.Modifieddurationincreasesasthecoupondecreases.ii.Modifieddurationdecreasesasmaturitydecreases.d.Convexitymeasuresthecurvatureofthebond’sprice-yieldcurve.Suchcurvaturemeansthatthedurationruleforbondpricechange(which课后答案网isbasedonlyontheslopeofthecurveattheoriginalyield)isonlyanapproximation.Addingatermtoaccountfortheconvexityofthebondincreasestheaccuracyoftheapproximation.Thatconvexityadjustmentisthelastterminthefollowingequation:∆P⎡12⎤=(−D*×∆y)+×Convexity×(∆y)⎢⎥Pwww.hackshp.cn⎣2⎦4.a.(i)Currentyield=Coupon/Price=$70/$960=0.0729=7.29%(ii)YTM=3.993%semiannuallyor7.986%annualbondequivalentyield.Onafinancialcalculator,enter:n=10;PV=–960;FV=1000;PMT=35Computetheinterestrate.16-14若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfolios(iii)Horizonyieldorrealizedcompoundyieldis4.166%(semiannually),or8.332%annualbondequivalentyield.Toobtainthisvalue,firstfindthefuturevalue(FV)ofreinvestedcouponsandprincipal.Therewillbesixpaymentsof$35each,reinvestedsemiannuallyat3%perperiod.Onafinancialcalculator,enter:PV=0;PMT=$35;n=6;i=3%.Compute:FV=$226.39Threeyearsfromnow,thebondwillbesellingattheparvalueof$1,000becausetheyieldtomaturityisforecasttoequalthecouponrate.Therefore,totalproceedsinthreeyearswillbe$1,226.39.Thenfindtherate(yrealized)thatmakestheFVofthepurchasepriceequalto$1,226.39:$960×(1+y6realized)=$1,226.39⇒yrealized=4.166%(semiannual)b.Shortcomingsofeachmeasure:(i)Currentyielddoesnotaccountforcapitalgainsorlossesonbondsboughtatpricesotherthanparvalue.Italsodoesnotaccountforreinvestmentincomeoncouponpayments.(ii)Yieldtomaturityassumesthebondishelduntilmaturityandthatallcouponincomecanbereinvestedatarateequaltotheyieldtomaturity.(iii)Horizonyieldorrealizedcompoundyieldisaffectedbytheforecastofreinvestmentrates,holdingperiod,andyieldofthebondattheendoftheinvestor"sholdingperiod.Note:Thiscriticismofhorizonyieldisabitunfair:whileYTMcanbecalculatedwithoutexplicitassumptionsregardingfutureYTMandreinvestmentrates,youimplicitlyassumethatthesevaluesequalthecurrentYTMifyouuseYTMasameasureofexpectedreturn.5.a.(i)Theeffectivedurationofthe4.75%Treasurysecurity课后答案网is:∆P/P(116.887−86.372)/100−==15.2575∆r.002(ii)Thedurationoftheportfoliowww.hackshp.cnistheweightedaverageofthedurationsoftheindividualbondsintheportfolio:PortfolioDuration=w1D1+w2D2+w3D3+…+wkDkwherewi=marketvalueofbondi/marketvalueoftheportfolioDi=durationofbondik=numberofbondsintheportfolioTheeffectivedurationofthebondportfolioiscalculatedasfollows:[($48,667,680/$98,667,680)×2.15]+[($50,000,000/$98,667,680)×15.26]=8.7916-15若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfoliosb.VanHusen’sremarkswouldbecorrectiftherewereasmall,parallelshiftinyields.Durationisafirst(linear)approximationonlyforsmallchangesinyield.Forlargerchangesinyield,theconvexitymeasureisneededinordertoapproximatethechangeinpricethatisnotexplainedbyduration.Additionally,portfoliodurationassumesthatallyieldschangebythesamenumberofbasispoints(parallelshift),soanynon-parallelshiftinyieldswouldresultinadifferenceinthepricesensitivityoftheportfoliocomparedtothepricesensitivityofasinglesecurityhavingthesameduration.6.a.TheAabondinitiallyhasahigherYTM(yieldspreadof40b.p.versus31b.p.),butitisexpectedtohaveawideningspreadrelativetoTreasuries.Thiswillreducetherateofreturn.TheAaaspreadisexpectedtobestable.Calculatecomparativereturnsasfollows:IncrementalreturnoverTreasuries=Incrementalyieldspread−(Changeinspread×duration)Aaabond:31bp−(0×3.1years)=31bpAabond:40bp−(10bp×3.1years)=9bpTherefore,choosetheAaabond.b.Othervariablestobeconsidered:•Potentialchangesinissue-specificcreditquality.Ifthecreditqualityofthebondschanges,spreadsrelativetoTreasurieswillalsochange.•Changesinrelativeyieldspreadsforagivenbondrating.Ifqualityspreadsinthegeneralbondmarketchangebecauseofchangesinrequiredriskpremiums,theyieldspreads课后答案网ofthebondswillchangeevenifthereisnochangeintheassessmentofthecreditqualityoftheseparticularbonds.•Maturityeffect.Asbondsneartheirmaturity,theeffectofcreditqualityonspreadscanalsochange.Thiscanaffectbondsofdifferentinitialcreditqualitydifferently.www.hackshp.cn7.a.%pricechange=(−Effectiveduration)×ChangeinYTM(%)CIC:(−7.35)×(−0.50%)=3.675%PTR:(−5.40)×(−0.50%)=2.700%16-16若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfoliosb.Sinceweareaskedtocalculatehorizonreturnoveraperiodofonlyonecouponperiod,thereisnoreinvestmentincome.Couponpayment+Year-endprice−InitialPriceHorizonreturn=Initialprice$31.25+,1$055.50−,1$017.50CIC:=.006806=.6806%,1$017.50$36.75+,1$041.50−,1$017.50PTR:=.005971=.5971%,1$017.50c.NoticethatCICisnon-callablebutPTRiscallable.Therefore,CIChaspositiveconvexity,whilePTRhasnegativeconvexity.Thus,theconvexitycorrectiontothedurationapproximationwillbepositiveforCICandnegativeforPTR.8.Theeconomicclimateisoneofimpendinginterestrateincreases.Hence,wewillseektoshortenportfolioduration.a.Choosetheshortmaturity(2012)bond.b.TheArizonabondlikelyhaslowerduration.TheArizonacouponsarelower,buttheArizonayieldishigher.c.Choosethe123/8%couponbond.Thematuritiesareapproximatelyequal,butthe123/8%couponismuchhigher,resultinginalowerduration.d.ThedurationoftheShellbondisloweriftheeffectofthehigheryieldtomaturityandearlierstart课后答案网ofsinkingfundredemptiondominatesitsslightlylowercouponrate.e.Thefloatingratenotehasadurationthatapproximatestheadjustmentperiod,whichisonly6months.www.hackshp.cn9.a.Amanagerwhobelievesthatthelevelofinterestrateswillchangeshouldengageinarateanticipationswap,lengtheningdurationifratesareexpectedtofall,andshorteningdurationifratesareexpectedtorise.16-17若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfoliosb.Achangeinyieldspreadsacrosssectorswouldcallforanintermarketspreadswap,inwhichthemanagerbuysbondsinthesectorforwhichyieldsareexpectedtofallrelativetootherbondsandsellsbondsinthesectorforwhichyieldsareexpectedtoriserelativetootherbonds.c.Abeliefthattheyieldspreadonaparticularinstrumentwillchangecallsforasubstitutionswapinwhichthatsecurityissoldifitsyieldisexpectedtoriserelativetotheyieldofothersimilarbonds,orisboughtifitsyieldisexpectedtofallrelativetotheyieldofothersimilarbonds.10.a.Theadvantagesofabondindexingstrategyare:•Historically,themajorityofactivemanagersunderperformbenchmarkindexesinmostperiods;indexingreducesthepossibilityofunderperformanceatagivenlevelofrisk.•Indexedportfoliosdonotdependonadvisorexpectationsandsohavelessriskofunderperformingthemarket.•Managementadvisoryfeesforindexedportfoliosaredramaticallylessthanfeesforactivelymanagedportfolios.Feeschargedbyactivemanagersgenerallyrangefrom15to50basispoints,whilefeesforindexedportfoliosrangefrom1to20basispoints(withthehighestofthoserepresentingenhancedindexing).Othernon-advisoryfees(i.e.,custodialfees)arealsolessforindexedportfolios.•Plansponsorshavegreatercontroloverindexedportfoliosbecauseindividualmanagersdonothaveasmuchfreedomtovaryfromtheparametersofthebenchmarkindex.Someplansponsorsevendecidetomanageindexportfolioswithin-houseinvestmentstaff.•Indexingisessentially“buyingthemarket.”Ifmarketsareefficient,anindexingstrategyshouldreduceunsystematicdiversifiablerisk,andshouldgenerate课后答案网maximumreturnforagivenlevelofrisk.Thedisadvantagesofabondindexingstrategyare:•Indexedportfolioreturnsmaymatchthebondindex,butdonotnecessarilyreflectoptimalperformance.Insometimeperiods,manyactivemanagersmaywww.hackshp.cnoutperformanindexingstrategyatthesamelevelofrisk.•Thechosenbondindexandportfolioreturnsmaynotmeettheclientobjectivesortheliabilitystream.•Bondindexingmayrestrictthefundfromparticipatinginsectorsorotheropportunitiesthatcouldincreasereturns.16-18若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfoliosb.Thestratifiedsampling,orcellular,methoddividestheindexintocells,witheachcellrepresentingadifferentcharacteristicoftheindex.Commoncellsusedinthecellularmethodcombine(butarenotlimitedto)duration,coupon,maturity,marketsectors,creditrating,andcallandsinkingfundfeatures.Theindexmanagerthenselectsoneormorebondissuestorepresenttheentirecell.Thetotalmarketweightofissuesheldforeachcellisbasedonthetargetindex’scompositionofthatcharacteristic.c.Trackingerrorisdefinedasthediscrepancybetweentheperformanceofanindexedportfolioandthebenchmarkindex.Whentheamountinvestedisrelativelysmallandthenumberofcellstobereplicatedislarge,asignificantsourceoftrackingerrorwiththecellularmethodoccursbecauseoftheneedtobuyoddlotsofissuesinordertoaccuratelyrepresenttherequiredcells.Oddlotsgenerallymustbepurchasedathigherpricesthanroundlots.Ontheotherhand,reducingthenumberofcellstolimittherequirednumberofoddlotswouldpotentiallyincreasetrackingerrorbecauseofthemismatchwiththetarget.11.a.Foranoption-freebond,theeffectivedurationandmodifieddurationareapproximatelythesame.Usingthedataprovided,thedurationiscalculatedasfollows:∆P/P(100.71−99.29)/100−==.7100∆r.0002b.Thetotalpercentagepricechangeforthebondisestimatedasfollows:Percentagepricechangeusingduration=–7.90×–0.02×100=15.80%Convexityadjustment=1.66%课后答案网Totalestimatedpercentagepricechange=15.80%+1.66%=17.46%c.Theassistant’sargumentisincorrect.Becausemodifiedconvexitydoesnotrecognizethefactthatcashflowsforbondswithanembeddedoptioncanchangeasyieldschange,modifiedconvexityremainspositiveasyieldsmovebelowthecallablebond’sstatedcouponrate,justaswww.hackshp.cnitwouldforanoption-freebond.Effectiveconvexity,however,takesintoaccountthefactthatcashflowsforasecuritywithanembeddedoptioncanchangeasinterestrateschange.Whenyieldsmovesignificantlybelowthestatedcouponrate,thelikelihoodthatthebondwillbecalledbytheissuerincreasesandtheeffectiveconvexityturnsnegative.16-19若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter16-ManagingBondPortfolios12.∆P/P=−D*∆yForStrategyI:5-yearmaturity:∆P/P=−4.83×(−0.75%)=3.6225%25-yearmaturity:∆P/P=−23.81×0.50%=−11.9050%StrategyI:∆P/P=(0.5×3.6225%)+[0.5×(−11.9050%)]=−4.1413%ForStrategyII:15-yearmaturity:∆P/P=−14.35×0.25%=−3.5875%13.a.i.Strongeconomicrecoverywithrisinginflationexpectations.Interestratesandbondyieldswillmostlikelyrise,andthepricesofbothbondswillfall.Theprobabilitythatthecallablebondwillbecalledwoulddecrease,andthecallablebondwillbehavemorelikethenon-callablebond.(Notethattheyhavesimilardurationswhenpricedtomaturity).Theslightlylowerdurationofthecallablebondwillresultinsomewhatbetterperformanceinthehighinterestratescenario.ii.Economicrecessionwithreducedinflationexpectations.Interestratesandbondyieldswillmostlikelyfall.Thecallablebondislikelytobecalled.Therelevantdurationcalculationforthecallablebondisnowmodifieddurationtocall.Priceappreciationislimitedasindicatedbythelowerduration.Thenon-callablebond,ontheotherhand,continuestohavethesamemodifieddurationandhencehasgreaterpriceappreciation.b.Projectedpricechange=(modifiedduration)×(changeinYTM)=(–6.80)×(–0.75%)=5.1%Therefore,theprice课后答案网willincreasetoapproximately$105.10fromitscurrentlevelof$100.c.ForBondA,thecallablebond,bondlifeandthereforebondcashflowsareuncertain.Ifoneignoresthecallfeatureandanalyzesthebondona“tomaturity”basis,allcalculationsforyieldanddurationaredistorted.Durationsaretoolongandyieldsarewww.hackshp.cntoohigh.Ontheotherhand,ifonetreatsthepremiumbondsellingabovethecallpriceona“tocall”basis,thedurationisunrealisticallyshortandyieldstoolow.Themosteffectiveapproachistouseanoptionvaluationapproach.Thecallablebondcanbedecomposedintotwoseparatesecurities:anon-callablebondandanoption:Priceofcallablebond=Priceofnon-callablebond–priceofoptionSincethecalloptionalwayshassomepositivevalue,thepriceofthecallablebondisalwayslessthanthepriceofthenon-callablesecurity.16-20若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter17-MacroeconomicandIndustryAnalysisCHAPTER17:MACROECONOMICMACROECONOMICANDANDANDINDUSTRYINDUSTRYINDUSTRYANALYSISANALYSISPROBLEMPROBLEMSETSSETS1.Expansionary(looser)monetarypolicytolowerinterestrateswouldstimulatebothinvestmentandexpendituresonconsumerdurables.Expansionaryfiscalpolicy(i.e.,lowertaxes,increasedgovernmentspending,increasedwelfaretransfers)wouldstimulateaggregatedemanddirectly.2.AdepreciatingdollarmakesimportedcarsmoreexpensiveandAmericancarslessexpensivetoforeignconsumers.ThisshouldbenefittheU.S.autoindustry.3.Thisexerciseislefttothestudent;answerswillvary.4.Atop-downapproachtosecurityvaluationbeginswithananalysisoftheglobalanddomesticeconomy.Analystswhofollowatop-downapproachthennarrowtheirattentiontoanindustryorsectorlikelytoperformwell,giventheexpectedperformanceofthebroadereconomy.Finally,theanalysisfocusesonspecificcompanieswithinanindustryorsectorthathasbeenidentifiedaslikelytoperformwell.Abottom-upapproachtypicallyemphasizesfundamentalanalysisofindividualcompanystocks,andislargelybasedonthebeliefthatundervaluedstocks课后答案网willperformwellregardlessoftheprospectsfortheindustryorthebroadereconomy.Themajoradvantageofthetop-downapproachisthatitprovidesastructuredapproachtoincorporatingtheimpactofeconomicandfinancialvariables,ateverylevel,intoanalysisofacompany’sstock.Onewouldexpect,forexample,thatprospectsforaparticularindustryarehighlydependentonbroadereconomicvariables.Similarly,theperformanceofanindividualcompany’sstockislikelytobegreatlyaffectedwww.hackshp.cnbytheprospectsfortheindustryinwhichthecompanyoperates.5.Firmswithgreatersensitivitytobusinesscyclesareinindustriesthatproducedurableconsumergoodsorcapitalgoods.Consumersofdurablegoods(e.g.,automobiles,majorappliances)aremorelikelytopurchasetheseproductsduringaneconomicexpansion,butcanoftenpostponepurchasesduringarecession.Businesspurchasesofcapitalgoods(e.g.,purchasesofmanufacturingequipmentbyfirmsthatproducetheirownproducts)declineduringarecessionbecausedemandforthefirms’endproductsdeclinesduringarecession.17-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter17-MacroeconomicandIndustryAnalysis6.a.GoldMining.Goldtraditionallyisviewedasahedgeagainstinflation.Expansionarymonetarypolicymayleadtoincreasedinflation,andthuscouldenhancethevalueofgoldminingstocks.b.Construction.Expansionarymonetarypolicywillleadtolowerinterestrateswhichoughttostimulatehousingdemand.Theconstructionindustryshouldbenefit.7.Supply-sideeconomistsbelievethatareductioninincometaxrateswillmakeworkersmorewillingtoworkatcurrentorevenslightlylower(gross-of-tax)wages.Suchaneffectoughttomitigatecostpressuresontheinflationrate.8.a.Theroboticsprocessentailshigherfixedcostsandlowervariable(labor)costs.Therefore,thisfirmwillperformbetterinaboomandworseinarecession.Forexample,costswillriselessrapidlythanrevenuewhensalesvolumeexpandsduringaboom.b.Becauseitsprofitsaremoresensitivetothebusinesscycle,theroboticsfirmwillhavethehigherbeta.9.a.Housingconstruction(cyclicalbutinterest-ratesensitive):(iii)Healthyexpansionb.Healthcare(anon-cyclicalindustry):(i)Deeprecessionc.Goldmining(counter-cyclical):(iv)Stagflationd.Steelproduction(cyclicalindustry)(ii)Superheatedeconomy课后答案网10.a.Oilwellequipment:Relativedecline(Environmentalpressures,declineineasily-developednewoilfields)b.Computerhardware:Consolidationc.Computersoftware:www.hackshp.cnConsolidationd.Geneticengineering:Start-upe.Railroads:Relativedecline11.a.GeneralAutos.Pharmaceuticalsarelessofadiscretionarypurchasethanautomobiles.b.FriendlyAirlines.Travelexpenditureismoresensitivetothebusinesscyclethanmovieconsumption.17-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter17-MacroeconomicandIndustryAnalysis12.Theindexofconsumerexpectationsisausefulleadingeconomicindicatorbecause,ifconsumersareoptimisticaboutthefuture,theywillbemorewillingtospendmoney,especiallyonconsumerdurables,whichwillincreaseaggregatedemandandstimulatetheeconomy.13.Laborcostperunitisausefullaggingindicatorbecausewagestypicallystartrisingonlywellintoaneconomicexpansion.Atthebeginningofanexpansion,thereisconsiderableslackintheeconomyandoutputcanexpandwithoutemployersbiddingupthepriceofinputsorthewagesofemployees.Bythetimewagesstartincreasingduetohighdemandforlabor,theboomperiodhasalreadyprogressedconsiderably.14.TheexpirationofthepatentmeansthatGeneralWeedkillerswillsoonfaceconsiderablygreatercompetitionfromitscompetitors.Wewouldexpectpricesandprofitmarginstofall,andtotalindustrysalestoincreasesomewhataspricesdecline.Theindustrywillprobablyentertheconsolidationstageinwhichproducersareforcedtocompetemoreextensivelyonthebasisofprice.15.a.Expectedprofit=Revenues–Fixedcosts–Variablecosts=$120,000–$30,000–[(1/3)×$120,000]=$50,000fixedcosts$30,000b.DOL=1+=1+=.160profits$50,000c.Ifsalesareonly$108,000,profitwillfallto:$108,000–$30,000–[(1/3)×$108,000]=$42,000Thisisa16%declinefromtheforecastedvalue.课后答案网d.Thedecreaseinprofitis16%,whichisequaltoDOLtimesthe10%dropinsales.e.Profitmustdropmorethan100%toturnnegative.Forprofittofall100%,revenuemustfallby:www.hackshp.cn100%100%==625.%DOL.160Therefore,revenuewouldbeonly37.5%oftheoriginalforecast.Atthislevel,revenuewillbe:0.375×$120,000=$45,000f.Ifrevenueis$45,000,profitwillbe:$45,000–$30,000–(1/3)×$45,000=$017-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter17-MacroeconomicandIndustryAnalysisCFACFAPROBLEMSPROBLEMS1.a.Loweringreserverequirementswouldallowbankstolendoutahigherfractionofdepositsandthusincreasethemoneysupply.b.TheFedwouldbuyTreasurysecurities,therebyincreasingthemoneysupply.c.Thediscountratewouldbereduced,allowingbankstoborrowadditionalfundsatalowerrate.2.a.Expansionarymonetarypolicyislikelytoincreasetheinflationrate,eitherbecauseitmayoverstimulatetheeconomy,orultimatelybecausetheendresultofmoremoneyintheeconomyishigherprices.b.Realoutputandemploymentshouldincreaseinresponsetotheexpansionarypolicy,atleastintheshortrun.c.Therealinterestrateshouldfall,atleastintheshort-run,asthesupplyoffundstotheeconomyhasincreased.d.Thenominalinterestratecouldeitherincreaseordecrease.Ontheonehand,therealratemightfall[seepart(c)],buttheinflationpremiummightrise[seepart(a)].Thenominalrateisthesumofthesetwocomponents.3.a.Theconceptofanindustriallifecyclereferstothetendencyofmostindustriestogothroughvariousstagesofgrowth.Therate课后答案网ofgrowth,thecompetitiveenvironment,profitmarginsandpricingstrategiestendtoshiftasanindustrymovesfromonestagetothenext,althoughitisgenerallydifficulttoidentifypreciselywhenonestagehasendedandthenextbegun.Thestart-upstageischaracterizedbyperceptionsofalargepotentialmarketandbyahighlevelofoptimismforpotentialprofits.However,thisstageusuallywww.hackshp.cndemonstratesahighrateoffailure.Inthesecondstage,oftencalledstablegrowthorconsolidation,growthishighandaccelerating,themarketsarebroadening,unitcostsaredecliningandqualityisimproving.Inthisstage,industryleadersbegintoemerge.Thethirdstage,usuallycalledslowinggrowthormaturity,ischaracterizedbydeceleratinggrowthcausedbyfactorssuchasmaturingmarketsand/orcompetitiveinroadsbyotherproducts.Finally,anindustryreachesastageofrelativedeclineinwhichsalessloworevendecline.17-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter17-MacroeconomicandIndustryAnalysisProductpricing,profitabilityandindustrycompetitivestructureoftenvarybystage.Thus,forexample,thefirststageusuallyencompasseshighproductprices,highcosts(R&D,marketing,etc.)anda(temporary)monopolisticindustrystructure.Instagetwo(stablegrowth),newentrantsbegintoappearandcostsfallrapidlyduetothelearningcurve.Pricesgenerallydonotfallasrapidly,however,allowingprofitmarginstoincrease.Instagethree(slowinggrowth),growthbeginstoslowastheproductorservicebeginstosaturatethemarket,andmarginsareerodedbysignificantpricereductions.Inthefinalstage,industrycumulativeproductionissohighthatproductioncostshavestoppeddeclining,profitmarginsarethin(assumingcompetitionexists),andthefateoftheindustrydependsonreplacementdemandandtheexistenceofsubstituteproducts/services.b.ThepassengercarbusinessintheUnitedStateshasprobablyenteredthefinalstageintheindustriallifecyclebecausenormalizedgrowthisquitelow.Theinformationprocessingbusiness,ontheotherhand,isundoubtedlyearlierinthecycle.Dependingonwhetherornotgrowthisstillaccelerating,itiseitherinthesecondorthirdstage.c.Cars:Inthefinalstagesofthelifecycle,demandtendstobepricesensitive.Thus,Universalcannotraisepriceswithoutlosingvolume.Moreover,giventheindustry’smaturity,coststructuresarelikelytobesimilaracrossallcompetitors,andanypricecutscanbematchedimmediately.Thus,Universal’scarbusinessisboxedin:Productpricingisdeterminedbythemarket,andthecompanyisa“price-taker.”Idata:Idatashouldhavemuchmorepricingflexibilitygivenitsearlierstageintheindustriallifecycle.Demandisgrowingfasterthansupply,and,dependingonthepresenceand/oractionsofanindustryleader,Idatamaysetpriceshightomaximizecurrentprofitsandgeneratecashforproductdevelopment,orsetpriceslowinanefforttogainmarketshare.课后答案网4.a.Abasicpremiseofthebusinesscycleapproachtoinvestmenttimingisthatstockpricesanticipatefluctuationsinthebusinesscycle.Forexample,thereisevidencethatstockpricestendtomoveaboutsixmonthsaheadoftheeconomy.Infact,stockpricesarealeadingindicatorfortheeconomy.Overthecourseofabusinesscycle,thisapproachtoinvestingwouldworkwww.hackshp.cnroughlyasfollows.Astheinvestorperceivesthatthetopofabusinesscycleisapproaching,stockspurchasedshouldnotbevulnerabletoarecession.Whentheinvestorperceivesthatadownturnisathand,stockholdingsshouldbelightenedwithproceedsinvestedinfixed-incomesecurities.Oncetherecessionhasmaturedtosomeextent,andinterestratesfall,bondpriceswillrise.Astheinvestorperceivesthattherecessionisabouttoend,profitsshouldbetakeninthebondsandreinvestedinstocks,particularlythoseincyclicalindustrieswithahighbeta.17-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter17-MacroeconomicandIndustryAnalysisGenerally,abnormalreturnscanbeearnedonlyiftheseassetallocationswitchesaretimedbetterthanthoseofotherinvestors.Switchesmadeaftertheturningpointsmaynotleadtoexcessreturns.b.Basedonthebusinesscycleapproachtoinvestmenttiming,theidealtimetoinvestinacyclicalstocksuchasapassengercarcompanywouldbejustbeforetheendofarecession.Iftherecoveryisalreadyunderway,Adam’srecommendationwouldbetoolate.Theequitiesmarketgenerallyanticipatesthechangesintheeconomiccycle.Therefore,sincethe“recoveryisunderway,”thepriceofUniversalAutoshouldalreadyreflecttheanticipatedimprovementsintheeconomy.5.a.•Theindustry-wideROEislevelingoff,indicatingthattheindustrymaybeapproachingalaterstageofthelifecycle.•AverageP/Eratiosaredeclining,suggestingthatinvestorsarebecominglessoptimisticaboutgrowthprospects.•Dividendpayoutisincreasing,suggestingthatthefirmseeslessreasontoreinvestearningsinthefirm.Theremaybefewergrowthopportunitiesintheindustry.•Industrydividendyieldisalsoincreasing,eventhoughmarketdividendyieldisdecreasing.b.•Industrygrowthrateisstillforecastat10%to15%,higherthanwouldbetrueofamatureindustry.•Non-U.S.marketsarestilluntapped,andsomefirmsarenowenteringthesemarkets.•Mailordersalesegment课后答案网isgrowingat40%ayear.•Nichemarketsarecontinuingtodevelop.•Newmanufacturerscontinuetoenterthemarket.6.a.Relevantdatafromthetablesupportingtheconclusionthatthewww.hackshp.cnretailautopartsindustryasawholeisinthematuritystageoftheindustrylifecycleare:•Thepopulationof18-29yearolds,amajorcustomerbasefortheindustry,isgraduallydeclining.•Thenumberofhouseholdswithincomelessthan$35,000,anotherimportantconsumerbase,isnotexpanding.•Thenumberofcarsfivetofifteenyearsold,animportantendmarket,hasexperiencedlowannualgrowth(oractualdeclineinsomeyears),sothenumberofunitsthatpotentiallyneedpartsisnotgrowing.17-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter17-MacroeconomicandIndustryAnalysis•Automotiveaftermarketindustryretailsaleshavebeengrowingslowlyforseveralyears.•Consumerexpendituresonautomotivepartsandaccessorieshavegrownslowlyforseveralyears.•Averageoperatingmarginsofallretailautopartscompanieshavesteadilydeclined.b.(i)RelevantdatafromthetablesupportingtheconclusionthatWigwamAutopartsHeaven,Inc.(WAH)anditsprincipalcompetitorsareintheconsolidationstageoftheirlifecycleare:•Salesgrowthofretailautopartscompanieswith100ormorestoreshavebeengrowingrapidlyandatanincreasingrate.•Marketshareofretailautopartsstoreswith100ormorestoreshasbeenincreasingbutisstilllessthan20percent,leavingroomformuchmoregrowth.•Averageoperatingmarginsforretailautopartscompanieswith100ormorestoresarehighandrising.(ii)Becauseofindustryfragmentation(i.e.,mostofthemarketshareisdistributedamongmanycompanieswithonlyafewstores),theretailautopartsindustryapparentlyisundergoingmarketinginnovationandconsolidation.Theindustryismovingtowardthe“categorykiller”format,inwhichafewmajorcompaniescontrollargemarketsharesthroughproliferationofoutlets.Theevidencesuggeststhatanew“industrywithinanindustry”isemergingintheformofthe“categorykiller”largechain-storecompany.Thisindustrysubgroupisinitsconsolidationstage(i.e.,rapidgrowthwithhighoperatingprofitmarginsandemergingmarketleaders)despitethefactthattheindustryisinthematuritystageofitslifecycle.7.i.Substitutes–oneyearfromnow:课后答案网CurrentlytheCarrycom,andotherproductsintheirindustrysegment,haveautomaticlanguageconversionfunctionalityandgeographicregionflexibility.Thismarketsegmentiscurrentlyinastrongposition.Substitutes–fiveyearsfromnow:Whiteexpectsthatotherproductsinthebroaderconsumerelectronicsindustry,suchasPDAs,PCs,andotherconsumerelectronics,willeventuallybeabletoincorporatebothfunctionalitiesandsothereforediminishthestrengthofthisforceforCarrycomandotherproductsintheirmarketsegment.www.hackshp.cnii.Threatofnew(orpotential)entrants–oneyearfromnow:Wadehasnothreatofentrantsintoitsmarketforthenextthreeyearsbecause:(a)Wadehastheexclusiveabilitytomanufacturewithordinarycopper,whileotherpotentialentrantsdonothaveaccesstopari-copper,and;(b)PotentialentrantsdonothaveaccesstotheexclusiveproductionlicenseforCarrycomtechnology.17-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter17-MacroeconomicandIndustryAnalysisThreatofnew(orpotential)entrants–fiveyearsfromnow:Beyondthenextthreeyears,however,thethreatishigh.Whiteexpectscompetitorstomarketcopper-basedproducts,eliminatingCarrycom’suniquecompetitiveadvantage.Inaddition,thethree-yearexclusiveproductionlicenseexpires.iii.Intensityofrivalry–oneyearfromnow:Wadewillexperienceonlymodestrivalryforthreeyearsasithasanexclusiveproductionlicenseforthenextthreeyears,whichlimitstheavailabilityofsimilarproducts.However,thebroaderelectronicsmarketmaybeintegratingtheautomaticlanguageconversionfeatureintoitsproductsafteroneyear.Intensityofrivalry–fiveyearsfromnow:Afterthelicenseexpiresinthreeyears,Whiteexpectsothercompetitorstoproduceanumberofsimilarproductswhichwilllimittheirpricingpower.Thisdemonstratesahighintensityofrivalry.8.a.(iii)b.(iii)c.(iv)d.(iii)课后答案网www.hackshp.cn17-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter18-EquityValuationModelsCHAPTER18:EQUITYEQUITYVALUATIONVALUATIONVALUATIONMODELSMODELSPROBLEMPROBLEMSETSSETS1.Theoretically,dividenddiscountmodelscanbeusedtovaluethestockofrapidlygrowingcompaniesthatdonotcurrentlypaydividends;inthisscenario,wewouldbevaluingexpecteddividendsintherelativelymoredistantfuture.However,asapracticalmatter,suchestimatesofpaymentstobemadeinthemoredistantfuturearenotoriouslyinaccurate,renderingdividenddiscountmodelsproblematicforvaluationofsuchcompanies;freecashflowmodelsaremorelikelytobeappropriate.Attheotherextreme,onewouldbemorelikelytochooseadividenddiscountmodeltovalueamaturefirmpayingarelativelystabledividend.2.Itismostimportanttousemulti-stagedividenddiscountmodelswhenvaluingcompanieswithtemporarilyhighgrowthrates.Thesecompaniestendtobecompaniesintheearlyphasesoftheirlifecycles,whentheyhavenumerousopportunitiesforreinvestment,resultinginrelativelyrapidgrowthandrelativelylowdividends(or,inmanycases,nodividendsatall).Asthesefirmsmature,attractiveinvestmentopportunitiesarelessnumeroussothatgrowthratesslow.3.Theintrinsicvalueofashareofstockistheindividualinvestor’sassessmentofthetrueworthofthestock.Themarketcapitalizationrateisthemarketconsensusfortherequiredrateofreturnforthestock.Iftheintrinsicvalueofthestockisequaltoitsprice,thenthemarketcapitalizationrate课后答案网isequaltotheexpectedrateofreturn.Ontheotherhand,iftheindividualinvestorbelievesthestockisunderpriced(i.e.,intrinsicvaluek,pricewillfall.b.(i)Anincreaseindividendpayoutwillreducethesustainablegrowthrateaslessfundsarereinvestedinthefirm.Thesustainablegrowthrate(i.e.,ROE×plowback)willfallasplowbackratiofalls.(ii)Theincreaseddividendpayoutratewillreducethegrowthrateofbookvalueforthesamereason--lessfundsarereinvestedinthefirm.4.Usingatwo-stagedividenddiscountmodel,thecurrentvalueofashareofSundanciiscalculatedasfollows.D3DD(k−g)12V=++0122(1+k)(1+k)(1+k).0$5623.0$3770.0$4976(.014−.013)=++=$43.98122.114.114.114where:E0=$0.952D0=$0.286E1课后答案网1=E0(1.32)=$0.952×1.32=$1.2566D1=E1×0.30=$1.2566×0.30=$0.3770E2=E0(1.32)2=$0.952×(1.32)2=$1.6588D2=E2×0.30=$1.6588www.hackshp.cn×0.30=$0.4976E233=E0×(1.32)×1.13=$0.952×(1.32)×1.13=$1.8744D3=E3×0.30=$1.8743×0.30=$0.562318-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter18-EquityValuationModels5.a.Freecashflowtoequity(FCFE)isdefinedasthecashflowremainingaftermeetingallfinancialobligations(includingdebtpayment)andaftercoveringcapitalexpenditureandworkingcapitalneeds.TheFCFEisameasureofhowmuchthefirmcanaffordtopayoutasdividends,butinagivenyearmaybemoreorlessthantheamountactuallypaidout.Sundanci"sFCFEfortheyear2008iscomputedasfollows:FCFE=Earningsaftertax+Depreciationexpense−Capitalexpenditures−IncreaseinNWC=$80million+$23million−$38million−$41million=$24millionFCFEpershare=FCFE/numberofsharesoutstanding=$24million/84millionshares=$0.286Atthegivendividendpayoutratio,Sundanci"sFCFEpershareequalsdividendspershare.b.TheFCFEmodelrequiresforecastsofFCFEforthehighgrowthyears(2009and2010)plusaforecastforthefirstyearofstablegrowth(2011)inordertotoallowforanestimateoftheterminalvaluein2010basedonperpetualgrowth.BecauseallofthecomponentsofFCFEareexpectedtogrowatthesamerate,thevaluescanbeobtainedbyprojectingtheFCFEatthecommonrate.(Alternatively,thecomponentsofFCFEcanbeprojectedandaggregatedforeachyear.)ThefollowingtableshowstheprocessforestimatingSundanci"scurrentvalueonapersharebasis.课后答案网www.hackshp.cn18-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter18-EquityValuationModelsFreeCashFlowtoEquityBaseAssumptionsSharesoutstanding:84millionRequiredreturnonequity(r):14%ActualProjectedProjectedProjected2008200920102011Growthrate(g)27%27%13%TotalPershareEarningsaftertax$80$0.952$1.2090$1.5355$1.7351Plus:Depreciationexpense$23$0.274$0.3480$0.4419$0.4994Less:Capitalexpenditures$38$0.452$0.5740$0.7290$0.8238Less:Increaseinnetworkingcapital$41$0.488$0.6198$0.7871$0.8894Equals:FCFE$24$0.286$0.3632$0.4613$0.5213Terminalvalue$52.1300*Totalcashflowstoequity$0.3632$52.5913**Discountedvalue$0.3186***$40.4673***Currentvaluepershare$40.7859*****Projected2010Terminalvalue=(Projected2011FCFE)/(r−g)**Projected2010Totalcashflowstoequity=Projected2010FCFE+Projected2010Terminalvalue***Discountedvaluesobtainedusingr=14%****Currentvaluepershare=SumofDiscountedProjected2009and2010Totalcashflowstoequityc.i.TheDDMusesastrictdefinition课后答案网ofcashflowstoequity,i.e.theexpecteddividendsonthecommonstock.Infact,takentoitsextreme,theDDMcannotbeusedtoestimatethevalueofastockthatpaysnodividends.TheFCFEmodelexpandsthedefinitionofcashflowstoincludethebalanceofresidualcashflowsafterallfinancialobligationsandinvestmentneedshavebeenmet.ThustheFCFEmodelexplicitlyrecognizesthefirm’sinvestmentandfinancingpoliciesaswww.hackshp.cnwellasitsdividendpolicy.Ininstancesofachangeofcorporatecontrol,andthereforethepossibilityofchangingdividendpolicy,theFCFEmodelprovidesabetterestimateofvalue.TheDDMisbiasedtowardfindinglowP/Eratiostockswithhighdividendyieldstobeundervaluedandconversely,highP/Eratiostockswithlowdividendyieldstobeovervalued.Itisconsideredaconservativemodelinthatittendstoidentifyfewerundervaluedfirmsasmarketpricesriserelativetofundamentals.TheDDMdoesnotallowforthepotentialtaxdisadvantageofhighdividendsrelativetothecapitalgainsachievablefromretentionofearnings.18-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter18-EquityValuationModelsii.Bothtwo-stagevaluationmodelsallowfortwodistinctphasesofgrowth,aninitialfiniteperiodwherethegrowthrateisabnormal,followedbyastablegrowthperiodthatisexpectedtolastindefinitely.Thesetwo-stagemodelssharethesamelimitationswithrespecttothegrowthassumptions.First,thereisthedifficultyofdefiningthedurationoftheextraordinarygrowthperiod.Forexample,alongerperiodofhighgrowthwillleadtoahighervaluation,andthereisthetemptationtoassumeanunrealisticallylongperiodofextraordinarygrowth.Second,theassumptionofasuddenshiftfromhighgrowthtolower,stablegrowthisunrealistic.Thetransformationismorelikelytooccurgradually,overaperiodoftime.Giventhattheassumedtotalhorizondoesnotshift(i.e.,isinfinite),thetimingoftheshiftfromhightostablegrowthisacriticaldeterminantofthevaluationestimate.Third,becausethevalueisquitesensitivetothesteady-stategrowthassumption,over-orunder-estimatingthisratecanleadtolargeerrorsinvalue.Thetwomodelsshareotherlimitationsaswell,notablydifficultiesinaccuratelyforecastingrequiredratesofreturn,indealingwiththedistortionsthatresultfromsubstantialand/orvolatiledebtratios,andinaccuratelyvaluingassetsthatdonotgenerateanycashflows.6.a.Theformulaforcalculatingapriceearningsratio(P/E)forastablegrowthfirmisthedividendpayoutratiodividedbythedifferencebetweentherequiredrateofreturnandthegrowthrateofdividends.IftheP/Eiscalculatedbasedontrailingearnings(year0),thepayoutratioisincreasedbythegrowthrate.IftheP/Eiscalculatedbasedonnextyear’searnings(year1),thenumeratoristhepayoutratio.P/Eontrailingearnings:P/E=[payoutratio×(1+g)]/(r−g)=[0.30×1.13]/(0.14−0.13)=33.9P/Eonnextyear"searnings:P/E=payoutratio/(r课后答案网−g)=0.30/(0.14−0.13)=30.0b.TheP/Eratioisadecreasingfunctionofriskiness;asriskincreases,theP/Eratiodecreases.IncreasesintheriskinessofSundancistockwouldbeexpectedtolowertheP/Eratio.TheP/Eratioisanincreasingfunctionofthegrowthrateofthefirm;thehighertheexpectedgrowth,thehighertheP/Eratio.SundanciwouldcommandahigherP/Ewww.hackshp.cnifanalystsincreasetheexpectedgrowthrate.TheP/Eratioisadecreasingfunctionofthemarketriskpremium.Anincreasedmarketriskpremiumincreasestherequiredrateofreturn,loweringthepriceofastockrelativetoitsearnings.AhighermarketriskpremiumwouldbeexpectedtolowerSundanci"sP/Eratio.18-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter18-EquityValuationModels7.a.Thesustainablegrowthrateisequalto:plowbackratio×returnonequity=b×ROEwhereb=[NetIncome–(Dividendpershare×sharesoutstanding)]/NetIncomeROE=NetIncome/BeginningofyearequityIn2005:b=[208–(0.80×100)]/208=0.6154ROE=208/1380=0.1507Sustainablegrowthrate=0.6154×0.1507=9.3%In2008:b=[275–(0.80×100)]/275=0.7091ROE=275/1836=0.1498Sustainablegrowthrate=0.7091×0.1498=10.6%b.i.Theincreasedretentionratioincreasedthesustainablegrowthrate.Retentionratio=[NetIncome–(Dividendpershare×sharesoutstanding)]/NetIncomeRetentionratioincreasedfrom0.6154in2005to0.7091in2008.Thisincreaseintheretentionratiodirectlyincreasedthesustainablegrowthratebecausetheretentionratioisoneofthetwofactorsdeterminingthesustainablegrowthrate.ii.Thedecreaseinleveragereducedthesustainablegrowthrate.Financialleverage=(TotalAssets/Beginningofyearequity)Financialleveragedecreasedfrom2.34(=3230/1380)atthebeginningof2005to2.10atthebeginningof2008(=3856/1836)课后答案网ThisdecreaseinleveragedirectlydecreasedROE(andthusthesustainablegrowthrate)becausefinancialleverageisoneofthefactorsdeterminingROE(andROEisoneofthetwofactorsdeterminingthesustainablegrowthrate).8.a.TheformulafortheGordonmodelwww.hackshp.cnis:V0=[D0×(1+g)]/(r–g)where:D0=dividendpaidattimeofvaluationg=annualgrowthrateofdividendsr=requiredrateofreturnforequityIntheaboveformula,P0,themarketpriceofthecommonstock,substitutesforV0andgbecomesthedividendgrowthrateimpliedbythemarket:P0=[D0×(1+g)]/(r–g)Substituting,wehave:58.49=[0.80×(1+g)]/(0.08–g)⇒g=6.54%18-13若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter18-EquityValuationModelsb.UseoftheGordongrowthmodelwouldbeinappropriatetovalueDynamic’scommonstock,forthefollowingreasons:i.TheGordongrowthmodelassumesasetofrelationshipsaboutthegrowthratefordividends,earnings,andstockvalues.Specifically,themodelassumesthatdividends,earnings,andstockvalueswillgrowatthesameconstantrate.InvaluingDynamic’scommonstock,theGordongrowthmodelisinappropriatebecausemanagement’sdividendpolicyhashelddividendsconstantindollaramountalthoughearningshavegrown,thusreducingthepayoutratio.ThispolicyisinconsistentwiththeGordonmodelassumptionthatthepayoutratioisconstant.ii.ItcouldalsobearguedthatuseoftheGordonmodel,givenDynamic’scurrentdividendpolicy,violatesoneofthegeneralconditionsforsuitabilityofthemodel,namelythatthecompany’sdividendpolicybearsanunderstandableandconsistentrelationshipwiththecompany’sprofitability.9.a.Theindustry’sestimatedP/Ecanbecomputedusingthefollowingmodel:P0/E1=payoutratio/(r−g)However,sincerandgarenotexplicitlygiven,theymustbecomputedusingthefollowingformulas:gind=ROE×retentionrate=0.25×0.40=0.10rind=governmentbondyield+(industrybeta×equityriskpremium)=0.06+(1.2×0.05)=0.12Therefore:P0/E1=0.60/(0.12−0.10)=30.0课后答案网b.i.ForecastgrowthinrealGDPwouldcauseP/EratiostobegenerallyhigherforCountryA.HigherexpectedgrowthinGDPimplieshigherearningsgrowthandahigherP/E.ii.GovernmentbondyieldwouldcauseP/EratiostobegenerallyhigherforCountryB.Alowergovernmentbondyieldimpliesalowerrisk-freerateandwww.hackshp.cnthereforeahigherP/E.iii.EquityriskpremiumwouldcauseP/EratiostobegenerallyhigherforCountryB.AlowerequityriskpremiumimpliesalowerrequiredreturnandahigherP/E.18-14若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter18-EquityValuationModels10.a.k=rf+β[Ε(rM)–rf]=4.5%+1.15(14.5%−4.5%)=16%b.YearDividend2009$1.722010$1.72×1.12=$1.932011$1.72×1.122=$2.162012$1.72×1.123=$2.422013$1.72×1.123×1.09=$2.63Presentvalueofdividendspaidin2010–2012:YearPVofDividend2010$1.93/1.161=$1.662011$2.16/1.162=$1.612012$2.42/1.163=$1.55Total=$4.82D2013.2$63Priceatyear-end2012===$37.57k−g.016−.009$37.57PVin2009ofthisstockprice==$24.073.116Intrinsicvalueofstock=$4.82+$24.07=$28.89c.ThedataintheproblemindicatethatQuickBrushissellingatapricesubstantiallybelowitsintrinsicvalue,whilethecalculationsabovedemonstratethatSmileWhiteissellingatapricesomewhatabovetheestimateofitsintrinsicvalue.Basedonthisanalysis,QuickBrushoffersthepotentialforconsiderableabnormalreturns,whileSmileWhiteoffersslightlybelow-marketrisk-adjustedreturns.课后答案网d.Strengthsoftwo-stageversusconstantgrowthDDM:•Two-stagemodelallowsforseparatevaluationoftwodistinctperiodsinacompany’sfuture.Thiscanaccommodatelifecycleeffects.Italsocanavoidthedifficultiesposedbyinitialgrowththatishigherthanthediscountrate.•Two-stagemodelallowsforinitialperiodofabove-sustainablegrowth.www.hackshp.cnItallowstheanalysttomakeuseofherexpectationsregardingwhengrowthmightshiftfromoff-trendtoamoresustainablelevel.AweaknessofallDDMsisthattheyareverysensitivetoinputvalues.Smallchangesinkorgcanimplylargechangesinestimatedintrinsicvalue.Theseinputsaredifficulttomeasure.18-15若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter18-EquityValuationModels11.a.ThevalueofashareofRioNationalequityusingtheGordongrowthmodelandthecapitalassetpricingmodelis$22.40,asshownbelow.Calculatetherequiredrateofreturnusingthecapitalassetpricingmodel:k=rf+β(kM–rf)=4%+1.8(9%–4%)=13%CalculatethesharevalueusingtheGordongrowthmodel:D×(1+g).0$20×(1+.012)oP===$22.400k−g.013−.012b.ThesustainablegrowthrateofRioNationalis9.97%,calculatedasfollows:g=b×ROE=EarningsRetentionRate×ROE=(1–PayoutRatio)×ROE=⎛Dividends⎞NetIncome⎛.3$20⎞$30.16⎜1−⎟×=⎜1−⎟×=.00997=.997%⎝NetIncome⎠BeginningEquity⎝$30.16⎠$270.3512.a.Toobtainfreecashflowtoequity(FCFE),thetwoadjustmentsthatShaarshouldmaketocashflowfromoperations(CFO)are:1.Subtractinvestmentinfixedcapital:CFOdoesnottakeintoaccounttheinvestingactivitiesinlong-termassets,particularlyplantandequipment.ThecashflowscorrespondingtothosenecessaryexpendituresarenotavailabletoequityholdersandthereforeshouldbesubtractedfromCFOtoobtainFCFE.2.Addnetborrowing:CFOdoesnottakeintoaccounttheamountofcapitalsuppliedtothefirmbylenders(e.g.,bondholders).Thenewborrowings,netofdebtrepayment,arecashflowsavailabletoequityholdersandshouldbeaddedtoCFOtoobtainFCFE.课后答案网b.Note1:RioNationalhad$75millionincapitalexpendituresduringtheyear.Adjustment:negative$75millionThecashflowsrequiredforthosecapitalexpenditures(–$75million)arenolongeravailabletotheequityholdersandshouldbesubtractedfromnetincometoobtainFCFE.www.hackshp.cn18-16若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter18-EquityValuationModelsNote2:Apieceofequipmentthatwasoriginallypurchasedfor$10millionwassoldfor$7millionatyear-end,whenithadanetbookvalueof$3million.EquipmentsalesareunusualforRioNational.Adjustment:positive$3millionIncalculatingFCFE,onlycashflowinvestmentsinfixedcapitalshouldbeconsidered.The$7millionsalepriceofequipmentisacashinflownowavailabletoequityholdersandshouldbeaddedtonetincome.However,thegainoverbookvaluethatwasrealizedwhensellingtheequipment($4million)isalreadyincludedinnetincome.Becausethetotalsaleiscash,notjustthegain,the$3millionnetbookvaluemustbeaddedtonetincome.Therefore,theadjustmentcalculationis:$7millionincashreceived–$4millionofgainrecordedinnetincome=$3millionadditionalcashreceivedaddedtonetincometoobtainFCFE.Note3:Thedecreaseinlong-termdebtrepresentsanunscheduledprincipalrepayment;therewasnonewborrowingduringtheyear.Adjustment:negative$5millionTheunscheduleddebtrepaymentcashflow(–$5million)isanamountnolongeravailabletoequityholdersandshouldbesubtractedfromnetincometodetermineFCFE.Note4:OnJanuary1,2008,thecompanyreceivedcashfromissuing400,000sharesofcommonequityatapriceof$25.00pershare.NoadjustmentTransactionsbetweenthefirmanditsshareholdersdonotaffectFCFE.TocalculateFCFE,therefore,noadjustmenttonetincomeisrequiredwithrespecttotheissuanceofnewshares.课后答案网Note5:Anewappraisalduringtheyearincreasedtheestimatedmarketvalueoflandheldforinvestmentby$2million,whichwasnotrecognizedin2008income.NoadjustmentTheincreasedmarketvalueofthelanddidnotgenerateanycashflowandwasnotreflectedinnetincome.TocalculateFCFE,therefore,www.hackshp.cnnoadjustmenttonetincomeisrequired.18-17若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter18-EquityValuationModelsc.Freecashflowtoequity(FCFE)iscalculatedasfollows:FCFE=NI+NCC–FCINV–WCINV+NetBorrowingwhereNCC=non-cashchargesFCINV=investmentinfixedcapitalWCINV=investmentinworkingcapitalMillion$ExplanationNI=$30.16FromTable18GNCC=+$67.17$71.17(depreciationandamortizationfromTable18G)–$4.00*(gainonsalefromNote2)FCINV=–$68.00$75.00(capitalexpendituresfromNote1)–$7.00*(cashonsalefromNote2)WCINV=–$24.00–$3.00(increaseinaccountsreceivablefromTable18F)+–$20.00(increaseininventoryfromTable18F)+–$1.00(decreaseinaccountspayablefromTable18F)NetBorrowing=+(–$5.00)–$5.00(decreaseinlong-termdebtfromTable18F)FCFE=$0.33*SupplementalNote2inTable18HaffectsbothNCCandFCINV.13.RioNational’sequityisrelativelyundervaluedcomparedtotheindustryonaP/E-to-growth(PEG)basis.RioNational’sPEGratioof1.33isbelowtheindustryPEGratioof1.66.ThelowerPEGratioisattractivebecauseitimpliesthatthegrowthrateatRioNationalisavailableatarelativelylowerpricethanisthecasefortheindustry.ThePEGratiosforRioNationalandtheindustryarecalculatedbelow:RioNational课后答案网CurrentPrice=$25.00NormalizedEarningsperShare=$1.71Price-to-EarningsRatio=$25/$1.71=14.62GrowthRate(asapercentage)=11PEGRatio=14.62/11=1.33www.hackshp.cnIndustryPrice-to-EarningsRatio=19.90GrowthRate(asapercentage)=12PEGRatio=19.90/12=1.6618-18若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter19-FinancialStatementAnalysisCHAPTER19:FINANCIALFINANCIALSTATEMENTSTATEMENTSTATEMENTANALYSISANALYSISPROBLEMPROBLEMSETSSETS1.ThemajordifferenceinapproachofinternationalfinancialreportingstandardsandU.S.GAAPaccountingstemsfromthedifferencebetween‘principles’and‘rules.’U.S.GAAPaccountingisrules-based,withextensivedetailedrulestobefollowedinthepreparationoffinancialstatements;manyinternationalstandards,includingthosefollowedinEuropeanUnioncountries,allowmuchgreaterflexibility,aslongasconformitywithgeneralprinciplesisdemonstrated.EventhoughU.S.GAAPisgenerallymoredetailedandspecific,issuesofcomparabilitystillariseamongU.S.companies.Comparabilityproblemsarestillgreateramongcompaniesinforeigncountries.2.Earningsmanagementshouldnotmatterinatrulyefficientmarket,whereallpubliclyavailableinformationisreflectedinthepriceofashareofstock.Investorscanseethroughattemptstomanageearningssothattheycandetermineacompany’strueprofitabilityand,hence,theintrinsicvalueofashareofstock.However,iffirmsdoengageinearningsmanagement,thentheclearimplicationisthatmanagersdonotviewfinancialmarketsasefficient.3.Bothcreditratingagenciesandstockmarketanalystsarelikelytobemoreorlessinterestedinalloftheratiosdiscussedinthischapter(aswellasmanyotherratiosandformsofanalysis).SincetheMoody课后答案网’sandStandardandPoor’sratingsassessbonddefaultrisk,theseagenciesaremostinterestedinleverageratios.Astockmarketanalystwouldbemostinterestedinprofitabilityandmarketpriceratios.4.ROA=ROS×ATOwww.hackshp.cnTheonlywaythatCrustyPiecanhaveanROShigherthantheindustryaverageandanROAequaltotheindustryaverageisforitsATOtobelowerthantheindustryaverage.5.ABC’sAssetturnovermustbeabovetheindustryaverage.19-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter19-FinancialStatementAnalysis6.ROE=(1–Taxrate)×[ROA+(ROA–Interestrate)Debt/Equity]ROEA>ROEBFirmsAandBhavethesameROA.AssumingthesametaxrateandassumingthatROA>interestrate,thenFirmAmusthaveeitheralowerinterestrateorahigherdebtratio.CFACFAPROBLEMSPROBLEMS1.ROE=Netprofits/Equity=Netprofits/Sales×Sales/Assets×Assets/Equity=Netprofitmargin×Assetturnover×Leverageratio=5.5%×2.0×2.2=24.2%2.SmileWhitehashigherqualityofearningsforthefollowingreasons:•SmileWhiteamortizesitsgoodwilloverashorterperiodthandoesQuickBrush.SmileWhitethereforepresentsmoreconservativeearningsbecauseithasgreatergoodwillamortizationexpense.•SmileWhitedepreciatesitsproperty,plantandequipmentusinganaccelerateddepreciationmethod.Thisresultsinrecognitionofdepreciationexpensesoonerandalsoimpliesthatitsincomeismoreconservativelystated.•SmileWhite’sbaddebtallowanceisgreaterasapercentofreceivables.SmileWhiteisrecognizinggreaterbad-debtexpensethanQuickBrush.Ifactualcollectionexperiencewillbecomparable,thenSmileWhitehasthemoreconservativerecognitionpolicy.课后答案网3.a.ROE=Netprofits=Netprofits×Sales×AssetsEquitySalesAssetsEquity=Netprofitmarginwww.hackshp.cn×Totalassetturnover×Assets/equityNetprofits510==.00992=.992%Sales,5140Sales,5140==.166Assets,3100Assets,3100==.141Equity,220019-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter19-FinancialStatementAnalysis510,5140,3100b.ROE=××=.992%×.166×.141=232.%,5140,3100,2200.196−.060c.g=ROE×plowback=232.%×=161.%.1964.a.PalombaPizzaStoresStatementofCashFlowsFortheyearendedDecember31CashFlowsfromOperatingActivitiesCashCollectionsfromCustomers$250,000CashPaymentstoSuppliers(85,000)CashPaymentsforSalaries(45,000)CashPaymentsforInterest(10,000)NetCashProvidedbyOperatingActivities$110,000CashFlowsfromInvestingActivitiesSaleofEquipment38,000PurchaseofEquipment(30,000)PurchaseofLand(14,000)NetCashUsedinInvestingActivitiesCashFlowsfromFinancingActivities(6,000)RetirementofCommonStock(25,000)PaymentofDividends(35,000)NetCashUsedinFinancingActivities(60,000)NetIncreaseinCash课后答案网44,000CashatBeginningofYear50,000CashatEndofYear$94,000b.Cashflowfromoperations(CFO)focusesonmeasuringthecashflowgeneratedbyoperationsandnotonmeasuringprofitability.Ifusedasameasureofperformance,CFOwww.hackshp.cnislesssubjecttodistortionthanthenetincomefigure.AnalystsuseCFOasacheckonthequalityofearnings.CFOthenbecomesacheckonthereportednetearningsfigure,butisnotasubstitutefornetearnings.CompanieswithhighnetincomebutlowCFOmaybeusingincomerecognitiontechniquesthataresuspect.Theabilityofafirmtogeneratecashfromoperationsonaconsistentbasisisoneindicationofthefinancialhealthofthefirm.Formostfirms,CFOisthe“lifeblood”ofthefirm.AnalystssearchfortrendsinCFOtoindicatefuturecashconditionsandthepotentialforcashflowproblems.19-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter19-FinancialStatementAnalysisCashflowfrominvestingactivities(CFI)isanindicationofhowthefirmisinvestingitsexcesscash.Theanalystmustconsidertheabilityofthefirmtocontinuetogrowandtoexpandactivities,andCFIisagoodindicationoftheattitudeofmanagementinthisarea.Analysisofthiscomponentoftotalcashflowindicatesthetypeofcapitalexpendituresbeingmadebymanagementtoeitherexpandormaintainproductiveactivities.CFIisalsoanindicatorofthefirm’sfinancialflexibilityanditsabilitytogeneratesufficientcashtorespondtounanticipatedneedsandopportunities.AdecreasingCFImaybeasignofaslowdowninthefirm’sgrowth.Cashflowfromfinancingactivities(CFF)indicatesthefeasibilityoffinancing,thesourcesoffinancing,andthetypesofsourcesmanagementsupports.Continueddebtfinancingmaysignalafuturecashflowproblem.Thedependencyofafirmonexternalsourcesoffinancing(eitherborrowingorequityfinancing)maypresentproblemsinthefuture,suchasdebtservicingandmaintainingdividendpolicy.AnalystsalsouseCFFasanindicationofthequalityofearnings.Itoffersinsightsintothefinancialhabitsofmanagementandpotentialfuturepolicies.5.a.CFfromoperatingactivities=$260–$85–$12–$35=$128b.CFfrominvestingactivities=–$8+$30–$40=–$18c.CFfromfinancingactivities=–$32–$37=–$696.a.QuickBrushhashadhighersalesandearningsgrowth(pershare)thanSmileWhite.Marginsarealsohigher.ButthisdoesnotmeanthatQuickBrushisnecessarilyabetterinvestment.SmileWhitehasahigherROE,which课后答案网hasbeenstable,whileQuickBrush’sROEhasbeendeclining.WecanseethesourceofthedifferenceinROEusingDuPontanalysis:ComponentDefinitionQuickBrushSmileWhiteTaxburden(1–t)Netprofits/pretaxprofits67.4%66.0%InterestburdenPretaxprofits/EBIT1.0000.955Profitmarginwww.hackshp.cnEBIT/Sales8.5%6.5%AssetturnoverSales/Assets1.423.55LeverageAssets/Equity1.471.48ROENetprofits/Equity12.0%21.4%Whiletaxburden,interestburden,andleveragearesimilar,profitmarginandassetturnoverdiffer.AlthoughSmileWhitehasalowerprofitmargin,ithasafarhigherassetturnover.19-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter19-FinancialStatementAnalysisSustainablegrowth=ROE×plowbackratioLudlow’sPlowbackSustainableROEestimateofratiogrowthrategrowthrateQuickBrush12.0%1.0012.0%30%SmileWhite21.4%0.347.3%10%Ludlowhasoverestimatedthesustainablegrowthrateforbothcompanies.QuickBrushhaslittleabilitytoincreaseitssustainablegrowth–plowbackalreadyequals100%.SmileWhitecouldincreaseitssustainablegrowthbyincreasingitsplowbackratio.b.QuickBrush’srecentEPSgrowthhasbeenachievedbyincreasingbookvaluepershare,notbyachievinggreaterprofitsperdollarofequity.AfirmcanincreaseEPSevenifROEisdecliningasistrueofQuickBrush.QuickBrush’sbookvaluepersharehasmorethandoubledinthelasttwoyears.Bookvaluepersharecanincreaseeitherbyretainingearningsorbyissuingnewstockatamarketpricegreaterthanbookvalue.QuickBrushhasbeenretainingallearnings,buttheincreaseinthenumberofoutstandingsharesindicatesthatithasalsoissuedasubstantialamountofstock.7.a.ROE=operatingmargin×interestburden×assetturnover×leverage×taxburdenROEforEastover(EO)andforSouthampton(SHC)in2007arefoundasfollows:EBITSHC:145/1,793=8.1%profitmargin=SalesEO:795/7,406=10.7%PretaxprofitsSHC:137/145=0.95interestburden=课后答案网EBITEO:600/795=0.75SalesSHC:1,793/2,104=0.85assetturnover=AssetsEO:7,406/8,265=0.90AssetsSHC:2,140/1,167=1.80leverage=EquityEO:8,265/3,864=2.14www.hackshp.cnNetprofitsSHC:91/137=0.66taxburden=PretaxprofitsEO:394/600=0.66SHC:7.8%ROEEO:10.2%19-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter19-FinancialStatementAnalysisb.ThedifferencesinthecomponentsofROEforEastoverandSouthamptonare:ProfitmarginEOhasahighermarginInterestburdenEOhasahigherinterestburdenbecauseitspretaxprofitsarealowerpercentageofEBITAssetturnoverEOismoreefficientatturningoveritsassetsLeverageEOhashigherfinancialleverageTaxBurdenNomajordifferenceherebetweenthetwocompaniesROEEOhasahigherROEthanSHC,butthisisonlyinpartduetohighermarginsandabetterassetturnover--greaterfinancialleveragealsoplaysapart.c.Thesustainablegrowthratecanbecalculatedas:ROEtimesplowbackratio.ThesustainablegrowthratesforEastoverandSouthamptonareasfollows:PlowbackSustainableROEratio*growthrateEastover10.2%0.363.7%Southampton7.8%0.584.5%*Plowback=(1–payoutratio)EO:Plowback=(1–0.64)=0.36SHC:Plowback=(1–0.42)=0.58Thesustainablegrowthratesderivedinthismannerarenotlikelytoberepresentativeoffuturegrowthbecause2007wasprobablynota“normal”year.ForEastover,earningshadnotyetrecoveredto2004-2005levels;earningsretentionofonly0.36seemslowforacompanyinacapitalintensiveindustry.Southampton’searnings课后答案网fellbyover50percentin2007anditsearningsretentionwillprobablybehigherthan0.58inthefuture.Thereisadanger,therefore,inbasingaprojectionononeyear’sresults,especiallyforcompaniesinacyclicalindustrysuchasforestproducts.8.a.Theformulafortheconstantgrowthdiscounteddividendmodelwww.hackshp.cnis:D(1+g)0P=0k−gForEastover:.1$20×.108P==$43.200.011−.008Thiscompareswiththecurrentstockpriceof$28.Onthisbasis,itappearsthatEastoverisundervalued.19-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter19-FinancialStatementAnalysisb.Theformulaforthetwo-stagediscounteddividendmodelis:DDDP1233P=+++01233(1+k)(1+k)(1+k)(1+k)ForEastover:g1=0.12andg2=0.08D0=1.20D11=D0(1.12)=$1.34D22=D0(1.12)=$1.51D33=D0(1.12)=$1.69D34=D0(1.12)(1.08)=$1.82D4.1$82P===$60.673k−g.011−.0082.1$34.1$51.1$69$60.67P=+++=$48.0301233(.111)(.111)(.111)(.111)ThisapproachmakesEastoverappearevenmoreundervaluedthanwasthecaseusingtheconstantgrowthapproach.c.Advantagesoftheconstantgrowthmodelinclude:(1)logical,theoreticalbasis;(2)simpletocompute;(3)inputscanbeestimated.Disadvantagesinclude:(1)verysensitivetoestimatesofgrowth;(2)gandkdifficulttoestimateaccurately;(3)onlyvalidforgXCall(long)C=5.180ST–50Put(short)–P=4.00–(50–ST)050Lendingposition=48.8250504/1.11050TotalC–P+=50.00STST4/1.110Bytheput-callparitytheorem,theinitialoutlayequalsthestockprice:S0=$50Ineitherscenario,youendupwiththesamepayoffasyouwouldifyouboughtthestockitself.9.a.OutcomeST≤XST>XStockST+DST+DPutX–ST0TotalX+DST+Db.OutcomeST≤XST>XCall0ST–XZeros课后答案网X+DX+DTotalX+DST+DThetotalpayoffsforthetwostrategiesareequalregardlessofwhetherSTexceedsX.c.Thecostofestablishingthestock-plus-putportfoliois:S0+PThecostofestablishingthecall-plus-zeroportfoliowww.hackshp.cnis:C+PV(X+D)Therefore:S0+P=C+PV(X+D)Thisresultisidenticaltoequation20.2.20-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter20-OptionsMarkets:Introduction10.a.PositionST105Writecall,X=$10500–(ST–105)Writeput,X=$100–(100–ST)00TotalST–1000105–STPayoff100105STWriteputWritecallb.Proceedsfromwritingoptions:Call:$4.40Put:$2.53Total:$6.93IfIBMsellsat$103ontheoptionexpirationdate,bothoptionsexpireoutofthemoney,andprofit=$6.93.IfIBMsellsat$110ontheoptionexpirationdate,thecallwrittenresultsinacashoutflowof$5atexpiration,andanoverallprofitof:$6.93–$5.00=$1.93c.Youbreakevenwheneithertheputorthecallresultsinacashoutflowof$6.93.课后答案网Fortheput,thisrequiresthat:$6.93=$100.00–ST⇒ST=$93.07Forthecall,thisrequiresthat:$6.93=STwww.hackshp.cn–$105⇒ST=$111.93d.TheinvestorisbettingthatIBMstockpricewillhavelowvolatility.Thispositionissimilartoastraddle.20-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter20-OptionsMarkets:Introduction18.Theputwiththehigherexercisepricemustcostmore.Therefore,thenetoutlaytoestablishtheportfolioispositive.PositionST<9090≤ST≤95ST>95Writeput,X=$90–(90–ST)00Buyput,X=$9595–ST95–ST0Total595–ST0Thepayoffandprofitdiagramis:5PayoffNetoutlaytoestablishposition0ST9095Profit19.BuytheX=62put(whichshouldcostmorebutdoesnot)andwritetheX=60put.Sincetheoptionshavethesameprice,yournetoutlayiszero.Yourproceedsatexpirationmaybepositive,butcannotbenegative.PositionST<6060≤ST≤62ST>62Buyput,X=$62课后答案网62–ST62–ST0Writeput,X=$60–(60–ST)00Total262–ST0Payoff=Profit(becausenetinvestment=0)www.hackshp.cn20ST606220-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter20-OptionsMarkets:Introduction20.Thefollowingpayofftableshowsthattheportfolioisrisklesswithtime-Tvalueequalto$10:PositionST≤10ST>10BuystockSTSTWritecall,X=$100–(ST–10)Buyput,X=$1010–ST0Total1010Therefore,therisk-freerateis:($10/$9.50)–1=0.0526=5.26%21.a.,b.PositionST<100100≤ST≤110ST>110Buyput,X=$110110–ST110–ST0Writeput,X=$100–(100–ST)00Total10110–ST0Thenetoutlaytoestablishthispositionispositive.Theputyoubuyhasahigherexercisepricethantheputyouwrite,andthereforemustcostmorethantheputthatyouwrite.Therefore,netprofitswillbelessthanthepayoffattimeT.10课后答案网Payoff0ST100110Profitwww.hackshp.cnc.Thevalueofthisportfoliogenerallydecreaseswiththestockprice.Therefore,itsbetaisnegative.20-13若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter20-OptionsMarkets:Introduction22.a.Joe’sstrategyPositionCostPayoffST≤400ST>400Stockindex400STSTPutoption,X=$40020400–ST0Total420400STProfit=payoff–$420–20ST–420Sally’sstrategyPositionCostPayoffST≤390ST>390Stockindex400STSTPutoption,X=$39015390–ST0Total415390STProfit=payoff–$415–25ST–415ProfitSallyJoe课后答案网390400ST-20-25b.Sallydoesbetterwhenthestockpriceishigh,butworsewhenthestockpriceislow.Thebreak-evenpointoccursatSwww.hackshp.cnT=$395,whenbothpositionsprovidelossesof$20.c.Sally’sstrategyhasgreatersystematicrisk.Profitsaremoresensitivetothevalueofthestockindex.20-14若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter20-OptionsMarkets:Introduction23.a.,b.(Seegraphbelow)Thisstrategyisabearspread.Initialproceeds=$9–$3=$6Thepayoffiseithernegativeorzero:PositionST<5050≤ST≤60ST>60Buycall,X=$6000ST–60Writecall,X=$500–(ST–50)–(ST–50)Total0–(ST–50)–10c.Breakevenoccurswhenthepayoffoffsetstheinitialproceedsof$6,whichoccursatstockpriceST=$56.Theinvestormustbebearish:thepositiondoesworsewhenthestockpriceincreases.606050ST-4Profit-10Payoff24.Buyashareofstock,writeacallwithX=$50,writeacallwithX=$60,andbuyacall课后答案网withX=$110.PositionST<5050≤ST≤6060110BuystockSTSTSTSTWritecall,X=$50www.hackshp.cn0–(ST–50)–(ST–50)–(ST–50)Writecall,X=$6000–(ST–60)–(ST–60)Buycall,X=$110000ST–110TotalST50110–ST0Theinvestorismakingavolatilitybet.ProfitswillbehighestwhenvolatilityislowandthestockpriceSTisbetween$50and$60.20-15若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter20-OptionsMarkets:Introduction25.a.PositionST≤780ST>780BuystockSTSTBuyput780–ST0Total780STPositionST≤840ST>840Buycall0ST–840BuyT-bills840840Total840STPayoffBillspluscalls840780Protectiveputstrategy课后答案网ST780840b.ThebillspluscallstrategyhasagreaterpayoffforsomevaluesofSTandneveralowerpayoff.Sinceitspayoffsarealwaysatleastasattractiveandsometimeswww.hackshp.cngreater,itmustbemorecostlytopurchase.20-16若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter20-OptionsMarkets:Introductionc.Theinitialcostofthestockplusputpositionis:$900+$6=$906Theinitialcostofthebillspluscallpositionis:$810+$120=$930ST=700ST=840ST=900ST=960Stock700840900960+Put80000Payoff780840900960Profit–126–66–654Bill840840840840+Call0060120Payoff840840900960Profit–90–90–30+30ProfitProtectiveputBillspluscalls780840ST-90-126d.Thestockandputstrategyisriskier.Thisstrategyperformsworsewhenthemarketisdownandbetterwhenthemarketisup.Therefore,itsbetaishigher.e.Parityisnotviolatedbecausetheseoptionshavedifferentexerciseprices.Parity课后答案网appliesonlytoputsandcallswiththesameexercisepriceandexpirationdate.26.Accordingtoput-callparity(assumingnodividends),thepresentvalueofapaymentof$105canbecalculatedusingtheoptionswithFebruaryexpirationandexercisepriceof$105.www.hackshp.cnPV(X)=S0+P–CPV($105)=$104.69+$4.40–$4.40=$104.6927.Fromput-callparity:C–P=ST0–X/(l+rf)Iftheoptionsareatthemoney,thenS0=Xand:C–P=X–X/(l+rf)TTheright-handsideoftheequationispositive,andweconcludethatC>P.20-17若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter20-OptionsMarkets:IntroductionCFACFAPROBLEMSPROBLEMS1.a.Donieshouldchoosethelongstranglestrategy.Alongstrangleoptionstrategyconsistsofbuyingaputandacallwiththesameexpirationdateandthesameunderlyingasset,butdifferentexerciseprices.Inastranglestrategy,thecallhasanexercisepriceabovethestockpriceandtheputhasanexercisepricebelowthestockprice.Aninvestorwhobuys(goeslong)astrangleexpectsthatthepriceoftheunderlyingasset(TRTMaterialsinthiscase)willeithermovesubstantiallybelowtheexercisepriceontheputorabovetheexercisepriceonthecall.WithrespecttoTRT,thelongstrangleinvestorbuysboththeputoptionandthecalloptionforatotalcostof$9.00,andwillexperienceaprofitifthestockpricemovesmorethan$9.00abovethecallexercisepriceormorethan$9.00belowtheputexerciseprice.ThisstrategywouldenableDonie"sclienttoprofitfromalargemoveinthestockprice,eitherupordown,inreactiontotheexpectedcourtdecision.b.i.Themaximumpossiblelosspershareis$9.00,whichisthetotalcostofthetwooptions($5.00+$4.00).ii.Themaximumpossiblegainisunlimitedifthestockpricemovesoutsidethebreakevenrangeofprices.iii.Thebreakevenpricesare$46.00and$69.00.Theputwilljustcovercostsifthestockpricefinishes$9.00belowtheputexerciseprice(i.e.,$55−$9=$46),andthecallwilljustcovercostsifthestockpricefinishes$9.00abovethecallexerciseprice(i.e.,$60+$9=$69).2.i.Equityindex-linkednote:Unliketraditionaldebtsecuritiesthatpayascheduled课后答案网rateofcouponinterestonaperiodicbasisandtheparamountofprincipalatmaturity,theequityindex-linkednotetypicallypayslittleornocouponinterest;atmaturity,however,aunitholderreceivestheoriginalissuepriceplusasupplementalredemptionamount,thevalueofwhichdependsonwheretheequityindexsettledrelativetoapredeterminedinitiallevel.www.hackshp.cnii.Commodity-linkedbearbond:Unliketraditionaldebtsecuritiesthatpayascheduledrateofcouponinterestonaperiodicbasisandtheparamountofprincipalatmaturity,thecommodity-linkedbearbondallowsaninvestortoparticipateinadeclineinacommodity’sprice.Inexchangeforalowerthanmarketcoupon,buyersofabeartranchereceivearedemptionvaluethatexceedsthepurchasepriceifthecommoditypricehasdeclinedbythematuritydate.20-18若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter20-OptionsMarkets:Introduction3.i.Conversionvalueofaconvertiblebondisthevalueofthesecurityifitisconvertedimmediately.Thatis:Conversionvalue=marketpriceofthecommonstock×conversionratio=$40×22=$880ii.Marketconversionpriceisthepricethataninvestoreffectivelypaysforthecommonstockiftheconvertiblebondispurchased:Marketconversionprice=marketpriceoftheconvertiblebond/conversionratio=$1,050/22=$47.734.a.i.Thecurrentmarketconversionpriceiscomputedasfollows:Marketconversionprice=marketpriceoftheconvertiblebond/conversionratio=$980/25=$39.20ii.Theexpectedone-yearreturnfortheYtelconvertiblebondis:Expectedreturn=[(endofyearprice+coupon)/currentprice]–1=[($1,125+$40)/$980]–1=0.1888=18.88%iii.Theexpectedone-yearreturnfortheYtelcommonequityis:Expectedreturn=[(end课后答案网ofyearprice+dividend)/currentprice]–1=($45/$35)–1=0.2857=28.57%b.Thetwocomponentsofaconvertiblebond’svalueare:•thestraightbondvalue,whichistheconvertiblebond’svalueasabond,and;•theoptionvalue,whichwww.hackshp.cnisthevalueassociatedwiththepotentialconversionintoequity.(i.)InresponsetotheincreaseinYtel’scommonequityprice,thestraightbondvalueshouldstaythesameandtheoptionvalueshouldincrease.TheincreaseinequitypricedoesnotaffectthestraightbondvaluecomponentoftheYtelconvertible.Theincreaseinequitypriceincreasestheoptionvaluecomponentsignificantly,becausethecalloptionbecomesdeep“inthemoney”whenthe$51pershareequitypriceiscomparedtotheconvertible’sconversionpriceof:$1,000/25=$40pershare.20-19若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter20-OptionsMarkets:Introduction(ii.)Inresponsetotheincreaseininterestrates,thestraightbondvalueshoulddecreaseandtheoptionvalueshouldincrease.Theincreaseininterestratesdecreasesthestraightbondvaluecomponent(bondvaluesdeclineasinterestratesincrease)oftheconvertiblebondandincreasesthevalueoftheequitycalloptioncomponent(calloptionvaluesincreaseasinterestratesincrease).Thisincreasemaybesmallorevenunnoticeablewhencomparedtothechangeintheoptionvalueresultingfromtheincreaseintheequityprice.5.a.(ii)[Profit=$40–$25+$2.50–$4.00]b.(i)课后答案网www.hackshp.cn20-20若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuationCHAPTER21:OPTIONOPTIONVALUATIONVALUATIONPROBLEMPROBLEMSETSSETS1.Thevalueofaputoptionalsoincreaseswiththevolatilityofthestock.Weseethisfromtheput-callparitytheoremasfollows:P=C–S0+PV(X)+PV(Dividends)GivenavalueforSandarisk-freeinterestrate,then,ifCincreasesbecauseofanincreaseinvolatility,Pmustalsoincreaseinordertomaintaintheequalityoftheparityrelationship.2.A$1increaseinacalloption’sexercisepricewouldleadtoadecreaseintheoption’svalueoflessthan$1.Thechangeinthecallpricewouldequal$1onlyif:(i)therewerea100%probabilitythatthecallwouldbeexercised,and(ii)theinterestratewerezero.3.Holdingfirm-specificriskconstant,higherbetaimplieshighertotalstockvolatility.Therefore,thevalueoftheputoptionincreasesasbetaincreases.4.Holdingbetaconstant,thestockwithalotoffirm-specificriskhashighertotalvolatility.Theoptiononthestockwithhigherfirm-specificriskisworthmore.5.Acalloptionwithahighexercisepricehasalowerhedgeratio.Thiscalloptionislessinthemoney.Bothd课后答案网1andN(d1)arelowerwhenXishigher.6.a.PutAmustbewrittenonthestockwiththelowerprice.Otherwise,giventhelowervolatilityofStockA,PutAwouldsellforlessthanPutB.b.PutBmustbewrittenwww.hackshp.cnonthestockwiththelowerprice.Thiswouldexplainitshigherprice.c.CallBmusthavethelowertimetoexpiration.DespitethehigherpriceofStockB,CallBischeaperthanCallA.Thiscanbeexplainedbyalowertimetoexpiration.d.CallBmustbewrittenonthestockwithhighervolatility.Thiswouldexplainitshigherprice.e.CallAmustbewrittenonthestockwithhighervolatility.Thiswouldexplainitshigherprice.21-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuation7.ExerciseHedgePriceRatio1200/30=0.00011010/30=0.33310020/30=0.6679030/30=1.000Astheoptionbecomesmoreinthemoney,thehedgeratioincreasestoamaximumof1.0.8.Sd1N(d1)45-0.02680.4893500.50000.6915550.97660.83569.a.uS0=130⇒Pu=0dS0=80⇒Pd=30Pu−Pd0−303Thehedgeratiois:H===−uS−dS130−80500b.RisklessS=80S=130Portfolio课后答案网Buy3shares240390Buy5puts1500Total390390Presentvalue=$390/1.10=$354.545www.hackshp.cnc.Theportfoliocostis:3S+5P=300+5PThevalueoftheportfoliois:$354.545Therefore:P=$54.545/5=$10.9121-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuationCu−Cd20−0210.Thehedgeratioforthecallis:H===uS−dS130−80500RisklessS=80S=130PortfolioBuy2shares160260Write5calls0-100Total160160Presentvalue=$160/1.10=$145.455Theportfoliocostis:2S–5C=$200–5CThevalueoftheportfoliois:$145.455Therefore:C=$54.545/5=$10.91DoesP=C+PV(X)–S?10.91=10.91+110/1.10–100=10.9111.d1=0.3182⇒N(d1)=0.6248d2=–0.0354⇒N(d2)=0.4859Xe−rT=47.56C=$8.1312.P=$5.69ThisvalueisderivedfromourBlack-Scholesspreadsheet,butnotethatwecouldhave课后答案网derivedthevaluefromput-callparity:P=C+PV(X)–S0=$8.13+$47.56−$50=$5.6913.a.Cfallsto$5.5541www.hackshp.cnb.Cfallsto$4.7911c.Cfallsto$6.0778d.Crisesto$11.5066e.Crisesto$8.718721-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuation14.AccordingtotheBlack-Scholesmodel,thecalloptionshouldbepricedat:[$55×N(d1)]–[50×N(d2)]=($55×0.6)–($50×0.5)=$8Sincetheoptionactuallysellsformorethan$8,impliedvolatilityisgreaterthan0.30.15.Astraddleisacallandaput.TheBlack-Scholesvaluewouldbe:C+P=S0N(d1)−Xe–rTN(d2)+Xe–rT[1−N(d2)]−S0[1−N(d1)]=S0[2N(d1)−1]+Xe–rT[1−2N(d2)]OntheExcelspreadsheet(Spreadsheet21.1),thevaluationformulawouldbe:B5*(2*E4−1)+B6*EXP(−B4*B3)*(1−2*E5)16.Therateofreturnofacalloptiononalong-termTreasurybondshouldbemoresensitivetochangesininterestratesthanistherateofreturnoftheunderlyingbond.Theoptionelasticityexceeds1.0.Inotherwords,theoptioniseffectivelyaleveredinvestmentandtherateofreturnontheoptionismoresensitivetointerestrateswings.17.Impliedvolatilityhasincreased.Ifnot,thecallpricewouldhavefallenasaresultofthedecreaseinstockprice.18.Impliedvolatilityhasincreased.Ifnot,theputpricewouldhavefallenasaresultofthedecreasedtimetoexpiration.19.Thehedgeratioapproachesone.AsSincreases,theprobabilityofexerciseapproaches1.0.N(d1)approaches1.0.课后答案网20.Thehedgeratioapproaches–1.0.AsSdecreases,theprobabilityofexerciseapproaches1.[N(d1)–1]approaches–1asN(d1)approaches0.21.Astraddleisacallandaput.Thehedgeratioofthestraddlewww.hackshp.cnisthesumofthehedgeratiosoftheindividualoptions:0.4+(–0.6)=–0.221-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuation22.a.Thespreadsheetappearsasfollows:INPUTSOUTPUTSStandarddeviation(annual)0.3213d10.0089Expiration(inyears)0.5d2-0.2183Risk-freerate(annual)0.05N(d1)0.5036StockPrice100N(d2)0.4136Exerciseprice105B/Scallvalue8.0000Dividendyield(annual)0B/Sputvalue10.4076Thestandarddeviationis:0.3213b.Thespreadsheetbelowshowsthestandarddeviationhasincreasedto:0.3568INPUTSOUTPUTSStandarddeviation(annual)0.3568d10.0318Expiration(inyears)0.5d2-0.2204Risk-freerate(annual)0.05N(d1)0.5127StockPrice100N(d2)0.4128Exerciseprice105B/Scallvalue9.0000Dividendyield(annual)0B/Sputvalue11.4075Impliedvolatilityhasincreasedbecausethevalueofanoptionincreaseswithgreatervolatility.c.Impliedvolatilityincreasesto0.4087whenexpirationdecreasestofourmonths.Theshorterexpirationdecreasesthevalueoftheoption;therefore,inorderfortheoptionpricetoremainunchangedat$8,impliedvolatilitymustincrease.INPUTSOUTPUTSStandarddeviation(annual)0.4087d1-0.0182Expiration(inyears)课后答案网0.33333d2-0.2541Risk-freerate(annual)0.05N(d1)0.4928StockPrice100N(d2)0.3997Exerciseprice105B/Scallvalue8.0001Dividendyield(annual)0B/Sputvalue11.2646d.Impliedvolatilitydecreasesto0.2406whenexercisepricedecreasesto$100.Thewww.hackshp.cndecreaseinexercisepriceincreasesthevalueofthecall,sothat,inordertotheoptionpricetoremainat$8,impliedvolatilitydecreases.INPUTSOUTPUTSStandarddeviation(annual)0.2406d10.2320Expiration(inyears)0.5d20.0619Risk-freerate(annual)0.05N(d1)0.5917StockPrice100N(d2)0.5247Exerciseprice100B/Scallvalue8.0010Dividendyield(annual)0B/Sputvalue5.532021-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuatione.Thedecreaseinstockpricedecreasesthevalueofthecall.Inorderfortheoptionpricetoremainat$8,impliedvolatilityincreases.INPUTSOUTPUTSStandarddeviation(annual)0.3566d1-0.0484Expiration(inyears)0.5d2-0.3006Risk-freerate(annual)0.05N(d1)0.4807StockPrice98N(d2)0.3819Exerciseprice105B/Scallvalue8.0000Dividendyield(annual)0B/Sputvalue12.407523.a.Thedeltaofthecollariscalculatedasfollows:PositionDeltaBuystock1.0Buyput,X=$45N(d1)–1=–0.40Writecall,X=$55–N(d1)=–0.35Total0.25Ifthestockpriceincreasesby$1,thenthevalueofthecollarincreasesby$0.25.Thestockwillbeworth$1more,thelossonthepurchasedputwillbe$0.40,andthecallwrittenrepresentsaliabilitythatincreasesby$0.35.b.IfSbecomesverylarge,thenthedeltaofthecollarapproacheszero.BothN(d1)termsapproach1.Intuitively,forverylargestockprices,thevalueoftheportfolioissimplythe(presentvalueofthe)exercisepriceofthecall,andisunaffectedbysmallchangesinthestockprice.AsSapproacheszero,thedeltaalsoapproacheszero:bothN(d1)termsapproach0.Forverysmallstockprices,thevalueoftheportfolioissimplythe(presentvalueofthe)exercisepriceoftheput,and课后答案网isunaffectedbysmallchangesinthestockprice.24.PutXDeltaA10−0.1www.hackshp.cnB20−0.5C30−0.925.a.ChoiceA:Callshavehigherelasticitythanshares.Forequaldollarinvestments,acall’scapitalgainpotentialisgreaterthanthatoftheunderlyingstock.b.ChoiceB:Callshavehedgeratioslessthan1.0,sotheshareshavehigherprofitpotential.Foranequalnumberofsharescontrolled,thedollarexposureofthesharesisgreaterthanthatofthecalls,andtheprofitpotentialisthereforegreater.21-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuation26.a.uS0=110⇒Pu=0dS0=90⇒Pd=10P−P0−101udThehedgeratiois:H===−uS−dS110−90200Aportfoliocomprisedofoneshareandtwoputsprovidesaguaranteedpayoffof$110,withpresentvalue:$110/1.05=$104.76Therefore:S+2P=$104.76$100+2P=$104.76⇒P=$2.38b.Costofprotectiveputportfolio=$100+$2.38=$102.38c.Ourgoalisaportfoliowiththesameexposuretothestockasthehypotheticalprotectiveputportfolio.Sincetheput’shedgeratiois–0.5,theportfolioconsistsof(1–0.5)=0.5sharesofstock,whichcosts$50,andtheremainingfunds($52.38)investedinT-bills,earning5%interest.PortfolioS=90S=110Buy0.5shares4555InvestinT-bills5555Total100110Thispayoffisidenticaltothatoftheprotectiveputportfolio.Thus,thestockplusbillsstrategyreplicatesboththecostandpayoffoftheprotectiveput.27.Theputvaluesinthesecondperiodare:课后答案网Puu=0Pud=Pdu=110−104.50=5.50Pdd=110−90.25=19.75www.hackshp.cnTocomputePu,firstcomputethehedgeratio:P−P0−.5501uuudH===−uuS−udS121−104.5030021-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuationFormarisklessportfoliobybuyingoneshareofstockandbuyingthreeputs.Thecostoftheportfoliois:S+3Pu=$110+3PuThepayofffortherisklessportfolioequals$121:RisklessS=104.50S=121PortfolioBuy1share104.50121.00Buy3puts16.500.00Total121.00121.00Therefore,findthevalueoftheputbysolving:$110+3Pu=$121/1.05⇒Pu=$1.746TocomputePd,computethehedgeratio:P−P.550−19.75duddH===−0.1duS−ddS104.50−90.2500Formarisklessportfoliobybuyingoneshareandbuyingoneput.Thecostoftheportfoliois:S+Pd=$95+PdThepayofffortherisklessportfolioequals$110:RisklessS=90.25S=104.50PortfolioBuy1share90.25104.50Buy1put19.755.50Total110.00110.00Therefore,findthevalue课后答案网oftheputbysolving:$95+Pd=$110/1.05⇒Pd=$9.762TocomputeP,computethehedgeratio:Pu−Pd.1746−.9762H===−.05344uS−dS110−9500www.hackshp.cnFormarisklessportfoliobybuying0.5344ofashareandbuyingoneput.Thecostoftheportfoliois:0.5344S+P=$53.44+P21-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuationThepayofffortherisklessportfolioequals$60.53:RisklessPortfolioS=95S=110Buy0.5344share50.76858.784Buy1put9.7621.746Total60.53060.530Therefore,findthevalueoftheputbysolving:$53.44+P=$60.53/1.05⇒P=$4.208Finally,weverifythisresultusingput-callparity.RecallfromExample21.1that:C=$4.434Put-callparityrequiresthat:P=C+PV(X)–S$4.208=$4.434+($110/1.052)−$100Exceptforminorroundingerror,put-callparityissatisfied.28.Ifr=0,thenoneshouldneverexerciseaputearly.Thereisno“timevaluecost”towaitingtoexercise,butthereisa“volatilitybenefit”fromwaiting.Toshowthismorerigorously,considerthefollowingportfolio:lend$Xandshortoneshareofstock.Thecosttoestablishtheportfoliois(X–S0).ThepayoffattimeT(withzerointerestearningsontheloan)is(X–ST).Incontrast,aputoptionhasapayoffattimeTof(X–ST)ifthatvalueispositive,andzerootherwise.Theput’spayoffisatleastaslargeastheportfolio’s,andtherefore,theputmustcostatleastasmuchastheportfoliotopurchase.Hence,P≥(X–S0),andtheputcanbesoldformorethantheproceedsfromimmediateexercise.Weconcludethatitdoesn’tpaytoexerciseearly.课后答案网29.a.Xe−rTb.Xc.0www.hackshp.cnd.0e.Itisoptimaltoexerciseimmediatelyaputonastockwhosepricehasfallentozero.ThevalueoftheAmericanputequalstheexerciseprice.Anydelayinexerciselowersvaluebythetimevalueofmoney.21-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuation30.Step1:Calculatetheoptionvaluesatexpiration.Thetwopossiblestockpricesandthecorrespondingcallvaluesare:uS0=120⇒Cu=20dS0=80⇒Cd=0Step2:Calculatethehedgeratio.Cu−Cd20−01H===uS−dS120−80200Therefore,formarisklessportfoliobybuyingoneshareofstockandwritingtwocalls.Thecostoftheportfoliois:S–2C=100–2CStep3:Showthatthepayofffortherisklessportfolioequals$80:RisklessS=80S=120PortfolioBuy1share80120Write2calls0-40Total8080Therefore,findthevalueofthecallbysolving:$100–2C=$80/1.10⇒C=$13.636Noticethatwedidnotusetheprobabilitiesofastockpriceincreaseordecrease.Thesearenotneededtovaluethecalloption.31.Thetwopossiblestockpricesandthecorrespondingcallvaluesare:uS0=130⇒Cu=30dS0=70⇒Cd课后答案网=0Cu−Cd30−01Thehedgeratiois:H===uS0−dS0130−702Formarisklessportfoliobybuyingoneshareofstockandwritingtwocalls.Thecostoftheportfoliois:S–2C=100–2Cwww.hackshp.cnThepayofffortherisklessportfolioequals$70:RisklessS=70S=130PortfolioBuy1share70130Write2calls0-60Total7070Therefore,findthevalueofthecallbysolving:$100–2C=$70/1.10⇒C=$18.182Here,thevalueofthecallisgreaterthanthevalueinthelower-volatilityscenario.21-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuation32.Thetwopossiblestockpricesandthecorrespondingputvaluesare:uS0=120⇒Pu=0dS0=80⇒Pd=20Pu−Pd0−201Thehedgeratiois:H===−uS−dS120−80200Formarisklessportfoliobybuyingoneshareofstockandbuyingtwoputs.Thecostoftheportfoliois:S+2P=100+2PThepayofffortherisklessportfolioequals$120:RisklessS=80S=120PortfolioBuy1share80120Buy2puts400Total120120Therefore,findthevalueoftheputbysolving:$100+2P=$120/1.10⇒P=$4.545Accordingtoput-callparity:P+S=C+PV(X)Ourestimatesofoptionvaluesatisfythisrelationship:$4.545+$100=$13.636+$100/1.10=$104.54533.Ifweassumethattheonlypossibleexercisedateisjustpriortotheex-dividenddate,thentherelevantparametersfortheBlack-Scholesformulaare:S0=60r=0.5%permonth课后答案网X=55σ=7%T=2monthsInthiscase:C=$6.04Ifinstead,onecommitstoforegoingearlyexercise,thenwereducethestockpricewww.hackshp.cnbythepresentvalueofthedividends.Therefore,weusethefollowingparameters:S0=60–2e−(0.005×2)=58.02r=0.5%permonthX=55σ=7%T=3monthsInthiscase,C=$5.05Thepseudo-Americanoptionvalueisthehigherofthesetwovalues:$6.0421-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuation34.True.Thecalloptionhasanelasticitygreaterthan1.0.Therefore,thecall’spercentagerateofreturnisgreaterthanthatoftheunderlyingstock.HencetheGMcallrespondsmorethanproportionatelywhentheGMstockpricechangesinresponsetobroadmarketmovements.Therefore,thebetaoftheGMcallisgreaterthanthebetaofGMstock.35.True.Theelasticityofacalloptionishigherthemoreoutofthemoneyistheoption.(Eventhoughthedeltaofthecallislower,thevalueofthecallisalsolower.Theproportionalresponseofthecallpricetothestockpriceincreases.Youcanconfirmthiswithnumericalexamples.)Therefore,therateofreturnofthecallwiththehigherexercisepricerespondsmoresensitivelytochangesinthemarketindex,andthereforeithasthehigherbeta.36.Asthestockpriceincreases,conversionbecomesincreasinglymoreassured.Thehedgeratioapproaches1.0.Thepriceoftheconvertiblebondwillmoveone-for-onewithchangesinthepriceoftheunderlyingstock.37.Salomonbelievesthatthemarketassessmentofvolatilityistoohigh.Therefore,Salomonshouldselloptionsbecausetheanalysissuggeststheoptionsareoverpricedwithrespecttotruevolatility.Thedeltaofthecallis0.6,whilethatoftheputis0.6–1=–0.4.Therefore,Salomonshouldsellputsandcallsintheratioof0.6to0.4.Forexample,ifSalomonsells2callsand3puts,thepositionwillbedeltaneutral:Delta=(2×0.6)+[3×(–0.4)]=038.Ifthestockmarketindexincreases1%,the1millionsharesofstockonwhichtheoptionsarewrittenwouldbeexpectedtoincrease课后答案网by:0.75%×$5×1million=$37,500Theoptionswouldincreaseby:delta×$37,500=0.8×$37,500=$30,000Inordertohedgeyourmarketexposure,youmustwww.hackshp.cnsell$3,000,000ofthemarketindexportfoliosothata1%changeintheindexwouldresultina$30,000changeinthevalueoftheportfolio.21-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuation39.S=100;currentvalueofportfolioX=100;floorpromisedtoclients(0%return)σ=0.25;volatilityr=0.05;risk-freerateT=4years;horizonofprograma.UsingtheBlack-Scholesformula,wefindthat:d1=0.65,N(d1)=0.7422,d2=0.15,N(d2)=0.5596Putvalue=$10.27Therefore,totalfundstobemanagedequals$110.27million:$100millionportfoliovalueplusthe$10.27millionfeefortheinsuranceprogram.Theputdeltais:N(d1)–1=0.7422–1=–0.2578Therefore,selloff25.78%oftheequityportfolio,placingtheremainingfundsinT-bills.Theamountoftheportfolioinequityistherefore$74.22million,whiletheamountinT-billsis:$110.27million–$74.22million=$36.05millionb.Atthenewportfoliovalue,theputdeltabecomes:–0.2779Thismeansthatyoumustreducethedeltaoftheportfolioby:0.2779–0.2578=0.0201Youshouldsellanadditional2.01%oftheequitypositionandusetheproceedstobuyT-bills.Sincethestockpriceisnowatonly97%ofitsoriginalvalue,youneedtosell:$97million×0.0201=$1.950millionofstock40.Usingthetruevolatility(32%)andtimetoexpiration课后答案网T=0.25years,thehedgeratioforExxonisN(d1)=0.5567.Becauseyoubelievethecallsareunder-priced(sellingatanimpliedvolatilitythatistoolow),youwillbuycallsandshort0.5567sharesforeachcallyoubuy.www.hackshp.cn41.Thecallsarecheap(impliedσ=0.30)andtheputsareexpensive(impliedσ=0.34).Therefore,buycallsandsellputs.Usingthe“true”volatilityofσ=0.32,thecalldeltais0.5567andtheputdeltais:0.5567–1.0=–0.4433Therefore,foreachcallpurchased,buy:0.5567/0.4433=1.256puts21-13若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuation42.a.Tocalculatethehedgeratio,supposethatthemarketindexincreasesby1%.Thenthestockportfoliowouldbeexpectedtoincreaseby:1%×1.5=1.5%or0.015×$1,250,000=$18,750Giventheoptiondeltaof0.8,theoptionportfoliowouldincreaseby:$18,750×0.8=$15,000Salomon’sliabilityfromwritingtheseoptionswouldincreasebythesameamount.Themarketindexportfoliowouldincreaseinvalueby1%.Therefore,SalomonBrothersshouldpurchase$1,500,000ofthemarketindexportfolioinordertohedgeitspositionsothata1%changeintheindexwouldresultina$15,000changeinthevalueoftheportfolio.b.Thedeltaofaputoptionis:0.8–1=–0.2Therefore,forevery1%themarketincreases,theindexwillriseby10pointsandthevalueoftheputoptioncontractwillchangeby:delta×10×contractmultiplier=–0.2×10×100=–$200Therefore,Salomonshouldwrite:$12,000/$200=60putcontractsCFACFAPROBLEMSPROBLEMS1.Statementa:Thehedgeratio(determiningthenumberoffuturescontractstosell)oughttobeadjustedbythebetaoftheequityportfolio,whichis1.20.Thecorrecthedgeratiowouldbe:$100million×课后答案网β=2,000×β=,2000×2.1=,2400$100×500Statementb:Theportfoliowillbehedged,andshouldthereforeearntherisk-freerate,notzero,astheconsultantclaims.Givenafuturespriceof100andanequitypriceof100,therateofreturnoverthe3-monthperiodis:(100−99)/99=1.01%=approximately4.1%annualizedwww.hackshp.cn2.a.Thevalueofthecalloptionisexpectedtodecreaseifthevolatilityoftheunderlyingstockpricedecreases.Thelessvolatiletheunderlyingstockprice,thelessthechanceofextremepricemovementsandthelowertheprobabilitythattheoptionexpiresinthemoney.Thismakestheparticipationfeatureontheupsidelessvaluable.Thevalueofthecalloptionisexpectedtoincreaseifthetimetoexpirationoftheoptionincreases.Thelongerthetimetoexpiration,thegreaterthechancethattheoptionwillexpireinthemoneyresultinginanincreaseinthetimepremiumcomponentoftheoption’svalue.21-14若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuationb.i.WhenEuropeanoptionsareoutofthemoney,investorsareessentiallysayingthattheyarewillingtopayapremiumfortheright,butnottheobligation,tobuyorselltheunderlyingasset.Theout-of-the-moneyoptionhasnointrinsicvalue,but,sinceoptionsrequirelittlecapital(justthepremiumpaid)toobtainarelativelylargepotentialpayoff,investorsarewillingtopaythatpremiumeveniftheoptionmayexpireworthless.TheBlack-Scholesmodeldoesnotreflectinvestors’demandforanypremiumabovethetimevalueoftheoption.Hence,ifinvestorsarewillingtopayapremiumforanout-of-the-moneyoptionaboveitstimevalue,theBlack-Scholesmodeldoesnotvaluethatexcesspremium.ii.WithAmericanoptions,investorshavetheright,butnottheobligation,toexercisetheoptionpriortoexpiration,eveniftheyexercisefornon-economicreasons.ThisincreasedflexibilityassociatedwithAmericanoptionshassomevaluebutisnotconsideredintheBlack-Scholesmodelbecausethemodelonlyvaluesoptionstotheirexpirationdate(Europeanoptions).3.a.Americanoptionsshouldcostmore(haveahigherpremium).AmericanoptionsgivetheinvestorgreaterflexibilitythanEuropeanoptionssincetheinvestorcanchoosewhethertoexerciseearly.Whenthestockpaysadividend,theoptiontoexerciseacallearlycanbevaluable.Butregardlessofthedividend,aEuropeanoption(putorcall)neversellsformorethananotherwise-identicalAmericanoption.b.C=S0+P−PV(X)=$43+$4−$45/1.055=$4.346Note:weassumethatAbacodoesnotpayanydividends.c.i)Anincreaseinshort-terminterestrate⇒PV(exerciseprice)islower,andcallvalueincreases.课后答案网ii)Anincreaseinstockpricevolatility⇒thecallvalueincreases.iii)Adecreaseintimetooptionexpiration⇒thecallvaluedecreases.4.a.Thetwopossiblevaluesoftheindexinthefirstperiodare:www.hackshp.cnuS0=1.20×50=60dS0=0.80×50=40Thepossiblevaluesoftheindexinthesecondperiodare:uuS20=(1.20)×50=72udS0=1.20×0.80×50=48duS0=0.80×1.20×50=48ddS0=(0.80)2×50=3221-15若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuationb.Thecallvaluesinthesecondperiodare:Cuu=72−60=12Cud=Cdu=Cdd=0SinceCud=Cdu=0,thenCd=0.TocomputeCu,firstcomputethehedgeratio:Cuu−Cud12−01H===uuS−udS72−48200Formarisklessportfoliobybuyingoneshareofstockandwritingtwocalls.Thecostoftheportfoliois:S–2Cu=$60–2CuThepayofffortherisklessportfolioequals$48:RisklessS=48S=72PortfolioBuy1share4872Write2calls0-24Total4848Therefore,findthevalueofthecallbysolving:$60–2Cu=$48/1.06⇒Cu=$7.358TocomputeC,computethehedgeratio:Cu−Cd.7358−0H===.03679uS−dS60−4000Formarisklessportfolio课后答案网bybuying0.3679ofashareandwritingonecall.Thecostoftheportfoliois:0.3679S–C=$18.395–CThepayofffortherisklessportfolioequals$14.716:RisklessPortfolioS=40S=60Buy0.3679sharewww.hackshp.cn14.71622.074Write1call0.000−7.358Total14.71614.716Therefore,findthevalueofthecallbysolving:$18.395–C=$14.716/1.06⇒C=$4.51221-16若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuationc.Theputvaluesinthesecondperiodare:Puu=0Pud=Pdu=60−48=12Pdd=60−32=28TocomputePu,firstcomputethehedgeratio:Puu−Pud0−121H===−uuS−udS72−48200Formarisklessportfoliobybuyingoneshareofstockandbuyingtwoputs.Thecostoftheportfoliois:S+2Pu=$60+2PuThepayofffortherisklessportfolioequals$72:RisklessS=48S=72PortfolioBuy1share4872Buy2puts240Total7272Therefore,findthevalueoftheputbysolving:$60+2Pu=$72/1.06⇒Pu=$3.962TocomputePd,computethehedgeratio:Pdu−Pdd12−28H===−0.1duS−ddS48−3200Formarisklessportfoliobybuyingoneshareandbuyingoneput.Thecostoftheportfolio课后答案网is:S+Pd=$40+PdThepayofffortherisklessportfolioequals$60:RisklessS=32S=48PortfolioBuy1sharewww.hackshp.cn3248Buy1put2812Total6060Therefore,findthevalueoftheputbysolving:$40+Pd=$60/1.06⇒Pd=$16.604TocomputeP,computethehedgeratio:P−P.3962−16.604udH===−.06321uS−dS60−400021-17若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuationFormarisklessportfoliobybuying0.6321ofashareandbuyingoneput.Thecostoftheportfoliois:0.6321S+P=$31.605+PThepayofffortherisklessportfolioequals$41.888:RisklessPortfolioS=40S=60Buy0.6321share25.28437.926Buy1put16.6043.962Total41.88841.888Therefore,findthevalueoftheputbysolving:$31.605+P=$41.888/1.06⇒P=$7.912d.Accordingtoput-call-parity:C=S+P−PV(X)=$50+$7.912−$60/(1.062)=$4.5120Thisisthevalueofthecallcalculatedinpart(b)above.5.a.(i)Indexincreasesto1402.Thecombinedportfoliowillsufferaloss.Thewrittencallsexpireinthemoney;theprotectiveputpurchasedexpiresworthless.Let’sanalyzetheoutcomeonaper-sharebasis.Thepayoutforeachcalloptionis$52,foratotalcashoutflowof$104.Thestockisworth$1,402.Theportfoliowillthusbeworth:$1,402−$104=$1,298Thenetcostoftheportfoliowhentheoptionpositionsareestablishedis:$1,336+$16.10(put)−[2×$8.60](callswritten)=$1,334.90(ii)Indexremainsat1336.Bothoptionsexpireoutofthemoney.Theportfoliowillthusbeworth$1,336(pershare),comparedtoaninitialcost30daysearlierof$1,334.90.Theportfolioexperiencesaverysmall课后答案网gainof$1.10.(iii)Indexdeclinesto1270.Thecallsexpireworthless.Theportfoliowillbeworth$1,330,theexercisepriceoftheprotectiveput.Thisrepresentsaverysmalllossof$4.90comparedtotheinitialcost30daysearlierof$1,334.90b.(i)Indexincreasesto1402.Thedeltaofthecallapproaches1.0asthestockgoesdeepintothemoney,whileexpirationwww.hackshp.cnofthecallapproachesandexercisebecomesessentiallycertain.Theputdeltaapproacheszero.(ii)Indexremainsat1336.Bothoptionsexpireoutofthemoney.Deltaofeachapproacheszeroasexpirationapproachesanditbecomescertainthattheoptionswillnotbeexercised.(iii)Indexdeclinesto1270.Thecallisoutofthemoneyasexpirationapproaches.Deltaapproacheszero.Conversely,thedeltaoftheputapproaches−1.0asexercisebecomescertain.21-18若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter21-OptionValuationc.Thecallsellsatanimpliedvolatility(11.00%)thatislessthanrecenthistoricalvolatility(12.00%);theputsellsatanimpliedvolatility(14.00%)thatisgreaterthanhistoricalvolatility.Thecallseemsrelativelycheap;theputseemsexpensive.课后答案网www.hackshp.cn21-19若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter22-FuturesMarketsCHAPTER22:FUTURESFUTURESMARKETSMARKETSPROBLEMPROBLEMSETSSETS1.Thereislittlehedgingorspeculativedemandforcementfutures,sincecementpricesarefairlystableandpredictable.Thetradingactivitynecessarytosupportthefuturesmarketwouldnotmaterialize.2.Theabilitytobuyonmarginisoneadvantageoffutures.Anotheristheeasewithwhichonecanalterone’sholdingsoftheasset.Thisisespeciallyimportantifoneisdealingincommodities,forwhichthefuturesmarketisfarmoreliquidthanthespotmarket.3.Shortsellingresultsinanimmediatecashinflow,whereastheshortfuturespositiondoesnot:ActionInitialCFFinalCFShortSale+P0–PTShortFutures0F0–PT4.a.False.Foranygivenlevelofthestockindex,thefuturespricewillbelowerwhenthedividendyieldishigher.Thisfollowsfromspot-futuresparity:FT0=S0(1+课后答案网rf–d)b.False.Theparityrelationshiptellsusthatthefuturespriceisdeterminedbythestockprice,theinterestrate,andthedividendyield;itisnotafunctionofbeta.c.True.Theshortfuturespositionwillprofitwhenthemarketfalls.Thisisanegativebetaposition.www.hackshp.cn5.Thefuturespriceistheagreed-uponpricefordeferreddeliveryoftheasset.Ifthatpriceisfair,thenthevalueoftheagreementoughttobezero;thatis,thecontractwillbeazero-NPVagreementforeachtrader.6.Becauselongpositionsequalshortpositions,futurestradingmustentaila“cancelingout”ofbetsontheasset.Moreover,nocashisexchangedattheinceptionoffuturestrading.Thus,thereshouldbeminimalimpactonthespotmarketfortheasset,andfuturestradingshouldnotbeexpectedtoreducecapitalavailableforotheruses.22-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter22-FuturesMarkets7.a.TheclosingfuturespricefortheMarchcontractwas1,477.20,whichhasadollarvalueof:$250×1,477.20=$369,300Therefore,therequiredmargindepositis:$36,930b.Thefuturespriceincreasesby:1,500.00–1,477.20=22.80Thecredittoyourmarginaccountwouldbe:22.80×$250=$5,700Thisisapercentgainof:$5,700/$36,930=0.1543=15.43%Notethatthefuturespriceitselfincreasedbyonly1.543%.c.Followingthereasoninginpart(b),anychangeinFismagnifiedbyaratioof(l/marginrequirement).Thisistheleverageeffect.Thereturnwillbe–10%.8.a.F0=S0(1+rf)=$150×1.06=$159b.F330=S0(1+rf)=$150×1.06=$178.65c.F30=150×1.08=$188.969.a.TakeashortpositioninT-bondfutures,tooffsetinterestraterisk.Ifratesincrease,thelossonthebondwillbeoffsettosomeextentbygainsonthefutures.b.Again,ashortpositioninT-bondfutureswilloffsettheinterestraterisk.c.Youwanttoprotectyourcashoutlaywhenthebondispurchased.Ifbondpricesincrease,youwillneedextracashtopurchasethebond.Thus,youshouldtakealongfuturespositionthat课后答案网willgenerateaprofitifpricesincrease.10.F0=S0×(l+rf–d)=1,500×(1+0.05–0.02)=1,54511.Theput-callparityrelationstateswww.hackshp.cnthat:P=C–ST0+X/(1+rf)IfX=F,then:P=C–ST0+F/(1+rf)Butspot-futuresparitytellsusthat:F=ST0(1+rf)Substituting,wefindthat:P=C–STT0+[S0(1+rf)]/(1+rf)=C–S0+S0whichimpliesthatP=C.22-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter22-FuturesMarkets12.Accordingtotheparityrelation,theproperpriceforDecemberfuturesis:F1/21/2Dec=FJune(l+rf)=846.30×1.05=867.20TheactualfuturespriceforDecemberislowrelativetotheJuneprice.YoushouldtakealongpositionintheDecembercontractandshorttheJunecontract.13.a.120×1.06=$127.20b.Thestockpricefallsto:120×(1–0.03)=$116.40Thefuturespricefallsto:116.4×1.06=$123.384Theinvestorloses:(127.20–123.384)×1,000=$3,816c.Thepercentagelossis:$3,816/$12,000=0.318=31.8%14.a.TheinitialfuturespriceisF0=1300×(1+0.005–0.002)12=$1,347.58Inonemonth,thefuturespricewillbe:F0=1320×(1+0.005–0.002)11=$1,364.22Theincreaseinthefuturespriceis16.64,sothecashflowwillbe:16.64×$250=$4,160.00b.Theholdingperiodreturnis:$4,160.00/$13,000=0.3200=32.00%15.Thetreasurerwouldliketobuythebondstoday,butcannot.Asaproxyforthis课后答案网purchase,T-bondfuturescontractscanbepurchased.Ifratesdoinfactfall,thetreasurerwillhavetobuybackthebondsforthesinkingfundatpriceshigherthanthepricesatwhichtheycouldbepurchasedtoday.However,thegainsonthefuturescontractswilloffsetthishighercosttosomeextent.www.hackshp.cn16.TheparityvalueofFis:1,300×(1+0.04–0.01)=1,339Theactualfuturespriceis1,330,toolowby9.ArbitragePortfolioCFnowCFin1yearShortIndex1,300−ST−(0.01×1,300)BuyFutures0ST−1,330Lend−1,3001,300×1.04Total0922-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter22-FuturesMarkets17.a.Futurespricesaredeterminedfromthespreadsheetasfollows:SpotSpotFuturesFuturesFuturesParityParityParityandandandTimeTimeTimeSpreadsSpreadsSpotprice1,500Incomeyield(%)1.5FuturespricesversusmaturityInterestrate(%)3.0Today"sdate1/1/2008Spotprice1,500.00Maturitydate12/14/2008Futures11,502.67Maturitydate25/21/2008Futures21,508.71Maturitydate311/18/2008Futures31,519.79Timetomaturity10.12Timetomaturity20.39Timetomaturity30.88LEGEND:EnterEnterdatadataValueValuecalculatedcalculatedSeeSeecommentcommentb.Thespreadsheetdemonstratesthatthefuturespricesnowdecreasewithincreasedtimetomaturity:SpotSpotFuturesFuturesFuturesParityParityParityandandandTimeTimeTimeSpreadsSpreadsSpotprice1,500Incomeyield(%)4.0FuturespricesversusmaturityInterestrate(%)3.0Today"sdate1/1/2008Spotprice1,500.00Maturitydate12/14/2008Futures11,498.20Maturitydate25/21/2008Futures21,494.15Maturitydate3课后答案网11/18/2008Futures31,486.78Timetomaturity10.12Timetomaturity20.39Timetomaturity30.88LEGEND:EnterEnterdatadatawww.hackshp.cnValueValuecalculatedcalculatedSeeSeecommentcomment18.a.ThecurrentyieldforTreasurybonds(coupondividedbyprice)playstheroleofthedividendyield.b.Whentheyieldcurveisupwardsloping,thecurrentyieldexceedstheshortrate.Hence,T-bondfuturespricesonmoredistantcontractsarelowerthanthoseonnear-termcontracts.22-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter22-FuturesMarkets19.a.CashFlowsActionNowT1T2LongfutureswithmaturityT10P1–F(T1)0ShortfutureswithmaturityT200F(T2)–P2BuyassetatT1,sellatT20–P1+P2AtT(T2–T1)1,borrowF(T1)0F(T1)–F(T1)×(1+rf)(T2–T1)Total00F(T2)–F(T1)×(1+rf)b.SincetheT2cashflowisrisklessandthenetinvestmentwaszero,thenanyprofitsrepresentanarbitrageopportunity.c.Thezero-profitno-arbitragerestrictionimpliesthatF(T2)=F(T1)×(1+rf)(T2–T1)CFACFAPROBLEMSPROBLEMS1.a.Thestrategythatwouldtakeadvantageofthearbitrageopportunityisa“reversecashandcarry.”Areversecashandcarryopportunityresultswhenthefollowingrelationshipdoesnotholdtrue:F0≥S0(1+C)Ifthefuturesprice课后答案网islessthanthespotpriceplusthecostofcarryingthegoodstothefuturesdeliverydate,thenanarbitrageopportunityexists.Atraderwouldbeabletoselltheassetshort,usetheproceedstolendattheprevailinginterestrate,andthenbuytheassetforfuturedelivery.Atthefuturedelivery,thetraderwouldthencollecttheproceedsoftheloanwithinterest,acceptdeliveryoftheasset,andcovertheshortpositioninthecommodity.www.hackshp.cnb.CashFlowsActionNowOneyearfromnowSellthespotcommodityshort+$120.00−$125.00Buythecommodityfuturesexpiringin1year$0.00$0.00Contracttolend$120at8%for1year−$120.00+$129.60Totalcashflow$0.00+$4.6022-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter22-FuturesMarkets2.a.Thecalloptionisdistinguishedbyitsasymmetricpayoff.IftheSwissfrancrisesinvalue,thenthecompanycanbuyfrancsforagivennumberofdollarstoserviceitsdebt,andtherebyputacaponthedollarcostofitsfinancing.Ifthefrancfalls,thecompanywillbenefitfromthechangeintheexchangerate.Thefuturesandforwardcontractshavesymmetricpayoffs.Thedollarcostofthefinancingislockedinregardlessofwhetherthefrancappreciatesordepreciates.Themajordifferencefromthefirm’sperspectivebetweenfuturesandforwardsisinthemark-to-marketfeatureoffutures.Theconsequenceofthisisthatthefirmmustbereadyforthecashmanagementissuessurroundingcashinflowsoroutflowsasthecurrencyvaluesandfuturespricesfluctuate.b.Thecalloptiongivesthecompanytheabilitytobenefitfromdepreciationinthefranc,butatacostequaltotheoptionpremium.Unlessthefirmhassomespecialexpertiseincurrencyspeculation,itseemsthatthefuturesorforwardstrategy,whichlocksinadollarcostoffinancingwithoutanoptionpremium,maybethebetterstrategy.3.Theimportantdistinctionbetweenafuturescontractandanoptionscontractisthatthefuturescontractisanobligation.Whenaninvestorpurchasesorsellsafuturescontract,theinvestorhasanobligationtoeitheracceptordeliver,respectively,theunderlyingcommodityontheexpirationdate.Incontrast,thebuyerofanoptioncontractisnotobligatedtoacceptordelivertheunderlyingcommoditybutinsteadhastheright,orchoice,toacceptdelivery(forcallholders)ormakedelivery(forputholders)oftheunderlyingcommodityanytimeduringthelifeofthecontract.Futuresandoptionsmodifyaportfolio’sriskindifferentways.Buyingorsellingafuturescontractaffectsaportfolio’supsideriskanddownsideriskbyasimilarmagnitude.Thisiscommonlyreferredtoassymmetricalimpact.Ontheotherhand,theadditionofacallorputoptiontoaportfoliodoesnotaffectaportfolio’supsideriskanddownsiderisktoasimilarmagnitude.Unlikefuturescontracts,theimpact课后答案网ofoptionsontheriskprofileofaportfolioisasymmetric.4.a.Theinvestorshouldselltheforwardcontracttoprotectthevalueofthebondagainstrisinginterestratesduringtheholdingperiod.Becausetheinvestorintendstotakealongpositionintheunderlyingasset,thehedgerequiresashortpositionwww.hackshp.cninthederivativeinstrument.b.Thevalueoftheforwardcontractonexpirationdateisequaltothespotpriceoftheunderlyingassetonexpirationdateminustheforwardpriceofthecontract:$978.40–$1,024.70=–$46.30Thecontracthasanegativevalue.Thisisthevaluetotheholderofalongpositionintheforwardcontract.Inthisexample,theinvestorshouldbeshorttheforwardcontract,sothatthevaluetothisinvestorwouldbe+$46.30sincethisisthecashflowtheinvestorexpectstoreceive.22-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter22-FuturesMarketsc.Thevalueofthecombinedportfolioattheendofthesix-monthholdingperiodis:$978.40+$46.30=$1,024.70Thechangeinthevalueofthecombinedportfolioduringthissix-monthperiodis:$24.70Thevalueofthecombinedportfolioisthesumofthemarketvalueofthebondandthevalueoftheshortpositionintheforwardcontract.Atthestartofthesix-monthholdingperiod,thebondisworth$1,000andtheforwardcontracthasavalueofzero(becausethisisnotanoff-marketforwardcontract,nomoneychangeshandsatinitiation).Sixmonthslater,thebondvalueis$978.40andthevalueoftheshortpositionintheforwardcontractis$46.30,ascalculatedinpart(b).Thefactthatthecombinedvalueofthelongpositioninthebondandtheshortpositionintheforwardcontractattheforwardcontract’smaturitydateisequaltotheforwardpriceontheforwardcontractatitsinitiationdateisnotacoincidence.Bytakingalongpositionintheunderlyingassetandashortpositionintheforwardcontract,theinvestorhascreatedafullyhedged(andhencerisk-free)position,andshouldearntherisk-freerateofreturn.Thesix-monthrisk-freerateofreturnis5.00%(annualized),whichproducesareturnof$24.70overasix-monthperiod:($1,000×1.05(1/2))–$1,000=$24.70TheseresultssupportVanHusen’sstatementthatsellingaforwardcontractontheunderlyingbondprotectstheportfolioduringaperiodofrisinginterestrates.Thelossinthevalueoftheunderlyingbondduringthesixmonthholdingperiodisoffsetbythecashpaymentmadeatexpirationdatetotheholderoftheshortpositionintheforwardcontract;thatis,ashortpositionintheforwardcontractprotects(hedges)thelongpositionintheunderlyingasset.课后答案网5.a.Accurate.Futurescontractsaremarkedtothemarketdaily.Holdingashortpositiononabondfuturescontractduringaperiodofrisinginterestrates(decliningbondprices)generatespositivecashinflowfromthedailymarktomarket.Ifaninvestorinafuturescontracthasalongpositionwhenthepriceoftheunderlyingassetincreases,www.hackshp.cnthenthedailymarktomarketgeneratesapositivecashinflowthatcanbereinvested.Forwardcontractssettleonlyatexpirationdateanddonotgenerateanycashflowpriortoexpiration.b.Inaccurate.Accordingtothecostofcarrymodel,thefuturescontractpriceisadjustedupwardbythecostofcarryfortheunderlyingasset.Bonds(andotherfinancialinstruments),however,donothaveanysignificantstoragecosts.Moreover,thecostofcarryisreducedbyanycouponpaymentspaidtothebondholderduringthelifeofthefuturescontract.Any“convenienceyield”fromholdingtheunderlyingbondalsoreducesthecostofcarry.Asaresult,thecostofcarryforabondislikelytobenegative.22-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagementCHAPTER23:FUTURES,FUTURES,SWAPS,SWAPS,SWAPS,ANDANDANDRISKRISKRISKMANAGEMENTMANAGEMENTPROBLEMPROBLEMSETSSETS1.Informulatingahedgeposition,astock’sbetaandabond’sdurationareusedsimilarlytodeterminetheexpectedpercentagegainorlossinthevalueoftheunderlyingassetforagivenchangeinmarketconditions.Then,ineachofthesemarkets,theexpectedpercentagechangeinvalueisusedtocalculatetheexpecteddollarchangeinvalueofthestockorbondportfolios,respectively.Finally,thedollarchangeinvalueoftheunderlyingasset,alongwiththedollarchangeinthevalueofthefuturescontract,determinesthehedgeratio.Themajordifferenceinthecalculationsnecessarytoformulateahedgepositionineachmarketliesinthemannerinwhichthefirststepidentifiedaboveiscomputed.Forahedgeintheequitymarket,theproductoftheequityportfolio’sbetawithrespecttothegivenmarketindexandtheexpectedpercentagechangeintheindexforthefuturescontractequalstheexpectedpercentagechangeinthevalueoftheportfolio.Clearly,iftheportfoliohasapositivebetaandtheinvestorisconcernedabouthedgingagainstadeclineintheindex,theresultofthiscalculationisadecreaseinthevalueoftheportfolio.Forahedgeinthefixedincomemarket,theproductofthebond’smodifieddurationandtheexpectedchangeinthebond’syieldequalstheexpectedpercentagechangeinthevalueofthebond.Here,theinvestorwhohasalongpositioninabond(orabondportfolio)isconcernedaboutthepossibilityofanincreaseinyield,andtheresultingchangeinthebond’svalueisaloss.Asecondarydifferenceinthecalculationsnecessarytoformulateahedgepositionineachmarketarisesinthecalculationofthehedgeratio.Intheequitymarket,thehedgeratioistypicallycalculatedbydividingthe课后答案网totalexpecteddollarchangeinthevalueoftheportfolio(foragivenchangeintheindex)bytheprofit(i.e.,thedollarchangeinvalue)ononefuturescontract(forthegivenchangeintheindex).Inthebondmarket,thecomparablecalculationisgenerallythoughtofintermsofthepricevalueofabasispoint(PVBP)forthebondandthePVBPforthefuturescontract,ratherthanintermsofthetotaldollarchangeinboththevalueoftheportfolioandthevalueofasinglefutureswww.hackshp.cncontract.23-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagement2.OneoftheconsiderationsthatwouldenterintothehedgingstrategyforaU.S.exportingfirmwithoutstandingbillstoitscustomersdenominatedinforeigncurrencyiswhethertheU.S.firmalsohasoutstandingpayablesdenominatedinthesameforeigncurrency.Sincethefirmreceivesforeigncurrencywhenitscustomers’billsarepaid,thefirmhedgesbytakingashortpositionintheforeigncurrency.TheU.S.firmwouldreduceitsshortpositioninfuturestotheextentthatoutstandingpayablesoffsetoutstandingreceivableswiththesamematuritybecausetheoutstandingpayableseffectivelyhedgetheexchangerateriskoftheoutstandingreceivables.Equivalently,iftheU.S.firmexpectstoincurongoingobligationsdenominatedinthesameforeigncurrencyinordertomeetexpensesrequiredtodeliveradditionalproductstoitscustomers,thenthefirmwouldreduceitsshortpositionintheforeigncurrencyfutures.Ingeneral,iftheU.S.firmincursexpensesinthesameforeigncurrency,thenthefirmwouldtakeashortpositioninthecurrencyfuturestohedgeitsprofitsmeasuredintheforeigncurrency.IftheU.S.firmincursallofitsexpensesinU.S.dollars,butbillsitscustomersintheforeigncurrency,thenthefirmwouldtakeapositiontohedgetheoutstandingreceivables,notjusttheprofit.AnotherconsiderationthataffectstheU.S.exportingfirm’swillingnesstohedgeitsexchangerateriskistheimpactofdepreciationoftheforeigncurrencyonthefirm’spricesforitsproducts.ForaU.S.firmthatsetsitspricesintheforeigncurrency,thedollar-equivalentpriceofthefirm’sproductsisreducedwhentheforeigncurrencydepreciates,sothatthefirmislikelytofinditdesirabletoincreaseitsshortpositionincurrencyfuturestohedgeagainstthisrisk.IftheU.S.firmisnotabletoincreasethepriceofitsproductsintheforeigncurrencyduetocompetition,thedepreciationoftheforeigncurrencyhasanimpactonprofitssimilartotheimpactofforeigncurrencydepreciationontheU.S.firm’sreceivables.3.Thehedgewillbemuchmoreeffectiveforthegold-producingfirm.Pricesfordistantmaturityoilfuturescontractshavesurprisinglylowcorrelationwithcurrentpricesbecauseconvenienceyieldsandstoragecostsfor课后答案网oilcanchangedramaticallyovertime.Whennear-termoilpricesfall,theremaybelittleornochangeinlonger-termprices,sinceoilpricesforverydistantdeliverygenerallyrespondonlyslightlytochangesinthecurrentmarketforshort-horizonoil.Becausethecorrelationbetweenshort-andlong-maturityoilfuturesissolow,hedginglongtermcommitmentswithshortmaturitycontractsdoeslittletoeliminaterisk;thatis,suchahedgeeliminatesverylittleofthevarianceentailedinuncertainfutureoilprices.www.hackshp.cnIncontrast,bothconvenienceyieldsandstoragecostsforgoldaresubstantiallysmallerandmorestable;theresultisthatthecorrelationbetweenshort-termandmoredistantgoldfuturespricesissubstantiallygreater.Inotherwords,thebasisbetweennearanddistantmaturitygoldfuturespricesisfarlessvariable,sohedginglong-termpriceswithshort-termgoldcontractsresultsinasubstantiallygreaterpercentagereductioninvolatility.23-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagement4.Municipalbondyields,whicharebelowT-bondyieldsbecauseoftheirtax-exemptstatus,areexpectedtocloseinonTreasuryyields.Becauseyieldsandpricesareinverselyrelated,thismeansthatmunicipalbondpriceswillperformpoorlycomparedtoTreasuries.Thereforeyoushouldestablishaspreadposition,buyingTreasury-bondfuturesandsellingmunicipalbondfutures.Thenetbetonthegenerallevelofinterestratesisapproximatelyzero.Youhavesimplymadeabetonrelativeperformancesinthetwosectors.5.a.S0×(1+rM)−D=(1,425×1.06)–15=1,495.50b.S0×(1+rf)−D=(1,425×1.03)–15=1,452.75c.Thefuturespriceistoolow.Buyfutures,shorttheindex,andinvesttheproceedsoftheshortsaleinT-bills:CFNowCFin6monthsBuyfutures0ST−1,422Shortindex1,425−ST−15BuyT-bills−1,4251,467.75Total030.756.a.Thevalueoftheunderlyingstockis:$250×1,350=$337,500$25/$337,500=0.000074=0.0074%ofthevalueofthestockb.$40×0.000074=$0.0030(lessthanhalfofonecent)课后答案网c.$0.15/$0.0030=50Thetransactioncostinthestockmarketis50timesthetransactioncostinthefuturesmarket.www.hackshp.cn23-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagement7.a.Youshouldbeshorttheindexfuturescontracts.Ifthestockvaluefalls,youneedfuturesprofitstooffsettheloss.b.Eachcontractisfor$250timestheindex,currentlyvaluedat1,350.Therefore,eachcontractcontrolsstockworth:$250×1,350=$337,500Inordertohedgea$13.5millionportfolio,youneed:$13,500,000=40contracts$337,500c.Now,yourstockswingsonly0.6asmuchasthemarketindex.Hence,youneed0.6asmanycontractsasin(b):0.6×40=24contracts8.Ifthebetaoftheportfoliowere1.0,shewouldsell$1millionoftheindex.Becausebetais1.25,sheshouldsell$1.25millionoftheindex.9.Youwouldshort$0.50ofthemarketindexcontractand$0.75ofthecomputerindustrystockforeachdollarheldinIBM.10.Thedollarisdepreciatingrelativetotheeuro.ToinduceinvestorstoinvestintheU.S.,theU.S.interestratemustbehigher.1+rUS.10411.a.Fromparity:F=E×=.200×=.1962001+r.106课后答案网UKb.SupposethatF0=$2.03/£.Thendollarsarerelativelytoocheapintheforwardmarket,orequivalently,poundsaretooexpensive.Therefore,youshouldborrowthepresentvalueof£1,usetheproceedstobuypound-denominatedbillsinthespotmarket,andsell£1forward:ActionNowwww.hackshp.cnCFin$Actionatperiod-endCFin$Collect$2.03,Sell£1forwardfor$2.030$2.03–$E1deliver£1Buy£1/1.06inspotmarket;–2.00/1.06=–$1.887Exchange£1for$E1$E1investattheBritishrisk-freerateRepayloan;Borrow$1.887$1.887–$1.962U.S.interestrate=4%Total0Total$0.06823-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagement12.a.LendintheU.K.b.BorrowintheU.S.c.BorrowingintheU.S.offersa4%rateofreturn.BorrowingintheU.K.andcoveringinterestrateriskwithfuturesorforwardsoffersarateofreturnof:⎡F0⎤⎡.198⎤r=(1+r)×⎥−1=.107×−1=.00593=.593%US⎢UK⎢⎥⎣E0⎦⎣.200⎦ItappearsadvantageoustoborrowintheU.S.,whereratesarelower,andtolendintheU.K.Anarbitragestrategyinvolvessimultaneouslendingandborrowingwiththecoveringofinterestraterisk:ActionNowCFin$Actionatperiod-endCFin$Borrow$2.00inU.S.$2.00Repayloan–$2.00×1.04ConvertborroweddollarstoCollectrepayment;exchange–$2.001.07×E1pounds;lend£1poundinU.K.proceedsfordollarsSellforward£1.07atF0=$1.980Unwindforward1.07×($1.98–E1)Total0Total$0.038613.Thefarmermustsellforward:100,000×(1/0.90)=111,111bushelsofyellowcornThisrequiresselling:111,111/5,000=22.2contracts14.Theclosingfuturespricewillbe:100−4.80=95.20Theinitialfuturespricewas95.4525,sothelosstothelongsideis25.25basispointsor:课后答案网25.25basispoints×$25perbasispoint=$631.25Thelosscanalsobecomputedas:0.002525×¼×$1,000,000=$631.2515.Supposetheyieldonyourportfolioincreasesby1.5basispoints.Thentheyieldwww.hackshp.cnontheT-bondcontractislikelytoincreaseby1basispoint.Thelossonyourportfoliowillbe:$1million×∆y×D*=$1,000,000×0.00015×4=$600Thechangeinthefuturesprice(per$100parvalue)willbe:$95×0.0001×9=$0.0855Thisisachangeof$85.50ona$100,000parvaluecontract.Thereforeyoushouldsell:$600/$85.50=7contracts23-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagement816.Shemustsell:1$million×=8.0$millionofT-bonds1017.Ifyieldchangesonthebondandthecontractsareeach1basispoint,thenthebondvaluewillchangeby:$10,000,000×0.0001×8=$8,000Thecontractwillresultinacashflowof:$100,000×0.0001×6=$60Therefore,thefirmshouldsell:8,000/60=133contractsThefirmsellsthecontractsbecauseyouneedprofitsonthecontracttooffsetlossesasabondissuerifinterestratesincrease.18.F=S(l+r)T=880×1.04=915.2000fIfF0=920,youcouldearnarbitrageprofitsasfollows:CFNowCFin1yearBuygold−880STShortfutures0920−STBorrow$880880−915.20Total04.80Theforwardpricemustbe915.20inorderforthisstrategytoyieldnoprofit.19.Ifapoorharvesttodayindicatesaworsethanaverageharvestinfutureyears,thenthefutures课后答案网priceswillriseinresponsetotoday’sharvest,althoughpresumablythetwo-yearpricewillchangebylessthantheone-yearprice.Thesamereasoningholdsifcornisstoredacrosstheharvest.Nextyear’spriceisdeterminedbytheavailablesupplyatharvesttime,whichistheactualharvestplusthestoredcorn.Asmallerharvesttodaymeanslessstoredcornfornextyearwhichcanleadtohigherprices.www.hackshp.cnSupposefirstthatcornisneverstoredacrossaharvest,andsecondthatthequalityofaharvestisnotrelatedtothequalityofpastharvests.Underthesecircumstances,thereisnolinkbetweenthecurrentpriceofcornandtheexpectedfuturepriceofcorn.Thequantityofcornstoredwillfalltozerobeforethenextharvest,andthusthequantityofcornandthepriceinoneyearwilldependsolelyonthequantityofnextyear’sharvest,whichhasnothingtodowiththisyear’sharvest.23-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagement20.Therequiredrateofreturnonanassetwiththesameriskascornis:1%+0.5(1.8%–1%)=1.4%permonthThus,intheabsenceofstoragecosts,threemonthsfromnowcornwouldsellfor:$2.75×1.0143=$2.867Thefuturevalueof3month’sstoragecostsis:$0.03×FA(1%,3)=$0.091whereFAstandsforthefuturevaluefactorforalevelannuitywithagiveninterestrateandnumberofpayments.Thus,inordertoinducestorage,theexpectedpricewouldhavetobe:$2.867+$0.091=$2.958Becausetheexpectedspotpriceisonly$2.94,youwouldnotstorecorn.21.Iftheexchangeofcurrencieswerestructuredasthreeseparateforwardcontracts,theforwardpriceswouldbedeterminedasfollows:Forwardexchangerate×$1millioneuros=dollarstobedeliveredYear1:1.50×(1.04/1.03)×$1millioneuros=$1.5146millionYear2:1.50×(1.04/1.03)2×$1millioneuros=$1.5293millionYear3:1.503×(1.04/1.03)×$1millioneuros=$1.5441millionInstead,wedeliverthesamenumberofdollars(F*)eachyear.ThevalueofF*isdeterminedbyfirstcomputingthepresentvalueofthisobligation:F*F*F*.15146.15293.15441++=++=.424301231231.041.04课后答案网1.04.104.104.104F*equals$1.5290millionperyear.22.a.TheswapratemovedinfavoroffirmABC.ABCshouldhavereceived1%moreperyearthanitcouldreceiveinthecurrentswapmarket.Basedonnotionalprincipalof$10million,thelosswww.hackshp.cnis:0.01×$10million=$100,000peryear.b.Themarketvalueofthefixedannuallossisobtainedbydiscountingatthecurrent7%rateon3-yearswaps.Thelossis:$100,000×Annuityfactor(7%,3)=$262,432c.IfABChadbecomeinsolvent,XYZwouldnotbeharmed.XYZwouldbehappytoseetheswapagreementcancelled.However,theswapagreementoughttobetreatedasanassetofABCwhenthefirmisreorganized.23-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagement23.Thefirmreceivesafixedratethatis2%higherthanthemarketrate.Theextrapaymentof(0.02×$10million)haspresentvalueequalto:$200,000×Annuityfactor(8%,5)=$799,54224.a.Fromparity:F0=1,200×(1+0.03)–15=1,221ActualF0is1,218;sothefuturespriceis3belowthe“proper”level.b.Buytherelativelycheapfutures,selltherelativelyexpensivestockandlendtheproceedsoftheshortsale:CFNowCFin6monthsBuyfutures0ST−1,218Sellshares1,200−ST−15Lend$1,200−1,2001,236Total03c.Ifyoudonotreceiveinterestontheproceedsoftheshortsales,thenthe$1200youreceivewillnotbeinvestedbutwillsimplybereturnedtoyou.Theproceedsfromthestrategyinpart(b)arenownegative:anarbitrageopportunitynolongerexists.CFNowCFin6monthsBuyfutures0ST−1,218Sellshares1,200−ST−15Place$1,200inmarginaccount−1,2001,200Total0−33课后答案网d.IfwecalltheoriginalfuturespriceF0,thentheproceedsfromthelong-futures,short-stockstrategyare:CFNowCFin6monthsBuyfutures0ST−F0Sellshareswww.hackshp.cn1,200−ST−15Place$1,200inmarginaccount−1,2001,200Total01,185−F0Therefore,F0canbeaslowas1,185withoutgivingrisetoanarbitrageopportunity.Ontheotherhand,ifF0ishigherthantheparityvalue(1,221),thenanarbitrageopportunity(buystocks,sellfutures)willexist.Thereisnoshort-sellingcostinthiscase.Therefore,theno-arbitragerangeis:1,185≤F0≤1,22123-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagement25.a.Callpthefractionofproceedsfromtheshortsaletowhichwehaveaccess.Ignoringtransactioncosts,thelowerboundonthefuturespricethatprecludesarbitrageisthefollowingusualparityvalue(exceptforthefactorp):S0(l+rfp)–DThedividend(D)equals:0.012×1,350=$16.20Thefactorparisesbecauseonlythisfractionoftheproceedsfromtheshortsalecanbeinvestedintherisk-freeasset.Wecansolveforpasfollows:1,350×(1+0.022p)–16.20=1,351⇒p=0.579b.Withp=0.9,theno-arbitragelowerboundonthefuturespriceis:1,350×[1+(0.022×0.9)]–16.20=1,360.53Theactualfuturespriceis1,351.Thedeparturefromtheboundistherefore9.53.Thisdeparturealsoequalsthepotentialprofitfromanarbitragestrategy.Thestrategyistoshortthestock,whichcurrentlysellsat1,350.Theinvestorreceives90%oftheproceeds(1,215)andtheremainder(135)remainsinthemarginaccountuntiltheshortpositioniscoveredin6months.Theinvestorbuysfuturesandlends1,215:CFNowCFin6monthsBuyfutures0ST−1,351Sellshares1350−135135−ST−16.20Lend−1,2151,215×1.022=1,241.73Total09.53Theprofitis:9.53×$250percontract=$2,382.50CFACFAPROBLEMSPROBLEMS课后答案网1.a.Byspot-futuresparity:F0=S0×(l+rf)=185×[1+(0.06/2)]=190.55b.Thelowerboundwww.hackshp.cnisbasedonthereversecash-and-carrystrategy.ActionNowCFin$Actionatperiod-endCFin$BuyoneTOBECindexSelloneTOBECindex0$100×(F1−F0)futurescontractfuturescontractSellspotTOBECindex+$18,500BuyspotTOBECindex−$100×S1Lend$18,500−$18,500Collectloanrepayment$18,500×1.03=+$19,055Paytransactioncosts−$15.00Total0Total−$100F0+$19,040(NotethatF1=S1atexpiration.)ThelowerboundforF0is:19,040/100=190.4023-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagement2.a.ThestrategywouldbetosellJapanesestockindexfuturestohedgethemarketriskofJapanesestocks,andtosellyenfuturestohedgethecurrencyexposure.b.Somepossiblepracticaldifficultieswiththisstrategyinclude:•Contractsizeonfuturesmaynotmatchsizeofportfolio.•Stockportfoliomaynotcloselytrackindexportfoliosonwhichfuturestrade.•Cashflowmanagementissuesfrommarkingtomarket.•Potentialmispricingoffuturescontracts(violationsofparity).3.a.Thehedgedinvestmentinvolvesconvertingthe$1milliontoforeigncurrency,investinginthatcountry,andsellingforwardtheforeigncurrencyinordertolockinthedollarvalueoftheinvestment.Becausetheinterestratesarefor90-dayperiods,weassumetheyarequotedasbondequivalentyields,annualizedusingsimpleinterest.Therefore,toexpressratesonaperquarterbasis,wedividetheseratesby4:JapanesegovernmentSwissgovernmentConvert$1million$1,000,000×133.05=$1,000,000×1.5260=tolocalcurrency¥133,050,000SF1,526,000Investinlocalcurrency¥133,050,000×[1+(0.076/4)]=SF1,526,000×[1+(0.086/4)]=for90days¥135,577,950SF1,558,809Convertto$at1,558,809/1.5348=135,577,950/133.47=$1,015,79390-dayforwardrate$1,015,643b.Theresultsinthetwocurrenciesarenearlyidentical.Thisnear-equalityreflectstheinterestrateparitytheorem.Thistheoryassertsthatthepricingrelationshipsbetween课后答案网interestratesandspotandforwardexchangeratesmustmakecovered(thatis,fullyhedgedandriskless)investmentsinanycurrencyequallyattractive.c.The90-dayreturninJapanis1.5793%,whichrepresentsabond-equivalentyieldof1.5793%×365/90=6.405%.The90-dayreturninSwitzerlandis1.5643%,whichrepresentsabond-equivalentyieldof1.5643%www.hackshp.cn×365/90=6.344%.Theestimateforthe90-dayrisk-freeU.S.governmentmoneymarketyieldisinthisrange.23-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagement4.TheinvestorcanbuyXamountofpesosatthe(indirect)spotexchangerate,andinvestthepesosintheMexicanbondmarket.Then,inoneyear,theinvestorwillhave:X×(1+rMEX)pesosThesepesoscanthenbeconvertedbackintodollarsusingthe(indirect)forwardexchangerate.Interestrateparityassertsthatthetwoholdingperiodreturnsmustbeequal,whichcanberepresentedbytheformula:(1+rUS)=E0×(1+rMEX)×(1/F0)TheleftsideoftheequationrepresentstheholdingperiodreturnforaU.S.dollar-denominatedbond.Ifinterestrateparityholds,thenthistermalsocorrespondstotheU.S.dollarholdingperiodreturnforthecurrency-hedgedMexicanone-yearbond.Therightsideoftheequationistheholdingperiodreturn,indollarterms,foracurrency-hedgedpeso-denominatedbond.SolvingforrUS:(1+rUS)=9.5000×(1+0.065)×(1/9.8707)(1+rUS)=1.0250rUS=2.50%ThusrUS=2.50%,whichisthesameastheyieldfortheone-yearU.S.bond.0.50.5⎛⎜1+rUS⎞⎟⎛.10010⎞5.a.Fromparity:F0=E0×⎜⎟=124.30×⎜⎟=122.06453⎝1+rJapan⎠⎝.10380⎠b.ActionNowCFin$Actionatperiod-endCFin¥−($1,000,000×1.0350.25)=Borrow$1,000,000inU.S.课后答案网$1,000,000Repayloan−$1,008,637.45Convertborroweddollarstoyen;Collectrepayment¥124,300,000×1.0050.25=–$1,000,000lend¥124,300,000inJapaninyen¥124,455,084.52Sellforward$1,008,637.45−(1,008,637.45×¥123.2605)=0UnwindforwardatF0=¥123.2605www.hackshp.cn−¥124,325,156.40Total0Total¥129,928.12Thearbitrageprofitis:¥129,928.126.a.Delsingshouldsellstockindexfuturescontractsandbuybondfuturescontracts.Thisstrategyisjustifiedbecausebuyingthebondfuturesandsellingthestockindexfuturesprovidesthesameexposureasbuyingthebondsandsellingthestocks.Thisstrategyassumeshighcorrelationbetweenthebondfuturesandthebondportfolio,aswellashighcorrelationbetweenthestockindexfuturesandthestockportfolio.23-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter23-Futures,Swaps,andRiskManagementb.Thenumberofcontractsineachcaseis:i.5×$200,000,000×0.0001=$100,000$100,000/97.85=1022contractsii.$200,000,000/($1,378×250)=581contracts7.SituationA.Themarketvalueoftheportfoliotobehedgedis$20million.Themarketvalueofthebondscontrolledbyonefuturescontractis$63,330.Ifweweretoequatethemarketvaluesoftheportfolioandthefuturescontract,wewouldsell:$20,000,000/$63,330=315.806contractsHowever,wemustadjustthis“naive”hedgeforthepricevolatilityofthebondportfoliorelativetothefuturescontract.Pricevolatilitiesdifferaccordingtoboththedurationandtheyieldvolatilityofthebonds.Inthiscase,theyieldvolatilitiesmaybeassumedequal,becauseanyyieldspreadbetweentheTreasuryportfolioandtheTreasurybondunderlyingthefuturescontractislikelytobestable.However,thedurationoftheTreasuryportfolioislessthanthatofthefuturescontract.Adjustingthenaivehedgeforrelativedurationandrelativeyieldvolatility,weobtaintheadjustedhedgeposition:6.7315.806××0.1=300contracts0.8SituationB.Here,thetreasurerseekstohedgethepurchasepriceofthebonds;thisrequiresalonghedge.Themarketvalueofthebondstobepurchasedis:$20million×0.93=$18.6millionThedurationratiois7.2/8.0,andtherelativeyieldvolatilityis1.25.Therefore,thehedgerequiresthetreasurertotakealongposition课后答案网in:18,600,0002.7××.125=330contracts63,3300.88.a.%changeinT-bondprice=modifieddurationwww.hackshp.cn×changeinYTM=7.0×0.50%=3.5%b.WhentheYTMoftheT-bondchangesby50basispoints,thepredictedchangeintheyieldontheKCbondis1.22×50=61basispoints.Therefore:%changeinKCprice=modifiedduration×changeinYTM=6.93×0.61%=4.23%23-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluationCHAPTER24:PORTFOLIOPORTFOLIOPERFORMANCEPERFORMANCEPERFORMANCEEVALUATIONEVALUATIONPROBLEMPROBLEMSETSSETS1.Asestablishedinthefollowingresultfromthetext,theSharperatiodependsonbothalphafortheportfolio(∀P)andthecorrelationbetweentheportfolioandthemarketindex(ρ):E(rP−rf)αP=+ρSMσσPPSpecifically,thisresultdemonstratesthatalowercorrelationwiththemarketindexreducestheSharperatio.Hence,ifalphaisnotsufficientlylarge,theportfolioisinferiortotheindex.Anotherwaytothinkaboutthisconclusionistonotethat,evenforaportfoliowithapositivealpha,ifitsdiversifiableriskissufficientlylarge,therebyreducingthecorrelationwiththemarketindex,thiscanresultinalowerSharperatio.2.TheIRR(i.e.,thedollar-weightedreturn)cannotberankedrelativetoeitherthegeometricaveragereturn(i.e.,thetime-weightedreturn)orthearithmeticaveragereturn.Undersomeconditions,theIRRisgreaterthaneachoftheothertwoaverages,andsimilarly,underotherconditions,theIRRcanalsobelessthaneachoftheotheraverages.Anumberofscenarioscanbedevelopedtoillustratethisconclusion.Forexample,considerascenariowheretherateofreturneachperiodconsistentlyincreasesoverseveraltimeperiods.Iftheamountinvestedalsoincreaseseachperiod,andthenalloftheproceedsarewithdrawnattheendofseveralperiods,theIRR课后答案网isgreaterthaneitherthegeometricorthearithmeticaveragebecausemoremoneyisinvestedatthehigherratesthanatthelowerrates.Ontheotherhand,ifwithdrawalsgraduallyreducetheamountinvestedastherateofreturnincreases,thentheIRRislessthaneachoftheotheraverages.(Similarscenariosareillustratedwithnumericalexamplesinthetext,onpage824,wheretheIRRisshowntobelessthanthegeometricaverage,andinConceptCheck1,wheretheIRRwww.hackshp.cnisgreaterthanthegeometricaverage.)3.Itisnotnecessarilywisetoshiftresourcestotimingattheexpenseofsecurityselection.Thereisalsotremendouspotentialvalueinsecurityanalysis.Thedecisionastowhethertoshiftresourceshastobemadeonthebasisofthemacro,comparedtothemicro,forecastingabilityoftheportfoliomanagementteam.24-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluation4.a.Arithmeticaverage:rABC=10%;rXYZ=10%b.Dispersion:σABC=7.07%;σXYZ=13.91%StockXYZhasgreaterdispersion.(Note:Weused5degreesoffreedomincalculatingstandarddeviations.)c.Geometricaverage:r1/5ABC=(1.20×1.12×1.14×1.03×1.01)–1=0.0977=9.77%r1/5XYZ=(1.30×1.12×1.18×1.00×0.90)–1=0.0911=9.11%Despitethefactthatthetwostockshavethesamearithmeticaverage,thegeometricaverageforXYZislessthanthegeometricaverageforABC.ThereasonforthisresultisthefactthatthegreatervarianceofXYZdrivesthegeometricaveragefurtherbelowthearithmeticaverage.d.Intermsof“forwardlooking”statistics,thearithmeticaverageisthebetterestimateofexpectedrateofreturn.Therefore,ifthedatareflecttheprobabilitiesoffuturereturns,10%istheexpectedrateofreturnforbothstocks.5.a.Time-weightedaveragereturnsarebasedonyear-by-yearratesofreturn:YearReturn=(capitalgains+dividend)/price2005−2006[($120–$100)+$4]/$100=24.00%2006−2007[($90–$120)+$4]/$120=–21.67%2007−2008课后答案网[($100–$90)+$4]/$90=15.56%Arithmeticmean:(24%–21.67%+15.56%)/3=5.96%Geometricmean:(1.24×0.7833×1.1556)1/3–1=0.0392=3.92%www.hackshp.cn24-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluationb.CashDateFlowExplanation1/1/05–$300Purchaseofthreesharesat$100each1/1/06–$228Purchaseoftwosharesat$120lessdividendincomeonthreesharesheld1/1/07$110Dividendsonfivesharesplussaleofoneshareat$901/1/08$416Dividendsonfoursharesplussaleoffoursharesat$100each416110Date:1/1/051/1/061/1/071/1/08−228−300Dollar-weightedreturn=Internalrateofreturn=–0.1607%6.TimeCashflow课后答案网Holdingperiodreturn03(–$90)=–$2701$100(100–90)/90=11.11%2$1000%3$1000%a.Time-weightedgeometricaverageratewww.hackshp.cnofreturn=(1.11111/3×1.0×1.0)–1=0.0357=3.57%b.Time-weightedarithmeticaveragerateofreturn=(11.11%+0+0)/3=3.70%Thearithmeticaverageisalwaysgreaterthanorequaltothegeometricaverage;thegreaterthedispersion,thegreaterthedifference.c.Dollar-weightedaveragerateofreturn=IRR=5.46%[Usingafinancialcalculator,enter:n=3,PV=–270,FV=0,PMT=100.Thencomputetheinterestrate.]TheIRRexceedstheotheraveragesbecausetheinvestmentfundwasthelargestwhenthehighestreturnoccurred.24-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluation7.a.Thealphasforthetwoportfoliosare:αA=12%–[5%+0.7(13%–5%)]=1.4%αB=16%–[5%+1.4(13%–5%)]=–0.2%Ideally,youwouldwanttotakealongpositioninPortfolioAandashortpositioninPortfolioB.b.Ifyouwillholdonlyoneofthetwoportfolios,thentheSharpemeasureistheappropriatecriterion:12−5S==.0583A1216−5S==.0355B31UsingtheSharpecriterion,PortfolioAisthepreferredportfolio.8.a.StockAStockB(i)Alpha=regressionintercept1.0%2.0%(ii)Informationratio=αP/σ(eP)0.09710.1047(iii)*Sharpemeasure=(rP–rf)/σP0.49070.3373(iv)**Treynormeasure=(rP–rf)/βP8.83310.500*TocomputetheSharpemeasure,notethatforeachstock,(rP–rf)canbecomputedfromtheright-handsideoftheregressionequation,usingtheassumedparametersrM=14%andrf=6%.Thestandarddeviationofeachstock’sreturnsisgivenintheproblem.课后答案网**ThebetatousefortheTreynormeasureistheslopecoefficientoftheregressionequationpresentedintheproblem.b.(i)Ifthisistheonlyriskyassetheldbytheinvestor,thenSharpe’smeasureistheappropriatemeasure.SincetheSharpemeasurewww.hackshp.cnishigherforStockA,thenAisthebestchoice.(ii)Ifthestockismixedwiththemarketindexfund,thenthecontributiontotheoverallSharpemeasureisdeterminedbytheappraisalratio;therefore,StockBispreferred.(iii)Ifthestockisoneofmanystocks,thenTreynor’smeasureistheappropriatemeasure,andStockBispreferred.24-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluation9.Weneedtodistinguishbetweenmarkettimingandsecurityselectionabilities.Theinterceptofthescatterdiagramisameasureofstockselectionability.Ifthemanagertendstohaveapositiveexcessreturnevenwhenthemarket’sperformanceismerely“neutral”(i.e.,haszeroexcessreturn),thenweconcludethatthemanagerhasonaveragemadegoodstockpicks.Stockselectionmustbethesourceofthepositiveexcessreturns.Timingabilityisindicatedbythecurvatureoftheplottedline.Linesthatbecomesteeperasyoumovetotherightalongthehorizontalaxisshowgoodtimingability.Thesteeperslopeshowsthatthemanagermaintainedhigherportfoliosensitivitytomarketswings(i.e.,ahigherbeta)inperiodswhenthemarketperformedwell.Thisabilitytochoosemoremarket-sensitivesecuritiesinanticipationofmarketupturnsistheessenceofgoodtiming.Incontrast,adecliningslopeasyoumovetotherightmeansthattheportfoliowasmoresensitivetothemarketwhenthemarketdidpoorlyandlesssensitivewhenthemarketdidwell.Thisindicatespoortiming.Wecanthereforeclassifyperformanceforthefourmanagersasfollows:SelectionTimingAbilityAbilityA.BadGoodB.GoodGoodC.GoodBadD.BadBad10.a.Bogey:(0.60×2.5%)+(0.30×1.2%)+(0.10×0.5%)=1.91%Actual:(0.70×2.0%)+(0.20×1.0%)+(0.10×0.5%)=1.65%Underperformance:0.26%b.SecuritySelection:课后答案网(1)(2)(3)=(1)×(2)DifferentialreturnManager"sContributiontoMarketwithinmarketportfolioweightperformance(Manager–index)www.hackshp.cnEquity–0.5%0.70−0.35%Bonds–0.2%0.20–0.04%Cash0.0%0.100.00%Contributionofsecurityselection:−0.39%24-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluationc.AssetAllocation:(1)(2)(3)=(1)×(2)ExcessweightIndexContributiontoMarket(Manager–benchmark)ReturnperformanceEquity0.10%2.5%0.25%Bonds–0.10%1.2%–0.12%Cash0.00%0.5%0.00%Contributionofassetallocation:0.13%Summary:Securityselection–0.39%Assetallocation0.13%Excessperformance–0.26%11.a.Managerreturn:(0.30×20)+(0.10×15)+(0.40×10)+(0.20×5)=12.50%Benchmark(bogey):(0.15×12)+(0.30×15)+(0.45×14)+(0.10×12)=13.80%Addedvalue:–1.30%b.Addedvaluefromcountryallocation:(1)(2)(3)=(1)×(2)ExcessweightIndexReturnContributiontoCountry(Manager–benchmark)minusbogeyperformanceU.K.0.15%−1.8%−0.27%Japan–0.20%1.2%–0.24%U.S.−0.05%0.2%−0.01%Germany0.10%−1.8%−0.18%课后答案网Contributionofcountryallocation:−0.70%c.Addedvaluefromstockselection:(1)(2)(3)=(1)×(2)DifferentialreturnManager’sContributiontoCountrywithincountrywww.hackshp.cncountryweightperformance(Manager–Index)U.K.8%0.30%2.4%Japan0%0.10%0.0%U.S.−4%0.40%−1.6%Germany−7%0.20%−1.4%Contributionofstockselection:−0.6%Summary:Countryallocation–0.70%Stockselection−0.60%Excessperformance–1.30%24-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluation12.Support:Amanagercouldbeabetterperformerinonetypeofcircumstancethaninanother.Forexample,amanagerwhodoesnotiming,butsimplymaintainsahighbeta,willdobetterinupmarketsandworseindownmarkets.Therefore,weshouldobserveperformanceoveranentirecycle.Also,totheextentthatobservingamanageroveranentirecycleincreasesthenumberofobservations,itwouldimprovethereliabilityofthemeasurement.Contradict:Ifweadequatelycontrolforexposuretothemarket(i.e.,adjustforbeta),thenmarketperformanceshouldnotaffecttherelativeperformanceofindividualmanagers.Itisthereforenotnecessarytowaitforanentiremarketcycletopassbeforeevaluatingamanager.13.Theuseofuniversesofmanagerstoevaluaterelativeinvestmentperformancedoes,tosomeextent,overcomestatisticalproblems,aslongasthosemanagergroupscanbemadesufficientlyhomogeneouswithrespecttostyle.14.a.Themanager’salphais:10%–[6%+0.5(14%–6%)]=0b.FromBlack-Jensen-Scholesandothers,weknowthat,onaverage,portfolioswithlowbetahavehistoricallyhadpositivealphas.(TheslopeoftheempiricalsecuritymarketlineisshallowerthanpredictedbytheCAPM.)Therefore,giventhemanager’slowbeta,performancemightactuallybesub-pardespitetheestimatedalphaofzero.15.Thisexerciseislefttothestudent;answerswillvary.CFACFAPROBLEMSPROBLEMS课后答案网1.a.ManagerAStrength.AlthoughManagerA’sone-yeartotalreturnwassomewhatbelowtheinternationalindexreturn(–6.0percentversus–5.0percent),thismanagerapparentlyhassomecountry/securityreturnexpertise.Thislargelocalmarketwww.hackshp.cnreturnadvantageof2.0percentexceedsthe0.2percentreturnfortheinternationalindex.Weakness.ManagerAhasanobviousweaknessinthecurrencymanagementarea.Thismanagerexperiencedamarkedcurrencyreturnshortfall,withareturnof–8.0percentversus–5.2percentfortheindex.24-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluationManagerBStrength.ManagerB’stotalreturnexceededthatoftheindex,withamarkedpositiveincrementapparentinthecurrencyreturn.ManagerBhada–1.0percentcurrencyreturncomparedtoa–5.2percentcurrencyreturnontheinternationalindex.Basedonthisoutcome,ManagerB’sstrengthappearstobeexpertiseinthecurrencyselectionarea.Weakness.ManagerBhadamarkedshortfallinlocalmarketreturn.Therefore,ManagerBappearstobeweakinsecurity/marketselectionability.b.Thefollowingstrategieswouldenablethefundtotakeadvantageofthestrengthsofeachofthetwomanagerswhileminimizingtheirweaknesses.1.Recommendation:OnestrategywouldbetodirectManagerAtomakenocurrencybetsrelativetotheinternationalindexandtodirectManagerBtomakeonlycurrencydecisions,andnoactivecountryorsecurityselectionbets.Justification:ThisstrategywouldmitigateManagerA’sweaknessbyhedgingallcurrencyexposuresintoindex-likeweights.ThiswouldallowcaptureofManagerA’scountryandstockselectionskillswhileavoidinglossesfrompoorcurrencymanagement.ThisstrategywouldalsomitigateManagerB’sweakness,leavinganindex-likeportfolioconstructandcapitalizingontheapparentskillincurrencymanagement.2.Recommendation:AnotherstrategywouldbetocombinetheportfoliosofManagerAandManagerB,withManagerAmakingcountryexposureandsecurityselectiondecisionsandManagerBmanagingthecurrencyexposurescreatedbyManagerA’sdecisions(providinga“currencyoverlay”).Justification:ThisrecommendationwouldcapturethestrengthsofbothManagerAandManager课后答案网Bandwouldminimizetheircollectiveweaknesses.2.a.Indeed,theoneyearresultswereterrible,butoneyearisapoorstatisticalbasefromwhichtodrawinferences.Moreover,theboardoftrusteeshaddirectedKarltoadoptalong-termhorizon.TheBoardspecificallyinstructedtheinvestmentmanagertogiveprioritytolongtermresults.www.hackshp.cnb.ThesampleofpensionfundshadamuchlargershareinvestedinequitiesthandidAlpine.Equitiesperformedmuchbetterthanbonds.YetthetrusteestoldAlpinetoholddownrisk,investingnotmorethan25%oftheplan’sassetsincommonstocks.(Alpine’sbetawasalsosomewhatdefensive.)Alpineshouldnotbeheldresponsibleforanassetallocationpolicydictatedbytheclient.c.Alpine’salphameasuresitsrisk-adjustedperformancecomparedtothemarket:α=13.3%–[7.5%+0.90(13.8%–7.5%)]=0.13%(actuallyabovezero)24-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluationd.Notethatthelast5years,andparticularlythemostrecentyear,havebeenbadforbonds,theassetclassthatAlpinehadbeenencouragedtohold.Withinthisassetclass,however,Alpinedidmuchbetterthantheindexfund.Moreover,despitethefactthatthebondindexunderperformedboththeactuarialreturnandT-bills,Alpineoutperformedboth.Alpine’sperformancewithineachassetclasshasbeensuperioronarisk-adjustedbasis.Itsoveralldisappointingreturnswereduetoaheavyassetallocationweightingtowardsbonds,whichwastheBoard’s,notAlpine’s,choice.e.Atrusteemaynotcareaboutthetime-weightedreturn,butthatreturnismoreindicativeofthemanager’sperformance.Afterall,themanagerhasnocontroloverthecashinflowsandoutflowsofthefund.3.a.MethodIdoesnothingtoseparatelyidentifytheeffectsofmarkettimingandsecurityselectiondecisions.Italsousesaquestionable“neutralposition,”thecompositionoftheportfolioatthebeginningoftheyear.b.MethodIIisnotperfect,butisthebestofthethreetechniques.Itatleastattemptstofocusonmarkettimingbyexaminingthereturnsforportfoliosconstructedfrombondmarketindexesusingactualweightsinvariousindexesversusyear-averageweights.Theproblemwiththismethodisthattheyear-averageweightsneednotcorrespondtoaclient’s“neutral”weights.Forexample,whatifthemanagerwereoptimisticovertheentireyearregardinglong-termbonds?Heraverageweightingcouldreflectheroptimism,andnotaneutralposition.c.MethodIIIusesnetpurchasesofbondsasasignalofbondmanageroptimism.Butsuchnetpurchasescanbemotivatedbywithdrawalsfromorcontributionstothefundratherthanthemanager’sdecisions.(Notethatthisisanopen-endedmutualfund.)Therefore,课后答案网itisinappropriatetoevaluatethemanagerbasedonwhethernetpurchasesturnouttobereliablebullishorbearishsignals.4.Treynormeasure=(17–8)/1.1=8.182www.hackshp.cn5.Sharpemeasure=(24–8)/18=0.88824-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluation6.a.TreynormeasuresPortfolioX:(10–6)/0.6=6.67S&P500:(12–6)/1.0=6.00SharpemeasuresPortfolioX:(10–6)/18=0.222S&P500:(12–6)/13=0.462PortfolioXoutperformsthemarketbasedontheTreynormeasure,butunderperformsbasedontheSharpemeasure.b.Thetwomeasuresofperformanceareinconflictbecausetheyusedifferentmeasuresofrisk.PortfolioXhaslesssystematicriskthanthemarket,asmeasuredbyitslowerbeta,butmoretotalrisk(volatility),asmeasuredbyitshigherstandarddeviation.Therefore,theportfoliooutperformsthemarketbasedontheTreynormeasurebutunderperformsbasedontheSharpemeasure.7.Geometricaverage=(1.15×0.90)1/2–1=0.0173=1.73%8.Geometricaverage=(0.91×1.23×1.17)1/3–1=0.0941=9.41%9.Internalrateofreturn=7.5%10.d.11.Time-weightedaveragereturn=(15%+10%)/2=12.5%课后答案网Tocomputedollar-weightedrateofreturn,cashflowsare:CF0=−$500,000CF1=−$500,000www.hackshp.cnCF2=($500,000×1.15×1.10)+($500,000×1.10)=$1,182,500Dollar-weightedrateofreturn=11.71%12.b.13.a.24-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluation14.a.Eachofthesebenchmarkshasseveraldeficiencies,asdescribedbelow.Marketindex:•Amarketindexmayexhibitsurvivorshipbias.Firmsthathavegoneoutofbusinessareremovedfromtheindex,resultinginaperformancemeasurethatoverstatesactualperformancehadthefailedfirmsbeenincluded.•Amarketindexmayexhibitdoublecountingthatarisesbecauseofcompaniesowningothercompaniesandbothbeingrepresentedintheindex.•Itisoftendifficulttoexactlyandcontinuallyreplicatetheholdingsinthemarketindexwithoutincurringsubstantialtradingcosts.•Thechosenindexmaynotbeanappropriateproxyforthemanagementstyleofthemanagers.•Thechosenindexmaynotrepresenttheentireuniverseofsecurities.Forexample,theS&P500Indexrepresents65%to70%ofU.S.equitymarketcapitalization.•Thechosenindex(e.g.,theS&P500)mayhavealargecapitalizationbias.•Thechosenindexmaynotbeinvestable.Theremaybesecuritiesintheindexthatcannotbeheldintheportfolio.Benchmarknormalportfolio:•Thisisthemostdifficultperformancemeasurementmethodtodevelopandcalculate.•Thenormalportfoliomustbecontinuallyupdated,requiringsubstantialresources.•Consultantsandclientsareconcernedthatmanagerswhoareinvolvedindevelopingandcalculatingtheirbenchmarkportfoliomayproduceaneasily-beatennormalportfolio,makingtheirperformanceappearbetterthanitactuallyis.Medianofthemanageruniverse:•Itcanbedifficulttoidentifyauniverseofmanagersappropriateforthe课后答案网investmentstyleoftheplan’smanagers.•Selectionofamanageruniverseforcomparisoninvolvessome,perhapsmuch,subjectivejudgement.•Comparisonwithamanageruniversedoesnottakeintoaccounttherisktakenintheportfolio.•Themedianofamanageruniversedoesnotrepresentan“investable”portfolio;www.hackshp.cnthatis,aportfoliomanagermaynotbeabletoinvestinthemedianmanagerportfolio.•Suchabenchmarkmaybeambiguous.Thenamesandweightsofthesecuritiesconstitutingthebenchmarkarenotclearlydelineated.•Thebenchmarkisnotconstructedpriortothestartofanevaluationperiod;itisnotspecifiedinadvance.•Amanageruniversemayexhibitsurvivorshipbias;managerswhohavegoneoutofbusinessareremovedfromtheuniverse,resultinginaperformancemeasurethatoverstatestheactualperformancehadthosemanagersbeenincluded.24-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluationb.i.TheSharperatioiscalculatedbydividingtheportfolioriskpremium(i.e.,actualportfolioreturnminustherisk-freereturn)bytheportfoliostandarddeviation:Sharperatio=(rP–rf)/σPTheTreynormeasureiscalculatedbydividingtheportfolioriskpremium(i.e.,actualportfolioreturnminustherisk-freereturn)bytheportfoliobeta:Treynormeasure=(rP–rf)/βPJensen’salphaiscalculatedbysubtractingthemarketriskpremium,adjustedforriskbytheportfolio’sbeta,fromtheactualportfolioexcessreturn(riskpremium).ItcanbedescribedasthedifferenceinreturnearnedbytheportfoliocomparedtothereturnimpliedbytheCapitalAssetPricingModelorSecurityMarketLine:αP=rP–[rf+βP(rM−rf)]ii.TheSharperatioassumesthattherelevantriskistotalrisk,anditmeasuresexcessreturnperunitoftotalrisk.TheTreynormeasureassumesthattherelevantriskissystematicrisk,anditmeasuresexcessreturnperunitofsystematicrisk.Jensen’salphaassumesthattherelevantriskissystematicrisk,anditmeasuresexcessreturnatagivenlevelofsystematicrisk.15.i.Thestatementisincorrect.Validbenchmarksareunbiased.Medianmanagerbenchmarks,however,aresubjecttosignificantsurvivorshipbias,whichresultsinseveraldrawbacks,includingthefollowing:•Theperformanceofmedianmanagerbenchmarksisbiasedupwards.•Theupwardbiasincreaseswithtime.•Survivorbiasintroducesuncertaintywithregardtomanagerrankings.•Survivorbiasskewstheshapeofthedistributioncurve.课后答案网ii.Thestatementisincorrect.Validbenchmarksareunambiguousandabletobereplicated.Themedianmanagerbenchmark,however,isambiguousbecausetheweightsoftheindividualsecuritiesinthebenchmarkarenotknown.Theportfolio’scompositioncannotbeknownbeforetheconclusionofameasurementperiodbecauseidentificationasamedianmanagerwww.hackshp.cncanoccuronlyafterperformanceismeasured.Validbenchmarksarealsoinvestable.Themedianmanagerbenchmarkisnotinvestable.Thatis,amanagerusingamedianmanagerbenchmarkcannotforegoactivemanagementand,takingapassive/indexedapproach,simplyholdthebenchmark.Thisisaresultofthefactthattheweightsofindividualsecuritiesinthebenchmarkarenotknown.iii.Thestatementiscorrect.Themedianmanagerbenchmarkmaybeinappropriatebecausethemedianmanageruniverseencompassesmanyinvestmentstylesand,therefore,maynotbeconsistentwithagivenmanager’sstyle.24-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter24-PortfolioPerformanceEvaluation16.a.Sharperatio=(rP–rf)/σPWilliamsonCapital:Sharperatio=(22.1%−5.0%)/16.8%=1.02JoynerAssetManagement:Sharperatio=(24.2%−5.0%)/20.2%=0.95Treynormeasure=(rP–rf)/βPWilliamsonCapital:Treynormeasure=(22.1%−5.0%)/1.2=14.25JoynerAssetManagement:Treynormeasure=(24.2%−5.0%)/0.8=24.00b.ThedifferenceintherankingsofWilliamsonandJoynerresultsdirectlyfromthedifferenceindiversificationoftheportfolios.JoynerhasahigherTreynormeasure(24.00)andalowerSharperatio(0.95)thandoesWilliamson(14.25and1.202,respectively),soJoynermustbelessdiversifiedthanWilliamson.TheTreynormeasureindicatesthatJoynerhasahigherreturnperunitofsystematicriskthandoesWilliamson,whiletheSharperatioindicatesthatJoynerhasalowerreturnperunitoftotalriskthandoesWilliamson.课后答案网www.hackshp.cn24-13若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter25-InternationalDiversificationCHAPTER25:INTERNATIONALINTERNATIONALDIVERSIFICATIONDIVERSIFICATIONPROBLEMPROBLEMSETSSETS1.“InternationalInvestingRaisesQuestions”waspublishedintheWallStreetJournalin1997.Someoftheargumentspresentedinthearticlemaynolongerbecompellingmorethanadecadelater.Forexample,thefollowingstatementfromthearticleisnolongertrueformanyU.S.multinationals:“Whenyoulookatthesemultinationals,thefactorthatdrivestheirperformanceistheirhomemarket.”Thesamecanalsobesaidoftheassertionthat“…mostoftheircosts−especiallylaborcosts–willbeincurredintheU.S.”However,thefollowingargumentfromthearticleisstillvalid:“U.S.multinationalstendtobeownedbyU.S.investors,whowillbeswayedbytheupsanddownsoftheU.S.market.”Anadditionalargumentthatisnotmentionedinthepieceisthefactthat,wheninvestinginU.S.multinationals,itisessentiallyimpossibletodeterminethedegreeofone’sinternationalexposure.Aportfolioofforeignstocksprovidesaninvestorabetterunderstandingofthisexposure.ThecorrelationbetweenportfoliosofforeignstocksandtheU.S.equitymarketislikelytobelessthanthecorrelationofaportfolioofU.S.multinationalswiththeU.S.market.2.Whichofthereturnsismorerelevanttoaninvestordependsonwhethertheinvestorhedgesthelocalcurrency.Iftheforeignexchangeriskhasbeenhedged,thentherelevantfigureisthestockmarketreturnsmeasuredinthelocalcurrency.Iftheforeignexchangeriskisnothedged,thentherelevantreturnsarethedollar-denominatedreturns.3.a.$10,000/2=£5,000课后答案网£5,000/£40=125sharesb.Tofillinthetable,weusetherelation:E11+r(US)=[(1+r(UK)]Ewww.hackshp.cn0Dollar-DenominatedReturn(%)PriceperPound-DenominatedforYearEndExchangeRateShare(£)Return(%)$1.80/£$2.00/£$2.20/££35-12.5%-21.25%-12.5%-3.75%£400.0%-10.00%0.0%10.00%£4512.5%1.25%12.5%23.75%c.Thedollar-denominatedreturnequalsthepound-denominatedreturnwhentheexchangerateisunchangedovertheyear.25-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter25-InternationalDiversification4.Thestandarddeviationofthepound-denominatedreturn(using3degreesoffreedom)is10.21%.Thedollar-denominatedreturnhasastandarddeviationof13.10%(using9degreesoffreedom),greaterthanthepound-denominatedstandarddeviation.Thisisduetotheadditionofexchangeraterisk.5.a.Firstwecalculatethedollarvalueofthe125sharesofstockineachscenario.Thenweaddtheprofitsfromtheforwardcontractineachscenario.DollarValueofStockPriceperatGivenExchangeRateShare(£)ExchangeRate:$1.80/£$2.00/£$2.20/££357,8758,7509,625£409,00010,00011,000£4510,12511,25012,375ProfitsonForwardExchange:1,500500-500[=5000(2.10–E1)]TotalDollarProceedsPriceperatGivenExchangeRateShare(£)ExchangeRate:$1.80/£$2.00/£$2.20/££359,3759,2509,125£4010,50010,50010,500£4511,62511,75011,875Finally,calculatethedollar-denominatedrateofreturn,recallingthattheinitialinvestmentwas$10,000:Rateofreturn(%)PriceperatGivenExchangeRateShare(£)ExchangeRate:课后答案网$1.80/£$2.00/£$2.20/££35-6.25%-7.50%-8.75%£405.00%5.00%5.00%£4516.25%17.50%18.75%b.Thestandarddeviationisnow10.24%.Thisislowerthantheunhedgeddollar-denominatedstandarddeviation,andwww.hackshp.cnisonlyslightlyhigherthanthestandarddeviationofthepound-denominatedreturn.25-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter25-InternationalDiversification6.CurrencySelectionEAFE:[0.30×(–10%)]+(0.10×0%)+(0.60×10%)=3.0%Manager:[0.35×(–10%)]+(0.15×0%)+(0.50×10%)=1.5%Lossof1.5%relativetoEAFE.CountrySelectionEAFE:(0.30×20%)+(0.10×15%)+(0.60×25%)=22.50%Manager:(0.35×20%)+(0.15×15%)+(0.50×25%)=21.75%Lossof0.75%relativetoEAFE.StockSelection[(18%–20%)×0.35]+[(20%–15%)×0.15]+[(20%–25%)×0.50]=–2.45%Lossof2.45%relativetoEAFE.7.1+r(US)=[1+rf(UK)]×(F0/E0)=1.08×(1.85/1.75)=1.1417⇒r(US)=14.17%8.Youcannowpurchase:$10,000/$1.75=£5,714.29Thiswillgrowwith8%interestto£6,171.43.Therefore,tolockinyourreturn,youwouldsellforward£6,171.43attheforwardexchangerate.9.AnaïveinvestmentbyaninvestorwhoresidesinForeignCountryAmightincludeonlyasmallfractionoftheportfolioinvestedinthehomecountry,andarelativelygreaterweightinvestedinU.S.securities.Thismightnotbeanappropriateapproachforaforeigninvestorwhoislikelytobecomfortablewithahomebias,justasAmericaninvestorsseemtobe.Areasonablewaytoscaledowntheweightinvestedinforeign课后答案网countries(forexample,theportfolioweightmaintainedbytheinvestorfromForeignCountryAinU.S.securities)istofocusontheweightofU.S.importsintheentireconsumptionbasketoftheinvestor(includingdurablegoods)ratherthanemphasizingmarketcapitalization.Sincethisconsumptionbasketincludeshealthcare,forexample,aswellasothersubstantialitemsthathavenoimportcomponent,theresultantdesiredweightinU.S.securitieswww.hackshp.cnwillbesmallerthanmarketcapitalizationwouldsuggest.CFACFAPROBLEMSPROBLEMS1.Initialinvestment=2,000×$1.50=$3,000Finalvalue=2,400×$1.75=$4,200Rateofreturn=($4,200/$3,000)−1=0.40=40%25-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter25-InternationalDiversification2.a.3.c.4.a.Theprimaryrationaleistheopportunityfordiversification.Factorsthatcontributetolowcorrelationsofstockreturnsacrossnationalboundariesare:i.imperfectcorrelationofbusinesscyclesii.imperfectcorrelationofinterestratesiii.imperfectcorrelationofinflationratesiv.exchangeratevolatilityb.Obstaclestointernationalinvestingare:i.Availabilityofinformation,includinginsufficientdataonwhichtobaseinvestmentdecisions.Interpretingandevaluatingdatathatisdifferentinformand/orcontentthantheroutinelyavailableandwidelyunderstoodU.S.dataisdifficult.Also,muchforeigndataisreportedwithaconsiderablelag.ii.Liquidity,intermsoftheabilitytobuyorsell,insizeandinatimelymanner,withoutaffectingthemarketprice.Mostforeignexchangesoffer(relativetoU.S.norms)limitedtrading,andexperiencegreaterpricevolatility.Moreover,onlya(relatively)smallnumberofindividualforeignstocksenjoyliquiditycomparabletothatintheU.S.,althoughthissituationisimprovingsteadily.iii.Transactioncosts,particularlywhenviewedasacombinationofcommissionplusspreadplusmarketimpactcosts,arewellaboveU.S.levelsinmostforeignmarkets.This,ofcourse,adverselyaffectsreturnrealization.iv.Politicalrisk.v.Foreigncurrencyrisk,althoughtoagreatextent,thiscanbehedged.c.Theasset-classperformancedataforthisparticularperiodrevealthatnon-U.S.dollar课后答案网bondsprovidedasmallincrementalreturnadvantageoverU.S.dollarbonds,butataconsiderablyhigherlevelofrisk.EachcategoryoffixedincomeassetsoutperformedtheS&P500IndexmeasureofU.S.equityresultswithregardtobothriskandreturn,whichiscertainlyanunexpectedoutcome.Withintheequityarea,non-U.S.stocks,representedbytheEAFEIndex,outperformedU.S.stocksbyaconsiderablemarginwww.hackshp.cnwithonlyslightlymorerisk.IncontrasttoU.S.equities,thisassetcategoryperformedasitshouldrelativetofixedincomeassets,providingmorereturnforthehigherriskinvolved.ConcerningtheAccountPerformanceIndex,itspositiononthegraphrevealsanaggregateoutcomethatissuperiortothesumofitscomponentparts.Tosomeextent,thisisduetothebeneficialeffectonperformanceresultingfrommulti-marketdiversificationandthedifferentialcovariancesinvolved.Inthiscase,theportfoliomanager(s)(apparently)achievedanon-balancepositivealpha,addingtototalportfolioreturnbytheiractions.Theadditionofinternational(i.e.,non-U.S.)securitiestoaportfoliothatwouldotherwisehaveheldonlydomestic(U.S.)securitiesclearlyworkedtotheadvantageofthisfundoverthistimeperiod.25-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter25-InternationalDiversification5.ThereturnontheCanadianbondisequaltothesumof:couponincome+gainorlossfromthepremiumordiscountintheforwardraterelativetothespotexchangerate+capitalgainorlossonthebond.Overthesix-monthperiod,thereturnis:Coupon+forwardpremium/discount+capitalgain=.750%+(−.075%)+Pricechangein%=3.00%+%capitalgain2TheexpectedsemiannualreturnontheU.S.bondis3.25%.SincetheU.S.bondissellingatparanditsyieldisexpectedtoremainunchanged,thereisnoexpectedcapitalgainorlossontheU.S.bond.Therefore,inordertoprovidethesamereturn,theCanadianbondmustprovideacapitalgainof0.25%(i.e.,1/4pointrelativetoparvalueof100)overandaboveanyexpectedcapitalgainontheU.S.bond.6.a.Weexchange$1millionforforeigncurrencyatthecurrentexchangerateandsellforwardtheamountofforeigncurrencywewillaccumulate90daysfromnow.Fortheyeninvestment,weinitiallyreceive:1million/0.0119=¥84.034millionInvestfor90daystoaccumulate:¥84.034×[1+(0.0252/4)]=¥84.563million(Notethatwedividethequoted90-dayrateby4becausequotedmoneymarketinterestratestypicallyareannualizedusingsimpleinterest,assuminga360-dayyear.)课后答案网Ifwesellthisnumberofyenforwardattheforwardexchangerateof0.0120¥//dollar,wewillendupwith:84.563million×0.0120=$1.0148millionThe90-daydollarinterestratewww.hackshp.cnis1.48%.Similarly,thedollarproceedsfromthe90-dayCanadiandollarinvestmentwillbe:1$million⎛.00674⎞×⎜1+⎟×.07269=.1$0148million.07284⎝4⎠The90-daydollarinterestrateis1.48%,thesameasthatintheyeninvestment.25-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter25-InternationalDiversificationb.Thedollar-hedgedrateofreturnondefault-freegovernmentsecuritiesinbothJapanandCanadais1.48%.Therefore,the90-dayinterestrateavailableonU.S.governmentsecuritiesmustalsobe1.48%.ThiscorrespondstoanAPRof5.92%,whichisgreaterthantheAPRinJapan,andlessthantheAPRinCanada.Thisresultmakessense,astherelationshipbetweenforwardandspotexchangeratesindicatesthattheU.S.dollarisexpectedtodepreciateagainsttheyenandappreciateagainsttheCanadiandollar.7.a.Incorrect.Therehavebeenperiodsofstrongperformancedespiteweakcurrencies.Itisalsopossiblethatanappreciatingcurrencycouldenhanceperformance.b.Correct.c.Correct.d.Incorrect.Correlationsarenotstableovertime.Also,theportfoliocanmovedramaticallyawayfromtheefficientfrontierfromoneperiodtothenext.8.a.Thefollowingargumentscouldbemadeinfavorofactivemanagement:Economicdiversity:thediversityoftheOtunianeconomyacrossvarioussectorsmayoffertheopportunityfortheactiveinvestortoemploy"topdown"sectortimingstrategies.Hightransactioncosts:veryhightransactioncostsmaydiscouragetradingactivitybyinternationalinvestorsandleadtoinefficienciesthatmaybeexploitedsuccessfully课后答案网byactiveinvestors.Goodfinancialdisclosureanddetailedaccountingstandards:goodfinancialdisclosureanddetailedaccountingstandardsmayprovidethewell-trainedanalystanopportunitytoperformfundamentalresearchanalysisinordertoidentifyinefficientlypricedsecurities.Capitalrestrictionswww.hackshp.cn:restrictionsoncapitalflowsmaydiscourageforeigninvestorparticipationandservetosegmenttheOtunianmarket,thuscreatingexploitablemarketinefficienciesfortheactiveinvestor.Developingeconomyandsecuritiesmarket:developingeconomiesandmarketsareoftencharacterizedbyinefficientlypricedsecuritiesandbyrapideconomicchangeandgrowth.Theactiveinvestormayexploitthesecharacteristics.Settlementproblems:longdelaysinsettlingtradesbynon-residentsmayservetodiscourageinternationalinvestors,leadingtoinefficientlypricedsecuritieswhichmaybeexploitedbyactivemanagement.25-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter25-InternationalDiversificationThefollowingargumentscouldbemadeinfavorofindexing:Economicdiversity:economicdiversityacrossabroadsectorofindustriesimpliesthatindexingmayprovideadiverserepresentativeportfoliothatisnotsubjecttotherisksassociatedwithconcentratedsectors.Hightransactioncosts:indexingwouldbefavoredbytheimpliedlowerlevelsoftradingactivityandcosts.Settlementproblems:indexingwouldbefavoredbytheimpliedlowerlevelsoftradingactivityandsettlementrequirements.Financialdisclosureandaccountingstandards:widepublicavailabilityofreliablefinancialinformationpresumablyleadstogreatermarketefficiency,reducingthevalueofbothfundamentalanalysisandactivemanagement,andfavoringindexing.Restrictionsofcapitalflows:indexingwouldbefavoredbytheimpliedlowerlevelsoftradingactivityandthussmalleropportunityforregulatoryinterference.b.Arecommendationforactivemanagementwouldfocusonshort-terminefficienciesin,andlongtermprospectsfor,thedevelopingOtunianmarketsandeconomy,inefficienciesandprospectswhichwouldnotgenerallybefoundinmoredevelopedmarkets.Arecommendationforindexingwouldfocusonthefactorsofeconomicdiversity,hightransactioncosts,settlementdelays,capitalflowrestrictions,andlowermanagementfees.课后答案网www.hackshp.cn25-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter26-HedgeFundsCHAPTER26:HEDGEHEDGEFUNDSFUNDSPROBLEMPROBLEMSETSSETS1.No,amarket-neutralhedgefundwouldnotbeagoodcandidateforaninvestor’sentireretirementportfoliobecausesuchafundisnotadiversifiedportfolio.Theterm‘market-neutral’referstoaportfoliopositionwithrespecttoaspecifiedmarketinefficiency.However,therecouldbearoleforamarket-neutralhedgefundintheinvestor’soverallportfolio;themarket-neutralhedgefundcanbethoughtofasanapproachfortheinvestortoaddalphatoamorepassiveinvestmentpositionsuchasanindexmutualfund.2.Theincentivefeeofahedgefundispartofthehedgefundcompensationstructure;theincentivefeeistypicallyequalto20%ofthehedgefund’sprofitsbeyondaparticularbenchmarkrateofreturn.Therefore,theincentivefeeresemblesthepayofftoacalloption,whichismorevaluablewhenvolatilityishigher.Consequently,thehedgefundportfoliomanagerismotivatedtotakeonhigh-riskassetsintheportfolio,therebyincreasingvolatilityandthevalueoftheincentivefee.3.Thereareanumberoffactorsthatmakeithardertoassesstheperformanceofahedgefundportfoliomanagerthanatypicalmutualfundmanager.Someofthesefactorsare:•Hedgefundstendtoinvestinmoreilliquidassetssothatanapparentalphamaybeinfactsimplycompensationforilliquidity.•Hedgefunds’valuationoflessliquidassets课后答案网isquestionable.•Survivorshipbiasandbackfillbiasresultinhedgefunddatabasesthatreportperformanceonlyformoresuccessfulhedgefunds.•Hedgefundstypicallyhaveunstableriskcharacteristicsmakingperformanceevaluationthatdependsonaconsistentriskprofileproblematic.•Taileventsskewthedistributionofhedgefundoutcomes,makingitdifficulttoobtainarepresentativesampleofreturnsoverrelativelyshortperiodsoftime.www.hackshp.cn4.No,statisticalarbitrageisnottruearbitragebecauseitdoesnotinvolveestablishingrisk-freepositionsbasedonsecuritymispricing.Statisticalarbitrageisessentiallyaportfolioofriskybets.Thehedgefundtakesalargenumberofsmallpositionsbasedonapparentsmall,temporarymarketinefficiencies,relyingontheprobabilitythattheexpectedreturnforthetotalityofthesebetsispositive.26-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter26-HedgeFunds5.Managementfee=0.02×$1billion=$20millionPortfoliorateIncentivefeeIncentivefeeTotalfeeTotalfeeofreturn(%)(%)($million)($million)(%)a.-500202b.000202c.500202d.1020103036.a.SincethehedgefundmanagerhasalongpositionintheWaterworksstock,heshouldsellsixcontracts,computedasfollows:$3,000,000×0.75=6contracts$250×1,500b.Thestandarddeviationofthemonthlyreturnofthehedgedportfolioisequaltothestandarddeviationoftheresiduals,whichis6%.Thestandarddeviationoftheresidualsforthestockisthevolatilitythatcannotbehedgedaway.Foramarket-neutral(zero-beta)position,thisisalsothetotalstandarddeviation.c.Theexpectedrateofreturnofthemarket-neutralpositionisequaltotherisk-freerateplusthealpha:0.5%+2.0%=2.5%Weassumethatmonthlyreturnsareapproximatelynormallydistributed.Thez-valueforarateofreturnofzerois:−2.5%/6.0%=−0.4167Therefore,theprobabilityofanegativereturn课后答案网is:N(−0.4167)=0.33857.a.Theresidualstandarddeviationoftheportfolioissmallerthaneachstock’sstandarddeviationbyafactorof100=10or,equivalently,theresidualvarianceoftheportfolioiswww.hackshp.cnsmallerbyafactorof100.So,insteadofaresidualstandarddeviationof6%,residualstandarddeviationisnow0.6%.b.Theexpectedreturnofthemarket-neutralpositionisstillequaltotherisk-freerateplusthealpha:0.5%+2.0%=2.5%Nowthez-valueforarateofreturnofzerois:−2.5%/0.6%=−4.1667Therefore,theprobabilityofanegativereturnis:N(−4.1667)=1.55×10−5Anegativereturnisveryunlikely.26-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter26-HedgeFunds8.a.Forthe(nowimproperly)hedgedportfolio:Variance=(0.252×52)+62=37.5625Standarddeviation=6.129%b.SincethemanagerhasmisestimatedthebetaofWaterworks,themanagerwillsellfourS&P500contracts(ratherthanthesixcontractsinProblem6):$3,000,000×0.50=4contracts$250×1,500Theportfolioisnotcompletelyhedgedsotheexpectedrateofreturnisnolonger2.5%.Wecandeterminetheexpectedrateofreturnbyfirstcomputingthetotaldollarvalueofthestockplusfuturesposition.Thedollarvalueofthestockportfoliois:$3,000,000×(1+rportfolio)=$3,000,000×[1+0.005+0.75(rM–0.005)+0.02+e]=$3,063,750+($2,250,000×rM)+($3,000,000×e)Thedollarproceedsfromthefuturespositionequal:4×$250×(F0−F1)=$1,000×[(S0×1.005)–S1]=$1,000×S0[1.005–(1+rM)]=$1,000×[1,500×(0.005–rM)]=$7,500−($1,500,000×rM)Thetotalvalueofthestockplusfuturespositionattheendofthemonthis:$3,071,250+($750,000×rM)+($3,000,000×e)=$3,071,250+($750,000×0.01)+($3,000,000×e)=课后答案网$3,078,750+($3,000,000×e)Theexpectedrateofreturnforthe(improperly)hedgedportfoliois:($3,078,750/$3,000,000)–1=0.02625=2.625%Nowthez-valueforaratewww.hackshp.cnofreturnofzerois:−2.625%/6.129%=−0.4283Theprobabilityofanegativereturnis:N(−0.4283)=0.3342Here,theprobabilityofanegativereturnisveryclosetotheprobabilitycomputedinProblem6.26-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter26-HedgeFundsc.Thevarianceforthediversified(butimproperlyhedged)portfoliois:(0.252×52)+0.62=1.9225Standarddeviation=1.3865%Thez-valueforarateofreturnofzerois:−2.625%/1.3865%=−1.8933Theprobabilityofanegativereturnis:N(−1.8933)=0.0292TheprobabilityofanegativereturnisnowfargreaterthantheresultwithproperhedginginProblem7.d.Themarketexposurefromimproperhedgingisfarmoreimportantincontributingtototalvolatility(andriskoflosses)inthecaseofthe100-stockportfoliobecausetheidiosyncraticriskofthediversifiedportfolioissosmall.9.Theincentivefeeistypicallyequalto20%ofthehedgefund’sprofitsbeyondaparticularbenchmarkrateofreturn.However,ifafundhasexperiencedlossesinthepast,thenthefundmaynotbeabletochargetheincentivefeeunlessthefundexceedsitsprevioushighwatermark.Theincentivefeeislessvaluableifthehigh-watermarkis$67,ratherthan$66.Withahigh-watermarkof$67,thenetassetvalueofthefundmustreach$67beforethehedgefundcanassesstheincentivefee.Thehigh-watermarkforahedgefundisequivalenttotheexercisepriceforacalloptiononanassetwithacurrentmarketvalueequaltothenetassetvalueofthefund.10.a.First,computetheBlackScholesvalueofacalloptionwiththefollowingparameters:课后答案网S0=62X=66R=0.04σ=0.50T=1yearwww.hackshp.cnTherefore:C=$11.685Thevalueoftheannualincentivefeeis:0.20×C=0.20×$11.685=$2.337b.HereweusethesameparametersusedintheBlack-Scholesmodelinpart(a)withtheexceptionthat:X=62Now:C=$13.253Thevalueoftheannualincentivefeeis0.20×C=0.20×$13.253=$2.65126-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter26-HedgeFundsc.HereweusethesameparametersusedintheBlack-Scholesmodelinpart(a)withtheexceptionthat:X=S0.040.040×e=62×e=64.5303Now:C=$12.240Thevalueoftheannualincentivefeeis0.20×C=0.20×$12.240=$2.448d.HereweusethesameparametersusedintheBlack-Scholesmodelinpart(a)withtheexceptionthat:X=62andσ=0.60Now:C=$15.581Thevalueoftheannualincentivefeeis0.20×C=0.20×$15.581=$3.11611.a.Thespreadsheetindicatesthattheend-of-monthvaluefortheS&P500inSeptember1977was96.53,sotheexercisepriceoftheputwrittenatthebeginningofOctober1977wouldhavebeen:0.95×96.53=91.7035AttheendofOctober,thevalueoftheindexwas92.34,sotheputwouldhaveexpiredoutofthemoneyandtheputwriter’spayoutwaszero.SinceitisunusualfortheS&P500tofallbymorethan5percentinonemonth,allbuttenofthe120monthsbetweenOctober1977andSeptember1987wouldhaveapayoutofzero.ThefirstmonthwithapositivepayoutwouldhavebeenJanuary1978.TheexercisepriceoftheputwrittenatthebeginningofJanuary1978wouldhavebeen:课后答案网0.95×95.10=90.3450AttheendofJanuary,thevalueoftheindexwas89.25(morethana6%decline),sotheoptionwriter’spayoutwouldhavebeen:90.3450–89.25=1.0950www.hackshp.cnTheaveragegrossmonthlypayoutfortheperiodwouldhavebeen0.2437andthestandarddeviationwouldhavebeen1.0951.26-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter26-HedgeFundsb.InOctober1987,theS&P500decreasedbymorethan21%,from321.83to251.79.TheexercisepriceoftheputwrittenatthebeginningofOctober1987wouldhavebeen:0.95×321.83=305.7385AttheendofOctober,theoptionwriter’spayoutwouldhavebeen:305.7385–251.79=53.9485TheaveragegrossmonthlypayoutfortheperiodOctober1977throughOctober1987wouldhavebeen0.6875andthestandarddeviationwouldhavebeen5.0026.Apparently,tailriskinnakedputwritingissubstantial.12.a.InordertocalculatetheSharperatio,wefirstcalculatetherateofreturnforeachmonthintheperiodOctober1982-September1987.TheendofmonthvaluefortheS&P500inSeptember1982was120.42,sotheexercisepricefortheOctoberputis:0.95×120.42=114.3990SincetheOctoberendofmonthvaluefortheindexwas133.72,theputexpiredoutofthemoneysothatthereisnopayoutforthewriteroftheoption.Therateofreturnthehedgefundearnsontheindexisthereforeequalto:(133.72/120.42)–1=0.11045=11.045%Assumingthatthehedgefundinveststhe$0.25millionpremiumalongwiththe$100millionbeginningofmonthvalue,thentheendofmonthvalueofthefundis:$100.25million×1.11045=$111.322millionTherateofreturnforthemonth课后答案网is:($111.322/$100.00)–1=0.11322=11.322%ThefirstmonththattheputexpiresinthemoneyisMay1984.TheendofmonthvaluefortheS&P500inApril1984was160.05,sotheexercisepricefortheMayputis:0.95×160.05=152.0475www.hackshp.cnTheMayendofmonthvaluefortheindexwas150.55,andthereforethepayoutforthewriterofaputoptionononeunitoftheindexis:152.0475–150.55=1.4975Therateofreturnthehedgefundearnsontheindexisequalto:(150.55/160.05)–1=-0.05936=–5.936%26-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter26-HedgeFundsThepayoutof1.4975perunitoftheindexreducesthehedgefund’srateofreturnby:1.4975/160.05=0.00936=0.936%Therateofreturnthehedgefundearnsisthereforeequalto:–5.936%–0.936%=–6.872%Theendofmonthvalueofthefundis:$100.25million×0.93128=$93.361millionTherateofreturnforthemonthis:($93.361/$100.00)–1=–0.06639=–6.639%FortheperiodOctober1982-September1987:Meanmonthlyreturn=1.898%Standarddeviation=4.353%Sharperatio=(1.898%–0.7%)/4.353%=0.275b.FortheperiodOctober1982-October1987:Meanmonthlyreturn=1.238%Standarddeviation=6.724%Sharperatio=(1.238%–0.7%)/6.724%=0.08013.a.,b.,c.Stand-HedgeHedgeHedgeFund课后答案网AloneFund1Fund2Fund3ofFundsFundStartofyearvalue(millions)$100.0$100.0$100.0$300.0$300.0Grossportfoliorateofreturn20%10%30%Endofyearvalue(beforefee)$120.0$110.0$130.0$360.0Incentivefee(Individualfunds)www.hackshp.cn$4.0$2.0$6.0$12.0Endofyearvalue(afterfee)$116.0$108.0$124.0$348.0$348.0Incentivefee(FundofFunds)$9.6Endofyearvalue(FundofFunds)$338.4Rateofreturn(afterfee)16.0%8.0%24.0%12.8%16.0%Notethattheendofyearvalue(after-fee)fortheStand-Alone(SA)FundisthesameastheendofyearvaluefortheFundofFunds(FF)beforeFFchargesitsextralayerofincentivefees.Therefore,theinvestor’srateofreturninSA(16.0%)ishigherthaninFF(12.8%)byanamountequaltotheextralayeroffees($9.6million,or3.2%)chargedbytheFundofFunds.26-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter26-HedgeFundsd.Stand-HedgeHedgeHedgeFundAloneFund1Fund2Fund3ofFundsFundStartofyearvalue(millions)$100.0$100.0$100.0$300.0$300.0Grossportfoliorateofreturn20%10%-30%Endofyearvalue(beforefee)$120.0$110.0$70.0$300.0Incentivefee(Individualfunds)$4.0$2.0$0.0$0.0Endofyearvalue(afterfee)$116.0$108.0$70.0$294.0$300.0Incentivefee(FundofFunds)$0.0Endofyearvalue(FundofFunds)$294.0Rateofreturn(afterfee)16.0%8.0%-30.0%-2.0%0.0%Now,theendofyearvalue(afterfee)forSAis$300,whiletheendofyearvalueforFFisonly$294,despitethefactthatneitherSAnorFFchargeanincentivefee.ThereasonforthedifferenceisthefactthattheFundofFundspaysanincentivefeetoeachofthecomponentportfolios.Ifevenoneoftheseportfoliosdoeswell,therewillbeanincentivefeecharged.Incontrast,SAchargesanincentivefeeonlyiftheaggregateportfoliodoeswell(atleastbetterthana0%return).Thefundoffundsstructurethereforeresultsintotalfeesatleastasgreatas(andusuallygreaterthan)thestand-alonestructure.课后答案网www.hackshp.cn26-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter27-TheTheoryofActivePortfolioManagementCHAPTER27:THETHETHEORYTHEORYTHEORYOFOFACTIVEACTIVEPORTFOLIOPORTFOLIOPORTFOLIOMANAGEMENTMANAGEMENTPROBLEMPROBLEMSETSSETS1.Viewsabouttherelativeperformanceofbondscomparedtostockscanhaveasignificantimpactonhowsecurityanalysisisconducted.Forexample,supposethat,asaresultofapredicteddecreaseininterestrates,bondsarenowexpectedtoperformbetterthanhadpreviouslybeenexpected.Inthisscenario,theperformanceforecastmayalsoreflectforecastsaboutthequality(credit)spreadsforbonds.Inadditiontotheimplicationsofmacroforecasts,theplayonyieldscanhaveimportantimplicationsforcorporationsinfinancialdistressthathavehighdegreesofleverage.Thehierarchyofuseofthemodelsuggestsatop-downanalysis,startingwiththeBLmodelinputs.Thisdoesnotruleoutfeedbackintheoppositedirectionif,forexample,thepreponderanceofsecurityanalysissuggestsanunexpectedlygood(orbad)economy(orsectoroftheeconomy).2.Thespecifictasksfortheeconometricsunitmightentailthefollowing:(1)Helpthemacroforecasterswiththeirforecastsforassetallocationandinsettingup‘views’fortheBLmodel.(2)HelptheQualityControlunittoestimateforecastingrecords.(3)Providearesourcetohandleanyproblemofstatisticsthatotherunitsmayencounter.3.Exerciselefttostudent;answerswillvary.课后答案网4.Exerciselefttostudent;answerswillvary.5.Toassignadollarvaluetoanimprovementinperformance,wewouldstartwiththeexpectedvalueofM2.Thisistheexpectedincrementalreturn(adjustedforrisk)fromactivemanagement.First,applythisincrementalMwww.hackshp.cn2tothedollarvalueoftheportfoliooverfutureperiods,and,second,computethepresentvalueofthesedollarincrementstodeterminethedollarvalueoftheactivity.Thus,weproceedtoobtaintheincrementalM2inatop-downmanner.FirstweneedtoestimatetheimprovementintheSharperatio.Thiscomesasaresultofanincreaseintheinformationratio(IR)oftheactiveportfolio.27-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter27-TheTheoryofActivePortfolioManagementTheactivityenvisionedinthisproblemamountstoanimprovementintheforecastingaccuracyofananalystwhoexaminesasetnumberofsecurities.ThislimitstheimprovementoftheoverallIRtothatofthosesecurities.(RecallthattheoverallsquaredIRisthesumofsquaredIRsoftheindividualsecurities.)Improvedaccuracymeansweassigngreaterweighttotheanalyst’sforecasts.ThisconstitutesanincrementtotheexpectedIRoftheanalyst.TheexpectedIRofsecuritiescoveredbytheanalyst(thatmayarisefromeitherpositiveornegativealphaforecasts)maybeobtainedintwoways:(1)directlyfromtheanalyst’spastforecasts;or,(2)fromestimatesofthedistributionofpastabnormalreturnsofthestockinquestion.(Notethatthiscouldbeanothertaskfortheeconometricsunit,asdiscussedinProblem2.)课后答案网www.hackshp.cn27-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteCHAPTER28:INVESTMENTINVESTMENTPOLICYPOLICYANDTHEFRAMEWORKFRAMEWORKOFOFOFTHETHETHECFACFACFAINSTITUTEINSTITUTEPROBLEMPROBLEMSETSSETS1.Youwouldadvisethemtoexploitallavailableretirementtaxshelters,suchas403b,401k,KeoghplansandIRAs.Sincetheywillnotbetaxedontheincomeearnedfromtheseaccountsuntiltheywithdrawthefunds,theyshouldavoidinvestingintax-preferredinstrumentslikemunicipalbonds.Iftheyareveryrisk-averse,theyshouldconsiderinvestingalargeproportionoftheirfundsininflation-indexedCDs,whichofferarisklessrealrateofreturn.2.a.Theleastriskyassetforapersoninvestingforherchild’scollegetuitionisanaccountdenominatedinunitsofcollegetuition.SuchanaccountistheCollegeSureCDofferedbytheCollegeSavingsBankofPrinceton,NewJersey.AunitofthisCDpays,atmaturity,anamountguaranteedtoequalorexceedtheaveragecostofayearofundergraduatetuition,asmeasuredbyanindexpreparedbytheCollegeBoard.b.Theleastriskyassetforadefinedbenefitpensionfundwithbenefitobligationsthathaveanaveragedurationoftenyearsisabondportfoliowithadurationoftenyearsandapresentvalueequaltothepresentvalueofthepensionobligation.Thisisanimmunizationstrategythatprovidesafuturevalueequalto(orgreaterthan)thepensionobligation,regardlessofthedirectionofchangeininterestrates.Notethatimmunizationrequiresperiodicrebalancingofthebondportfolio.c.Theleastriskyassetforadefinedbenefitpensionfundthatpaysinflation-protectedbenefitsisaportfolio课后答案网ofimmunizedTreasuryInflation-IndexedSecuritieswithadurationequaltothedurationofthepensionobligation(i.e.,inthisscenario,adurationoftenyears).(Note:ThesesecuritiesarealsoreferredtoasTreasuryInflation-ProtectedSecurities,orTIPS.)3.a.GeorgeMore’sexpectedaccumulationatage65:www.hackshp.cnniPVPMTFVFixedincome253%$100,000$1,500⇒FV=$264,067Commonstocks256%$100,000$1,500⇒FV=$511,484b.Expectedretirementannuity:niPVFVPMTFixedincome153%$264,0670⇒PMT=$22,120Commonstocks156%$511,4840⇒PMT=$52,66428-1若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstitutec.Inordertogetafixed-incomeannuityof$30,000peryear,hisaccumulationatage65wouldhavetobe:niPMTFVPVFixedincome153%$30,0000⇒PV=$358,138Hisannualcontributionwouldhavetobe:niPVFVPMTFixedincome253%$100,000-$358,138⇒PMT=$4,080Thisisanincreaseof$2,580peryearoverhiscurrentcontributionof$1,500peryear.4.a.Theanswertothisquestiondependsontheassumptionsmadeabouttheinvestor’seffectiveincometaxratesfortheperiodofaccumulationandfortheperiodofwithdrawals.First,weassumethat(i)taxratesremainconstantthroughouttheentiretimehorizon;and,(ii)theinvestor’staxableincomeremainsrelativelyconstantthroughout.Consequently,theinvestor’seffectivetaxratedoesnotchange,andwefindthattheRothIRAandtheconventionalIRAprovidethesameafter-taxbenefits.Alternatively,wemightconsiderascenarioinwhichahouseholdhasalowincomeearlyintheaccumulationperiodandhigherincomelaterintheaccumulationperiodandduringthewithdrawalperiod.Iftaxratesareconstantthroughoutthetimehorizon,thentheinvestor’seffectivetaxratewouldbelowerthroughouttheaccumulationperiodthanduringthewithdrawalperiod,and,asaresult,theRothIRAwouldprovidehigherafter-taxbenefits.Thisisaconsequenceofthefactthataninvestor’sRothIRAcontributionsduringtheaccumulationperiodaretaxedatthelowerrate,whilewithdrawalsfromaconventionalIRAwouldbetaxedatthehigherrate.Similarly,theconventionalIRAprovideshigherafter-taxbenefitsintheeventthattheeffectivetaxrateishigherduringtheaccumulationperiodthan课后答案网itisduringtheperiodofwithdrawals.Clearly,eachofthescenariosdescribedhererepresentsanextremelyunrealisticsimplification.Theissuebecomesmorecomplexifweconsiderthemanypossiblechanges,bothintaxlawandintheinvestor’sindividualcircumstances,thatcanhaveanimpactontheeffectivetaxrate.www.hackshp.cn28-2若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteb.FortheRothIRA,contributionsaremadewithafter-taxdollars,sothetaxrateisknown(andtaxesarepaid)duringtheaccumulationperiod;thetaxrateforwithdrawalsatretirementfromaRothIRAiszero,andisthereforealsoknownwithcertainty.Ontheotherhand,contributionstoaconventionalIRAduringtheaccumulationperiodaretax-free,butthetaxrateforwithdrawalsisnotknownuntilthewithdrawalsaremadeatretirement.ThistaxrateuncertaintyforaconventionalIRAhastwosources.First,theinvestorisunabletoanticipatelegislatedchangesinfuturetaxrates;and,second,eveniftaxratesweretoremainconstant,theinvestorcannotdetermineherfuturetaxbracketbecauseshecannotaccuratelyforecasthertaxableincomeatretirement.Consequently,theRothIRAprovidesprotectionagainsttax-rateuncertainty,whiletheconventionalIRAsubjectstheinvestortosubstantialtaxrateuncertainty.课后答案网www.hackshp.cn28-3若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteCFACFAPROBLEMSPROBLEMS1.a.i.ReturnRequirement:IPSYhastheappropriatelanguage.SincethePlaniscurrentlyunder-funded,theprimaryobjectiveshouldbetomakethepensionfundfinanciallystronger.Theriskinherentinattemptingtomaximizetotalreturnswouldbeinappropriate.ii.RiskTolerance:IPSYhastheappropriatelanguage.Becauseofthefund’sunder-fundedstatus,thePlanhaslimitedrisktolerance;shouldthefundincurasubstantialloss,paymentstobeneficiariescouldbejeopardized.iii.TimeHorizon:IPSYhastheappropriatelanguage.Althoughgoing-concernpensionplansusuallyhavealongtimehorizon,theAcmeplanhasashortertimehorizonbecauseofthereducedretirementageandtherelativelyhighmedianageoftheworkforce.iv.Liquidity:IPSXhastheappropriatelanguage.Becauseoftheearlyretirementfeaturestartingnextmonthandtheageoftheworkforce(whichindicatesanincreasingnumberofretireesinthenearfuture),thePlanneedsamoderatelevelofliquidityinordertofundmonthlybenefitpayments.b.Thecurrentportfolioisthemostappropriatechoiceforthepensionplan’sassetallocation.Thecurrentportfoliooffers:i.AnexpectedreturnthatexceedsthePlan’sreturnrequirement;ii.AnexpectedstandarddeviationthatonlyslightlyexceedsthePlan’starget;and,iii.Alevelofliquiditythatshouldbesufficientforfutureneeds.ThehigherexpectedreturnwillamelioratethePlan’sunder-fundedstatussomewhat,andthechangeinthefund’sriskprofilewillbeminimal.TheportfoliohassignificantallocationstoU.K.bonds(42percent)andlarge-capequities(13percent)inadditiontocash(5percent).Theavailability课后答案网ofthesehighlyliquidassetsshouldbesufficienttofundmonthlybenefitpaymentswhentheearlyretirementfeaturetakeseffectnextmonth,particularlyinviewofthestableincomeflowsfromtheseinvestments.TheGrahamportfoliooffers:i.AnexpectedreturnthatisslightlybelowthePlan’srequirement;ii.Anexpectedstandarddeviationthatwww.hackshp.cnissubstantiallybelowthePlan’starget;and,iii.Alevelofliquiditythatshouldbemorethansufficientforfutureneeds.GiventhePlan’sunder-fundedstatus,theportfolio’slevelofriskisunacceptable.28-4若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteTheMichaelportfoliooffers:i.AnexpectedreturnthatissubstantiallyabovethePlan’srequirement;ii.AnexpectedstandarddeviationthatfarexceedsthePlan’starget;andiii.Alevelofliquiditythatshouldbesufficientforfutureneeds.GiventhePlan’sunder-fundedstatus,theportfolio’slevelofriskisunacceptable.2.c.Liquidity3.b.Organizingthemanagementprocessitself.4.a.AnapproachtoassetallocationthatGSScoulduseistheonedetailedinthechapter.Itconsistsofthefollowingsteps:1.Specifyassetclassestobeincludedintheportfolio.Themajorclassesusuallyconsideredarethefollowing:Moneymarketinstruments(usuallycalledcash)Fixedincomesecurities(usuallycalledbonds)StocksRealestatePreciousmetalsOther2.Specifycapitalmarketexpectations.Thisstepconsistsofusingbothhistoricaldataandeconomicanalysistodetermineyourexpectationsoffutureratesofreturnovertherelevantholdingperiodontheassetstobeconsideredforinclusionintheportfolio.3.Derivetheefficientportfoliofrontier.Thisstepconsistsoffindingportfoliosthatachievethemaximumexpectedreturnforanygivendegreeofrisk.课后答案网4.Findtheoptimalassetmix.Thisstepconsistsofselectingtheefficientportfoliothatbestmeetsyourriskandreturnobjectiveswhilesatisfyingtheconstraintsyouface.b.Aguardianinvestortypicallyisanindividualwhowishestopreservethepurchasingpowerofhisassets.ExtremeguardianswouldbeexclusivelyinAAAshorttermcredits.www.hackshp.cnGSSshouldfirstdeterminehowlongthetimehorizonisandhowhighthereturnexpectationsare.Assumingalongtimehorizonand8-10%return(pretax)expectations,theportfoliocouldbeallocated30-40%bonds,30-40%stocks,andmodestallocationstoeachoftheotherassetgroups.28-5若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstitute5.a.OBJECTIVES1.ReturnTherequiredtotalrateofreturnfortheJUendowmentfundisthesumofthespendingrateandtheexpectedlong-termincreaseineducationalcosts:Spendingrate=$126million(currentspendingneed)dividedby($2,000millioncurrentfundbalanceless$200millionlibrarypayment)=$126million/$1,800million=7percentTheexpectededucationalcostincreaseis3percent.Thesumofthetwocomponentsis10percent.Achievingthisrelativelyhighreturnwouldensurethattheendowment’srealvalueismaintained.2.RiskEvaluationofrisktolerancerequiresanassessmentofboththeabilityandthewillingnessoftheendowmenttotakerisk.Ability:AverageRisk•Endowmentfundsarelong-terminnature,havinginfinitelives.Thislongtimehorizonbyitselfwouldallowforabove-averagerisk.•However,creativetensionexistsbetweentheJUendowment’sdemandforhighcurrentincometomeetimmediatespendingrequirementsandtheneedforlong-termgrowthtomeetfuturerequirements.Thisneedforaspendingrate(inexcessof5percent)andtheuniversity’sheavydependenceonthosefundsallowforonlyaveragerisk.Willingness:AboveAverageRisk•Universityleadersandendowmentdirectorshavesetaspendingrateinexcessof5percent.Toachievetheir7percentrealrateofreturn,thefundmustbeinvestedin课后答案网above-averagerisksecurities.Thus,the7percentspendingrateindicatesawillingnesstotakeabove-averagerisk.•Inaddition,thecurrentportfolioallocation,withitslargeallocationstodirectrealestateandventurecapital,indicatesawillingnesstotakeabove-averagerisk.Takingbothabilityandwillingnessintoconsideration,theendowmentwww.hackshp.cn’srisktoleranceisbestcharacterizedas“aboveaverage.”CONSTRAINTS1.TimeHorizon.Atwo-stagetimehorizonisneeded.Thefirststagerecognizesshort-termliquidityconstraints($200millionlibrarypaymentineightmonths).Thesecondstageisaninfinitetimehorizon(endowmentfundsareestablishedtoprovidepermanentsupport).28-6若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstitute2.Liquidity.Generally,endowmentfundshavelongtimehorizons,andlittleliquidityisneededinexcessofannualdistributionrequirements.However,theJUendowmentrequiresliquidityfortheupcominglibrarypaymentinadditiontothecurrentyear’scontributiontotheoperatingbudget.Liquidityneedsforthenextyearare:LibraryPayment+$200millionOperatingBudgetContribution+$126millionAnnualPortfolioIncome−$29millionTotal+$297millionAnnualportfolioincome=(0.04×$40million)+(0.05×$60million)+(0.01×$300million)+(0.001×$400million)+(0.03×$700million)=$29million3.Taxes.U.S.endowmentfundsaretax-exempt.4.Legal/Regulatory.U.S.endowmentfundsaresubjecttopredominantlystate(butsomefederal)regulatoryandlegalconstraints,andstandardsofprudencegenerallyapply.RestrictionsimposedbyBremnermayposealegalconstraintonthefund(nomorethan25percentoftheinitialBertocchiOilandGassharesmaybesoldinanyone-yearperiod).5.UniqueCircumstances.Only25percentofdonatedBertocchiOilandGassharesmaybesoldinanyone-yearperiod(constraintimposedbydonor).Asecondaryconsiderationistheneedtobudgettheone-time$200millionlibrarypaymentineightmonths.b.U.S.MoneyMarketFund:15%(Range:14%-17%)Liquidityneedsforthenextyearare:Librarypayment课后答案网+$200millionOperatingbudgetcontribution+$126millionAnnualportfolioincome−$29millionTotal+$297millionTotalliquidityofatleast$297millionisrequired(14.85percentofcurrentendowmentassets).Additionalallocations(morethan2percentabovethesuggested15percent)www.hackshp.cnwouldbeoverlyconservative.Thiscushionshouldbesufficientforanytransactionneeds(i.e.,mismatchofcashinflows/outflows).IntermediateGlobalBondFund:20%(Range:15%-25%)Toachievea10percentportfolioreturn,thefundneedstotakeaboveaveragerisk(e.g.,20percentinGlobalBondFundand30percentinGlobalEquityFund).Anallocationbelow15percentwouldinvolvetakingunnecessaryriskthatwouldputthesafetyandpreservationoftheendowmentfundinjeopardy.Anallocationinthe21percentto25percentrangecouldstillbetoleratedbecausetheslightreductioninportfolioexpectedreturnwouldbepartiallycompensatedbythereductioninportfoliorisk.Anallocationabove25percentwouldnotsatisfytheendowmentfundreturnrequirements.28-7若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteGlobalEquityFund:30%(Range:25%-35%)Toachievea10percentportfolioreturn,thefundneedstotakeaboveaveragerisk(e.g.,30percentinGlobalEquityFundand20percentinGlobalBondFund).Anallocationabove35percentwouldinvolvetakingunnecessaryriskthatwouldputthesafetyandpreservationoftheendowmentfundinjeopardy.Anallocationinthe25percentto29percentrangecouldstillbetolerated,astheslightreductioninportfolioexpectedreturnwouldbepartiallycompensatedbythereductioninportfoliorisk.Anallocationbelow25percentwouldnotsatisfytheendowmentfundreturnrequirements.BertocchiOilandGasCommonStock:15%Thereisasingleissuerconcentrationriskassociatedwiththecurrentallocation,anda25percentreduction($100million),whichisthemaximumreductionallowedbythedonor,isrequired($400million−$100million=$300millionremaining).DirectRealEstate:10%VentureCapital:10%Thesuggestedallocations(pointestimates)wouldallowtheJUendowmentfundtomeetthe10percentreturnrequirement,calculatedasfollows:SuggestedExpectedWeightedAssetAllocationReturnReturnU.S.MoneyMarketFund0.154.0%0.60%IntermediateGlobalBondFund0.205.0%1.00%GlobalEquityFund0.3010.0%3.00%BertocchiCommonStock0.1515.0%2.25%DirectRealEstate0.1011.5%1.15%VentureCapital0.1020.0%2.00%Total1.0010.000%Theallowableallocationranges,takeninpropercombination,wouldalsobeconsistentwiththe10percentreturnrequirement.课后答案网6.a.Overview.Fairfaxis58yearsoldandhassevenyearsuntilaplannedretirement.Shehasafairlylavishlifestylebutfewmoneyworries.Herlargesalarypaysallcurrentexpenses,andshehasaccumulated$2millionincashequivalentsfromsavingsinpreviousyears.Herhealthisexcellent,andherhealthinsurancecoveragewillcontinueafterretirementandisemployerpaid.WhileFairfax’sjobisahigh-levelone,sheisnotwellversedininvestmentmattersandwww.hackshp.cnhashadthegoodsensetoconnectwithprofessionalcounseltostartplanningforherinvestmentfuture,afuturethatiscomplicatedbyownershipofa$10millionblockofcompanystockthat,whilelistedontheNYSE,paysnodividendsandhasazero-costbasisfortaxpurposes.Allsalary,investmentincome(exceptinterestonmunicipalbonds)andrealizedcapitalgainsaretaxedtoFairfaxata35percentrate;thistaxrateanda4percentinflationrateareexpectedtocontinueintothefuture.Fairfaxwouldaccepta3percentreal,after-taxreturnfromtheinvestmentportfoliotobeformedfromher$2millioninsavings(“theSavingsPortfolio”)ifthatreturncouldbeobtainedwithonlymodestportfoliovolatility(i.e.,lessthana10percentannualdecline).Sheisdescribedasbeing“conservativeinallthings.”28-8若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteOBJECTIVES•ReturnRequirement.Fairfax’sneedforportfolioincomebeginssevenyearsfromnow,atthedateofretirement.TheinvestmentfocusforherSavingsPortfolioshouldbeongrowingtheportfolio’svalueintheinteriminawaythatprovidesprotectionagainstlossofpurchasingpower.Her3%real,after-taxreturnpreferenceimpliesagrosstotalreturnrequirementofatleast10.8%,assumingherinvestmentsarefullytaxable(asisthecasenow)andassuming4%inflationanda35percenttaxrate.ForFairfaxtomaintainhercurrentlifestyle,then,atretirement,shewouldhavetogenerateinflation-adjustedannualincomeof:7$500,000×1.04=$658,000IfthemarketvalueofReston’sstockdoesnotchange,andifsheisabletoearna10.8%returnontheSavingsPortfolio(or7%nominalafter-taxreturn),then,byretirementage,sheshouldaccumulate:$10,000,000+($2,000,000×1.077)=$13,211,500Togenerate$658,000peryear,a5.0%returnonthe$13,211,500wouldbeneeded.•RiskTolerance.TheinformationprovidedindicatesthatFairfaxisquiteriskaverse;shedoesnotwanttoexperienceadeclineofmorethan10%inthevalueoftheSavingsPortfolioinanygivenyear.Thiswouldindicatethattheportfolioshouldhavebelowaverageriskexposureinordertominimizeitsdownsidevolatility.Intermsofoverallwealth,Fairfaxcouldaffordtotakemorethanaveragerisk,butbecauseofherpreferencesandthenon-diversifiednatureofthetotalportfolio,abelow-averageriskobjectiveisappropriatefortheSavingsPortfolio.Itshouldbenoted,however,thattrulymeaningfulstatementsabouttheriskofFairfax’stotalportfolioaretiedtoassumptionsregardingboththevolatilityofReston’sstock(ifitisretained)andwhenandatwhatpricetheRestonstockwillbesold.BecausetheRestonholdingconstitutes83%ofFairfax’stotal课后答案网portfolio,itwilllargelydeterminetherisksheactuallyexperiencesaslongasthisholdingremainsintact.CONSTRAINTS•TimeHorizon.TwotimehorizonsareapplicabletoFairfax’slife.ThefirsttimehorizonrepresentstheperiodduringwhichFairfaxshouldsetupherfinancialsituationinpreparationforthebalanceofthesecondtimehorizon,herretirementperiodofindefinitelength.www.hackshp.cnOfthetwohorizons,thelongertermtotheexpectedendofherlifeisthedominanthorizonbecauseitisoverthisperiodthattheassetsmustfulfilltheirprimaryfunctionoffundingherexpenses,asanannuity,inretirement.•Liquidity.Withliquiditydefinedeitherasincomeneedsorascashreservestomeetemergencyneeds,Fairfax’sliquidityrequirementisminimal.Fivehundredthousanddollarsofsalaryisavailableannually,healthcostconcernsarenonexistent,andweknowofnoplannedneedsforcashfromtheportfolio.28-9若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstitute•Taxes.Fairfax’staxableincome(salary,taxableinvestmentincome,andrealizedcapitalgainsonsecurities)istaxedata35%rate.Carefultaxplanningandcoordinationwithinvestmentplanningisrequired.Investmentstrategyshouldincludeseekingincomethatisshelteredfromtaxesandholdingsecuritiesforlengthytimeperiodsinordertoproducelargerafter-taxreturns.SaleoftheRestonstockwillhavesizeabletaxconsequencesbecauseFairfax’scostbasisiszero;specialplanningwillbeneededforthiseventuality.Fairfaxmaywanttoconsidersomeformofcharitablegiving,eitherduringherlifetimeoratdeath.Shehasnoimmediatefamily,andweknowofnootherpotentialgiftorbequestrecipients.•LawsandRegulations.Fairfaxshouldbeawareof,andabideby,anysecurities(orother)lawsorregulationsrelatingtoher“insider”statusatRestonandherholdingofRestonstock.Althoughthereisnotrustinstrumentinplace,ifFairfax’sfutureinvestingishandledbyaninvestmentadvisor,theresponsibilitiesassociatedwiththePrudentPersonRulewillcomeintoplay,includingtheresponsibilityforinvestinginadiversifiedportfolio.Also,shehasaneedtoseekestateplanninglegalassistance,eventhoughtherearenoapparentgiftorbequestrecipients.•UniqueCircumstancesand/orPreferences.ThevalueoftheRestonstockdominatesthevalueofFairfax’sportfolio.Awell-definedexitstrategyneedstobedevelopedforthestockassoonasispracticalandappropriate.Ifthevalueofthestockincreases,oratleastdoesnotdeclinebeforeitisliquidated,Fairfax’spresentlifestylecanbemaintainedafterretirementwiththecombinedportfolio.AsignificantandprolongedsetbackforRestonIndustries,however,couldhavedisastrousconsequences.SuchcircumstanceswouldrequireadramaticdownscalingofFairfax’slifestyleorgenerationofalternatesourcesofincomeinordertomaintainhercurrentlifestyle.Aworst-casescenariomightbecharacterizedbya50%dropinthemarketvalueofReston’sstockandsaleofthatstocktodiversifytheportfolio,wherethesaleproceedswouldbesubjecttoa35%taxrate.Inthisscenario,thenetproceeds课后答案网oftheRestonpartoftheportfoliowouldbe:$10,000,000×0.5×(1−0.35)=$3,250,000WhenaddedtotheSavingsPortfolio,totalportfoliovaluewouldbe$5,250,000.Forthisportfoliotogenerate$658,000inincome,a12.5%returnwouldberequired.Synopsis.ThepolicygoverninginvestmentinFairfax’sSavingsPortfoliowillputemphasisonrealizinga3%real,after-taxreturnfromamixwww.hackshp.cnofhigh-qualityassetswithlessthanaveragerisk.OngoingattentionwillbegiventoFairfax’staxplanningandlegalneeds,herprogresstowardretirement,andthevalueofherRestonstock.TheRestonstockholdingisauniquecircumstanceofdecisivesignificanceinthissituation.Developmentsshouldbemonitoredclosely,andprotectionagainsttheeffectsofaworst-casescenarioshouldbeimplementedassoonaspossible.28-10若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteb.Critique.TheCoastalproposalproducesareal,after-taxexpectedreturnofapproximately5.18%,whichexceedsthe3%levelsoughtbyFairfax.Theexpectedreturnforthisproposalcanbecalculatedbyfirstsubtractingthetax-exemptyieldfromthetotalcurrentyield:4.9%−0.55%=4.35%Next,convertthistoanafter-taxyield:4.35%×(1−0.35)=2.83%Thetaxexemptincomeisthenaddedbacktothetotal:2.83%+0.55%=3.38%Theappreciationportionofthereturn(5.8%)isthenaddedtotheafter-taxyieldtogetthenominalportfolioreturn:3.38%+5.80%=9.18%Finally,the4%inflationrateissubtractedtoproducetheexpectedrealafter-taxreturn:9.18%–4.0%=5.18%Thisresultcanalsobeobtainedbycomputingthesereturnsforeachoftheindividualholdings,weightingeachresultbytheportfoliopercentageandthenaddingtoderiveatotalportfolioresult.Fromthedataavailable,itisnotpossibletodeterminespecificallytheinherentdegreeofportfoliovolatility.Despitemeetingthereturncriterion,theallocationisneitherrealisticnor,initsdetail,appropriatetoFairfax’ssituationinthecontextofaninvestmentpolicyusefullyapplicabletoher.Theprimaryweaknessesarethefollowing:•AllocationofEquityAssets.ExposuretoequityassetswillbenecessaryinordertoachievethereturnrequirementsspecifiedbyFairfax;however,greaterdiversificationoftheseassetsamongotherequityclassesisneededtoproduceamoreefficient,potentiallylessvolatileportfoliothatwouldmeetbothherrisktoleranceparametersandherreturnrequirements.AnallocationthatfocusesequityinvestmentsinU.S.large-capand/orsmall-capholdingsandalsoincludessmallerinternationalandRealEstateInvestmentTrustexposureismorelikelytoachievethereturnandrisktolerancegoals.Ifmoreinformationwereavailableconcerningthereturnsandvolatilityofthe课后答案网Restonstock,anargumentcouldbemadethatthisholdingistheU.S.equitycomponentofherportfolio.ButthelackofinformationonthisissueprecludestakingitintoaccountfortheSavingsPortfolioallocationandcreatestheneedforbroaderequitydiversification.•Cashallocation.Withintheproposedfixed-incomecomponent,the15%allocationwww.hackshp.cntocashisexcessivegiventhelimitedliquidityrequirementandthelowreturnforthisassetclass.•Corporate/MunicipalBondAllocation.Thecorporatebondallocation(10percent)isinappropriategivenFairfax’staxsituationandthesuperiorafter-taxyieldonmunicipalbondsrelativetocorporate(5.5%vs.4.9%after-taxreturn).•VentureCapitalAllocation.TheallocationtoventurecapitalisquestionablegivenFairfax’spolicystatementindicatingthatsheisquiteriskaverse.Althoughventurecapitalmayprovidediversificationbenefits,venturecapitalreturnshistoricallyhavebeenmorevolatilethanotherriskyassetssuchasU.S.large-andsmall-capstocks.Hence,evenasmallpercentageallocationtoventurecapitalmaybeinappropriate.28-11若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstitute•LackofRisk/VolatilityInformation.Theproposalconcentratesonreturnexpectationsandignoresrisk/volatilityimplications.Specifically,theproposalshouldhaveaddressedtheexpectedvolatilityoftheentireportfoliotodeterminewhetheritfallswithintherisktoleranceparametersspecifiedbyFairfax.c.i.Fairfaxhasstatedthatsheisseekinga3%real,after-taxreturn.Table28Gprovidesnominal,pre-taxfigures,whichmustbeadjustedforbothtaxesandinflationinordertoascertainwhichportfoliosmeetFairfax’sreturnobjective.Asimplesolutionistosubtractthemunicipalbondreturncomponentfromthestatedreturn,thensubjecttheresultingfiguretoa35%taxrate,andthenaddbacktax-exemptmunicipalbondincome.Thisproducesanominal,after-taxreturn.Finally,subtract4%percentinflationtoarriveatthereal,after-taxreturn.Forexample,AllocationAhasarealafter-taxreturnof3.4%,calculatedasfollows:{[0.099–(0.072×0.4)]×(1-0.35)}+(0.072×0.4)–0.04=3.44%Alternatively,thiscanbecalculatedasfollows:multiplythetaxablereturnsbytheirrespectiveallocations,sumtheseproducts,adjustforthetaxrate,addtheresulttotheproductofthenontaxable(municipalbond)returnanditsallocation,anddeducttheinflationratefromthissum.ForAllocationA:[(0.045×0.10)+(0.13×0.20)+(0.15×0.10)+(0.15×0.10)+(0.10×0.10)]×(1−0.35)+[(0.072×0.4)]–0.04=3.46%AllocationReturnMeasureABCDENominalReturn9.9%11.0%8.8%14.4%10.3%RealAfter-TaxReturn3.5%3.1%2.5%5.3%3.5%Table28Galsoprovidesafter-taxreturnsthatcouldbeadjustedforinflationandthenusedtoidentifythoseportfoliosthatmeetFairfax’sreturnguidelines.AllocationsA,B,D,and课后答案网EmeetFairfax’sreal,after-taxreturnobjectives.ii.Fairfaxhasstatedthataworstcasereturnof–10%inany12-monthperiodwouldbeacceptable.Theexpectedreturnlesstwotimestheportfoliorisk(expectedstandarddeviation)istherelevantrisktolerancemeasure.Inthiscase,threeallocationsmeetthecriterion:A,C,andE.www.hackshp.cnAllocationParameterABCDEExpectedReturn9.9%11.0%8.8%14.4%10.3%Exp.Std.Deviation9.4%12.4%8.5%18.1%10.1%WorstCaseReturn−8.9%−13.8%−8.2%−21.8%−9.9%d.i.TheSharpeRatioforAllocationD,usingthecashequivalentrateof4.5percentastherisk-freerate,is:(0.144−0.045)/0.181=0.547ii.ThetwoallocationswiththebestSharpeRatiosareAandE;theratioforeachoftheseallocationsis0.574.28-12若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstitutee.TherecommendedallocationisA.Theallocationsthatmeetboththeminimumreal,after-taxobjectiveandthemaximumrisktoleranceobjectiveareAandE.TheseallocationshaveidenticalSharpeRatiosandbothoftheseallocationshavelargepositionsinmunicipalbonds.However,AllocationEalsohasalargepositioninREITs,whereasthecomparableequitypositionforAllocationAisadiversifiedportfoliooflargeandsmallcapdomesticstocks.BecauseofthediversificationvalueofthelargeandsmallstockpositionsinAllocationA,asopposedtothespecializedornon-diversifiednatureofREITstocksandtheirlimiteddatahistory,onewouldhavegreaterconfidencethattheexpectationaldataforthelarge-andsmall-capstockportfolioswillberealizedthanfortheREITportfolio.7.a.Thekeyelementsthatshoulddeterminethefoundation’sgrant-making(spending)policyare:1.Averageexpectedinflationoveralongtimehorizon;2.Averageexpectednominalreturnontheendowmentportfoliooverthesamelonghorizon;and,3.The5%-of-asset-valuepayoutrequirementimposedbytaxauthoritiesasaconditionforongoingU.S.taxexemption,arequirementthatisexpectedtocontinueindefinitely.Topreservetherealvalueofitsassetsandtomaintainitsspendinginrealterms,thefoundationcannotpayoutmore,onaverageovertime,thantherealreturnitearnsfromitsinvestmentportfolio,sincenofund-raisingactivitiesarecontemplated.Ineffect,theportionofthetotalreturnrepresentingtheinflationratemustberetainedandreinvestedifthefoundation’sprincipalistogrowwithinflationand,thus,maintainitsrealvalueandtherealvalueoffuturegrants.b.OBJECTIVESReturnRequirement课后答案网:Productionofcurrentincome,thecommittee’sfocusbeforeMr.Franklin’sgift,isnolongeraprimaryobjective,giventheincreaseintheassetbaseandtheCommittee’sunderstandingthatinvestmentpolicymustaccommodatelong-termaswellasshort-termgoals.Theneedforaminimumannualpayoutequalto5%ofassetsmustbeconsidered,aswellastheneedtomaintaintherealvalueoftheseassets.Atotalwww.hackshp.cnreturnobjective(roughlyequaltothegrantrateplustheinflationrate,butnotlessthanthe5%requiredformaintenanceofthefoundation’stax-exemptstatus)isappropriate.RiskTolerance:Theincreaseinthefoundation’sfinancialflexibilityarisingfromMr.Franklin’sgiftandthecommittee’sspendingpolicychangehaveincreasedthefoundation’sabilitytoassumerisk.Theorganizationhasamoreorlessinfiniteexpectedlifespanand,inthecontextofthislong-termhorizon,hastheabilitytoaccepttheconsequencesofshort-termfluctuationsinassetvalues.Moreover,adoptionofaclear-cutspendingrulewillpermitcashflowstobeplannedwithsomeprecision,addingstabilitytoannualbudgetingandreducingtheneedforprecautionaryliquidity.Overall,thefoundation’srisktoleranceisaboveaverageandorientedtolong-termconsiderations.28-13若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteCONSTRAINTSLiquidityRequirements:Liquidityneedsarelow,withlittlelikelihoodofunforeseendemandsrequiringeitherforcedassetsalesorimmensecash.Suchneedsasexist,principallyforannualgrant-making,areknowninadvanceandrelativelyeasytoplanforinasystematicway.TimeHorizon:Thefoundationhasavirtuallyinfinitelife;theneedtoplanforfutureaswellascurrentfinancialdemandsjustifiesalong-termhorizonwithperhapsafiveyearcycleofplanningandreview.Taxes:Tax-exemptunderpresentU.S.lawiftheannualminimumpayoutrequirement(currently5%ofassetvalue)ismet.LegalandRegulatory:GovernedbystatelawandPrudentPersonstandards;ongoingattentionmustbepaidtomaintainingthetax-exemptstatusbystrictobservanceofIRSandanyrelatedFederalregulations.UniqueCircumstances:Theneedtomaintainrealvalueaftergrantsisakeyconsideration,asisthe5%ofassetsrequirementfortaxexemption.Therealreturnachievedmustmeetorexceedthegrantrate,withthe5%levelaminimumrequirement.Narrative:Investmentactionsshalltakeplaceinalong-term,tax-exemptcontext,reflectaboveaveragerisktolerance,andemphasizeproductionofrealtotalreturns,butwithatleasta5%nominalreturn.c.Tomeetrequirementsofthisscenario,itisfirstnecessarytoidentifyaspendingratethatisbothsufficient(i.e.,5%orhigherinnominalterms)andfeasible(i.e.,prudentandattainableunderthecircumstancesrepresentedbytheTable26Hdataandtheempiricalevidenceofhistoricalriskandreturnforthevariousassetclasses).Therealreturnfromtherecommendedallocationshouldbeshowntoequalorexceedtheminimumpayoutrequirement(i.e.,equaltoorgreaterthan5%innominalterms).课后答案网Theallocationphilosophywillreflectthefoundation’sneedforrealreturnsatorabovethegrantrate,itstotalreturnorientation,itsaboveaveragerisktolerance,itslowliquidityrequirements,anditstaxexemptstatus.WhiletheTable26Hdataandhistoricalexperienceprovideneededinputstotheprocess,severalgeneralizationsarealsoappropriate:www.hackshp.cn1.Allocationstofixedincomeinstrumentswillbelessthan50%asbondshaveprovidedinferiorrealreturnsinthepast,andwhileforecastedrealreturnsfrom1993to2000arehigher,theyarestilllowerthanforstocks.Realreturnneedsarehighandliquidityneedsarelow.Bondswillbeincludedprimarilyfordiversificationandriskreductionpurposes.Theongoingcashflowfrombondportfoliosofthissizeshouldeasilyprovideforallnormalworkingcapitalneeds.2.Allocationstoequitieswillbegreaterthan50%,andthisassetclasswillbetheportfolio’s“workhorseasset.”Expectedandhistoricalrealreturnsarehigh,thehorizonislong,risktoleranceisaboveaverage,andtaxesarenotaconsideration.28-14若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstitute3.Withintheequityuniversethereisroominthissituationforsmall-capaswellaslarge-capissues,forinternationalaswellasdomesticissuesand,perhaps,forventurecapitalinvestmentaswell.Diversificationwillcontributetoriskreduction,andtotalreturncouldbeenhanced.Allcouldbeincluded.4.Givenitsvalueasanalternativetostocksandbondsasawaytomaintainrealreturnandprovidediversificationbenefits,realestatecouldbeincludedinthisportfolio.Inalongtermcontext,realestatehasprovidedgoodinflationprotection,helpingtoprotectrealreturnproduction.Anexampleofanappropriate,modestlyaggressiveallocationisshownbelow.Table28Hcontainsanarrayofhistoricalandexpectedreturndatawhichwasusedtodeveloprealreturnforecasts.Inthiscase,theobjectivewastoreachaspendinglevelinrealtermsascloseto6%aspossible,alevelappearingtomeetthedualgoalsofthecommitteeandthatisalsofeasible.Theactualexpectedrealportfolioreturnis5.8%.IntermediateTermRecommendedRealReturnForecastofAllocationContributionRealReturnsCash(U.S.)Tbills0.7%*0%Bonds:Intermediate2.350.115%LongTreasury4.2100.420Corporate5.3100.530International4.9100.490Stocks:LargeCap5.5301.650SmallCap8.5100.850International6.6100.660VentureCapital课后答案网12.050.600RealEstate5.0100.500TotalExpectedReturn100%5.815%*Nocashisincludedbecauseongoingcashflowfromtheportfolioshouldbesufficienttomeetallnormalworkingcapitalneeds.www.hackshp.cn8.a.TheMaclins’overallriskobjectivemustconsiderbothwillingnessandabilitytotakerisk.Willingness:TheMaclinshaveabelow-averagewillingnesstotakerisk,basedontheirunhappinesswiththeportfoliovolatilityinrecentyearsandtheirdesiretoavoidshortfallriskinexcessof–12percentreturninanyoneyearinthevalueoftheinvestmentportfolio.28-15若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteAbility:TheMaclinshaveanaverageabilitytotakerisk.Whiletheirlargeassetbaseandalongtimehorizonwouldotherwisesuggestanabove-averageabilitytotakerisk,theirlivingexpenses(£74,000)aresignificantlygreaterthanChristopher’safter-taxsalary(£48,000),causingthemtobeverydependentonprojectedportfolioreturnstocoverthedifference,andtherebyreducingtheirabilitytotakerisk.Overall:TheMaclins’overallrisktoleranceisbelowaverage,astheirbelow-averagewillingnesstotakeriskdominatestheiraverageabilitytotakeriskindeterminingtheiroverallrisktolerance.b.TheMaclins’returnobjectiveistogrowtheportfoliotomeettheireducationalandretirementneedsaswellastoprovideforongoingnetexpenses.TheMaclinswillrequireannualafter-taxcashflowsof£26,000(calculatedbelow)tocoverongoingnetexpenses,andtheywillneed£2millionin18yearstofundtheirchildren’seducationandtheirownretirement.Tomeetthisobjective,theMaclins’pre-taxrequiredreturnis7.38percent,whichiscalculatedbelow.Theafter-taxreturnrequiredtoaccumulate£2millionin18years,beginningwithaninvestablebaseof£1,235,000(calculatedbelow)andwithannualoutflowsof£26,000,is4.427percent.Whenadjustedforthe40percenttaxrate,thisresultsina7.38percentpretaxreturn:4.427%/(1−0.40)=7.38%AnnualCashFlow=–£26,000Christopher’sAnnualSalary80,000Less:Taxes(40%)–32,000LivingExpenses–74,000NetAnnualCashFlow–£26,000AssetBase=£1,235,000Inheritance900,000BarnettCo.CommonStock220,000StocksandBonds课后答案网160,000Cash5,000Subtotal£1,285,000LessOne-timeNeeds:DownPaymentonHouse–30,000CharitableDonationwww.hackshp.cn–20,000TotalAssets£1,235,000Note:NoinflationadjustmentisrequiredinthereturncalculationbecauseincreasesinlivingexpenseswillbeoffsetbyincreasesinChristopher’ssalary.28-16若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstitutec.TheMaclins’investmentpolicystatementshouldincludethefollowingconstraints:i.Timehorizon:TheMaclinshaveatwo-stagetimehorizonbecauseoftheirchangingcashflowandresourceneeds.Thefirststageisthenext18years.Thesecondstagebeginswiththeirretirementandtheuniversityeducationyearsfortheirchildren.ii.Liquidityrequirements:TheMaclinshaveone-timeimmediateexpenses(£50,000)thatincludethedepositonthehousetheyarepurchasingandthecharitabledonationinhonorofLouise’sfather.iii.Taxconcerns:TheU.K.hasa40percentmarginaltaxrateonbothordinaryincomeandcapitalgains.Thereforethereisnopreferenceforinvestmentreturnsfromtaxabledividendsorinterestovercapitalgains.Taxeswillbeadragoninvestmentperformancebecauseallexpenditureswillbeaftertax.iv.Uniquecircumstances:ThelargeholdingoftheBarnettCo.commonstock(representing18percentoftheMaclins’totalportfolio)andtheresultinglackofdiversificationisakeyfactortobeincludedinevaluatingtheriskoftheMaclins’portfolioandinthefuturemanagementoftheMaclins’assets.TheMaclins’desirenottoinvestinalcoholandtobaccostocksisanotherconstrainingfactor,especiallyintheselectionofanyfutureinvestmentstyleormanager.9.a.1.Thecashreserveistoohigh.•The15percent(or£185,250)cashallocationisnotconsistentwiththeliquidityconstraint.•Thelargeallocationtoalow-returnassetcontributestoashortfallinreturnrelativetorequiredreturn.2.The15percentallocationtoBarnettCo.commonstockistoohigh.•Theriskofholdinga15percentpositioninBarnettstock,withastandarddeviation课后答案网of48,isnotappropriatefortheMaclins’below-averagerisktoleranceand–12percentshortfallrisklimitation.•ThelargeholdinginBarnettstockisinconsistentwithadequateportfoliodiversification.3.Shortfallriskexceedsthelimitationwww.hackshp.cnof–12percentreturninanyoneyear.•TheMaclinshavestatedthattheirshortfallrisklimitationis–12percentreturninanyoneyear.Subtracting2timesthestandarddeviationfromtheportfolio’sexpectedreturn,wefind:6.70percent–(2×12.40percent)=–18.10percentThisisbelowtheirshortfallrisklimitation.4.Theexpectedreturnistoolow(theallocationbetweenstocksandbondsisnotconsistentwithreturnobjective).•Theportfolio’sexpectedreturnof6.70percentislessthanthereturnobjectiveof7.38percent.28-17若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteb.Note:TheMaclinshavepurchasedtheirhomeandmadetheircharitablecontribution.Cash:0%to3%TheMaclinsdonothaveanongoingneedforaspecificcashreservefund.Liquidityneedsarelowandonlyasmallallocationforemergenciesneedbeconsidered.Portfolioincomewillcovertheannualshortfallinlivingexpenses.Thereforethelowestallocationtocashismostappropriate.U.K.CorporateBonds:50%to60%TheMaclinsneedsignificantexposuretothislessvolatileassetclass,giventheirbelow-averagerisktolerance.Stablereturn,derivedfromcurrentincome,willalsobeneededtooffsettheannualcashflowshortfall.ThereforethehighestallocationtoU.K.CorporateBondsismostappropriate.U.S.Equities:20%to25%TheMaclinsmustmeettheirreturnobjectivewhileaddressingtheirrisktolerance.U.S.Equitiesofferhigherexpectedreturnsthanbondsandalsoofferinternationaldiversificationbenefits.Therisk/returnprofileisalsorelativelymorefavorablethanitisforeitherU.K.BondsorBarnettstock.ThereforethehighestallocationtoU.S.Equitiesismostappropriate.BarnettCo.CommonStock:0%to5%TheMaclins’belowaveragerisktoleranceincludesashortfallrisklimitationof–12percentreturninanyoneyear,andtheBarnettstockisveryvolatile.Thereistoomuchstock-specific(non-systematic)riskinthisconcentratedpositionforsuchaninvestor.Theyalsohave“employmentrisk”withBarnett.ThereforethelowestallocationtoBarnettstockismostappropriate.Thefollowingsampleallocationsareprovidedtoillustratethatselectedrangesmeetthereturnobjective.Sampleallocation1:课后答案网WeightedWeight(%)Return(%)AssetClassReturn(%)Cash11.00.01U.K.CorporateBonds555.02.75U.K.Small-capitalization1011.01.10EquitiesU.K.Large-capitalizationwww.hackshp.cn109.00.90EquitiesU.S.Equities2010.02.00BarnettCo.CommonStock416.00.64PortfolioExpectedReturn7.4028-18若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn 课后答案网：www.hackshp.cnChapter28-InvestmentPolicyandtheFrameworkoftheCFAInstituteSampleallocation2:WeightedWeight(%)Return(%)AssetClassReturn(%)Cash11.00.01U.K.CorporateBonds505.02.50U.K.Small-capitalization1011.01.10EquitiesU.K.Large-capitalization109.00.90EquitiesU.S.Equities2410.02.40BarnettCo.CommonStock516.00.80PortfolioExpectedReturn7.71课后答案网www.hackshp.cn28-19若侵犯了您的版权利益，敬请来信告知！www.hackshp.cn'