《金融学》（第二版） 课件 （英文） Chapter13、14 Capital Market Equilibrium；Forward and Futures Markets

Chapter13:

CapitalMarket EquilibriumObjectiveTheTheoryoftheCAPMUseofCAPMinbenchmarkingUsingCAPMtodeterminecorrectratefordiscounting1Chapter13Contents13.1TheCapitalAssetPricingModelinBrief13.2DeterminingoftheRiskPremiumontheMarketPortfolio13.3BetaandRiskPremiumsonIndividualSecurities13.4UsingtheCAPMinPortfolioSelection13.5Valuation&RegulatingRatesofReturn13.6ModificationsandAlternativestotheCAPM2IntroductionCAPMisatheoryaboutequilibriumpricesinthemarketsforriskyassetsItisimportantbecauseitprovidesajustificationforthewidespreadpracticeofpassiveinvestingcalledindexingawaytoestimateexpectedratesofreturnforuseinevaluatingstocksandprojects313.1TheCapitalAssetPricingModelinBriefDevelopedinthe1960’sbySharp,andindependentlybyLintner,andMossinItanswersthequestionWhatwouldequilibriumriskpremiumsbeifpeoplehadthesamesetofforecastsofexpectedreturns,risk,andcorrelationsallchosetheirportfoliosaccordingtheprinciplesofefficientdiversification4Sowhat’swrongwithms-analysisTheassumptionsofthelastchapterappearedfullyacceptableInfactitmayappeartobepedantictomentionthematallWhydevelopanewmodelforrisk-returnifthepresentmodelain’tbroke?5ms-analysis:EstimationWedidnotspellitout,butifyourecallthemnemonicforobtainingtheportfoliovolatilityinthems-model,(givenn-sharesintheportfolio,)weneededn-means(noproblem)n-standarddeviations(noproblem)n*(n-1)/2correlations(?problem)6ms-analysis:EstimationAllparametersneedestimation,andtherearen*(n+1)/2+nparametersAssumeaportfolioof,say,2,000sharesrepresentthemarket,thenweneedtoestimatemorethan2,000,000parameters,mostofwhicharecorrelations7ms-analysis:EstimationRecallthatwhenyouestimateparameters,itisdonewithonlyagivenlevelofconfidenceConfidenceimproveswiththenumberofobservationsInpracticetheparametershavetimedependence,soolddataintroduceserrorFor2,000shares,anda99%confidence,about20,000parameterswillbeinerror8ms-analysis:EstimationTheerrorsmay,ormaynot,besignificanttoyourinvestmentdecision,buttheirexistencecallsforfurtheranalysisInanycase,thedatacollection,verification,andprocessing,isasignificantuseofanalyticalresources9ms-analysis:WishesAfterwehavetheestimatedparameters,findingtheoptimalportfoliorequiresquadraticprogramming,andthisagainrequiresheavyuseofcomputationalresourcesTheproblemissimilartoknowingthepositionandvelocityofeverystarintheMilkyWay,andattemptingtopredicttheirfuturesbycomputingindividualinteractions10ms-analysis:GuidancePrinciplesforSimplificationAnimportantprincipleoffinancialmodelingistocreateequationsthatcapturethekeyfactorsparsimoniouslyAnotherimportantprincipleistoattempttodevelopsimplemodelsLinearmodelsarethenpreferredtoquadraticmodels11TheAstrophysicsofFinanceIntheMilkyWayproblem,anastronomershouldspecifyexactlywhatneedstobepredicted,andgiveattentiontothevariablesthatmostaffectitSo,ifhewantstoknowwhenthenextstarwillcomecloseenoughtoSoltodisturbtheOortcloudthenclosestarsneedindividualanalysisdistantstarsmaybetreatedhomogeneously12SpecifyingtheModelInthelastchapterweexamineddiversifyingahomogenousportfolio,andweobservedthatthereweretwokindsofriskdiversifiableorindividualriskNondiversifiableormarketrisk13SpecifyingtheModelWealsoobservedthatinthelimitasthenumberofsecuritiesbecomeslarge,weobtainedtheformulaThisformulatellsusthatthecorrelationsareofcrucialimportanceintherelationshipbetweenaportfolioriskandthestockrisk14SpecifyingtheModelInthehomogenousmodel,wesawthattherewasindividual-andmarket-riskAssumethateachequity’sreturnisthecompositionoftworandomvariables:oneassociatedwiththemarket’sreturnoneassociatedwiththecompany-specificreturn15SpecifyingtheModel:AssumptionsCompany-specificreturnonanystockxisnotcorrelatedtothecompany-specificreturnonanyotherstockyiscorrelatedwiththemarketreturnTherisk-freerateisconstantduringtheinvestmenttheperiod16AssumptionsInvestorsforecastsagreewithrespecttoexpectations,standarddeviations,andcorrelationsofthereturnsofriskysecuritiesThereforeallinvestorsholdriskyassetsinthesamerelativeproportionsInvestorsbehaveoptimallyInequilibrium,pricesadjustsothataggregatedemandforeachsecurityisequaltoitssupply17MarketPortfolioSinceeveryinvestor’srelativeholdingsoftheriskysecurityisthesame,theonlywaytheassetmarketcanclearisifthoseoptimalrelativeproportionsaretheproportionsinwhichtheyarevaluedinthemarketplaceMarketPortfolio18CMLandtheCAPMCAPMsaysthatinequilibrium,anyinvestor’srelativeholdingofriskyassetswillbethesameasinthemarketportfolioDependingontheirriskaversions,differentinvestorsholdportfolioswithdifferentmixesofrisklessassetandthemarketportfolio19CAPMFormula20TheCapitalMarketLine21Activev.PassiveManagementCAPMimpliesthat,onaverage,theperformancesofactiveportfoliomanagersisequaltothatofpassivemanagersemployingjustthemarketportfolioandtherisk-freesecurityDiligentmanagersdooutperformpassivemanagers,butonlytothedegreethattheirdiligenceisrewarded22RewardOnlyforMarketRiskTheriskpremiumonanyindividualsecurityisproportionalonlytoitscontributiontotheriskofthemarketportfolio,anddoesnotdependonitsstand-aloneriskInvestorsarerewardedonlyforbearingmarketrisk2313.2DeterminingtheRiskPremiumontheMarketPortfolioCAPMstatesthattheequilibriumriskpremiumonthemarketportfolioistheproductofvarianceofthemarket,s2Mweightedaverageofthedegreeofriskaversionofholdersofrisk,A24CommentCAPMexplainsthedifferencebetweentherisklessinterestrateandtheexpectedrateofreturnonthemarketportfolio,butnottheirabsolutelevelsTheabsoluteleveloftheequilibriumexpectedrateofreturnonthemarketportfolioisdeterminedbysuchfactorsasexpectedproductivityhouseholdinter-temporalpreferencesforconsumption25Example:ToDetermine‘A’2613.3BetaandRiskPremiumsonIndividualSecuritiesIfriskisdefinedasthatmeasuresuchthatasitincreases,arisk-averseinvestorwouldhavetobecompensatedbyalargerexpectedreturninorderthatshewouldcontinuetoholditinheroptimalportfolio,thenthemeasureofasecurity’sriskisitsbeta,bbtellsyouhowmuchthesecurity’srateofreturnchangeswhenthereturnonthemarketportfoliochanges27Comment:b=1Asecuritywithab=1onaveragerisesandfallswiththemarketa10%(say)unexpectedrise(fall)inthemarketreturnpremiumwill,onaverage,resultina10%rise(fall)inthesecurity’sreturnpremium28Comment:b

³1Asecuritywithab

³1onaveragerisesandfallsmorethanthemarketWithab=1.3,a10%(say)unexpectedrise(fall)inthemarketreturnpremiumwill,onaverage,resultina13%rise(fall)inthesecurity’sreturnpremiumSuchasecurityissaidtobeaggressive29Comment:b

£1Asecuritywithab

£1onaveragerisesandfallslessthanthemarketWithab=0.7,a10%(say)unexpectedrise(fall)inthemarketreturnpremiumwill,onaverage,resultina7%rise(fall)inthesecurity’sreturnpremiumSuchasecurityissaidtobedefensive30CAPMRiskPremiumonanyAssetAccordingthetheCAPM,inequilibrium,theriskpremiumonanyassetisequaltheproductof

b(or‘Beta’)theriskpremiumonthemarketportfolio31TheSecurityMarketLine32SecurityMarketLineTheplotofasecurity’sriskpremium(orsometimessecurityreturns)againstsecuritybetaNotethattheslopeofthesecuritymarketlineisthemarketpremiumByCAPMtheory,allsecuritiesmustfallpreciselyontheSML(henceitsname)33PracticalExampleSomesimulateddatawasgeneratedundertheassumptionsthat:themarketportfolioreturnhasanexpectedvalueof0.15,avolatilityof0.20,andindex0=50thesharezhasareturnof0.12,avolatilityof0.25,andprice0=30(nodividends)thecorrelationbetweenthereturnsis0.90;andtherisk-freerateis0.053435DataSetUsedInordertodisplaythematerialclearly,onlyoneyearofdataisgenerated,andiscollectedmonthly,resultingin13setsofpricesInarealsimulation,muchmoredatamustbecollectedinordertoprovideanadequateconfidenceintervalforparameterestimates36TransformationofPricesintoReturnsThepricesaretransformedintomonthlyholdingperiodreturns(mhpr_Ind,andmhpr_Z)Themhprsaretransformedintoannualrates,compoundedannuallyTheannualratescompoundedannuallyaretransformedtoannualratescompoundedcontinuously37TableofPrices3839FinancialCalculatorsEverythingcouldhavebeendoneusingamodernstandard-issuefinancialorscientificcalculatorRemember,thecorrectratetouseistheannualratecompoundedcontinuously,andthatmonth-to-yearconversionsofstandarddeviationinvolveasquarerootof12Takecaretoenterthemarketrateastheindependentvariable,x40AccuracyIssueWeassumedthatthes’sandr’sareconstants,buttheyarerandomvariablestooInordertoachieveadequateconfidence,alargesampleisneededSmallmovementsinpricearemaskedbytransactionpricesTheresultisacompromisebetweencurrencyandconfidence41ModelandMeasuredValuesofStatisticalParameters42CommentTheillustratedtrajectoryistypicalformonthlydatacollectedoverayearCaution:avoidusingsmalldatasetstoestimateCAPMparameters43RegressionLineTheslopeoftheregressionlineofdependentstockagainstindependentmarketreturnsisbeta4445ObservationAllsecurities,(notjustefficientportfolios)plotontotheSML,iftheyarecorrectlypricedaccordingtotheCAPM46TheBetaofaPortfolioWhendeterminingtheriskofaportfoliousingstandarddeviationresultsinaformulathat’squitecomplexusingbeta,theformulaislinear47ComputingBetaHerearesomeusefulformulaeforcomputingbeta4813.4UsingtheCAPMinPortfolioSelectionWhetherornotCAPMisavalidtheory,indexingisattractivetoinvestorsbecausehistoricallyithasperformedbetterthanmostactivelymanagedportfoliositcostslesstoimplementthatactivemanagement49AParadoxResolvedThelastchapterposedaparadoxwithtwosecuritiesco-existing,onehavingalowerstandarddeviationandhigherreturnthantheotherIfweaccepttheCAPMasavalidtheory,wehavearesolutionBothsecuritieslieontheSML,andbothsecuritiesliebelowtheCML50s-riskandb-riskAsecurityhastwokindsofrisk:riskthatmaybediversifiedaway,andriskthatisassociatedwiththemarketTheCAPMtheorystatesthatthelowerreturnonthes-riskiersecurityimpliesthatithasalowerlevelofmarketb-risk,andthisistheonlyrelevantriskThes-riskiersecuritycontainsrelativelymore(irrelevant)security-specificrisk51ABrandManagerMostinvestorshavetheopportunitytoeliminatemostindividualriskfromtheirportfolio;butconsideraproductmanager’sexposuretoriskIfabrandmanager’sproductsperformwell,promotion,highersalary,andgreaterautonomyfollowperformbadly,humiliation,unemploymentandpovertyfollow52ABrandManagerNowassumethatanewproductisavailableforinclusioninthebrand,butgivenitsb-riskandexpectedreturn,itfallsbelowthesml,andhenceisnotintheinvestors’interestsThemanagerdiscoversthatthenewproductreduceshistotalrisk,andactsinhisowninterests(ratherthantheinvestors’),andacceptstheproduct(agencyproblem)53ThePortfolioManagerRemember(lastchapter)wehadnotresolvedtheissuehowtoevaluatetheperformanceofaportfoliomanager,butgiventheCAPMaresolutionisathandIfyourportfolioisproducingactualreturnswithalowerbetathanthesmlspecifies(withstatisticalsignificance),thenyoushouldcertainlynotbefired54ThePortfolioManagerThefurtherawelldiversifiedportfolioconsistentlyliesabove(below)thesml,thebetter(worse)thefundmanager’sperformanceThereareseveralmeasuresofthisdistance,butthistopicisbetterleftforanotherday55AlphaFundandtheSecurityMarketLine56AlphaFundandtheCapitalMarketLine57HowtoWinInvestmentGamesYoumayhavebeenaskedtotakepartinaninvestmentgamewhereyou‘given’$100,000tomanageforasemester;winnertakesallTheoverwhelmingchancesarethatthewinningstudentusespoorfinancialpractices58HowtoWinInvestmentGames(Continued)Thecriteriaofsuccessforthegamedifferssignificantlyfromreal-lifeinvesting,soyourstrategyforwinningislikelytobedifferentIfyoudiversifyawayunsystematicrisk--evenifyouhavesomekindofinformationaladvantageoveryourcompetition--youareveryunlikelytowinthegameTowin,youneedindividualrisktoseparateyoufromthecrowdUnlikearealinvestoryoudon’thaverealdownside-riskyourupside-potentialmaterializesonlybybeingfirst5913.5ValuationandRegulatingRatesofReturnBetamaybeusedtoobtainthediscountfactorforaprojectAssumeaprojectissimilartotheprojectsundertakenbyanotherfirm,‘Betaful’Betafulisfinancedby20%short-termdebt,and80%equity,anditsbis1.3(assumedebtisrisk-free)Youroptimalcapitalstructureis40%(risk-free)debt,and60%equity60ValuationandRegulatingRatesofReturnAssumethemarketrateis15%,andtherisk-freerateis5%ComputethebetaofBetaful’soperations61ValuationandRegulatingRatesofReturnBetaofBetaful’soperationsisequaltothebetaofournewoperationTofindtherequiredreturnonthenewproject,applytheCAPM62ValuationandRegulatingRatesofReturnAssumethatyourcompanyisjustavehicleforthenewproject,thenthebetaofyourunquotedequityis63ValuationandRegulatingRatesofReturnAssumethatyourcompanyhasanexpecteddividendof$6nextyear,andthatitwillgrowannuallyatarateof4%forever,thevalueofashareis64ValuationandRegulatingRatesofReturnRegulatorsusetheCAPMtoestablisha‘fair’rateofreturnoninvestedcapitalinpublicutilities,giventhelevelofrisk6513.6ModificationsandAlternativestotheCAPMStartinginthe1970sresearchersfoundthatCAPMdidnotseemtofullyexplainthestructureofexpectedreturnsonassets.AconsensusemergedthattheoriginalversionoftheCAPMneededtobemodified.66PotentialexplanationsfortheapparentdeviationsfromtheCAPM:CAPMactuallydoeshold,butthe“market”portfoliosusedinthetestingwereincompleteandinadequaterepresentationsofthetruemarketportfolio.67PotentialexplanationsfortheapparentdeviationsfromtheCAPM:ThefocusonmarketimperfectionsisnotcontemplatedintheCAPM.Suchas:borrowingcostsandconstraintsshortsalesrestrictionsandcostsdifferenttaxtreatmentsforvariousassetsThenontradabilityofsomeimportantassetssuchashumancapital68PotentialexplanationsfortheapparentdeviationsfromtheCAPM:Addgreaterrealismtothemodelingassumptions,whilemaintainingtheCAPM’sbasicmethodology.OnesuchmodelisthemultifactorIntertemporalCapitalAssetPricingModel(ICAPM)69IntertemporalCapitalAssetPricingModel(ICAPM)InICAPMequilibriumriskpremiumsonsecuritiesinthisdynamicmodelcomefromseveraldimensionofrisksreflectednotonlybytheirreturnsensitivitiesorbetaonthemarketportfoliobutalsobytheirsensitivitytoothersystematicriskssuchas:changesininterestratesexpectedreturnsonassetschangesinconsumptiongoodprices.70AlternativeTheoriesArbitragePricingTheory(APT)APTstatesthatarelationsimilartotheSecurityMarketLinecanexistevenifinvestorsarenotmean-varianceoptimizers.71ArbitragePricingTheory(APT)Ifthereareenoughdifferentsecuritiesto“diversifyaway”allbutmarketriskThenanexpected-return-to-betarelationwillexistasaconsequenceoftherenotbeinganyarbitrageopportunities72Chapter14:

ForwardandFutures MarketsObjectiveHowtopriceforwardandfuturesStorageofcommoditiesCostofcarryUnderstandingfinancialfutures73Chapter14:Contents14.1DistinctionBetweenForward&FuturesContracts14.2TheEconomicFunctionofFuturesMarkets14.3TheRoleofSpeculators14.4RelationBetweenCommoditySpot&FuturesPrices14.5ExtractingInformationfromCommodityFuturesPrices14.6Forward-SpotPriceParityforGold14.7FinancialFutures14.8The“Implied”RisklessRate14.9TheForwardPriceisnotaForecastoftheSpotPrice14.10Forward-SpotPrice-ParitywithCashPayouts14.11“Implied”Dividends14.12TheForeign-ExchangeParityRelation14.13TheRoleofExpectationsinDeterminingExchangeRates7414.1DistinctionBetweenForward&FuturesContractspartiesagreetoexchangesomeiteminthefutureatadeliverypricespecifiednowtheforwardpriceisdefinedasthedeliverypricewhichmakesthecurrentmarketvalueofthecontractzeronomoneyispaidinthepresentbyeitherpartytotheotherthefacevalueofthecontractisthequantityoftheitemspecifiedinthecontractmultipliedbytheforwardpricethepartywhoagreestobuythespecifiedtakesthelongposition,andthepartywhoagreestoselltheitemtakestheshortposition75TermsOpen,High,Low,Settle,Change,Lifetimehigh,Lifetimelow,OpeninterestMark-to-marketMarginrequirementMargincall76CharacteristicsofFuturesFuturesare:standardcontractsimmunefromthecreditworthinessofbuyerandsellerbecauseexchangestandsbetweentraderscontractsmarkedtomarketdailymarginrequirements7714.2TheEconomicFunctionofFuturesMarketsThefuturesmarketsfacilitatethere-allocationofexposuretocommoditypriceriskamongmarketparticipantsBut:78byprovidingameanstohedgethepriceriskassociatedwithstoringacommodity,futurescontractsmakeitpossibletoseparatethedecisionofwhethertophysicallystoreacommodityfromthedecisiontohavefinancialexposuretopricechanges79TheEconomicFunctionofFuturesMarkets(Continued)Adistributor,j,mayhedgebysellingthecommodityonthespotmarketnowatapriceSsellingshortafuturescontractatapriceFanddeliverthecommodityataspecifiedtimeinthefuturetherewillbeacarryingcostCjfordistributorj,andshewillstoreonlyifCj<F-S80TheEconomicFunctionofFuturesMarkets(Continued)Thedifferencebetweenthefuturespriceandthespotprice,F-S,iscalledthespread,andgovernshowmuchwheatwillbestored,andbywhom81TheEconomicFunctionofFuturesMarkets(Continued)Supposethecommodityiswheat,andnextyear’scropisexpectedtobemuchhigherthanaverage,thenfuturespricesmaybelowerthanthespot,(thespreadmaybenegative,)nobodywillstorewheat82TheEconomicFunctionofFuturesMarkets(Continued)Theexistenceofthefuturesmarketforwheatconveysinformationtoallproducers,distributors,andconsumers;andthiseliminatesthenecessityformarketparticipantstogatherandprocessinformationinordertoforecastthefuturespotprice8314.3TheRoleofSpeculatorsHedgeranyoneusingafuturesmarkettoreduceriskSpeculatoranyonewhotakesapositioninthemarket(increasinghisrisk)inordertoprofitfromhisforecastsoffuturespotprices(Aproducer,distributororconsumerwhochoosesnottohedgeherriskmaybeconsideredtobeaspeculator)84TheRoleofSpeculators:ExampleSupposethatthecurrent1-monthfuturesinwheatis$1.5/bushel,andafarmingfamilywithstoredwheatbelievesthatthepricewillriseto$2.00Nothedgingthestoredwheatresultsinthefamilybeingexposedtothevagranciesofthewheatmarket,anditbecomes,ineffect,awheatspeculator(justliketheircobblercousinswhoarelongwheatfutures)85TheRoleofSpeculators:GamblersandWastersCritic:“Speculatorshavenosocialvalue”Answer:Successfulspeculatorsmakethemarketmoreefficientasaninformationresourceprovideliquiditywhenitisneeded,whichiswhenproducers,distributors,andconsumerscan’torwon’thedgemoreefficientbycontributingtowardsrecoveringthefixedcostsofprovidingafuturesexchange8614.4RelationshipBetweenCommoditySpotandFuturesPricesArbitrageursplaceanupperboundonfuturespricesbylockinginasureprofitonfuturespricesifthespreadbetweenthefuturespriceandspotpricebecomesgreaterthanthecostofcarry,F-S£Cthecostofcarryvariesasafunctionoftimeandwarehousingorganization8714.5ExtractingInformationfromCommodityFuturesPricesCase1If(FuturesPrice<CurrentSpot)ThenthefuturespriceisanindicatoroftheexpectedfuturespotpriceThefuturespriceisabiasedestimatebecausethereareriskpremiumsanddiscountsassociatedwithholdingthecommodity88ExtractingInformationfromCommodityFuturesPricesCase2If(FuturesPrice>CurrentSpot)ThenthefuturespriceisnotanindicatoroftheexpectedfuturespotpriceThespreadcannotexceedthecostofcarry8914.6Spot-FuturesPriceParityforGoldInthecaseofgoldfutures,arbitrageestablishesanupper-andlower-boundonthespreadbetweenthefuturesandspotprices,resultinginthespot-futuresprice-parityrelationship90Spot-FuturesPriceParityforGoldTherearetwowaystoinvestingoldbuyanounceofgoldatS0,storeitforayearatastoragecostof$h/$S0,andsellitforS1investS0ina1-yearT-billwithreturnrf,andpurchasea1-ounceofgoldforward,F,fordeliveryin1-year91Spot-FuturesPriceParityforGoldAcontractwithlifeT:Thisisnotacausalrelationship,buttheforwardandcurrentspotjointlydeterminethemarketIfweknowone,thentheruleofonemarketdeterminesthatweknowtheother92Spot-FuturesPriceParityforGoldThefollowingdiagramshowshowtocreatesyntheticgold,T-bills,orgoldforwardcontractfromtheothertwoAllpricesarepredetermined,exceptthepriceoftheoneyearoftheforwardandthepriceinoneyearofthegold,butthedifferencebetweenthemisequaltotheknownfinancingandstoragecosts93RuleofOnePrice:NoArbitrageProfitsPurchaseActualAuSellT-BillSellAuForwardSellActualAuSettleT-BillSettleAuForwardAu=Gold94ImpliedCostofCarryAsaconsequenceoftheforward-spotpriceparityrelationship,youcan’textractinformationabouttheexpectedfuturespotpriceofgold(unlikeonewheatcase)fromfuturespricesTheimpliedcostofcarry(per$spot)is h=(F-S0)/S0-rf9514.7FinancialFuturesWenowfocusonfinancialfuturesstandardizedcontractsforfuturedeliveryofstocks,bonds,indices,andforeigncurrencytheyhavenointrinsicvalue,butrepresentclaimsonfuturecashflowstheyhaveverylowstoragecostssettlementisusuallyincash96FinancialFuturesWithnostoragecost,therelationshipbetweentheforwardandthespotisAnydeviationfromthiswillresultinanarbitrageopportunity97FinancialFutures:ExampleConsidersharesinBablonics,Inc,tradingat$50each,($5,000foraroundlot);assume6-monthT-billsyield6%(compoundedsemiannually)98Bablonics,Inc(Continued)1PurchaseoneroundlotofstockatspotThisresultsinanegativecashflowtodayof$5,000(out),andwillgenerateacashflowof100*Spot6m(in)

insixmonths99Bablonics,Inc(Continued)2Covertoday’snegativecashflowbysellingshort$5,000worthof6-monthT-billswithafacevalueof5000(1+0.06/2)^0.5=$5,150Thecashflowtodayis$5,000(in),andthecashflowinsixmonthstimewillbe$5,150(out)100Bablonics,Inc(Continued)3Covertheriskexposurebyselling100sharesforwardattheequilibriumpriceof5000*(1+0.06/2)^0.5=$5,150Thereisnocashflowtoday,butthevalueofthisforwardcontractinsixmonthstimewillbe$(Spot6m-5,150)101Bablonics,Inc(Continued)-$5,000(longstock)+$5,000(shortbond)+$0(shortforward)=$0102Bablonics,Inc(Continued)CashFlowin6-Months+$Spot6m(settlelongstock)-$5,150(settleshortbond)+($5,150-$Spot6m)(settleforward)=$0103Bablonics,Inc(Conclusion)Ifyournetrisk-freeinvestmentwaszero,andyoureceivenothingthatiswhatyoushouldexpectandyouexpectto:receivedpositivevaluewithnorisk,thentheruleofonepricehasbeenviolatedlosevaluewithnorisk,thenreversethedirectionofalltransactions,andagainyouprofitwithnorisk10414.8The“Implied”RisklessRateRearrangingtheformula,theimpliedinterestrateonaforw