《金融学》（第二版） 课件 （英文） -Chapter7、8 Principles of Market Valuation；Valuation of Known Cash Flows Bonds

Chapter7:

Principlesof MarketValuationObjectiveExplaintheprinciplesofassetevaluation1Chapter7Contents7.1Therelationshipbetweenanasset’svalue&itsprice7.2Valuemaximization&financialdecisions7.3Thelawofoneprice&arbitrage7.4Arbitrage&thelawofoneprice7.5Interestrates&thelawofoneprice7.6Exchangerates&triangulararbitrage7.7Valuationusingcomparables7.8ValuationModels7.9Accountingmeasuresofvalue7.10Howinformationisreflectedinsecurityprices7.11Theefficientmarketshypothesis2IntroductionRecallthatthethreepillarsoffinancearetimevalueofmoneyriskmanagementassetvaluationManyfinancialdecisionsare,inessence,thedeterminationofanasset’svalue3Introduction(Continued)ThekeytoassetvaluationiscomparisonoftheassettobevaluedwithasetofassetswithsimilarcharacteristicsandknownvaluesBythelawofoneprice,thepriceofallequivalentassetsmustbethesame47.1RelationshipbetweenAsset’sValueandItsPriceDefinition:Anasset’sfundamentalvalueisthepricewellinformedinvestorsmustpaytopurchaseitinafreeandcompetitivemarket5RelationshipbetweenAssetValueandPriceTherecanexisttemporarydifferencesbetweenthemarketpriceofanassetanditsfundamentalvalueSecurityanalystsmaketheirlivingbydiscoveringtheseaberrationsManywell-informedprofessionalsarelookingfortheseaberrations.Areasonableinitialassumptionisthataberrationsaresmall67.2ValueMaximizationandFinancialDecisionsFinancialdecisionscanbemaderationallypurelyonthebasisofvaluemaximization,andwithoutregardtoriskpreferencesandexpectationsMarketsforfinancialassetsprovidetheinformationneededtochoosebetweensomealternatives77.3TheLawofOnePriceandArbitrageLawofOnePrice:Inacompetitivemarket,iftwoassetsareequivalent,theywilltendtohavethesameprice8TheLawofOnePriceandArbitrageThelawofonepriceisenforcedbyaprocesscalledarbitrageArbitrageisthepurchasingofasetofassets,andimmediatesaleofanothersetofassets,insuchawayastoearnasureprofitfrompricedifferences9TheLawofOnePriceandArbitrageArbitrageursengageinthebusinessoftradingsimilarassetswithapricedifferentialthatcannotbejustifiedbytransaction-andtransformation-costsExample:Goldinanytwopartsofthecountryshouldnotdifferbymorethanthetransactioncostsofmovingit107.4ArbitrageandthePricesofFinancialAssetsArbitragingbyshippingaphysicalcommodity(gold)involveshighertransactioncoststhanarbitragingfinancialassets(sharesofstock)Weexpectthesamefinancialcommoditytradingontwomarketstobepricedveryclosely11ArbitrageandthePricesofFinancialAssetsTheruleofonepriceisthemostfundamentalvaluationprincipleinfinance.Iftwoverysimilarsecuritiestradeatsignificantlydifferentprices,wefirstsuspectInterferencewithnormalmarketoperationSomeunrecognizeddifferencebetweenthetwoassets12ArbitrageandthePricesofFinancialAssetsNotwonon-identicalassetsareexactlyalike,andtheremaybeoccasionswhentwosimilarassetstradeatdifferentpricesDollarbillswithcertainserialnumbersareveryvaluabletoplayersofliar’spokerNotevenadollarisalwaysworthadollar!137.5InterestRatesandtheLawofOnePriceIftwoorganizationswithsimilarcreditworthinessissuebondswithsimilarterms,thentheirinterestrateswillbesimilarTakecaretoensurethattherearenosubtledifferencesinthetaxstatusofthebondsthevalueofcollateralorbackingofthebonds147.6ExchangeRatesandTriangularArbitrageThelawofonepricealsoappliestoforeignexchangemarketsIfthreecurrenciesarefreelyconvertibleincompetitivemarkets,thenitisenoughknowanytwoexchangeratestocomputethethirdexchangerate15TriangularArbitrageUSAJapanUK¥100/$or$0.01/¥£0.005/¥or¥200/£$2/£or£0.5/$16TriangularArbitrageEverycountryhasitsownconventionsforexpressingexchangeratesTradersintheU.K.expressexchangeratesasforeigncurrencyperpoundTradersintheU.S.A.expressexchangeratesasdollarsperunitofforeigncurrencyInthecaseof$/£exchangerates,dealersinbothcountriesusethesamerate,say2$/£17TriangularArbitrageIfweselecttheformoftheratecorrectly,weobtaintherelationshipR£/¥=R£/$*R$/¥Undertheconditionsspecified,thisequilibriumrelationshipmusthold(orarisk-free,almostcost-less,arbitragewillimmediatelyreestablishtheequilibrium)18TriangularArbitrageMoregenerallyRA/C=RA/B*RB/CRA/B=1/RB/A19TriangularArbitrageMorespecifically,intheexampleR£/¥=R£/$*R$/¥=0.5*0.01=0.005R¥/£=1/R£/¥=1/0.005=200Theothertwopairfollowthesameform20TriangularArbitrageIfthisrelationshipweretofailsignificantly,thentraderswouldprofitbyimmediatelymovinglargesumsofmoneyroundthediagramclockwiseoranti-clockwiseCurrencytradersmayborrowlargeamountsofmoneyatclosetogovernmentratesAberrationshaveonlyfleetingexistences217.7ValuationUsingComparablesSomeassetsarenottraded,orareonlytradedinfrequently,butwestillneedtoevaluatethemThelawofonepricemaybeusedtoevaluateassets,evenwhenarbitragecannotbeusedtoenforcethelaw22ValuationUsingComparablesTwocasesaworkofartinanestatethatneedstobeevaluatedforcomputationofestatetaxesahomethatneedstobeevaluatedtoensurethefairnessofpropertytaxes23ValuationUsingComparablesToevaluatethenon-tradingasset,onefindscomparablepricesoftradedassetsItisusefultothinkofassetpricesinafeature-timeframeworkSimilarassetshavepricesthattendtomoveupanddowntogetherintimeAtaparticulartime,differencesinassetpricesarelargelyaccountableintermsofdifferencesinfeatures24ValuationUsingComparablesToevaluateaworkofart,itisnecessarytofindassetsthatare“close”infeature-timespaceThecloserthefeaturesmatch,thelongerthedatacollectionperiodmaybeTheclosertothepresenttimeanassetwassold,themorediversethefeaturesmaybeBothkindsof“closeness”areneeded25PastFeatureDifferentialOldsaleofthisworkRecentsaleofunrelatedworkRecentwell-matchedsale26ValuationUsingComparablesIntheabovediagram,theblackstarsindicateusablepriceexemplars,andthepinkstarsindicatepoorexemplarsThevariable“feature”isaaggregateofmanyfactors,someobjective,somesubjective27ValuationUsingComparablesExampleCollectpricesandfeaturedifferentialsforartbythesameartist:10-yearsartofthesamequality:5-yearsartfromthesameschool:5-yearsbroadlysimilarart:2-years28ValuationUsingComparablesFromthisinformationyoucandeterminepricetrendsinthegeneralartmarketobtaintrend-adjustedbenchmarkpricesgainanunderstandingofhowtoadjustthebenchmarkforfeaturedifferences297.8ValuationModelsAvaluationmodelisaquantitativemethodusedforestimatinganasset’svaluefromknownpricesofotherassetsthatarenotitsexactequivalentThevaluationmodelemployedmaydependonthepurposeoftheevaluationtraditionalshareholderv.take-overspecialist30StockEvaluationusingP/EsTheprice-over-earningsratiosofsimilarcompaniesaredeterminedBasedonthese,anestimateismadeofthep/eratioofthenon-pricedfirmTheearningsofthefirmaremultipliedbythisp/eratiotoobtainanevaluation31StockEvaluationusingP/EsTheaccuracyofthismethoddependsontheappropriatenessoftheexemplarfirmsFutureprofitability,accountingmethods,leverage,technology,andahostofotherfactors,willaffecttheexemplars’p/eratios32ValuationModelRefinementYouareasecurityanalystforanassetYouhavedevelopedavaluationmodelyoubelieveissuperiortovaluationmodelsusedbyothertradersAssumingthesuperiormodelremainsproprietary,itmaybedifficulttoexploitit33ValuationModelRefinementWhenamarketisdrivenbyavaluationmodel,usingasuperiormodelmayleadtoinferiortradingperformancearbitragestrategiescreatedusingthe“superiormodel”aresometimeslesseffectivethanthoseofthestandardmodelwhenusingasuperiorproprietymodel,youneedtobeselectiveaboutwhentoemployit34P/ERatioandSmallBusinessesYoualreadyhaveenoughtheoreticalknowledgetopriceasmallbusinesscorrectlyusingNPVTraditionally,smallbusinesseswerepricedusingP/Es(sub-optimalmodel)Thisleadstopriceaberrationsfromwhichyoucanstillbenefit(useNPV)35TaxCheatsSomesmallbars,restaurants,hairdressers,andothercashbusinessescheattheIRSbykeepingtwosetsofbooksAssumingap/eratioof8,suchabusinesswilllose$8forevery$1/yearcheatedwhenitcomestosellingthebusinessSuchbusinessesare“dressedforsale”acoupleofyearspriortotheplannedsale367.9AccountingMeasuresofValueOwner’sequityisnotanaccurateindicatorofthefirm’smarketvalueAssetsandliabilitiesarenotmarketpricedmarkingthebalancesheettomarkethelpsIntangiblesareunder-includedafirmisagoingconcern,notjustitsphysicalassetsandliabilities377.10HowInformationisreflectedinSecurityPricesSometimesastockpricewillrisesharplywiththereleaseofinformationAnimportantdrughasachievedanimportantsteponitsroadtobeingmarketedPoortradingresultsareannounced,buttheyarebetterthanthoseanticipatedbytradersAnunanticipatedpositiveFedannouncement38HowInformationisreflectedinSecurityPricesMarkettradersformprobabilitydistributionsofkeystock-pricedeterminants(Example,salesrevenue)Whenthesedistributionschangetoassimilatenewinformation,thestockmarketreacts,andthepricechangesThisleadstotheefficientmarkethypothesis397.11EfficientMarketHypothesisTheefficientmarkethypothesisstatesanasset’scurrentpricereflectsallpubliclyavailableinformationaboutfutureeconomicfundamentalsaffectingmarketprice40EfficientMarketHypothesisThemechanismleadingtotheefficientmarket’shypothesisCollectionofrelevantinformationAnalysisofthisinformationtoobtainapriceTradingonthisanalysisuntilthepriceaberrationiseliminated41CollectionofRelevantInformationCollectinformationor“facts”aboutacompany,andthefactorsthatmayaffectitSECfilings,annualreports,clippingservices,conferenceswithCEO/CFO,industryanalyses,patentfilings,rumors,discussionswithcompetitorsandcustomers,informalmarketsurveys,advertisingcampaigns,recruitmentactivity,technologicalsurveys…42AnalysisofthisInformationAtonetime,analystswerecontenttoformjustapointestimateofthepriceToday,analyststrytoincorporateprobabilityintotheirpricing,byworkingwithranges,forinstanceThemoreaccuratetheinformation,thesmallerthepricedispersion->lessrisk43TradingonthisAnalysisBasedonherestimates,theanalystmayrecommendatradeThemagnitudeofresultingtradesdependonherpastsuccessesandhercurrentstatusBarrierstoentryarelow,andsuccessfulanalystsarewellrewarded&gaininfluenceResult:Knowledgeableindividualskeepthemarketefficient44Chapter8:

ValuationofKnown CashFlows:BondsObjectiveValuationoffixedincomesecuritiesExplainwhybondpriceschange45Chapter8Contents8.1UsingPresentValueFormulastoValueKnownFlows8.2TheBasicBuildingBlocks:PureDiscountBonds8.3CouponBonds,CurrentYield,andYield-to-Maturity8.4ReadingBondListings8.5WhyYieldsforthesameMaturityDiffer8.6TheBehaviorofBondPricesOverTime468.1UsingPresentValueFormulastoValueKnownFlowsYouhavebeenofferedtheopportunitytopurchaseamortgage.ItwasoriginallypartofacreativefinancingpackagewheretheoriginalownerfinancedthebuyerTheremaininglifeofthemortgageis60months,withpaymentof$400.Yourrequiredrateofreturnis1.5%/month47CalculationUsingthepresentvalueofanannuityformuladiscussedinchapter4,youwillpaynomorethan48FinancialCalculatorAlternatively,usingyourfinancialcalculator(remembertosetthecorrectdefaults)youobtain49ChangeinRequiredRateIfyourrequiredrateofreturnincreasedto1.6%/month50UsingPresentValueFormulastoValueKnownFlowsObservethatthemaximumyouwouldpayforthebondhasdecreasedAnincreaseintherequiredrateofreturnalwaysleadstoadecreaseinthevalueofafixedincomesecurityTheproofisveryeasy51BondPricesRiseastheInterestRatesFallWritethePVofthefixedincomesecurityasthesumterms52BondPricesRiseastheInterestRatesFallIfigoesup,1+igoesup,1/(1+i)goesdownfori>-1,(1/(1+i))jgoesdownfori>0.Soifthepaymentsarepositive,thenthesummustalsogodownSimilarly,idown->PVup53BondPricesRiseastheInterestRatesFallBasicprincipleinevaluatingknownflowsAchangeinmarketinterestratescausesachangeintheoppositedirectioninthemarketvaluesofallexistingcontractspromisingfixedpaymentsinthefuture54NoteVolatilemarketratesimplyvolatilemarketvalues55FindingtheCorrectDiscountRateBondanalysisisnotaseasyasthisanalysisappearstoimplyWeneedaninterestratetouseintheformulaWesawinChapter2thatinterestratesareafunctionoftime-to-maturityTwodefault-freebondswithidenticalmaturitiesmayhavedifferentYTMs56YieldCurveAtypicalyieldcurve:578.2TheBasicsBuildingBlocks:PureDiscountBondsWecanalwaysanalyzeanyfixedincomecontractintoasumofpurediscountbondsApurediscountbondisasecuritythatpromisestopayaspecifiedsinglecashpayment(facevalueorparvalue)ataspecifieddatecalleditsmaturitydate58PureDiscountBondsNoteThereisnocashflowassociatedwithinterestPurediscountbondsarepurchasedatadiscountfromtheirfaceorparvalue59PureDiscountBondsThepurediscountbondisanexampleofthepresentvalueofalumpsumequationweanalyzedinChapter4Solvingthis,theyield-to-maturityonapurediscountbondisgivenbytherelationship:60PureDiscountBondsInthisequation,PisthepresentvalueorpriceofthebondFisthefaceorfuturevaluenistheinvestmentperiodiistheyield-to-maturity61PureDiscountBondsExampleYoucanpurchaseapurediscountbondfor$9,000,anditmaturesintwoyearswithafacevalueof$10,000Whatistheytm?62PureDiscountBonds638.3CouponBonds,CurrentYield,andYieldtoMaturityAcouponbondobligatestheissuertomakeperiodicpaymentsofinterest(calledcouponpayments)tothebondholderuntilthebondmaturesatwhichtimethefacevalueofthebondisalsopaidtothebondholderandthecontractissatisfied64CouponRateThecouponrateistheinterestrateappliedtothefacevaluetocomputethecouponpaymentAbondwithafacevalueof$1,000andacouponrateof10%paysanannualcouponof$100Atmaturity,thepaymentis$1,000+$10065CashFlowsfor10%$1,000CouponBond66Par,premium,andDiscountBondsAcouponbondwithitscurrentpriceequaltoitsparvalueisaparbondIfitistradingbelowparitisadiscountbondIfitistradingaboveparitisapremiumbond(nottobeconfusedwiththeU.K.lotterybondofthesamename!)67BondsTradingatParBondPricingPrinciple#1:(ParBonds)Ifabond’spriceequalsitsfacevalue,thenitsyield-to-maturity=currentyield=couponrate. Proof:68CouponBonds,CurrentYield,andYield-to-MaturityTheyield-to-maturityisthediscountratethatmakesthepresentvalueofthecashflowsfromthebondequaltothecurrentpriceofthebondAnexcellentwaytocomputetheytmisgiveninChapter469UsingPureDiscountBondstoValueotherBondsValueabondthatpaysits$100couponattheendofeachyearfor3-years,anditsparvalueof$1,000in3-yearsYouhavediscoveredthreepurediscountbonds(eachwitha$1,000parvalue)thatmaturein1,2,and3years,andthataretradingat$960,$890,and$810respectively70FirstSolutionMethod71SecondSolutionMethod72ConclusionThefirstmethodusesthefactthatacouponbondisthesumofpurediscountbondsitisfastanddirectThesecondmethodfirstdeterminestheyields-to-maturityofeachdiscountbondcashflowsarethenevaluatedusingthem73TheYTMoftheCouponBondWehavethepriceofthecouponbond,andthetimingandmagnitudeofitsfuturecashflows,sowecandetermineitsYTMWeusethefinancialcalculator,butanumericalmethodwasprovidedinchapter4forthisclassofproblems74TheYTMoftheCouponBond75ObservationTheyieldtomaturityonthe3-yearpurediscountbondwas7.28%andtheyield-to-maturityonthe3-yearcouponbondwas7.10%Theyield-curvefordefault-freebondsisnotauniquevalue76BondPricingPrinciple#2&3BondPrinciple#2:PremiumBonds bondprice>facevalueÞytm<currentyield<couponrateBondPrinciple#3:DiscountBonds bondprice<facevalueÞytm>currentyield>couponrate77ProofofRelationshipbetweenYTMandCurrentYieldForcouponbonds,wehavethefollowingrelationshipsNotethe(sensible)restrictionsonthevariablerangesNotethat1/((1+i)^n-1)isalwayspositive7879ProofofRelationshipbetweenCurrentandCouponYieldsForcouponbonds,wehavethefollowingrelationshipderivedfromthebondformulaNotethatthedifferencesbetweenthereciprocalshavethesamesign,sotheactualdifferencesalsohavethesamesignNotethatsizerelationshipisdeterminedbythediscountfactorwhichisalways<18081HowtoRememberPrinciplesImaginethatthebondwasissuedatpartheyield-to-maturitymovesfromthecouponyieldintheoppositedirectiontopricethecouponrateisunchangingThisdiagrammayhelp:8283HighYieldT-BondFundsYieldcurveswithlargepositiveslopesmakelonger-termT-bondstemptingbecause,likeT-bills,theyaredefault-freeTheabovediagramwasbasedon:par=$1000,coupon=$100,n=10-years,flatObservethelargeeffectofmodestchangesininterestoncapitalAcloseupisgivenbelow8485ClarificationThelastexampleusedaflatyieldcurveLetuslookatanexamplewithshort-termratesremainingfixedlonger-termratesrisingonincreasedexpectationofageneralriseininterestrates8687InvestmentImplicationsAssumea20-yearbondwithacouponrateof6%Purchasefor$1016.54whenthelowercurveprevailsWhenyieldcurverises,thebondisworthonly$814.05ThisisamassivecapitalriskAdditionally,long-termratesaremorevolatilethanshort-termrates888.4ReadingBondListings

Therearetraditionsforreportingyieldsandcomputingearnedinterestthatneedtobeunderstoodbeforetr