Investment and Portfolio Management 5
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Transcript of Investment and Portfolio Management 5
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INVESTMENT ANALYSIS ANDPORTFOLIO MANAGEMENT
CAPITAL ASSET PRICING MODEL
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OBJECTIVES OF OUR STUDY
Whataretheassumptionsofthe capitalasset
pricingmodel? Whatisarisk-freeassetand whatareitsrisk-
return characteristics?
Whatisthe covarianceand correlation between
therisk-freeassetandariskyassetorportfolioofriskyassets?
Whatistheexpectedreturn whenyou combinetherisk-freeassetandaportfolioofrisky
assets? Whatisthestandarddeviation whenyou
combinetherisk-freeassetandaportfolioofriskyassets?
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OBJECTIVES OF OUR STUDY Whenyou combinetherisk-freeassetanda
portfolioofriskyassetsonthe Markowitzefficientfrontier, whatdoesthesetofpossibleportfolioslooklike?
Giventheinitialsetofportfoliopossibilities with
arisk-freeasset, whathappens whenyouaddfinancialleverage (thatis, borrow)?
Whatisthemarketportfolio, whatassetsareincludedinthisportfolio,and whatarethe
relative weightsforthealternativeassetsincluded?
Whatisthe capitalmarketline (CML)?
Whatdo wemean by completediversification?
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OBJECTIVES OF OUR STUDY
How do wemeasurediversificationforanindividualportfolio?
Whataresystematic andunsystematic risk?
Giventhe CML, whatistheseparationtheorem?
Giventhe CML, whatistherelevantriskmeasureforanindividualriskyasset?
Whatisthesecuritymarketline (SML),andhowdoesitdifferfromthe CML?
Whatisbeta, and whyisitreferredtoasastandardizedmeasureofsystematic risk?
How canyouusethe SML todeterminetheexpected (required) rateofreturnforarisky
asset?
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OBJECTIVES OF OUR STUDY
Usingthe SML, whatdo wemean byanundervaluedandovervaluedsecurity,andhowdo wedetermine whetheranassetisundervaluedorovervalued?
Whatisanassets characteristic line,andhow doyou computethe characteristic lineforanasset?
Whatistheimpactonthe characteristic linewhenyou computeitusingdifferentreturnintervals (suchas weeklyversusmonthly) and
whenyouemploydifferentproxies (thatis,benchmarks) forthemarketportfolio
Whathappenstothe capitalmarketline (CML)whenyouassumetherearedifferencesintherisk-free borrowingandlendingrates?
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OBJECTIVES OF OUR STUDY
Whatisazero-betaassetandhow doesitsuseimpactthe CML?
Whathappenstothesecurityline (SML) whenyouassumetransactions costs,heterogeneousexpectations,differentplanningperiods,andtaxes?
Whatarethemajorquestions considered whenempiricallytestingthe CAPM?
Whataretheempiricalresultsfromteststhatexaminethestabilityofbeta?
How doalternativepublishedestimatesofbetacompare?
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OBJECTIVES OF OUR STUDY
Whataretheresultsofstudiesthatexaminetherelationship betweensystematic riskandreturn?
Whatothervariables besides betahavehadasignificantimpactonreturns?
Whatisthetheoryregardingthe marketportfolioandhow doesthisdifferfromthe
marketproxyusedforthemarketportfolio?
Assumingthereisa benchmarkproblem,whatvariablesareaffected byit?
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RECALLING PORTFOLIO THEORY
One basic assumptionofportfoliotheoryisthatasaninvestoryou wanttomaximizethereturnsfromyour
investmentsforagivenlevelofrisk.
Investorsare basicallyrisk averse,meaningthat,given
a choice betweentwoassets withequalratesofreturn,
they willselecttheasset withthelowerlevelofrisk.
Thisdoesnotimplythateverybodyisriskaverseorthat
investorsare completelyriskaversiveregardingall
financial commitments.
Certainpeople buylotteryticketsandgambleatracetracksorin casinos, whereitisknownthattheexpected
returnsarenegative, whichmeansthatparticipantsare
willingtopayfortheexcitementoftheriskinvolved.
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RECALLING PORTFOLIO THEORY
Ourbasic assumptionisthatmostinvestors committinglargesumsofmoneytodevelopinganinvestmentportfolioareriskaversive.
Itgivesapositiverelationship betweenexpectedreturnandexpectedrisk.
Historically wealsofindthatthereis
generallyapositiverelationship betweentheratesofreturnonvariousassetsandtheirmeasuresofrisk.
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RECALLING PORTFOLIO THEORY
Riskisthe uncertainty of future outcomes Analternativedefinitionmight bethe probability of an
adverse outcome.
Intheearly 1960s,theinvestment communitytalked
aboutrisk, butthere wasnospecific measurefortheterm.
The basic portfoliomodel wasdeveloped byHarryMarkowitz, whoderivedtheexpectedrateofreturnforaportfolioofassetsandanexpectedriskmeasure.
Markowitzshowedthatthevarianceoftherateofreturnwasameaningfulmeasureofrisk.
Thisportfoliovarianceformulaindicatedtheimportanceofdiversifyingyourinvestmentstoreducethetotalriskofaportfolio butalsoshowedhowtoeffectivelydiversify.
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Althoughtherearenumerouspotential
measuresofrisk,varianceorstandard
deviationofreturnsareused because:
thismeasureissomewhatintuitive;
itisa correctand widelyrecognizedrisk
measure;and
ithas beenusedinmostofthetheoreticalassetpricingmodels.
RECALLING PORTFOLIO THEORY
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Expectedreturnofanindividualstock
ComputationofExpected Returnforan
individualriskystock
Expected Return
E( R )=
RECALLING PORTFOLIO THEORY
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Expectedreturnonportfolioofriskyassets
ComputationofExpected Returnforaportfolio
ofriskyassets:
RECALLING PORTFOLIO THEORY
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MeasurementofRisk
Varianceorthestandarddeviationofexpected
returnsisusedasthemeasureofrisk.
Measurementofriskforanindividual
Investment:
Piis the probability of the possible rate of return,
Ri
RECALLING PORTFOLIO THEORY
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COMPUTATIONOFTHE VARIANCEOFTHE EXPECTED RATE
OFRETURNFORAN INDIVIDUAL RISKY ASSET
RECALLING PORTFOLIO THEORY
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MeasurementofRisk (contd)
Measurement of Risk for a portfolio:
Two basic conceptsinstatistics covariance;and
correlation,
must beunderstood before wediscuss
theformulaforthevarianceoftherateofreturnforaportfolio.
RECALLING PORTFOLIO THEORY
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RECALLING PORTFOLIO THEORY
Covariance isameasureofthedegreeto whichtwovariables movetogetherrelativetotheirindividualmeanvaluesovertime. A positive covariancemeansthattheratesofreturnfortwo
investmentstendtomoveinthesamedirectionrelativetotheir
individualmeansduringthesametimeperiod. anegative covarianceindicatesthattheratesofreturnfortwo
investmentstendtomoveindifferentdirectionsrelativetotheirmeansduringspecifiedtimeintervalsovertime.
Themagnitude ofthe covariancedependsonthevariancesoftheindividualreturnseries,as wellasontherelationship
betweentheseries. Fortwoassets,iandj, the covarianceofratesofreturnis
definedas:
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RECALLING PORTFOLIO THEORY
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RECALLING PORTFOLIO THEORY
Standard Deviation of a Portfolio
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RECALLING PORTFOLIO THEORY
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RECALLING PORTFOLIO THEORY
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RECALLING PORTFOLIO THEORY
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RECALLING PORTFOLIO THEORY
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RECALLING PORTFOLIO THEORY
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CAPITAL ASSET PRICING MODEL
Followingthedevelopmentofportfoliotheory by
Markowitz,twomajortheorieshave beenputforththatderiveamodelforthevaluationofriskyassets.
Infirstsession I willintroduceoneofthesetwomodelsthatis,the capitalassetpricingmodel (CAPM).
The backgroundonthe CAPM isimportantatthispoint
becausetheriskmeasureimplied bythismodelisanecessaryinputforoursubsequentdiscussiononthevaluationofriskyassets.
Thepresentation concerns capitalmarkettheoryandthecapitalassetpricingmodelthat wasdevelopedalmostconcurrently bythreeindividuals.
Subsequently,analternativemultifactorassetvaluationmodel wasproposed,thearbitragepricingtheory (APT).
Thishasledtothedevelopmentofnumerousothermultifactormodelsthatarethesubjectof2ndsession.
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CAPITAL ASSET PRICING MODEL
Capitalmarkettheoryextendsportfoliotheory
anddevelopsamodelforpricingallriskyassets.Thefinalproduct,thecapital asset pricingmodel (CAPM), willallow youtodeterminetherequiredrateofreturnforanyriskyasset.
We begin withthe backgroundofcapitalmarkettheorythatincludestheunderlyingassumptionsofthetheoryandadiscussionofthefactorsthatledtoitsdevelopment.This includes ananalysis of the effect of assuming the
existence of a risk-free asset. Notably,assumingtheexistenceofarisk-free
ratehassignificantimplicationsforthepotentialreturnandriskandalternativerisk-returncombinations.
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CAPITAL ASSET PRICING MODEL
AssumptionsofCapital Market Theory
1. Allinvestorsare Markowitzefficientinvestors who wanttotargetpointsontheefficientfrontier. Theexactlocationontheefficientfrontierand,therefore,thespecific portfolioselected willdependontheindividualinvestorsrisk-returnutilityfunction.
2. Investors can borrow orlendanyamountofmoneyattherisk-freerateofreturn(RFR).
3. Allinvestorshavehomogeneousexpectations;thatis,theyestimateidenticalprobabilitydistributionsforfutureratesofreturn.
4. Allinvestorshavethesameone-periodtimehorizon
5. Allinvestmentsareinfinitelydivisible,
6. Therearenotaxesortransaction costsinvolvedin buyingorsellingassets.
7. Thereisnoinflationorany changeininterestrates,orinflationisfullyanticipated.
8. Capitalmarketsareinequilibrium.
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CAPITAL ASSET PRICING MODEL
Theassumptionofarisk-freeassetintheeconomyiscriticaltoassetpricingtheory. Therefore,first we willunderstandthemeaningofarisk-freeassetandshowsitseffectontheriskandreturnmeasures whenthisrisk-free
assetis combined withaportfolio. Astheexpectedreturnonarisk-freeassetisentirely
certain,thestandarddeviationofitsexpectedreturniszero . Therateofreturnearnedonsuchanassetshould betherisk-freerateofreturn(RFR),
When weintroducethisrisk-freeassetintotherisky worldofthe Markowitzportfoliomodel wefindthe covarianceoftherisk-freeasset withanyriskyassetorportfolioofassets willalwaysequalzero.
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CAPITAL ASSET PRICING MODEL
Combining a Risk-Free Asset with a RiskyPortfolio
Whathappenstotheaveragerateofreturnand
thestandarddeviationofreturns whenyou
combinearisk-freeasset withaportfolioofriskyassets?
1. ExpectedReturn Liketheexpectedreturnfora
portfoliooftworiskyassets,theexpectedrateof
returnforaportfoliothatincludesarisk-freeassetisthe weightedaverageofthetworeturns:
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CAPITAL ASSET PRICING MODEL
Combining a Risk-Free Asset with a Risky Portfolio
2. Standard Deviation theexpectedvarianceforatwo-assetportfoliois:
Substitutingforthevaluesforriskfreeassets:
Weknow thatthevarianceoftherisk-freeassetiszero,thatis, 2RF =0. Becausethe correlation betweentherisk-freeassetandanyriskyasset isalsozero,thefactorrRF,i intheprecedingequationalsoequalszero. Therefore,any componentofthevarianceformulathathaseitheroftheseterms willequalzero.Whenyoumaketheseadjustments,theformula becomes:
Thestandarddeviationis
Therefore,thestandarddeviationofaportfoliothat combinestherisk-freeasset withriskyassetsisthe linear proportion of the standarddeviation of the risky asset portfolio.
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CAPITAL ASSET PRICING MODEL
Combining a Risk-Free Asset with a Risky Portfolio
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CAPITAL ASSET PRICING MODEL
Combining a Risk-Free Asset with a Risky Portfolio Therefore,both return and risk increase in a
linear fashion along the original Line RFR-M, and
thisextensiondominateseverything below the
lineontheoriginalefficientfrontier. Thus,youhaveanew efficientfrontier:the
straightlinefromtheRFRtangentto Point M.
Thislineisreferredtoasthecapital market line
(CML)
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CAPITAL ASSET PRICING MODEL
The Market Portfolio
Because Portfolio M liesatthepointoftangency,ithasthehighestportfoliopossibilityline,andeverybody willwanttoinvestin Portfolio M and borrow orlendto besomewhereonthe CML. Thisportfoliomust,therefore,
includeall risky assets. Thisportfoliothatincludesallriskyassetsisreferredtoas
themarket portfolio.
Becausethemarketportfolio containsallriskyassets,itisacompletely diversified portfolio, whichmeansthatall
theriskuniquetoindividualassetsintheportfolioisdiversifiedaway.
Specifically,a completelydiversifiedportfolio wouldhavea correlation withthemarketportfolioof+1.00. Thisislogical because completediversificationmeanstheeliminationofalltheunsystematic oruniquerisk.
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CAPITAL ASSET PRICING MODEL
The Market Portfolio
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CAPITAL ASSET PRICING MODEL
Now we canproceedtouseittodetermineanappropriateexpectedrateofreturnonariskyasset. Thissteptakesusintothecapital assetpricing model (CAPM), whichisamodelthatindicates whatshould betheexpectedorrequiredratesofreturnonriskyassets.
Toaccomplishtheforegoing, wedemonstratethecreationofasecuritymarketline (SML) thatvisuallyrepresentstherelationship betweenriskandtheexpectedortherequiredrateofreturnon
anasset. Theequationofthis SML,togetherwithestimates
forthereturnonarisk-freeassetandonthemarketportfolio, cangenerateexpectedorrequiredratesofreturnforanyasset basedonits
systematic risk.
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CAPITAL ASSET PRICING MODEL Weknow thattherelevantriskmeasureforanindividualriskyassetis
its covariance withthemarketportfolio (Covi,M). Therefore, we candraw therisk-returnrelationshipasshown below
withthesystematic covariancevariable (Covi,M) astheriskmeasure.
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CAPITAL ASSET PRICING MODEL
Thereturnforthemarketportfolio (RM) should be
consistent withitsownrisk, whichisthe covarianceofthemarket withitself. Ifyourecalltheformulaforcovariance,you willseethatthe covarianceofanyasset withitselfisitsvariance,
Covi,i= i2.
Inturn,the covarianceofthemarket withitselfisthevarianceofthemarketrateofreturn CovM,M = M2.
Therefore,theequationfortherisk-returnlineinthepreviousgraph will be:
Defining CoviM / M2 as beta, (i),thisequation can be
stated:
E(Ri) =RFR+ i(RM RFR)
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CAPITAL ASSET PRICING MODEL
Beta can beviewedasastandardizedmeasureofsystematicrisk.
Specifically, wealreadyknow thatthe covarianceofanyassetiwiththemarketportfolio (CoviM) istherelevantriskmeasure.
Betaisastandardizedmeasureofrisk becauseitrelatesthiscovariancetothevarianceofthemarketportfolio.
Asaresult,themarketportfoliohasa betaof1. Therefore,ifthe
iforanassetisabove 1.0,theassethashighernormalized
systematic riskthanthemarket, whichmeansthatitismorevolatilethantheoverallmarketportfolio.
Giventhisstandardizedmeasureofsystematic risk,the SMLgraph can beexpressedasshownonnextpage. Thisisthesamegraphasshownonpreviouspage,exceptthereisadifferentmeasureofrisk. Specifically,thegraph (nextpage)replacesthe covarianceofanassetsreturns withthemarketportfolioastheriskmeasure withthestandardizedmeasureofsystematic risk (beta), whichisthe covarianceofanasset withthemarketportfoliodivided bythevarianceof themarketportfolio.
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CAPITAL ASSET PRICING MODEL
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CAPITAL ASSET PRICING MODEL
Determiningthe Expected RateofReturnfora Risky Asset Todemonstratehow you would computetheexpectedorrequired
ratesofreturn, considerthefollowingexamplestocksassumingyouhavealready computed betas:
Assumethat weexpecttheeconomysRFRto be 6 percent (0.06) andthereturnonthemarketportfolio (RM) to be 12 percent (0.12). Thisimpliesamarketriskpremiumof6 percent (0.06).Withtheseinputs,the SML equation wouldyieldthefollowingexpected (required) rates
ofreturnforthesefivestocks:
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CAPITAL ASSET PRICING MODEL
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CAPITAL ASSET PRICING MODEL
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CAPITAL ASSET PRICING MODEL
Stock A haslowerriskthantheaggregatemarket,soyoushouldnotexpect (require) itsreturnto beashighasthereturnonthemarketportfolioofriskyassets. Youshouldexpect (require) Stock A toreturn 10.2 percent.
Stock B hassystematic riskequaltothemarkets (beta=
1.00),soitsrequiredrateofreturnshouldlikewise beequaltotheexpectedmarketreturn (12 percent).
Stocks C and D havesystematic riskgreaterthanthemarkets,sotheyshouldprovidereturns consistent withtheirrisk.
Finally, Stock E hasanegative beta (whichisquiterareinpractice),soitsrequiredrateofreturn,ifsuchastockcould befound, would be below theRFR.
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CAPITAL ASSET PRICING MODEL
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CAPITAL ASSET PRICING MODEL
EMPIRICAL TESTSOFTHECAPM Whentestingthe CAPM,therearetwomajorquestions.
First,How stable is the measure of systematic risk(beta)?Because betaisourprincipalriskmeasure,itisimportanttoknow whetherpast betas can beusedasestimatesoffuture betas.Also,how dothealternativepublishedestimatesofbeta compare?
Second,Is there a positive linear relationship ashypothesized between beta and the rate of return onrisky assets?Morespecifically,how welldoreturnsconformtothefollowing SML equation,discussedearlier
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CAPITAL ASSET PRICING MODEL
EMPIRICAL TESTSOFTHECAPM Numerousstudieshaveexaminedthestabilityofbeta
andgenerally concludedthattheriskmeasure wasnotstableforindividualstocks butthestabilityofthe betafor
portfolios ofstocksincreaseddramatically. Thelargertheportfolioofstocks (e.g.,over50 stocks)
Thelongertheperiod (over26 weeks),themorestablethe betaoftheportfolio.
Also,the betastendedtoregresstowardthemean.
Specifically,high-betaportfoliostendedtodeclineovertimetowardunity (1.00), whereaslow-betaportfoliostendedtoincreaseovertimetowardunity.
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CAPITAL ASSET PRICING MODEL
Anotherfactorthataffectsthestabilityofbetaishowmanymonthsareusedtoestimatethe original betaandthetest beta. Roenfeldt, Griepentrog,and Pflamm (RGP)compared betasderivedfrom48monthsofdatatosubsequent betasfor12, 24,36,and48months.
The48- month betas werenotgoodforestimatingsubsequent 12-month betas but werequitegoodforestimating 24-,36-,and48-month betas.
Tosummarize,individual betas weregenerallyvolatileovertime whereaslargeportfolio betas werestable.
Also,itisimportanttouseatleast36 monthsofdatatoestimate betaand be consciousofthestockstradingvolumeandsize.
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CAPITAL ASSET PRICING MODEL
ARBITRAGEPRICING THEORY
Whatisthearbitragepricingtheory (APT)
and whatareitssimilaritiesand
differencesrelativetothe CAPM?
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CAPITAL ASSET PRICING MODEL
ARBITRAGEPRICING THEORY Arbitrage Pricing Theory (APT), was
developed by Rossinthemid-1970s withthreemajorassumptions:1. Capitalmarketsareperfectly competitive.
2. Investorsalwaysprefermore wealthtoless wealthwith certainty.
3. Thestochastic processgeneratingassetreturns can
beexpressedasalinearfunctionofasetofKriskfactors (orindexes).
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CAPITAL ASSET PRICING MODEL
ARBITRAGEPRICING THEORY