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Foundationsof

FinancialAnalysisandInvestmentsLecture3: CapitalAssetPricingModel(CAPM)DrEkaterinaSvetlovaFoundationsof

FinancialAnalToday‘slectureBriefrevision:Lecture2Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateMPTandCAPM:PreliminaryremarksTheCapitalAssetPricingModel(CAPM)FirstconsiderationsaboutthelimitationsofCAPMDrEkaterinaSvetlovaToday‘slectureBriefrevision:TheportfolioconsistsoftworiskyassetsD(debt)andE(equity)TheirweightsintheportfolioareWeconstructriskyportfoliosvaryingtoprovidethelowestpossibleriskforanygivenlevelofexpectedreturnE(rp)=wDE(rD)+wEE(rE)

DrEkaterinaSvetlovaxD

and

xE(xD+xE=1;xD≥0,xE≥0)xD

and

xE Cov(rD,rE)=DEDESuccessofdiversificationdependsonthecorrelationcoefficientBodieetal.2014,Ch.71.Briefrevision:Lecture2

TheportfolioconsistsoftwoDrEkaterinaSvetlovaDebtEquityExpectedreturnE(r)8%13%Standarddeviation12%20%Bodieetal.(2014),Table7.1,p.208Bodieetal.(2014),Table7.3,p.211ABBodieetal.(2014),p.2141.Briefrevision:Lecture2

DrEkaterinaSvetlovaDebtEquitDrEkaterinaSvetlovaDebtEquityExpectedreturnE(r)8%13%Standarddeviation12%20%Bodieetal.(2014),Table7.1,p.208Bodieetal.(2014),Table7.3,p.211WhenρDE=-1,

WhenρDE=0,

1.Briefrevision:Lecture2

DrEkaterinaSvetlovaDebtEquit1.Briefrevision:Lecture2

Source:Bodieetal.2014:p.220DrEkaterinaSvetlova1.Briefrevision:Lecture2

SDrEkaterinaSvetlovaDiversifiable(nonsystematic)riskvsundiversifiable(systematic)risk1.Briefrevision:Lecture2

Bodieetal.(2014),p.207DrEkaterinaSvetlovaDiversifiDrEkaterinaSvetlovaHowdoesdiversificationmatter?DrEkaterinaSvetlovaHowdoesDrEkaterinaSvetlovaSponsorsTrusteesTheInvestmentManagementFirmInvestmentconsultantstheTampafirefightersandpoliceofficerspensionfundCityofTampa,FloridaHaroldJ.BowenIIIHowdoesdiversificationmatter?Asforbeingdiversified,whichisthemantraofnearlyallinstitutionalmoneymanagersandconsultants,[theTampafund]isn’t.…[T]hefund’sassetsareconcentratedinarelativelysmallnumberofstocksandfixed-incomeinvestments.Inshort,theTampapensionfundprettymuchbreaksalltheconventionalrulesoffundmanagement.DrEkaterinaSvetlovaSponsorsT2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlova2.Mean-varianceoptimizatiUnlimitedborrowingandlendingatarisk-freerate:Risklessassetisanassetwithacertainreturnforthegiventimehorizon.Forexample:USTreasurybondsthatautomaticallyadjustforinflation(TIPS:Treasuryinflationprotectedsecurities)orshorttermUSTreasurybills(UST-bills)Standarddeviationofthereturn:σ=0

DrEkaterinaSvetlova2.Mean-varianceoptimizationwithunlimitedborrowingandlending atarisk-freerateUnlimitedborrowingandlendinIfyouinvestinassetHandrisklessasset:xHandxf=1-xHErp=(1-xH)Rf+xHRH=

Rf+xH(ErH-Rf)σp=(1-xH)2σf+xH2σH2+2xH(1-xH)ρfHσfσHAsσf=0,weobtain:σp=xHσH2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004IfyouinvestinassetHandrDrEkaterinaSvetlovaCombiningequationsforportfolioreturnandrisk,weobtain:

ErH-Rf Erp=Rf+ σp

σH2.Mean-varianceoptimizationwithunlimitedborrowingandlending atarisk-freerateSource:Perold2004DrEkaterinaSvetlovaCombining

ErH-Rf

σHTheslope:Sharperatio(ErH-Rf)Riskpremium2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004

Theslope:Sharperatio(ErHSharperatioofassetH:(12%-5%)/40%=0.175Important:allcombinationsofassetHwithrisk-freeborrowingandlendinghavethesameSharperatio:itistheslopeofastraightlineSharperatioofassetM:(10%-5%)/20%=0.252.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004SharperatioofassetH:ImportUseofSharperatioinpractice:ShaperatioisusedtomeasuretheperformanceofaportfolioAdvantage:theriskadjustedperformancemeasurement2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaUseofSharperatioinpracticSharperatioofH<SharperatioofMThecombinationofrisk-freeassetandMdominatesthecombinationofrisk-freeassetandH2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004SharperatioofH<SharperatHowmuchofeachriskyassetshouldoneholdintheportfolio?Sharperatio:0.305(higherthan0.25forMand0.175forH)AllinvestorswillholdassetsMandHinproportions74/26Newefficiencylinewhenrisk-freelending/borrowingisallowed2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004CorrelationbetweenMandHassumedtobezeroHowmuchofeachriskyassetsIncaseofmanyriskyassets:Tobinseparationtheorem:Portfoliochoiceproblemcanbeseparatedintwotasks:IdentifytheoptimalriskyportfolioIdentifythecapitalallocationbetweenriskyandrisklessinvestmentsRiskaversionRiskseeking3.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004Incaseofmanyriskyassets:TUseofTobinseparationinpractice:

2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaUseofTobinseparationinpraCapitalMarketLine(CML)=setofpotentialallocationsbetweenariskyassetandano-riskyasset(oraportfoliothatcontainsonlyriskyassetsandrisk-freeassets)MM–themarketportfolioAllinvestorsholdportfolioM(notdependentoninvestors’toleranceforrisk)

Themarketportfolioistheonewherethesupplyequalsdemand(marketclearing)2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaCapitalMarketLine(CML)=se

3.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlova

3.Mean-varianceoptimizat

ErM-Rf ErP=Rf+ σP

σMMarketpriceofriskTheamountofriskintheportfolioAllrationalinvestorswillholdthesamemarketportfolio(M)ForanyefficientportfolioontheCMLapplies:Generalformula:Expectedreturn=(Priceoftime)+(Priceofrisk)x(Amountofrisk)2.Mean-varianceoptimizationwithunlimitedborrowingandlending atarisk-freerateDrEkaterinaSvetlovaMarketpriceofriskTheamount3.MPTandCAPM:PreliminaryremarksDrEkaterinaSvetlova3.MPTandCAPM:Preliminaryr3.MPTandCAPM:preliminaryremarksPortfoliotheory(normative): givenexpectations(expectedreturns,volatilities,correlations) Howshouldarisk-averseinvestorstructureanefficientportfolio?Howtoachieveanoptimaltrade-offbetweenriskandreturn?(differencesinexpectationscompositionofthetangentialportfolio)TheCapitalAssetPricingModel(positive): underveryrestrictiveassumptionswhatthemarketshouldlooklikeinequilibrium?

CAPMidentifiesaportfoliothatmustbeefficientifassetpricesaretoclearthemarketofallassets(demandforsecurities=supply)

CAPMisanequilibriummodel

DrEkaterinaSvetlova3.MPTandCAPM:preliminaryThemodelgivesusaprecisepredictionoftherelationshipthatweshouldobservebetweentheriskofanassetanditsexpectedreturninequilibriumFunctionsoftheCAPMmodel:Toprovideabenchmarkrateofreturnforevaluatinginvestments(“fair”returngivenarisk)Tomakeaguessfornewsecurities(e.g.,IPOs)Tomeasuretheriskofanindividualsecurity3.MPTandCAPM:preliminaryremarksDrEkaterinaSvetlovaThemodelgivesusaprecisepAllinvestorsaremean-varianceoptimizersandestimatetheirportfoliosaccordingtoE(R)andvariance(allMPTassumptionsapply)AllinvestorshavehomogeneousexpectationsconcerningE(R),VarianceundCovariances(everyinvestorhasthesamerisk-returnexpectationforanygivenstock)identifyefficientfrontierCapitalmarketsareperfect(allassetsareinfinitelydivisable,therearenotransactioncosts,notaxes,allinvestorsarepricetakersandhaveanequalaccesstomarket/informationandinvestmentopportunities)Thereistheunlimitedborrowingandlendingatarisk-freerateofinterestsCAPMassumptions3.MPTandCAPM:preliminaryremarksDrEkaterinaSvetlovaAllinvestorsaremean-varianc4.TheCapitalAssetPricingModel(CAPM)DrEkaterinaSvetlova4.TheCapitalAssetPricingMDrEkaterinaSvetlova4.TheCapitalAssetPricingModel(CAPM)Whatistheriskofanindividualsecurityinthecontextofthebestportfolioyoucanhold?Inotherwords,whatareequilibriumreturnsandrisksofanindividualsecurity?Intuition:Ifweinvestinrisk-freeassetandtheoptimalriskyportfolio,thenouronlysourceofriskisthevarianceofthereturnontheriskyportfolio.Theriskofanindividualsecurityistheamountthatsecuritycontributestothevarianceofthereturnontheoptimalriskyportfolio.Whatistherateofchangeinthemarketportfoliovariancegiventhatwechangetheweightontheithsecurityalittlebit?DrEkaterinaSvetlova4.TheCaAbasicprincipleofequilibriumisthatallinvestmentsshouldofferthesamereward-to-riskratio.Thereward-to-risksratiooftheithsecurityandthemarketportfolioshouldbeequal2.Mean-varianceoptimizationwithunlimitedborrowingandlending atarisk-freerateDrEkaterinaSvetlova

-thecontributionofthesecurityitothevarianceofthemarketportfolioTheCAPMformulaBodieetal.(2014),p.295ffAbasicprincipleofequilibri4.TheCapitalAssetPricingModel(CAPM)

ThebetaofasecuritywithrespecttothemarketportfolioisthemeasureofriskforthatsecurityTheconceptualmeaningofthe“Beta”The“beta”isameasureofthevolatility(systematicrisk)ofasecurityoraportfolioincomparisontothemarketasawholeIfbeta>1,itindicatesthatthesecurity’spricewillbemorevolatilethanthemarketExample:abetaequalsto1.3meansthatthesecurityis30%morevolatilethanthemarketDrEkaterinaSvetlova4.TheCapitalAssetPricingMUseofbetainpractice:BetaasameasureofriskofamutualfundExample:TheBlackRockGlobalSmallCapFund(factsheet)4.TheCapitalAssetPricingModel(CAPM)

DrEkaterinaSvetlovaUseofbetainpractice:4.TheThesecuritymarketlineprovidesabenchmarkfortheevaluationofinvestmentperformanceAssetplotsabovetheSMLofferagreaterexpectedreturnsthanindicatedbytheCAPM(underpricedassets)AssetplotsbelowtheSMLofferalowerexpectedreturnsthanindicatedbytheCAPM(overpricedassets)4.TheCapitalAssetPricingModel(CAPM)

DrEkaterinaSvetlova

ThesecuritymarketlineproviExample:Marketreturnisexpectedtobe14%,thestockbetais1.2,theT-billrateis6%.Theexpectedreturnonthestockis:6+1.2(14–6)=15.6%Ifyouexpect17%returnforthestock,theimpliedalphais1.4%4.TheCapitalAssetPricingModel(CAPM)

DrEkaterinaSvetlova

Example:MarketreturnisexpeImplicationsoftheCAPM:TheexpectedreturnofastockdoesnotdependonitsidiosyncraticriskIntheCAPM,astock’sexpectedreturndoesnotdependonthegrowth rateofitsexpectedfuturecashflowsBetameasurestheriskofanassetthatcannotbediversifiedaway

Overallriskofanasset=SystematicriskCompanyspecificrisk+β4.TheCapitalAssetPricingModel(CAPM)

DrEkaterinaSvetlova

ImplicationsoftheCAPM:Overa

ImplicationsoftheCAPMfordiversificationDiversificationreducesrisksbutdoesnoteliminatethemThetypeofriskthatdiversificationreducesisthecompanyspecific=idiosyncraticrisk=ariskspecifictoeachparticularasset=itisnotcorrelatedacrossassetsWhenweincreaseanumberofassetsinaportfolio,weexpectthatonaveragetheidiosyncraticriskscanceleachotherandthattheactualreturngetsclosertotheexpectedreturn

thereisnoreasontoexpectcompensationforbearingthisriskSystematicriskiscommonacrossassets–youcannotreducethisriskthroughdiversificationSourcesofsystematicrisk:theoveralleconomyorfinancialmarkets

risk-aversinvestorsrequirecompensationforbearingthisriskFullenkamp20124.TheCapitalAssetPricingModel(CAPM)DrEkaterinaSvetlovaImplicationsoftheCAPMforQuickcheck:Arethefollowingtrueorfalse?Explain.Stockswithabetaofzeroofferanexpectedrateofreturnofzero.TheCAPMimpliesthatinvestorsrequireahigherreturntoholdhighlyvolatilesecuritiesYoucanconstructaportfoliowithbetaof0.75byinvesting75%oftheinvestmentbudgetinT-billsandtheremainderinthemarketportfolio.Source:Bodieetal.2014:317DrEkaterinaSvetlova4.TheCapitalAssetPricingModel(CAPM)Quickcheck:Source:BodieetaQuickcheck:Whichofthefollowingfactorsreflectpuremarketriskforagivencorporation?Increasedshort-terminterestrates.FireinthecorporationwarehouseIncreasedinsurancecostsDeathoftheCEOIncreasedlabourcosts.Source:Bodieetal.2014:235DrEkaterinaSvetlova4.TheCapitalAssetPricingModel(CAPM)Quickcheck:Source:BodieetaMainpredictionsoftheCAPMAllinvestorswillalwayscombineariskfreeassetwiththemarketportfoliowillhavethesameportfolioofriskyassets(themarketportfolio)agreeontheexpectedreturnandontheexpectedvarianceofthemarketportfolioandofeveryassetagreeonthemarketriskpremiumandonthebetaofeveryassetagreeonthemarketportfoliobeingontheminimumvariancefrontierandbeingmean-varianceefficientexpectreturnsfromtheirinvestmentsaccordingtothebetasTradingvolumeoffinancialmarketswillbeverysmall

4.TheCapitalAssetPricingModel(CAPM)

DrEkaterinaSvetlovaMainpredictionsoftheCAPM4.5.FirstconsiderationsaboutthelimitationsofCAPMDrEkaterinaSvetlova5.FirstconsiderationsaboutCAPM=equilibriummodel(“snapshot”ofthemarketatonepointintime)Whatis“marketportfolio”?Indices,ernational…RiskpremiumsdependoninvesmentclimateandbusinesscycleWarrenBuffett:“Riskcomesfromnotknowingwhatyou’redoing.” Doesthefundamentalcashflowanalysisreallynotmatter?CAPMhasnotbeenconfirmedempirically(nextlecture)DrEkaterinaSvetlovaCAPM=equilibriummodel(“snaβdoesn‘texplainthevarianceofreturns: Basu(1977):earning-price-ratioeffect Banz(1981):sizeeffect Bhandari(1988):highdebt-equity-ratioeffect Statmanetal.(1980):book-to-market-ratioeffectBenjaminGraham,thelegendaryinvestor:Betaisamoreorlessusefulmeasureofpastpricefluctuationsofcommonstocks.Whatbothersmeisthatauthoritiesnowequatethebetaideawiththeconceptofrisk.Pricevariabilityyes;riskno.Realinvestmentriskismeasurednotbythepercentthatastockmaydeclineinpriceinrelationtothegeneralmarketinagivenperiod,butthedangerofalossofqualityandearningpowerthrougheconomicchangesordeteriorationofmanagement.Isbetatherealsourceofrisk?5.FirstconsiderationsaboutthelimitationsofCAPMDrEkaterinaSvetlovaβdoesn‘texplainthevarianceIsCAPMjustCRAP(completelyredundantassetpricing)?Montier(2007):“Institutionalmoneymanagersdon‘tthinkintermsofvarianceasadescriptionofrisk.NeveryethaveImetalongonlyinvestorwhocaresaboutup-sidestandarddeviation;thisgetslumpedintoreturn.”“Anentireindustryappearstohavearisenobsessedwithαandβ.“Fama/French(2004):

?TheCAPM,likeMarkowitz’(1952,1959)portfoliomodelonwhichitisbuilt,isneverthelessatheoreticaltourdeforce.WecontinuetoteachtheCAPMasanintroductiontothefundamentalconceptsofportfoliotheoryandassetpricing,tobebuiltonbymorecomplicatedmodelslikeMerton’s(1973)ICAPM.Butwealsowarnstudentsthatdespiteitsseductivesimplicity,theCAPM’sempiricalproblemsprobablyinvalidateitsuseinapplications.”5.FirstconsiderationsaboutthelimitationsofCAPMDrEkaterinaSvetlovaIsCAPMjustCRAP(completelyReferencesBodie,KaneandMarkus(2014),Investments,McGrauwHill,section7.3andchapter9Perold,Andre(2004),TheCapitalAssetPricingModel,JournalofEconomicPerspectives18(3),pp.773-806.DrEkaterinaSvetlovaReferencesBodie,KaneandMarkFoundationsof

FinancialAnalysisandInvestmentsLecture3: CapitalAssetPricingModel(CAPM)DrEkaterinaSvetlovaFoundationsof

FinancialAnalToday‘slectureBriefrevision:Lecture2Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateMPTandCAPM:PreliminaryremarksTheCapitalAssetPricingModel(CAPM)FirstconsiderationsaboutthelimitationsofCAPMDrEkaterinaSvetlovaToday‘slectureBriefrevision:TheportfolioconsistsoftworiskyassetsD(debt)andE(equity)TheirweightsintheportfolioareWeconstructriskyportfoliosvaryingtoprovidethelowestpossibleriskforanygivenlevelofexpectedreturnE(rp)=wDE(rD)+wEE(rE)

DrEkaterinaSvetlovaxD

and

xE(xD+xE=1;xD≥0,xE≥0)xD

and

xE Cov(rD,rE)=DEDESuccessofdiversificationdependsonthecorrelationcoefficientBodieetal.2014,Ch.71.Briefrevision:Lecture2

TheportfolioconsistsoftwoDrEkaterinaSvetlovaDebtEquityExpectedreturnE(r)8%13%Standarddeviation12%20%Bodieetal.(2014),Table7.1,p.208Bodieetal.(2014),Table7.3,p.211ABBodieetal.(2014),p.2141.Briefrevision:Lecture2

DrEkaterinaSvetlovaDebtEquitDrEkaterinaSvetlovaDebtEquityExpectedreturnE(r)8%13%Standarddeviation12%20%Bodieetal.(2014),Table7.1,p.208Bodieetal.(2014),Table7.3,p.211WhenρDE=-1,

WhenρDE=0,

1.Briefrevision:Lecture2

DrEkaterinaSvetlovaDebtEquit1.Briefrevision:Lecture2

Source:Bodieetal.2014:p.220DrEkaterinaSvetlova1.Briefrevision:Lecture2

SDrEkaterinaSvetlovaDiversifiable(nonsystematic)riskvsundiversifiable(systematic)risk1.Briefrevision:Lecture2

Bodieetal.(2014),p.207DrEkaterinaSvetlovaDiversifiDrEkaterinaSvetlovaHowdoesdiversificationmatter?DrEkaterinaSvetlovaHowdoesDrEkaterinaSvetlovaSponsorsTrusteesTheInvestmentManagementFirmInvestmentconsultantstheTampafirefightersandpoliceofficerspensionfundCityofTampa,FloridaHaroldJ.BowenIIIHowdoesdiversificationmatter?Asforbeingdiversified,whichisthemantraofnearlyallinstitutionalmoneymanagersandconsultants,[theTampafund]isn’t.…[T]hefund’sassetsareconcentratedinarelativelysmallnumberofstocksandfixed-incomeinvestments.Inshort,theTampapensionfundprettymuchbreaksalltheconventionalrulesoffundmanagement.DrEkaterinaSvetlovaSponsorsT2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlova2.Mean-varianceoptimizatiUnlimitedborrowingandlendingatarisk-freerate:Risklessassetisanassetwithacertainreturnforthegiventimehorizon.Forexample:USTreasurybondsthatautomaticallyadjustforinflation(TIPS:Treasuryinflationprotectedsecurities)orshorttermUSTreasurybills(UST-bills)Standarddeviationofthereturn:σ=0

DrEkaterinaSvetlova2.Mean-varianceoptimizationwithunlimitedborrowingandlending atarisk-freerateUnlimitedborrowingandlendinIfyouinvestinassetHandrisklessasset:xHandxf=1-xHErp=(1-xH)Rf+xHRH=

Rf+xH(ErH-Rf)σp=(1-xH)2σf+xH2σH2+2xH(1-xH)ρfHσfσHAsσf=0,weobtain:σp=xHσH2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004IfyouinvestinassetHandrDrEkaterinaSvetlovaCombiningequationsforportfolioreturnandrisk,weobtain:

ErH-Rf Erp=Rf+ σp

σH2.Mean-varianceoptimizationwithunlimitedborrowingandlending atarisk-freerateSource:Perold2004DrEkaterinaSvetlovaCombining

ErH-Rf

σHTheslope:Sharperatio(ErH-Rf)Riskpremium2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004

Theslope:Sharperatio(ErHSharperatioofassetH:(12%-5%)/40%=0.175Important:allcombinationsofassetHwithrisk-freeborrowingandlendinghavethesameSharperatio:itistheslopeofastraightlineSharperatioofassetM:(10%-5%)/20%=0.252.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004SharperatioofassetH:ImportUseofSharperatioinpractice:ShaperatioisusedtomeasuretheperformanceofaportfolioAdvantage:theriskadjustedperformancemeasurement2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaUseofSharperatioinpracticSharperatioofH<SharperatioofMThecombinationofrisk-freeassetandMdominatesthecombinationofrisk-freeassetandH2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004SharperatioofH<SharperatHowmuchofeachriskyassetshouldoneholdintheportfolio?Sharperatio:0.305(higherthan0.25forMand0.175forH)AllinvestorswillholdassetsMandHinproportions74/26Newefficiencylinewhenrisk-freelending/borrowingisallowed2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004CorrelationbetweenMandHassumedtobezeroHowmuchofeachriskyassetsIncaseofmanyriskyassets:Tobinseparationtheorem:Portfoliochoiceproblemcanbeseparatedintwotasks:IdentifytheoptimalriskyportfolioIdentifythecapitalallocationbetweenriskyandrisklessinvestmentsRiskaversionRiskseeking3.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaSource:Perold2004Incaseofmanyriskyassets:TUseofTobinseparationinpractice:

2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaUseofTobinseparationinpraCapitalMarketLine(CML)=setofpotentialallocationsbetweenariskyassetandano-riskyasset(oraportfoliothatcontainsonlyriskyassetsandrisk-freeassets)MM–themarketportfolioAllinvestorsholdportfolioM(notdependentoninvestors’toleranceforrisk)

Themarketportfolioistheonewherethesupplyequalsdemand(marketclearing)2.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlovaCapitalMarketLine(CML)=se

3.Mean-varianceoptimizationwithunlimitedborrowingandlendingatarisk-freerateDrEkaterinaSvetlova

3.Mean-varianceoptimizat

ErM-Rf ErP=Rf+ σP

σMMarketpriceofriskTheamountofriskintheportfolioAllrationalinvestorswillholdthesamemarketportfolio(M)ForanyefficientportfolioontheCMLapplies:Generalformula:Expectedreturn=(Priceoftime)+(Priceofrisk)x(Amountofrisk)2.Mean-varianceoptimizationwithunlimitedborrowingandlending atarisk-freerateDrEkaterinaSvetlovaMarketpriceofriskTheamount3.MPTandCAPM:PreliminaryremarksDrEkaterinaSvetlova3.MPTandCAPM:Preliminaryr3.MPTandCAPM:preliminaryremarksPortfoliotheory(normative): givenexpectations(expectedreturns,volatilities,correlations) Howshouldarisk-averseinvestorstructureanefficientportfolio?Howtoachieveanoptimaltrade-offbetweenriskandreturn?(differencesinexpectationscompositionofthetangentialportfolio)TheCapitalAssetPricingModel(positive): underveryrestrictiveassumptionswhatthemarketshouldlooklikeinequilibrium?

CAPMidentifiesaportfoliothatmustbeefficientifassetpricesaretoclearthemarketofallassets(demandforsecurities=supply)

CAPMisanequilibriummodel

DrEkaterinaSvetlova3.MPTandCAPM:preliminaryThemodelgivesusaprecisepredictionoftherelationshipthatweshouldobservebetweentheriskofanassetanditsexpectedreturninequilibriumFunctionsoftheCAPMmodel:Toprovideabenchmarkrateofreturnforevaluatinginvestments(“fair”returngivenarisk)Tomakeaguessfornewsecurities(e.g.,IPOs)Tomeasuretheriskofanindividualsecurity3.MPTandCAPM:preliminaryremarksDrEkaterinaSvetlovaThemodelgivesusaprecisepAllinvestorsaremean-varianceoptimizersandestimatetheirportfoliosaccordingtoE(R)andvariance(allMPTassumptionsapply)AllinvestorshavehomogeneousexpectationsconcerningE(R),VarianceundCovariances(everyinvestorhasthesamerisk-returnexpectationforanygivenstock)identifyefficientfrontierCapitalmarketsareperfect(allassetsareinfinitelydivisable,therearenotransactioncosts,notaxes,allinvestorsarepricetakersandhaveanequalaccesstomarket/informationandinvestmentopportunities)Thereistheunlimitedborrowingandlendingatarisk-freerateofinterestsCAPMassumptions3.MPTandCAPM:preliminaryremarksDrEkaterinaSvetlovaAllinvestorsaremean-varianc4.TheCapitalAssetPricingM

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