资本资产定价模型(CAPM.ppt

FoundationsofFinancialAnalysisandInvestments Lecture3 CapitalAssetPricingModel CAPM DrEkaterinaSvetlova Today slecture Briefrevision Lecture2Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerateMPTandCAPM PreliminaryremarksTheCapitalAssetPricingModel CAPM FirstconsiderationsaboutthelimitationsofCAPM DrEkaterinaSvetlova TheportfolioconsistsoftworiskyassetsD debt andE equity TheirweightsintheportfolioareWeconstructriskyportfoliosvaryingtoprovidethelowestpossibleriskforanygivenlevelofexpectedreturnE rp wDE rD wEE rE DrEkaterinaSvetlova xDandxE xD xE 1 xD 0 xE 0 xDandxE Cov rD rE DE D E Successofdiversificationdependsonthecorrelationcoefficient Bodieetal 2014 Ch 7 1 Briefrevision Lecture2 DrEkaterinaSvetlova Bodieetal 2014 Table7 1 p 208 Bodieetal 2014 Table7 3 p 211 A B Bodieetal 2014 p 214 1 Briefrevision Lecture2 DrEkaterinaSvetlova Bodieetal 2014 Table7 1 p 208 Bodieetal 2014 Table7 3 p 211 When DE 1 When DE 0 1 Briefrevision Lecture2 1 Briefrevision Lecture2 Source Bodieetal 2014 p 220 DrEkaterinaSvetlova DrEkaterinaSvetlova Diversifiable nonsystematic riskvsundiversifiable systematic risk 1 Briefrevision Lecture2 Bodieetal 2014 p 207 DrEkaterinaSvetlova Howdoesdiversificationmatter DrEkaterinaSvetlova Sponsors Trustees TheInvestmentManagementFirm Investmentconsultants theTampafirefightersandpoliceofficerspensionfund CityofTampa Florida HaroldJ BowenIII Howdoesdiversificationmatter Source Asforbeingdiversified whichisthemantraofnearlyallinstitutionalmoneymanagersandconsultants theTampafund isn t T hefund sassetsareconcentratedinarelativelysmallnumberofstocksandfixed incomeinvestments Inshort theTampapensionfundprettymuchbreaksalltheconventionalrulesoffundmanagement 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova Unlimitedborrowingandlendingatarisk freerate Risklessassetisanassetwithacertainreturnforthegiventimehorizon Forexample USTreasurybondsthatautomaticallyadjustforinflation TIPS Treasuryinflationprotectedsecurities orshorttermUSTreasurybills UST bills Standarddeviationofthereturn 0 DrEkaterinaSvetlova 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate IfyouinvestinassetHandrisklessasset xHandxf 1 xH Erp 1 xH Rf xHRH Rf xH ErH Rf p 1 xH 2 f xH2 H2 2xH 1 xH fH f H As f 0 weobtain p xH H 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova Source Perold2004 DrEkaterinaSvetlova Combiningequationsforportfolioreturnandrisk weobtain ErH RfErp Rf p H 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate Source Perold2004 ErH Rf H Theslope Sharperatio ErH Rf Riskpremium 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova Source Perold2004 SharperatioofassetH 12 5 40 0 175 Important allcombinationsofassetHwithrisk freeborrowingandlendinghavethesameSharperatio itistheslopeofastraightline SharperatioofassetM 10 5 20 0 25 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova Source Perold2004 UseofSharperatioinpractice ShaperatioisusedtomeasuretheperformanceofaportfolioAdvantage theriskadjustedperformancemeasurement 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova SharperatioofH SharperatioofMThecombinationofrisk freeassetandMdominatesthecombinationofrisk freeassetandH 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova Source Perold2004 Howmuchofeachriskyassetshouldoneholdintheportfolio Sharperatio 0 305 higherthan0 25forMand0 175forH AllinvestorswillholdassetsMandHinproportions74 26 Newefficiencylinewhenrisk freelending borrowingisallowed 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova Source Perold2004 CorrelationbetweenMandHassumedtobezero Incaseofmanyriskyassets Tobinseparationtheorem Portfoliochoiceproblemcanbeseparatedintwotasks IdentifytheoptimalriskyportfolioIdentifythecapitalallocationbetweenriskyandrisklessinvestments Riskaversion Riskseeking 3 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova Source Perold2004 UseofTobinseparationinpractice Source 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova CapitalMarketLine CML setofpotentialallocationsbetweenariskyassetandano riskyasset oraportfoliothatcontainsonlyriskyassetsandrisk freeassets M M themarketportfolio AllinvestorsholdportfolioM notdependentoninvestors toleranceforrisk Themarketportfolioistheonewherethesupplyequalsdemand marketclearing 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova 3 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova ErM RfErP Rf P M Marketpriceofrisk Theamountofriskintheportfolio Allrationalinvestorswillholdthesamemarketportfolio M ForanyefficientportfolioontheCMLapplies Generalformula Expectedreturn Priceoftime Priceofrisk x Amountofrisk 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova 3 MPTandCAPM Preliminaryremarks DrEkaterinaSvetlova 3 MPTandCAPM preliminaryremarks Portfoliotheory normative givenexpectations expectedreturns volatilities correlations Howshouldarisk averseinvestorstructureanefficientportfolio Howtoachieveanoptimaltrade offbetweenriskandreturn differencesinexpectations compositionofthetangentialportfolio TheCapitalAssetPricingModel positive underveryrestrictiveassumptions whatthemarketshouldlooklikeinequilibrium CAPMidentifiesaportfoliothatmustbeefficientifassetpricesaretoclearthemarketofallassets demandforsecurities supply CAPMisanequilibriummodel DrEkaterinaSvetlova ThemodelgivesusaprecisepredictionoftherelationshipthatweshouldobservebetweentheriskofanassetanditsexpectedreturninequilibriumFunctionsoftheCAPMmodel Toprovideabenchmarkrateofreturnforevaluatinginvestments fair returngivenarisk Tomakeaguessfornewsecurities e g IPOs Tomeasuretheriskofanindividualsecurity 3 MPTandCAPM preliminaryremarks DrEkaterinaSvetlova Allinvestorsaremean varianceoptimizersandestimatetheirportfoliosaccordingtoE R andvariance allMPTassumptionsapply AllinvestorshavehomogeneousexpectationsconcerningE R VarianceundCovariances everyinvestorhasthesamerisk returnexpectationforanygivenstock identifyefficientfrontierCapitalmarketsareperfect allassetsareinfinitelydivisable therearenotransactioncosts notaxes allinvestorsarepricetakersandhaveanequalaccesstomarket informationandinvestmentopportunities Thereistheunlimitedborrowingandlendingatarisk freerateofinterests CAPMassumptions 3 MPTandCAPM preliminaryremarks DrEkaterinaSvetlova 4 TheCapitalAssetPricingModel CAPM DrEkaterinaSvetlova DrEkaterinaSvetlova 4 TheCapitalAssetPricingModel CAPM Whatistheriskofanindividualsecurityinthecontextofthebestportfolioyoucanhold Inotherwords whatareequilibriumreturnsandrisksofanindividualsecurity Intuition Ifweinvestinrisk freeassetandtheoptimalriskyportfolio thenouronlysourceofriskisthevarianceofthereturnontheriskyportfolio Theriskofanindividualsecurityistheamountthatsecuritycontributestothevarianceofthereturnontheoptimalriskyportfolio Whatistherateofchangeinthemarketportfoliovariancegiventhatwechangetheweightontheithsecurityalittlebit Abasicprincipleofequilibriumisthatallinvestmentsshouldofferthesamereward to riskratio Thereward to risksratiooftheithsecurityandthemarketportfolioshouldbeequal 2 Mean varianceoptimizationwithunlimitedborrowingandlendingatarisk freerate DrEkaterinaSvetlova thecontributionofthesecurityitothevarianceofthemarketportfolio TheCAPMformula Bodieetal 2014 p 295ff 4 TheCapitalAssetPricingModel CAPM Thebetaofasecuritywithrespecttothemarketportfolioisthemeasureofriskforthatsecurity Theconceptualmeaningofthe Beta The beta isameasureofthevolatility systematicrisk ofasecurityoraportfolioincomparisontothemarketasawholeIfbeta 1 itindicatesthatthesecurity spricewillbemorevolatilethanthemarketExample abetaequalsto1 3meansthatthesecurityis30 morevolatilethanthemarket DrEkaterinaSvetlova Useofbetainpractice BetaasameasureofriskofamutualfundExample TheBlackRockGlobalSmallCapFund factsheet Source 4 TheCapitalAssetPricingModel CAPM DrEkaterinaSvetlova Thesecuritymarketlineprovidesabenchmarkfortheevaluationofinvestmentperformance AssetplotsabovetheSMLofferagreaterexpectedreturnsthanindicatedbytheCAPM underpricedassets AssetplotsbelowtheSMLofferalowerexpectedreturnsthanindicatedbytheCAPM overpricedassets 4 TheCapitalAssetPricingModel CAPM DrEkaterinaSvetlova Example Marketreturnisexpectedtobe14 thestockbetais1 2 theT billrateis6 Theexpectedreturnonthestockis 6 1 2 14 6 15 6 Ifyouexpect17 returnforthestock theimpliedalphais1 4 4 TheCapitalAssetPricingModel CAPM DrEkaterinaSvetlova ImplicationsoftheCAPM TheexpectedreturnofastockdoesnotdependonitsidiosyncraticriskIntheCAPM astock sexpectedreturndoesnotdependonthegrowthrateofitsexpectedfuturecashflowsBetameasurestheriskofanassetthatcannotbediversifiedaway Overallriskofanasset Systematicrisk Companyspecificrisk 4 TheCapitalAssetPricingModel CAPM DrEkaterinaSvetlova ImplicationsoftheCAPMfordiversification DiversificationreducesrisksbutdoesnoteliminatethemThetypeofriskthatdiversificationreducesisthecompanyspecific idiosyncraticrisk ariskspecifictoeachparticularasset itisnotcorrelatedacrossassetsWhenweincreaseanumberofassetsinaportfolio weexpectthatonaveragetheidiosyncraticriskscanceleachotherandthattheactualreturngetsclosertotheexpectedreturn thereisnoreasontoexpectcompensationforbearingthisriskSystematicriskiscommonacrossassets youcannotreducethisriskthroughdiversificationSourcesofsystematicrisk theoveralleconomyorfinancialmarkets risk aversinvestorsrequirecompensationforbearingthisrisk Fullenkamp2012 4 TheCapitalAssetPricingModel CAPM DrEkaterinaSvetlova Quickcheck Arethefollowingtrueorfalse Explain Stockswithabetaofzeroofferanexpectedrateofreturnofzero TheCAPMimpliesthatinvestorsrequireahigherreturntoholdhighlyvolatilesecuritiesYoucanconstructaportfoliowithbetaof0 75byinvesting75 oftheinvestmentbudgetinT billsandtheremainderinthemarketportfolio Source Bodieetal 2014 317 DrEkaterinaSvetlova 4 TheCapitalAssetPricingModel CAPM Quickcheck Whichofthefollowingfactorsreflectpuremarketriskforagivencorporation Increasedshort terminterestrates FireinthecorporationwarehouseIncreasedinsurancecostsDeathoftheCEOIncreasedlabourcosts Source Bodieetal 2014 235 DrEkaterinaSvetlova 4 TheCapitalAssetPricingModel CAPM MainpredictionsoftheCAPMAllinvestorswillalwayscombineariskfreeassetwiththemarketportfoliowillhavethesameportfolioofriskyassets themarketportfolio agreeontheexpectedreturnandontheexpectedvarianceofthemarketportfolioandofeveryassetagreeonthemarketriskpremiumandonthebetaofeveryassetagreeonthemarketportfoliobeingontheminimumvariancefrontierandbeingmean varianceefficientexpectreturnsfromtheirinvestmentsaccordingtothebetasTradingvolumeoffinancialmarketswillbeverysmall 4 TheCapitalAssetPricingModel CAPM DrEkaterinaSvetlova 5 FirstconsiderationsaboutthelimitationsofCAPM DrEkaterinaSvetlova CAPM equilibriummodel snapshot ofthemarketatonepointintime Whatis marketportfolio Indices nationalvs international RiskpremiumsdependoninvesmentclimateandbusinesscycleWarrenBuffett Riskcomesfromnotknowingwhatyou redoing Doesthefundamentalcashflowanalysisreallynotmatter CAPMhasnotbeenconfirmedempirically nextlecture DrEkaterinaSvetlova doesn texplainthevarianceofreturns Basu 1977 earning price ratioeffectBanz 1981 sizeeffectBhandari 1988 highdebt equity ratioeffectStatmanetal 1980 book to market ratioeffect BenjaminGraham thelegendaryinvestor Betaisamoreorlessusefulmeasureofpastpricefluctuationsofcommonstocks Whatbothersmeisthatauthorit