资本资产定价模型(CAPM-文档资料.ppt

Foundations of Financial Analysis and InvestmentsLecture 3:Capital Asset Pricing Model(CAPM)1Todays lecture1.Brief revision:Lecture 22.Mean-variance optimization with unlimited borrowing and lending at a risk-free rate3.MPT and CAPM:Preliminary remarks 4.The Capital Asset Pricing Model(CAPM)5.First considerations about the limitations of CAPM2The portfolio consists of two risky assets D(debt)and E(equity)Their weights in the portfolio are We construct risky portfolios varying to provide the lowest possible risk for any given level of expected returnE(rp)=wD E(rD)+wEE(rE)x xD Dandx xE E(xD+xE=1;xD0,xE0)x xD Dandx xE ECov(rD,rE)=DEDESuccess of diversification depends on the correlation coefficientBodieetal.2014,Ch.71.Brief revision:Lecture 23DebtEquityExpected return E(r)8%13%Standard deviation 12%20%Bodie et al.(2014),Table 7.1,p.208Bodie et al.(2014),Table 7.3,p.211ABBodie et al.(2014),p.2141.Brief revision:Lecture 24DebtEquityExpected return E(r)8%13%Standard deviation 12%20%Bodie et al.(2014),Table 7.1,p.208Bodie et al.(2014),Table 7.3,p.211WhenDE=-1,WhenDE=0,1.Brief revision:Lecture 251.Brief revision:Lecture 2Source:Bodieetal.2014:p.2206Diversifiable(non systematic)risk vs undiversifiable(systematic)risk 1.Brief revision:Lecture 2Bodie et al.(2014),p.2077How does diversification matter?8SponsorsTrusteesThe Investment Management FirmInvestment consultantsthe Tampa firefighters and police officers pension fundCity of Tampa,FloridaHaroldJ.BowenIIIHow does diversification matter?Source:http:/ for being diversified,which is the mantra of nearly all institutional money managers and consultants,the Tampa fund isnt.The funds assets are concentrated in a relatively small number of stocks and fixed-income investments.In short,the Tampa pension fund pretty much breaks all the conventional rules of fund management.92.Mean-variance optimization with unlimited borrowing and lending at a risk-free rate10Unlimited borrowing and lending at a risk-free rate:-Riskless asset isanassetwithacertainreturnforthegiventimehorizon.-For example:USTreasurybondsthatautomaticallyadjustforinflation(TIPS:Treasuryinflationprotectedsecurities)orshorttermUS Treasury bills(US T-bills)-Standarddeviationofthereturn:=02.Mean-variance optimization with unlimited borrowing and lending at a risk-free rate11IfyouinvestinassetHandrisklessasset:xHandxf=1-xHErErp p=(1-xH)Rf+xHRH=R Rf f+x+xH H(Er(ErH H-R Rf f)p=(1-xH)2f+xH2H2+2xH(1-xH)fHfHAsf=0,weobtain:p p=x=xH H H H2.Mean-variance optimization with unlimited borrowing and lending at a risk-free rateSource:Perold200412Combiningequationsforportfolioreturnandrisk,weobtain:ErH-RfErp=Rf+pH2.Mean-variance optimization with unlimited borrowing and lending at a risk-free rateSource:Perold200413ErH-RfHTheslope:Sharpe ratio(Er(ErH H-R-Rf f)Risk premium2.Mean-variance optimization with unlimited borrowing and lending at a risk-free rateSource:Perold200414Sharpe ratio of asset H:(12%-5%)/40%=0.175Important:allcombinationsofassetHwithrisk-freeborrowingandlendinghavethe same Sharpe ratio:itistheslopeofastraightlineSharpe ratio of asset M:(10%-5%)/20%=0.252.Mean-variance optimization with unlimited borrowing and lending at a risk-free rateSource:Perold200415Use of Sharpe ratio in practice:Shaperatioisusedtomeasure the performance of a portfolioAdvantage:theriskadjustedperformancemeasurement2.Mean-variance optimization with unlimited borrowing and lending at a risk-free rate16Sharpe ratio of H 1,itindicatesthatthesecurityspricewillbemorevolatilethanthemarketExample:abetaequalsto1.3meansthatthesecurityis30%morevolatilethanthemarket31Use of beta in practice:Beta as a measure of risk of a mutual fundExample:TheBlackRockGlobalSmallCapFund(factsheet)Source:https:/ Capital Asset Pricing Model(CAPM)32ThesecuritymarketlineprovidesabenchmarkfortheevaluationofinvestmentperformanceAssetplotsabove the SML offeragreaterexpected returns than indicated by theCAPM(underpriced assets)Assetplotsbelow the SML offeralowerexpected returns than indicated by theCAPM(overpriced assets)4.The Capital Asset Pricing Model(CAPM)33Example:Marketreturnisexpectedtobe14%,thestockbetais1.2,theT-billrateis6%.Theexpectedreturnonthestockis:6+1.2(146)=15.6%Ifyouexpect17%returnforthestock,theimpliedalphais1.4%4.The Capital Asset Pricing Model(CAPM)34Implications of the CAPM:1.Theexpectedreturnofastockdoesnotdependonitsidiosyncraticrisk2.IntheCAPM,astocksexpectedreturndoesnotdependonthegrowthrateofitsexpectedfuturecashflows3.BetameasurestheriskofanassetthatcannotbediversifiedawayOverall riskof an asset=Systematic riskCompany specific risk+4.The Capital Asset Pricing Model(CAPM)35 Implications of the CAPM for diversificationDiversificationreducesrisksbutdoesnoteliminatethemThetypeofriskthatdiversificationreducesisthecompanyspecific=idiosyncratic risk=ariskspecifictoeachparticularasset=itisnotcorrelatedacrossassetsWhenweincreaseanumberofassetsinaportfolio,weexpectthatonaveragetheidiosyncraticriskscanceleachotherandthattheactualreturngetsclosertotheexpectedreturnthereisnoreasontoexpectcompensationforbearingthisriskSystematic riskiscommonacrossassetsyoucannotreducethisriskthroughdiversificationSourcesofsystematicrisk:theoveralleconomyorfinancialmarketsrisk-aversinvestorsrequirecompensationforbearingthisriskFullenkamp20124.The Capital Asset Pricing Model(CAPM)36Quick check:Arethefollowingtrueorfalse?Explain.a.Stockswithabetaofzeroofferanexpectedrateofreturnofzero.b.TheCAPMimpliesthatinvestorsrequireahigherreturntoholdhighlyvolatilesecuritiesc.Youcanconstructaportfoliowithbetaof0.75byinvesting75%oftheinvestmentbudgetinT-billsandtheremainderinthemarketportfolio.Source:Bodieetal.2014:3174.The Capital Asset Pricing Model(CAPM)37Quick check:Whichofthefollowingfactorsreflectpure marketriskforagivencorporation?a.Increasedshort-terminterestrates.b.Fireinthecorporationwarehousec.Increasedinsurancecostsd.DeathoftheCEOe.Increasedlabourcosts.Source:Bodieetal.2014:2354.The Capital Asset Pricing Model(CAPM)38Main predictions of the CAPMAllinvestors-willalwayscombineariskfreeassetwiththemarketportfolio-willhavethesameportfolioofriskyassets(themarketportfolio)-agreeontheexpectedreturnandontheexpectedvarianceofthemarketportfolioandofeveryasset-agreeonthemarketriskpremiumandonthebetaofeveryasset-agreeonthemarketportfoliobeingontheminimumvariancefrontierandbeingmean-varianceefficient-expectreturnsfromtheirinvestmentsaccordingtothebetas-Tradingvolumeoffinancialmarketswillbeverysmall4.The Capital Asset Pricing Model(CAPM)395.First considerations about the limitations of CAPM40CAPM=equilibriummodel(“snapshot”ofthemarketatonepointintime)Whatis“market portfolio”?Indices,nationalvs.internationalRisk premiums dependoninvesmentclimateandbusinesscycleWarrenBuffett:“Risk comes from not knowing what youre doing.”Doesthefundamentalcashflowanalysisreallynotmatter?CAPMhasnot been confirmed empirically(nextlecture)41doesntexplainthevarianceofreturns:Basu(1977):earning-price-ratioeffectBanz(1981):sizeeffectBhandari(1988):highdebt-equity-ratioeffectStatmanetal.(1980):book-to-market-ratioeffectBenjaminGraham,thelegendaryinvestor:Betaisamoreorlessusefulmeasure of past price fluctuationsofcommonstocks.Whatbothersmeisthatauthoritiesnowequatethebetaideawiththeconceptofrisk.Price variability yes;risk no.Realinvestmentriskismeasurednotbythepercentthatastockmaydeclineinpriceinrelationtothegeneralmarketinagivenperiod,butthedangerofalossofqualityandearningpowerthrougheconomicchangesordeteriorationofmanagement.Is beta the real source of risk?5.First considerations about the limitations of CAPM42Is CAPM just CRAP(completely redundant asset pricing)?Montier(2007):“Institutionalmoneymanagersdontthinkintermsofvarianceasadescriptionofrisk.NeveryethaveImetalongonlyinvestorwhocaresaboutup-sidestandarddeviation;thisgetslumpedintoreturn.”“Anentireindustryappearstohavearisenobsessed with and.“Fama/French(2004):TheCAPM,likeMarkowitz(1952,1959)portfoliomodelonwhichitisbuilt,isneverthelessatheoreticaltourdeforce.WecontinuetoteachtheCAPMasanintroductiontothefundamentalconceptsofportfoliotheoryandassetpricing,tobebuiltonbymorecomplicatedmodelslikeMertons(1973)ICAPM.Butwealsowarn studentsthatdespiteitsseductivesimplicity,theCAPMsempiricalproblemsprobablyinvalidateitsuseinapplications.”5.First considerations about the limitations of CAPM43ReferencesBodie,Kane and Markus(2014),Investments,McGrauw Hill,section 7.3 and chapter 9Perold,Andre(2004),The Capital Asset Pricing Model,Journal of Economic Perspectives 18(3),pp.773-806.44