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1、Lecture8CAPMCAPMasaRegression•TheCAPMputsstructure–i.e.,howinvestorsformefficientportfolios-toMarkowitz’s(1952)mean-varianceoptimizationtheory.•TheCAPMassumesonlyonesourceofsystematicrisk:MarketRisk.•Systematicrisk:(1)Cannotbediversified(2)Hastobehedged(
2、3)Inequilibriumitiscompensatedbyariskpremium•Thestockmarketexposesinvestorstoacertaindegreetomarketrisk.=>Investorswillbecompensated.•Thecompensationwillbeproportionaltoyourriskexposure.•ThedatageneratingCAPMis:R-r=α+β(R-r)+εi=1,..,Nandt=1,…,Ti,tfiim,tfi
3、,tR=returnonassetiattimet.i,trf=returnofrisklessassetattimet.R=returnonthemarketportfolioattimet.m,tαiandβarethecoefficientstobeestimated.iCov((R,ε)=0m,ti,tTheDGPmodelisalsocalledtheSecurityCharacteristicLine(SCL).•Ifα=0,.theniE[R-r]=βE[(R-r)](ThisistheS
4、harpe-LitnerCAPM.)i,tfim,tfE[(R-r)]iscalledthemarketriskpremium:thedifferencebetweenm,tfthereturnonthemarketportfolioandthereturnonarisklessbond.Theexpectedreturnonassetioverrisproportionaltothemarketriskfpremium.βistheproportionalityfactor(sensitivityto
5、marketrisk).iIfβ=0,assetiisnotexposedtomarketrisk.Thus,theinvestorisnoticompensatedwithhigherreturn.Zero-βasset,marketneutral.Ifβ>0,assetiisexposedtomarketriskandR≥r,providedthatii,tfE[R−r]>0.m,tfQ:WhatistheMarketPortfolio?Itrepresentsallwealth.Weneedtoi
6、ncludenotonlyallstocks,butallbonds,realestate,privatelyheldcapital,publiclyheldcapital(roads,universities,etc.),andhumancapitalintheworld.(Easytostate,butcomplicatedtoform.)Q:HowdowecalculateE[R]andr?m,tf•TheCAPMcanberepresentedasarelationbetweenE[R]andβ
7、:E[R]=r+βλ(SecurityMarketLine=SML)ifi•TheCAPMisverysimple:Onlyonesourceofrisk–marketrisk–affectsexpectedreturns.-Advantage:(1)Simplicity.(2)Itprovidesagoodbenchmark(performanceevaluation,etc.)(3)Itdistinguishesbetweendiversifiableandnon-diversifiablerisk
8、.-Disadvantages:(1)Itislikelythatothersourcesofriskexist.(Omittedvariablebiasintheestimatesofβ.)i(2)Themarketportfolioisunobservable.Thus,Rwillbem,tproxiedbyanobservedmarketporfolio(say,EW-CRSP).(Measurementerrorisintroduc
