ch3资本资产定价模型

Ch3Ch3CMLCMLββCAPMCAPMSMLSML„„(risk(risk--freeasset)freeasset)ƒƒ//ƒƒ11σσ22=0=022σσfifi=0=0ƒƒ……1¾FrFσF=0ArAσAwwAAwwFF(=1(=1--wwAA))AAFFPPPPrrPP==wwFFrrFF++wwAArrAA==rrFF++wwAA((rrAA--rrFF))™™PPE(rE(rPP)=)=rrFF++wwAA[E[ErrAA--rrFF]]ƒƒƒƒ™™PPσσPP22=Var=VarwwAArrAA+w+wFFrrFF=w=wAA22σσAA22+w+wFF22σσFF22+2w+2wAAwwFFσσAFAF=w=wAA22σσAA22σσPP=w=wAAσσAAwwAAPAfAfPr)r(Er)r(Eσσ−+=CALCapitalAllocationLine)PP2σrfE(r)σACALAFE(rA)Y„„CALCALFAFA0w0wAA11wwffFF————““””loanloan„„CALCALAYAYwwAA11wwff00rrffwwffFF————““””(borrow)(borrow)rf´s´=[E(rA)-rf´]/σAσrfE(r)σACALAFE(rA)E(r)σrfσACALAFE(rA)rf´sss´´22AABB————E(rE(rAA))E(rE(rBB))σσAAσσBBσrfE(r)AB™TABTσrfE(r)AB™PFTCAL(T)rfE(r)σTAE(rT)BTPσPPwwTTwwff(=(=11--wwTT))PPrrPP=w=wffrrff+w+wTTrrTTE(rE(rPP)=w)=wffrrff+w+wTTE(rE(rTT)=r)=rff+w+wTT[[E(rE(rTT))--rrff]]σσPP=w=wTTσσTTCAL(T)PTfTfPr)r(Er)r(Eσσ−+=CAL(T)σrfE(r)ABTNFCAL(N)33CALCALCAL(N)CAL(N)CAL(N)CAL(N)————NN————FNFN————FNFN1122NNAABBTT————AABBFFTTCAL(T)CAL(T)⎪⎩⎪⎨⎧=+σ−=1yyt.sr)r(ESmaxBATfTTTfTTr)r(ESσ−=„„““22””AABB————σrfE(r)ABPσrfE(r)σACALAFE(rA)““1+11+1””————CALCALPAfAfPr)r(Er)r(Eσσ−+=CALCapitalAllocationLine)““2+12+1””————CALCALCAL(T)σrfE(r)ABTNFCAL(N)CMLCML9CapitalAssetPricingModelCAPMStanford9CAPM9CAPMCMLSML„William.Sharpe(1964)John.Lintner1965Jan.Mossin1966WilliamF.SharpeHarry.M.Markowitz••CAPMCAPM999999Homogeneousexpectations„Marketportfolio„M=w1……wn••CapitalMarketLineCapitalMarketLineE(r)E(rM)rfMCMLCMLσmσP““n+1n+1””————CALCAL•CMLCMLPMfMfPr)r(Er)r(Eσ⋅σ−+=(3-1)•¾“”¾“”„CML„CML„CML„CML1CML2CMLββ„„P∑∑==σ=σ1i1jijji2PwwM=w1……wn∑∑==σ=σn1in1jijji2Mww∑∑∑∑∑∑======σ++σ=σ=σ=σn1jnjjnn1jj1j1n1in1jijjin1in1jijji2M)w((3-2)nn11Mrwrwr++=iMijn1jjjin1jjnn11iMiiMw)r,rCovw)rwrw,r(Cov)r,r(Covσ==++==σ∑∑==(3-3)4-2MnMniMiM112Mσ++σ+σ=σƒƒσiMƒPFMƒMσ2Mƒσ2M„„ββ————2MiMiσσ=β3-5™βiiβ™β(σ2M™βββ„Mβ12M2M2MMMM=σσ=σσ=β:=¾β¾β1™βi1βi=1.51%i1.5%iCAPMCAPM¾iiM,σrfE(r)MFCMLE(rM)σMiMfMr)r(Eσ−iMMCAPM[]2MiMMMi)r(E)r(Eσ−σσ⋅−(iM2MfMfir)r(Er)r(Eσ⋅σ−+=(4-6)**CAPMCAPM[]fMifir)r(Er)r(E−β+=(4-7)CAPM12‹‹CAPMCAPMCAPMCAPMββiM2MfMfir)r(Er)r(Eσ⋅σ−+=[]ifMfir)r(Er)r(Eβ⋅−+=Sharpe,1964Lintner,1965Mossin,1966CAPMβE(r)„„iSMLTheSecuritiesMarketLine[]ifMfir)r(Er)r(Eβ⋅−+=••βrfE(r)MSMLSMLE(ri)1E(rM)βi1ii[]fMifir)r(Er)r(E−β+=FF„CAPM-(securitymarketline,SML)••11PmP=w1w2……wmσFCMLPE(rp)∑∑====miiimiiiPrEwrwErE11)()()([]∑=−β+=m1ifMifi)r)r(E(rw∑=−β+=m1ifMiif)r)r(E(wrPPPPββ),(1122MPMPMMPrrCovσσσβ==∑∑==σ=σ=m1iMii2MMm1iii2M)r,r(Covw1)r,rw(Cov12MiMm1iiwσσ=∑=im1iiwβ=∑=])([)(fMPfPrrErrE−+=βCMLσFCMLPE(rp)FE(rp)SMLβMP••PCMLMPMρPM=1/σCMLPMEFPMσPM=ρPMσPσM=σPσMMPMPσσ=σ2MPMfMfP]r)r(E[r)r(Eσσ⋅−+=PfMfP]r)r(E[r)r(Eβ⋅−+=„„1SML2SML11CMLCMLSMLSML„„a)a)CMLSMLβb)b)CMLCMLSMLSML22)))¾“”¾SML3344αα¾α0ββ1βE(ri)rfFME(r)SMLE(rM)Aαα0Aα0A