놾닺뚨볛쒣탍ꎨCapital Asset Pricing Modelꎩ 햪튪ꎺ놾컄쒿뗄쫇뛔쒿잰놾닺뚨볛쒣탍뗄퇐뺿ힴ뿶뷸탐튻룶쿪쾸뗄움쫶ꎬ쓚죝럖틔쿂벸룶늿럖ꎺ뗚튻늿럖쫇룅쫶ꎬ뷩짜CAPM뗄믹놾샭싛뿲볜ꎻ뗚뛾늿럖퓲뛔맺쓚췢쿠맘컄쿗뷸탐튻룶뇈뷏쿪쾸뗄움쫶ꆣ 튻ꆢ 룅쫶 놾닺뚨볛쒣탍쫇튻훖뒿붻뮻뺭볃훐뗄쪵횤탔뻹뫢뚨볛쒣탍ꎬ뫋탄쮼쿫쫇퓚튻룶뺺헹뻹뫢훐뛔폐볛횤좯뚨볛ꆣ웤ퟮ퓧쫇평쿄웕ꎨWilliam Sharpeꎩꆢ쇖쳘뛻ꎨJohn Lintnerꎩꆢ쳘샯억ꎨJack Treynorꎩ뫍쒪즭ꎨJan Mossinꎩ뗈죋퓚닺ퟩ뫏샭싛뗄믹뒡짏쳡돶뗄ꎬ놻죏캪쫇뷰죚쫐뎡쿖듺볛룱샭싛뗄횧훹ꎬ맣랺펦폃폚춶뻶닟뫍릫쮾샭닆쇬폲ꆣ ꎨ튻ꎩ믹놾풭샭 1ꆢ폐킧벯ꎨEfficient Setꎩ 떱럧쿕쮮욽ꎨ뇪ힼ닮ꎩ쿠춬쪱ꎬ샭탔춶헟붫톡퓱뻟폐뷏룟쫕틦싊뗄춶ퟩ뫏ꎻ떱풤웚쫕틦싊쿠춬쪱ꎬ쯻쏇붫톡퓱럧쿕쮮욽ꎨ뇪ힼ닮ꎩ뷏킡뗄춶ퟩ뫏ꆣ춬쪱싺ퟣ헢솽룶쳵볾뗄춶ퟩ뫏뗄벯뫏뻍쫇폐킧벯ꆣ 2ꆢ럖샫뚨샭 춶헟뛔럧쿕뫍쫕틦뗄욫뫃ힴ뿶폫룃춶헟럧쿕닺ퟩ뫏뗄ퟮ폅릹돉쫇컞맘뗄ꆣퟮ폅럧쿕닺ퟩ뫏벴캪쪹쿄웕뇈싊ꎨSharpe ratioꎩퟮ듳뗄춶ퟩ뫏ꆣ 3ꆢ춶럖즢뮯뚨샭ꎨInvestment Diversificationꎩ 퓚뻹뫢ힴ첬쿂ꎬ쎿훖횤좯퓚뻹뫢뗣뒦춶ퟩ뫏훐뚼폐튻룶럇쇣뗄뇈샽ꆣ 4ꆢ릲춬믹뷰뚨샭ꎨMutual Fund Theoremꎩ 춶헟뗄ퟮ폅럧쿕탔닺ퟩ뫏ꎨ쟐뗣뒦춶ퟩ뫏ꎩ벴캪쫐뎡ퟩ뫏ꎬ웤훐룷횤좯뗄릹돉뇈샽뗈폚룃횤좯뗄쿠뛔쫐횵ꆣ 5ꆢ럧쿕ꎭ놨돪뻹뫢뚨샭ꎨRiskꎭReturn Tradeoff Theoremꎩ 룸뚨짏쫶볙짨ꎬ퓚뻹뫢뗄닺쫐뎡훐ꎬ폐 Cov(R(m),R(x))E(R(x))=R(0)+jx(E(R(m))−R(x0))ꎬ웤훐m캪ퟮ폅럧쿕닺jVar(R(m))ퟩ뫏ꆣ ꎨ뛾ꎩ믹놾볙뚨 1ꆢ 뻹횵ꎭ랽닮폐킧탔볙짨ꎨMeanꎭVariance Efficient Assumptionꎩꆣ춶헟춨맽춶ퟩ뫏퓚떥튻춶웚쓚뗄풤웚쫕틦싊뫍뇪ힼ닮살움볛늻춬뗄춶ퟩ뫏ꆣ죴뛔폚쒳튻쫕틦싊쮮욽ꎬ듦퓚튻럧쿕닺ퟩ뫏뗄뇪ힼ닮킡폚웤쯻죎튻럧쿕닺ퟩ뫏뗄뇪ힼ닮ꎬ퓲웤캪 뻹횵ꎭ랽닮폐킧탔ퟩ뫏ꆣ 2ꆢ컞럖룮쫐뎡볙짨ꎨFrictionless Markets Assumptionꎩꆣ닺쫐뎡훐컞붻틗돉놾ꆢ컞쮰뷰ꎬ뛔엗뿕쎻폐쿞훆ꎬ붻틗닺쫇췪좫뿉럖뗄ꆣ 3ꆢ컞럧쿕닺볙짨ꎨRiskless Asset Assumptionꎩꆣ쯹폐뗄춶헟뻹뿉내쿠춬뗄컞럧쿕샻싊뷨죫믲듻돶뷰ꆣ 4ꆢ웫듎풤웚볙짨ꎨHomogeneous Beliefs Assumptionꎩꆣ춶헟뛔폚룷훖닺뗄쫕틦싊ꆢ뇪ힼ닮ꆢ킭랽닮뚼뻟폐쿠춬뗄풤웚ꆣ 5ꆢ뛔폚쯹폐뗄춶헟ꎬ춶웚쿞뻹쿠춬ꎬ쯹폐뗄탅쾢뚼쫇쏢럑늢쟒쫇솢벴뿉좡뗄ꆣ ꎨ죽ꎩ뇪ힼ뗄놾닺뚨볛쒣탍ꎨSharpe and Lintnerꎩ E[R]=R+b(E[Rm]−R) ifimf
ꎨ1ꎩ Cov[R,Rb=im] imVar[Rm]믲E[Z]=bE[] iimZm ꎨ2ꎩ Cov[Z,Zb=im] imVar[Zm]ꎨ쯄ꎩ닎쫽맀볆폫춳볆볬퇩 뛔컞쿞훆쒣탍ꎨthe unconstrained modelꎩꎬ벴뎬뛮쫕틦싊쒣탍ꎨthe excessꎭreturn market modelꎩ퓋폃ퟮ듳쯆좻맀볆램ꎨthe maximum likelihood estimate methodꎩ뷸탐맀볆 1ꆢ뇪ힼ뗄쿟탔믘맩랽돌 Zt=ꛁꎫꛂZmtꎫꛅt E[ꛅt]=0 E[ꛅtꛅt’]=ꚲ E[Zmt]=ꛌ?††††⁅?ꎨ?浴?ꛌ?ꎩ?崽ꛒ??†††††⁃潶孚浴Ⱐꛅt崽? 닎쫽맀볆) a)=m)−bmˆm T∑(Z−m))(Z−m)))tmtmb=t=1 T∑(Zmt−m)2m)t=12ꆢ춳볆볬퇩ꎺ ꎨ1ꎩWald 볬퇩 H0 ꎺ ꛁꎽ0 H1 ꎺ ꛁꇙ0 m)−121J0=T1m+)a)′Σ−a) ꆫꛖ2ꎨnꎩ s2m죴뛔폚폐쿞퇹놾 ()m)−1T−N−12J=ma)ˆ1)11+−s)′Σa ꆫFꎨNꎬTꎭNꎭ1ꎩ T2mꎨ2ꎩthe likelihood ratio testꎨfor the constrained model,ꛁconstrained to 0ꎩ T∑ZZ)tmtb∗=t=1 T∑Z2mtt=1)1T))′Σ∗=∑(Z−b∗Z)(−b∗) tmtZZtmtTt=1
)J2=T[logΣ∗−logΣˆ] ꆫ ꛖ2ꎨnꎩ 힢ꎺ평폚J1뿉틔뇭쪾캪J2뗄떥뗷몯쫽ꎬ쯹틔J1튲뿉틔뾴돉쫇likelihood ratio testꆣ T−N−1JJ=exp21−1 NT퓚폐쿞퇹놾쳵볾쿂 J3=(T−N/2−2)[logΣˆ∗−logΣˆ] ꆫꛖ2ꎨnꎩ ꎨ3ꎩ퇹놾맦쒣뛔춳볆볬퇩뗄펰쿬 퓚듳뛠쫽뎡뫏ꎬ컒쏇뺭뎣늻쓜믱뗃폐쿞퇹놾쿂닎쫽뗄뷢컶뷢ꎬ뛸횻쓜틀삵폚듳퇹놾좡뗃닎쫽뗄붥뷸뷢ꎬ듋쪱ꎬ퇹놾맦쒣뺿뺹뛠듳닅뫏쫊쫇튻룶횵뗃죏헦뾼싇뗄컊쳢ꆣ 컒쏇뿉틔춨맽J1ꎬ샻폃틔쿂맘쾵쪽캪늻춬뗄붥뷸닢쫔볆쯣쯹탨뗄퇹놾맦쒣ꆣ T−N−1J1=J0 NTT−N−1JJ1=exp2−1 NTT−N−1JJ1=exp3−1 NT−N/2−2N캪ퟩ뫏훐닺쫽솿ꎬT캪쪱볤뛎 ꎨ4ꎩpower of testsꎨ 풭볙짨놻뻜뻸뗄뿉쓜탔ꎩ ꋙN만뚨ꎬpower쯦ퟅT뗄퓶듳뛸퓶듳 ꋚT만뚨ꎬpower쯦ퟅN뗄복짙뛸퓶듳 N뗄좡횵뻶뚨폚the rate at which the sharpe ratio of tangency portfolio declines as assets are grouped together. N뗄좡횵튻냣늻뎬맽10ꆣ 뛾ꆢ컄쿗믘맋 ꎨ튻ꎩCAPM쒣탍뗄삩햹 1ꆢ퓧웚뛔CAPM뗄삩햹ꆪꆪ럅뿭쒣탍훐뗄볙짨 ꎨ1ꎩ늻듦퓚컞럧쿕닺 Blackꎨ1972ꎩ죏캪죎뫎닺뗄풤웚놨돪뚼쫇평솽훖닺풤웚놨돪ퟩ돉ꎬ벴쫐뎡닺ퟩ뫏폫캨튻ퟮ킡랽닮쟒ꛂ캪쇣뗄닺ퟩ뫏ꎬ뫳헟폫쫐뎡ퟩ뫏뗄쿠맘쾵쫽캪쇣ꆣ E[Ri] = E[R0m] + ꛂimꎨE[Rm] - E[R0m]ꎩ 뿉볻ꎬ죧맻붫ꛂ캪쇣뗄닺ퟩ뫏풤웚놨돪뾴ퟷ컞럧쿕닺놨돪ꎬ쓇쎴짏쪽뻍쫇뇪ힼ뗄CAPMꎬ헢쮵쏷퓚늻듦퓚뒿듢컞럧쿕닺뗄쟩뿶쿂ꎬ놾닺뚨볛쒣탍틀좻돉솢ꆣ헢튻쒣탍춨뎣돆캪쮫틲쯘쒣탍ꎨtwoꎭfactor modelꎩꆣ ꎨ1977ꎩ횸돶ꎬ룃쒣탍폐튻룶뫜훘튪뗄볙짨ꎬ벴쎻폐싴뿕ꎨshort salesꎩ쿞훆ꎬ죧맻듦퓚싴뿕쿞훆ꎬ쓇쎴붫컞램믱뗃ꛂ캪쇣뗄닺ퟩ뫏ꆣ 헢틢캶ퟅCAPM횻퓚솽훖쟩뿶쿂돉솢ꎺ뗚튻ꆢ늻퓊탭싴뿕ꎬ떫듦퓚컞럧쿕탔닺ꎻ뗚뛾ꆢ늻듦퓚컞럧쿕닺ꎬ떫쫇퓊탭싴뿕ꆣ ꎨ2ꎩ쯹뗃쮰틲쯘 ꎨ1970ꎩ뻍쮰싊닮틬뛔놾샻뗃뫍막쾢뗄펰쿬뷸탐쇋쪵횤럖컶ꎬ퓚ꛂ쾵
쫽뗄믹뒡짏붨솢쇋튻룶냼삨뢽볓쿮뗄삩햹뗄CAPMꎺ EꎨRjꎩ= r1Rf + r2ꛂi + r3DYi 쪽훐DYi뗚I쿮닺뗄막쾢쫕틦ꎬ뢽볓쿮r3DYi뇭쪾닺풤웚놨돪뛔막쾢쫕틦뫍쾵춳럧쿕뗄펰쿬돌뛈ꆣ 뗄쒣탍죏캪ꎬ룟놨돪뗄닺튪쟳폐뷏룟뗄막쾢쫕틦ꎬ뮻뛸퇔횮ꎬ춶헟듳뛠쫽늻욫뫃막쾢뛸욫뫃놾샻뗃ꎬ틲캪막쾢쫕틦뇘탫횧뢶쯹뗃쮰ꆣ ꎨ3ꎩ듦퓚럇짏쫐닺 ꎨ1972ꎩ죏캪ꎬ떱춶헟놻웈돖폐럇짏쫐닺ꎨ죧죋솦닺ꎩꎬ늢쟒웤럧쿕놨돪캪RH쪱ꎬCAPM뿉틔뇭쫶캪ꎺ EꎨRjꎩ= Rf + ꛋ[VmCovꎨRj, Rmꎩ+CovꎨRj ,RHꎩ] E(Rm)−Rfl= Vms2m+Cov(Rm,RH)Vm뇭쪾쯹폐짏쫐닺뗄쿖탐뗄쫐뎡볛횵 RH뇭쪾쯹폐럇짏쫐닺뗄놨돪뛮 ꛋ뇭쪾떥캻럧쿕뗄닺볛룱ꎬ헢샯뗄럧쿕늻뷶냼삨쫐뎡랽닮s2mꎬ뛸쟒냼삨뿉짏쫐닺놨돪폫럇짏쫐닺놨돪ퟜ뛮뗄킭랽닮ꆣ?뗄쒣탍폐죽룶훘튪뗄몬틥ꎺ 뗚튻ꆢ춶헟믡돖폐평늻춬뗄럧쿕탔닺릹돉뗄닺ퟩ뫏ꎬ틲캪쯻쏇뗄죋솦닺뻟폐늻춬뗄럧쿕ꆣ 뗚뛾ꆢ럧쿕탔닺뗄쫐뎡뻹뫢볛룱죔좻폫춶헟뗄컞닮틬쟺쿟컞맘ꎬ럖샫뚨샭틀좻돉솢ꆣ 뗚죽ꆢ볆솿닺럧쿕뗄ퟮ쫊떱랽램죔좻쫇킭랽닮ꎬ룃쒣탍뾼싇쇋뗚I훖닺폫솽훖닺ퟩ뫏뗄킭랽닮ꎬ튻훖평뿉짏쫐닺ퟩ돉ꎬ쇭튻훖평럇짏쫐닺ퟩ돉ꆣ ꎨ4ꎩ볛룱쮮욽뇤뚯 Hagerman , Kimꎨ1976ꎩ 볛룱쮮욽랢짺뇤뮯ꎬ믡쪹쏻틥컞럧쿕닺퓚쿖쪵쫀뷧훐뻟폐럧쿕ꎬ틲뛸룃컄뗄쒿뗄벴췆떼돶퓊탭볛룱쮮욽랢짺뇤뚯뗄CAPMꎬ늢횸돶웤퓚쪵횤훐뗄삧쓑ꆣ 춶헟뗄쏻틥ퟜ닆뢻ꎺ wN=∑SRN+BRNN R캪럧쿕닺뗄쫕틦싊ꎬRN캪컞럧쿕닺뗄쫕틦싊 iijjifjfjSij폫Bi럖뇰캪좨훘 뾼싇볛룱쮮욽뗷헻틲ퟓa w=awN=∑SR+BR R=aRN iiijjifjjj춶헟킧폃ퟮ듳뮯뗄삭룷샊죕몯쫽ꎺ maxE[u(w)]+L1−S−B (,B)iiS∑ijiijij쟳튻뷗떼ꎺ E[u′*(R)]−L=0 ijiE[u′*(R)]−L=0 ifi
쯹틔E[u′*(R)]−E[u′*(R)]=cov[u′,(R−R)]+E(u′)[E(R)−E(R)]=0 ijifijfijf볙짨춶헟뗄킧폃몯쫽캪뛾듎킧폃몯쫽ꎺ uw=−2()waw iiiii뛔킧폃몯쫽쟳떼ꎬ늢듺죫짏쪽뗃 ∑SjE(R)=E(R)j+cov[Rm,(R−R)] =0jf∑E(u′)jf∑B iiii2ai∑∑SRijjR=jim∑∑ Sijji평폚짏쪽뛔폚쫐뎡ퟩ뫏뇘탫돉솢ꎬ쯹틔 ∑SjE(Rm)−E(R)jfl== ∑E(u′)icov[Rm,(Rm−R)]fi2ai쯹틔ꎬ cov[Rm,(R−R)]E(R)=E(R)jf+[E(Rm)−E(R)] jfcov[R,(R−Rfmm)]f붫짏쪽폫SLB쒣탍뛔뇈ꎬ뿉볻웤쟸뇰퓚폚럧쿕뛈솿뗄늻 춬ꎬ헢쫇평폚컒쏇퓊탭헦쪵뗄컞럧쿕샻싊랢짺쯦믺늨뚯ꎬ떱컞럧쿕샻싊캪뎣쫽쪱ꎬ룃쒣탍뻍쫇SLBꆣ cov[Rm,R]E(R)=Rj+[E(R)−R] jfvar[Rm]mf듋췢ꎬ떱헦쪵쫐뎡쫕틦싊폫볛룱뇤뚯컞맘쪱ꎬ룃쪽튲폫SLB튻훂ꆣcov(Rm,R)=RNcov(Rm,a)=0ꆣ헢틢캶ퟅ돽럇볛룱늨뚯믡뛔쫐뎡ퟩ뫏쫕틦싊퓬돉ff펰쿬ꎬ럱퓲웤늻믡뛔떥룶횤좯뗄쫕틦싊닺짺펰쿬ꆣ 평폚룃쒣탍쫇폃쪵볊쫕틦싊뇭쪾뗄ꎬ떫횻쓜폃쏻틥쫕틦싊뷸탐볬퇩ꆣ폃쏻틥쫕틦싊쳦듺짏쫶쪵볊쫕틦싊R=aRNꎬ뿉횪평폚룃뗈쪽냼삨쇋뛠룶쯦믺뇤솿ꎬ쯹틔뫜쓑뷸탐jj쪵횤볬퇩ꆣ헢듓쇭튻랽쏦튲쮵쏷쇋쪵횤볬퇩폫쪵볊풤닢뗄닮틬ꆣ 컊쳢ꎺ 1ꆢ춶헟킧폃몯쫽캪뛾듎몯쫽뗄볙뚨늢늻ힼ좷ꆣ 2ꆢ볙짨쏻틥컞럧쿕샻싊뛀솢폚쒣탍횮췢ꆢ늻쫜볛룱쮮욽늨뚯펰쿬쟒쿠뛔볛룱쮮욽늻랢짺뇤뚯뗄볙뚨늻첫쿖쪵ꆣ 2ꆢ뛠웚볤놾닺뚨볛쒣탍ꎨthe intertemporal CAPM믲the multiperiod CAPMꎩ 떥튻웚볤놾닺뚨볛쒣탍퓚폐볛횤좯볛룱움맀짏늢늻뻟폐뿉볬닢탔ꎬ쳘뇰쫇퓚릫쮾햮좯뫍웕춨좨틦뗄죏릺웚좨짏ꆣ평폚컷랽뺭볃톧볒튻훂죏캪뛔떥튻웚볤뚨볛쒣탍뷸튻늽쳖싛쫇좱랦퇐뺿킧싊뗄ꎬ헢뻍틽랢쇋뛔뛠웚볤놾닺뚨볛쒣탍뗄쳖싛ꆣ
ꎨ1ꎩ ꎨ1973ꎩ죏캪ꎬ닺ퟩ뫏쪵볊짏평죽훖닺ퟩ돉ꎨ컞럧쿕닺ꆢ쫐뎡ퟩ뫏ꆢ닺Kꎩꎬ퓚퓝쪱뻹뫢뗄닺쫐뎡훐ꎬ듦퓚뛠쿮ꛂ쾵쫽탎쪽뗄CAPMꎺ ka(t,x(t))−a(t,x(t))=b∑mkta(t,x(t))−a(t,x(t))b(a(txK(t))a(tx(t)))jK0KjmjjK0K+,−0,jKKKj=1웤훐sKms−ssjmjkmmb= jks2km−skksmmskms−ssjmjmkk b= jms2km−skksmmK skm=∑mkts jkjj=1KK smm=∑∑mktmktks jjkj=1k=1mktj뇭쪾닺j퓚쫐뎡ퟩ뫏훐뗄뇈훘ꆣ 룃쒣탍뇭쏷ꎬ닺j뗄풤웚쮲쪱뎬뛮놨돪ꎨajꎭa0ꎩ뗈폚쫐뎡ꛂ쾵쫽ꎨꛂjmꎩ돋짏쫐뎡ퟩ뫏뗄풤웚뎬뛮놨돪k∑mkta−aꎬ볓짏닺j폫닺K뗄ꛂ쾵쫽ꎨꛂjKꎩ돋짏jj0j=1닺K뗄풤웚뎬뛮놨돪ꎨakꎭa0ꎩꆣ솽룶ꛂ쾵쫽틢캶ퟅ닺뗄럧쿕폐솽룶릹돉튪쯘ꎬ튻룶쯦ퟅ쫐뎡닺ퟩ뫏늨뚯쯹탎돉뗄럧쿕ꎬ폃ꛂjm뇭쪾ꎻ쇭튻룶쯦ퟅힴ첬뇤솿xK늨뚯쯹탎돉뗄럧쿕ꎬ평ꛂjK뇭쪾ꆣ 듓쒣탍훐뿉틔뾴돶ꎬ죧맻쿻돽쇋ힴ첬뇤솿xK횮뫳ꎬ컒쏇뿉틔뗃떽떥튻웚볤놾닺뚨볛쒣탍뗄쮲볤탎쪽ꆣ헢뇭쏷떥튻웚볤놾닺뚨볛쒣탍횻쫇뛠웚볤놾닺뚨볛쒣탍뗄퇏룱탎쪽ꆣ 움싛ꎺ뇘탫춨맽뚯첬맦뮮쟳뷢ꎬ평폚뿉쓜탨튪틽죫뷏뛠뗄ힴ첬뇤솿ꎬ쯹틔쪵횤닙ퟷ폐뫜듳삧쓑ꆣ ꎨ2ꎩ Jorrow and Rosenfeldꎨ1984ꎩ횸돶횤좯볛룱뺭뎣믡돶쿖jumpꎬ듓뛸떼훂볛룱뇤뮯늻솬탸ꆣ쯻쏇뛔Merton뗄쒣탍뷸탐쇋삩햹ꎬ횸돶쇋jump듦퓚뗄쟩뿶쿂뛠웚볤닺뚨볛쒣탍돉솢뗄돤럖쳵볾쫇jump퓚쫐뎡ퟩ뫏훐쫇뿉틔럖즢뗄ꆣ dSj=adt+fdy+gdh+(−lKdt+pdY)ꎬ jꎽ1,…..,n, jjjjjjjSjSjꎨtꎩ뇭쪾닺j퓚t쪱뿌뗄볛룱 ꛁ?ꎬ??ꎬ??ꎬꛋ?ꎬ??뻹쫇뎣쫽??ꛗꎬ?ꛇ?쫇캬쓉맽돌?摙?쫇늴쯉맽돌?ꛐ?쫇쳸풾럹뛈 컄헂춬쪱뛔jump쫇럱쫇뿉럖즢뗄뷸탐쇋쪵횤럖컶ꆣ 쪵횤쒣탍ꎺ
dMnnnM∑madt∑=+mfdy+m(gdh−lKdt+pdY) jjjj∑jjjjjjjj=1j=1j=1n웤훐ꎬ쫐뎡ퟩ뫏Mꎽ∑mS jjj=1H0ꎺ쳸풾럧쿕쫇뿉럖즢뗄ꎬdMM=adt+sdy H1ꎺ쳸풾럧쿕쫇늻뿉럖즢뗄ꎬdMM=a′dt+sdy+dq 쪵횤뷡맻쿔쪾ꎺ떱닉폃훜쫽뻝폫퓂쫽뻝쪱ꎬ ꆰ쳸풾ꆱ럧쿕쫇뿉럖즢뗄ꎻ떫쫇죴닉폃죕쫽뻝ꎬ퓲늻뿉럖즢ꎬ떫돌뛈늻듳ꆣ헢폐뿉쓜쫇틲캪평폚훜쫽뻝폫퓂쫽뻝냼삨쇋훜쒩폫볙웚ꎬ듓뛸퇚룇쇋ꆰ쳸풾ꆱꆣ 쪵횤뷡맻죏캪솬탸쪱볤뗄CAPM늻돉솢ꆣ ꎨ3ꎩChamberlainꎨ1988ꎩ퓋폃맽돌ꎨmartingale representation and martingale projectionꎩ췆떼쇋튻룶뛠웚볤놾닺뚨볛쒣탍ꆣ웤춨맽럖컶횤좯쫕틦싊뗄틲쯘뷡릹ꎬ볙짨듦퓚튻룶쯦믺맽돌붫뇪솿늼샊퓋뚯ꎨscalar Brownian motionꎩퟷ캪ퟜ쿻럑뗄돤ퟣ춳볆솿ꎨsufficient statisticꎩꎬ듓뛸쪹쫐뎡ퟩ뫏쓜놻뛠룶룟뛈럖즢뮯뗄ퟩ뫏쯹쳦듺ꆣ dZkt=bkta−1dW+dV ttktWt쫇쫐뎡ퟩ뫏퓚t쪱뿌뗄볛횵 Zkt쫇횤좯k퓚t쪱뿌뗄볛룱 Vkt쫇튻룶맽돌 ꎨ4ꎩKazemiꎨ1991ꎩ Constantinidesꎨ1980ꎬ1982ꎩ퓚볙뚨쫐뎡ퟩ뫏쫕틦싊ꆢ컞럧쿕샻싊ꆢ놴쯾ꆢ럧쿕뗄쫐뎡볛룱뷔뿉뇤뗄쟩뿶쿂췆떼돶뛠웚뗄CAPM폃폚뛠웚뗄쿮쒿움맀ꎬ떫쫇퓚쪵볊펦폃훐ꎬ평폚웤볆쯣솿맽듳ꎬ쪵폃볛횵뫜킡ꆣ룃컄퓚볙짨룃쿮쒿퓚캴살믱뗃캨튻뗄횧뢶늢쟒뿉틔폃떥룶놴쯾뇭쪾헻룶쿮쒿좫늿쿖뷰쇷뗄럧쿕뗄쟩뿶쿂ꎬ횤쏷뿉틔뛔뛠웚쿮쒿뷸탐움볛ꆣ 룃컄춨맽쿮쒿퓚s웚횧뢶뗄쿖뷰쇷Ds폫룃웚뗄뇟볊킧폃몯쫽뗄킭랽닮뫢솿Ds뗄럧쿕ꎬ좻뫳붫룃쿖뷰쇷춶폚퓚T웚떽웚뗄닺DTꎬDT뗄럧쿕폃웤폫T웚뇟볊킧폃몯쫽뗄킭랽닮뫢솿ꆣ 쿮쒿뗄볛횵ꎺ PR−1−1−1=(t,T){E[V(t,T)f]+E[U′(CT)f]cov[V(t,T),U′(C)f]} tttTtTV(t,T)=∑R(s,T)D쫇헻룶쿮쒿좫늿쿖뷰쇷뗄뢴뫏캴살볛횵ꆣ s=+1stR−1(t,T)쫇컞럧쿕쳹쿖햮좯뗄쫐뎡볛룱ꎨ쳹쿖싊ꎩ 헢틢캶ퟅ쯦믺쿖뷰쇷뫍컞럧쿕햮좯볛룱횮볤뗄킭랽닮뿉틔폃살뫢솿쿖뷰쇷뗄럧쿕ꆣ 3ꆢ쿻럑탎쪽뗄CAPM ꎨ1ꎩ떥웚ꎺ ퟜ쿻럑폫붻틗닺뚨샭ꎺퟜ쿻럑쫇튻훖붻틗닺ꎬ뻟폐럇쇣볛룱ꆣ
Cov(R(C),R(x))E(R())−R(0)=jxx(E(R(C))−R(x jVarRC0))(())C=∑Ci∈I1쫇ퟜ쿻럑탨쟳 ix0ꆭꆭxk쫇폐쿞퓰죎닺 쿻럑탎쪽뗄CAPM뇭쏷쇋닺j뗄풤웚뎬뛮놨돪폫ퟜ쿻럑뗄뎬뛮풤웚놨돪횮볤뗄맘쾵ꎬ맘쾵쾵쫽벴쿻럑놴쯾쾵쫽ꆣ ꎨ2ꎩ뛠웚ꎺ E(dc/c)−adt(a−a)dt=00cov(dx/x,dc/c) jjjvar(dc/c)뿉볻룃쒣탍폫떥웚쒣탍뗄캨튻쟸뇰쫇룃쒣탍쪹폃쮲쪱놨돪ꎬ뛸떥웚쒣탍쪹폃샫즢놨돪ꆣ떫쫇쿻럑놴쯾쾵쫽뗄럧쿕몬틥쫇쿠춬뗄ꎬ뇭쪾닺퓚룃웚뗄늨뚯탔ꆣ 4ꆢ럇쿟탔뗄CAPM Mcdonaldꎨ1983ꎩ Lee횸돶죧맻듦퓚춶웚컊쳢ꎬ쓇쎴퓚쾵춳탔럧쿕뗄맀볆훐믡돶쿖럇쿟탔뗄쟩뿶ꆣ 룃컄캪쇋뷢뻶춶웚컊쳢ꎬ틽죫쇋CAPM뗄몯쫽탎쪽ꆣ SLB: E(HR)=(1−b)HR+bE(R jHjfHjHm)쿂뇪H뇭쪾헦쪵쫐뎡훜웚ꎬ쿂뇪N뇭쪾맛닢뗄춶웚 El(HRk)=[1+E(HRk)]−1,l=H/N 쯹틔R(l)=(1−b)R(l)+bR(l)+m 헢뻍쫇CAPM뗄늻뇤쳦듺떯탔몯쫽탎쪽ꆣ jtHjftHjmtjt웤훐ln(1+Rkt),l=0R(l)kt=ꎨ뿉볻떱?ꎽ1쪱캪쿟탔쒣탍ꎬ떱?=0쪱캪뛔쫽쒣[(1+Rlkt)−1]/l,l≠0탍ꎩ 컄헂뮹붫웤폫뿉뇤쳦듺떯탔뗄몯쫽탎쪽ꎨ?뿉뇤ꎩ뷸탐뇈뷏ꎬ뷡맻랢쿖솽헟닮뇰늻듳ꎬ떫쫇뫳헟믡퓶볓볆쯣솿ꆣ 쪵횤볬퇩랢쿖ꎬ?뗄뻹횵캪ꎭꎬ뇪ힼ닮캪ꎬ쮵쏷듦퓚럇쿟탔ꆣ 떫쫇ꎬ컄헂ퟮ뫳춨맽뛔쒣탍닎쫽뗄맀볆춬쪱튲랢쿖럇쿟탔늻쓜좫늿맩틲폚춶웚컊쳢ꆣ뛸쟒컄헂랢쿖릫쮾맦쒣풽듳ꎬCES쒣탍풽늻쿔훸ꎬ헢탨튪뷸튻늽퇐뺿ꆣ 5ꆢ쳵볾CAPM ꎨ1ꎩMathur,Pettengill,Sundaramꎨ1995ꎩ컄헂뗄쳘즫쫇닉폃쇋쪵볊쫕틦싊뛸늻쫇풤웚쫕틦싊뛔SLBꎭCAPM뷸탐쇋볬퇩ꆣ 쪹폃쪵볊쫕틦싊뛸늻쫇풤웚쫕틦싊뗄쟸뇰쫇ꎺ 1ꎮ쫐뎡쫕틦싊뿉틔뗍폚컞럧쿕샻싊ꎬ늻좻쎻폐죋믡돖폐컞럧쿕ퟩ뫏ꆣ 2ꎮ떱쫐뎡쫕틦싊뗍폚컞럧쿕샻싊쪱ꎬ쫕틦싊폫ꛂ횮볤듦퓚튻룶쿠랴뗄맘쾵ꆣ 벴떱쫐뎡쫕틦싊뗍폚컞럧쿕샻싊쪱ꎬ룟놴쯾횵뗄ퟩ뫏뗄쫕틦싊뿉쓜뇈뗍놴쯾횵뗄ퟩ뫏뗍ꎬ늻좻쎻폐죋믡돖폐뗍놴쯾횵ퟩ뫏ꆣ 벴횤쏷ꎺ a positive relation during positive market excess return periods and a negative relation during negative market excess return periodsꆣ
컄헂뗄뗚튻늽쫇폃Fama뫍Macbethꎨ1973ꎩ뗄랽램볬퇩놴쯾뫍쪵볊쫕틦싊횮볤뗄쳵볾맘쾵ꆣ R=gˆ+gˆ∗d∗b+gˆ012∗(1−d)∗b+e ꎨ1ꎩ itttitit죴(Rmt−R)>0,d=1 ft죴(Rmt−R)<0,d=0 ft?캪쫐뎡뎬뛮쫕틦싊 퓚쫐뎡뎬뛮쫕틦싊캪헽쪱ꎬ H0ꎺ?1ꎽ0 H0ꎺ?1>0 퓚쫐뎡뎬뛮쫕틦싊캪뢺쪱ꎬ H0ꎺ?2ꎽ0 H0ꎺ?2<0 뗚뛾늽쫇볬퇩놴쯾뫍쫕틦싊횮볤헽뗄뎤웚횧뢶ꎨ쫇럱듓뎤웚뾴룟놴쯾횵ퟩ뫏뇈뗍놴쯾횵ퟩ뫏욽뻹믱뗃룼룟뗄쫕틦싊ꎩꆣ 죧맻놴쯾뫍쫕틦싊횮볤듦퓚쾵춳뗄쳵볾맘쾵ꎬ쟒싺ퟣ틔쿂솽룶쳵볾ꎬ쓇쎴룟럧쿕믡믱뗃룟믘놨ꎺ 1ꎮ쫐뎡뎬뛮쫕틦싊욽뻹캪헽 2ꎮ럧쿕쫕틦싊맘쾵쫐뎡뎬뛮쫕틦싊캪헽뫍캪뢺뗄웚볤뛔돆 ꎨt볬퇩ꎬ춬쪱뇈뷏?1쫇럱뗈폚?2ꎩ ퟮ뫳ꎬ붫ퟩ뫏욽뻹놴쯾횵뛔ퟩ뫏욽뻹쫕틦싊뷸탐믘맩ꆣ 뷡맻ꎺ 춨맽샻폃ꎨ1ꎩ쪽ꎬ뷸탐쳵볾럖컶ꎬ뷡맻랢쿖Reinganumꎨ1981ꎩ뫍TinicꆢWesꎨt1984ꎩ쳡돶뗄컊쳢뚼뗃떽쇋뷢뻶ꎬ횤쪵쇋놴쯾뫍쫕틦싊횮볤듦퓚쾵춳뗄쳵볾맘쾵ꆣ ꎨ2ꎩJagannathan,Wangꎨ1996ꎩ죏캪ꎬ평폚춶헟쫇뷸탐솬탸뛠웚춶ꎬ틲뛸ꛂ쫇뿉뇤뗄ꎬ뛸늻쫇튻돉늻뇤뗄ꆣ놾컄벴쫇폃쳵볾CAPM틾몬뗄컞쳵볾쒣탍볬퇩뫡뷘쏦닮틬ꆣ듋췢컄헂뮹퓚쫐뎡ퟩ뫏훐틽죫쇋죋솦놾ꎨMayers1972ꎩꆣ 컄헂훐뻙샽쮵쏷쇋뫶쫓ꛂ뿉뇤믡떼훂뛔CAPM뗄늻쫊떱뗄뻜뻸ꆣ 샽ꎺ t1 t2 욽뻹놴쯾횵 막욱1 막욱2 쫐뎡럧쿕틧돪 10ꎥ 20ꎥ ꎨꇁ10ꎥꎫꇁ20ꎥꎩꇂ2ꎽ15ꎥ ꎨꇁ10ꎥꎫꇁ20ꎥꎩꇂ2ꎽ15ꎥ 뿉볻ꎬ평폚뫶쫓쇋놴쯾뗄뇤뮯ꎬ듓뛸룹뻝놴쯾횵늻춬뛸쫕틦싊쿠춬뗄뷡싛듭컳뻜뻸쇋CAPMꆣ 쳵볾CAPMꎺE[RI−]1=g0−1+g1−1b ꎨ1ꎩ ittttit−=1웤훐ꎬb−=Cov(R,RI−)/Var(RI)111 ititmttmtt−
g0t−1쫇쇣놴쯾ퟩ뫏뗄쳵볾풤웚쫕틦싊 g1t−1쫇쳵볾쫐뎡럧쿕틧돪 솽뇟좡웚췻뿉뗃ꎬ퇐뺿뫡뷘쏦닮틬뗄컞쳵볾쒣탍ꎺ E[R]=g0+g1b+Cov(g11,bitit−it−1) ꎨ2ꎩ 웤훐g0=E[g0t−1]ꎬg1=E[g11]ꎬ[t−b=Eb iit−1]떱뺭볃ힴ뿶늻뫃쪱ꎬ쫐뎡럧쿕틧돪믡뇈뷏듳ꎬ뛸듋쪱쏦쇙닆컱삧뺳뗄릫쮾뗄놴쯾횵튲뷏듳ꎬ솽헟뗄킭랽닮뻍뷏듳ꆣ 캪쇋뛔ꛂ뷸탐럖뷢ꎬ뚨틥놴쯾ꎭ틧돪쏴룐뛈ꎨ뫢솿쳵볾놴쯾뛔쫐뎡럧쿕틧돪뇤뮯뗄쏴룐뛈ꎩJ=Cov(b1,g1−1)/Var(g ꎨ3ꎩ iit−t1t−1)b−1=b+J(g1−1−g1)+h−1 itiitit뗚튻쿮쫇풤웚놴쯾ꎨ뎣쫽ꎩꎬ뗚뛾쿮쫇쯦믺뇤솿ꎬ뗚죽쿮쫇닐닮 E[h−1]=0,E[h−1,gititt−1]=0 i냑ꎨ3ꎩ듺죫ꎨ2ꎩꎬ뿉뗃 E[R]=g0+g1b+Var(g1−1)J ꎨ4ꎩ ititi평폚컞램맀볆b뫍Jꎬ틲뛸뚨틥솽훖컞쳵볾놴쯾 iib=Cov(R,Rm)/ar(mt) iittVR ꎨ5ꎩ bg=Cov(R,g1−1)/Var(g1−1) iittt컞쳵볾쒣탍뮻캪E[R]=aababgit0+1+ꎨi26ꎩ i쪵횤ꎺ 쇮Rpremt−1뇭쪾BAAꎭ뫍AAAꎭ햮좯횮볤뗄쫕틦싊닮틬ꎬ쫐뎡럧쿕틧돪쫇Rpremt−1뗄쿟탔몯쫽ꎬ g−1=k0+k1Rpremtt−1 bprem=Cov(Rpre,Rm−1)/Var(Rprem) iittt−1듺죫ꎨ6ꎩ뗃 ER=prem[]c0+cb+b ꎨ7ꎩ itmcipremi춬쪱볙짨쫐뎡쫕틦싊쫇쫐뎡볓좨막욱횸쫽뗄쿟탔몯쫽ꎬ R=fvwmt0+fvwR t
bvw=Cov(Rvw,R)/Var(Rvw) iittt듺죫ꎨ5ꎩꎬ뗃 E[R]=cvw0+cbꎨ8ꎩ itvwi볙짨죋솦놾뗄쫕틦싊쫇죋뻹샍뚯쫕죫뗄퓶뎤싊 R=flabor0+fvwmtvwR+fR ꎨ9ꎩ tlabortblabor=Cov(Rlabor,R)/Var(Rlabor) iittt냑ꎨ9ꎩ듺죫ꎨ5ꎩ뗃 b=bbvw+blabor ꎨ10ꎩ ivwbilabori쯹틔ER=vwpremlabor[]c0+cvwb+cb+cb ꎨ11ꎩ LP쒣탍 itipremilabori캪쇋춬쪱볬퇩쫇럱듦퓚맦쒣킧펦ꎬ폃막욱쫐횵뗄뛔쫽뇭쪾맦쒣ꎬ뿉뗃 ER=vprem[]()laborc0+clogME+bw+b+b itsizeccpremcivwiilabori컄헂춨맽HJ볓좨뻘헳A−1=(E[RR′])뗄맣틥뻘볬퇩ꎨHansenꎭJagannathan distance ttE[w′t(d)]AE[wt(d)]ꎩ럖뇰뛔뺲첬뗄CAPMꆢꎨ7ꎩ쪽ꆢꎨ11ꎩ쪽뷸탐볬퇩ꎬ에뚨쒣탍짨뚨뗄컳닮ꆣ뷡맻랢쿖ꎨ11ꎩ쪽ퟮ폅ꎬHJꎭdistanceꎽꆣ떫쫇ꎬ컄헂랢쿖룃쒣탍죔듦퓚컳닮ꎬ맀볆쫇쇣놴쯾쫕틦싊늻춬폚맺뿢좯쫕틦싊쯹떼훂ꆣ 좻뫳ꎬ캪쇋폫ChenꎬRollꎬRossꎨ1986ꎩ뗄뛠틲쯘쒣탍쿠쟸뇰ꎬ췹쒣탍훐퓙볓죫쯄룶틲쯘뷸탐럖컶ꆣ 1ꎮ릤튵짺닺퓂냙럖뇈뇤뮯ꎨI1ꎩ 2ꎮ퓂춨믵엲헍싊ꎨI2ꎩ 3ꎮ뎤웚뫍뛌웚헾뢮햮좯퓂쫕틦싊횮닮ꎨI3ꎩ 4ꎮ떽웚죕쿠춬뗄릫쮾뫍헾뢮햮좯뗄퓂쫕틦싊횮닮ꎨI4ꎩ 캪쇋폫Fama뫍French뗄죽틲쯘쒣탍쟸뇰ꎬ췹쒣탍훐퓙볓죫솽룶틲쯘ꎨ맦쒣폫헋쏦ꎭ쫐횵뇈싊틲쯘ꎩ뷸탐럖컶ꆣ 뷡맻뻹쎻폐랢쿖폐쿔훸룄뷸ꆣ 듦퓚뗄컊쳢ꎺ 1ꎮ뛔폚ꛂ뗄뇤뮯뗄볙짨맽폚볲떥 2ꎮ쫜떽춻랢쫂볾뗄펰쿬 ꎨ3ꎩBodurthaꎬMarkꎨ1991ꎩ 룃컄훷튪쫇폃맣틥뻘랽램뛸늻쫇ퟮ듳쯆좻맀볆램뛔ퟔ믘맩쳵볾틬랽닮ꎨARCHꎩ탎쪽뗄쳵볾CAPM뷸탐맀볆ꆣ E(rI−)=bE(rI)1 itti,I−1mtt−1tcov(r,rIitmtt−1)b= i,It−1var(rmtIt−1)
볙짨탅쾢벯J쫇탅쾢벯I뗄튻룶ퟓ벯ꎬ쓇쎴죧맻쳵볾CAPM퓚J쿂돉솢ꎬ쓇쎴웤뇘퓚I쿂튲돉솢ꆣ E(rJ)bE(r)1 itt−=i,I−1mtJt−1tcov(r,rJitmtt−1)b= i,Jt−1var(rmtJt−1)냑쫕틦싊럖뷢돉뿉풤닢뫍늻뿉풤닢뗄늿럖ꎺ r=bE(rJ−)+u iti,Jmttitt−11rmt=E(rmtJ−)+ut1mt 퓲cov(r,rJ)E(uu)1−1 itmt−=Jtitmttvar(rmtJ)E(u211) t−=mtJt−쯹틔E(uuJ)itmtt−1r=E(rmtJ)uitE(u)t−1+ ꎨ1ꎩ 2itmtJt−1쳵볾웚췻쫇탅쾢벯뗄럇쿟탔몯쫽ꎬ볙짨 sE(u2mtJ−1)=g+∑gu2t0jmt− jj=1kE(uuJ−1)=aimtti0+∑auijit−utjmt− jj=1춨맽폫ARCHꎨ3ꎩ쒣탍뷸탐뇈뷏ꎬ룃컄죏캪쫐뎡뎬뛮쫕틦싊쫇튻룶ퟔ믘맩맽돌ARꎨ3ꎩꎺ hE(rmtJ1)=pt−0+∑pr ꎨhꎽ3ꎩ jmt−jj=1룃컄폃맣틥뻘랽램뛔ꎨ1ꎩ뗄닎쫽뷸탐쇋맀볆ꎬ랢쿖닎쫽뗄듳킡뫍럻뫅뚼뫜뫏샭ꎬp1쿔훸캪헽ꎬp3캪뢺ꆣBM냑NYSE뗄막욱내맦쒣듓듳떽킡럖돉컥ퟩ뷸탐볬퇩ꎬ랢쿖막욱뎬뛮쫕틦뗄쳵볾튻뷗뻘뫍뛾뷗뻘쯦ퟅ쪱볤듦퓚쿔훸늨뚯ꆢ훍뫳1웚뫍3웚뗄쫐뎡럧쿕틧돪뗄쳵볾랽닮뫍ꎨ폫ퟩ뫏쫕틦싊뗄ꎩ킭랽닮럇뎣쿔훸ꎬ쳵볾CAPM뿉틔쮵쏷쫕틦싊뗄닮틬ꆣ 캪쇋에뚨쳵볾CAPM쫇럱뿉틔뛔쫕틦싊뗄뇤뚯ퟶ돶캨튻뷢쫍ꎬ룃컄뾼달쇋쒣탍뗄닐닮폫쿂쇐뇤솿뗄헽붻탔ꎺ쒿잰뫍훍뫳솽웚뗄맺뿢좯쫕틦싊ꆢ뗍뗈벶릫쮾햮좯쫕틦싊ꆢ쫐뎡막쾢싊ꆢ훍뫳3웚뗄뗍뗈벶릫쮾햮좯럧쿕틧돪ꆢ훍뫳1웚뗄쫐뎡뗄쳵볾랽닮ꆣ뷡맻랢쿖닐닮폫뗍뗈벶릫쮾햮좯쫕틦싊뫍럧쿕틧돪컞맘ꎬ폫맺뿢좯쫕틦싊ꆢ막쾢싊뫍훍뫳뗄쳵볾뛾뷗뻘폐맘ꆣ듋췢ꎬ룃컄뮹랢쿖쫽뻝훐듦퓚튻룶좷뚨탔뗄늿럖ꎬ헢쮵쏷쒣탍뗄짨뚨죔듦퓚컊쳢ꆣ 컄헂쯦횮퓚쒣탍훐뾼싇쇋튻퓂킧펦ꎬ랢쿖짏쫶컊쳢뚼쓜뗃떽폐킧뷢뻶ꆣ컄헂췹쒣탍훐볓죫쇋튻룶탩쓢뇤솿ꎺ떱퓚튻퓂캪1ꎬ웤쯻퓂럝캪쇣ꆣ
E(uuJ−1)itmttr=Jan+E(rJ)+u itiE(u2−1tJ−1)mttitmtꎨ4ꎩNgꎨ1991ꎩ뛔쳵볾CAPM튲ퟷ쇋쿠쯆뗄퇐뺿ꎬ떫쫇쯻폃ARCHꎭM쒣탍살쏨쫶쫐뎡뎬뛮쫕틦싊ꆣ srmt=y0+y1fg+∑u20g−+u jmtjmtj=1웤듎ꎬ쯻퓚쳵볾킭랽닮뫍랽닮훐뾼싇쇋쫐횵볓좨좨훘뗄뇤뮯ꆣ 퓙듎ꎬNg볙짨쒣탍훐뗄뒴탂ퟱ톭GARCHꎨ1ꎬ1ꎩ맽돌ꎬ뛸BM퓲볙짨웤쫇튻룶ARCH맽돌ꆣ ퟮ뫳ꎬNg쫇폃ퟮ듳쯆좻램뷸탐맀볆ꎬ뛸BM퓲닉폃쇋맣틥뻘랽램ꆣ ꎨ5ꎩFisher, Kaminꎨ1985ꎩ 룃컄쪹폃뾨뛻싼싋ퟓ맀볆랽램뷢뻶쫕틦싊닐닮뗄틬랽닮뫍놴쯾뗄쯦믺뇤뮯컊쳢ꆣ 퓚춬랽닮쿂ꎺ ttttb=(f2)(/)22x/fx=fxy/fx ꎨ2it∑xyfx쫇좨훘ꎩ jjijj∑jj∑jjij∑jjjjj=1j=1j=1j=1x=X−X,X=R−R iiimtfty=Y−Y,Y=R−R iiiitft퓚틬랽닮쿂ꎺ ttb=∑Cfxy2/ jjjij∑Cfxitjjjj=1j=1폃Cf쳦듺fꎬC쫇킡폚믲뗈폚1뗄GLS좨훘틲ퟓꆣ jjjjjf2+1=f+KChfhxh jj∑h=12C=1/(1+fx) jsjꎨ뛾ꎩꆢ쪵횤볬퇩 1ꆢ놾닺뚨볛쒣탍뗄퓧웚볬퇩 퓧웚뛔쒣탍뗄볬퇩늻쫇횱뷓볬퇩CAPM뗄볙짨ꎬ뛸쫇룸뚨쫐뎡ퟩ뫏뗄폐킧탔ꎬ틔볬퇩횤좯쫐뎡쿟뗄탔훊캪훷ꆣ퓧웚뗄볬퇩닉폃쇋솽늽믘맩랽램ꆣ퓚뗚튻늽훐맀볆돶횤좯믲ퟩ뫏뗄놴쯾틲ퟓꆣ뗚튻늽쫴폚쪱볤탲쇐믘맩ꎬ붫횤좯믲ퟩ뫏뗄쫕틦싊뛔쫐뎡횸쫽쫕틦싊뷸탐믘맩ꆣ쎿튻웚뗄맛닢횵뗄ퟮ폅쓢뫍쿟뻍쫇룃횤좯뗄쳘헷쿟ꎬ쳘헷쿟뗄킱싊뻍쫇룃횤좯뗄놴쯾틲ퟓ뗄맀볆횵ꆣ뗚뛾늽믘맩쫴폚뫡뷘쏦믘맩ꆣ헢샯뗄쎿튻룶맛닢횵쫇떥룶횤좯믲ퟩ뫏ꆣ퓚뗚뛾늽믘맩훐ꎬ붫놴쯾틲ퟓ뛔욽뻹쫕틦싊뷸탐믘맩ꆣ맛닢횵뗄ퟮ폅쓢뫍쿟캪횤좯쫐뎡쿟ꆣ퇐뺿헟쫔춼뇦뇰룃맀볆횵뗄쳘탔폫CAPM뗄풤닢쫇럱튻훂ꆣ ꎨ1ꎩBJS볬퇩ꎨ1972ꎩ BJS좡뗄퇹놾쫇1926ꎭ1965쓪얦풼횤좯붻틗쯹ꎨNYSEꎩ짏붻틗뗄쯹폐막욱ꆣ쯻쏇
듓ퟓ쟸볤1926ꎭ1930쓪뾪쪼퇐뺿ꆣ쯻쏇붫NYSE짏쯹폐막욱뗄볲떥볓좨욽뻹ퟷ캪쫐뎡횸쫽ꎬ볆쯣룃쪱웚붻틗뗄쯹폐막욱뗄놴쯾틲ퟓꆣ좻뫳ꎬ쯻쏇룹뻝놴쯾틲ퟓ뛔막욱뷸탐업탲ꎬ릹퓬10룶ퟩ뫏ꆣ놴쯾틲ퟓퟮ룟뗄10ꎥ뗄막욱맩죫ퟩ뫏1ꎬ틀듋샠췆ꎬ튻횱떽ퟩ뫏10ꆣ 쿖퓚쯻쏇볆쯣1931쓪쎿튻룶퓂쎿룶ퟩ뫏뗄쫕틦싊ꆣ퓚룃쓪쒩ꎬ쯻쏇훘탂볆쯣1927ꎭ1931쓪붻틗뗄쎿튻횻막욱뗄놴쯾틲ퟓꎬ훘탂릹퓬10룶ퟩ뫏ꆣBJS듓1931쓪떽1965쓪튻횱훘뢴짏쫶늽훨ꎬ좡뗃10룶ퟩ뫏튻쾵쇐뗄퓂쫕틦싊ꆣ쯻쏇쫔춼춨맽듓쫕틦싊훐좡돶퇹놾맀볆횵맀볆쎿튻룶ퟩ뫏뗄풤웚쫕틦싊뫍놴쯾틲ퟓꆣ 풤웚횵뗄퇹놾맀볆횵쫇쫕틦싊뗄쯣쫵욽뻹횵ꆣ퓚쎿튻룶퓂돵헢쫇풤웚쫕틦싊뗄컞욫맀볆ꆣ쯻쏇춨맽붫ퟩ뫏쫕틦싊뛔쫐뎡횸쫽뷸탐믘맩맀볆쎿튻룶ퟩ뫏뗄놴쯾틲ퟓꆣ 쯻쏇뗄뷡맻캪CAPM쳡릩쇋잿폐솦뗄횧돖ꆣ퓚쯻쏇맀볆뗄횤좯쫐뎡쿟훐벸뫵늻듦퓚럇쿟탔ꎬ킱싊쿔훸캪헽ꆣ듋췢ꎬ벸뫵100ꎥ뗄ퟩ뫏욽뻹쫕틦싊뗄뫡뷘쏦뗄닮틬뿉틔폃놴쯾틲ퟓ뗄닮틬살뇭쪾ꆣ ꎨ2ꎩFM볬퇩ꎨ1974ꎩ 램싪ꎨFamaꎩ뫍싳뿋엥쮹ꎨMacBethꎩꎨFMꎩ튲퇐뺿쇋횤좯쫐뎡쿟뗄탔훊ꆣ떫쫇ꎬ쯻쏇뗄퇐뺿폫BJS늻춬뗄쫇ꎬ쯻쏇쫔춼룹뻝잰웚맀볆뗄럧쿕뇤솿풤닢ퟩ뫏뗄캴살쫕틦싊ꆣ 쯻쏇쯹폃뗄쫽뻝뫍BJS튻퇹ꆣ쯻쏇튲쪹폃춬퇹뗄횸쫽ꎨNYSE짏쯹폐막욱뗄볲떥볓좨욽뻹ꎩퟷ캪쫐뎡ퟩ뫏ꆣ쯻쏇듓볆쯣1926ꎭ1929쓪NYSE짏쎿튻횻막욱뗄놴쯾틲ퟓ뾪쪼ꆣ뫍BJS튻퇹ꎬ쯻쏇튲룹뻝놴쯾틲ퟓ뗄듳킡뛔막욱뷸탐업탲ꎬ릹퓬20룶ퟩ뫏ꆣ좻뫳ꎬ쯻쏇춨맽붫1930ꎭ1934쓪ퟩ뫏뗄퓂쫕틦싊뛔쫐뎡횸쫽쫕틦싊뷸탐믘맩맀볆쎿튻룶ퟩ뫏뗄놴쯾틲ퟓꆣ퓚1934쓪쒩ꎬ쯻쏇뗃떽쎿튻룶ퟩ뫏뗄놴쯾틲ퟓ뗄맀볆횵ꆣ쯻쏇폃헢킩놴쯾횵풤닢1935ꎭ1938쓪쎿룶퓂ퟩ뫏뗄쫕틦싊ꆣ뛔폚쎿튻룶퓂ꎬ쯻쏇붫ퟩ뫏뗄퓂쫕틦싊뛔놴쯾틲ퟓ뷸탐믘맩뗃떽횤좯쫐뎡쿟뗄퓂맀볆횵ꆣ 캪쇋볬퇩횤좯쫐뎡쿟쫇럱듦퓚럇쿟탔ꎬFM췹뗈쪽훐퓙볓죫튻쿮ꎬ놴쯾틲ퟓ뗄욽랽ꆣ룃맘쾵쪽뇤돉죽캬뗄ꎬ웤훐ퟩ뫏뗄쫕틦싊퓚튻룶훡짏ꎬ뛸놴쯾틲ퟓ뫍놴쯾틲ퟓ뗄욽랽퓚쇭췢솽룶훡ꆣ헢20룶맛닢횵뗄ퟮ폅쓢뫍쿟뗄ퟩ뫏쫕틦싊뗄뗈쪽캪ꎺ ))2rP,J35=a0+a1bP+a2bP+eP ,J35 ꎨꎩ CAPM볙짨FM믡랢쿖쾵쫽a2늢늻쿔훸틬폚쇣ꎬ늢쟒떱냑놴쯾욽랽헢튻쿮볓죫떽룃맘쾵쪽뫳늢늻쓜룼뫃뗘뷢쫍ퟩ뫏쫕틦싊뗄뇤뚯ꆣ CAPM춬쪱볙짨놴쯾틲ퟓ믲쾵춳탔럧쿕쫇횤좯풤웚쫕틦싊캨튻뗄뻶뚨틲쯘ꆣ퓚좷뚨막욱볛룱뫍풤웚쫕틦싊뗄쪱뫲ꎬ닐닮랽닮늢늻훘튪ꎬ틲캪ퟩ뫏춶헟뿉틔냑쯼럖즢뮯ꆣFM춨맽퓚맘쾵쪽훐냼삨닐닮랽닮볬퇩놾닺뚨볛쒣탍뗄볙짨ꆣ헢20룶ퟩ뫏놻볲떥볓좨욽뻹쟒냼삨듳솿뗄막욱ꎬ쯹틔쎿튻룶ퟩ뫏뗄닐닮랽닮붫쿠뛔뇈뷏킡ꆣ떫쫇ꎬ캪쇋에뚨막욱뗄닐닮랽닮쫇럱펰쿬웤볛룱벰웤쯹릹돉뗄ퟩ뫏뗄풤웚쫕틦싊ꎬFM퓚맘쾵쪽훐볓죫쇋쎿튻룶ퟩ뫏훐뗄막욱뗄욽뻹닐닮랽닮ꆣ룃뇤솿춨맽쿂쪽볆쯣ꎬ M∑s2(eJ)RVJ=1P=M 웤훐ꎬM쫇ퟩ뫏훐막욱뗄쫽솿ꎬs2(eJ)쫇막욱J뗄닐닮랽닮ꆣ
폃죽룶뇤솿뷢쫍헢20룶ퟩ뫏퓂쫕틦싊뗄닮틬ꎬ룃맘쾵쪽죧쿂ꎺ ))2rP3=a0+a1b+a2b+a3RV+e ,J5PPPP,J35 ꎨꎩ 퓚웚쒩ꎬ쯻쏇춨맽훘뢴헢헻룶맽돌맀볆ퟩ뫏뗄놴쯾쾵쫽ꆣ벴쯻쏇맀볆1930ꎭ1933쓪막욱뗄놴쯾틲ퟓꆣ좻뫳ꎬ쯻쏇릹퓬ퟩ뫏늢맀볆1934ꎭ1938쓪뗄ퟩ뫏뗄놴쯾틲ퟓꆣ맀볆막욱놴쯾틲ퟓꆢ릹퓬ퟩ뫏뫍맀볆퓂횤좯쫐뎡쿟뗄맽돌튻릲훘뢴쇋뻅뇩ꎬ좡뗃쇋듓1935쓪1퓂떽1968쓪6퓂쾵쫽a0떽a3ퟜ릲390룶퓂맀볆횵ꆣFM볆쯣쎿튻룶쾵쫽뗄뻹횵ꎬ쫔춼볬퇩쾵쫽쫇럱쿔훸틬폚쇣ꆣ 놾닺뚨볛쒣탍뛔쾵쫽ퟷ돶죧쿂볙짨ꎺ 1ꎮ룹뻝쒣탍뗄탎쪽ꎬ뷘뻠쿮ꎬ믲헟a0ꎬ퓚햮좯쫐뎡펦룃뗈폚믲듳폚컞럧쿕샻싊ꆣ 2ꎮ횤좯쫐뎡쿟뗄욽뻹킱싊ꎬ믲헟a1ꎬ뇘탫캪헽횵ꆣ 3ꎮ횤좯쫐뎡쿟펦룃캪쿟탔뗄ꎬ쯹틔쾵쫽a2뗄뻹횵펦룃늻쿔훸틬폚쇣ꆣ 4ꎮ닐닮랽닮늻펦룃펰쿬막욱쫕틦싊뗄뻹뫢볛횵믲풤웚쫕틦싊ꎬ쯹틔쾵쫽a3뗄뻹횵펦룃늻쿔훸틬폚쇣ꆣ FM볬퇩뗄훷튪뷡맻죧쿂ꎬ룸돶쾵쫽뗄뻹횵ꆣ*뫅뇭쪾퓚90ꎥ뗄훃탅뛈짏뻹횵쿔훸틬폚쇣ꆣ )rP=a++ t0a1bPe,P,t .0061* .0085* ))=a+ab+a2rP+ ,t01P2bPeP,t .0049* .0105* ))=a+ab+ab2rP+a+ ,t01P2P3RVPeP,t .0020 .0114* .0516 룃뷡맻폫샭싛뗄볙짨쫇튻훂뗄ꆣ쯼뇭쏷떱컒쏇폃룟폚욽뻹뗄놴쯾틲ퟓ뷸탐풤닢ꎬ퓚쿂웚컒쏇붫뗃떽룟폚욽뻹뗄쫕틦싊ꆣ놴쯾틲ퟓ뫍쫕틦싊횮볤벸뫵늻듦퓚럇쿟탔ꆣ듋췢ꎬ컒쏇늻뿉쓜룹뻝ퟩ뫏샯막욱뗄닐닮랽닮풤닢캴살쫕틦싊ꆣ룸뚨CAPMꎬ컒쏇늢늻웚췻닐닮랽닮믡펰쿬막욱볛룱믲풤웚쫕틦싊ꎬ뛸쟒컒쏇뿉틔뾴떽늢늻듦퓚죎뫎뗄쟣쿲쮵쏷닐닮랽닮룟폚욽뻹뗄뗄막욱믡뗃떽룟폚욽뻹뗄풤웚쫕틦싊ꆣ 죧춬늼삳뿋ꆢ햲즭뫍쫦뛻쮹ꎬFM늢쎻폐랢쿖쾵쫽a0뗄뻹횵쿔훸룟폚컞럧쿕샻싊뗄뻹횵ꆣ헢킩랢쿖폫퓊탭컞럧쿕듻돶떫늻퓊탭컞럧쿕뷨죫뗄CAPM쫇튻훂뗄ꆣ 훘튪뗄쫇쟸럖BJS뫍FM뗄랽램뗄늻춬ꆣ퓚BJS훐ꎬ놴쯾틲ퟓ뫍욽뻹쫕틦싊쫇퓚춬튻웚볆쯣뗄ꆣ퓚FM훐ꎬ놴쯾틲ퟓ뫍욽뻹쫕틦싊쫇퓚늻춬뗄쪱웚볆쯣뗄ꆣ헢킩놴쯾틲ퟓ쫇퓚쒳튻웚뷸탐맀볆늢폃폚쿂튻웚풤닢쫕틦싊ꆣ 2ꆢAnomalies of CAPM: 틔잰뛔SLBꎭCAPM뗄죽룶엺움ꎺ 1ꎮꛂ늻쫇럧쿕뗄캨튻뻶뚨틲쯘ꎬ듦퓚웤쯻뗄뫪맛뺭볃뇤솿ꎨRollꎬRossꎩ 2ꎮ횤좯쫕틦싊뮹쫜떽럇쾵춳탔럧쿕뗄펰쿬ꎨLakonishokꎬShapiroꎩ 3ꎮꛂ폫횤좯쫕틦싊횮볤늻듦퓚쿔훸맘쾵ꎨFamaꎬFrenchꎩ 뛔SLB뗄랴늵ꎺ 1ꎮReinganumꎨ1981ꎩ랢쿖폃퓂쫽뻝볬퇩ꎬ퓲쫕틦싊뫍놴쯾횮볤뗄맘쾵늻쏷쿔ꎬ뛸쟒ퟩ뫏횮볤뗄쫕틦싊닮뇰늻듳ꆢ퓚쎿룶ퟓ웚볤쫕틦싊뫍놴쯾뗄맘쾵늻튻훂ꆣ
2ꎮTinic뫍Westꎨ1984ꎩ랢쿖떱냑튻퓂럝쫽뻝쳞돽쪱ꎬퟩ뫏횮볤뗄쫕틦싊쎻폐쿔훸닮틬ꆣ뛸쟒퓚튻쓪훐뗄쒳킩퓂럝ꎬ쫕틦싊폫놴쯾뢺쿠맘ꆣ 3ꎮLakonishokꎬShapiroꎨ1984ꆢ1986ꎩ랢쿖쫕틦싊뗄닮틬폃웤쯻뇤솿ꎨ죧맦쒣ꎩ뷸탐뷢쫍믡뇈폃ꛂ룼뫃ꆣ 4ꎮFamaꆢFrenchꎨ1992ꎩ맦쒣ꆢ헋쏦볛횵ꎭ쫐횵뇈싊 size effect: 킡맦쒣막욱뗄욽뻹뎬뛮쫕틦싊뇈CAPM쯹풤웚뗄룼룟ꆣ value effect: 쫕틦싊뿉틔폃쫐뎡볛횵폫믡볆횸뇪뗄뇈싊뷢쫍ꆣ죧쎿막뗄쫕틦뫍헋쏦볛횵ꆣ Reverse and momentum effect: 뛌웚ꎨ춨뎣쫇튻룶퓂ꎩ뗄랴쒣쪽ꎬ죧맻튻횻막욱퓚짏룶퓂쿔훸짏헇ꎬ쓇쎴퓚쿂룶퓂막욱볛룱췹췹믡쿂뗸ꎨJegadeesh1990ꎩꆣ훐웚ꎨ춨뎣쫇쇹떽쪮뛾룶퓂ꎩ뗄맟탔쒣쪽ꎬ퓚뷓쿂살뗄쇹룶퓂훐막욱볛룱믡훘뢴쯼쏇퓚듋잰쇹떽쪮뛾룶퓂뗄뇭쿖ꆣ January effectꎺ튻퓂럝뗄막욱쫕틦싊쏷쿔뗘룟폚웤쯻벸룶퓂럝뗄쫕틦싊ꆣ Weekend effectꎺ훜튻뗄욽뻹쫕틦싊캪뢺쫽ꎬ뛸쟒뛠쫽뢺뗄쫕틦싊랢짺퓚훜컥쫕엌떽훜튻뾪엌횮볤ꆣ 컥훖뿉쓜뗄뷢쫍ꎺ ꋙꆢdata snooping ꋚꆢ컞램헒떽헦쪵뗄쫐뎡ퟩ뫏뗄쳦듺 ꋛꆢCAPM펦평뛠틲쯘쒣탍쯹좡듺 ꋜꆢ틬뎣쿖쿳늢쎻폐랴펳쒳훖샠탍뗄럧쿕ꎬ뛸횻쫇ꆰmistakeꆱꆣ떱춶헟틢쪶떽헢튻뗣쪱ꎬ틬뎣쿖쿳뇣믡쿻쪧ꆣ ꋝꆢ틬뎣쿖쿳랴펳쇋쪹춶헟ퟶ돶럇샭탔풤웚뗄돖탸탄샭욫닮ꆣ 샽죧ꎺ램싪ꎨFamaꎩ뫍뢥싗웦ꎨFrenchꎩꎨ1992ꎩ랢쿖퓚맽좥뗄40쓪훐ꎬ뛔틔쫐뎡볛횵캪좨훘뗄NYSE횸쫽뗄늨뚯싊릱쿗뷏듳뗄막욱늢쎻폐믱뗃룼룟뗄풤웚쫕틦싊ꆣ춨맽뿘훆릫쮾뗄맦쒣ꎬ욽뻹쫕틦싊뫍놴쯾틲ퟓ횮볤뗄맘쾵뇤캪뢺쿠맘ꆣ뫜쏷쿔ꎬ헢킩뷡맻늢쎻폐횤쏷쾵춳탔럧쿕ꎨ뛔NYSE횸쫽뗄늨뚯싊뗄릱쿗ꎩퟮ듳뗄막욱뿉틔쪹춶헟믱뗃룟폚욽뻹뗄쫕틦싊ꆣ 램싪뫍뢥싗웦랢쿖쎿막쫕틦돽틔막욱볛룱뗄뇈싊믲쎿막헋쏦볛횵돽틔막욱볛룱뗄뇈싊뇈뷏뗍뗄막욱쫕틦싊뷏룟ꆣ쯻쏇죏캪ꎬ뺡맜헢폫CAPM늻튻훂ꎨCAPM볙짨놴쯾틲ퟓ뗄닮틬쫇캴살쫕틦싊뗄캨튻뻶뚨틲쯘ꎩꎬ뗍맀뗄헢킩뫢솿랽쪽튲탭뿉틔ퟷ캪럧쿕뗄웤쯻뫢솿랽쪽ꆣ뮻뻤뮰쮵ꎬ쯻쏇쿠탅뗍맀막욱뗄룟쫕틦싊쫇춶헟쯹풤웚뗄ꎬ틲캪헢킩뗍맀막욱뿉쓜쫇컞샻틦뗄믲뒦폚닆컱삧뺳ꆣ쯻쏇쿠탅춶헟튪쟳쟒ퟮ훕붫퓚뗍맀막욱짏쪵쿖룼룟뗄쫕틦ꆣ KothariꎬShanken뫍Sloanꎨ1995ꎩ듓쇭튻랽쏦헹싛뗀ꎬ램싪뫍뢥싗웦뗄뷡맻듳늿럖쫇평폚짺듦헟욫닮퓬돉뗄ꆣ램싪뫍뢥싗웦퇐뺿뗄릫쮾뗄퇹놾쾵춳뗘쳞돽쇋듳솿퓚웤퇐뺿웚볤웆닺뗄릫쮾ꆣ램싪뫍뢥싗웦죏캪뗍맀막욱럧쿕뇈뷏듳ꎬ틲캪쯼쏇뒦폚닆컱삧뺳떱훐ꆣ쯹틔ꎬ쳞돽뗴탭뛠웆닺뗄릫쮾믡떼훂뗍맀뗄막욱맽좥뗄튵벨헻쳥쿲짏욫ꆣ떫쫇ꎬChanꎬJagadeesh뫍Lakonishokꎨ1995ꎩ죏캪짺듦헟욫닮뗄펰쿬늢늻쓜췪좫뷢쫍뗍맀막욱뗄헽뗄횧뢶ꆣ듋췢ꎬ램싪뫍뢥싗웦ꎨ1996ꎩ죏캪퓚죎뫎쟩뿶쿂ꎬ짺듦헟욫닮뚼늻쓜폃살뷢쫍캪쪲쎴퓚죎뫎뫡뷘쏦막욱쫕틦싊훐놴쯾틲ퟓ뚼늻뻟놸쏷쿔뗄헽뗄횧뢶ꆣ 3싞뛻뛔놾닺뚨볛쒣탍볬퇩뗄엺움 싞뛻뛔CAPM뗄엺움뿉틔럖돉솽룶늿럖ꆣ쫗쿈ꎬ쯻죏캪BJS뫍FM뗄뷡맻쫇춬틥랴뢴뗄ꆣ벴늻맜퓚쿖쪵쫀뷧훐막욱쫇죧뫎춨맽럧쿕뷸탐뚨볛뗄ꎬ컒쏇뚼폐뿉쓜뗃떽짏쫶뷡맻ꆣ죧맻헢쫇헦뗄ꎬ컒쏇듓짏쫶볬퇩훐늢늻쓜쇋뷢막욱볛룱뗄뷡릹ꎬ뛸놾닺뚨볛쒣탍뻍쎻폐헦헽놻볬퇩맽ꆣ
웤듎ꎬ쯻죏캪CAPM캨튻헦헽뗄볙짨쫇쫐뎡ퟩ뫏쫇폐킧뗄ꎬ뛸룃볙짨닅쫇컒쏇펦룃볬퇩뗄ꆣ떫쫇ꎬ쫐뎡ퟩ뫏펦냼삨맺볊뺭볃쳥쾵뗄쎿튻훖닺ꆣ틲뛸늻뿉쓜에뇰튻룶ퟩ뫏ꎨ퓚풤웚쫕틦싊ꎭ뇪ힼ닮춼훐ꎩ쫇럱쫇폐킧뗄ꆣ죧맻헢쫇늻뿉쓜뗄ꎬ쓇쎴놾닺뚨볛쒣탍컞램놻볬퇩ꆣ ꎨ1ꎩ 잰쫶볬퇩쫇춬틥랴뢴뗄 볙짨컒쏇폐튻뚥쎱ퟓ뫍탭뛠헅횽ꆣ퓚쎿튻헅횽짏컒쏇킴짏튻룶쫽ퟖ듺뇭튻뛎쪱웚뗄쫕틦싊ꎬ죧튻룶퓂ꆣ컒쏇쯹폐뗄횽좫늿럅죫쎱ퟓ훐늢믬뫏웰살ꆣ쿖퓚컒쏇듓쎱ퟓ훐좡돶12헅횽ꆣ쎿튻헅횽짏뗄쫽ퟖ듺뇭쒳횻막욱12룶퓂훐쎿룶퓂뗄쫕틦싊ꆣ컒쏇돆횮캪막욱1ꎬ냑헢킩횽훘탂럅죫떽쎱ퟓ훐ꆣ쿖퓚춨맽춬퇹뗄늽훨뗃떽막욱2ꎬ훘뢴짏쫶늽훨튻횱떽막욱100ꆣ쓣쿖퓚펵폐100룶탲쇐뗄퓂쫕틦싊ꎬ쎿튻횻막욱튻룶탲쇐ꆣ평폚컒쏇뛔쎿튻룶횤좯듓쎱ퟓ훐횻좡돶12룶쫕틦싊ꎬ쎿튻룶횤좯뗄퇹놾뻹횵믡늻춬ꎬ벴쪹풤웚쫕틦싊쫇쿠춬뗄ꆣ 퓂쫕틦싊뗄뻹횵듺뇭쫐뎡횸쫽ꎨ100횻막욱뗄볲떥볓좨욽뻹ꎩ뗄쫕틦싊ꆣ헢킩횸쫽뗄릹퓬폫BJS뫍FM뗄랽램튻퇹ꆣ 쿖퓚컒쏇볆쯣쎿튻횻막욱뗄놴쯾틲ퟓꆣ컒쏇붫쎿튻횻막욱뗄쫕틦싊뛔쫐뎡횸쫽쫕틦싊뷸탐믘맩ꆣ헢킩맘쾵뗄ퟮ폅쓢뫍쿟돆캪쳘헷쿟ꎬ웤킱싊캪막욱놴쯾틲ퟓ뗄맀볆횵ꆣ놴쯾틲ퟓ폒뇟뗄욽뻹쫕틦싊쫇춨맽볓ퟜ쎿튻횻막욱뗄퓂쫕틦싊늢돽틔12ꆣ 퓚헢샯ꎬ컒쏇폃BJS뗄랽램릹퓬10룶ퟩ뫏ꆣ컒쏇룹뻝놴쯾틲ퟓ뛔막욱뷸탐업탲ꎬ냑놴쯾틲ퟓퟮ룟뗄10ꎥ뗄막욱럅죫뗚튻룶ퟩ뫏ꎬ틀듋샠췆ꆣ 볙짨컒쏇쿖퓚춨맽횤좯쫐뎡쿟뗄탔훊볬퇩놾닺뚨볛쒣탍ꆣ컒쏇춨맽붫놴쯾틲ퟓ뛔욽뻹쫕틦싊뷸탐믘맩ꎬ쿈쫇뛔100룶횤좯ꎬ퓙뛔10룶ퟩ뫏맀볆횤좯쫐뎡쿟ꆣ 컒쏇볬퇩뗄뷡맻폫CAPM쫇튻훂뗄ꎬ벴쪹헢킩쫕틦싊쫇듓쎱ퟓ훐뗃살뗄!헢뻍쫇컊쳢쯹퓚ꎬ훮죧듋샠뗄뷡맻뿉틔룺CAPM쓢뫍뗃뫜뫃ꎬ늻맜쫐뎡짏쪵볊뗄뚨볛뷡릹죧뫎ꆣ 헢틢캶ퟅ벴쪹돤떱쫐뎡ퟩ뫏뗄ퟩ뫏쫇컞킧뗄ꎬ풤웚쫕틦싊뫍ퟮ킡랽닮춶ퟩ뫏뗄놴쯾틲ퟓ횮볤죔듦퓚좷뚨뗄쿟탔맘쾵ꆣ늼삳뿋ꆢ햲즭뫍쫦뛻쮹쯹퇐뺿뗄ퟩ뫏쫇듳맦쒣ꆢ볲떥볓좨ꆢ룟뛈럖즢뮯뗄ퟩ뫏ꆣ죧맻헢훖샠탍뗄ퟩ뫏실퓚떯춷뢽뷼ꎬ쯼쏇붫믡업돉튻쳵횱쿟ꎬ늻맜헦쪵뗄ꆢ쫐횵볓좨욽뻹쫐뎡ퟩ뫏쫇럱폐킧ꆣ 헽죧잰쫶볬퇩늻쓜뇭쏷막욱쫕틦싊쫇듓쎱ퟓ훐좡돶뗄ꎬ릹붨퓚헦쪵쫽뻝믹뒡짏뗄볬퇩튲늢늻쓜룦쯟컒쏇쫐뎡짏뚨볛뷡릹뗄탔훊ꆣ떱쯼쏇룦쯟컒쏇쯹쪹폃뗄쫐뎡횸쫽틔풤웚쫕틦싊뗄탎쪽뫜뿉쓜실퓚ퟜ뗄ퟮ킡랽닮춶ퟩ뫏짏ꎬ쯼쏇늢쎻폐룦쯟컒쏇횸쫽뗄쿠뛔폐킧탔ꆣ쫂쪵짏ꎬ죧맻퓚죎뫎쟩뿶쿂뾼달BJS뫍FM쪹폃뗄횸쫽뗄폐킧탔ꎬ헢쫇럇뎣횵뗃뮳틉뗄ꆣ캪쇋볬퇩CAPMꎬ컒쏇뇘탫볬퇩쫐횵볓좨쫐뎡ퟩ뫏뗄폐킧탔ꆣ뛸BJS뫍FM쪹폃뗄쫇NYSE짏쯹폐막욱뗄볲떥볓좨ퟩ뫏ꆣ 컊쳢퓚폚BJS뫍FM늢쎻폐횱뷓볬퇩CAPM뗄볙짨ꎺ쫐뎡ퟩ뫏실퓚폐킧벯짏ꆣ쿠랴ꎬ쯻쏇뾼달뗄쫇룹뻝튻룶볲떥볓좨ퟩ뫏릹붨뗄횤좯쫐뎡쿟뗄탔훊ꆣ죧맻룃쫐뎡ퟩ뫏쫇폐킧뗄ꎬ쓇쎴놴쯾틲ퟓ뫍풤웚쫕틦싊횮볤붫듦퓚헽쿠맘뗄쿟탔맘쾵ꆣ떫쫇ꎬ늻탒뗄쫇ꎬ떱컒쏇랢쿖ퟩ뫏놴쯾틲ퟓ뫍풤웚쫕틦싊횮볤붫듦퓚ퟅ췪좫쿟탔맘쾵ꎬ늢늻틢캶ퟅ쫐뎡ퟩ뫏쫇폐킧뗄ꆣ ꎨ2ꎩ 놾닺뚨볛쒣탍뿉틔놻볬퇩싰ꎿ 싞뛻뗄뗚뛾룶맛뗣쫇CAPM놾훊짏늻쫇튻룶뿉볬퇩뗄샭싛ꆣ 볙짨쓣쏦쇙튻룶닺ퟜ쳥ꎬ쿠뛔폚룃ퟜ쳥뗄ퟮ킡랽닮벯ꎬ헢킩닺뗄쫐뎡ퟩ뫏쫇폐킧뗄ꆣ죧맻쓣쿖퓚돖폐헢킩닺뗄튻룶ퟓ벯ꎬ쿠뛔폚룃ퟓ벯뗄ퟮ킡랽닮벯ꎬ룃ퟓ벯뗄튻룶쫐횵볓좨ퟩ뫏늻듳뿉쓜쫇폐킧뗄ꆣ쯹틔ꎬ벴쪹헦쪵뗄ퟮ킡랽닮벯쫇폐킧뗄ꎬ쿠뛔폚룹뻝NYSE뗄막욱릹붨뗄ퟮ킡랽닮벯ꎬNYSE횸쫽튲늻듳뿉쓜쫇폐킧뗄ꆣ
튪쿫뻜뻸CAPMꎬ쓣뇘탫뻜뻸쫐뎡ퟩ뫏뗄폐킧탔ꆣ헢벴쪹늻쫇늻뿉쓜뗄ꎬ튲붫쫇럇뎣삧쓑뗄ꆣ쓣붫늻뗃늻냑쓣뗄퇐뺿삩햹떽웤쯻쯹폐붻틗쯹ꎬ냼삨뎡췢붻틗쫐뎡뗄쯹폐막욱ꆣ쓣뮹붫늻뗃늻냼삨햮좯ꆢ폅쿈막뫍웤쯻샠탍뗄횤좯ꆣ탭뛠햮좯쫇평릫쮾쮽쿂돖폐ꎬ듓늻붻틗ꆣ쓣컞램맛닢떽헢킩횤좯뗄쫕틦싊ꆣ쓣튲컞램맛닢떽웤쯻탭뛠닺뗄쫕틦싊ꎬ훮죧얩뎡뫍쯹폐좨ꆣퟩ뫏춶헟뮹뿉틔맺볊뮯ꎬ쯹틔쓣뇘탫퓚쓣뗄쫐뎡ퟩ뫏샯냼삨쫀뷧짏쎿튻룶맺볒뗄쯹폐닺ꆣ쓣쏦쇙뗄쫇튻볾늻뿉쓜뗄죎컱ꆣ 퓚헢샯폐솽뗣뫜훘튪ꆣ쫗쿈ꎬ벴쪹CAPM쫇헦쪵뗄ꎬ튲쎻폐샭평쿠탅냼삨뺭볃쾵춳훐튻듳늿럖ퟜ닺뗄쫐뎡ퟩ뫏맘폚룃늿럖닺뗄ퟮ킡랽닮벯쫇폐킧뗄ꆣ웤듎ꎬ룸뚨뿉틔믱뗃뗄탅쾢ꎬ컒쏇횻뿉틔맛닢떽튻킡늿럖ퟜ닺뗄쫕틦싊ꆣShankenꎨ1984ꎩ죏캪냼삨퓚쫐뎡ퟩ뫏샯뗄쓇늿럖닺늢늻훘튪ꎬ훘튪뗄쫇쳦듺뗄쫐뎡ퟩ뫏뗄쫕틦싊뫍쫐뎡ퟩ뫏쫕틦싊뗄쿠맘뛈ꆣ룃늿럖뗄뇈샽뿉쓜뫜킡ꎬ떫쫇쿠맘뛈뿉쓜뫜듳ꆣ쯻춬쪱횸돶폫CAPM뗄쪵횤볬퇩훐쪹폃뗄횤좯컞맘뗄닺늻뇘냼삨퓚쳦듺뗄쫐뎡ퟩ뫏샯ꆣ헢킩뗣쫇컞킧뗣ꎬ웤퓚쒳훖돌뛈짏뗷뫍쇋뛔쒣탍뗄엺움ꆣ떫쫇ꎬ뇘탫횸쏷컒쏇폀풶컞램맛닢떽헦쪵쫐뎡ퟩ뫏뗄쫕틦싊ꆣ틲뛸ꎬ컒쏇붫폀풶컞램뗃횪죎뫎쳦듺ퟩ뫏폫헢킩쫕틦싊뗄쿠맘돌뛈ꆣ듋췢ꎬ컒쏇폀풶컞램뗃횪폫냼삨퓚룃볬퇩훐뗄횤좯쿠맘뗄닺퓚뛠듳돌뛈짏냼삨퓚쫐뎡ퟩ뫏훐떫쎻폐냼삨퓚쳦듺ퟩ뫏훐ꆣ 룹뻝틔짏맛뗣ꎬ탭뛠죋죏캪쎻폐튻룶죋퓸뺭릹퓬돶뛔놾닺뚨볛쒣탍폐킧뗄볬퇩ꎬ틔뫳튲늻믡폐ꆣ쯻쏇죏캪CAPM쫇컞램볬퇩뗄ꆣ 2ꆢ놾닺뚨볛쒣탍뗄뷼웚볬퇩ꆪꆪ뻹횵랽닮폐킧뗄볬퇩 CAPM뗄뷼웚볬퇩ퟅ훘폚웤훷튪볙짨ꎺ쫐뎡ퟩ뫏캻폚ퟜ뗄뻹횵ꎭ랽닮폐킧벯짏ꆣ ꋙ Mackinlay,Richardsonꎨ1991ꎩ 평폚믹폚쫕틦싊ퟱ톭쳘뚨럖늼뗄볙짨볬퇩췹췹믡떼훂폐욫뗄뷡싛ꎬ쯹틔룃컄닉폃쇋맣틥뻘랽램뛔쫐뎡횸쫽뗄뻹횵랽닮폐킧탔뷸탐쇋볬퇩ꎬ폫틔췹뗄볬퇩늻춬ꎬ룃컄늢쎻폐볙짨쫕틦싊ퟱ톭헽첬럖늼ꆣ 뻹횵랽닮폐킧탔뗄볬퇩릫쪽ꎺ r=a+br+eitiiptitE[e]=0it E[eritpt]=0a=0ir캪뎬뛮쫕틦싊 it퓚룸뚨뛀솢춬럖늼뫍뛠풪헽첬럖늼뗄볙짨쿂ꎬ춨뎣폃Wald춳볆솿볬퇩뻹횵랽닮폐킧탔ꆣ 맣틥뻘볬퇩뻹횵랽닮폐킧탔튻냣폐솽훖랽램ꎺ 1ꎮ맀볆컞쿞훆쾵춳늢폃룃컞쿞훆맀볆솿볬퇩a=0뗄볙짨ꆣ)[−1−1fTaR[D−11TSTDT]R]a)=′′′~c2N R=IN⊗(10) Rd=ˆaˆ
e1(a1,b1)te1(a1,b1)rtpt:e1(a,b)tii2ꎮ붫풼쫸쳵볾a=0듺죫f(d)=ꎬ맀볆쿞훆쾵춳ꎬ좻뫳볬퇩맽te1(a,b)rtiipt:e1(a,b)tNNe1(a,b)rtNNpt럖쪶뇰뗄풼쫸쳵볾ꆣ )′)f=Tg()−1TbSTgT(b)c22~N 볬퇩뷡맻뇭쏷ꎺ뛔폚CRSP쫐횵볓좨횸쫽뫍볲떥볓좨횸쫽ꎬWald춳볆솿럖뇰뇈GMM춳볆솿뗍맀ꎥ뫍ꎥꆣ쯹틔Wald춳볆솿뺭뎣늻믡뻜뻸뻹횵랽닮폐킧탔ꎬ뛸폃GMM춳볆솿퓲횤쏷쫐뎡ퟩ뫏늢늻쫇뻹횵랽닮폐킧뗄ꆣ 캪쇋볬퇩룃닮틬쫇풴폚Wald춳볆솿뗄늻ힼ좷뮹쫇풴폚GMM춳볆솿퓚킡퇹놾훐늻쫊폃ꎬ룃컄뇈뷏쇋Wald춳볆솿뫍GMM춳볆솿퓚킡퇹놾훐뗄뷡맻ꎬ랢쿖늢쎻폐듦퓚쿔훸닮틬ꆣ쮵쏷쇋룃닮틬쫇풴폚Wald춳볆솿뗄늻ힼ좷ꆣ ꋚRollꆢRossꎨ1994ꎩ 떱쫐뎡횸쫽쫇뻹횵랽닮폐킧뗄ꎬ쓇쎴쫕틦싊뫍ꛂ횮볤듦퓚쿟탔뗄맘쾵ꎬ떫쫇쪵횤볬퇩췹췹랢쿖쫕틦싊뫍ꛂ횮볤늢늻듦퓚쿟탔맘쾵ꎬ쯹틔튻룶뿉쓜뗄뷢쫍쫇톡퓱뗄쫐뎡횸쫽늻쫇뻹횵랽닮폐킧뗄ꆣ룃컄뗄쒿뗄벴럖컶쫐뎡횸쫽뗄톡퓱뛔쫕틦싊뫍ꛂ횮볤맘쾵뗄펰쿬ꆣ 룃컄쫗쿈쏨쫶쇋떼돶쳘뚨쫕틦싊뫍놴쯾뗄뫡뷘쏦맘쾵뗄횸쫽뗄뷢컶쳘헷ꆣ 캻폚폐킧벯쓚늿뗄쳦듺쫐뎡횸쫽쟺쿟뇭쪾캪ꎺ Bs4+Crs2+Dr2+Fs2+Gr+H=0 B=k2(ac−b2),C=−2dkcD=gcF=dkb−g(ac−b2)+cd2G=−gbH=ag−d2,,2,2,a≡R−1−11222′VR,b≡R′V1c≡−,1′V1,d≡sR,g≡msR−1 V캪쫕틦싊킭랽닮뻘헳ꎬ1캪떥캻헳 µ캪쫕틦싊뗄뫡뷘쏦뻹횵 s2R−1뫡뷘쏦믲쪱볤탲쇐랽닮 k캪R폫ꛂ뗄뫡뷘쏦킭랽닮 떱kꎽ0쪱ꎬ쳦듺쫐뎡횸쫽쟺쿟캪폫폐킧벯쿠쟐폚ퟜ뗄ퟮ킡랽닮ퟩ뫏뗄엗컯쿟ꆣꎨ춼1ꎩ
ퟜ뗄ퟮ킡랽닮ퟩ뫏뗄ꛂ뗈폚1ꎬcov(R,1)=0ꎬ폐킧ퟩ뫏훐횻폐ퟜ뗄ퟮ킡랽닮ퟩ뫏뗄k캪0ꎬ웤쯻뷔캪1ꆣ 떱쫐뎡횸쫽캻폚폐킧벯쓚늿쪱ꎬ웤늻쫇뻹횵랽닮폐킧뗄ꆣ 폐킧벯뫍kꎽ0뗄쫐뎡횸쫽뗄ퟮ뛌뻠샫폃쫕틦싊닮틬뇭쪾캪ꎺ M≡∗−={[(s2−)(ac−b21/2)]−[(cs2−)(ac−b2−cd21/2rrc11/g)]}/c r쫇룃쫐뎡횸쫽뗄쫕틦싊ꎬr*쫇폫룃쫐뎡횸쫽랽닮쿠춬뗄폐킧ퟩ뫏뗄쫕틦싊ꆣ 캻폚폐킧벯ꎨkꎽ1ꎩ뫍뗄쫐뎡횸쫽쟺쿟ꎨkꎽ0ꎩ횮볤뗄ퟩ뫏ꎬcov(R,b)=k캪헽횵ꆣ 떱kꇙ0쪱ꎬ쳦듺쫐뎡횸쫽쟺쿟캪췖풲ꎬ쎿룶췖풲뗄훡뻹뷘ퟝ훡폚ퟜ뗄ퟮ킡랽닮ퟩ뫏뗄쫕틦싊ꎬ뛸쟒k풽듳ꎬ췖풲풽킡ꆣꎨ춼2ꎩ
캪쇋럖컶뻹횵랽닮볬퇩뛔쫐뎡횸쫽톡퓱뗄쏴룐뛈ꎬ룃컄횸돶ꎬ평폚kꎽ0뗄컞킧ퟩ뫏폫폐킧ퟩ뫏뻠샫뿉쓜쿠닮늻풶ꎬ틲뛸짔캢뗄퇹놾컳닮폐뿉쓜쪹뻹횵랽닮볬퇩쪧킧ꆣ헢뻍뛔맽좥뗄뫜뛠볬퇩뷡맻ퟶ돶쇋뷢쫍ꎬcov(R,b)=k뛔쫐뎡횸쫽뗄톡퓱럇뎣쏴룐ꎬ폫쫐뎡ퟩ뫏뫜뷓뷼뗄횸쫽폐뿉쓜뗃돶헽ꆢ뢺ꆢ믲쇣뗄cov(R,b)=kꎨ죧FamaꆢFrench죏캪놴쯾늻쓜뷢쫍쫕틦싊닮틬폐뿉쓜쫇틲캪쫐뎡ퟩ뫏톡퓱늻떱뗄뷡맻ꆣꎩ 룃컄뮹랢쿖ꎬ춳볆랽램뗄톡퓱뛔쫕틦싊뫍놴쯾맘쾵뗄볬퇩튲믡닺짺펰쿬ꆣ폃GLS뿉틔뷢뻶OLS뗄짏쫶컊쳢ꎬ틲캪횻튪쳦듺횸쫽뗄풤웚쫕틦싊룟폚ퟜ뗄ퟮ킡랽닮ퟩ뫏뗄쫕틦싊ꎬ쓇쎴cov(R,b)=k뻍캪헽횵ꆣ헢틢캶ퟅ횻튪횸쫽늻쫇췪좫컞킧ꎬ쓇쎴퓚듳퇹놾훐cov(R,b)=k뇘캪헽ꆣ떫쫇헢좴듸살쇭튻룶컊쳢ꎬ벴늻쓜볬퇩쳦듺횸쫽쫇럱폐킧ꆣ ꋛShankenꎨ1987ꎩ ꆾKandelꎬstambaughꎨ1987ꎬ1989ꎩShankenꎨ1987ꎩ뻹춨맽헒돶쳦듺쫐뎡횸쫽폫헦쪵쫐뎡ퟩ뫏뗄쿠맘뛈췆떼돶뛔CAPM뗄볬퇩ꆣꆿ 떫쫇평폚떱쫐뎡횸쫽캻폚폐킧벯쓚늿쪱ꎬ퓚쿠춬뗄cov(R,b)=k쿂폐늻횹튻룶쫐뎡횸쫽ꎬ쯹틔늻뿉쓜춨맽헒돶쳦듺쫐뎡횸쫽퓚뻹횵ꎭ랽닮춼훐뗄캻훃좷뚨kꆣ 볙짨쓣쏦쇙튻룶횤좯ퟜ쳥뫍믹폚룃ퟜ쳥릹붨뗄쳦듺쫐뎡ퟩ뫏ꆣ춬쪱볙짨ퟓ벯횻쫇맺볊짏쯹폐놾춶ퟜ쳥뗄튻킡늿럖ꎬ늢쟒믹폚룃ퟓ벯뗄폐킧벯뫜뿉쓜실퓚믹폚쯹폐놾춶ퟜ쳥뗄ퟜ뗄ퟮ킡랽닮벯쓚늿ꆣ뗣M듺뇭쳦듺쫐뎡ퟩ뫏ꎬ뗣M∗듺뇭헦쪵뗄ퟜ쫐뎡ퟩ
뫏ꆣ쿠뛔폚웤룷ퟔ뗄폐킧벯ꎬ늻맜M믲헟M∗뚼쫇컞킧뗄ꆣ 쿖퓚M∗뫍ퟜ뗄폐킧벯뚼컞램맛닢떽ꎬ떫쫇쓣뿉틔맛닢떽M뫍ퟓ벯뗄폐킧벯ꆣ쓣튲뿉틔볬퇩쿠뛔폚ퟓ벯뗄폐킧벯M쫇럱컞킧ꆣ 룸뚨M뫍M∗뗄쫕틦싊뗄쿠맘뛈뫍풤웚쫕틦싊폫M∗뗄킭랽닮쿟탔쿠맘뗄볙짨ꎬ쓣뿉틔볬퇩M∗쿠뛔폚ퟓ벯뗄폐킧벯쫇럱컞킧ꆣ틲캪웤살ퟔ폚ퟓ벯ꎬퟓ벯뗄폐킧벯뇘뚨실퓚ퟜ뗄폐킧벯샯쏦ꆣ쯹틔ꎬ죧맻M∗쿠뛔폚ퟓ벯뗄폐킧벯컞킧ꎬ퓲뿉틔풤닢웤맘폚ퟜ뗄폐킧벯튲쫇컞킧뗄ꆣ룸뚨룃풤웚쫕틦싊뗄볙짨뗄맘쾵뫍M뫍M∗횮볤뗄쿠맘쾵쫽ꎬ헢뾴웰살쯆뫵폐뿉쓜뻜뻸CAPMꆣShanken뷓ퟅ횤쏷죧맻쓣풸틢돐죏램싪뫍싳뿋엥쮹쯹쪹폃뗄쳦듺쫐뎡ퟩ뫏뫍늼삳뿋ꎬ햲즭뫍쫦뛻쮹쯹쪹폃뗄쳦듺쫐뎡ퟩ뫏횮볤뗄쿠맘쾵쫽캪.8ꎬ쓇쎴CAPM뿉틔퓚95ꎥ뗄훃탅뛈짏놻뻜뻸ꆣ 헢쫇튻룶폐좤뗄쮼쿫ꎬ떫쫇웤틀좻듦퓚튻룶퇏훘뗄컊쳢ꆣ평폚듳늿럖쫐뎡ퟩ뫏쫇늻뿉쇷춨뗄ꎬ쯹틔웤쫕틦싊쫇컞램맛닢뗄ꎬ쓇컒쏇죧뫎횪뗀.8쫇튻룶뫏샭뗄쿠맘쾵쫽ꎿ죧맻쫐뎡ퟩ뫏냼삨죋솦놾뫍웤쯻럇뎣훘튪떫쫇췪좫늻뿉맛닢뗄릹돉돉럖ꎬ쓇쎴뫜죝틗ퟶ돶뿉틔맛닢뗄쳦듺ퟩ뫏뫍헦쪵뗄쫐뎡ퟩ뫏횮볤뗄쿠맘쾵쫽뫜뗍뗄에뛏ꆣ본폚듋ꎬ튻룶늻뿉뻜뻸뗄쿈죫횮볻쫇럱쫇뛔튻룶늻뿉뻜뻸뗄샭싛뗄룄뷸쓘ꎿ ꋜ Jarrow, Madanꎨ1997ꎩ Dybvig and Ingersoll (1982)ퟮ퓧횤쏷쇋퓚췪좫쫐뎡훐ꎬCAPM뫍웚좨붻틗횮볤듦퓚ퟅ늻튻훂ꆣ뛸놾컄횤쏷룃늻튻훂늻쫇풴폚쫐뎡늻췪좫ꎬ뛸쫇틲캪뻹횵랽닮욫뫃놾짭믡떼훂쳗샻믺믡뗄돶쿖ꆣ 컄헂죏캪퓚춶헟뻟폐뻹횵랽닮욫뫃늢뿉틔뷸탐맣랺뗄퇜짺닺욷붻틗뗄뻹뫢뺭볃훐듦퓚ퟅ쳗샻믺믡ꎬ듓뛸횤쏷뻹횵랽닮럖컶쫇컞킧뗄ꆣ Dana (1994)횤쏷쇋CAPM틢캶ퟅ틔쫐뎡ퟩ뫏캪뇪뗄웚좨붻틗듦퓚ퟅ쳗샻믺믡ꆣ 뚨볛몯쫽f[z]=E[pz] zꇊZ ꎨRiesz representation theoremꎩ Z쫇욽랽뿉믽뗄쯦믺뇤솿뿕볤뗄뇕ퟓ듺쫽ꆣ p=a−be aꆢb뻹캪뇪솿 cE[+=(a−be)(e−k)]<0 j떱eꎨퟜ?뢳ꎩ컞쟮듳쪱ꎬc캪뢺횵ꎬk캪횴탐볛룱ꆣ j볙짨킧폃몯쫽u(x)=U[E(x),var(x)] i떱쇮zꎽx+yꎬ쪱ꎬꎨy캪럇뢺뗄룟늨뚯싊뇤솿ꎩ U[E(z),var(z)]<U[E(x),var(x)] 뿉볻ꎬ쯤좻z폅폚xꎬ떫쫇룹뻝뻹횵랽닮럖컶ꎬ춶헟뗄킧폃랴뛸붵뗍ꆣ쮵쏷샭싛짏듦퓚ퟅ쳗샻믺믡ꆣ 떱좻ꎬ헢횻퓚폐쿞뗄쮮욽ꎨh>0ꎩ쿂듦퓚늻튻훂ꎨ뻹횵랽닮욫뫃쫇럇떥뗷뗄ꎬ뛸쫐뎡ퟩ
뫏뗄볛룱쫇쿟탔뗄ꎩꎬ뛔폚솬탸쪱볤뗄BS늢늻돉솢ꎨ룹뻝쒬뛙뗄솬탸쪱볤뻹뫢ꎩꆣ 캪쇋퇩횤쪵볹훐쫇럱헦헽듦퓚쳗샻믺믡ꎬ컄헂릹퓬쇋튻룶CAPM뺭볃훐뗄웚좨뚨볛쒣탍ꎬ늢틔쫐뎡ퟩ뫏캪뇪뗄뷸탐웚좨붻틗ꎬ랢쿖떱횴탐볛룱뒦폚탩횵웚좨솽룶뇪ힼ닮쪱ꎬ뾴헇웚좨볛룱캪뢺횵ꎬ듓뛸듦퓚ퟅ쳗샻믺믡ꆣ 볙짨뻹횵랽닮욫뫃틔웚쒩T쪱뿌ퟜ닆뢻뗄뻹횵랽닮몯쫽뇭쪾ꎬeꎨퟜ?뢳ꎩퟱ톭벸뫎늼샊퓋뚯ꆣ 폫BS릫쪽늻춬뗄쫇ꎬ룃웚좨뚨볛쒣탍믹폚죎틢뗄ꆢ샫즢뗄맦뮮풶뺰ꆣ wV()()뾴헇웚좨볛룱(,K,m,s,,h,r)=(aer+bKem+rh−t)VemttN(dttttt1) −aer(h−t)KNd−be(m+r)(h−t)22mt+s2t(2)VeN(dttt3)(뾴뗸웚좨볛룱w(V,K,m,s−tm+−tmt′,t,h=−rh+rh,r)(ae)bKe()())VeN(−d)ttttt1 +aer(h−t)KN−d+be(m+r)(h−t)V2e2mt+s2t(2)N(−dttt3)((m)(t))m(m)(t)(s2w−wVKe−rTVer−h−1bV2e2her−h−h′=−+−+1−e−(−t)) tttttt뿉볻ꎬ짏쪽늢늻싺ퟣ뾴헇ꎭ뾴뗸웚좨욽볛릫쪽ꎬ횻폐떱h=t쪱ꎬ욽볛릫쪽돉솢ꎨt=s−t,h=T−tꎬs캪떽웚죕ꎬT캪헻룶쮮욽웚ꎩꆣ 평폚쒣탍볙짨듦퓚컞쿞뗄횴탐볛룱ꎬ캪쇋횤쏷웤쫇럱뎬돶쪵볊뗄붻틗랶캧ꎬ컄헂퓋폃BS릫쪽뛔룃쒣탍뗃돶뗄웚좨볛룱볆쯣돶틾몬늨뚯싊ꆣ샽ꎺ막욱쿖볛캪100ꎬ풤웚쫕틦싊캪15ꎥꎬ늨뚯싊캪20ꎥꎬ컞럧쿕샻싊캪5ꎥꎬ떱횴탐볛룱캪140쪱ꎬBS릫쪽볆쯣돶뗄웚좨볛룱캪ꎬ뛸룃쒣탍볆쯣돶뗄웚좨볛룱캪뢺횵ꆣ 컄헂뮹뇈뷏쇋BS릫쪽뫍CAPM웚좨뚨볛쒣탍뛔뇪ힼ웕뛻웚믵웚좨볛룱쫽뻝뗄볆쯣뷡맻ꎬ랢쿖CAPM웚좨뚨볛쒣탍뗄욽뻹컳닮캪ꎥꎬ룟폚BS릫쪽뗄ꎥꆣ 컄헂ퟮ뫳뗃돶뷡싛ꎬ평폚뻹횵랽닮럖컶쫇컞킧뗄ꎬ쯹틔믹폚뻹횵랽닮폐킧뗄CAPM늢늻돉솢ꆣ 닎뾼컄쿗ꎺ Campbell,, 2000,“Asset Pricing at the Millennium”, The Journal of Finance, ,1515-1568. Black,F.,1972, “Capital market equilibrium with restricted borrowing”, Journal of Business, ,444-455. Hagerman,.,,1976,“Capital asset pricing with price level changes”, Journal of Financial and Quantitative Analysis, , 381-391 Merton,.,1973,“An intertemporal capital asset pricing model”,Economitrica,,867-887 Jorrow,.,,1984,“Jump risks and the intertemporal capital asset pricing model”, Journal of Business, ,337-351 Chamberlain,G.,1988,“Asset pricing in Multiperiod securities markets”,Econometrica,,1283-1300 Kazemi,.,1991,“The multi period CAPM and the valuation of Multi-period stochastic cash flows”, Journal of Financial and Quantitative Analysis, ,223-231 Mcdonald,B.,1983,“Functional forms and the capital asset pricing model”, Journal of Financial and Quantitative Analysis, ,319-329
Mathur,I.,,,1995,“Conditional relation between beta and returns”, Journal of Financial and Quantitative Analysis, ,101-116 Jagannathan,R.,,1996,“the Conditional CAPM and the cross-section of expected returns”, Journal of Finance ,,3-53 Bodurtha,.,,1991,“Testing the CAPM with Time varying risks and returns”, Journal of Finance, ,1485-1505 Ng,L.,1991,“Tests of the CAPM with time varying covariances: a multivariate GARCH approach”, Journal of Finance, ,1507-1521 Fisher,L.,, 1985,“Forecasting systematic risk: estimates of “raw” beta that take account of the tendency of beta to change and heteroskedasticity of residual returns”, Journal of Financial and Quantitative Analysis, ,127-149 Mackinlay,.,,1991,“Using Generalized method of moments to test mean variance efficiency”, Journal of Finance, ,511-527 .,,1994,“Relation between expected returns and betas”, Journal of Finance, ,101-121 Jarrow, .,. Madan,1997,“Is Mean-Variance Analysis Vacuous: Or was Beta Still Born?”, European Finance Review,, 15–30.
