폐맘쯦믺쳹쿖틲ퟓ뗄튻킩쮼뾼 쇖몣 ꎨ쿃쏅듳톧뷰죚쾵ꎬꎳꎶꎱꎰꎰꎵꎩ 잰퇔 Cochrane(1996,2000)쳡돶쇋튻룶쯦믺쳹쿖틲ퟓ뗄샭싛뿲볜ꎬ헢룶샭싛뿲볜뿉틔폃폚뷢쫍튻냣뗄닺뚨볛컊쳢ꆣ헢룶샭싛뿲볜ퟮ쿔훸뗄튻룶쳘헷뻍쫇뿉틔붫쯹폐뗄닺뚨볛쒣탍ꎬ죧놾닺뚨볛쒣탍ꎨb쒣탍ꎩꆢ틲쯘쒣탍뗈ꎬ쓉죫떽헢룶튻냣뮯뗄샭싛뿲볜훐ꆣKan and Zhou(1999)샻폃쒣쓢뗄랽램뛔듋쳡돶쇋훊틉ꆣ쯻쏇뗃돶뷡싛죏캪뒫춳뗄뚨볛쒣탍뗄쫽뻝맀볆뷡맻ꎬ쳘뇰쫇퓚럧쿕볛룱뗄맀볆짏ꎬ튪뇈쯦믺쳹쿖쒣탍컈뚨뫍ힼ좷뗃뛠ꎬ뛸쟒쯦믺쳹쿖쒣탍퓚쪶뇰듭컳쒣탍짏뗄쓜솦튲쫇폐쿞뗄ꆣ놾컄퓲퓚헢믹뒡짏ꎬ솦쟳톰헒돶닺짺헢룶컊쳢뗄풭틲ꆣ뺭맽럖컶뿉틔랢쿖ꎬ헢쪵볊짏쫇퓚볬퇩늻춬뗄쒣탍ꎬ뒫춳뗄볬퇩쒣탍쪵볊짏퓚볬퇩틲쯘쒣탍ꎬ뛸쯦믺쳹쿖틲ퟓ쪵볊짏볬퇩뗄쫇b쒣탍ꆣ평폚쒣쓢뗄쫽뻝쫇룹뻝틲쯘쒣탍뷸탐쒣쓢뗄ꎬ떱좻늻뿉뇜쏢뗘뗃돶뒫춳볬퇩랽램뗄맀볆뷡맻폅폚쯦믺쳹쿖틲ퟓ뗄뷡싛ꆣ틲듋ꎬ뛾헟횮볤뗄닮틬늻퓚폚쯦믺쳹쿖틲ퟓ뗄랽램놾짭ꎬ뛸퓚폚쎻폐헒떽튻룶헽좷뗘폃폚뇭쪾틲쯘쒣탍뗄쯦믺쳹쿖틲ퟓꆣ 평폚쯦믺쳹쿖틲ퟓ뷢뻶뗄쫇b쒣탍ꎬ퓚b쒣탍훐ꎬ럇쾵춳탔뗄닢솿컳닮틔벰퓫틴뚼늻믡뛔풤웚럧쿕틧돪닺짺펰쿬ꎬKan and Zhou(1999)뛔퓚쯦믺쳹쿖틲ퟓ쿂뗄헢룶뷡싛쳡돶쇋훊틉ꆣ떫쫇뇊헟뺭맽럖컶ꎬ죏캪ꎬ헢룶뷡싛벴쪹쪹폃쯦믺쳹쿖틲ퟓ뗄랽램ꎬ죔좻돉솢ꆣKan and Zhou(1999)횮쯹틔뗃돶듭컳뗄뷡싛ꎬ훷튪풭틲퓚폚쯻쏇횻뾼싇쇋틲쯘뇤뚯뛔럧쿕볛룱뗄펰쿬ꎬ뛸쎻폐뾼싇틲쯘뇤뚯뛔틲쯘쿠맘쾵쫽뗄펰쿬ꆣ뛾헟쪵볊짏쫇뮥쿠뗖쿻뗄ꎬ틲듋ퟮ뫳뗄풤웚럧쿕틧돪놣돖늻뇤ꆣ 컄헂뗄뗚죽룶컊쳢튪첽쳖뗄뻍쫇뚨볛듭컳컊쳢ꆣ떱쯦믺쳹쿖틲ퟓ캻폚틲쯘뿕볤횮쓚쪱ꎬ튲뻍쫇쮵ꎬ뿉틔폃틲쯘살뷸탐뇭쪾쪱ꎬ뚨볛듭컳캪쇣ꆣ떫쫇죧맻쯦믺쳹쿖틲ퟓ늻퓚틲쯘뿕볤횮쓚ꎬ뚨볛듭컳뻍뿉쓜듦퓚ꆣ쯦믺쳹쿖틲ퟓ샫뾪틲쯘뿕볤풽풶ꎬ뚨볛듭컳뻍풽듳ꆣ헢뿉틔뷢쫍캪쪲쎴믹폚쿻럑뗄놾닺뚨볛쒣탍늻쓜릻뗃떽뫜뫃뗄킧맻뗄훷튪풭틲ꆣ퓚헢룶닺뚨볛쒣탍훐ꎬ쯦믺쳹쿖틲ퟓ뫍쿻럑뗄뇟볊킧폃폐맘Mu'(Cbt+1)t+1=ꎬ튻냣늻퓚틲쯘뿕볤횮쓚ꎬu'(C)t쯹틔뻍믡듦퓚ퟅ뚨볛듭컳ꆣ 쿠펦뗄ꎬ놾컄튲럖캪죽룶늿럖ꎺ뗚튻룶늿럖뻍쫇뛔b쒣탍뫍틲쯘쒣탍뷸탐퇏룱뗄뇈뷏뫍쟸럖ꎬ늢퓚듋믹뒡짏헽쪽쯦믺쳹쿖틲ퟓ볬퇩뗄쪵볊짏쫇b쒣탍ꎻ뗚뛾늿럖뻍쫇튪뛔b쒣탍쿂ퟛ뫏뾼싇틲쯘쿠맘쾵쫽뫍럧쿕볛룱믹뒡짏뛔럧쿕틧돪컊쳢뷸탐럖컶ꎻ뗚죽늿럖퓲쫇뛔뚨
볛듭컳뗄튻킩볲떥쳖싛ꆣ캪쇋쮵쏷뗄랽뇣ꎬ놾컄좫늿쪹폃떥룶펰쿬틲ퟓꎬ벴쫐뎡쫕틦싊rmꆣ 튻ꆢb쒣탍ꆢ틲쯘쒣탍뫍쯦믺쳹쿖틲ퟓ ꎨ튻ꎩb쒣탍뫍틲쯘쒣탍 튻룶ퟮ뗤탍뗄b쒣탍뻍쫇놾닺뚨볛쒣탍: E(r)=r+b[E(r)−r],jfjmfcov(r,r) b=jmjvar(rm)튻룶떥틲쯘쒣탍뇭쪾캪ꎺr=E(r)+bf+e, f쫇뺭맽뒦샭뗄틲ퟓꎬf=rm−E(rm)ꆣ jjjj볙짨kq캪뚨볛뫋ꎬ벴p=E(kqxj)ꎬ jEkkqr=kE(r)fkjq+b+keꎬ(qx)Ekr=j(=ꎬ jjqqjqj)1pj1=E(kq)E(rj)+bE(kf)+E(kqej)ꎬ jq1E(kqf)E(kqeEr=+b−−j)()(ꎬ jEj(kq)E(kq)E(kq)죧맻컞럧쿕쫕틦싊캻폚닺뿕볤쓚ꎬ E(kq)=1/rf, E(r)=r−brp(f),p(f)뇭쪾틲쯘f뗄볛룱ꆣ jfjfcov(r,f)cov(r,r)b=j=jmꎬ 뗈폚b쒣탍ꆣ jvar()var(m)E(r)q(f)=E(kq(rm−E(rm)=1−mꎬ rfE(r)=r+b(E(r)−r) jfmfr=E(r+bf+e=r+b(E(r)−r)+bf+e, jjjfmfjr−r=b(E(r)−r)+bf+eꎬ 럧쿕볛룱캪 l=E(rm)−rf, 튲뗈폚b쒣탍쿂뗄럧쿕jfmfj볛룱ꆣ 쯹틔ꎬ퓚b쒣탍쿂ꎬr=r+bꎨE(rm)−r)+h jfjfj퓚틲쯘쒣탍쿂ꎬ r=r+b(E(rm)−r)+bf+eꆣ죧맻폃뎬뛮쫕틦싊rꎽr−rꎨ벴jfjfjjjjf
뎬맽컞럧쿕샻싊뗄늿럖ꎩ뫍럧쿕볛룱a뇭쪾ꎬ퓲뿉틔뇭쪾캪ꎺ rfb쒣탍ꎺr=ba+hꎬcov(,)b=jꆣ jjjjvar(f)틲쯘쒣탍ꎺr=ba+bf+eꆣ jjjj뛔펰쿬틲ퟓ뿉틔뷸탐뇪ힼ뮯ꎬ쪹뗃펰쿬틲ퟓ뗄랽닮뇤캪ꎱꎬ벴뿉틔짨ff'=ꎬ듋쪱퓚bs(f)쒣탍훐ꎬb'=cov(r,f')=E(rf')ꎬ틲캪E(f')=01ꆣ쯹틔뺭맽뇪ힼ뮯뒦샭횮뫳ꎺ jjjb쒣탍ꎺ'r=ba'+hꎬb'=E(rf')ꆣ jjjjj틲쯘쒣탍ꎺ''r=ba'+bf'+eꆣ jjjjꎨ뛾ꎩ볆솿럖컶 †짏쏦뗄럖컶뚼쫇뫡뷘쏦럖컶ꎬ퓚쪵볊볆솿럖컶뗄쪱뫲튪삩햹떽쪱볤탲쇐럖컶ꆣ평폚솽룶쒣탍뗄늻춬ꎬ틲듋ꎬ쪹폃뗄쪱볤탲쇐GMM볆솿쒣탍튲늻튻퇹ꆣ T∑(r−rfl)ttt†뛔b쒣탍뛸퇔ꎬGMM랽램캪ꎺ볆쯣뻘g=t=11TꎬTgT1T:N(0N,S1)ꆣ 춨맽ퟮ킡뮯))argminlgT(l)'W1TgT(l)쟳돶lꎬ듋쪱l=WD−1(DT'1TT)(DT'W1Tr2T)ꆣ웤훐ꎬ TT∑rftt∑rtD=t=1Tꎬr=t=1TꎬWTT1T쫇S−11뗄폐킧맀볆ꆣ †뛸뛔틲쯘쒣탍뛸퇔ꎬ쯼뗄GMM랽램캪ꎺ E(e)=E(r−bl−bf)=0;tttꆣ쯼뗄뻘쳵볾캪 E(f)=E[r−bl−bf)f]=0ttt1Tg2T(l,b)=∑[z⊗(r−bl−bf)]ꎬTg2T(l,b):(02N,S2),zt=[1,ft] Ttttt=1?쯹틔닎쫽l,b춨맽argminlbgT(l,b)'WTgT(l,b)ꆣ ,222쯹틔ꎬ퓚b쒣탍훐ꎬGMM랽램횻폐튻룶맀볆닎쫽ꎬ쓇뻍쫇럧쿕볛룱ꎬ뛸럧쿕쾵쫽횱뷓춨맽 1 뿉틔랢쿖ꎬ듋쪱bb'=jꎬ쯹틔a'=as(f)ꎬ펰쿬틲ퟓ뗄뇤뚯춬쪱펰쿬럧쿕볛룱뫍럧쿕쾵쫽ꆣ js(f)2 쪽ퟓ훐뗄r쫇튻룶N×1쿲솿ꎬ듺뇭쪱뿌t쫐뎡짏N룶닺뗄뎬뛮쫕틦싊ꆣ t
TE(rf)=1/Tt∑rf뷸탐맀볆ꆣ뛸퓚틲쯘쒣탍훐ꎬGMM랽램춬쪱뛔럧쿕쾵쫽뫍럧쿕볛룱ttt=1춬쪱뷸탐맀볆ꎬ쪹뗃ퟮ뫳뗄컳닮ퟮ킡ꆣ틲듋ꎬ쫕틦싊쪱볤탲쇐ꎬb쒣탍붫쯹폐뗄컳닮뚼쳥쿖퓚럧쿕볛룱훐ꎬ쪹뗃럧쿕볛룱뇤뗃쿠뛔늻컈뚨ꎻ뛸틲쯘쒣탍퓲붫컳닮춬쪱럖룸럧쿕쾵쫽뫍럧쿕볛룱ꎬ틲듋럧쿕볛룱뻍쿔뗃쿠뛔뇈뷏컈뚨ꆣퟜ뗄살쮵ꎬ틲쯘쒣탍쫇솪뫏쟳뷢ꎬ뛸b쒣탍퓲쫇떥뛀쟳뷢ꆣ ꎨ죽ꎩ쯦믺쳹쿖틲ퟓ †퓚쯦믺쳹쿖틲ퟓ쒣탍훐ꎬCochrane(2000)뗈죏캪ꎬ죧맻떥틲쯘쒣탍돉솢ꎬ퓲듦퓚튻룶쯦믺쳹쿖틲ퟓM쪹뗃E(rM)=0ꎬM=d−df3ꎬ퓲 tttt01tE(rM)=E[r(d0−d1f)]=0,?E[r(1−lf)]=0,l=d/dꎬ tttttt10E(r)=E(rfl)=E(rf)lꎬ뗈폚뺭맽뇪ힼ뮯뒦샭횮뫳뗄b쒣탍ꆣ tttt†쯹틔ꎬ죧맻헢폐헢룶쯦믺쳹쿖틲ퟓ뗄쳵볾ꎬ퓲쯼볬퇩뗄쫇b쒣탍ꎬ뛸늻쫇틲쯘쒣탍ꆣ죧맻튪볬퇩틲쯘쒣탍ꎬ퓲탨튪쇭췢뗄쳵볾ꆣ †틲듋ꎬ퓚Kan and Zhou(1999)훐ꎬ쯹쪹폃뗄쒣쓢쫽뻝살풴폚틲쯘쒣탍ꎬ쯹틔폃쯦믺쳹쿖쒣탍ꎬ컞램뷸탐튻룶폐킧뗄볬퇩ꎬ쿠펦뗄럧쿕볛룱튲뫜늻컈뚨ꆣ 뛾ꆢb쒣탍뫍럧쿕틧돪 Kan and Zhouꎨ1999ꎩ죏캪ꎬ쪹폃쯦믺쳹쿖틲ퟓ뿉쓜컞램ힼ좷에뇰헦헽뗄럧쿕틲쯘ꎬ틲캪뿉쓜춬쪱듦퓚ퟅ벸룶뇤솿싺ퟣ쯦믺쳹쿖틲ퟓ뗈쪽ꆣ볙짨헦쪵뗄뺭맽뇪ힼ뮯뒦샭뗄럧쿕틲쯘캪fꎬ퓲E[r(1−lf)]=0ꆣ떫쫇듦퓚솽훖쟩뿶튲쓜싺ퟣ쯦믺쳹쿖틲ퟓ뗈쪽ꎺ tttf+n1ꆢg=ttl=l+s2,1ꎻn쫇튻룶뒿듢뗄닢솿컳닮ꎻ t2gnt1+sn12ꆢb'∑−eh=tꎬl=∑−1hlb'bꆣ b∑−1'b뛸g,h뚼늻쫇헦헽뗄럧쿕틲쯘ꆣ틲듋ꎬ샻폃쯦믺쳹쿖틲ퟓ컞램헒떽헦헽뗄럧쿕볛룱ꆣ tt떫쫇ꎬ컒쏇헦헽맘탄뗄늻쫇럧쿕볛룱놾짭ꎬ뛸쫇럧쿕틧돪ꎬ벴럧쿕볛룱뫍럧쿕쾵쫽뗄돋믽ꆣ럧쿕틲ퟓ뗄뇤뚯늻뷶믡펰쿬럧쿕볛룱ꎬ튲믡펰쿬럧쿕쾵쫽ꎻ컒쏇튪럖컶쯦믺쳹쿖틲ퟓ뛔b쒣탍뗄볬퇩쓜솦ꎬ뻍뇘탫ퟛ뫏럖컶럧쿕틲쯘뇤뚯뛔럧쿕볛룱뫍럧쿕쾵쫽뗄펰쿬ꆣ 3 쪵볊짏ꎬ평듋뿉횪d0=1/rꎬ틲캪E(M)=d0=1/r ftf
쟩뿶f+n1ꎺ죧맻쪹폃탂뗄럧쿕틲쯘g=ttl=l+s2,1ꎬ퓲듋쪱ꎬ t+s2gn1nˆf+ncov(r,fn)bb=covrtt=tttg(t,)=ꎬ틲캪cov(r,n)=0ꆣ듋쪱뗄럧쿕틧돪tt1s21+s21+s2nnn캪ꎺ bgˆlg=blꎬ죔좻뗈폚헦쪵틲쯘쿂뗄럧쿕틧돪ꎬ쯹틔볓죫튻룶닢솿컳닮늢늻믡뛔럧쿕틧돪뗄맀볆닺짺펰쿬ꆣ 쟩뿶2ꎺ죧맻쪹폃탂뗄b∑−1럧쿕틲쯘'eh=tꎬl=∑−1bꎬ듋쪱ꎬ b∑−1hlb''b1ˆb'∑−ebb=tcov(r,)=ꎬ럧쿕틧돪캪ꎺ tbbb∑−1'b)bhlh=blꎬ튲죔좻뗈폚헦쪵틲쯘쿂뗄럧쿕틧돪ꆣ 쯹틔컞싛퓚뫎훖쳵볾쿂ꎬ펰쿬틲쯘뗄럇쾵춳탔룄뇤믡룄뇤쿠펦뗄럧쿕볛룱뫍럧쿕쾵쫽ꎬ떫쫇늻믡룄뇤뛔럧쿕틧돪뗄맀볆ꆣ럇쾵춳탔룄뇤쪵볊짏쫇퓚늻룄뇤럧쿕틧돪뗄쳵볾쿂뛔럧쿕틧돪뗄솽룶ퟩ돉늿럖ꎬ벴럧쿕볛룱뫍럧쿕쾵쫽뷸탐훘탂럖엤ꆣ듋쪱ꎬ헦헽뗄틲쯘죔좻쫇fꎬt뛔쯼뗄럇쾵춳탔룄뇤늻믡뛔뷡싛닺짺펰쿬ꆣ헢튲뻍퇩횤쇋ꎬ퓚b쒣탍쿂ꎬ럇쾵춳탔뗄럧쿕틲쯘늻믡뛔럧쿕틧돪닺짺펰쿬ꆣ 죽ꆢ뚨볛듭컳뫍뚨볛뫋4 룹뻝짏쏦뛔b쒣탍뗄럖컶ꎬ뚨볛듭컳 E(kqe)=E−−−=−j(r)rb(E(r)r)jjfmf=−rq(e) Efj(kq)붫뚨볛뫋kq펳짤떽틲쯘뿕볤FFF, kq=kq+h,kq∈F,h⊥Fꆣ퓲 E(ke)=E(he),qjj, |E(he)|≤|h|||e||jj≤sFF||re|k−k||,|kjfqqq−kq||뫢솿뚨볛뫋뫍틲쯘뿕볤횮볤뗄뻠샫ꆣ쯹틔죧맻kqj뷓뷼폚틲쯘뿕볤ꎬ뚨볛듭컳뻍뫜킡ꆣ죧맻쯼퓚틲쯘뿕볤쓚ꎬ뚨볛듭컳캪0ꆣ떫쫇죧맻헢룶뚨볛뫋풶샫틲쯘뿕볤ꎬ뚨볛듭컳뻍뿉쓜뇈뷏듳ꆣ 샻폃헢룶풭샭ꎬ컒쏇뻍뿉틔럖컶늻춬뚨볛쒣탍뗄뚨볛컊쳢ꎺ 4 닎볻Leroy and Werner(2000)ꆣ
CAPMꎺ쫇b쒣탍뗄뗤탍ꎬ뚨볛뫋캻폚틲쯘뿕볤쓚ꎬ틲듋ꎬ뚨볛듭컳캪0ꆣ쯹틔듋쪱a=bl5ꆣ쯹틔ꎬ퓚CAPM훐ꎬ죧맻돶쿖컳닮믲헟듭컳ꎬ쫇평CAPM쒣탍놾짭틽웰ꎬ듋쪱뗄뚨볛뫋늻믡듸살컳닮ꆣ 믹폚쿻럑뗄CAPMꎺ뚨볛뫋캪u'(Cdt+1)ꎬ쿖쪵맀볆쪱튻냣쪹폃튻킩ힴ첬뇤솿ꎬ뇈죧닆u'(C)t뢻뗈ꎬퟷ캪틲쯘뿕볤ꎬ틲듋뚨볛뫋뿉쓜늻캻폚틲쯘뿕볤쓚ꎬ듋쪱뻍뿉쓜듦퓚ퟅ뇈뷏듳뗄뚨볛듭컳ꆣ듋쪱ꎬa=bl+jꆣ쯹틔ꎬ듋쪱뗄맀볆컳닮뻍폐뿉쓜살ퟔ폚솽룶랽쏦ꎺ튻룶쫇쒣탍놾짭ꎬ쇭튻룶뻍쫇평폚뚨볛뫋틽웰ꆣ틲듋벴쪹헢룶쒣탍뗄맀볆킧맻닮ꎬ뿉쓜헢룶풭틲살ퟔ폚뚨볛뫋늻퓚틲쯘뿕볤쓚ꎬ뛸늻쫇쒣탍놾짭뗄컊쳢ꆣ쯹틔ꎬ늻쓜틲캪믹폚쿻럑뗄CAPM쒣탍맀볆킧맻닮뻍볲떥뗄뻜뻸헢룶쒣탍ꆣ 닎뾼컄쿗ꎺ Cochrane, J. H., 1996, “A Cross Sectional Test of an Investment-based Asset Pricing Models”, Journal of Political Economy 104, 574-621. Cochrane, J. H., 2000, Asset Pricing, Princeton University Press. Kan, R. and G. Zhou, 1999, “A Critique of the Stochastic Discount Factor Methodology”, Journal of Finance, vol. LIV, 1221-1248. Leroy, ., and J. Werner, 2000, Principles of Financial Economics, Cambridge University Press. 5
