놴쯾쾵쫽뗄뻹횵믘맩맽돌1 The Mean Reversion Process of Beta 십쾲뗂 횣헱쇺 ꎨ쿃쏅듳톧뷰죚쾵ꎬ쿃쏅″㘱〰?ꎩ? Ma Xideꎬ Zheng Zhenlong (Department of Finance, Xiamen University, 361005) 햪튪ꎺCAPM훐뗄놴쯾쾵쫽놻죏캪쫇횤좯ퟩ뫏뫍떥룶횤좯럧쿕듳킡뗄뫢솿횸뇪ꎬ뷼쓪살샭싛뷧뛔폚CAPM훐뗄놴쯾쾵쫽늢럇뎣쫽틑뺭듯돉쇋릲쪶ꎬ뛸쟒훚뛠벣쿳뇭쏷ꎬ놴쯾쾵쫽뗄뇤뮯뫜뿉쓜ퟱ톭튻룶뻹횵믘맩맽돌ꆣ놾컄뗄훷튪쒿뗄벴틔짮랢햹캪샽ꎬ볬퇩웤놴쯾쾵쫽쫇럱ퟱ톭튻룶뻹횵믘맩맽돌ꆣ 맘볼듊ꎺCAPMꎬ놴쯾쾵쫽ꎬ뻹횵믘맩 JEL럖샠ꎺG120 G140 Abstract: The beta coefficient of CAPM is widely accepted as relevant measure of risk in portfolio and security analysis. Recently economists have reached an agreement on the fact that beta is not constant. There are many evidences showing that betas have mean reversion tendencies. The authors test if the beta of Bank of ShenZhen development has mean reversion tendency. Key words: CAPM, beta coefficient, mean reversion JEL ClassificationꎺG120 G140 놾닺뚨볛쒣탍ꎨCAPMꎩ쫇닺뚨볛샭싛뗄뫋탄ꎬ좻뛸뛔폚웤쪵횤볬퇩좴튻횱듦퓚헹틩ꆣ쫽쪮쓪살ꎬ뒫춳뗄CAPM늻뛏퓢떽훊틉ꎬ춬쪱튲늻뛏뗃떽늹돤뫍삩햹ꆣퟮ뷼뗄퇐뺿뇭쏷ꎬCAPM훐뗄놴쯾쾵쫽쯤좻쫇튻룶쯦믺쾵쫽ꎬ떫쫇쯼뫜뿉쓜ퟱ톭튻룶뻹횵믘맩맽돌ꎬ헢쪹뗃뛔놴쯾쾵쫽뗄풤닢뇤캪뿉쓜ꎬ튲쪹CAPM뗃틔훘탂므랢짺믺ꆣ 튻ꆢ컄쿗ퟛ쫶 ퟮ퓧쳡돶떥룶횤좯뗄놴쯾쾵쫽폐뿉쓜ퟱ톭뻹횵믘맩맽돌뗄쫇Blumeꎨ1975ꎩꎬ쯻죏캪평폚짏쫐릫쮾풭쿈벫뛋룟ꎨ뗍ꎩ럧쿕뗄뺭펪쿮쒿퓚뺭맽튻뛎쪱볤뫳럧쿕폐뿉쓜붵뗍ꎨ짽룟ꎩꎬ믲헟웤탂췘햹뗄쿮쒿럧쿕뇈뻉쿮쒿뗍ꎨ룟ꎩꎬ쓇쎴ퟷ캪뫢솿떥룶횤좯럧쿕뗄놴쯾쾵쫽튲믡랢짺쿠펦뗄뇤뮯ꆣBlume횤쏷ꎬퟩ뫏놴쯾쾵쫽뗄뇤뮯돶쿖뻹횵믘맩늢늻쫇ퟩ뫏톡퓱욫닮ꆰorder biasꆱ뗄풵맊ꎬ뛸쫇ퟩ뫏훐횤좯놴쯾쾵쫽ퟔ짭뇤뮯뗄뷡맻ꆣ Blume뗄뷡싛뗃떽쇋톧뷧뗄맣랺죏뿉ꎬBrenner뫍Smidꎨt1977ꎩꆢFabozzi뫍Francisꎨ1978ꎩꆢFrancis (1979)쿈뫳뚼퇩횤쇋놴쯾쾵쫽ퟱ톭뻹횵믘맩맽돌ꆣ뺡맜Kolb뫍Rodriguez(1989)쳡돶쇋 1놾컄쫇뷌폽늿폅탣쟠쓪뷌쪦훺볆뮮ꆰ훐맺탅폃럧쿕뛈솿뫍뿘훆쒣탍ꆱ쿮쒿뗄훐웚퇐뺿돉맻횮튻ꆣ룐킻쿃쏅듳톧뷰죚쾵늩쪿짺쇖몣뫍쿃쏅듳톧쫽톧쾵쮶쪿짺췵놣뫏뛔놾컄쯹쳡뗄틢볻뫍붨틩ꆣ떱좻ꎬ컄퓰ퟔ뢺ꆣ 1
튻킩틬틩ꎬ떫쫇훚뛠톧헟뮹쫇룹뻝룃볙짨닉폃놴튶쮹벼쫵뛔놴쯾쾵쫽뷸탐쇋돉릦뗄풤닢ꎬ늢뻍죧뫎붵뗍풤닢컳닮뫍뒦샭놴쯾쾵쫽돶쿖틬뎣횵뗄쟩뿶쳡돶쇋탭뛠붨틩ꎬ죧Klemkosky뫍Martinꎨ1975ꎩꆢEubank뫍Zumwaltꎨ1979ꎩꆢStatmanꎨ1981ꎩꆢFrost뫍Savarinoꎨ1986ꎩ뗈ꆣ GangemiꆢRobert뫍Robertꎨ1999ꎩ퓲햾퓚맺볊춶헟뗄뷇뛈ꎬ폃쒦룹쮹첹샻좫쟲쫐뎡횸쫽뫍펢ꆢ쏀뗈18룶맺볒뗄막욱쫐뎡횸쫽뷸탐볬퇩ꎬ랢쿖맺뇰놴쯾ꎨcountry betaꎩ튲ퟱ톭뻹횵믘맩맽돌ꎬ듓뛸캪뛈솿맺뇰럧쿕쳡릩쇋폐폃뗄횸뇪ꆣ 평듋뿉볻ꎬ죧맻놴쯾쾵쫽듦퓚뻹횵믘맩쟷쫆뗄뮰ꎬ쓇쎴뛔놴쯾쾵쫽뷸탐ힼ좷풤닢붫뇤돉뿉쓜ꎬ헢틢캶ퟅ벴쪹놴쯾쾵쫽뿉뇤ꎬ컒쏇죔좻뿉틔샻폃CAPM뷸탐ퟩ뫏춶믲튵벨움볛ꆣ럱퓲뗄뮰ꎬCAPM뗄펦폃붫믡쫜떽뫜듳뗄쿞훆ꆣ놾컄뗄쒿뗄벴틔짮랢햹캪샽ꎬ볬퇩놴쯾쾵쫽쫇럱듦퓚뻹횵믘맩쟷쫆ꆣ 뛾ꆢ뻹횵믘맩볬퇩뗄짨볆 ꎨ튻ꎩ퇐뺿랽램 뻹횵믘맩맽돌뗄튻냣쒣탍캪ꎺ dx=(p−qx)dt+sxgdW ꎨ1ꎩ 웤훐ꎬx쫇쯦믺뇤솿ꎬq쫇믘맩쯙뛈ꎬp/q쫇뎤웚뻹횵ꎬꛒ쫇랽닮ꎬdW쫇캬쓉맽돌뗄퓶솿ꎬ dW=edt ꎨ2ꎩ te쫇뻹횵캪쇣ꆢ랽닮캪1뗄뇪ힼ헽첬럖늼쯦믺뇤솿ꆣ t떱g=0쪱ꎬ뻍쫇ퟮ볲떥뗄뻹횵믘맩쒣탍ꎺ dx=(p−qx)dt+sdW ꎨ3ꎩ 킴돉샫즢탎쪽캪ꎺ x+1−x=p−qx+e′ ꎨ4ꎩ tttt웤훐ꎬe′=se tt캪쇋볬퇩놴쯾쾵쫽쫇럱ퟱ톭뻹횵믘맩맽돌ꎬ뿉틔닉폃솽늽믘맩뗄랽램ꆣ뗚튻늽볙짨놴쯾쾵쫽퓚뛌웚쓚쫇늻뇤뗄ꎬ늢뷸탐럖웚ꎬ닉폃뒫춳뗄CAPM맀볆돶쎿튻웚뗄놴쯾쾵쫽bˆꎺ tZ=a+bZ+e itmt ꎨ5ꎩ it웤훐ꎬZ쫇횤좯i퓚t쪱뿌뗄뎬뛮쫕틦싊ꎨZ=r−rꎩꎬZitititftmt 쫇t쪱뿌쫐뎡뗄뎬뛮쫕틦싊ꎨZmt=rmt−rꎩꆣ ft뗚뛾늽벴룹뻝ꎨ4ꎩ쪽ꎬ뛔쿂쪽뷸탐ퟮ킡뛾돋믘맩ꎬ맀볆돶pꆢqꎺ b+1−b=p−qb+e′ ꎨ6ꎩ tttt 2
웤훐ꎬb뇭쪾t쪱뿌뗄놴쯾쾵쫽ꎬb쾵쫽ꆣ tt+1뇭쪾tꎫ1쪱뿌뗄놴쯾죧맻0<p<1ꎬ0<q<1ꎬ쓇쎴쮵쏷놴쯾쾵쫽듦퓚뻹횵믘맩쟷쫆ꎬ뛸쟒pꆢq풽쟷뷼폚1ꎬ뻹횵믘맩쟷쫆풽쏷쿔ꎬ웤훐놴쯾쾵쫽뗄뎤웚뻹횵b=p/qꆣ 듋췢ꎬ놴쯾쾵쫽뗄뎤웚뻹횵튲뿉틔춨맽맣틥ퟮ킡뛾돋뷸탐맀볆ꎺ ∑Z∑Z2ˆnnmtimtb=/i22222 ꎨ7ꎩ +=sst1eibimtt=1se+sibimt웤훐ꎬs2e쫇횤좯i퓚t쪱뿌뗄닐닮e뗄랽닮ꎬs2itb쫇횤좯i퓚t쪱뿌뗄놴쯾쾵쫽b뗄iiit랽닮ꆣ ꎨ뛾ꎩ쫽뻝쮵쏷 놾컄틔짮랢햹캪퇐뺿뛔쿳ꎬ톡좡뗄쪱볤뛎쫇듓1991쓪8퓂26죕떽2001쓪12퓂31죕ꎬ쳞돽짮랢햹춣없뗄붻틗죕ꎬ튻릲폐2550룶붻틗죕쫽뻝ꎬ쎿30룶붻틗죕쫽뻝캪튻웚ꎬ튻릲럖85웚ꎬ헢훷튪쫇틲캪ꎺꎨ1ꎩ놾컄캪쇋뷸탐럖웚ꎬ탨튪뷏뛠뗄쫽뻝솿ꎬ뛸훐맺막욱쫐뎡랢햹샺돌뷏뛌ꎬ싺ퟣ쳵볾뗄막욱캪쫽늻뛠ꎬ짮랢햹늻뷶쫇ퟮ퓧랢탐짏쫐뗄막욱횮튻ꎬ뛸쟒웤폖쫇뷰죚냥뿩뗄벨폅막ꎬ뻟폐튻뚨뗄듺뇭탔ꎻꎨ2ꎩ평폚뛔놴쯾쾵쫽뷸탐맀볆쪱ꎬ쫽뻝솿첫짙믡떼훂놴쯾쾵쫽뇪ힼ컳맽듳ꎬ뛸쫽뻝솿첫뛠퓲믡쿠펦복짙폃폚뻹횵믘맩뗄쫽뻝ꎬ틲뛸ퟮ뫳좷뚨캪쎿30룶붻틗죕쫽뻝캪튻웚ꆣ 퓚맺췢뗄퇐뺿떱훐ꎬ튻냣틔죽룶퓂뗄뛌웚맺햮샻싊ퟷ캪컞럧쿕샻싊ꎬ떫쫇컒맺쒿잰맺햮듳뛠캪뎤웚욷훖ꎬ틲듋컞램폃맺햮샻싊ퟷ캪컞럧쿕샻싊ꎬ쯹틔놾컄틔튻쓪웚틸탐뚨웚듦뿮샻싊ퟷ캪컞럧쿕샻싊ꆣ 짮랢햹뗄죕쫕틦싊춨맽쿂쪽볆쯣ꎺ r=ln(P+D)−ln(P ꎨ8ꎩ iti,ti,ti,t−1)웤훐ꎬr쫇t쪱뿌뗄쫕틦싊ꎬP쫇t쪱뿌뗄쫕엌볛ꎬPDiti,ti,t−1쫇tꎭ1쪱뿌뗄쫕엌볛ꎬi,t쫇t쪱뿌뗄쎿막뫬샻ꆣ 듋췢ꎬ놾컄닉폃짮?ퟛ뫏횸쫽ퟷ캪쫐뎡횸쫽볆쯣쫐뎡쫕틦싊ꎺ rmt=lnindex−lnindex tt−1 ꎨ9ꎩ 웤훐ꎬrmt쫇t쪱뿌뗄쫐뎡쫕틦싊ꎬindex쫇t쪱뿌뗄쫕엌횸쫽ꎬindex쫇tꎭ1쪱뿌tt−1뗄쫕엌횸쫽ꆣ 죽ꆢ쪵횤뷡맻뫍럖컶 샻폃뇠돌ꎬ컒쏇쫗쿈뿉틔폃ퟮ킡뛾돋믘맩맀볆돶쎿튻웚뗄놴쯾쾵쫽bˆꎬ듓춼t훐뿉틔뾴떽ꎬ쯤좻짮랢햹뗄놴쯾쾵쫽퓚쒳킩쓪럝늨뚯뷏킡ꎬ퓚쒳킩쓪럝늨뚯뷏듳ꎬ떫쫇뚼듳훂퓚ퟳ폒늨뚯ꎬ뇭쿖돶뫜쏷쿔뗄뻹횵믘맩쟷쫆ꆣ캪쇋뷸탐퇩횤ꎬ컒쏇뷸탐뗚뛾늽믘맩ꆣ 3
짮랢햹놴쯾쾵쫽늨뚯ힴ뿶?ㄮ??〮????ㄳㄹ㈵㌱㌷㐳㐹㔵㘱㘷㜳㜹㠵? 샻폃ꎬ컒쏇뛔ꎨ6ꎩ쪽뷸탐ퟮ킡뛾돋믘맩ꎬ뿉틔뗃떽ꎺ b+1−b=− ꎨ10ꎩ ttt()(−)R2= F= 웤훐ꎬpꆢq럖뇰캪뫍ꎬ늻뷶뚼퓚0뫍1횮볤ꎬ뛸쟒뚼쫇룟뛈쿔훸뗄ꎬt춳볆솿럖뇰캪뫍ꎭꆣ믘맩랽돌뗄쓢뫏폅뛈R2캪ꎬF횵튲뫜쿔훸ꎬ쮵쏷룃쓢뫏쒣탍폐킧ꎬ헢뷸튻늽퇩횤쇋놴쯾쾵쫽ퟱ톭뻹횵믘맩맽돌뗄뷡싛ꆣ듓ꎨ10ꎩ쪽훐ꎬ컒쏇뿉틔맀쯣돶놴쯾쾵쫽뗄뎤웚뻹횵b=p/q=ꎬ컒쏇냑쯼폫듓ꎨ7ꎩ쪽맀볆돶살뗄뷡맻ꎨb=ꎩ뷸탐뇈뷏ꎬ랢쿖솽헟쿠닮늻듳ꎬ헢쮵쏷뿉틔샻폃ꎨ7ꎩ쪽뛔놴쯾쾵쫽뷸탐풤닢ꆣ 쯄ꆢ뷡싛 춨맽짏쫶럖컶ꎬ컒쏇뿉틔뗃떽틔쿂뷡싛ꎺ 1ꆢ떥룶횤좯뗄놴쯾쾵쫽쫇튻룶ퟱ톭뻹횵믘맩맽돌뗄쯦믺뇤솿ꆣ짏쫐릫쮾막욱뗄놴쯾쾵쫽퓚쿠뛔뛌웚쓚믡늻뛏뗘랢짺뇤뮯ꎬ떫쫇듓뎤웚살뾴ꎬ쯼ퟜ쫇캧죆쒳룶뻹횵짏쿂늨뚯ꆣ헢쫇평룃짏쫐릫쮾뗄뺭펪탔훊쯹뻶뚨뗄ꎬ웤쯹뒦뗄탐튵ꆢ튵컱탔훊ꆢ쿠뛔폚웤쯻웳튵뗄맦쒣퓚뫜듳돌뛈짏뻶뚨쇋놴쯾쾵쫽뗄뎤웚뻹횵ꆣ듓헢튻뗣살뾴ꎬ헢튻뷡싛폫뒫춳뗄CAPM늢늻쎬뛜ꆣ떫쫇평폚놴쯾쾵쫽놾짭듦퓚럧쿕풴ꎬ죧릫쮾뗄춶쿮쒿뗄럧쿕랢짺뇤뮯ꆢ뺭샺늻춬뗄뺭볃쪱웚ꎨ얣쫐믲태쫐ꎩꆢ돶쿖훘듳죋쫂뇤뚯뗈ꎬ뻹믡떼훂놴쯾쾵쫽퓚쿠뛔뛌웚쓚랢짺늨뚯ꎬ틲듋헢폫뒫춳뗄CAPM뗄볙짨폖늻쿠럻ꆣ횵뗃힢틢뗄쫇ꎬ퓚벫뛌웚쓚ꎬ놴쯾쾵쫽폖쫇늻뇤뗄ꎬ틲캪쯼랴펳쇋짏쫐릫쮾뗄뺭펪쳘뗣ꎬ늻뿉쓜쯦쪱랢짺뇤뮯ꎬ틲듋붫쯼ퟷ캪쾵춳탔럧쿕뗄뫢솿횸뇪폖캴뎢늻뿉ꆣ 2ꆢ놴쯾쾵쫽쯤좻쫇뿉뇤뗄ꎬ떫쫇튲쫇뿉풤닢뗄ꆣ룹뻝짏쫶췆싛ꎬ컒쏇쫗쿈뿉틔맀볆돶놴쯾쾵쫽뗄뎤웚뻹횵ꆣ평폚놴쯾쾵쫽뿉뇤ꎬ쯹틔죴폃ퟮ킡뛾돋맀볆붫늻쫇랽닮ퟮ킡뗄ꎬ펦룃폃맣틥ퟮ킡뛾돋뷸탐맀볆ꎬ듓뗈쪽ꎨ7ꎩ컒쏇뻍뿉틔뗃떽놴쯾쾵쫽뎤웚뻹횵뗄맀볆솿bꆣ웤듎ꎬ컒쏇룹뻝뒫춳뗄CAPM맀볆돶뷼웚뗄놴쯾쾵쫽bꆣퟮ뫳ꎬ룹뻝뻹횵믘맩뗄쯙뛈q컒쏇t뻍뿉틔듳훂맀볆돶쿂튻웚뗄놴쯾쾵쫽bt+1ꆣ틲듋죧맻쓜릻ힼ좷뗘맀볆돶놴쯾쾵쫽ꎬ쓇쎴 4 ꛂ
CAPM죔붫쫇폐폃뗄ꆣ쪵횤퇐뺿뇭쏷ꎬ쯦ퟅ횤좯ퟩ뫏뗄맦쒣퓶듳뫍놴튶쮹벼쫵뗄틽죫ꎬ뛔ퟩ뫏놴쯾쾵쫽풤닢뗄뺫좷뛈튲늻뛏쳡룟ꆣ쒿잰ꎬ맺췢뗄ퟮ탂퇐뺿헽늻뛏룄뷸뛔놴쯾쾵쫽뗄풤닢ꎬ쳵볾CAPM뗃떽쇋톸쏍랢햹ꎬ헢붫쫇뷱뫳뷸튻늽퇐뺿뗄랽쿲ꆣ 닎뾼컄쿗 1. Blume,., 1975, ꆰBetas and their Regression Tendencies: Some Further Evidenceꆱ, Journal of Finance 30, 785-795. 2. Brenner, M., and S. Smidt , 1977, ꆰA simple model of non-stationarity of systematic riskꆱ, Journal of Finance 32, 1081–1092. 3. Eubank, A., and J. Zumwalt, 1979, ꆰAn analysis of the forecast error impact of alternative beta adjustment techniques and risk classesꆱ, Journal of Finance 30, 761–776. 4. Fabozzi, F., and J. Francis, 1978, ꆰBeta as a random coefficientꆱ, Journal of Financial and Quantitative Analysis 13, 101–116. 5. Francis, J., 1979, ꆰStatistical analysis of risk surrogates for NYSE stocksꆱ, Journal of Financial and Quantitative Analysis 14, 981–997. 6. Frost, P., and J. Savarino, 1986, ꆰAn empirical Bayes approach to efficient portfolio selectionꆱ, Journal of Financial and Quantitative Analysis 21, 293–305. 7. Gangemi, M., B. Robert, and F. Robert, 1999, ꆰMean reversion and the forecasting of country betas: a noteꆱ, Global Finance Journal 10, 231-245 8. Klemkosky, R., and J. Martin, 1975, ꆰThe adjustment of beta forecastsꆱ, Journal of Finance 30, 1123–1128. 9. Kolb, R., and R. Rodriguez, 1989, ꆰThe regression tendencies of betas: a reappraisalꆱ, Financial services Review 24, 319–334. 10. Statman, M., 1981, ꆰBetas compared: Merill Lynch vs. value lineꆱ, Journal of Portfolio Management 7, 41–44. 5
