뗚15뻭ꆡ뗚1웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ,쓪ꆡꆡ2퓂ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ훐맺맜샭뿆톧ChineseJournalofManagementScienceFeb.,ꆡ2007컄헂뇠뫅:1003-207(2007)01-0027-07뷰죚쫐뎡쳵볾룟뷗뻘럧쿕폫뚯첬ퟩ뫏춶붯들쿀1,2,탭웴랢2,헅쫀펢1(1.쳬뷲듳톧맜샭톧풺,쳬뷲ꆡ300072;2.즽뚫릤짌톧풺쫽톧폫탅쾢뿆톧톧풺,즽뚫퇌첨ꆡ264005)햪ꆡ튪:헫뛔뒫춳ퟩ뫏춶샭싛쎻폐뾼싇룟뷗뻘럧쿕뫍뺲첬뒦샭컊쳢솽듳좱쿝,쳡돶뛠풪GARCHSK쒣탍폃폚뫢솿쪱뇤뗄룟뷗뻘럧쿕,믹폚킧폃몯쫽뗄Taylor햹뾪췆떼돶듸폐룟뷗뻘럧쿕뗄뚯첬ퟩ뫏춶닟싔,늢샻폃틅뒫쯣램뷸탐쟳뷢ꆣ쪵횤퇐뺿뇭쏷,훐맺막쫐늻뷶듦퓚룟뷗뻘럧쿕,뛸쟒럧쿕뻟폐쪱뇤쳘헷;캪럀랶룟뷗뻘럧쿕,춶헟탨튪뚯첬뗘탞헽쯻뗄닺엤훃좨훘ꆣ맘볼듊:룟뷗뻘럧쿕;뚯첬ퟩ뫏춶;뛠풪GARCHSK쒣탍;틅뒫쯣램훐춼럖샠뫅:F22410ꆡꆡꆡ컄쿗뇪쪶싫:A1ꆡ틽퇔ퟩ뫏춶샭싛쎻폐뛔듋뷸탐쳖싛ꆣ맺볊짏,튻킩톧헟퓸뛔룟뷗뻘ퟩ뫏춶컊쳢뷸Markowitz(1952)샻폃뻹횵-랽닮럖컶틔벰뛾탐맽퇐뺿ꆣLai(1991),Chunhachinda뗈(1997),듎맦뮮랽램,뷢뻶쇋ퟮ폅횤좯ퟩ뫏컊쳢[1],쯻쯹쳡돶Prakash뗈(2003)뫍Sunh뗈(2003)쪹폃뛠쒿뇪맦뗄횤좯ퟩ뫏샭싛놻쫓캪쿖듺뷰죚샭싛뗄믹쪯ꆣ룃쒣뮮벼쫵뷢뻶쇋ퟮ듳뮯웚췻쫕틦뫍욫뛈ꆢퟮ킡뮯랽닮탍훷튪볙짨춶헟뗄킧폃몯쫽평쫕틦뗄뻹횵뫍랽닮죽룶쒿뇪횮볤뗄폅뮯컊쳢,뛔듸폐욫뛈럧쿕뗄닺솽룶뇤솿좷뚨,웤훐쫕틦뗄랽닮랴펳쇋춶럧쿕ꆣퟩ뫏뷸탐톡퓱[2ꆫ5];Jondeau뗈(2004)샻폃웚췻킧폃늻뿉럱죏,Markowitz뗄ퟩ뫏춶샭싛뾪뒴쇋몯쫽Taylor햹뾪쳖싛쇋럇헽첬쳵볾쿂닺엤훃컊뛔뷰죚럧쿕뷸탐뚨솿닢뛈폫럀랶뗄쿈뫓,쫇뫳탸탭쳢,랢쿖욫뛈럧쿕폫럥뛈럧쿕뗄듦퓚뛔뷰죚춶뻶뛠웤쯼샭싛퇐뺿뗄믹뒡ꆣ쯦ퟅ뷰죚샭싛폫쪵볹늻뛏닟듦퓚쿔훸펰쿬[6];Gustavo뗈(2004)뫍Joro뗈짮뮯뫍뷰죚볆솿붨쒣벼쫵늻뛏랢햹,룃샭싛뗄늻ퟣ(2005)튲쳖싛쇋듸폐욫뛈럧쿕뗄ퟩ뫏춶컊쳢,룸횮뒦튲훰붥쿔쿖돶살돶쇋ퟮ폅ퟩ뫏춶좨훘뗄볆쯣랽램,늢뷸튻늽퓚죽,춻돶뇭쿖퓚솽룶랽쏦ꆣ뗚튻,평폚춶쫕틦폫럧쿕뗄쪱뇤탔,춶헟탨튪늻뛏움캬뿕볤훐룸돶웤뿉탐폲ꆢ폐킧잰퇘뫍뛔펦뗄벸뫎탔맀웤춶쫕틦폫럧쿕훊[7-8]ꆣ맺쓚,헅쫷뇳뗈(2004)뾼싇쇋몬폐붻틗돉,쯦쪱ힼ놸탞룄웤펵폐뗄닺ퟩ뫏뗄훖샠폫좨훘ꆣ좻뛸뒫춳뗄ퟩ뫏춶샭싛쎻폐놾뗄뻹횵-랽닮-욫뛈ퟩ뫏춶쒣탍,늢뛔쒣탍뗄틽뷸쪱볤틲쯘,횻쫇뺲첬뗘뾼달춶쫕틦폫럧쿕쇩쏴뛈뷸탐쇋닢쫔,랢쿖욫뛈럧쿕뗄듦퓚믡벫듳뗘,쓑틔폐킧뗘뷢뻶뚯첬춶뻶닟컊쳢ꆣ뗚뛾,뷰죚쫐뎡룄뇤닺ퟩ뫏뗄톡퓱[9]ꆣ훐늻뷶듦퓚랽닮럧쿕좻뛸,쯹폐헢킩쳖싛튲뚼쫇뺲첬뗄,쎻폐뾼싇뛾,뛸쟒듦퓚욫뛈럧쿕뫍럥뛈럧쿕,죧:뢺욫뛈뗄듦퓚쪹뗃닺쫕틦쿂붵뗄뿉쓜탔풶뷗뻘쓋훁룟뷗뻘럧쿕뗄쪱뇤탔ꆣ웹뷱,짐컞컄쿗쳖듳폚짏짽뗄뿉쓜탔;뎬뛮럥뛈뗄듦퓚쪹뗃벫횵쫂볾싛듸폐룟뷗뻘럧쿕뗄뚯첬ퟩ뫏춶컊쳢ꆣ룟뷗뻘뚯랢짺뗄뿉쓜탔벫듳뗘퓶볓,붫웤돆캪룟뷗뻘럧쿕첬ퟩ뫏춶럖컶틀삵폚룟뷗뻘늨뚯탔붨쒣,Leon뗈(냼삨(2005)퇘쾮GARCH쒣탍뷡릹,쳡돶쇋튻풪ퟔ믘맩:죽뷗뻘럧쿕뫍쯄뷗뻘럧쿕)ꆣ헢킩룟뷗뻘럧쿕뗄듦퓚쫆뇘믡펰쿬떽춶헟뗄춶뻶닟쳵볾틬랽닮ꆢ욫뛈ꆢ럥뛈(GARCHSK)쒣탍폃폚춬쪱,좻뛸뒫춳뗄쏨쫶뷰죚쪱볤탲쇐뛾뷗뻘ꆢ죽뷗뻘뫍쯄뷗뻘럧쿕뗄쫕룥죕웚:2006-05-15;탞뚩죕웚:2007-01-15뚯첬쳘헷[10]ꆣ믹뷰쿮쒿:맺볒ퟔ좻뿆톧믹뷰훺쿮쒿(70471050)ퟷ헟볲뷩:붯들쿀(1973-),얮(몺ퟥ),낲믕즽죋,쳬뷲듳톧맜뾼싇떽뷰죚쫐뎡늻뷶듦퓚룟뷗뻘럧쿕,뛸쟒헢샭톧풺늩쪿짺,즽뚫릤짌톧풺쫽톧폫탅쾢뿆톧톧풺붲킩럧쿕쫇쪱뇤뗄,놾컄튻랽쏦,퓚Leon뗈(2005)룸쪦,퇐뺿랽쿲:쫽솿뺭볃랽램ꆢ뷰죚볆솿.돶뗄튻풪GARCHSK쒣탍뗄믹뒡짏,쳡돶쇋뛠풪GARCHSK쒣탍폃폚쏨쫶뛠룶뷰죚닺믲쫐뎡뗄
ꆤ28ꆤ훐맺맜샭뿆톧ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ2007쓪룟뷗뻘럧쿕횮볤뚯첬맘쾵,늢믹폚뛀솢돉럖럖뷢룸ꛌp,t=Et-1[Rp,t]=wꇤꛌtt돶뛠풪쳵볾룟뷗뻘늨뚯싊뗄맀볆;쇭튻랽쏦,퓚ꛒ22p,t=Et-1[(Rp,t-ꛌp,t)]=Et-1[(Wt-W-2t)]Jondeau뗈(2004)퇐뺿뗄믹뒡짏,믹폚킧폃몯쫽뗄3sp,t=Et-1[(R3p,t-ꛌp,t)]=Et-1[(Wt-W-3t)]Taylor햹뾪룸돶쳵볾룟뷗뻘뚯첬ퟩ뫏춶랽램,늢4샻폃틅뒫쯣램뷸탐쇋쟳뷢ꆣ듓뛸,퓚솽룶닣쏦짏뛔kp,t=E44t-1[(Rp,t]-ꛌp,t)]=Et-1[(Wt-W-t)]뒫춳뗄ퟩ뫏춶샭싛뷸탐쇋룄뷸,튻쫇쳖싛쇋뚯첬(4)ퟩ뫏춶탐캪;뛾쫇뾼싇쇋룟뷗뻘럧쿕뛔뷰죚춶쪽훐,욫뛈폫럥뛈닉폃뷰죚짏뗄뚨틥,붫웤뚨틥캪룟뻶닟뗄펰쿬ꆣ뷗훐탄뻘,뛸늻쫇춳볆짏뗄뇪ힼ뮯룟뷗훐탄뻘ꆣ틲듋,쳵볾웚췻킧폃몯쫽쪽(3)뿉틔뮯캪평닺ퟩ2ꆡ뚯첬ퟩ뫏춶릹붨뫏쫕틦뗄쳵볾룟뷗뻘럧쿕살뷼쯆,벴211ꆡ춶뻶닟컊쳢Et-1[U(Wt)]ꇖU(W-(2)t)+1U(W-t)ꛒ2p,t+2평폚탨튪뾼싇룟뷗뻘럧쿕뛔춶뻶닟뗄펰쿬,1-컒쏇듓춶뗄킧폃몯쫽돶랢뷸탐폐맘쳖싛ꆣ볙뚨춶U(3)3(W)4t)sp,t+1U(4(W-t)kp,t(5)3!4!헟뗄웚돵닆뢻캪1,쯻믹폚뗚t웚쒩닆뢻Wt뗄킧룹뻝Scott뫍Horvath(1980)뗄퇐뺿뷡맻,쳵볾폃U(Wt)ퟮ듳뮯살뷸탐닺엤훃ꆣ짨t쪱뿌쯻퓚N웚췻킧폃폫쳵볾웚췻쫕틦뫍쳵볾욫뛈듦퓚헽쿠맘,룶닺짏춶좨훘캪wt=(w1t,w2t,ꆭ,wNt)ꇤ,N룶뛸폫쳵볾랽닮뫍쳵볾럥뛈듦퓚뢺쿠맘,벴춶헟쾲닺뗄쫕틦쿲솿Rt=(R1t,R2t,ꆭ,RNt)ꇤꆣ캪믱뗃쳵뮶헽뗄쫕틦뫍욫뛈뛸쳖퇡듳뗄랽닮뫍럥뛈[11]ꆣ볾룟뷗뻘럧쿕뛔ퟩ뫏춶뗄펰쿬,뛔킧폃몯쫽뷸탐212ꆡ뚯첬닺엤훃Taylor햹뾪,뗃떽룹뻝잰쏦뗄쳖싛,뿉틔샻폃닺ퟩ뫏쫕틦뗄쳵ꇞUW-kt)(Wt-W-t)볾웚췻ꆢ쳵볾랽닮ꆢ쳵볾욫뛈뫍쳵볾럥뛈뛔죎틢튻룶(Wt)=ꇆU(k)((1)k=0k!킧폃몯쫽뷸탐뷼쯆ꆣ퓚잰쏦쳖싛뗄N룶럧쿕닺쪽훐,W-t=Et-1(Wt)=1+wꇤꛌtt캪뗚t웚쒩뗄웚췻짏틽죫튻룶컞럧쿕닺,웤쫕틦캪R0,t,퓲뿉틔뗃떽닆뢻;ꛌt=Et-1(Rt)캪쳵볾웚췻쫕틦쿲솿;Et-1(ꆤ)쿂쏦뗄폅뮯컊쳢:캪쳵볾웚췻쯣ퟓꆣ평쪽(1)뿉틔뗃떽t쪱뿌뗄쳵볾웚maxU(ꛌ34p,t,ꛒ2p,t,sp,t,kp,t)췻킧폃캪wp,wi,tp0,t(6).ꆡwꇤt1+wp0,t=1Et-1[U(Wt)]=ꇞ쪽훐,wp0,t캪춶폚컞럧쿕닺짏뗄좨훘,wt=W-kEt)(Wt-W-t)t-1ꇆU(k)(=(wp1,t,ꆭ,wpN,t)ꇤ캪춶폚N룶럧쿕닺짏뗄좨훘k=0k!ꇞퟩ돉뗄닺ퟩ뫏좨훘쿲솿;1=(1,1,ꆭ,1)ꇤ캪NꇁꇆU(k)(W-t)Ekt-1[(Wt-W-t)](2)1쇐쿲솿;킧폃몯쫽훐쯄룶훷튪닎쫽,벴닺ퟩ뫏뗄k=0k!틲듋,쳵볾웚췻킧폃좡뻶폚웚쒩닆뢻럖늼뗄쯹쳵볾웚췻ꆢ쳵볾랽닮ꆢ쳵볾욫뛈뫍쳵볾럥뛈럖뇰캪쳵폐쳵볾훐탄뻘ꆣ탨튪횸돶뗄쫇볾웚췻:ꛌp,t=wp0,tR0,t+wꇤp,ꛌtt,춨맽Taylor햹뾪뗃떽뗄뛔쳵볾웚췻킧폃뗄뷼쯆폫춶헟뛔닆뢻럖늼뻘쳵볾랽닮:ꛒ2p,t=wꇤtEt-1[(Rt-ꛌt)(Rt-뗄욫뫃폐맘쾵,뛸헢킩뻘뿉틔평킧폃몯쫽뗄욫떼쫽ꛌt)ꇤ]wt=wꇤtꚧtwt=wꇤtꇆp,t뗃떽ꆣ쳵볾욫뛈3:sp,t=wꇤtEt-1[(Rt-ꛌt)(Rt-ꛌt)ꇤª쿖퓚뛔쪽(2)뷸탐쯄뷗뷘뛏,뗃떽(Rt-ꛌt)ꇤ](wtªwt)=wꇤtSt(wtªwt)=Et-1[U(Wt)]=U(W-t)+U(1)(W-t)Et-1[(Wtwꇤꚸp,t쳵볾럥뛈4:kp,t=wꇤtEt-1[(Rt-ꛌt)(Rt-ꛌt)ꇤª-W-2t)]+1U(2)(W-t)Et-1[(Wt-W-t)]+2(Rt-ꛌt)ꇤª(Rt-ꛌt)ꇤ](wtªwtªwt)=1U(3)(W-t)EwꇤtKt(wtªwtªwt)=wꇤtꚷp,tt-1[(Wt-W-3t)]+3!헢샯,1ꇆ=Hptwt캪킭랽닮쿲솿,쳥쿖쇋쪱뇤뛾,tU(4)(W-t)Et-1[(Wt-W-4t)]+O(W4t)(3)4!뷗뻘쾵춳럧쿕,ꚸp,t=St(wtªwt)캪킭욫뛈쿲솿,틲캪,닆뢻뗄쳵볾훐탄뻘뫍닺ퟩ뫏쫕틦뗄쳵볾훐쳥쿖쇋쪱뇤죽뷗뻘쾵춳럧쿕,ꚷp,t=Kt(wtªwtª탄뻘횮볤듦퓚죧쿂맘쾵wt)캪킭럥뛈쿲솿,쳥쿖쇋쪱뇤쯄뷗뻘쾵춳럧쿕;ª
뗚1웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ붯들쿀뗈:쳵볾룟뷗뻘럧쿕폫뚯첬ퟩ뫏춶ꆤ29ꆤ뇭쪾뻘헳뗄Kronecker믽ꆣ뗄뇤뮯,뻍뗃떽쪱뇤뗄좨훘쿲솿wt,듓뛸쪵쿖뚯첬샻폃삭룱샊죕쟳벫횵랽램,뿉틔뗃떽ퟩ뫏춶ꆣ평폚쪽(11)듦퓚룟뛈뗄럇쿟탔,헢샯믹L(wt,ꛑt)=U(ꛌp,t,ꛒ234p,t,sp,t,kp,t)-ꛋt(wꇤtl-1)폚틅뒫쯣램룸돶ퟩ뫏춶좨훘쿲솿wt뗄쟳뷢닟싔ꆣ(7)213ꆡ믹폚틅뒫쯣램뗄뚯첬ퟩ뫏춶룹뻝튻뷗쳵볾,뿉틔뗃떽ퟮ폅뷢싺ퟣ쳵볾틅뒫쯣램훐냼삨뇠싫ꆢ좺쳥맦쒣짨뚨ꆢ쫊펦횵몯ꛌt-R0,t=a1,tHtwt+a2,tSt(wtªwt)+쫽뚨틥ꆢ톡퓱ꆢ붻닦ꆢ뇤틬뫍춣횹뗈훘튪뮷뷚ꆣ뛔폚a3,tKt(wtªwtªwt)(8)럇쿟탔랽돌ퟩ(11)뷸탐쟳뷢,쿂쏦룸돶웤틅뒫쯣램쪽훐:R0,t=(R0,t,ꆭ,R0,t)ꇤ캪평컞럧쿕닺쫕틦ퟩ짨볆ꆣ돉뗄Nꇁ1캬쿲솿2U2,t1)뇠싫;a1,t=-U,a2,t=3U3,t-U,a3,t1,t1,t평폚좨훘닎쫽뻟폐튻뚨뗄좡횵랶캧,틲듋,놾컄=4U4,t-U;Ui,t(i=1닉폃쇋쪵횵뇠싫랽쪽ꆣ,2,3,4)럖뇰캪킧폃몯쫽맘폚1,t웤훐뗚i룶닎쫽34(ꛌ2)돵쪼훖좺짺돉p,t,ꛒ2p,t,sp,t,kp,t)뗄욫떼쫽ꆣ캪쇋믱뗃춶헟퓚뾼싇떽틅뒫쯣램뗄탔쓜폫볆쯣킧싊,놾컄톡퓱N룶럧쿕닺뫍튻룶컞럧쿕닺짏뗄쪱뇤닺ퟩ뫏좨훘,탨튪뛔킧폃몯쫽뷸좺쳥맦쒣캪10,짺돉좡횵퓚쟸볤짏뗄10ퟩ훖좺,쎿탐뻟쳥짨뚨ꆣ컄훐,뾼싇튻룶뎣뻸뛔럧쿕퇡뛱ퟩ훖좺폐4룶좾즫쳥ꆣ3)쫊펦횵몯쫽(CARA)킧폃몯쫽U(Wt)=-exp(-ꛑWt),ꛑ캪춶헟뎣뻸뛔럧쿕퇡뛱뗄닢뛈닎쫽,쪵횤쪱좡ꛑ틅뒫쯣램퓚뷸뮯쯑쯷훐믹놾짏늻폃췢늿탅쾢,=1ꆣ평쪽뷶틔쒿뇪몯쫽(튲뻍쫇쫊펦횵몯쫽)캪틀뻝ꆣ놾컄뚨(5),뿉뗃4Et-1[U(Wt)]ꇖ-exp(-ꛑW-t)틥쫊펦횵몯쫽캪:E2valt=ꇆei,t(t=1,2,ꆭ,T),i=11+ꛑ2ꛒ2ꛑ334p,t-sp웤훐ei캪쿲솿,t+ꛑ4kp,t23!4!(ꛌt-R0,t)-ꛗ1(wt)Htwt+ꛗ2(wt)St(wtªwt)=-exp(-ꛑꛌp,t)1+ꛑ2ꛒ2ꛑ334p,t-sp,t+ꛑ4kp,t(9)23-ꛗ!4!3(wt)Kt(wtªwtªwt)(12)춬쪱뿉틔믱뗃E뗄뗚i룶럖솿ꆣt-1[U(Wt)]럖뇰뛔U1,t,U2,t,U3,t,U4,t뗄욫떼쫽캪4)톡퓱닙ퟷ:톡퓱뗄쒿뗄쫇냑뷏폅뗄룶쳥횱뷓틅뒫떽쿂튻U1,t=9Et-1[U(Wt)]9ꛌp,t듺,믲춨맽엤뛔붻닦퓙틅뒫룸쿂튻듺ꆣ톡퓱닙ퟷ붨=ꛑ3솢퓚뛔좺쳥훐룶쳥쫊펦횵움맀믹뒡횮짏,놾컄닉폃exp(-ꛑꛌp,t)1+ꛑ2ꛒ2ꛑ3p,t-sp,t+ꛑ44kp,t23!4!쫊펦횵뇈샽램ꆣU25)붻닦닙ퟷ,t=9Et-1[U(Wt)]9ꛒ2=ꛑ2-exp(-ꛑꛌp,t)p,t2붻닦쫇횸냑솽룶뢸듺룶쳥뗄늿럖뷡릹볓틔쳦뮻U3,t=9Et-1[U(Wt)]ꛑ3exp(-ꛑꛌp,t)93=훘ퟩ뛸짺돉탂룶쳥뗄닙ퟷꆣ붻닦쫇틅뒫쯣램훐뗄뫋sp,t3!탄쯣ퟓꆣ붻닦싊풽룟,좺쳥훐믹틲뒮뗄룼탂뻍풽뿬,U4,t=9Et-1[U(Wt)]=ꛑ4-exp(-ꛑꛌp,t)94k붻닦싊맽룟,룟탔쓜뒮놻웆뮵뗄뿉쓜탔룼듳ꆣ죧맻p,t4!(10)붻닦싊맽뗍,쯑쯷뗄쯙뛈믡뫜싽ꆣ룹뻝뺭퇩횵,놾컄붫쪽(10)듺죫쪽(8)뗃닉폃뗄붻닦싊캪018,쪵쪩쇋떥뗣붻닦닟싔ꆣ(ꛌ6)뇤틬닙ퟷt-R0,t)-ꛗ1(wt)Htwt+ꛗ2(wt)St(wtªwt)-ꛗ3(wt)Kt(wtªwtªwt)=0(11)뇤틬쯣ퟓ뛔좺쳥훐룶쳥뒮뗄쒳킩믹틲횵뷸탐뇤쪽훐ꛑ-1뚯ꆣ틅뒫쯣램떼죫뇤틬쯣ퟓ뗄쒿뗄폐솽룶:튻쫇쪹,ꛗi(wt)=i1+ꛑ2ꛒ2ꛑ33p,t-sp,t+ꛑ44kp,t,ii!2!3!4!틅뒫쯣램뻟폐뻖늿쯦믺쯑쯷쓜솦,벴퓚뷓뷼ퟮ폅뷢=1,2,3,쯼쏇뚼쫇좨훘쿲솿wt뗄럇쿟탔몯쫽ꆣ뗄쇚폲,샻폃뇤틬쯣ퟓ살볓쯙쿲ퟮ폅뷢뗄쫕솲;뛾쫇쪽(11)쪵훊쫇틔좨훘쿲솿wt캪ퟔ뇤솿,평N쪹틅뒫쯣램캬돖좺쳥뗄뛠퇹탔,럀횹돶쿖퓧쫬쿖쿳ꆣ룶랽돌ퟩ돉뗄럇쿟탔랽돌ퟩꆣ퓚쪱뿌t만뚨쪱,춨맽튻룶룟쮮욽뗄뇤틬싊,믡닺짺뷓뷼뒿쯦믺뗄쯑쫽횵뷢램,뿉틔뗃떽좨훘쿲솿뗄뻟쳥좡횵ꆣ쯦ퟅ쪱뿌쯷뷡맻,뛸뗍쮮욽뗄뇤틬싊믡쪹쫕솲쯙뛈맽싽ꆣ헢
ꆤ30ꆤ훐맺맜샭뿆톧ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ2007쓪샯닉폃떥뗣뇤틬,뇤틬싊캪01001-0101ꆣ쒣탍쪵쿖뛔룷뷗뻘럧쿕뗄맀볆ꆣ7)춣횹ힼ퓲311ꆡ뛠풪GARCHSK쒣탍놾컄틔ퟮ듳쫔퇩듺쫽ퟷ캪춣횹ힼ퓲ꆣLeon뗈(2005)쳡돶쇋튻풪GARCHSK(1,1;1,1;1,13ꆡ쳵볾룟뷗뻘럧쿕뫢솿)쒣탍[10],룃쒣탍뿉폃폚쳖싛떥룶뷰죚닺뗄쳵볾룟뷗뻘럧쿕ꆣ죴튪퓚뛠룶뷰죚닺횮볤럖즢훁듋,쪽(11)훐폃폚쏨쫶뛾뷗뻘럧쿕뗄쳵볾랽랽닮럧쿕ꆢ욫뛈럧쿕뫍럥뛈럧쿕,탨튪볆쯣쳵볾랽닮닮-킭랽닮뻘헳Htꆢ쏨쫶죽뷗뻘럧쿕뗄쳵볾욫뛈--킭랽닮ꆢ쳵볾욫뛈-킭욫뛈뫍쳵볾럥뛈-킭럥뛈ꆣ킭욫뛈뻘헳St뫍쏨쫶쯄뷗뻘럧쿕뗄쳵볾럥뛈-킭캪듋,컒쏇붫튻풪뗄GARCHSK쒣탍삩햹떽뛠풪뗄럥뛈뻘헳Kt짐쫴캴횪,놾컄쳡돶뛠풪GARCHSK쟩탎,룸돶뛠풪GARCHSK쒣탍뗄쿲솿뇭듯죧쿂Yt=Mt+:tꆡ:t|It-1ꆫD(0,Ht,St,Kt)ꛇt=H-1/2t:t,ꛇt|It-1ꆫD(03,I,St,K3t)q1p1vech(Ht)=B0+ꇆB1,ivech(ꛇt-ꛇiꇤt-i)+ꇆB2,jvech(Ht-j)i=1j=1(13)q2p2vech(St)=ꚣ0+ꇆꚣ1,ivech((ꛇt-ꛇiꇤt-i)ªꛇꇤt-i)+ꇆꚣ2,jvech(St-j)i=1j=1q3p3vech(Kt)=ꛄ0+ꇆꛄ1,ivech((ꛇt-ꛇiꇤt-i)ªꛇꇤt-iªꛇꇤt-i)+ꇆꛄ2,jvech(Kt-j)i=1j=1쪽훐:ꛇt캪쯦믺컳닮쿲솿:t뺭H-1/2t:t뇪ힼ뮯뫳뗃떽312ꆡ뛠풪쳵볾룟뷗뻘늨뚯싊맀볆뗄컳닮쿲솿;i캪떥캻뻘헳,S3t,K3t럖뇰캪ꛇt뗄죧맻냑뷰죚쪱볤탲쇐뾴ퟷ뷰죚쾵춳쯹쫍럅돶살쳵볾욫뛈-킭욫뛈뻘헳뫍쳵볾럥뛈-킭럥뛈뻘헳;뗄탅뫅,퓲뿉틔붫웤쫓캪평죴룉룶쿠뮥뛀솢뗄풴탅B0캪ꆫN(H)ꇁ1캬쇐쿲솿,ꚣ0캪ꆫN(H)ꇁ1캬쇐쿲솿,뫅내헕쒳훖랽쪽믬뫏뛸돉ꆣ퓚쫽뻝췚뻲ꆢ믺웷톧쾰ꛄ0캪ꆫN(K)ꇁ1캬쇐쿲솿;B1뗈쇬폲훐뺭뎣쪹폃뗄뛀솢돉럖럖컶(ICA)랽램쓜릻,i,B2,j뻹캪ꆫN(H)캬랽뻘헳,ꚣ1,i,ꚣ2,j뻹캪ꆫN(S)캬랽뻘헳,ꛄ1,i,ꛄ2,j뻹캪ꆫN(K)춨맽뛔맛닢떽뗄탲쇐뷸탐럖뷢,듓뛸뗃떽잱퓚뗄풴캬랽뻘헳ꆫꆫ;N(H탅뫅ꆣ헢샯,뷨훺ICA랽램살뷢뻶쿲솿GARCHSK)=N(N+1)/2,N(S)=N(N+ꆫ1)(N+2)/6,N(K쒣탍뗄늨뚯싊맀볆컊쳢ꆣ)=N(N+1)(N+2)(N+죴ICt=(IC1t,IC2t,ꆭ,ICNt)ꇤ쫇쫕틦쿲솿Yt3)/24;vech(ꆤ)캪쿲솿냫쯣ퟓ,붫뻘헳내헕쿂죽뷇뛑돉튻룶쇐쿲솿ꆣ뗄N룶뛀솢돉럖,퓲ICit뫍ICjt(iꇙj)쫇춳볆뛀솢쒣탍뗄,뛸쟒듦퓚뿉쓦뻘헳U(돆ퟷ뮻뻘헳),쪹뗃(13)뇈뛠풪GARCH쒣탍듦퓚룼캪퇏훘뗄ꆰ캬쫽퓖쓑ꆱ컊쳢ꆣ쿂쏦믹폚뛀솢돉럖럖뷢벼쫵쳖ICt=UYt(14)싛뛠풪뛔쪽(14)솽뇟춬쪱쟳쳵볾랽닮ꆢ쳵볾욫뛈뫍쳵GARCHSK쒣탍훐쳵볾룟뷗뻘늨뚯싊맀볆컊쳢ꆣ볾럥뛈뿉뗃:var(ICt|It-1)=var(UYt|It-1)=Uvar(Yt|It-1)Uꇤ=UHtUꇤskew(ICt|It-1)=skew(UYt|It-1)=Uskew(Yt|It-1)(UꇤªUꇤ)=USt(UꇤªUꇤ)(15)kurt(ICt|It-1)=kurt(UYt|It-1)=Ukurt(Yt|It-1)(UꇤªUꇤªUꇤ)=UHt(UꇤªUꇤªUꇤ)쪽(15)쪵볊짏붨솢웰풭쪼쪱볤탲쇐뗄쳵볾랽닮-킭쯘럖뇰캪뛔펦돉럖뗄쳵볾랽닮ꆢ쳵볾욫뛈뫍쳵볾럥랽닮ꆢ쳵볾욫뛈-킭욫뛈ꆢ쳵볾럥뛈-킭럥뛈뻘헳폫뛈ꆣ웤뛀솢돉럖뗄쳵볾랽닮-킭랽닮ꆢ쳵볾욫뛈-킭욫틲듋,튻떩뗃떽Yt뗄뛀솢돉럖럖뷢ICt=UYt,뛈ꆢ쳵볾럥뛈-킭럥뛈뻘헳횮볤뗄뛔펦맘쾵ꆣ뛸뛀닉폃죧쪽(16)쯹쪾뗄튻풪GARCHSK쒣탍럖뇰맀솢돉럖뗄쳵볾랽닮-킭랽닮ꆢ쳵볾욫뛈-킭욫뛈뫍볆룷룶뛀솢돉럖뗄쳵볾랽닮ꆢ쳵볾욫뛈뫍쳵볾럥뛈ꆣ쳵볾럥뛈-킭럥뛈뻘헳쫇뛔뷇뻘헳,뛔뷇쿟짏뗄풪
뗚1웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ붯들쿀뗈:쳵볾룟뷗뻘럧쿕폫뚯첬ퟩ뫏춶ꆤ31ꆤq1p1ꛎ맻,뻜뻸쇋쫕틦탲쇐럾듓헽첬럖늼뗄볙뚨ꆣ틲듋,캪(H)(H)lt=w+ꇆꛁ(H)2(H)li(ꛇꆫ(H)l,t-i)+ꇆꛂ(H)ljꛎl,t-ji=1j=1쇋쏨쫶욫뛈뫍럥뛈뗄뚯첬쳘헷,뇘탫붨솢뛠풪쳵볾q2p룟뷗뻘늨뚯쒣탍ꆣꛎ(S)S)ꆫ2lt=w(+ꇆꛁ(S)li(ꛇ(S)3l,t-i)+ꇆꛂ(S)(S)ljꛎl,t-j;뇭1ꆡ쯄룶막횸쫕틦탲쇐뗄믹놾춳볆탔훊i=1j=1(16)(l=1,2,ꆭDJIAHKHSJNCISSM,N)욽뻹횵010317170106833101097413-01022085q3p3ꛎ뇪ힼ닮01008679010106480101278201013878(K)lt=w(K)+ꇆꛁ(K)4li(ꛇꆫ(K)l,t-i)+ꇆꛂ(K)ljꛎ(K)l,t-j욫뛈-0130321-01056713-014427-111589i=1j=1쪽훐,ꛎ(H)lt,ꛎ(S)lt,ꛎ(K)lt럖뇰캪뗚럥뛈415105612867614160915602l룶뛀솢돉럖뗄J-B볬퇩68147732801923323167312161603IClt(l=1,2,ꆭ,N)뗄쳵볾랽닮ꆢ쳵볾욫뛈뫍쳵볾ꆡꆡ힢:3뇭쪾1%쿔훸탔쮮욽쿂쿔훸ꆣ럥뛈ꆣ퓚믱뗃뛀솢돉럖뗄쳵볾룟뷗뻘늨뚯싊뫳,퓚쪽(15)룷랽돌뗄ퟳ폒솽뇟럖뇰ퟳ돋뫍폒돋뛔펦뻘헳412ꆡ뛠풪쳵볾룟뷗뻘럧쿕뗄쓦,듓뛸뗃떽Yt뗄쳵볾랽닮-킭랽닮뻘헳ꆢ쳵볾쫗쿈,샻폃(1997)룸돶뗄늻뚯뗣쯣램[13,14],뛔욫뛈-킭욫뛈뻘헳뫍쳵볾럥뛈-킭럥뛈뻘헳럖뇰쯄룶횸쫽쫕틦뷸탐뛀솢돉럖럖뷢,쟳뗃뮻뻘헳뗄캪맀볆캪:H281767-31763721579111393t=U-1ꚮ(H)tUt-1St=U-1ꚮ(S)t(UꇤªUꇤt-1)(17)1215331181916-181670-131639U1^=K-166155811910911714642181318t=U-1ꚮ(K)t(UꇤªUꇤªUꇤt-1)쪽훐-431256-1141647321729-581832:l=1,2,ꆭ,N럖뇰듺뇭뗚l룶뛀솢돉럖;ꚮ(H)t=diag(ꛎ(H)1t,ꛎ(H)2t,ꆭ,ꛎ(H)Nt)ꆢꚮ(S)(18)t=diag(ꛎ(S)1t,ꛎ(S)2t,ꆭ,ꛎ(S)Nt)뫍ꚮ(K)t=diag(ꛎ(K)1t,ꛎ(K)2t,ꆭ,ꛎ(K)Nt)럖뇰캪뛀평쪽(18),뿉틔뗃떽쯄룶뛀솢돉럖(IC1ꆢIC2ꆢIC3솢돉럖쳵볾랽닮-킭랽닮뻘헳ꆢ쳵볾욫뛈-킭욫뛈뫍^^IC4)뗄맀볆^ICt(ICt=UYt)ꆣ뻘헳뫍쳵볾럥뛈-킭럥뛈뻘헳,웤럇훷뛔뷇쿟짏풪웤듎,뛔쯄룶뛀솢돉럖럖뇰붨솢튻풪쯘캪GARCHSK쒣탍,뿉틔붨솢쯄룶뛀솢돉럖뗄튻풪0ꆣ듓뛸평쪽(17)뿉틔쪵쿖뛔뛠풪쳵볾룟뷗뻘늨뚯싊:쳵볾랽닮-킭랽닮ꆢ쳵볾욫뛈-킭욫뛈뫍쳵GARCHSK(1,1;1,1;1,1)쒣탍볾럥뛈yt=ꛅtꆡꛅt|It-1ꆫD(0,ht,st,kt)-킭럥뛈뗄맀볆ꆣꛇ-1/23t=htꛅt;ꛇt|It-1ꆫD(0,13,st,kt)4ꆡ쫽뻝뗄톡좡벰쪵횤ht=ꛂ0+ꛂ1ꛇ2t-1+ꛂ2ht-1(19)st=ꛃ0+ꛃ1ꛇ3411ꆡ쫽뻝뗄톡좡벰믹놾춳볆탔훊t-1+ꛃ2st-1톡퓱쯄룶횤좯횸쫽ퟷ캪퇐뺿뛔쿳,럖뇰폃럻뫅kt=ꛄ0+ꛄ1ꛇ4t-1+ꛄ2kt-1:D뇭2룸돶쇋쒣탍(19)뗄닎쫽맀볆뷡맻ꆣJIAꆢHKHSꆢJN뫍CISSM듺뇭뗀쟭쮹릤튵횸쫽ꆢ쿣룛뫣짺횸쫽ꆢ죕뺭횸쫽뫍짏횤ퟛ뫏횸쫽뗄죕뛈쫕뇭2ꆡGARCHSK(1,1;1,1;1,1)쒣탍맀볆뷡맻엌볛닎쫽IC1IC2IC3IC4,퇹놾쟸볤캪:2003/02/06훁2005/06/30,쳞돽ꛂ뷚볙죕뫍럇춬늽붻틗죕,퇹놾죝솿캪0010368010032010921010662:N=958ꆣ쫽랽닮랽돌ꛂ1010630010220010001010660뻝살ퟔ퇅뮢뷰죚췸햾ꛂ:
ꆤ32ꆤ훐맺맜샭뿆톧ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ2007쓪닮-킭랽닮ꆢ쳵볾욫뛈-킭욫뛈뫍쳵볾럥뛈-킭럥ퟩ뫏춶뗄펰쿬,룄뷸뫳뗄쒣탍붫룼볓뻟폐쫊펦탔ꆣ뛈뻘헳뗄맀볆뷡맻ꆣ414ꆡ폫뺲첬ퟩ뫏춶뗄뇈뷏413ꆡ뚯첬ퟩ뫏춶쟳뷢캪뾼싇뚯첬ퟩ뫏춶뗄킧맻,붫웤폫뺲첬ퟩ뫏퓚믹폚틅뒫쯣램뗄ퟮ폅닺ퟩ뫏좨훘쟳뷢맽돌춶뷸탐뇈뷏ꆣ늻럀짨쫐뎡짏뮹듦퓚튻룶춶헟,훐,뷢뗄뇤뮯폫훖좺욽뻹횵뇤뮯톸쯙쫕솲,폚100듺쯻닉폃릺싲-돖폐(buyandhold)춶닟싔,늢쟒횮뫳쯆좻몯쫽횵믹놾컈뚨,쎻폐쏷쿔뗄룄뷸ꆣ헢쪱,폃폚룷룶횤좯횸쫽뗄춶좨훘뻹쿠뗈,벴ꆣ쫗쿈,럖쫤돶뗄뷡맻캪ퟮ폅뷡맻,평쪽(11)좷뚨뗄ퟮ폅ퟩ뫏뇰샻폃뚯첬뗄좨훘뫍뺲첬뗄좨훘볆쯣돶닺ퟩ뫏뗄춶좨훘쫇룶뚯첬뗄뷡맻,쯦ퟅ쪱볤뗄뇤뮯뛸뇤뮯ꆣ쫕틦ꆢ랽닮ꆢ욫뛈뫍럥뛈퓚쎿쳬뗄좡횵,뇭3룸돶웤뚯첬ퟩ뫏춶좨훘뇭쏷,춶헟쎿쳬퓚룷횻막욱짏욽뻹횵뫍뇪ힼ닮;웤듎,샻폃쪽(9),퓚뗄쳵볾쿂,뿉뗄춶쟩뿶쫇늻튻퇹뗄,샭싛짏탨튪욵랱뗘뷸탐붻틔볆쯣돶뚯첬ퟩ뫏춶폫뺲첬ퟩ뫏춶뗄쳵볾웚췻틗틔캬돖웚췻킧폃ퟮ듳뮯ꆣ좻뛸,쿖쪵훐뗄붻틗듦킧폃몯쫽퓚쎿쳬뗄좡횵,뷸뛸뿉틔뗃떽웤욽뻹횵뫍퓚ퟅ붻틗돉놾,탨튪퓚붨쒣쪱쳖싛붻틗돉놾뛔뚯첬뇪ힼ닮,볆쯣뷡맻볻뇭3ꆣ뇭3ꆡ뚯첬ퟩ뫏춶폫뺲첬ퟩ뫏춶킧맻뛔뇈ퟩ뫏춶랽쪽킧폃쫕틦랽닮욫뛈럥뛈욽뻹횵뇪ힼ닮욽뻹횵뇪ힼ닮욽뻹횵뇪ힼ닮욽뻹횵뇪ힼ닮욽뻹횵뇪ힼ닮뚯첬-0191712133100105045190090100017116754-013962313466512275410982뺲첬-1120085136140104386101260100020117596-014748412527611483517729ꆡꆡ평뇭3뗄뷡맻뿉횪,뚯첬ퟩ뫏춶폫뺲첬ퟩ뫏(듓욽뻹킧폃살뾴)폅폚뺲첬ퟩ뫏춶,뛸쟒퓚룷룶춶믱뗃뗄욽뻹킧폃럖뇰캪:-019171뫍-떥쿮짏(럖뇰듓쫕틦ꆢ랽닮ꆢ욫뛈ꆢ럥뛈살뾴)뻹폅폚112008,뛸웤뇪ힼ닮럖뇰캪:213310뫍513614,헢틢뫳헟ꆣ캶ퟅ뚯첬ퟩ뫏춶늻뷶쓜퓚ퟜ쳥짏쳡룟춶헟뗄킧폃쮮욽,뛸쟒쓜릻쪹뗃춶헟믱뗃튻룶컈뚨뗄킧폃닎뾼컄쿗:쮮욽ꆣ늻뷶죧듋,퓚닺ퟩ뫏뗄쫕틦ꆢ랽닮ꆢ욫뛈뫍[1]MarkowitzH..Portfolioselection[J].JournalofFi2럥뛈쯄룶떥쿮횸뇪뗄춳볆훐,뚯첬ퟩ뫏춶뗄킧맻nance,1952,7:77-91.뻹폅폚뺲첬ퟩ뫏춶[2]..Portfolioselectionwithskewness:amulti2,뇭쿖퓚:웤튻,뚯첬ퟩ뫏춶뗄룷룶떥쿮횸뇪뗄뇪ힼ닮뻹뇈뺲첬ퟩ뫏춶뗄튪ple-objectiveapproach[J].ReviewofQuantitativeFi2킡nanceandAccounting,1991,1:293-305.,쿔쪾돶뷏잿뗄컈뚨탔;웤뛾,뚯첬ퟩ뫏춶뗄쫕틦ꆢ욫뛈뗄욽뻹횵뇈뺲첬ퟩ뫏춶뗄쫕틦ꆢ욫뛈뗄욽[3]ChunhachindaP.,DandapaniK.,HamidS.,etal..뻹횵튪룟,뛸잰헟뗄랽닮ꆢ럥뛈뗄욽뻹횵뇈뫳헟뗄튪Portfolioselectionandskewness:evidencefrominterna2tionalstockmarkets[J].JournalofBankingandFi2뗍,헢헽쫇춶헟쯹웚췻뗄,폫잰컄럖컶뷡싛튻훂ꆣnance,1997,21(2):143-167.[4]PrakashA.,ChangC.,PactwaT..Selectingaportfo25ꆡ뷡싛liowithskewness:recentevidencefromUS,European,틔췹뗄맺쓚췢컄쿗훐,뛾뷗뻘럧쿕(랽닮럧쿕)andLatinAmericanequitymarkets[J].Journalof쫜떽쇋웕뇩뗄맘힢ꆣ쯦ퟅ샭싛폫쪵볹뗄짮죫,룟뷗BankingandFinance,2003,27(7):1375-1390.뻘럧쿕(욫뛈럧쿕뫍럥뛈럧쿕)틑훰붥틽웰죋쏇뗄훘[5]SunhQ.,YanY..Skewnesspersistencewithoptimal쫓ꆣ놾컄쳖싛쇋듸폐룟뷗뻘럧쿕뗄뚯첬ퟩ뫏춶컊portfolioselection[J].JournalofBankingandFinance,쳢2003,27:1111-1121.,튻랽쏦쳡돶뛠풪GARCHSK쒣탍,폃폚뫢솿뷰죚쫐뎡뗄룟뷗뻘럧쿕;쇭튻랽쏦,믹폚킧폃몯쫽뗄[6]JondeauE.,RockingerM..Optimalportfolioallocationunderhighermoments[Z].BanqueDeFrance,workingTaylor햹뾪룸돶쳵볾룟뷗뻘뚯첬ퟩ뫏춶랽램,듓paper,2004.솽룶랽쏦뛔뒫춳뗄ퟩ뫏춶샭싛뷸탐쇋룄뷸ꆣ쪵횤[7].,..Findingamaxi2퇐뺿뇭쏷,훐맺막쫐늻뷶듦퓚룟뷗뻘럧쿕,뛸쟒럧쿕mumskewnessportfolio-ageneralsolutiontothree-뻟폐쪱뇤쳘헷;캪럀랶룟뷗뻘럧쿕,춶헟탨튪뚯첬momentsportfoliochoice[J].JournalofEconomicDy2뗘탞헽닺엤훃좨훘;뚯첬ퟩ뫏춶늻뷶퓚ퟜ쳥짏namics&Control,2004,28:1335-1352.
뗚1웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ붯들쿀뗈:쳵볾룟뷗뻘럧쿕폫뚯첬ퟩ뫏춶ꆤ33ꆤ[8]JoroT.,NaP..Portfolioperformanceevaluationina[11].,..Onthedirectionofpref2mean-variance-skewnessframework[J].EuropeanerenceformomentsofhigherorderthatthevarianceJournalofOperationalResearch,2005,(5):1-16.[J].JournalofFinance,1980,35:915-919.[9]헅쫷뇳,냗쯦욽,튦솢.몬폐붻틗돉놾뗄뻹횵-랽닮-욫[12]랮훇,헅쫀펢.뷰죚늨뚯탔벰쪵횤퇐뺿[J].훐맺맜샭뿆뛈닺ퟩ뫏폅뮯쒣탍[J].쫽톧뗄쪵볹폫죏쪶,2004,34톧,2002,10(6):27-30.(2):22-26.[13]A..KarhunenJ..OjaE..Independentcomponenta2[10]LeonA.,RubioG.,SernaG..Autoregresivecondi2nalysis[M].Wiley,NewYork,,skewnessandkurtosis[J].TheQuar2[14]A..OjaE..Afastfixed-pointalgorithmforinde2terlyReviewofEconomicsandFinance,2005,45:599pendentcomponentanalysis[J].NeuralComputation,,9:-xia1,2,XUQi-fa2,ZHANGShi-ying(,TianjinUnversity,Tianjin300072,China;,ShandongInstituteofBusinessandTechnology,Yantai264005,China)Abstract:Twodefectsintraditionalportfoliotheory,withoutconsideringhighermomentsriskandsettlingproblemstaticly,,,basedonTaylorseriesexpansionofutilityfunction,thedynamicportfoliomodelwithhighermomentsriskisderived,,:highermomentsrisk;dynamicportfolio;multivariateGARCHSKmodel;GeneticAlgorithm
