华中科技大学硕士学位论文背景风险下指数复制的混合规划算法姓名：郑金璐申请学位级别：硕士专业：企业管理指导教师：龚朴2010-12
햪 튪 막횸웚믵뗄짏쫐ꎬ돽쇋룄뇤쒿잰훐맺막쫐떥뇟쫐뗄쿖ힴꎬ캪춶죋쳡릩쇋쳗웚놣횵뗄믺믡ꎬ뮹룸폨쇋춶헟쇭췢튻훖펯샻쒣쪽——막횸웚믵쳗샻ꆣ웤풭샭쫇샻폃막횸웚믵쫐뎡듦퓚뗄늻뫏샭볛룱ꎬ춶헟춬쪱닎폫막욱쿖믵뫍막횸웚믵쫐뎡뗄붻틗ꎬ믲헟춬쪱뷸탐늻춬샠뇰막욱횸쫽뫏풼ꎬ믲헟늻춬웚쿞막욱횸쫽뫏풼뗄붻틗ꎬ살좡샻닮뗄탐캪ꆣ헢훖펯샻쒣쪽뻍캪횸쫽뢴훆벼쫵쳡릩쇋쪵볹뗄뿕볤ꆣ 폅뮯횸쫽뢴훆뿉틔룅삨돉튻룶럇쿟탔믬뫏헻쫽폅뮯컊쳢ꎬ뛔폚럇쿟탔뗄믬뫏헻쫽폅뮯컊쳢뗄쟳뷢쫇튻룶뇈뷏뢴퓓뗄맽돌ꎬ뛸쟒뫜짙톧헟붫놳뺰럧쿕쓉죫횸쫽뢴훆쒿뇪몯쫽뗄붨솢ꎬ폈웤쫇춶헟뗄뷷짷욫뫃ꎬ헢짦벰떽뛔죽뷗뻘쟳ퟮ횵ꆣ놾컄샻폃쿟탔뮯쫖뛎퓚벼쫵짏뿋럾쇋뛔죽뷗뻘쟳뷢ퟮ횵뗄쓑쳢ꎬ믹폚킧폃몯쫽뿲볜쿂뗄놳뺰럧쿕살릹붨뢴훆횸쫽쒣탍ꎬ룹뻝늻춬춶죋뗄춶욫뫃릹붨늻춬뗄뢴훆ퟩ뫏ꆣ컄훐훷튪짦벰떽솽샠춶죋ꎬ럧쿕퇡뛱뗄춶죋뫍뷷짷뗄럧쿕퇡뛱춶죋ꆣ퓚헢솽룶뿲볜쿂ꎬ쳡돶풼쫸쳵볾뫍쒿뇪몯쫽ꎬ붨솢횸쫽뢴훆뗄쫽톧쒣탍ꆣ놾컄톡퓱뮦짮300횸쫽ퟷ캪훷튪룺ퟙ쒿뇪ꎬ짏횤100ퟷ캪듎튪ힷퟙ쒿뇪ꎬ쳡릩튻킩뇈뷏틢틥ꆣ틀뻝쳡돶뗄늻춬쒣탍뛔짏쫶횸쫽릹붨뢴훆횸쫽ꎬ늢볆뷏쇋룷훖랽램뗄ힷퟙ킧맻ꆣ쪵퇩횤쏷죧맻뷶뷶뇈뷏ힷퟙ욫샫뛈ꎬ헫뛔럧쿕퇡뛱룶쳥릹붨뗄죽뷗뛎쒣탍뗄ힷퟙ킧맻ퟮ뫃ꎻ헫뛔뷷짷럧쿕퇡뛱춶헟릹붨뗄쒣탍믹놾듯떽쇋짨볆뗄쒿뇪ꎬ뢴훆횸쫽쿠뛔폚쒿뇪횸쫽폐룼듳뗄헽쿲욫틆ꆣ놾컄샻폃쿟탔뮯뗄쫖뛎붫횸쫽뢴훆뗄컊쳢볲뮯ꎬ뛸쟒듳듳쳡룟쇋퓋쯣쯙뛈ꎬ뗃떽뇈뷏뫃뗄횸쫽뢴훆킧맻ꎬ캪횸쫽뢴훆퓚쪵볹훐뗄펦폃쳡릩쇋뇣뷝ꆣ 맘볼듊ꎺ횸쫽뢴훆ꎻ믬뫏헻쫽폅뮯ꎻ놳뺰럧쿕ꎻ욫뛈 I
Abstract In addition to changing the current status of Chinese stock market, which is the investor can only get profit form the increase of stock price, the stock index future not only provide a hedge opportunity, but also give investor another profit model ,that is arbitrage. The principle is making use of the unreasonable price in stock index market. The investor take part in the transaction in the spot and future market, or different types of stock index contracts, or different periods of trading stock index contracts at the same time, in order to earn spreads. This profit model induces the development of index tracking. Optimization of index tracking can be summarized as a nonlinear mixed integer optimization problem, which is a much complex process. What’s more, when establishing the objective function, few scholars take the background risk into account, in particular prudent investor preference, which relates to the third moment for the most value. We use linear method to overcome the problem of getting the maximum value of the third order moment. Based on the background risk under the framework of utility function, we establish index tracking model. There are two kinks of investors, risk aversion and prudent. Based on the investor types we induce constrain conditions and objective functions to establish mathematic model. We choose HS300 as the first tracking target and the SZ100 as the second tracking target, which provide some comparisons. Based on different models we carry out the calculation and compare the tracking result. The result shows if we only care the tracking deviation, the three-period models which is for risk aversion investors, is the best. The tracked index using the model for prudent investors gets a positive deviation, just as we anticipant. We simplify the index tracking problem using linear method in this paper. At the same time the calculate speed is well developed and the result is as we anticipant, which provide convenient for the use of index tracking in practice. Keywords: Index tracking, Mix-integer programming, Background risk, Skewness II
뛀뒴탔짹쏷 놾죋짹쏷쯹돊붻뗄톧캻싛컄쫇컒룶죋퓚떼쪦횸떼쿂뷸탐뗄퇐뺿릤ퟷ벰좡뗃뗄퇐뺿돉맻ꆣ뺡컒쯹횪ꎬ돽컄훐틑뺭뇪쏷틽폃뗄쓚죝췢ꎬ놾싛컄늻냼몬죎뫎웤쯻룶죋믲벯쳥틑뺭랢뇭믲킴맽뗄퇐뺿돉맻ꆣ뛔놾컄뗄퇐뺿ퟶ돶릱쿗뗄룶죋뫍벯쳥ꎬ뻹틑퓚컄훐틔쏷좷랽쪽뇪쏷ꆣ놾죋췪좫틢쪶떽놾짹쏷뗄램싉뷡맻평놾죋돐떣ꆣ 톧캻싛컄ퟷ헟잩쏻ꎺ 죕웚ꎺ 쓪 퓂 죕 톧캻싛컄냦좨쪹폃쫚좨쫩 놾톧캻싛컄ퟷ헟췪좫쇋뷢톧킣폐맘놣쇴ꆢ쪹폃톧캻싛컄뗄맦뚨ꎬ벴ꎺ톧킣폐좨놣쇴늢쿲맺볒폐맘늿쏅믲믺릹쯍붻싛컄뗄뢴펡볾뫍뗧ퟓ냦ꎬ퓊탭싛컄놻닩퓄뫍뷨퓄ꆣ놾죋쫚좨뮪훐뿆벼듳톧뿉틔붫놾톧캻싛컄뗄좫늿믲늿럖쓚죝뇠죫폐맘쫽뻝뿢뷸탐볬쯷ꎬ뿉틔닉폃펰펡ꆢ쯵펡믲즨쏨뗈뢴훆쫖뛎놣듦뫍믣뇠놾톧캻싛컄ꆣ 놾싛컄쫴폚놣 쏜ꇵ 늻 놣 쏜 ꇵ 퓚___쓪뷢쏜뫳쫊폃놾쫚좨쫩ꆣ ꎨ쟫퓚틔짏랽뿲쓚듲“v”ꎩ 톧캻싛컄ퟷ헟잩쏻ꎺ 횸떼샏쪦잩쏻ꎺ 죕웚ꎺ 쓪 퓂 죕 죕웚ꎺ 쓪 퓂 죕
1 탷싛 퇐뺿놳뺰벰컊쳢쳡돶 쫀뷧짏돶쿖뗚튻횻횸쫽탍믹뷰ꎬ벴룺ퟙ쏀맺S&P500횸쫽뗄Vanguard500횸쫽믹뷰ꎬ훁듋횸쫽춶삭뾪쇋탲쒻ꆣ퓚듋횮잰ꎬ튻횱쫇믽벫춶닟싔햼뻝헻룶뷰죚춶쫐뎡뗄훷떼뗘캻ꎬ놻죋쏇쯹쫬쾤뫍펦폃ꆣVanguard500횸쫽닺짺틔뫳ꎬ믽벫춶뫍쿻벫춶놻럅떽쇋춬튻룶욽첨짏ꎬ맘폚솽헟뗄폅쇓쫆뗄쳖싛튲ퟔ듋뾪쪼ꆣ믽벫춶쫇떱춶헟쫔춼뎬풽쫐뎡뇭쿖믲헟쒳떥튻쫐뎡횸쫽쪱쯹닉폃뗄닟싔ꎬ믽벫춶튻냣냩쯦ퟅ춶럧룱ꆢ뷸돶쫐뎡쪱믺ꆢ탐튵틔벰막욱뗄톡퓱ꆣ쿻벫춶쫇튻훖뚢힡쫐뎡횸쫽ꎬ쎻폐톰쟳햽쪤쫐뎡뗄춶닟싔ꆣ쿻벫춶헟춨맽톡퓱튻ퟩ횤좯늢뎤웚돖폐ꎬ뺭샺웤볛룱룄뇤뛸믱뗃뎤웚쫕틦ꆣ횸쫽춶쫇쿻벫춶뗄튻훖훘튪탎쪽ꆣ ퟔ쫀뷧뗚튻횻횸쫽믹뷰닺짺ꎬ뷼쯄쪮쓪틑뺭맽좥쇋ꎬ맘폚훷뚯춶폫쿻벫춶쓄튻룶룼뫃뗄쳖싛듓살쎻폐춣횹ꎬ짐컞뚨싛ꆣ퓚돉쫬뗄놾쫐뎡ꎬ훷뚯춶쏦쇙뗄ퟮ듳쳴햽쫇닺뚨볛욫닮벴쪹듦퓚ꎬ튲쫇쮲벴쫅뗄ꆣ쯦ퟅ놾쫐뎡풽살풽돉쫬ꎬ헢훖뚨볛욫닮늻뛏복짙믲헟돖탸쪱볤늻뛏뇤뛌ꎬ떼훂훷뚯춶닟싔쫜떽벫듳쳴햽ꆣ훷뚯춶쏦쇙뗄쇭튻룶뻞듳쳴햽쫇웤뷏룟뗄붻틗돉놾ꎬ뷏룟뗄죋솦돉놾틔벰뢴퓓뗄뻶닟훆뚨뫍럧쿕뿘훆쯹듸살뗄돉놾ꆣ틲듋믹폚쿻벫춶뗄탭뛠폅쫆ꎬ폈웤쫇돉놾폅쫆ꆢ맜샭폅쫆뫍뷴룺쫐뎡욽뻹놨돪싊뗄놣횤탔ꎬ틔벰듓쪵볹훐뾴ꎬ쫐뎡횸쫽뎤웚쫇돊쿖짏짽뗄쟷쫆뫍떥횻막욱뫜쓑뎤웚엜펮쫐뎡횸쫽ꎬ쿻벫춶폈웤쫇횸쫽춶풽살풽뛠뗄놻닉폃ꆣ횸쫽뢴훆뗄쯣램퇐뺿풽살풽폐쫐뎡뫍랢햹뿕볤ꆣ 쒿잰맺췢쯹폃뗄뗃떽뢴훆ힷퟙ뗄ퟮ폅뮯쯣램냼삨뛾듎맦뮮ꆢ쿟탔맦뮮ꆢ쏉쳘뾨싥쒣쓢ꆢ틅뒫쯣램뫍웴랢쪽쯣램뗈ꎬ헢킩쯣램뗄쪹폃쪹뗃횸쫽뢴훆킧맻뗃떽쇋룼뫃뗄룄뷸ꆣ 퓚컒맺ꎬ1999쓪죽횻럢뇕탍횸쫽믹뷰쫗쿈컊쫀ꎺ믹뷰탋뫍ꆢ믹뷰웕럡뫍믹뷰뺰뢣ꆣ떫쫇헢죽횻믹뷰뿉틔쮵뚼늻쫇헦헽틢틥짏뗄횸쫽믹뷰ꎬ늻맽쫇튻훖믬뫏탍 1
뷰죚닺ꎬ웤ퟩ뫏훐냼삨쇋횸쫽춶ꆢ믽벫뗄막욱춶틔벰맺햮늿럖춶ꆣ2002쓪ꎬ짏몣횤좯붻틗쯹췆돶쇋짏횤180횸쫽ꎬ퓚춬튻쓪맺쓚돶쿖쇋뗚튻횻헦헽틢틥짏뗄횸쫽믹뷰——뮪낲180횸쫽퓶잿믹뷰ꆣ떫쫇ퟔ듋맺쓚뗄횸쫽뢴훆틔벰횸쫽믹뷰늢쎻폐랱죙랢햹웰살ꎬ뛸쫇뺭샺쇋뫜뎤쪱볤뗄돁볅ꆣ횱떽2003쓪3퓂ꎬ맺쓚뗚튻횻췪좫뢴훆탍횸쫽믹뷰——쳬춬180횸쫽믹뷰놻췆돶ꆣ뷼벸쓪ꎬ맺쓚횸쫽뮯믹뷰퓚맦쒣뫍쫽솿짏폐쯹랢햹ꎬ떫쫇웤쯙뛈틔벰맦쒣풶풶늻벰랢듯놾쫐뎡ꆣ뷼킩쓪퇇첫룷룶맺볒믽벫췆뷸짧믡놣헏쳥쾵붨솢뫍룄룯ꎬ쪹뗃퇸샏믹뷰맦쒣뗄ힳ듳ꎬ폐솦듙뷸쇋횸쫽믹뷰뗄랢햹ꆣ뛸ETF뗄돉릦폖튻뚨돌뛈짏췆뚯쇋횸쫽춶뗄뷸늽ꆣ틲캪횸쫽춶뗄돉놾뗍솮ꎬ폖럻뫏듳맦쒣뷰뗄놾엤훃틔벰뎤웚춶탨쟳ꎬ듓뎤풶뷇뛈뾼싇횸쫽춶뻟폐뫜듳랢햹뿕볤ꆣ뮦짮300막횸웚믵뗄췆돶ꎬ캪믹뷰ꎬ좯짌ꎬ웚믵릫쮾뗈뷰죚믺릹쳡릩쇋튻룶뷰죚뒴탂뗄릤뻟ꎬ쪹뗃헢킩믺릹춶헟뿉틔퓚“뷰죚릤돌”뗄샭싛뿲볜쿂좥첽쯷탂뗄펯샻쒣탍ꆣ웤훐막횸웚믵쳗샻뻍쫇튻훖훘튪뗄탂탍펯샻쒣쪽ꎬ횵뗃짮죫퇐뺿ꆣ뛸쟒뾪햹막횸웚믵쳗샻뛔폚믖뢴얤쟺뗄웚믵쫐뎡볛룱ꎬ틖훆맽뛈뗄쫐뎡춶믺탐캪ꎬ쳡룟쫐뎡뗄컈뚨뫍낲좫폐ퟅ훘튪뗄ퟷ폃ꆣ막횸웚믵쳗샻뗄튻훖훘튪탎쪽뻍쫇웚쿖쳗샻—샻폃웚믵뫍쿖믵뗄볛닮뷸탐쳗샻ꎬ헢룶맽돌훐뛔횸쫽웚믵욷훖뗄뢴훆폐뫜훘튪뗄ퟷ폃ꆣ 떫쫇쒿잰듦퓚뗄횸쫽뢴훆쒣탍뫜짙뾼싇떽놳뺰럧쿕ꎬ춶죋뗄럧쿕욫뫃ꆣ떱춶죋퓚ퟶ튻룶춶ퟩ뫏뗄뻶닟컊쳢쪱ꎬ늻뷶뷶튪쏦뛔ퟩ뫏럧쿕ꎬ뮹튪쏦뛔살ퟔ랽랽쏦쏦뗄놳뺰럧쿕ꎬ냼삨샍뚯솦쫕죫ꎬ쮽폐쫕죫ꎬ쪵컯닺짏뗄춶ꎬ틔벰튻킩늻뿉풤웚뗄럑폃뗈ꆣ퓚헢룶뿲볜쿂ꎬ튻냣볙짨퓚뷰죚쫐뎡뗄춶닺욷캪뷰죚닺ꎬ믲헟ퟩ뫏닺ꎬ믲헟붻틗닺ꆣ쓇쎴퓚뾼싇뷰죚닺춶ퟩ뫏뗄붨솢쪱ꎬ뻍튪붫놳뺰럧쿕쓉죫뾼싇뗄랶캧ꎬ놳뺰럧쿕뗄좱쪧믡뛔춶ퟩ뫏뗄붨솢뷡맻퓬돉펰쿬ꆣ틲듋놾컄퓚릹붨횸쫽뢴훆쒣탍뗄쪱뫲붫놳뺰럧쿕쳥쿖퓚뢴훆쒣탍뗄쒿뇪몯쫽훐ꎬ쟒샻폃쿟탔뮯뗄쫖뛎춻웆쇋쒿잰뛔죽뷗뻘쟳뷢벫횵뗄벼쫵쓑쳢ꆣ 2
횸쫽뢴훆뫍놳뺰럧쿕퇐뺿쿖ힴ 횸쫽뢴훆퇐뺿쿖ힴ 횸쫽뢴훆쯣램퇐뺿폐솽쳵훷쇷랽쿲ꎺ믹폚십뿋캬듄뗄춶ퟩ뫏샭싛퇐뺿틔벰믹폚틲쯘쒣탍뗄퇐뺿ꆣHaugen뫍Bakerꎨ1990ꎩ훷튪믹폚십뿋캬듄뗄춶ퟩ뫏샭싛ꆣ쯻쏇죏캪퓚뻹횵-랽닮뿲볜쿂뷸탐횸쫽뢴훆ꎬ뿉틔춨맽죽훖랽쪽뫢솿뢴훆ퟩ뫏뗄ힷퟙ쓜솦ꎺ웤튻쫇뢴훆ퟩ뫏뗄쳘헷쿟쟣킱뛈폫ힷퟙ쒿뇪쳘헷쿟쟣킱뛈뗄뇈뷏ꎻ웤뛾쫇뢴훆ퟩ뫏뗄늨뚯폫ힷퟙ쒿뇪늨뚯쿠맘뗄늿럖ꎻ웤죽쫇뢴훆ퟩ뫏폫ힷퟙ쒿뇪횮볤쫕틦싊닮틬뗄늨뚯탔ꆣ헢킩뫢솿횸뇪퓚튻뚨돌뛈짏캪횸쫽뢴훆쒿뇪몯쫽뗄짨뚨쳡릩쇋닎뾼볛횵ꆣ믹폚틲쯘쒣탍뗄퇐뺿쫇붫횸쫽뫍막욱뗄믘놨폫튻룶믲헟뛠룶뺭볃틲쯘솪쾵웰살ꆣ늻쓑샭뷢ꎬ헢훖쒣탍뗄뷢쫍쓜솦쯦ퟅ쒣탍훐틲쯘쫽쒿뗄퓶볓뛸퓶잿ꆣ떫쫇퓚쒣탍붨솢맽돌훐ꎬ탨튪뛔틲쯘뷸탐쪶뇰ꎬ웤쓑뒦쫇컞램쪶뇰쯹폐뗄쿠맘틲쯘ꎬ튲늻쓜ힼ좷뗄룸돶틲쯘뗄쫽쒿ꎬ틲듋틲쯘뗄톡퓱쫜룶죋훷맛에뛏펰쿬ꆣ 쿂쏦럖뇰뷩짜튻쿂맘폚횸쫽뢴훆뫍볓잿횸쫽뗄잰퇘컄쿗ꆣ 1ꎩ횸쫽뢴훆 횸쫽뢴훆웤뫋탄쫇복킡ힷퟙ컳닮ꎬ좡뗃폫쫐뎡횸쫽쿠춬뗄쫐뎡뇭쿖ꆣ쿂쏦쫇뷱쓪맘폚횸쫽뢴훆돶쿖뗄훷튪컄쿗ꆣJenson뫍van Dijkꎨ2002ꎩꎬ뾼싇쇋퓚룺ퟙퟩ뫏막욱쫽폐쿞뗘쟩뿶쿂ퟮ킡뮯룺ퟙ컳닮뗄컊쳢ꆣ퓚컄훐뗄랽램훐ꎬ쫇ퟮ킡뮯튻룶냼몬ꎨ솬탸뗄ꎩ룺ퟙ컳닮뫍ꎨ샫즢뗄ꎩ막욱쫽솿뗄볓좨쒿뇪몯쫽ꆣ튻떩막욱ퟩ뫏틑뺭놻톡뚨ꎬ컄훐춨맽뇪ힼ뛾듎맦뮮살뗃떽ퟮ폅뗄막욱좨훘ꆣ퓚컄헂훐룸돶쇋냼몬250횻막욱뗄횸쫽뗄볆쯣뷡맻ꎬ쎻폐룸돶쿪쾸뗄볆쯣쪱볤ꆣDerigs 뫍Nickelꎨ2003ꎩ룸돶쇋웴랢쒣쓢쯣램ꆣ퓚컄훐ꎬ막욱쫕틦뫍킭랽닮춨맽쿟탔뛠틲쯘쒣탍뗃떽ꎬ틲쯘뛠살ퟔ뫪맛뺭볃뇤솿ꆣ웤훐폐튻룶낸샽럖컶ꎬ쫇ힷퟙ뗂맺뗄DAX30횸쫽ꎨ뺡맜폐뛠폠뗄쿞훆쳵볾ꎬ튲쮵쏷쇋췪쏀뗄ힷퟙ쫇늻뿉쓜뗄ꎩꆣퟩ뫏훐좫늿202횻막욱ꎬ살ퟔDAX30뫍STOXX200ꆣ컄훐횻룸돶쇋튻늿럖볆쯣뷡맻ꆣOkey 뫍Akmanꎨ2003ꎩꎬ샻폃쇋쿞훆뻛벯샭싛ꆣ컄훐쫇틀뻝Beasley et al.ꎨ2003ꎩ룸돶뗄 3
릫쪽ꎬ늢쟒샻폃쿞훆뻛벯ꎬ뷢뻶쇋믬뫏헻쫽럇쿟탔맦뮮컊쳢ꆣ샻폃냼몬31횻살ퟔHang Seng막욱뗄쫽뻝ꎬ컄훐폃풭살뗄릫쪽뫍뻛벯릫쪽뗃돶쇋쿠쯆뗄뷡맻ꆣ뻙튻룶뛾듎닢쫔뗄샽ퟓꎬ풭살뗄릫쪽폃쇋487쏫ꎬ떫쫇뻛벯릫쪽뷶뷶폃쇋117쏫ꆣFocardi뫍Fabozziꎨ2004ꎩ쳖싛샻폃벯좺뗄랽램붨솢ힷퟙퟩ뫏ꆣ컄훐붨틩샻폃막욱볛룱탲쇐볤뗄얷쪽뻠샫ퟷ캪럖닣벯좺뗄튻룶믹뒡ꆣ튻떩막욱뗄벯좺틑뺭탎돉ꎬ컄훐붨틩듓쎿튻룶벯좺훐톡퓱튻횻막욱살탎돉룺ퟙퟩ뫏ꆣ컄훐쳡돶헢훖랽램춬퇹뿉틔폃퓚볓잿횸쫽ꆣ컄헂훐쎻폐햹쪾볆쯣뷡맻ꆣFang 뫍Wangꎨ2005ꎩ냑ힷퟙ횸쫽뗄컊쳢뾴ퟷ튻룶쮫쒿뇪맦뮮컊쳢ꆣ튻룶쒿뇪폫뛔막욱횸쫽뗄뻸뛔늻샻욫닮뗄뻹횵쿠맘ꎬ쇭튻룶쒿뇪폫뎬믘놨쿠맘ꆣ컄훐쳡돶뿉틔폃쿟탔맦뮮뷢뻶뗄쫽톧쒣탍——쒣뫽뻶닟샭싛ꆣ컄훐룸돶쇋탭뛠톡좡30횻막욱ힷퟙ짏횤180뗄샽ퟓꎬ떫쫇쎻폐룸돶볆쯣쪱볤ꆣGaivoronoski et al.ꎨ2005ꎩ쳖싛쇋탭뛠솿뮯ힷퟙퟩ뫏뫍막욱횸쫽횮볤뇭쿖닮틬뗄랽램틔벰욽뫢ힷퟙퟩ뫏뗄랽램ꆣ컄훐톡퓱막욱뗄랽램쫇쿈톡퓱튻룶늻볓쿞훆뗄ퟩ뫏ꎬ좻뫳퓚헢룶럇쿞훆ퟩ뫏훐틀뻝막욱뗄뇭쿖업탲ꆣ컄훐룸돶쇋뛔Oslo막욱붻틗쯹65횻막욱뗄볆쯣뷡맻ꎬ떫쫇쎻폐룸돶볆쯣쪱볤ꆣLi et al.ꎨ2005ꎩ냑횸쫽ힷퟙ떱ퟶퟮ킡뮯튻룶쫕틦좨훘욽랽닮틬ꎬ헢룶닮틬살ퟔ횸쫽훐뗄막욱좨훘뫍ힷퟙퟩ뫏훐뗄막욱좨훘ꆣ컄훐폃Stein램퓲맀볆뗷헻쫕틦ꆣ컄훐햹쪾쇋뛔짮?40횸쫽뗄뷡맻ꎬ떫쫇쎻폐룸돶볆쯣쪱볤ꆣOh et al.ꎨ2005ꎩ캪쎿튻횻막욱뚨틥쇋튻룶폅쿈좨몯쫽ꎬ헢룶몯쫽쫇평붻틗솿ꎬ쫐뎡놾뮯틔벰ß뗄좨훘뫍릹돉뗄ꆣ폅쿈좨몯쫽뗄튻룶볲떥폃램쫇뻶뚨ힷퟙퟩ뫏뗄ퟩ돉막욱ꆣ틅뒫쯣램놻폃살뻶뚨ힷퟙퟩ뫏훐쎿횻막욱뗄좨훘ꆣ컄훐룸돶쇋뛔몫맺KOPSI200횸쫽뗄볆쯣뷡맻ꎬ떫쎻폐룸돶볆쯣쪱볤ꆣ Coleman et al.ꎨ2006ꎩ뾼싇쇋퓚ힷퟙퟩ뫏뗄닺쫽쒿폐쿞뗘쟩뿶쿂ퟮ킡뮯ힷퟙ컳닮ꆣ퓚컄훐뗄랽램훐쫇춨맽ퟮ킡뮯튻룶좨훘쒿뇪몯쫽ꎬ몯쫽평ힷퟙ컳닮뫍ힷퟙퟩ뫏훐뗄닺쫽솿ퟩ릹돉ꆣ쒿뇪몯쫽훐뗄샫즢뇤솿춨맽튻룶솬탸몯쫽훰늽뇆뷼ꆣ컄훐햹쪾쇋샻폃릫뾪뿉틔믱뗃뗄Beasley et al.뗄쫽뻝볆쯣뗄뷡맻ꎬ떫쫇쎻폐룸돶볆쯣쪱볤ꆣColwell et al.ꎨ2007ꎩ냑횸쫽ힷퟙ컊쳢뾴ퟶ튻룶솬탸쪱볤뗄뛔돥컊쳢ꆣ컄훐닉폃튻룶뚯첬랽램——뻖늿럧쿕뗄ퟮ킡뮯살듓뢴훆횸쫽뗄솬탸붻틗닟싔톡퓱튻룶ퟮ폅ힷퟙퟩ뫏ꆣ컄훐뗄횸쫽ힷퟙ릫쪽훐쎻폐냼삨붻틗럑폃ꎬ늻쿞훆싴뿕ꆣ컄훐 4
햹쪾쇋S&P500 10횻ퟮ듳막욱훐톡퓱9횻뗄볆쯣뷡맻ꆣCorielli뫍Marcellinꎨo2006ꎩ쳡돶쇋튻룶횸쫽ힷퟙ랽램ꎬ헢훖랽램쫇믹폚막욱볛룱틲쯘쒣탍ꆣ퓚헢훖랽램훐ꎬ횸쫽틔벰ힷퟙퟩ뫏폐쿠춬뗄틲쯘뷡릹ꆣ컄훐닉좡튻훖볲떥뗄랽램쿲ힷퟙퟩ뫏훐볓죫탂뗄막욱ꆣ퓚헢룶맽돌훐ꎬ뗚튻늽쫇뷸탐틲쯘업탲ꎬ좻뫳틀쮳탲붫폫헢킩틲쯘쿠맘탔ퟮ뫃뗄막욱볓죫ힷퟙퟩ뫏ꆣ컄훐룸돶쇋헫뛔훘붨뗄EuroStoxx50횸쫽뗄ힷퟙ뷡맻ꎬ떫쫇쎻폐룸돶볆쯣쪱볤ꆣYao et al.ꎨ2006ꎩ뾼싇폃튻룶냼삨뫜짙닺뗄ퟩ뫏좥ힷퟙ튻룶뷰죚뇪룋ꆣ퓚컄훐뗄랽램훐ꎬힷퟙퟩ뫏훐뗄닺뇘탫쫇틑횪뗄ꆣ컄훐냑볆쯣ힷퟙ뗄컊쳢ퟷ캪튻룶쯦믺쿟탔뛾듎뿘훆컊쳢ꎬ늢폃냫헽뚨맦뮮뷢뻶쯼ꆣ컄훐룸돶쇋뷶폃4믲5횻막욱뗄ퟩ뫏ힷퟙ뫣짺횸쫽뗄뷡맻ꎬ떫쫇쎻폐룸돶볆쯣쪱볤ꆣYu et al.ꎨ2006ꎩ햹쪾쇋튻훖ힷퟙ횸쫽뗄십뿋캬듄쒣탍ꎬ퓚헢룶쒣탍훐볙짨횸쫽ힷퟙ뷡맻뫍뿘훆ힷퟙퟩ뫏뗄쫕틦붵떽뗍폚횸쫽뗄룅싊폐맘ꎨ늻샻럧쿕ꎩꎻ믲헟폫늻샻럧쿕뗄룟뷗뻠쿠맘ꆣ컄훐볙짨막욱믘놨싺ퟣ솪뫏헽첬럖늼ꎬ늢쟒퓊탭싴뿕ꆣ컄훐룸돶쇋맘폚뫣짺횸쫽막욱뗄튻룶볲떥쫽횵샽ퟓꆣStoyan 뫍Kwonꎨ2007ꎩ룸돶쇋튻훖믹폚솽뷗뛎쯦믺돌탲뗄횸쫽ힷퟙ랽램ꆣ웤쒿뇪쫇죽룶틲쯘뗄럇볓좨뫍ꎺힷퟙퟩ뫏뫍횸쫽횮볤뗄뻸뛔닮횵ꆢ퓚쳘뚨뗄탐튵욫샫샭쿫춶뗄뻸뛔횵ꆢ붻틗뗄막욱쫽솿ꆣ 2ꎩ볓잿횸쫽 튻킩춶헟늻뷶뷶싺ퟣ쫐뎡뇭쿖ꎬ쾣췻뗃떽뎬풽쫐뎡뇭쿖뗄쫕틦ꎬ퓚헢훖쟩뿶쿂ꎬ볓잿횸쫽펦퓋뛸짺ꎬ볓잿횸쫽뗄쒿뗄퓚폚훘쿖쫐뎡횸쫽뗄뇭쿖ꎬ춬쪱닺짺뎬맽쫐뎡횸쫽뗄쫕틦ꆣ볓잿횸쫽쫇퓚뿆톧컄쿗훐쿠뛔놻뾼싇뷏짙뗄쇬폲ꆣ쯹폐쿂쏦뷩짜뗄릤ퟷ뚼쫇쪼폚2005쓪ꆣ볓잿횸쫽뗄랽램짔볓탞룄뻍뿉틔폃퓚횸쫽ힷퟙꆣ틲듋쿂쏦뷩짜뗄쯣램튲뿉틔폃퓚횸쫽뢴훆ꆣAlexander 뫍Dimitriuꎨ2005ꎩ펦폃믹폚햽싔뗄킭헻ꆣ퓚헢훖랽램훐춨맽볓짏믲헟복좥튻룶뎣쫽뗄뎬뛮믘놨a살붨솢솽룶횸쫽탲쇐ꆣ닉폃킭헻뗄랽램좥ힷퟙ붨솢뗄헢솽횻횸쫽탲쇐ꆣ춨맽ퟶ뛠a볓짏ힷퟙퟩ뫏뫍ퟶ뿕a복좥ힷퟙퟩ뫏살믱뗃뎬뛮믘놨ꆣ퓚헢훖랽램훐쫇틀뻝막욱뗄볛룱뻶뚨쫇럱붫막욱쓉죫ힷퟙퟩ뫏ꆣ컄훐룸돶쇋헫뛔뗀쟭쮹횸쫽뗄ힷퟙ뷡맻ꎬ떫쫇쎻폐룸돶볆쯣쪱볤ꆣDose뫍Cincottiꎨ2005ꎩ뷨본Beasley et al.뗄릤ퟷꎬ샻폃솽횻막 5
욱샺쪷볛룱뗄닮틬ퟷ캪뻠샫살탎돉막욱벯좺ꆣ헢룶벯좺폃살뻶뚨쓄횻막욱놻냼삨퓚ힷퟙퟩ뫏ꆣ캪쇋뻶뚨퓚쎿횻막욱짏뗄춶ꎬ컄훐폃튻룶좨훘?살좨뫢ힷퟙ횸쫽뫍뎬뛮믘놨ꆣ컄훐붫헢훖랽램폃퓚뇪ힼ웕뛻500횸쫽ꎬ떫쫇쎻폐룸돶뻟쳥볆쯣쪱볤ꆣKonno뫍Hatagiꎨ2005ꎩ폃쇋욽뻹뻸뛔욫닮쒿뇪ꆣ퓚헢훖랽램훐쒿뇪쫇퓚쎿룶쪱볤웚볤뗄횸쫽볛횵폫ힷퟙ횸쫽볛횵뗄닮틬ꆣ랽램훐냼삨쇋붻틗럑폃틔벰튻룶듸폐쿟탔풼쫸뗄낼몯쫽뗄ퟮ킡뮯볆쯣ꆣ컄훐뷸탐쇋튻룶컊쳢복짙닢쫔ꎬ살쿻복뇤솿ꆣ컄훐뮹햹쪾쇋샻폃죕뺭225훐225횻막욱뗄볆쯣뷡맻ꆣ볆쯣쪱볤듓4쏫떽566쏫늻뗈ꆣ ퟜ뷡살쮵쎻폐튻룶잱퓚뗄볆쯣ힷퟙ횸쫽뫍볓잿횸쫽뗄쫽톧쒣탍쫇놻췪좫뷓쫜뗄ꆣ튻냣컄쿗뗄ퟷ헟뚼쫇뷢뻶쇋튻솽룶컊쳢ꎬ뺭뎣쎻폐룸돶쿪쾸뗄볆쯣뷡맻믲헟쪱볤튪쟳ꎬ늢쟒횻폃쇋ퟔ벺뗄쫽뻝ꎬ헢퇹쪹뗃룷룶뷡맻뿉뇈탔늻잿ꆣퟜ횮뛔폚ힷퟙ횸쫽뫍볓잿횸쫽뗄컄쿗쫇“럖룮뗄”ꎬ늻춬쒣탍ꎬ늻춬쫽뻝뗄뷡맻쫇뛀솢뗄ꆣ 놳뺰럧쿕퇐뺿쿖ힴ 놳뺰럧쿕쫇횸쓇킩늻쓜퓚뷰죚쫐뎡짏춨맽닺ퟩ뫏뷸탐럖즢뗄럧쿕(Baptista, 2008)ꆣ떱춶죋퓚ퟶ튻룶춶ퟩ뫏뗄뻶닟컊쳢쪱ꎬ늻뷶뷶튪쏦뛔ퟩ뫏럧쿕ꎬ뮹튪쏦뛔살ퟔ랽랽쏦쏦뗄놳뺰럧쿕ꎬ냼삨샍뚯솦쫕죫ꎬ쮽폐쫕죫ꎬ쪵컯닺짏뗄춶ꎬ틔벰튻킩늻뿉풤웚뗄럑폃뗈ꆣ퓚헢룶뿲볜쿂ꎬ튻냣볙짨퓚뷰죚쫐뎡뗄춶닺욷캪뷰죚닺ꎬ믲헟ퟩ뫏닺ꎬ믲헟붻틗닺ꆣ쓇쎴퓚뾼싇뷰죚닺춶ퟩ뫏뗄붨솢쪱ꎬ뻍튪붫놳뺰럧쿕쓉죫뾼싇뗄랶캧ꎬ놳뺰럧쿕뗄좱쪧믡뛔춶ퟩ뫏뗄붨솢뷡맻퓬돉펰쿬ꎨChonghui Jiang, Yongkai, 뫍 Yunbi An, 2010; Chiki Hara, James Huang, 뫍 Chistoph Kuzmics, 2009ꎩꆣ 듓von Neumann뫍Morgensternꎬ떽Arrow훰붥탎돉쇋닉폃킧폃몯쫽쒣탍뛔럧쿕뷸탐럖컶뗄샭싛쒣탍ꆣ떱튻룶룶쳥늻풸틢뷓쫜믲헟뛔폚죎뫎릫욽뗄뛄늩뚼컞쯹캽뗄쪱뫲ꎬ헢룶룶쳥춨뎣놻죏캪쫇럧쿕퇡뛱뗄ꆣ럧쿕퇡뛱뗄맛뗣뎤쪱볤틔살틑뺭돉캪퇐뺿럧쿕뗄믹뒡ꆣퟮ뷼ꎬEeckhoudt 뫍 Schlesingerꎨ2006ꎩ퓚컄헂훐닻쫶쇋Von Neumann-Morgenstern 킧폃몯쫽뗄솬탸떼쫽뿉틔펦폃퓚릺싲닊욱뗄뻶닟짏ꆣ떱좻ꎬ킧폃몯쫽뗄솬탸떼쫽뿉틔룸돶룼뛠맘폚뻶닟헟욫뫃뗄탅쾢ꎬ랴펳돶뛔럧쿕뗄룷훖 6
첬뛈ꆣ탎쪽짏ꎬ퓚웚췻킧폃쒣탍훐ꎬ뷷짷ꎨprudenceꎩꎬ뷚훆ꎨtemperanceꎩ뫍벱퓪(edginess)럖뇰뚨틥캪킧폃몯쫽죽뷗떼쫽캪헽횵ꎬ쯄뷗떼쫽캪뢺횵ꎬ컥뷗떼쫽캪헽횵ꆣ헢킩맛뗣퓚럇웚췻킧폃쒣탍훐튲볤뷓뗄돶쿖쇋ꎨBleichrodt 뫍 Eeckhoudtꎬ 2005ꎩꆣ뒫춳짏헢킩볙짨놻폃퓚뻶닟컊쳢ꎺ럖컶뷷짷춶헟뗄럀폹탔뒢탮뻶닟컊쳢ꎨKimballꎬ1990ꎩꎬ뷚훆춶헟퓚좱쪧놳뺰럧쿕뗄쟩뿶쿂뛔럧쿕닺뗄탨튪ꎨKimballꎬ1992ꎻGollier 뫍 Prattꎬ1996ꎩꎬ틔벰벱퓪춶헟퓚풤럀뚯믺짏뛔뛠풪럧쿕뗄랴펳ꎨLajeri-Chaherliꎬ2004ꎩꆣ믹폚뻟쳥뻶닟쒣탍뗄킧폃몯쫽죽뷗떼쫽ꎬ쯄뷗떼쫽뫍컥뷗떼쫽럻뫅뗄뷢쫍폫퓚욫뫃컞맘뗄뻟쳥뻶닟컊쳢훐뛾뷗떼쫽럻뫅뗄뷢쫍쫇룟뛈쿠맘뗄ꆣ떱뻶닟헟뇤뗃뢻폐쪱ꎬ죎뫎돌뛈뗄럧쿕럖첯뿉틔뷢쫍캪뛔늻샻룄뇤룼뗍뗄쏴룐탔ꎨMichel Denuit 뫍 Béatrice Reyꎬ2010ꎩꆣ뮻뻤뮰쮵ꎬ헢훖쏴룐탔폃킧폃몯쫽틧볛살뇭쪾ꎬ튲벴늻샻룄뇤잰뫳뗄웚췻킧폃뗄닮틬ꆣ샻폃Epstein 뫍Tannyꎨ1980ꎩ뚨틥뗄믹놾쿠맘탔퓶볓뇤뿉틔횤쏷뷷짷ꎬ뷚훆뫍벱퓪쫇믹폚퓚닆뢻퓶볓쪱4-ힴ첬닊욱훐뛔룅싊뿧뛈뗄퇡뛱ꆣ퓚쇭튻룶볙짨쿂ꎬ믹폚쇭튻룶튻냣욫뫃ꎬEeckhoudt 뫍 Schlesingeꎨr2006ꎩꎬ틔벰Eeckhoudt et al. (2009)튲퇩횤쇋뷷짷뫍뷚훆ꆣ퓚뗚튻욪컄헂훐쯻쏇쏨쫶캪뛔“pain disaggregation”뗄욫뫃ꎬ퓚뗚뛾욪컄헂훐쯻쏇틀삵“뫃쟩뿶뫍뮵쟩뿶뷡뫏”뗄쟷쫆ꆣ 튻냣ꎬ폃쿠뛔럧쿕퇡뛱ꎨrelative risk aversion (RRA)ꎩ뫍쿠뛔뷷짷ꎨrelative prudence (RP)ꎩ뗄쾵쫽횵살뿌뮭킧폃몯쫽뛾뷗떼쫽뫍죽뷗떼쫽ꆣ뛔폚쿠뛔럧쿕퇡뛱뛸퇔ꎨ탐캪쫇쿠뛔폚닆뢻뚨틥뗄ꎬ헢샯뗄닆뢻폃x뇭쪾ꎬ쿠뛔럧쿕퇡뛱뚨틥캪u(2)ꎨ(x)−xꎩꎬ웤쮮욽뗄훘튪탔틑뺭놻뫜뎤쪱볤맘힢떽쇋ꆣ쪵볊짏ꎬ튻쾵쇐뒦샭1u()(x)ퟩ뫏뻶닟ꎬ뒢탮뻶닟ꎬ믲헟믲폐쟳뎥쒣탍뗄컄쿗ꎨMitchell , 1994 뫍 Chiu and Madden , 2007)ꎬ쿔쪾퓚탭뛠쫂컯횮볤ꎬ뺭맽뇈뷏떥캻1뫍쿠뛔럧쿕퇡뛱쾵쫽ꎬ뇈뷏뺲첬뷡맻쫇쿠맘솪뗄ꆣ헢룶맛뗣뗄ퟮ뷼컄쿗쫇Meyerꎨ2005ꎩꆣ퓚좨틦틧볛횮쏕훐ꎬ쿠뛔럧쿕퇡뛱쾵쫽횵웰쇋맘볼탔뗄ퟷ폃ꆣ평폚뷷짷뗄맛뗣ꎨKimballꎬ1990ꎩ뇈럧(3쿕퇡뛱뗄맛뗣튪돶쿖뗄췭뫜뛠ꎬ쿠뛔뷷u)짷ꎨ뚨틥캪(x)−xꎩ뇈쿠뛔럧쿕퇡뛱룼u(2)(x)짙뗄퓚컄쿗훐뗃떽쳖싛ꆣ퓚쿖듦뗄짙쫽컄쿗훐죏캪쿠뛔뷷짷뗄뇪룋횵캪2ꎨChoi et 7
al. ꎬ2001ꎩꆣ퓚헢킩컄쿗훐쿔쪾ꎬ죧맻쿠뛔뷷짷뗄횵킡폚2ꎬ럧쿕쫕틦뗄퓶뎤믡뺭샺뛾뷗햼폅뇤ꎨGollierꎬ2001ꎩꆣWhiteꎨ2008ꎩ잿뗷쿠뛔뷷짷뫍2횮볤뗄쿠뛔뇈뷏쫇퓚튻룶쳖볛뮹볛뗄뿲볜쿂ꆣ틔짏헢킩컄쿗뗄쳖싛쮵쏷ꎬ쿠뛔럧쿕퇡뛱뫍떥캻1횮볤뗄뇈뷏ꎬ틔벰쿠뛔뷷짷뫍2횮볤뗄뇈뷏럖뇰쳥쿖쇋뛔럧쿕퇡뛱뫍뷷짷뗄맘힢돌뛈ꆣ퓚헢룶틢틥짏ꎬ뛔폚쿠뛔럧쿕퇡뛱뫍쿠뛔뷷짷뗄뇪룋횵떥캻1뫍2뿉틔붫뻶닟헟럖뇰솽샠ꎺ폐튻뗣럧쿕퇡뛱뫍뷷짷뗄뻶닟헟틔벰럇뎣럧쿕퇡뛱뫍뷷짷뗄뻶닟헟ꆣ 놾컄훷튪퇐뺿쓚죝 놾컄닉폃믬뫏헻쫽맦뮮뗄벼쫵랽램뷸탐횸쫽뢴훆퇐뺿ꆣ퓚횸쫽뢴훆맽돌훐ꎬ틽죫춶헟럧쿕욫뫃뗄룅쓮ꎬ헫뛔늻춬뗄춶헟ꎬ릹붨늻춬뗄뢴훆ퟩ뫏ꆣ튻샠럧쿕욫뫃룶쳥쫇럧쿕퇡뛱룶쳥ꎬ헢샠룶쳥ힷ쟳퓚뢴훆ퟩ뫏웚췻믘놨ퟮ듳뮯뗄잰쳡쿂ꎬퟮ킡뮯뢴훆ퟩ뫏뗄랽닮ꎬ믲헟퓚뢴훆ퟩ뫏랽닮ퟮ킡뮯뗄잰쳡쿂ꎬퟮ듳뮯뢴훆ퟩ뫏뗄웚췻믘놨ꎻ쇭튻샠럧쿕욫뫃룶쳥쫇뷷짷럧쿕퇡뛱룶쳥ꎬ헢샠룶쳥ힷ쟳퓚뢴훆ퟩ뫏웚췻믘놨튻뚨ꎬ랽닮튻뚨뗄잰쳡쿂ꎬퟮ듳뮯뢴훆ퟩ뫏뗄욫뛈ꆣ헫뛔헢솽훖샠탍뗄룶쳥ꎬ컄훐짨볆쇋솽룶뢴훆ퟩ뫏릹붨쒣탍——튻훖쫇믹폚CAPM떥틲쯘탎쪽뗄믘맩쒣탍ꎬ튻훖쫇뇪ힼ뻹횵—랽닮—욫뛈쒣탍ꆣ퓚솽듳샠쒣탍쿂폖폐튻킩ퟓ쒣탍ꎬ샻폃헢킩쒣탍릹붨ퟩ뫏ꎬ늢뛔ힷퟙ킧맻뷸탐쇋쮵쏷ꆣ 놾컄뗄뻟쳥뿲볜ꎺ놾컄뗚튻헂뻟쳥뷩짜쇋놾컄퇐뺿뗄놳뺰뫍틢틥ꎬ틔벰횸쫽뢴훆쿠맘쓚죝ꎬ냼삨횸쫽뢴훆뗄샭싛믹뒡ꎬ횸쫽뢴훆랽램럖샠ꎬ횸쫽뢴훆쯣램퇐뺿ꎻ뗚뛾헂훷튪뷩짜쇋솽랽쏦뗄쓚죝ꎬ웤튻쫇듓럧쿕욫뫃뫍킧폃몯쫽뗄뷇뛈닻쫶쇋놾컄뢴훆ퟩ뫏릹붨뗄믹놾풭샭ꎬ웤뛾쫇뷩짜쇋놾컄뢴훆ퟩ뫏릹붨뗄벼쫵랽램—헻쫽맦뮮쒣탍ꎬ뛔쒣탍룅쓮ꎬ쟳뷢뚼룸폨쿪쾸쮵쏷ꎻ뗚죽헂쳡돶쇋횸쫽뢴훆뗄뻟쳥쫽톧쒣탍ꎬ뛔럻뫅뗄뚨틥ꎬ풼쫸쳵볾뗄짨뚨ꎬ틔벰쒿뇪몯쫽뚼ퟶ쇋쿪쾸쮵쏷ꎻ뗚쯄헂쫇쪵퇩퇐뺿늿럖ꎬ폃쒣탍릹붨쇋뢴훆ퟩ뫏ꎬ늢룺ퟙ쇋뢴훆ퟩ뫏뗄ힷퟙ킧맻ꎻퟮ뫳튻헂쫇컄헂뗄ퟜ뷡ꎬퟜ뷡쇋좫컄ꎬ늢뷸탐쇋햹췻ꆣ 8
2 놳뺰럧쿕쿂횸쫽뢴훆쿠맘샭싛 횸쫽뢴훆쫽톧쒣탍 횸쫽뢴훆믹놾랽램 횸쫽뢴훆벼쫵룸폨횸쫽춶샭쓮쪵볹뗄뿉쓜ꎬ쫇쿻벫춶닟싔훐뫜훘튪뗄랽램ꎬ웤폐볡쪵뗄샭싛믹뒡ꆣ잰죋쳡돶뗄폐킧쫐뎡샭싛뫍춶ퟩ뫏샭싛룸쇋횸쫽뢴훆잿폐솦뗄횧돖ꆣ평폚폐킧쫐뎡뗄듦퓚ꎬ쪹뗃횸쫽춶뿉틔늻닮폚믽벫춶닟싔ꎬ캪횸쫽춶쳡릩쇋샭싛믹뒡ꎻ쿖듺닺ퟩ뫏샭싛뫍CAPM샭싛뇭쏷춶헟뗄폐킧춶ퟩ뫏쫇쫐뎡ퟩ뫏ꎬ뛸퓚튻뚨돌뛈짏ꎬ횸쫽쫇쫐뎡쟩뿶뇤뮯뗄ퟮ병쳥쿖ꎬ틲듋춶헟뗄ퟮ폅ퟩ뫏쫇쫐뎡횸쫽뗄ힷퟙꆣ평듋뿉볻ꎬ폐킧쫐뎡샭싛뫍ퟩ뫏샭싛캪횸쫽뢴훆쳡릩쇋잿듳뗄샭싛믹뒡ꆣ 릹붨ힷퟙퟩ뫏뗄랽램듳훂뿉틔럖캪죽샠ꎺ췪좫뢴훆ꆢ럖닣돩퇹뫍폅뮯톡퇹랽램ꆣ 1ꎩ췪좫뢴훆램 췪좫뢴훆쫇ힷퟙퟩ뫏릹붨훐ퟮ볲떥뗄랽램ꎬ벴룹뻝횸쫽릹돉ꎬ릺싲쫐뎡횸쫽훐쯹폐돉럖막ꎬ늢내헕쫐뎡횸쫽훐뗄좨훘살좷뚨ힷퟙퟩ뫏훐룷룶막욱뗄좨훘ꆣ웤폅뗣쫇볲떥ꎬ랽뇣닙ퟷꎻ랽램춸쏷틗폚샭뷢ꎬ죝틗놻춶헟뷓쫜ꎻퟮ뫃뗄쓢뫏쇋쫐뎡횸쫽ꎬힷퟙ컳닮ퟮ킡ꆣ쿠뛔폚폅뗣ꎬ췪좫뢴훆뗄좱뗣룼늻죝뫶쫓ꆣ쫗쿈쫇붻틗돉놾뗄뾼싇ꆣ릹붨ퟩ뫏맽돌틔벰쫐뎡횸쫽뗄뗷헻ꎬힷퟙퟩ뫏뚼쏦쇙듳솿막욱뗄싲싴ꎬ짦벰떽뻞듳뗄붻틗돉놾ꎬퟮ훕튲믡닺짺뷏듳뗄룺ퟙ컳닮돉놾ꎻ웤듎ꎬ쫐뎡횸쫽릹붨맽돌훐룼뛠뗄쫇뾼싇쫐뎡뗄헻쳥뇭쿖ꎬ틲듋뿉쓜냼몬튻킩쇷뚯탔늻룟뗄닺퓚돉럖막훐ꎬ쪹뗃릹붨ퟩ뫏늻틗닙ퟷꎬ믲헟쏦쇙릺싲돥믷돉놾ꆣ틲듋돽럇쫐뎡횸쫽돉럖막뫜짙ꎬ럱퓲닉폃췪좫뢴훆믡닺짺뷏룟뗄붻틗돉놾ꎬ짵훁뿉쓜뗖쿻췪좫뢴훆듸살뗄룟쓢뫏뛈ꆣ 2ꎩ럖닣돩퇹램 럖닣돩퇹쿈내헕튻뚨뗄뇪ힼ붫쫐뎡횸쫽뗄쯹폐돉럖막럖돉죴룉닣ꎬ쎿튻닣캪ퟜ쳥뗄튻룶퇹놾ꎬ룷룶닣횮볤뗄룶쳥횮볤쎻폐훘뢴ꆣ좻뫳내헕튻뚨뗄돩퇹랽램듓 9
룷룶닣훐돩돶튻뚨쫽솿뗄퇹놾ꎬ쯹폐닣뗄퇹놾릹돉ힷퟙퟩ뫏뗄ퟜ쳥ꆣ웤폅뗣퓚폚ꎺ쿠뛔폚췪좫뢴훆붵뗍쇋붻틗돉놾ꎻ뿉틔뇜쏢믲헟쿻돽튻킩틬뎣막뗄펰쿬ꎬ냼삨좱랦쇷뚯탔뗄막욱ꎬ듦퓚닆컱럧쿕뗄릫쮾막욱뗈ꆣ틲듋퓚쫐뎡횸쫽쪧헦믲헟룶뇰막욱늻쓜헽뎣붻틗뗈쟩뿶쿂ꎬ럖닣돩퇹쿠뛔폚췪좫뢴훆쓜릻룸돶튻룶룼ힼ좷뗄쓢뫏ꆣ떱좻ꎬ럖닣돩퇹튲듦퓚좱뗣ꎺힷퟙퟩ뫏뗄릹붨룼볓뢴퓓ꎬ룼쓑닙ퟷꎬ늢튪쪱쪱맘힢룺ퟙ컳닮ꎻ럖닣돩퇹짐쎻폐탎돉춳튻뗄뇪ힼꎬ돩퇹랽램늻릻춸쏷ꎬ뿉쓜떼훂춶헟뗄늻탅죎ꆣ 3ꎩ폅뮯톡퇹램 폅뮯톡퇹램쫇퓚럖컶쫐뎡횸쫽돉럖막쿠맘샺쪷쫽뻝뫍횸뇪뗄믹뒡짏ꎬ듓훐톡퓱쫊떱훖샠뫍쫽솿뗄횤좯릹붨ힷퟙퟩ뫏ꎬ살쓢뫏쫐뎡횸쫽ꆣ웤폅뗣퓚폚ꎺ폅뮯톡퇹램튻냣횻탨튪뷏짙쫽솿뗄횤좯살릹붨ힷퟙퟩ뫏ꎬ탨튪뷏짙뗄붻틗돉놾ꎻ톡퇹랽램룼볓뛠퇹ꎬ뿉틔듯떽늻춬뗄쒿뇪ꎬ뇈죧뿉틔쪹ힷퟙ컳닮ퟮ킡뮯ꎬ뿉틔뎬풽쫐뎡횸쫽뗄뇭쿖ꎨ튲뻍쫇춨뎣틢틥뗄볓잿횸쫽ꎩꎻ헽평폚톡퇹랽램뗄뛠퇹뮯ꎬ춶헟뿉톡퓱뗄랶캧룼맣ꎬ뿉틔틀뻝룶죋욫뫃톡퓱늻춬뗄톡퇹랽램ꆣ웤좱뗣ꎺퟩ뫏릹퓬맽돌뢴퓓ꎬ탨튪뢴퓓뗄쫽횵볆쯣뫍럖컶ꎬ틲듋볆쯣킧싊뫜훘튪ꆣ 틔짏뷩짜쇋ힷퟙ횸쫽릹돉뗄죽훖훘튪랽램ꎬ룷폐폅쇓ꆣ퓚톧헟뗄퇐뺿훐ꎬퟮ뛠뗄쫇맘폚폅뮯톡퇹램ꎬ웤뿉랢햹뿕볤튲ퟮ듳ꎬ놾컄튲쫇훂솦폚퇐뺿튻훖폅뮯톡퇹램ꎬ틲듋쿂쏦뗄쯣램퇐뺿뷼뿶ꎬ훘튪쫇헫뛔폅뮯톡퇹램ꆣ 횸쫽뢴훆쫽톧쒣탍 쫗쿈컒쏇맛달N훖막욱퓚쪱볤0,1,...,T뗄볛룱ꎬ틔벰놻ힷퟙ횸쫽퓚헢룶쪱볤뛎뗄뇭쿖ꆣ컄훐훂솦폚좷뚨ힷퟙퟩ뫏ퟮ폅릹돉ꎬK횻막욱뗄톡퓱ꎨK<Nꎩ,틔벰헢킩막욱뗄쫽솿믲헟춶뇈샽ꆣ횸쫽뢴훆훐짦벰뗄훷튪뇤솿폐ꎺeꎬힷퟙퟩ뫏훐좷뚨i춶막욱i뗄ퟮ킡춶뇈샽ꎻdꎬힷퟙퟩ뫏훐좷뚨춶막욱i뗄ퟮ듳춶뇈샽ꎻYꎬii떱잰ힷퟙퟩ뫏훐막욱i뗄막쫽ꎻVꎬ쪱볤t막욱i뗄볛룱ꎻIꎬ쪱볤t횸쫽뗄볛횵ꎻRꎬittt쪱볤t횸쫽떥웚뗄솬탸믘놨싊ꎬ샽죧R=ln(I/I−1)ꎻrꎬ쪱볤t막욱i뗄떥웚솬탸tttit 10
믘놨싊ꆣ샽죧r=ln(V/V1)ꎻCꎬ떱잰ititit−쪱볤Tힷퟙퟩ뫏[X]뗄ퟜ볛횵∑nXV볓i=1iiti짏쿖뷰뗄뇤뮯ꎨ냼삨쿖뷰뗄탂춶죫틔벰쿖뷰뗄뎷돶ꎩꎬ튲뻍쫇릹붨탂뗄ힷퟙퟩ뫏쪱뿉틔쪹폃뗄ퟜ뗄뷰솿ꎻsfꎬ폃럖쫽뇭쪾퓚쪱볤T싴돶튻떥캻막욱i뗄돉놾ꎻbfꎬii폃럖쫽뇭쪾퓚쪱볤T싲죫튻떥캻막욱i뗄돉놾ꎻgꎬC훐뿉틔폃폚ퟷ캪붻틗럑폃뗄뇈샽쿞훆ꎨ0≤g≤1ꎩꎻyꎬ퓚탂뗄ힷퟙퟩ뫏훐막욱i뗄막쫽ꎻGꎬ싲죫믲헟싴돶막ii욱랢짺뗄붻틗럑폃ꆣힷퟙퟩ뫏뗄놸톡막욱뿉틔쫇쯹폐N횻막욱훐뗄튻훖ꎬ횻튪헢횻막욱뻟폐샺쪷볛룱벯뫏[V]ꆣ it뢴훆ퟩ뫏뗄붨솢쪵볊뻍쫇튻룶ퟮ폅뮯컊쳢ꎬ짨뚨튻룶쒿뇪몯쫽ꎬ퓚튻킩풼쫸쿂듯떽쒿뇪몯쫽ꆣ뿉틔쮵ꎬ퓚폅뮯컊쳢훐ꎬ풼쫸쳵볾쫇튻룶뫜훘튪뗄늿럖ꆣ풼쫸쳵볾뿉틔뿌뮭뷰뗄쿞훆ꎬ돉놾뗄쿞훆ꎬ짵훁춶죋뗄욫뫃ꎬ횻튪뻟폐쓜릻솿뮯뗄튻킩쳘탔ꆣ쿂쏦뷩짜횸쫽뢴훆믹놾쒣탍훐뺭뎣짦벰떽뗄튻킩풼쫸쳵볾ꆣ N ∑z=K () ii=1 ez≤yVT/C≤dz i=1,...,N () iiiiii G≥fb(y−Y)V 1,...iiiiiTi=,N () G≥s f(Y−y)V i=1,...,N () N ∑G≤gC () ii=1NN ∑yV=−iiTC∑Gi () =1=1 y,G≥0 i=1,...,N () ii z∈[0,1] i=1,...,N () i풼쫸ꎨꎩ놣횤쇋탂뗄ힷퟙퟩ뫏훐폐K횻막욱ꎻ풼쫸ꎨꎩ쏨쫶쇋죧맻튻횻막욱i쎻폐퓚탂뗄ힷퟙퟩ뫏훐퓲y쫇0ꎬ죧맻막욱i냼삨퓚탂뗄ힷퟙퟩ뫏훐웤뇈샽싺i 11
ퟣ튪싺ퟣퟮ듳춶뇈샽뫍ퟮ킡춶뇈샽뗄튪쟳ꎻ풼쫸ꎨꎩ뫍ꎨꎩ뚨틥쇋붻틗돉놾ꎬ뻍쫇싲싴막욱뗄붻틗돉놾튪킡폚뗈폚퓊탭뮨럑뗄ퟜ뗄붻틗돉놾ꎻ풼쫸ꎨꎩ쿞훆쇋ퟜ뗄붻틗돉놾ꎻ풼쫸ꎨꎩ쫇튻룶뻹뫢뗈쪽ꎬ놣횤T쪱볤탂뗄ힷퟙퟩ뫏뗄횵뗈폚떱잰ힷퟙퟩ뫏뗄횵볓짏쿖뷰룄뇤복좥ퟜ뗄붻틗돉놾ꎻ풼쫸ꎨꎩ횻쫇놣횤쇋뇤솿뗄뺭볃톧틢틥ꎻ풼쫸ꎨꎩ뚨틥쇋z뗄0-1뇤솿쳘뗣ꆣ i퓚횸쫽뢴훆훐뮹짦벰떽튻룶훘튪뗄늿럖ꎬ뻍쫇횸쫽뢴훆킧맻뗄뛈솿ꎬ뿉틔톡퓱룺ퟙ튵벨ꎬ룺ퟙ컳닮ꆣ떱좻ꎬ룺ퟙ컳닮풽킡ꎬ쮵쏷뢴훆ퟩ뫏뗄룺ퟙ킧맻풽뫃ꆣ쿖퓚톧헟닉폃뗄뢴훆킧맻뛈솿랽램훷튪럖캪솽샠ꎬ뗚튻샠붫뢴훆ퟩ뫏폫쒿뇪횸쫽쫕틦싊횮볤닮틬뗄랽닮ퟷ캪룺ퟙ컳닮뚨틥ꎬ죧Rollꎨ1992ꎩꆣ튻킩뫳쏦뗄톧헟뛔룃훖뛈솿랽램뷸탐쇋뷸튻늽탞헽ꎬ죧BeasleyꎬMeade뫍Changꎨ2003ꎩꆣ쯻쏇죏캪내헕헢룶뚨틥ꎬ죧맻뢴훆ퟩ뫏폫쒿뇪횸쫽쫕틦횮볤뗄닮횵캪뎣쫽ꎬ웤랽닮뇘좻캪쇣ꎬ쓇쎴ힷퟙ컳닮캪쇣ꎬ쿔좻늻뫏쟩샭ꆣ틲듋쯻쏇죏캪펦룃닉폃뢴훆ퟩ뫏폫쒿뇪횸쫽쫕틦싊횮볤닮틬욽랽뫍좡뻹횵ퟷ캪룺ퟙ컳닮ꆣ뗚뛾샠뛈솿랽램쫇붫뢴훆ퟩ뫏폫쒿뇪횸쫽쫕틦횮볤뗄쿟탔닮틬ퟷ캪룺ퟙ컳닮ꎬ죧Rudolfꎨ1999ꎩꎬ쳡돶쇋쯄훖쿟탔뛈솿쒣탍ꎬ늢죏캪쿟탔탎쪽뇈뛾듎욽랽뫍탎쪽룼뷓뷼쿖쪵ꆣ놾컄훷튪뾼싇뗄뛈솿룺ퟙ컳닮랽램죧쿂ꎺ 쫗쿈쫇룺ퟙ컳닮욫닮ꎨTracking Differenceꎬ볲킴캪TDꎩ뗄룅쓮ꎬ쫇뢴훆ퟩ뫏t쫕틦싊폫놻ힷퟙ횸쫽쫕틦싊뗄닮횵ꎬ튻냣쫇룺ퟙ컳닮ퟮ볲떥뗄튻훖뇭쪾탎쪽ꆣ폃릫쪽뿉틔뇭쪾돉 K∑VyitiI TD=g=1tlologteKe () ∑VyIt−1it−1ii=1쿂쏦틽죫룺ퟙ욫샫뛈ꎨTracking Errorꎬ볲킴캪TEꎩ뗄룅쓮ꎬ웤쫇횸뢴훆ퟩ뫏쫕틦싊폫놻ힷퟙ횸쫽쫕틦싊죕닮횵뗄뇪ힼ닮ꎬ헢훖랽램쫇뛈솿룺ퟙ컳닮뗄ퟮ뎣폃횸뇪ꎬ놻맺쓚췢웕뇩닉폃ꆣ룃랽램쫇튻훖쿠뛔뗄랽램ꎬ쫇룺ퟙ컳닮욫닮뗄늨뚯싊ꎬ웤뻟쳥볆쯣릫쪽죧쿂 12
T∑2(TD−TDt)TE=t=1 () T−1T∑TDt웤훐TD=t=1ꎬT쫇볆쯣쟸볤ꆣ헢퇹볆쯣돶뗄쫇죕룺ퟙ컳닮ꎬ퓚쪵컱훐ꎬT뿉틔폃TE돋틔250뗄욽랽룹뗃떽쓪룺ퟙ컳닮ꆣ 놳뺰럧쿕틔벰뷷짷뗄춶헟 횸쫽뢴훆ퟩ뫏뗄붨솢춬튻냣닺ퟩ뫏뗄붨솢튻퇹ꎬ뿉틔샭뷢캪퓋돯톧훐뗄뛠쒿뇪맦뮮ꎬ붫웤훐뗄튻킩쒿뇪풼쫸퓚쒳튻쮮욽믲헟쒳튻쟸볤ꎬ쟳뷢웤쯻튻룶쒿뇪뗄ퟮ폅뮯ꎬ벴튻룶떥쒿뇪ퟮ폅뮯컊쳢ꆣ쟳뷢돶살뗄ퟮ폅뷢뻍쫇쒿뇪맦뮮뗄폐킧뷢ꆣ 맘폚춶ퟩ뫏붨솢뗄폅뮯쒣탍폐탭뛠훖ꎬ샽죧킧폃몯쫽쒣탍ꎬ뻹횵—랽닮쒣탍ꎬ뻹횵—VaR쒣탍틔벰뫳살뗄뻹횵—CVaR쒣탍뗈ꆣ놾컄훷튪닉폃뗄웚췻킧폃쒣탍ꆣ룃쒣탍ퟷ캪뺭뗤뗄춶ퟩ뫏폅뮯쒣탍ꎬ쫇볙짨쎿룶춶죋뚼뻟폐튻룶킧폃몯쫽ꎬ춶죋틀뻝킧폃몯쫽뗄ퟮ폅뮯뷸탐춶뻶닟ꆣ뻟쳥살쮵ꎬ뻍쫇춶죋퓚튻뚨뗄풼쫸쳵볾쿂ꎬ톰헒튻룶춶ퟩ뫏ꎬ쪹ퟔ벺뗄웚췻킧폃듯떽ퟮ듳뮯ꆣ 늻좷뚨쳵볾쿂쿖듺횤좯ퟩ뫏톡퓱샭싛뫜듳돌뛈짏쫇틔킧폃풤웚킧폃샭싛캪믹뒡뗄ꎬ웤쒿뇪컞럇쫇쪹춶헟뗄풤웚킧폃ퟮ듳ꎬ믲헟뷡뫏킧폃ퟮ듳뮯풭샭틔벰춶죋뗄룶죋럧쿕욫뫃좷뚨뗄쒿뇪몯쫽ꆣ 춶ퟩ뫏붨솢쪱ꎬ뫶싔놳뺰럧쿕믡뛔ퟩ뫏뗄붨솢뷡맻닺짺펰쿬ꆣ떱튻룶룶쳥늻풸틢뷓쫜믲헟뛔폚죎뫎릫욽뗄뛄늩뚼컞쯹캽뗄쪱뫲ꎬ헢룶룶쳥춨뎣놻죏캪쫇럧쿕퇡뛱뗄ꆣ럧쿕퇡뛱뗄맛뗣뎤쪱볤틔살틑뺭돉캪퇐뺿럧쿕뗄믹뒡ꆣ퓚볙뚨웚췻킧폃뗄뿲볜쿂ꎬ럧쿕퇡뛱틢캶ퟅvon Neumann-Morgenstern킧폃몯쫽쫇낼뗄ꎬ믲헟뿉캢뗄ꎬ쟒뛾뷗떼쫽킡폚0ꆣ힢틢떽ꎬ믹놾럧쿕퇡뛱뗄뚨틥횻짦벰떽킧폃몯쫽뗄뛾뷗떼쫽ꆣ탂뷼맘폚“뷷짷”럧쿕퇡뛱틑뺭돉캪튻룶놻웕뇩뷓쫜뗄볙짨ꆣ뛔폚뷷짷럧쿕퇡뛱뗄뚨틥쫇헢퇹뗄ꎬ퓚럧쿕퇡뛱뗄믹뒡짏ꎬ뚨틥뇟볊킧폃쫇춹뗄ꎬ튲벴죽듎떼쫽듳폚0ꎬ춬쪱튻킩톧헟튲춨맽춶헟뗄탐캪뛔“뷷짷”뷸탐쇋뚨틥ꆣ뷷짷럧쿕퇡뛱뗄 13
춶헢뛔헽쿲욫뛈뻟폐욫뫃ꆣ 볙짨R(=1,ꆭ,n)쫇듺뇭닺S(1,ꆭ?n)쫕틦싊뗄쯦믺뇤솿ꆣ춬쪱볙짨jjx=(x1,ꆭ?xn)쫇춶ퟩ뫏쿲솿ꎬ웤훐x듺뇭퓚닺S짏뗄춶뇈샽ꆣ폐쿂쏦뗄뇭jj듯쪽ꎺ X={x∈Rn:Ax=b,x≥0} () 웤훐A∈Rm×nꎬb∈RmꎬX쫇튻룶뿉틔춶벯뫏ꆣ 뛔폚춶벯훐뗄튻룶ퟩ뫏ꎬx∈X뗄춶믘놨R(x)폐죧쿂뗄뇭쪾ꎺ n R(x)=∑Rx () jjj=1죧맻볙짨킧폃몯쫽U(x)쫇뇭쪾폫ퟩ뫏x쿠맘뗄킧폃뇭쪾ꆣ쓇쎴킧펦몯쫽U붫쫇춶ퟩ뫏믘놨R(x)뗄몯쫽뇭쪾ꎬ벴 U(x)=u(R(x)) () 뛔믘놨R(x)뗄웚췻ퟶ죧쿂볙짨 E(R(x))=r(x) () 뛔킧폃몯쫽u(R(x))퓚웤웚췻횵r(x)뢽뷼뷸탐첩샕햹뾪ꎬ폐쿂쏦뗄뷡맻 ∞=+∑(k)k u(R(x))u(r(x))u(r(x))(R(x)−r(x))k! () k=1퓙뛔짏쏦뗄햹뾪쪽솽뇟좡웚췻폐 ∞uR=+kkE() ((x))u(r(x))u(r(x))E(R(x)−r(x))k!.16) ∑ (2k=1쿂쏦튻뷚붫냑횸쫽뢴훆폫럧쿕뷡뫏웰살ꆣ 14
놳뺰럧쿕쿂횸쫽뢴훆쒣탍 럧쿕퇡뛱쿂횸쫽뢴훆 퓚튻킩쟩뿶쿂ꎬ뛔킧폃몯쫽쟳뷢ퟮ폅횻탨튪햹뾪떽뛾듎떼쫽ꎬ튲벴뛔킧폃몯쫽뗄뛾뷗뇆뷼ꆣ뛔폚ꎨꎩ쪽ꎬ죧맻뗈쪽폒뇟횻햹뾪떽킧폃몯쫽뗄뛾듎떼쫽ꎬ폐 EuR=+(1)1(2xurxurxERx−rx+u) (())(())(())()()(r(x))v(x) () 2웤훐 2 v(x)=E(R(x)−r(x)) () 쿔좻ꎬꎨꎩ쪽뗈쪽폒뇟뗚뛾쿮캪쇣ꆣ쓇쎴ꎨꎩ쪽뻍뇤돉쇋쿂쏦뗄쪽ퟓ 1EuRx=urx+u(2) (())(())(r(x))v(x) () 2헢룶쪱뫲웚췻킧폃뗄몯쫽횵뷶좡뻶폚솽룶틲쯘ꎬ튻룶쫇ퟩ뫏쫕틦싊뗄웚췻ꎬ튻룶쫇ퟩ뫏쫕틦싊뗄랽닮ꆣ헢훖쟩뿶쿂킧폃몯쫽쒣탍폫Markowitz뗄뻹횵—랽닮쒣탍퓚킧맻짏벸뫵쎻폐닮틬ꆣ뻟쳥뛸퇔ꎬ죧맻춶죋쫇럧쿕퇡뛱뗄ꎬ떱ퟩ뫏뗄쫕틦싊쫇쇣뗄쪱뫲ꎬ웤킧폃쮮욽캪쇣ꎬ쯦ퟅퟩ뫏쫕틦싊뗄퓶볓ꎬ웤킧폃쮮욽믡퓶볓ꎬ떫퓶볓뗄쯙뛈좴믡뇤싽ꆣ튲뻍쫇쮵ꎬ쯦ퟅ춶죋뿉틔믱뗃쫕틦싊뗄퓶볓ꎬ쎿떥캻쫕틦싊듸살뗄킧폃좴쫇복짙뗄ꎬ헢룶폫캢맛뺭볃톧훐뗄뇟볊킧폃뗝복쫇튻훂뗄ꆣ퓚헢훖쟩탎쿂ꎬ킧폃몯쫽뗄뛾뷗떼쫽u(2)(r(x))p0ꆣ뻹횵—랽닮쒣탍훐ꎬ랽닮쫇폃살뛈솿럧쿕뗄ꎬ룃쒣탍뗄ퟮ폅뮯쫇ퟩ뫏쫕틦싊랽닮튻뚨뗄쟩뿶쿂ꎬ벴럧쿕튻뚨ꎬퟮ듳뮯ퟩ뫏쫕틦싊뗄뻹횵ꎬ믲헟ퟩ뫏쫕틦싊뻹횵튻뚨뗄쟩뿶쿂ꎬퟮ킡ퟩ뫏쫕틦싊뗄랽닮ꎬ벴ퟮ킡럧쿕ꆣ퓚u(2)(r(x))p0뗄쟩뿶쿂ꎬ쟳뷢ꎨꎩ쪽웚췻킧폃ퟮ듳뮯뻍쫇ퟮ듳뮯쫕틦싊뗄뻹횵ꎬ믲헟ퟮ킡뮯쫕틦싊뗄랽닮ꆣ 놾컄훐닉폃뗄쒿뇪몯쫽늻쫇횱뷓뗄쫕틦믲헟랽닮ꎬ뛸쫇솽룶쿠맘뗄룅쓮ꆣ헢샯튪틽죫CAPMꎨcapital asset pricing modelꎬ놾닺뚨볛쒣탍ꎩ뚨볛릫쪽ꆣ헢샯뛔CAPM릫쪽뗄췆떼늻ퟷ쿪쾸뗄쮵쏷ꎬ횱뷓틽폃웤탎쪽ꆣ퓚춨뎣뗄쪵횤럖컶훐ꎬCAPM쒣탍폐벸훖뇤탎탎쪽뿉틔놻닉폃ꎬ웤훐튻훖샻폃싊뇈뷏룟뗄뻍쫇떥틲쯘쒣탍ꎬ믲헟돆ퟷ쫐뎡쒣탍ꎬ웤뇭듯쪽 15
~ R=a+bjRM+e () jj웤훐R쫇럧쿕닺~S뗄쫕틦싊ꎬRM쫇쫐뎡ퟩ뫏뗄쫕틦싊ꎻe듺뇭뻹횵쫇0jjj뗄쯦믺컳닮쿮ꎬ웤랴펳쇋럧쿕닺S뗄럇쾵춳럧쿕ꎬ폐j~E(e)=0,covR,e=0,cov(e,e)=0맘쾵돉솢ꎻa쫇떥틲쯘쒣탍믘맩뗄뷘뻠jMjjij쿮ꎬ웤듺뇭럧쿕닺S폫쫐뎡ퟩ뫏늻쿠맘뗄쫕틦싊ꎬ뗈폚닺뗄럇맦퓲쫕틦싊뗄j뻹횵ꎻb싺ퟣ쿂쏦뗄맘쾵 jsb=jM () js2M웤듺뇭럧쿕닺S뗄쫕틦싊쿠뛔폚쫐뎡쫕틦싊뗄쏴룐돌뛈ꆣ퓚CAPM뗄볙짨j쿂ꎬ폐a=(1−b)R뗈쪽돉솢ꆣ떱뗈쪽늻돉솢쪱ꎬ틢캶ퟅ쫐뎡뛔럧쿕닺뗄쫕틦jjf싊듦퓚룟맀믲헟뗍맀뗄쟩뿶ꆣ 짏쏦럖컶뗄쫇떥룶럧쿕닺뗄쟩뿶ꎬ떱럧쿕닺S(1,ꆭ?n)릹돉튻룶ퟩ뫏쪱ꎬjퟩ뫏좨훘쿲솿캪x=(x1,ꆭ?xn)ꎬ럧쿕닺ퟩ뫏뗄a뫍b싺ퟣꎬ n a=∑xa () jjj=1n b=∑xb () jjj=1듓짏쏦뷩짜뗄헢킩맘쾵뿉틔뗃떽ퟩ뫏닺뗄튻뷗뻘—뻹횵ꎬ뛾뷗뻘—랽닮폫CAPM쒣탍훐뗄a뫍b퓚듦퓚쓚퓚솪쾵ꎬ웤뇤뚯랽쿲쫇튻훂뗄ꆣ틲듋ꎬ퓚ퟮ폅ퟩ뫏붨솢뗄맽돌훐ꎬ풼쫸쳵볾믲헟쒿뇪몯쫽훐뛔뻹횵뫍랽닮뗄튻킩쿞훆믲헟튪쟳뿉틔뮯돉캪뛔a뫍b뗄쿞훆믲헟튪쟳ꎬ퓚쒳킩쟩뿶쿂랽뇣컊쳢뗄쟳뷢ꆣ놾컄훐쓢닉폃헢훖랽램ꆣ 16
뷷짷럧쿕퇡뛱쿂횸쫽뢴훆 튻냣쟩뿶쿂ꎬ뻹횵—랽닮쒣탍쟳뷢춶ퟩ뫏ퟮ폅뮯컊쳢틑뺭ퟣ릻ꆣ떫쫇늻뿉뇜쏢ꎬ폐쪱쿠뛔폚킧폃몯쫽뛸퇔ꎬ뷶뷶맀볆닺쫕틦싊럖늼몯쫽뗄튻뷗뻘뫍뛾뷗뻘쫇늻릻뗄ꎬ늻쓜췪헻뗄뷸탐킧폃몯쫽럖컶ꎻ쇭췢폐쪱늻춬뗄춶죋뿉쓜폐늻춬뗄럧쿕욫뫃ꎬ믡뛔쫕틦싊럖늼몯쫽뗄룟뷗뻘듦퓚튪쟳ꎬ폈웤쫇뛔죽뷗뻘탎쪽—욫뛈뗄욫뫃ꆣ샽죧Maghrebiꎨ1992ꎩ샻폃TSE뗄쫽뻝퇩횤쇋춶죋뛔쫕틦싊몯쫽욫뛈뗄욫뫃뫍볡돖ꎬ쯻뗄컄헂훐쳡떽춶죋쾲뮶욫뛈캪헽뗄춶ퟩ뫏ꎬ뛸쟒죧맻쒳웚볤뗄욫뛈캪헽횵ꎬ쿂튻룶웚볤붫믡캬돖욫뛈뗄헽횵ꎬK. Muralidharꎨ1993ꎩ뗄컄헂훐ퟷ돶쇋쿠쯆뗄쏨쫶ꆣ 맘폚죽뷗뻘뗄퓚ퟩ뫏폅뮯훐뗄훘튪탔쫇평Samuelsonꎨ1958ꎩ퓚짏쫀볍50쓪듺쫗쿈쳡돶뗄ꎬ떫쫇퓚맽뫳뗄뫜뎤튻뛎쪱볤뚼쎻폐탎돉뛔죽뷗뻘뗄뚨솿럖컶ꎬ횱떽짏쫀볍80쓪듺ꆣ웤훐뗄풭틲냼삨틔쿂벸뗣ꎬ웤튻쫇떱닺ퟩ뫏훐돉럖쫽솿ꎬ벴n뫜듳쪱ꎬ뎬맽벸냙쪱ꎬ죽뷗뻘뗄맀볆뫜삧쓑ꎻ웤뛾쫇죽뷗뻘놾짭늻쫇춹몯쫽ꎬ헢퇹폃뇪ힼ뗄볆쯣랽램뫜쓑쟳뷢죽뷗뻘뗄ퟮ폅횵ꎻ웤죽쫇퓚퓊탭솬탸붻틗뗄쟩뿶쿂ꎬ뻹횵—랽닮쒣탍틑뺭ퟣ릻잿듳ꎬ튻냣쟩뿶쿂쟳뷢ퟩ뫏ퟮ폅뮯컊쳢틑뺭ퟣ릻ꆣ 떫쫇헢킩풭틲늢쎻쓜ퟨ횹헢룶쇬폲뗄랢햹ꆣퟮ쿈붫욫뛈뚨솿럖컶쓉죫ퟮ폅ퟩ뫏붨솢뗄쫇뻸뛔뻹횵욫닮욫뛈쒣탍ꎨmean-absolute-deviation-skewness modelꎬMADSꎩ쒣탍ꎨH. Konno뫍H. Yamazaki, 1993ꎩ뫍뻹횵—랽닮—욫뛈쒣탍ꎨmean-variance-skewness model, MVSꎩꎬ헢쫇퓚짏쫀볍90쓪듺ꎬ퓚컄훐틔뻹횵뫍폃랽닮뇭쪾뗄럧쿕틔벰뻸뛔욫샫ퟷ캪풼쫸ꎬퟮ듳뮯춶ퟩ뫏뗄욫뛈ꆣ헢킩퇐뺿훐뚼뛔죽듎몯쫽ퟶ쇋럖뛎쿟탔뇆뷼ꆣ퓚1998쓪ꎬH. Konno, T. Suzuli뫍D. Kobayashiꎨ1998ꎩ룸돶쇋쟳뷢MADS쒣탍뷢뗄럖횧뚨뷧쯣램ꆣ헢킩랽램퓚놣횤볆쯣솿퓶볓폐쿞뗄쳵볾쿂ꎬ쪹뗃샻폃죽뷗뻘붨솢ퟮ폅ퟩ뫏뇤돉뿉쓜ꆣ 짏쏦뛔죽뷗뻘ퟶ쇋헢쎴뛠뷩짜ꎬ쿂쏦뻟쳥듓킧폃몯쫽쒣탍훐틽죫죽뷗뻘뫍욫뛈룅쓮ꆣ쫗쿈뛔킧폃몯쫽ퟶ튻룶볙짨 볙짨ꎺ킧폃몯쫽U(R)쫇튻룶뗝복뗄럧쿕퇡뛱몯쫽ꎬ벴퓚쟸폲R(x),x∈X 17
훐ꎬU(R)싺ퟣu(1)Rf0u(2)Rpu(3)(),()0,(R)f0ꆣ 잰쏦뗄뗈쪽ꎨꎩ폐 ∞ Eu(R(k)k(x))u(r(x))∑u(r(x))E(R(x)r(x))k! =+−k=1붫헢룶뗈쪽폒뇟햹뾪떽죽뷗뻘ꎬ폐 EuRx=urx+u(2)(())(())(r(x))v(x)2+u3(r(x))k(x)6 () 웤훐2v(x)=E(R(x)−r(x))틑뺭퓚ꎨꎩ쪽훐뷸탐쇋쮵쏷ꎬ 3 k(x)=E(R(x)−r(x)) () 폐쇋볙짨ꎬ뛔뗈쪽ꎨꎩ뗄킧폃쟳뷢ퟮ듳횵ꎬퟔ좻냼삨k(x)쿮뗄ퟮ듳ꆣ퓚1998쓪ꎬH. Konno, T. Suzuli뫍D. Kobayashi뗄컄헂훐틑뺭룸돶쇋욫뛈뗄뚨틥쪽ꎬ벴욫뛈K캪 k(x) P= () {32v(x)}쿔좻욫뛈쫇튻룶폫죽뷗뻘횱뷓쿠맘뗄룅쓮ꎬ싺ퟣ쇋욫뛈뗄ퟮ듳뮯ꎬ튲벴싺ퟣ쇋죽뷗뻘뗄ퟮ듳뮯ꎬ싺ퟣ쇋뗝복럧쿕퇡뛱룶쳥뛔폚킧폃몯쫽뗄욫뫃ꆣ 헢튻랽램떼훂뗄횱뷓뷡맻뻍쫇뢴훆ퟩ뫏뻟폐튻뚨헽욫뛈ꎬ헢튻탔훊믡폐퓵퇹뗄펰쿬ꎿ잰컄쳡떽쇋CAPM뗄떥틲쯘뇭듯쪽ꎬ헢샯틽폃튻쿂웤튻냣뇭듯쪽 E(R)=r+b(E(R)−rf) () ifm웤훐E(R)쫇막욱i뗄웚췻쫕틦싊ꎬr쫇컞럧쿕샻싊ꎬE(Rm)쫇쫐뎡뗄웚췻쫕if틦싊ꆣꎬ폐쇋헢룶쒣탍ꎬ막욱i뗄뎬뛮쫕틦a뿉틔뇭쪾캪 i a=R−r+bE(R−rf(m)iif) () 춬샭ꎬ뿉틔뚨틥튻룶춶ퟩ뫏X뗄뎬뛮쫕틦aXꎬ aX=RX−rf+bX(E(Rm)−rf) () 18
죧맻볙짨횸쫽뗄쫕틦폫쫐뎡쫕틦쫇뗈볛뗄ꎬ뿉틔춨맽싴뿕막횸웚믵살뛔돥헢늿럖럧쿕ꆣ헢훖춨맽ퟶ뿕웚믵믲헟ퟶ뛠쿖믵ꎬ럖샫돶a뗄닟싔놻돆ퟷ낢뛻램닟싔ꆣ헢룶닟싔쫇릹붨튻룶쓜릻닺짺헽뗄뎬뛮믘놨뗄춶ퟩ뫏ꎬ좻뫳ퟶ뿕막횸웚믵럖샫돶춶ퟩ뫏뗄뎬뛮믘놨ꎬ벴낢뛻램ꆣ헢훖뻹횵—랽닮—욫뛈쒣탍뿉틔뗃떽헽뗄뎬뛮믘놨ꎬ틲듋뿉틔폃살릹붨낢뛻램닟싔ꆣ 잰컄틑뺭뛔놾컄뢴훆ퟩ뫏붨솢훐쓢닉폃풼쫸쳵볾뫍쒿뇪몯쫽뗄뺭볃톧놳뺰ퟶ쇋쿠맘뷩짜ꎬ쿂쏦뗄늿럖붫훘뗣뷩짜놾컄ퟮ폅뮯쟳뷢붫닉폃뗄랽램——믬뫏헻쫽쿟탔맦뮮ꆣ 놾헂킡뷡 놾헂훷튪뷩짜쇋횸쫽뢴훆뗄믹놾쫽톧쒣탍틔벰뢴훆ퟩ뫏붨솢뗄샭싛놳뺰ꆣ맘폚횸쫽뢴훆뷩짜쇋웤믹놾랽램ꎬ믹놾쒣탍틔벰룺ퟙ컳닮뗄뛈솿ꆣ뛔폚샭싛놳뺰ꎬ놾컄훷튪쫇듓ퟩ뫏쫕틦싊킧폃몯쫽뗄캪쟐죫뗣ꎬ뷡뫏놳뺰럧쿕뗄룅쓮ꎬ퓚ퟩ뫏붨솢뗄맽돌훐뾼싇떽쇋ퟩ뫏쫕틦싊뗄튻뷗뻘ꎬ뛾뷗뻘ꎬ틔벰죽뷗뻠ꎬ뫋탄쮼쿫쫇웚췻킧폃뗄ퟮ듳뮯ꆣ훐볤짦벰떽튻킩맘폚춶죋욫뫃뗄볙짨ꎬ헢킩쫇ퟩ뫏붨솢뗄틢틥쯹퓚ꎬ뾼싇늻춬룶쳥뗄럧쿕욫뫃ꎬ톡퓱늻춬ퟩ뫏붨솢랽쪽ꆣ 19
3 믬뫏헻쫽맦뮮횸쫽뢴훆 믬뫏헻쫽맦뮮쒣탍 ퟮ폅뮯뗄샭싛뫍쯣램쫇퓋돯톧뗄튻룶훘튪럖횧ꎬ웤퇐뺿죧뫎퓚튻킩풼쫸쳵볾쿂ꎬ듓훚뛠랽낸훐톡퓱ퟮ폅뗄뿉탐랽낸ꆣ헢샠컊쳢벸뫵퓚룷룶톧뿆쇬폲뚼듦퓚ꎬ헢퇹퓚뫜뛠컊쳢훐ꎬ샽죧릤뎧톡횷ꎬ죋풱업냠ꎬ퓋쫤쿟슷짨볆뗈ꎬ뺭뎣돶쿖헻쫽뇤솿ꆣ퓚맦뮮컊쳢훐뇤솿좫늿믲늿럖쫇헻쫽뗄맦뮮뻍돆캪헻쫽맦뮮ꆣ웤좷쟐뚨틥ꎺ헻쫽맦뮮쫇퓚튻킩뗈쪽뫍늻뗈쪽뗄풼쫸쳵볾쿂ꎬ튻킩뇤솿헻쫽뗄쿞훆쿂ꎬퟮ듳뮯믲헟ퟮ쿂뮯쒿뇪몯쫽뗄폅뮯맦뮮ꆣ늻쪧튻냣탔ꎬ쿂쏦룸돶튻룶볲떥뗄헻쫽맦뮮뗄쫽톧뇭듯 nmax z=∑cxjjj=1n∑ax≤b(i=1,2,ꆭ?m)ijjj j=1 () x≥0 (j=1,2,ꆭ?n)j쫇int (j=1,2,ꆭ,I;I≤n)j튻냣살쮵헻쫽맦뮮폐솽훖볲떥럖샠ꎬ웤튻쫇룹뻝풼쫸쳵볾믲헟쒿뇪몯쫽뗄쿟탔폫럱럖캪쿟탔헻쫽맦뮮뫍럇쿟탔헻쫽맦뮮ꎻ웤뛾쫇룹뻝헻쫽맦뮮훐뇤솿뗄좡횵쿞훆탎쪽럖샠ꎺꎨ1ꎩ뒿헻쫽맦뮮ꎨinteger programming, 볲볇캪IPꎩꎬ쯹폐뗄뻶닟뇤솿뚼쫇헻쫽ꆣꎨ2ꎩ믬뫏헻쫽맦뮮ꎨmixed integer programming, 볲볇캪MIPꎩꎬ늿럖뻶닟뇤솿쫇헻쫽ꆣꎨ3ꎩ0-1헻쫽맦뮮ꎨbinary programming, 볲볇캪BIPꎩꎬ헻쫽뇤솿횻쓜좡0믲헟1ꎬ0-1헻쫽맦뮮폖뿉틔뷸튻늽럖캪0-1뒿헻쫽맦뮮뫍0-1믬뫏헻쫽맦뮮ꆣ뛔헻쫽맦뮮뗄퇐뺿ꎬ늻쓜뷶뷶뻖쿞퓚웤훘튪탔뗄퇐뺿ꎬ훷튪죎컱쫇짨볆튻킩랽램살뷢뻶룷훖쪵볊뗄헻쫽맦뮮컊쳢ꆣ뎤웚틔살ꎬ헻쫽맦뮮컊쳢튻횱쫇놸쫜펦폃쫽톧ꎬ뻶닟뿆톧ꎬ맜샭뿆톧ꎬ퓋돯톧뗈톧뿆룟뛈맘힢뗄잰퇘컊쳢ꎬ쫇쫽톧맦뮮훐럇뎣뎣볻뗄ꎬ뫜뢴퓓뗄튻샠컊쳢ꆣ헻쫽맦뮮뗄쟳뷢쫇듓쿟탔헻쫽맦뮮뗄쟳뷢뾪 20
쪼뗄ꆣ1960쓪A. H. Land뫍A. G. Doig쫗쿈쳡돶쇋뷢뻶믵색떣컊쳢ꎨ믵색떣컊쳢뗄튻냣쳡램ꎺ튻룶믵색듓쒳돇헲돶랢ꎬ뺭맽죴룉돇헲튻듎ꎬ쟒뷶뺭맽튻듎ꎬퟮ뫳죔튪믘떽풭쪼돶랢뗄뗘랽ꎬ컊펦룃죧맻톡퓱탐ퟟ슷쿟뿉틔쪹ퟜ탐돌ퟮ뛌ꆣ헢룶컊쳢쫇퓋돯톧뗄뺭뗤컊쳢ꎬ폖놻돆ퟷ췆쿺풱컊쳢ꆣꎩ뗄럖횧뚨뷧랽램ꎬ쯦뫳헢룶랽램톸쯙돉캪뷢뻶쿟탔헻쫽맦뮮뗄튻훖훷쇷랽램ꆣ횱떽1979쓪ꎬM. Grotschel뫍M. W. Padberg뗈죋횤쏷쇋쫡ퟓ늻뗈쪽틔벰ퟓ좦늻뗈쪽뚼쫇믵색떣컊쳢뗄헻뗣춹뇟뷧쳵볾ꆣ쯻쏇틔헢킩뇟뷧쳵볾ퟷ캪룮욽쏦ꎬ폃헢훖랽램헒떽쇋120룶돇쫐뗄믵색떣컊쳢뗄ퟮ폅뷢ꎬ헢퇹룮욽쏦랽램돉캪쇋쟳뷢쿟탔헻쫽맦뮮컊쳢뗄탂춾뺶ꆣ좻뫳폖붫솽훖랽램펦폃떽쟳뷢럇쿟탔헻쫽맦뮮컊쳢짏ꆣ럇쿟탔헻쫽맦뮮컊쳢쫇쿖뷱ퟮ폅뮯퇐뺿뗄훘뗣뫍쓑뗣ꆣ퓚맽좥ꎬ죋쏇튻쿲맘힢뗄쫇쿟탔헻쫽맦뮮뗄퇐뺿ꎬ뛸뫶쫓뛶쇋럇쿟탔컊쳢ꎬ틲듋헢룶쇬폲뗄퇐뺿뮹뇈뷏돵늽ꆣ웤쯣램믹놾뿉틔럖돉솽샠ꎬ튻샠쫇믹폚쏉쳘뾨싥랽램뗄쯦믺랽램ꎬ죧Q. Zheng뫍D. Zhuang(1994)룸돶뗄쯣램ꎻ쇭튻샠쫇좷뚨탔뗄쯣램ꎬ죧V. Vassilev뫍K. Genova(1994)쳡돶뗄쯣램ꆣ떫쫇헢킩쯣램믹놾뚼쫇뻖늿쯣램ꎬ뿉틔뷢뻶벸뫵쯹폐뗄샫즢컊쳢ꎬ떫횻쫇헒떽쇋뻖늿ퟮ폅뷢ꆣ놾컄펦폃뗄훷튪쫇쿟탔헻쫽맦뮮뗄쟳뷢ꎬ틲듋쿂쏦훷튪뷩짜튻쿂룮욽쏦랽램뫍럖횦뚨뷧램ꆣ 1ꎩ룮욽쏦램 잰쏦쳡떽뗄ꎬ룮욽쏦램쫇평R. E. Gomory퓚1958쓪쳡돶살뗄ꎬ틲듋폖놻돆캪Gomory룮욽쏦램ꆣ헢룶랽램뗄뫋탄쮼쿫쫇폃쟳뷢쿟탔맦뮮뗄랽램좥쟳뷢헻쫽맦뮮컊쳢ꎬ믹놾쮼쿫쫇ꎺ쫗쿈뫶싔뇤솿쫇헻쫽헢튻쳵볾ꎬ좻뫳늻뛏퓶볓쿟탔풼쫸쳵볾ꎨ벸뫎짏돆캪룮욽쏦ꎩ쪹뗃풭살뗄뿉탐폲놻쟐룮뗴튻늿럖ꎬ놻쟐룮뗴뗄늿럖횻냼몬럇헻쫽뗄뷢ꎬ헻쫽뷢퓚놣쇴쿂살늿럖훐ꆣ헢퇹늻뛏뷸탐쿂좥ꎬ횱떽ퟮ뫳쟐룮떽놣쇴쿂살늿럖훐횻폐튻룶헻쫽ퟸ뇪ꎬ헢룶뻍쫇헻쫽맦뮮컊쳢뗄ퟮ폅뷢ꆣ룅싊살붲ꎬ웤늽훨쫇ꎺꎨ1ꎩ뫶싔뛔뇤솿헻쫽뗄쿞훆ꎬ냑맦뮮컊쳢ퟷ캪튻냣쿟탔컊쳢쟳뷢ꆣ죧맻쟳떽ퟮ폅뷢퓲뷡쫸ꎬ럱퓲뷸탐뗚뛾늽ꎻꎨ2ꎩ퓶볓뢨훺뗄풼쫸ꆣ헢튻늽쫇헻룶룮욽쏦랽램뗄뫋탄ꎻꎨ3ꎩ볬퇩쫇럱뗃돶ퟮ폅뷢ꎬ죧맻늻쫇략믘떽뗚뛾늽ꆣ 2ꎩ럖횧뚨뷧램 21
럖횧뚨뷧램폫룮욽쏦램뗄풭샭샠쯆ꆣ쿈럅뿭헻쫽맦뮮뗄쿞훆ꎬ쟳뷢헻쫽맦뮮뗄쿟탔맦뮮쯉돚컊쳢ꎬ죧맻뗃떽튻룶헻쫽뷢ꎬ헢룶뷢뻍쫇헻룶헻쫽맦뮮뗄ퟮ폅뷢ꎬ쟳뷢뻍떽듋뷡쫸ꎬ떱좻헢훖룅싊럇뎣킡ꎻ죧맻뗃떽뗄뷢늻쫇튻룶헻쫽뷢ꎬ쓇쎴쿟탔맦뮮쯉돚컊쳢뗄뷢쫇헻쫽맦뮮ퟮ폅헻쫽뷢뗄튻룶짏뷧ꎻ죧맻헒떽튻룶헻쫽뷢ꎬ쓇쎴헢룶헻쫽뷢쫇ퟮ폅헻쫽뷢뗄튻룶쿂뷧ꆣ죧맻쓜릻헒떽튻룶랽램ꎬ늻뛏뗄쳡룟쿂뷬ꎬ붵뗍짏뷧ꎬ쯵킡뛾헟횮볤뗄닮횵ꎬퟮ훕쪹뛾헟쿠뗈ꎬ뻍뿉틔헒떽ퟮ폅헻쫽뷢ꆣ룅싊살붲ꎬ웤튻냣늽훨캪ꎺꎨ1ꎩ돵쪼뮯ꆣ쫗쿈쟳뷢룸뚨뗄헻쫽맦뮮컊쳢뗄쿟탔쯉돚맦뮮ꎬ죧맻뗃떽뗄뷢쫇헻쫽뷢ꎬ퓲캪헻쫽맦뮮뗄ퟮ폅뷢ꆣ늻좻ꎬퟷ캪헢룶컊쳢ퟮ폅헻쫽뷢뗄돵쪼짏뷧ꎬ짨돵쪼쿂뷧캪뢺컞쟮ꆣꎨ2ꎩ럖횦폫럖횦쫷ꆣ퓚죎뫎튻룶컊쳢믲헟ퟓ컊쳢샯ꎬ듓쓇킩늻싺ퟣ헻쫽쿞훆뗄뇤솿훐톡퓱튻룶뷸탐뒦샭뗄맽돌돆ퟷ럖횦ꆣ럖횦맽돌쫇춨맽볓죫뮥돢뗄풼쫸붫튻룶컊쳢럖뷢캪쫜떽뷸튻늽풼쫸뗄솽룶컊쳢ꎬ헢퇹뿉틔쪹럇헻쫽뗄뇤솿뷸튻늽뇆뷼헻쫽ꆣ럖횦맽돌좥뗴쇋솽룶헻쫽횮볤뗄럇헻쫽폲ꎬ쯵킡쇋쟳뷢쟸폲ꆣ죧맻ퟓ컊쳢늻싺ퟣ헻쫽풼쫸뻍볌탸럖횦ꎬ헢퇹튻늽뷓튻늽뿉틔탎돉튻룶럖횦쫷ꆣꎨ3ꎩ뚨뷧폫보횦ꆣ헢퇹늻뛏럖횦쟳뷢룷룶ퟓ컊쳢ꎬ틔쪵쿖룄뇤웤짏쿂뷧뗄맽돌놻돆캪뚨뷧ꆣ짏뷧평짐쎻폐쟳뷢뗄ퟓ컊쳢훐ퟮ듳쒿뇪몯쫽횵좷뚨ꎬ쿂뷧평뗃돶뗄ퟮ뫃헻쫽뷢좷뚨ꆣꎨ4ꎩ쯑쯷뗼듺ꆣ쎿듎췪돉튻듎럖횦맽돌뻍쫇췪돉쇋튻듎쯑쯷맽돌ꆣ퓚헢룶맽돌훐ꎬ떱쿂뷧룄뇤뫳ꎬ튪볬닩쯹폐짐캴쟳뷢뗄ퟓ컊쳢늢보뗴쒿뇪몯쫽횵킡폚탂뗄쿂뷧뗄ퟓ컊쳢ꆣ죧맻쎻폐헒떽헻쫽뷢ꎬ쮵쏷헢룶컊쳢쎻폐ퟮ폅헻쫽뷢ꎻ럱퓲ꎬ럖횦쯑쯷맽돌뗃떽뗄ퟮ뫃헻쫽뷢뻍쫇헢룶컊쳢뗄ퟮ폅뷢ꆣ쯑쯷킧싊믡쫜떽럖횦뷡뗣뫍럖횦뇤솿톡퓱뗄펰쿬ꆣ럖횦뷡뗣톡퓱뗄훷튪랽램폐ꎺ짮첽램ꎬ맣첽램ꎬ풤맀램ꆣ럖횦뇤솿톡퓱뗄랽램훷튪폐ꎺ내쒿뇪몯쫽쾵쫽톡퓱ꎬ내럇헻쫽뇤솿톡퓱ꎬ내죋캪룸뚨뗄쮳탲톡퓱ꆣ 럇쿟탔컊쳢쿟탔뮯 퓚잰쏦헂뷚틑뺭뷩짜쇋놾컄퓚컊쳢쟳뷢맽돌훐짦벰떽뛔킧폃몯쫽죽뷗뻘쟳뷢ퟮ횵뗄컊쳢ꎬ떫쫇헢룶튻횱쫇룶벼쫵짏뗄쓑쳢ꎬ훷튪쳥쿖퓚솽룶랽쏦ꎺ웤튻쫇떱닺쫽솿맽뛠쪱ꎬ맀볆죽뷗뻘뫜삧쓑ꎬ킧싊뗍ꎻ웤뛾쫇죽뷗뻘늻쫇춹몯쫽ꎬ쓑쟳 22
ퟮ듳횵ꆣ놾컄닉폃튻훖쿟탔뮯랽램붫럇쿟탔컊쳢뮯캪쿟탔컊쳢ꆣ놾뷚훷튪뷩짜룃랽램뗄쮼쿫뫍쪵쿖ꆣ캪쇋쮵쏷뗄랽쏦ꎬ퓚놾뷚쿈뛔컄훐짦벰떽뗄훷튪럻뫅뷸탐쫇쮵쏷ꆣ 쫗쿈컒쏇맛달N훖막욱퓚쪱볤0,1,...,T뗄볛룱ꎬ틔벰놻ힷퟙ횸쫽퓚헢룶쪱볤뛎뗄뇭쿖ꆣ컄훐훂솦폚좷뚨ힷퟙퟩ뫏ퟮ폅릹돉ꎬK횻막욱뗄톡퓱ꎨK<Nꎩ,틔벰헢킩막욱뗄쫽솿믲헟춶뇈샽ꆣ쿂쏦뻟쳥쏨쫶튻킩ퟩ뫏릹붨맽돌훐붫튪폃떽뗄튻킩뇤솿틔벰뺭볃틢틥ꎺ 뇭3-1 훷튪뇤솿뗄뚨틥틔벰뷢쫍쮵쏷 뇤솿 틢틥 eힷퟙퟩ뫏훐좷뚨춶막욱i뗄ퟮ킡춶뇈샽 idힷퟙퟩ뫏훐좷뚨춶막욱i뗄ퟮ듳춶뇈샽 i떱잰ힷퟙퟩ뫏훐막욱i뗄막쫽ꎬ컒쏇냑ퟩ뫏뗄붨솢ퟷ캪튻룶ퟩ뫏훘붨뗄맽돌ꎬ뻍쫇퓚Y i쿖폐ퟩ뫏뗄믹뒡짏ꎬ뷸탐훘탂톡퓱ꎬ릹붨탂뗄ퟩ뫏 V쪱볤t막욱i뗄볛룱 itI쪱볤t횸쫽뗄볛횵 tR 쪱볤t횸쫽떥웚뗄솬탸믘놨싊ꎬ샽죧R=ln(I/Ittt−1) tr 쪱볤t막욱i뗄떥웚솬탸믘놨싊ꆣ샽죧r=ln(V/Vittit−1) iti떱잰쪱볤Tힷퟙퟩ뫏[X]뗄ퟜ볛횵i∑nXV볓짏쿖뷰뗄뇤뮯ꎨ냼삨쿖뷰뗄탂춶죫iitCi=1 틔벰쿖뷰뗄뎷돶ꎩꎬ튲뻍쫇릹붨탂뗄ힷퟙퟩ뫏쪱뿉틔쪹폃뗄ퟜ뗄뷰솿 sf폃럖쫽뇭쪾퓚쪱볤T싴돶튻떥캻막욱i뗄돉놾 ibf폃럖쫽뇭쪾퓚쪱볤T싲죫튻떥캻막욱i뗄돉놾 ig C훐뿉틔폃폚ퟷ캪붻틗럑폃뗄뇈샽쿞훆ꎨ0≤g≤1ꎩ y퓚탂뗄ힷퟙퟩ뫏훐막욱i뗄막쫽 i 23
탸뇭 G싲죫믲헟싴돶막욱랢짺뗄붻틗럑폃 i쫇튻룶0-1뇤솿ꎬ튲쫇놾컄뗄훷튪뻶닟뇤솿횮튻ꎬ죧맻탂뗄ힷퟙퟩ뫏훐냼삨막욱iꎬz i퓲z뗄횵뗈폚1,ꎬ럱퓲z뗄횵뗈폚 iia ힷퟙퟩ뫏훜믘놨뛔쫐뎡횸쫽훜믘놨믘맩뷘뻠 b ힷퟙퟩ뫏훜믘놨뛔쫐뎡횸쫽훜믘놨믘맩킱싊 볙짨(R1,...,RK)쫇샫즢퇹놾뿕볤짏뗄튻룶럖늼ꎬ뚨틥ꎺ f=P{(R1,...R)=(r1,..r)},t=1,..T tKt.,ttKTr 막욱i솬탸웚볤믘놨ꎬ벴r=ER=∑fr i[]iititt=1R 막욱ퟩ뫏떥웚믘놨뻹횵ꎬ벴KR=rxꎬ웤훐x=yV/itititiiiit∑yV =1jjtjTKk 틦뗄죽뷗뻘ꎬK3kR(X)=E∑(R−r)xiii=∑3fzꎬz=tt∑(r−R)x tititii=1t=1i=1e짨뚨훷튪쫇뾼싇떽K횵틑뺭톡뚨ꎬ뻍튪놣횤뢴훆ퟩ뫏훐막욱쫽솿뗄릹돉쫇iKꎬ죧맻쎻폐짨뚨ퟮ킡뇈샽ꎬ쒳횻막욱뗄뇈샽뿉쓜쫇쇣ꎬ헢룶쫇퓚닙ퟷ훐돶쿖맽뗄ꎬ쓇쎴K횵뗄짨뚨뻍쪧좥쇋틢틥ꎻd뗄짨뚨훷튪뾼싇떽쫐뎡쇷탐탔틔벰릺싲막욱뗄i돥믷돉놾ꎬ컒쏇횪뗀뗄ꎬ떱튻횻막욱놻듳솿놻릺싲쪱ꎬ평릩탨맘쾵뿉틔횪뗀뛌웚쓚탨쟳뗄벱뻧짏짽믡떼훂볛룱짏헇ꎬ헢퇹뻍믡퓶듳막욱뗄릺싲돉놾ꎬ늻샻폚뢴훆ퟩ뫏뗄릹붨ꎻsbf뫍f튻퇹ꎬ놾컄훐뛔폚돉놾횻뾼싇쇋펡뮨쮰ꎬ훁폚횤좯릫쮾뗄뺭ii볍럑폃쎻폐ퟶ뾼싇ꎬ풭틲훷튪폐솽룶ꎬ웤튻쫇쿠뛔폚ퟜ뗄뷰뛮ꎬ헢킩쿠맘럑폃쿠뛔뫜킡ꎬ뛔ퟩ뫏톡퓱쎻폐쪲쎴펰쿬ꎬ웤뛾쫇룷룶좯짌럑폃쫕좡늢늻튻훂ꎬ쓑폚볆솿ꎻ늻쪧튻냣탔ꎬ컒쏇뿉틔퓊탭[X]좡럖쫽횵ꎨ틲캪춶ퟜ뛮뫜듳ꎩꆣힷퟙퟩ뫏i뗄놸톡막욱뿉틔쫇쯹폐N횻막욱훐뗄튻훖ꎬ횻튪헢횻막욱뻟폐샺쪷볛룱벯뫏[V]ꆣ it 24
헢샯틽죫0-1뇤솿뷸탐쿟탔뮯ꆣ럻뫅뚨틥훐틑뺭쮵쏷뗄ꎬ볙짨(R1,...,Rk)쫇샫즢퇹놾뿕볤짏뗄튻룶럖늼ꎬ뚨틥ꎺ f=P{(R1, ꆭꆭ,R)=(r1,ꆭꆭ,r)},t=1,ꆭꆭ,T () tKtKt헢퇹뻍폐 T r=E[R]=ii∑fr () titt=1뮹폐 KK ER(x)=E∑Rxi∑rx () iii=1=1K2vR(x)=E∑(R−r)xiiii=1 () TK2 ∑f∑(r−r)xtitiit=1i=1K3vR(x)E∑=(R−r)xiiii=1 () TK3 ∑f∑(r−r)xtitiit=1i=1헢퇹뻹횵—랽닮—욫뛈쒣탍뻍뇤돉쟳뷢 Tmax∑3fzttt=1T22st ∑fz≤sttt=1K ∑rx=r () iii=1K z=∑(r−r)x,t=1,ꆭꆭ,Ttitiii=1 x∈X 25
쿂쏦닉폃뇪ힼ뗄럖뛎쿟탔뇆뷼뛔뛾듎몯쫽2z뫍죽듎몯쫽3z뷸탐쿟탔뮯ꎬ퓚헢tt룶맽돌훐탨튪틽죫튻쾵쇐뗄0-1뇤솿ꆣ쿂쏦붫쿪쾸뷩짜쿟탔뮯뗄맽돌ꆣ볙짨 KKz=min∑r−rx∑rx=r,x∈Xt0()}itiiii=1=1 () KKz=max∑(r−r)x∑rx=rx∈X}titiiii=1=1좻뫳붫쟸볤[z0,z]럖돉m뗈럖뎤뛈ꆣ쿂쏦틽죫뢨훺뇤솿lꎬ웤훐ttmtjt=1,2,ꆭꆭ,T,j=0,1ꆭꆭ,mꆣ헢퇹랽닮뫍욫뛈뿉틔뇭쪾돉쿂쏦뗄탎쪽ꎺ Tmv2R(x)=∑f∑zlttjtjt=1j=0Tmk3R(x)=∑f∑zlttjtjt=1j=0m z∑zl,=1,2,ꆭꆭ,T () ttjtjj=0m∑l=1,t=1,2ꆭꆭ,Ttjj=0l≥0, t=1,2,ꆭꆭ,T;j=0,1ꆭꆭ,mtj캪쇋놣횤욫뛈몯쫽뗄춹탔ꎬl탨튪싺ퟣ쿂쏦뗄쳵tk볾 ltl+1≤qtl+1ltl+2≤qtl+1+qtl+2 ꆭꆭ () l≤qtmtm−1웤훐q∈[0,1],j=l+1,l+2,ꆭꆭ?j−1ꆣ tj헢퇹뻹횵—랽닮—욫뛈쒣탍뻍뇤돉쿂쏦탎쪽뗄풼쫸쳵볾 Tm∑∑2l≤2 fzs () ttjtjt=1j=0K ∑rx=r () iii=1 26
Km ∑(r−r)x∑zl,=1,2,...,T () itiitjtj=1=0m ∑l=1,t=1,....,T () tjl=0 l≥0,t=1,...,T;j=0,1,...,m () tj l+1≤y+1,t=1,...T () tltltt l≤y+y−1,j=l+2,...,m−1;t==1,...T () tjtjtjt l≤−1,=1,..., () y=0or1,j=l+1,..m;t=1,...,T () tjtퟮ듳뮯욫뛈뇤캪쒿뇪ꎺ Tmmax3 ∑f∑zl () ttjtjt=1j=0헢퇹쒿뇪몯쫽욫뛈뻍쪵쿖쇋쿟탔뮯ꆣ 헻쫽맦뮮뢴훆쒣탍붨솢 ퟜ쳥살쮵놾컄뢴훆ퟩ뫏뗄붨솢닉폃쇋솽훖쮼쿫ꎬ웤튻쫇믘맩뗄쮼쿫ꎬ웤뛾쫇“뻘”뗄쮼쿫ꆣ믘맩뗄쮼쿫훷튪쫇믹폚잰쏦뷩짜뗄CAPM쒣탍뗄튻훖탎쪽——떥틲쯘쒣탍믲헟쫐뎡횸쫽쒣탍ꎬ훷튪폃퓚럧쿕퇡뛱춶죋뢴훆ퟩ뫏뗄붨솢ꆣ헢룶맛뗣뗄뫃뒦퓚폚뿉틔랢햹쿟탔뮯ꎬ랽뇣샻폃쿟탔헻쫽맦뮮쟳뷢ꎬ헢훖벼쫵쿠뛔폚럇쿟탔컊쳢벼쫵돉쫬ꎬ뛸쟒볆쯣킧싊룟ꆣ“뻘”뗄쮼쿫쫇맡뎹쪼훕뗄ꎬ횻쫇퓚ퟮ폅뮯욫뛈뗄맽돌훐쳥쿖뗄폈웤춻돶ꎬ펦폃폚뷷짷뗄럧쿕퇡뛱춶죋ꆣ퓚헢룶맽돌훐ꎬ쫇쿞훆튻뷗뻘뫍뛾뷗뻘뗄횵ꎬ듯떽죽뷗뻘몯쫽뗄ퟮ폅ꆣ룃늿럖붫룸돶뻟쳥뗄풼쫸쳵볾뫍쒿뇪몯쫽ꆣ 풼쫸쳵볾뗄톡퓱 뢴훆ퟩ뫏뗄붨솢쪵볊뻍쫇튻룶ퟮ폅뮯컊쳢ꎬ짨뚨튻룶쒿뇪몯쫽ꎬ퓚튻킩풼쫸 27
쿂듯떽쒿뇪몯쫽ꆣ뿉틔쮵ꎬ퓚폅뮯컊쳢훐ꎬ풼쫸쳵볾쫇튻룶뫜훘튪뗄늿럖ꆣ풼쫸쳵볾뿉틔뿌뮭뷰뗄쿞훆ꎬ돉놾뗄쿞훆ꎬ짵훁춶죋뗄욫뫃ꎬ횻튪뻟폐쓜릻솿뮯뗄튻킩쳘탔ꆣ쿂쏦쫇놾컄훐짦벰뗄늿럖풼쫸쳵볾ꎬ횮쯹틔쮵쫇늿럖풼쫸쳵볾ꎬ뛸늻쫇좫늿ꎬ쫇틲캪헢킩풼쫸쫇ퟮ믹놾뗄풼쫸ꎬ쫇퓚헻룶ퟩ뫏붨솢맽돌훐뚼믡쪹폃떽뗄ꎬ퓚쿂쏦뗄뷩짜훐뻍믡랢쿖ꎬ놾컄뗄쒣탍뿉틔럖돉벸룶뷗뛎ꎬ폐킩쒣탍쫇틔잰튻룶쒣탍뗄뷡맻ퟷ캪튻룶풼쫸ꎬ헢훖쟩뿶퓚헢샯쎻폐튻튻쇐돶ꆣ풼쫸쳵볾죧쿂ꎺ N ∑z=K () ii=1 ez≤yV/C≤dz =1,...,N () iiiiTii G≥fb(y−Y)V 1,...,iiiiiTi=N () Gs ≥f(Y−y)V i=1,...,N () iiiiiTN ∑G≤gC () ii=1NN ∑yV=C−∑G () iiTi=1=1 y,G≥0 i=1,...,N () ii z∈[0,1] i=1,...,N () i쿂쏦뻟쳥뷩짜튻쿂쎿룶풼쫸쳵볾뗄몬틥ꆣ풼쫸ꎨꎩ놣횤쇋탂뗄ힷퟙퟩ뫏훐폐K횻막욱ꎻ풼쫸ꎨꎩ쏨쫶쇋죧맻튻횻막욱i쎻폐퓚탂뗄ힷퟙퟩ뫏훐퓲y쫇0ꎬi죧맻막욱i냼삨퓚탂뗄ힷퟙퟩ뫏훐웤뇈샽싺ퟣ튪싺ퟣퟮ듳춶뇈샽뫍ퟮ킡춶뇈샽뗄튪쟳ꎻ풼쫸ꎨꎩ뫍ꎨꎩ뚨틥쇋붻틗돉놾ꎬ뻍쫇싲싴막욱뗄붻틗돉놾튪킡폚뗈폚퓊탭뮨럑뗄ퟜ뗄붻틗돉놾ꎻ풼쫸ꎨꎩ쿞훆쇋ퟜ뗄붻틗돉놾ꎻ풼쫸ꎨꎩ쫇튻룶뻹뫢뗈쪽ꎬ놣횤T쪱볤탂뗄ힷퟙퟩ뫏뗄횵뗈폚떱잰ힷퟙퟩ뫏뗄횵볓짏쿖뷰룄뇤복좥ퟜ뗄붻틗돉놾ꎻ풼쫸ꎨꎩ횻쫇놣횤쇋뇤솿뗄뺭볃톧틢틥ꎻ풼쫸ꎨꎩ뚨틥쇋z뗄0-1뇤솿쳘뗣ꆣ i 28
쒿뇪몯쫽뗄붨솢 잰쏦뷩짜쇋놾컄듓뺭볃톧놳뺰살붲ꎬ훷튪뾼싇쇋솽샠춶죋ꎬ웤튻쫇럧쿕퇡뛱헟ꎬ웤뛾쫇뷷짷뗄럧쿕퇡뛱헟ꆣ퓚헢늿럖쒿뇪몯쫽뗄좷뚨훐ꎬ컒쏇튲붫럖돉솽룶늿럖뷩짜ꎬ헢룶튲쫇쿂컄ퟶ쫽횵퓋쯣붫닉폃뗄릹볜ꆣ 쿈뷩짜뛔럧쿕퇡뛱춶헟붨솢ힷퟙퟩ뫏뗄쒿뇪몯쫽ꆣ잰컄뷩짜쇋놾컄훷튪닉폃쿟탔헻쫽맦뮮ꎬ헢훖볆쯣뇈뷏돉쫬ꎬ볆쯣킧싊룟ꎬ뛸컄훐짦벰떽튻킩럇쿟탔뇤솿ꎬ뻍틢캶ퟅ쫗쿈튪폐쿟탔뮯뗄맽돌ꆣ캪쇋쿟탔뮯ퟩ뫏뗄믘놨ꎬ컄훐볙짨ퟩ뫏뗄믘놨뿉틔뇭쪾돉떥룶막욱믘놨볓좨쟳뫍ꆣ웤훐좨훘뫍캪1ꆣ헢룶쫇뷰죚톧훐뇈뷏웕뇩뗄튻룶볙짨ꆣ벴쪱볤t뗄ힷퟙퟩ뫏믘놨N∑xrꎬ웤훐Nx=yV/itititiit∑yVꎬ쟒=1jjtji=1∑Nx=1ꆣ 1iti=쿖퓚x쫇맘폚튪쟳뷢뇤솿y뗄럇쿟탔뇭쪾ꆣ컄훐붫폃튻룶쪱볤뛀솢뗄쫽x살itii뇆뷼Nxꎬ웤훐x=yV/itiiiT∑yVꎬ듺뇭쪱볤T막욱i뗄춶뇈샽ꆣ헢퇹퓚쪱볤tힷ=1jjTjퟙퟩ뫏뗄믘놨∑N=xrꆣ =1iiti컒쏇폃CN−∑G듺쳦Nꎨꎩ훐컒쏇jj=1∑yV쪹x뗄뇭듯쿟탔뮯ꆣ듓풼쫸=1jjTij횪뗀N∑G≤gCꆣ틲듋x뿉틔뷼쯆뇭쪾캪 iii=1 x=yV/(C−gC),i=1,...,N () iiit뢴훆ퟩ뫏믘놨죧맻쿠뛔폚횸쫽믘놨뷸탐믘맩ꎬ틀뻝ퟮ킡뛾돋램뿉틔뗃떽뷘뻠뫍킱싊쿮ꆣ헢솽쿮튲뿉틔폃뢴훆ퟩ뫏훐돉캪막욱뗄뷘뻠뫍킱싊뇭쪾죧쿂ꎺ ∧N∧ a=∑xai () ii=1∧N∧ b=∑xb () iii=1웤훐∧a뫍∧b쪫떥룶막욱i믘놨뛔횸쫽믘놨믘맩뗄뷘뻠뫍킱싊ꆣ ii 29
떱좻뛔폚횸쫽ힷퟙ컒쏇쾣췻뗄뷡맻쫇톡퓱K횻막욱틔벰웤룷룶막욱뗄쫽솿쪹뗃∧a=0ꎬ∧b=1ꎬ헢퇹뻍쫇뢴훆ퟩ뫏췪좫뢴훆쇋횸쫽ꆣ쿂쏦뻍튻튻뷩짜룷룶쒿뇪몯쫽ꎺ 1ꎩ튻뷗뛎쒣탍 닉폃튻룶볲떥뗄볓좨쒿뇪ꎺ ∧∧ minla|−0|+lb|b−1| () 웤훐la,lb≥0ꎬ춶죋뿉틔룹뻝ퟔ벺뗄쾲뫃뚨틥뗄뷘뻠캪0뫍킱싊캪1뗄좨훘ꆣ죧맻춶죋뇈뷏퓚틢뢴훆ퟩ뫏뗄럧쿕ꎬ뿉틔룸폨lb룼듳뗄좨훘ꎻ죧맻춶죋늻퓚틢럧쿕ꎬ횻ힷ쟳뎬풽횸쫽뗄믘놨ꎬ뿉틔룸폨la룼듳뗄좨훘ꆣ 2ꎩ솽뷗뛎쒣탍 뗚튻훖랽램ꎺ 쿈∧min|a−0|ꎬ좻뫳퓙∧min|b−1| () 뗚뛾훖랽램ꎺ ∧ 쿈min|b−1|ꎬ좻뫳퓙∧min|a−0| () 헢솽훖랽램뿉틔쫓ퟷ쫇튻뷗뛎쒣탍뗄쳘쫢쟩뿶ꆣ뗚튻훖랽램쿠떱폚la풶듳폚lbꎬ튲뻍쫇춶죋룼볓뾴훘뗃떽뎬풽횸쫽뗄믘놨ꎻ뗚뛾훖랽램쿠떱폚lb풶듳폚laꎬ튲뻍쫇춶죋룼볓훘쫓뿘훆뢴훆ퟩ뫏뗄럧쿕ꆣ 힢틢떽짏쏦룸돶뗄쒿뇪몯쫽뚼쫇럇쿟탔뗄쪽ퟓꎬ퓚헢샯뿉틔춨맽뇪ힼ뮯뗄랽램뗃떽쿟탔쪽ퟓꆣ틽죫솽룶뇤솿R뫍Sꎬ웤훐 ∧ R≥a () ∧ R≥−a () ∧ S≥b−1 () ∧ S≥−b−1 () 30
R,S≥0 () 춨맽짏쏦뗄뇤솿짨훃ꎬ쒿뇪몯쫽뷸튻늽뇤캪 minlaR+lbS () 쿈minR,퓙minS () 쿈minS,퓙minR () 헢퇹쒿뇪몯쫽뚼쪵쿖쇋쿟탔뮯ꆣ 3ꎩ죽뷗뛎쒣탍 헢훖쒣탍쫇퓚잰쏦솽뷗뛎뗄믹뒡짏퓙ퟮ킡뮯붻틗돉놾ꎬ벴볓짏풼쫸쳵볾∧∧a=aopt뫍b=bopt뗄믹뒡짏ꎬ좻뫳퓙짨쒿뇪몯쫽 N min∑G () ii=1떱좻퓚헢샯튪쮵쏷튻뗣ꎬ헢튻늽쫇퓚솽뷗뛎쒣탍뗄믹뒡짏뷸탐뗄ꆣ솽룶솽뷗뛎쒣탍뗄뢴훆킧맻죧맻늻튻퇹ꎬ캪쇋뷚쪡볆쯣쪱볤ꎬ놾컄붫톡퓱뢴훆킧맻뫃뗄튻룶뷸탐죽뷗뛎쒣탍뗄쪵퇩퇐뺿ꆣ 뛔폚뷷짷뗄럧쿕퇡뛱룶쳥ꎬ룃랽램뗄풭샭잰쏦틑뺭ퟶ쇋뷩짜ꎬ뫋탄쒿뇪뻍쫇ퟮ듳뮯뢴훆ퟩ뫏뗄쫕틦싊럖늼뗄욫뛈ꆣ헢훖풼쫸헫뛔뻟폐뷷짷럧쿕퇡뛱뗄룶쳥ꎬ헢훖춶헟퓚쫕틦싊뫍랽닮튻퇹뗄쟩뿶쿂룼볓쾲뮶헽욫뛈ꆣ볲떥살쮵ꎬ헢룶쫇튻룶튻뷗뛎쒣탍ꎬ횻쫇퓚잰쏦룸돶뗄풼쫸쳵볾짏볓죫뛔뢴훆ퟩ뫏쫕틦싊웚췻뫍랽닮뗄풼쫸ꎬ좻뫳틔ퟮ듳뮯욫뛈ퟷ캪쒿뇪몯쫽ꎬ벴쿂쏦뗄쪽ퟓ maxP () 뺭맽잰컄뷚쿪쾸뷩짜뗄쿟탔뮯맽돌ꎬퟮ듳뮯욫뛈뇤캪쒿뇪ꎺ Tm max∑3ft∑zl () tjtjt=1j=0헢퇹쒿뇪몯쫽욫뛈뻍쪵쿖쇋쿟탔뮯ꆣ 31
놾헂킡뷡 놾헂붫헻쫽맦뮮춬뢴훆ퟩ뫏뗄붨솢솪쾵웰살ꆣ쫗쿈뷩짜쇋헻쫽맦뮮뗄쿠맘룅쓮ꎬ믹놾뷢램ꎻ좻뫳훘뗣뷩짜쇋놾컄벼쫵짏뗄튻룶춻웆ꎬ벴퓚뛔킧폃몯쫽죽뷗뻘쟳뷢ퟮ횵훐ꎬ튲벴놾컄훐짦벰뗄욫뛈쟳뷢ퟮ횵훐붫럇쿟탔컊쳢쿟탔뮯뗄맽돌ꆣퟮ뫳닻쫶뫍쮵쏷쇋놾컄퓚뻟쳥횸쫽뢴훆쒣탍훐풼쫸쳵볾뗄톡퓱뫍붨솢ꎬ틔벰쒿뇪몯쫽뗄톡퓱뫍붨솢ꆣ 32
4 쫽횵쪵퇩 2010쓪4퓂16죕ꎬ막횸웚믵뾪쪼짏쫐붻틗ꎬ헢뇪횾ퟅ돯놸뷼4쓪뗄막횸웚믵붫뾪뮨뷡맻ꎬ훐맺놾쫐뎡붫펭살“돉죋샱”ꆣ막횸웚믵뗄췆돶붫캪횸쫽뢴훆벼쫵뗄랢햹쳡릩룼맣삫뗄뿕볤뫍볬퇩뗄욽첨ꆣ훚쯹훜횪ꎬ막욱횸쫽웚믵ꎬ볲돆막횸웚믵ꎬ쫇뷰죚웚믵뗄튻훖ꎬ쫇틔믵뇒뮯뗄막볛횸쫽캪뇪뗄웚믵뫏풼ꆣ막횸웚믵뗄돶쿖ꎬ뛔폚춶죋살쮵ꎬ폐죽룶랽쏦뗄뫃뒦ꎬ웤튻쫇뿉틔웤뛔막횸쿖믵뷸탐쳗웚놣횵ꎬ맦뇜쾵춳럧쿕ꎨ쯗돆듳엌럧쿕ꎩꎬ웤뛾쫇춶믺ꎬ웤죽쫇웚쿖쳗샻ꆣ쯹캽쳗샻ꎬ쫇횸샻폃막횸웚믵뚨볛욫닮ꎬ춨맽싲죫막횸웚믵뇪뗄횸쫽돉럖막욱ꎬ춬쪱싴돶막횸웚믵ꎬ믲헟쫇싴뿕막횸웚믵뇪뗄횸쫽돉럖막ꎬ춬쪱싲죫막횸웚믵ꎬ살좡뗃컞럧쿕쫕틦뗄맽돌ꆣ막횸웚믵뗄쫗룶뇪뗄쫇뮦짮300횸쫽ꎬ뮦짮300횸쫽평훐횤횸쫽폐쿞릫쮾뇠훆ꎬ웤평뮦짮A막훐맦쒣듳ꎬ쇷뚯탔뫃ꎬ뻟폐듺뇭탔뗄300횻막욱ퟩ돉ꎬ폚2005쓪4퓂8죕헽쪽랢늼ꎬ웤쒿뗄쫇ퟛ뫏랴펳뮦짮A막쫐뎡헻쳥뗄뇭쿖ꆣ뮦짮300횸쫽틔2004쓪12퓂31죕캪믹죕ꎬ믹뗣캪1000뗣ꎬ냑믹죕300횻퇹놾막뗄뗷헻쫐횵ퟷ캪믹웚ꆣ뮦짮300횸쫽닉폃엉탭볓좨ퟛ뫏볛룱횸쫽릫쪽뷸탐볆쯣ꎬ뻟쳥볆쯣릫쪽죧쿂ꎺ 놨룦웚횸쫽횵 = 놨룦웚돉럖막뗄뗷헻쫐횵/믹웚×1000 웤훐ꎬ뗷헻쫐횵 = ?(막볛×뗷헻막놾쫽)ꎬ믹웚틠돆캪돽쫽ꆣ 떱뮦짮300횸쫽뗄퇹놾막랢짺돶쾢ꎬ돽좨ꎬ춣없ꎬ막놾뇤뚯ꎬ틔벰퇹놾막뗷헻쪱ꎬ훐횤횸쫽폐쿞릫쮾믡뛔횸쫽뷸탐쿠펦탞헽ꎬ틔놣횤횸쫽뗄솬탸탔ꆣ뮦짮300횸쫽틔뗷헻막놾ퟷ캪좨훘ꎬ틔뗷헻뫳뗄ퟔ평쇷춨막놾뛸럇좫늿막놾ퟷ캪좨훘ꎬ룼쓜헦쪵랴펳쫐뎡훐쪵볊뿉릩붻틗막럝뗄막볛뇤뚯쟩뿶ꎬ듓뛸폐킧뗄뇜쏢쇋춨맽듳엌막살닙ퟝ횸쫽뗄쟩뿶랢짺ꆣ 뮦짮300놻뺳쓚췢뛠볒믺릹뾪랢캪횸쫽믹뷰뫍ETF닺욷ꎬ룺ퟙ닺퓚A막막욱횸쫽훐룟뻓쫗캻ꆣ믹폚뮦짮300횸쫽뗄훘튪뗘캻ꎬ놾컄톡좡뮦짮300횸쫽ퟷ캪훷튪룺ퟙ횸쫽ꎬ춬쪱톡퓱훐횤100ퟷ캪듎튪룺ퟙ횸쫽ꎬ쳡릩튻킩뇈뷏틢틥ꆣ 쿂쏦뗄쪵퇩퇐뺿훷튪럖돉솽룶늿럖ꎬ웤튻쫇헫뛔럧쿕퇡뛱춶헟붨솢룺ퟙퟩ뫏ꎬ웤뛾쫇헫뛔뷷짷럧쿕퇡뛱춶헟붨솢룺ퟙퟩ뫏ꎬ늢뛔뛾헟뗄룺ퟙ킧맻ퟶ돶뇈뷏ꆣ 33
럧쿕퇡뛱쿂횸쫽뢴훆쫽횵쪵퇩 퓚헢늿럖틀뻝믘맩쒣탍ꎬ벴CAPM쒣탍뗄떥틲쯘탎쪽붨솢룺ퟙퟩ뫏ꎬ뻟쳥늽훨죧쿂ꎺ 1ꎩ맀볆뮦짮300뫍짏횤100뗄돉럖막뗄a횵뫍b횵ꎬ돉럖막뗄쫕엌볛쫽뻝살ퟔCCER쫽뻝뿢ꎬ뾼싇떽좡뗃a횵뫍b횵튪퓚뇈뷏뎤뗄쫽뻝쟸볤쓚ꎬ놾컄닉폃쇋100룶쪱볤쟸볤뗄쫽뻝ꎬ뢽슼훐붫믡룸돶뻟쳥뗄a횵뫍b뗄ꎻ 2ꎩ짨뚨닎쫽ꎬ틔벰붫1ꎩ뗃떽뗄a횵뫍b횵쫽뻝듺죫늻춬뗄볆쯣쒣탍ꎻ 3ꎩ폃헻쫽쿟탔맦뮮쟳뷢ퟩ뫏ꎬ퓚헢룶맽돌훐늻뛏룄뇤맘볼닎쫽뗄좡횵ꎬ좡뗃늻춬뗄룺ퟙퟩ뫏ꎻ 4ꎩ폫횸쫽뗄킧맻쿠뇈뷏ꎬ폃퇹놾췢뗄쫽뻝움볛룺ퟙퟩ뫏뗄룺ퟙ킧맻ꆣ 뛔ힷퟙ킧맻뗄럖컶ꎬ닉폃룺ퟙ욫샫뛈ퟷ캪룺ퟙ컳닮뗄뛈솿랽램ꆣ놾컄훐붨솢ퟩ뫏뗄죕웚캪2010쓪2퓂22죕ꎬ볆쯣쇋췹뫳30룶붻틗죕ꎬ떽2010쓪4퓂8죕뗄죕룺ퟙ컳닮ꆣ 튻뷗뛎쒣탍 퓚뗚죽헂룸돶쇋튻뷗뛎쒣탍뗄쒿뇪몯쫽ꎬ퓚ퟶ쪵퇩퇐뺿뗄쪱뫲ꎬ놾컄뛔la뫍lb뗄좡횵횻튪닉폃쇋죽훖랽쪽ꎬ웤튻쫇la=1,lb=0ꎬ볲떥뗄쮵ꎬ뻍쫇횱뷓쇮a횵뺡솿쟷폚0ꎻ웤뛾쫇la=0,lb=1ꎬ볲떥뗄쮵ꎬ뻍쫇횱뷓쇮b횵뺡솿쟷폚1ꎻ웤죽쫇쇮la+lb=1,la≠0쟒lb≠0ꎬ웤쪵잰솽훖좡횵랽쪽뻍쫇뗚죽훖랽쪽뗄쳘쫢탎쪽ꎬ틲캪웤뫜뻟듺뇭탔ꎬ쯹틔헢샯떥뛀쇐돶살쇋ꆣ뇈뷏볆쯣뗄뷡맻랢쿖ꎬ뗚죽훖랽쪽뗄ힷퟙ킧맻늢늻뫃ꎬ틲듋쿂쏦뛔뷡맻뗄럖컶붫훷튪쏨쫶랽램튻뫍랽램뛾ꆣ 뇭4-1룸돶돵쪼닎쫽뗄짨뚨ꆣ뾪쪼컒쏇톡퓱K=5ꎬ벴폃5횧막욱ힷퟙ횸쫽ꎬ캪쇋랴펳K횵뛔ힷퟙ킧맻뗄펰쿬ꎬ붫틔5캪뗈퓶쟸볤ꎬ퓶볓K뗄횵ꎬ쿂컄믡룸돶K횵뗄펰쿬ꎻ헢샯짨훃쇋붻틗럑폃쯹쓜햼폃뗄ퟮ듳좨훘ꎬ훷튪쫇돶폚좫쏦탔뗄뾼싇ꎬ뾼싇떽튻킩쟩뿶쿂싲싴막욱쮫쿲쫕럑ꎬ쪵볊짏퓚떱잰맺쓚뗄놾쫐뎡훐ꎬ횻폐퓚 34
싴돶막욱뗄쪱뫲쫕좡잧럖횮튻뗄펡뮨쮰ꎬ헢퇹붻틗럑폃쯹쓜햼폃뗄뷰ퟮ듳좨훘횻폐퓚킡폚잧럖횮튻뗄쪱뫲닅폐틢틥ꎬ놾컄헢샯짨훃캪웟럖횮튻ꎬ쿠떱폚럅뿭쇋뛔붻틗럑폃뗄풼쫸ꎬ퓚쿂컄죽뷗뛎쒣탍훐붫훷튪뾼달붻틗럑폃뗄펰쿬ꎻ탂춶죫뷰헢샯짨훃뗄캪0ꎬ잰컄쮵쏷쇋헢샯ힷퟙퟩ뫏뗄붨솢쪵볊짏쫇튻룶훘붨뗄맽돌ꎬ볙짨뾪쪼틑뺭폐튻룶춶ퟩ뫏ꎬ헢룶ퟩ뫏뗄ퟜ뷰솿캪1000000ꎬ욽뻹럖엤퓚K횻막욱짏ꎻ맘폚쎿횧막욱ퟮ듳춶뇈샽뫍ퟮ킡춶뇈샽뗄톡퓱쎻폐맽뛠뗄뾼싇ꎬ횻쫇놣횤쇋퓚헢솽룶풼쫸쳵볾쿂뿉틔릹붨ퟩ뫏ꎬ뇈죧ꎬퟮ킡춶뇈샽맽듳ꎬ뿉쓜폫K횵뗄톡퓱탎돉쎬뛜ꎬ듓뛸떼훂늻쓜릹붨룺ퟙퟩ뫏ꎬ컒쏇튲뎢쫔쇋룄뇤쎿횧막욱ퟮ듳춶뇈샽뫍ퟮ킡춶뇈샽뗄ퟩ뫏ꎬ횤쏷뛔ힷퟙퟩ뫏룺ퟙ킧맻쎻폐쿔훸펰쿬ꆣ 뇭4-1 돵쪼닎쫽뗄짨뚨 닎쫽쏻돆 닎쫽몬틥 닎쫽횵 tpSize 뢴훆ퟩ뫏막욱쫽 5maxCostRatio 붻틗럑폃쯹쓜햼폃뗄ퟮ듳좨훘 싲죫붻틗럑폃뇈싊 0sellFee 싴돶붻틗럑폃뇈싊 탂춶죫뷰 0maxRatio 쎿횧막욱뗄ퟮ듳춶뇈샽 쎿횧막욱뗄ퟮ킡춶뇈샽 ꎩla=1,lb=0쒣탍 캪쇋볲떥쮵쏷놾컄뗄볆쯣쇷돌ꎬ쿂쏦틔K=5쪱ꎬ뛔뮦짮300뗄ힷퟙ뷡맻뷸탐쮵쏷ꆣ퓚뢴훆ퟩ뫏훐ꎬ톡좡뗄2010쓪2퓂22죕뗄뮦짮300훐300횧돉럖막뗄쫕K∑Vyiti엌볛ퟷ캪쿖볛ꆣ뢴훆ퟩ뫏떥죕믘놨뗄볆쯣쪽쫇i1log=eKꎬ뮦짮300횸쫽뗄떥죕∑V−1yitii=1믘놨볆쯣쪽쫇Itlogeꎬힷퟙ컳닮욫닮쫇뢴훆ퟩ뫏떥죕믘놨복좥뮦짮300횸쫽떥죕It−1믘놨뗄닮횵ꆣ듓뇭룱훐뗄쫽뻝뿉틔뾴떽ꎬ퇹놾췢30룶붻틗죕뗄ힷퟙ컳닮욫닮캪ꎬ쫽솿벶퓚10뗄-3듎랽ꆣힷퟙ컳닮욫닮뗄ퟮ듳횵캪ꎬퟮ킡횵캪ꎬ헢룶ퟮ킡횵쫇듓쫽횵짏살붲뗄ꎬ죧맻횻맘힢뻸뛔ힷퟙ컳닮욫닮ꎬퟮ킡 35
뗄욫닮횵캪ꎻ30쳬뗄ힷퟙ컳닮욫닮뗄뻹횵캪ꎬ쒳룶돌뛈쮵쏷뢴훆ퟩ뫏뗄믘놨뻹횵튪룟폚뮦짮300믘놨ꎬ퓚30쳬훐ꎬ폐19쳬뢴훆ퟩ뫏뗄믘놨튪룟폚뮦짮300횸쫽ꎬ죧맻엗웺뢴훆뗄룅쓮ꎬ쮵쏷뢴훆ퟩ뫏뗄뇭쿖튪뫃튻킩ꎬ뿉틔폃살짨볆낢뛻램닟싔ꆣ헢룶ퟩ뫏30룶붻틗죕뗄죕ힷퟙ욫샫뛈캪ꎬ떥떥듓헢룶쫽뻝살뾴ꎬힷퟙ킧맻늢늻쯣뫃ꎬ튵쓚튻냣짨뚨뗄ힷퟙ욫샫뛈쫽솿벶퓚10뗄-3듎랽ꎬ듓쿂쏦뗄럖컶뿉틔횪뗀쫜떽K횵맽킡뗄튻늿럖펰쿬ꆣ 뇭4-2 K=5쪱뮦짮300ힷퟙ뇭쿖 죕웚 뢴훆ퟩ뫏떥죕믘놨 뮦짮300떥죕믘놨 ힷퟙ컳닮욫닮 20100223 20100224 20100225 20100226 20100301 20100302 20100303 20100304 20100305 20100308 20100309 20100310 20100311 20100312 20100315 20100316 20100317 20100318 20100319 20100322 20100323 20100324 20100325 20100326 20100329 20100330 20100331 20100401 20100402 20100406 max min aver TE 36
쿂쏦뗄뇭룱붫룸돶K횵뗄룄뇤뛔ힷퟙ킧맻뗄펰쿬ꎬK횵듓5뾪쪼ꎬ튻횱퓶볓떽50ꎬ춬쪱춳볆쇋퓚룷룶늻춬뗄K횵쿂볆쯣쪱볤ꆣ 뇭4-3 K횵룄뇤뛔뢴훆킧맻펰쿬ꎨ1ꎩ 룺ퟙ컳닮욫닮뻹횵 K뗄좡횵 룺ퟙ컳닮욫닮 뻸뛔횵 룺ퟙ욫샫뛈 볆쯣쪱볤ꎨ쏫ꎩ 5 10 15 20 25 30 35 40 45 50 max min aver 듓짏쏦뗄뇭룱뿉틔듳룅뾴돶K횵룄뇤뛔ힷퟙ욫샫뛈뗄펰쿬ꆣ퓚K=5뗄쪱뫲ힷퟙ욫샫뛈ퟮ듳ꎬ쫇ꎬ퓚K=25뗄쪱뫲ힷퟙ욫샫뛈ퟮ킡ꎬ쫇ꆣ듓ힷퟙ욫샫뛈뗄쟷쫆살뾴ꎬK=5쪱좡뗃ퟮ듳횵ꎬ좻뫳쯦ퟅK횵뗄퓶볓폐튻룶늻뛏복킡뗄맽돌ꎬ튻횱떽K=25ꎬ떽듯ퟮ킡뗄ힷퟙ욫샫뛈ꎻ짔뫳ꎬힷퟙ욫샫뛈퓶듳떽잧럖횮냋쫽솿벶ꎬ짏쿂늨뚯ꎬ쎻폐첫듳뗄룄뇤ꆣ뾼싇떽틔짏쫽뻝ꎬ퓚K=25쪱ꎬ튲뻍쫇폃25횧막욱뢴훆뮦짮300뗄킧맻뇈뷏뫃ꆣ듓퓋탐쪱볤뾴ꎬ쯦ퟅK횵퓶볓퓋탐쪱볤믹놾짏쫇늻뛏퓶볓뗄ꎬ횻폐퓚K=15뫍K=20뗄쪱뫲돶쿖쇋틬뎣ꆣퟜ쳥살쮵퓋탐킧싊뫜룟ꎬ욽뻹폃쪱캪쏫ꎬ풶풶킡폚웤쯻튻킩랽램ꎬ샽죧닮럖뷸뮯쯣램횸쫽뢴훆뗄퓋탐쪱볤ꎬ웤튻냣퓚튻럖훓틔짏ꎬ짵훁듯떽벸럖훓ꆣ룺ퟙ컳닮욫닮30쳬뻹횵뗄뻸뛔횵ퟮ듳캪ꎬퟮ킡캪ꎬ뻹횵캪ꆣ폃쇋춬퇹뗄랽램ꎬ톰헒짏횤100뗄ퟮ폅뢴훆ퟩ뫏돉럖막뗄쫽쒿ꎬ뗃떽뗄쫽뻝쫇떱K=10쪱ꎬ벴폃10횻막욱뢴훆짏횤100뗄킧맻뇈뷏뫃ꆣ쿂쏦룸돶솽럹뢴훆킧맻춼ꆣ 헢샯탨튪쮵쏷튻쿂뢴훆ퟩ뫏뗣캻뗄좷뚨ꆣ컒쏇틔2010쓪2퓂22죕ퟷ캪믹죕ꎬ틔헢튻쳬놻ힷퟙ횸쫽뗄뗣캻ퟷ캪믹뗣ꎬ틔헢튻쳬뢴훆ퟩ뫏뗄ퟜ쫐횵ퟷ캪믹웚ꎬ헢 37
퇹뢴훆ퟩ뫏쎿죕뗄뗣캻뻍뗈폚룃죕뗄ퟩ뫏뗷헻쫐횵/믹웚×믹뗣뗃떽ꆣ뛔폚뮦짮300횸쫽뗄뢴훆ꎬ30룶붻틗죕훐뢴훆ퟩ뫏뗣캻폫뮦짮300횸쫽뗣캻닮횵뗄뻸뛔횵ퟮ듳횵캪ꎬퟮ킡횵캪ꎬ뻹횵캪ꆣ뛔폚짏횤100횸쫽뗄뢴훆ꎬ30룶붻틗죕훐뢴훆ퟩ뫏뗣캻폫짏횤100횸쫽뗣캻닮횵뗄뻸뛔횵뗄ퟮ듳횵캪ꎬퟮ킡횵캪ꎬ뻹횵캪ꆣퟜ쳥살쮵믹놾뢴훆쇋횸쫽뗄쟷쫆ꆣ ㌴㔰㌴〰㌳㔰㌳〰㌲㔰㌲〰㌱㔰㌱〰㌰㔰?????ㄱㄳㄵㄷㄹ㈱㈳㈵㈷㈹뢴훆ퟩ뫏뮦짮㌰? 춼4-1 K=25쪱뛔뮦짮300뢴훆킧맻춼ꎨ1ꎩ ㌳〰㌲㔰㌲〰㌱㔰㌱〰㌰㔰㌰〰㈹㔰?????ㄱㄳㄵㄷㄹ㈱㈳㈵㈷㈹쿖ꐱ〰뢴훆ퟩ뫏 춼4-2 K=10쪱짏횤100뢴훆킧맻춼 38
퓚짏쫶볆쯣횮췢ꎬ캬돖K횵퓚25ꎬ컒쏇폖럖뇰룄뇤쇋쎿횧막욱뗄ퟮ듳춶뇈샽ꎬퟮ킡춶뇈샽ꎬ틔벰붻틗럑폃쯹쓜햼폃뗄ퟮ듳좨훘ꎬ뷡맻쿔쪾헢킩뇤솿뗄룄뇤늢쎻폐뛔뢴훆ퟩ뫏뗄ힷퟙ킧맻닺짺쏷쿔뗄ꎬ믲헟쟷쫆탔뗄펰쿬ꎬ틲듋퓚헢샯쎻폐붫퓋쯣뷡맻튻튻쇐돶ꆣ 2ꎩla=0,lb=1쒣탍 쿂쏦뾼싇튻뷗뛎쒣탍뗄쇭췢튻훖탎쪽ꎬ벴뺡솿쪹b뗄횵쟷폚1ꎬ뛸뫶싔뛔a뗄풼쫸ꆣퟜ쳥살쮵ꎬ헢훖쒣탍뛔뮦짮300횸쫽뗄뢴훆킧맻튪닮폚la=1,lb=0쒣탍뗄뢴훆킧맻ꎬ쿂쏦룸돶뻟쳥뗄볆쯣쫽뻝ꆣ퓚볆쯣맽돌훐짨훃쇋쿠춬뗄웰쪼닎쫽ꎬ횻쫇룄뇤쇋K뗄횵ꎬ춬퇹듓5튻횱떽50ꆣ 뇭4-4 K횵룄뇤뛔뢴훆킧맻뗄펰쿬ꎨ2ꎩ 룺ퟙ컳닮욫닮뻹횵 K뗄좡횵 룺ퟙ컳닮욫닮뻹횵 뻸뛔횵 룺ퟙ욫샫뛈 볆쯣쪱볤ꎨ쏫ꎩ 5 10 15 20 25 30 35 40 45 50 MAX MIN AVER 퓚헢룶쒣탍쿂ꎬ룺ퟙ욫샫뛈뗄뇤뮯쟷쫆늻쫇쓇쎴쏷쿔ꎬ퓚K=25쪱욫뛈뗄횵늻쫇ퟮ킡횵ꎬ뻓폚뗚뛾킡뗄캻훃ꎬ퓚K=40뗄쪱뫲좡떽ퟮ킡욫샫뛈ꆣ룺ퟙ욫샫뛈뗄ퟮ듳횵캪ꎬ튪킡폚la=1,lb=0쒣탍ꎬ떫쫇웤ퟮ킡횵캪ꎬ듳폚la=1,lb=0쒣탍뗄ퟮ킡횵ꎬ웤뻹횵캪ꎬ튲튪쿔훸듳폚쒣탍뗄룺ퟙ욫샫뛈뻹횵ꆣ헢룶쒣탍뗄볆쯣쪱볤쿠뛔뷏뛌ꎬ뻹횵횻폐쏫ꎬ짙폚la=1lb,=0쒣탍뗄쏫ꆣ쿂쏦룸돶K=40뗄튻룶룺ퟙ킧맻춼ꆣ 39
㌴㔰㌴〰㌳㔰㌳〰㌲㔰㌲〰㌱㔰㌱〰㌰㔰?????ㄱㄳㄵㄷㄹ㈱㈳㈵㈷㈹뢴훆ퟩ뫏뮦짮㌰? 춼4-3 K=40쪱뮦짮300뢴훆킧맻춼 짏춼퓚K=40쪱ꎬ뛔뮦짮300횸쫽뗄뢴훆ꎬ30룶붻틗죕훐뢴훆ퟩ뫏뗣캻폫뮦짮300횸쫽뗣캻닮횵뗄뻸뛔횵ퟮ듳횵캪ꎬퟮ킡횵캪ꎬ뻹횵캪ꆣ 솽뷗뛎쒣탍 솽뷗뛎쒣탍폐솽훖탎쪽ꎬ쿈∧∧∧min|a−0|ꎬ좻뫳퓙min|b−1|뫍쿈min|b−1|ꎬ좻뫳퓙∧min|a−0|ꎬ쿂쏦럖뇰룸돶솽훖쒣탍뗄뷡맻ꆣ ∧1ꎩ쿈min|a−0|ꎬ좻뫳퓙∧min|b−1|쒣탍 뇭4-5 K횵룄뇤뛔뢴훆킧맻뗄펰쿬ꎨ3ꎩ 룺ퟙ컳닮욫닮뻹횵K뗄좡횵 룺ퟙ컳닮욫닮뻹횵 뻸뛔횵 룺ퟙ욫샫뛈 볆쯣쪱볤ꎨ쏫ꎩ 5 10 15 20 25 30 35 40 45 50 max min aver 40
듓뇭훐뗄쫽뻝뿉틔랢쿖ꎬ헢룶솽뷗뛎쒣탍ힷퟙ킧맻튪쏷쿔뫃폚짏쏦뷩짜뗄솽룶튻뷗뛎쒣탍뗄뢴훆킧맻ꆣ맘힢룺ퟙ컳닮욫닮뻸뛔횵뻹횵ꎬ뇭4-3뫍뇭4-4훐튻뷗뛎쒣탍뗄횵캪ꎬ룃솽뷗뛎쒣탍뗄횵캪ꎬ뗍쇋42%ꎻ맘힢룺ퟙ욫샫뛈ꎬ뇭4-3훐뗄뻹횵캪ꎬퟮ킡횵캪ꎬ뇭4-4훐뗄뻹횵캪ꎬퟮ킡횵캪ꎬ뛸룃뇭4-5훐뻹횵횻폐ꎬퟮ킡횵횻폐ꎻ떱좻ꎬ룃쒣탍뗄퓋탐쪱볤튪뎤튻킩ꎬ욽뻹볆쯣쪱볤캪쏫ꎬ뇭4-3룸돶뗄욽뻹볆쯣쪱볤캪ꎬ뇭4-4룸돶뗄욽뻹볆쯣쪱볤캪ꆣ횻맘힢뇭4-5ꎬ쯦ퟅK횵뇤뮯ꎬ룺ퟙ욫샫뛈쎻폐쿔쪾돶뫜쏷쿔뗄쟷쫆뇤뮯ꎬ퓚K=25쪱ꎬ룺ퟙ욫샫뛈좡뗃ퟮ킡횵ꎬ퓚K=35틔뫳ꎬ룺ퟙ욫샫뛈캬돖퓚잧럖횮쇹쫽솿벶ꆣ쿂쏦룸돶K=25쪱뗄룺ퟙ킧맻춼ꆣ ㌴㔰㌴〰㌳㔰㌳〰㌲㔰㌲〰㌱㔰㌱〰㌰㔰?????ㄱㄳㄵㄷㄹ㈱㈳㈵㈷㈹뢴훆ퟩ뫏뮦짮㌰? 춼4-4 K=25쪱뮦짮300뢴훆킧맻춼 춼4-4ꎬ퓚K=25쪱ꎬ뛔뮦짮300횸쫽뗄뢴훆ꎬ30룶붻틗죕훐뢴훆ퟩ뫏뗣캻폫뮦짮300횸쫽뗣캻닮횵뗄뻸뛔횵ퟮ듳횵캪ꎬퟮ킡횵캪ꎬ뻹횵캪ꆣ ∧∧2ꎩ쿈min|b−1|ꎬ좻뫳퓙min|a−0|쒣탍 41
뇭4-6 K횵룄뇤뛔뢴훆킧맻뗄펰쿬ꎨ4ꎩ 룺ퟙ컳닮욫닮뻹K뗄좡횵 룺ퟙ컳닮욫닮뻹횵 횵뻸뛔횵 룺ퟙ욫샫뛈 볆쯣쪱볤ꎨ쏫ꎩ 5 10 15 20 25 30 35 40 45 50 max min aver 룃쒣탍뗄ힷퟙ킧맻늻죧뇭4-5룸돶뗄뛾뷗뛎쒣탍뗄ힷퟙ킧맻ꎬ듓ힷퟙ컳닮욫닮뻹횵뻸뛔횵살뾴짵훁늻죧솽룶튻뷗뛎쒣탍뗄ힷퟙ킧맻ꎬ룺ퟙ컳닮욫닮뻹횵뻸뛔횵룟듯ꆣ룃쒣탍뗄룺ퟙ욫샫뛈뻹횵캪ꎬ룟폚뇭4-5룸돶뗄ꎬ볆쯣쪱볤뻹횵쿠뛔폚뇭4-5룸돶뗄쪱볤뻹횵폐짙탭복짙ꆣ퓚K=25쪱ꎬ룺ퟙ욫샫뛈듯떽ퟮ킡횵ꎬ듓K=15틔뫳ꎬힷퟙ욫샫뛈캬돖퓚잧럖횮웟쫽솿벶ꆣ쿂쏦룸룶K=25쫇ힷퟙ킧맻춼ꆣ ㌵〰㌴㔰㌴〰㌳㔰㌳〰㌲㔰㌲〰㌱㔰㌱〰㌰㔰?????ㄱㄳㄵㄷㄹ㈱㈳㈵㈷㈹뢴훆ퟩ뫏뮦짮㌰? 춼4-5 K=25쪱뮦짮300뢴훆킧맻춼 42
춼4-5ꎬ퓚K=25쪱ꎬ뛔뮦짮300횸쫽뗄뢴훆ꎬ30룶붻틗죕훐뢴훆ퟩ뫏뗣캻폫뮦짮300횸쫽뗣캻닮횵뗄뻸뛔횵ퟮ듳횵캪ꎬퟮ킡횵캪ꎬ뻹횵캪ꆣ 죽뷗뛎쒣탍 볲뛸퇔횮ꎬ죽뷗뛎쒣탍뻍쫇틽죫쇋붻틗럑폃ꆣ웤쪵붻틗럑폃뗄틽죫뿉틔탎돉탭뛠탂뗄쒣탍ퟩ뫏ꎬ뇈죧퓚튻뷗뛎쒣탍뗄믹뒡짏틽죫붻틗럑폃탎돉솽뷗뛎쒣탍ꎬ뻍뿉틔탎돉튻횻튻훖탂쒣탍ꆣ쿖퓚컒쏇쫇퓚솽뷗뛎쒣탍뗄믹뒡짏틽죫붻틗럑폃ꎬ탎돉죽뷗뛎쒣탍ꎬ훷튪뾼싇떽솽뷗뛎쒣탍뗄ힷퟙ킧맻뇈튻뷗뛎뫃튻킩ꎬ퓚쪵볹훐ꎬ퓚늻탨튪첫듳뛮췢돉놾뗄쟩뿶쿂뿏뚨퓱폅톡퓱쒣탍ꎬ틲듋횻퓚컄훐쏨쫶쇋틽죫붻틗럑폃뗄죽뷗뛎쒣탍ꆣ폖퓚킡뷚훐ꎬ쿈∧min|a−0|ꎬ좻뫳퓙∧min|b−1|쒣탍뗄ힷퟙ킧맻룼뫃튻킩ꎬ틲듋퓚헢튻뷚횻룸돶퓚룃쒣탍믹뒡짏틽죫붻틗럑폃뗄죽뷗뛎쒣탍ꆣ퓚뇭4-5훐룸돶쇋쿈∧min|a−0|ꎬ좻뫳퓙∧min|b−1|쒣탍뗄쿠맘뷡맻ꎬ퓚K=30뗄쪱뫲ힷퟙ킧맻뇈뷏뫃ꎬ틲듋퓚헢늿럖죽뷗뛎쒣탍훐붫닉폃K=30ꎬ좻뫳룄뇤붻틗럑폃ퟮ듳뇈훘릹붨뢴훆ퟩ뫏ꎬ뇈뷏웤늻춬뗄ힷퟙ킧맻ꆣ 뇭4-7 죽뷗뛎쒣탍뗄ힷퟙ킧맻 붻틗럑폃쯹쓜햼룺ퟙ컳닮욫닮뻹폃ퟮ듳뇈훘 룺ퟙ컳닮욫닮뻹횵 횵뻸뛔횵 룺ퟙ욫샫뛈 볆쯣쪱볤ꎨ쏫ꎩ max min aver 43
퓚뇭4-7훐ꎬ늻뛏룄뇤뗄뇤솿쫇붻틗럑폃쯹쓜햼뗄ퟮ듳뇈훘ꎬ뇤뮯뗄웰뗣캪ꎬ헢훷튪쫇뷡뫏쒿잰훐맺막욱쫐뎡뗄쪵쟩ꎬ춶죋퓚싲싴막욱뗄맽돌훐횻폐싴돶막욱뗄쪱뫲탨튪붻쓉뗄펡뮨쮰ꎻ뇤뮯뗄훕뗣쫇ꎬ톡퓱헢룶훕뗣폐솽룶풭틲ꎬ쫗쿈쫇붻틗럑폃쯹쓜햼뗄ퟮ듳뇈훘킡폚쪱ꎬ쟳뷢컊쳢컞뷢ꎬ웤듎ꎬ듓뇭훐뗄쫽뻝뿉틔랢쿖붻틗럑폃쯹쓜햼뗄ퟮ듳뇈훘퓚뫳ꎬ뢴훆ퟩ뫏뗄ힷퟙ킧맻틑뺭쎻폐닮틬ꆣ맘힢뇭4-7훐뗄ힷퟙ욫샫뛈ꎬ컒쏇랢쿖죽뷗뛎쒣탍뗄ힷퟙ킧맻쏷쿔뫃폚튻뷗뛎쒣탍뫍솽뷗뛎쒣탍ꎬힷퟙ욫샫뛈뗄뻹횵횻폐ꎬퟮ킡캪ꎬ퓚짏컄뇭룱훐룸돶뗄ힷퟙ욫샫뛈뻹횵훐ퟮ뫃뗄뇭쿖튲폐ꎬ풶풶듳폚ꆣ맘힢뇭4-7훐룺ퟙ컳닮욫닮뻹횵뻸뛔횵ꎬ헢룶솿쿠뛔폚잰컄뗄쒣탍튪듳뫜뛠ꎬ떫쫇컒쏇믡랢쿖뇭4-7훐룺ퟙ컳닮욫닮뻹횵뚼쫇헽횵ꎬ헢룶쮵쏷퓚쎿훖쟩뿶쿂뢴훆ퟩ뫏쿠뛔폚뮦짮300횸쫽뚼폐룼룟뗄믘놨ꎬ헢쫇튻훖뫃탅뫅ꆣ죽뷗뛎쒣탍뗄욽뻹볆쯣쪱볤캪ꎬퟜ쳥살뾴쯦ퟅ붻틗럑폃쯹쓜햼뗄ퟮ듳뇈훘쿂붵ꎬ볆쯣쪱볤쫇짏짽뗄ꎬ떫쫇헢훖쟷쫆늻쫇떥뗷뇤뮯뗄ꆣ 뷷짷럧쿕퇡뛱쿂횸쫽뢴훆쫽횵쪵퇩 헢늿럖쓚죝훷튪틀뻝뻹횵—랽닮—욫뛈쒣탍ꎬ헫뛔뮦짮300붨솢ힷퟙퟩ뫏ꎬ뻟쳥늽훨죧쿂ꎺ 1ꎩ볆쯣뮦짮300횸쫽뗄300횧돉럖막듓2010쓪1퓂12죕떽2010쓪2퓂22죕25룶붻틗죕뗄떥죕쫕틦싊ꎻ 2ꎩ짨뚨닎쫽ꎬ틔벰붫1ꎩ뗃떽뗄쫽뻝듺죫볆쯣쒣탍ꎻ 3ꎩ폃헻쫽쿟탔맦뮮쟳뷢ퟩ뫏ꎬ퓚헢룶맽돌훐늻뛏룄뇤맘볼닎쫽뗄좡횵ꎬ좡뗃늻춬뗄룺ퟙퟩ뫏ꎻ 4ꎩ폫횸쫽뗄킧맻쿠뇈뷏ꎬ폃퇹놾췢뗄쫽뻝움볛룺ퟙퟩ뫏뗄룺ퟙ킧맻ꆣ 쿂쏦쿈뛔뢴훆ퟩ뫏릹붨훐뗄돵쪼닎쫽뷸탐튻쿂쮵쏷ꆣ 44
뇭4-8 돵쪼닎쫽뗄짨뚨 닎쫽쏻돆 닎쫽몬틥 닎쫽횵 tpSize 뢴훆ퟩ뫏막욱쫽 5maxCostRatio 붻틗럑폃쯹쓜햼폃뗄ퟮ듳좨훘 싲죫붻틗럑폃뇈싊 0sellFee 싴돶붻틗럑폃뇈싊 탂춶죫뷰 0T 믘쯝쪱볤 25xptRet 튪쟳뗄웚췻믘놨 튪쟳뗄뇪ힼ닮 쿟탔뮯쪱쟸볤뗈럖럖쫽 50쿠뛔폚럧쿕퇡뛱춶헟뢴훆ퟩ뫏붨솢뗄돵쪼쒣탍ꎬ헢샯짦벰뗄탂닎쫽훷튪폐뫳쏦쯄룶ꎬ믘쯝쪱볤ꎬ튪쟳뗄웚췻믘놨ꎬ튪쟳뗄뇪ힼ닮틔벰쿟탔뮯쪱쟸볤뗈럖럖쫽ꆣ믘쯝쟸볤뻍쫇횸쒣탍붨솢쪱쪹폃뗄퇹놾쓚쟸볤ꎬ퓚헢샯횸2010쓪1퓂12죕떽2010쓪2퓂22죕ꎻ튪쟳뗄웚췻믘놨벴풼쫸ꎨꎩ훐뗄rꎻ튪쟳뗄뇪ힼ닮벴풼쫸ꎨꎩ훐뗄sꎻ쿟탔뮯쪱쟸볤뗄뗈럖럖쫽퓚뷚훐ퟶ쇋쿪쾸쮵쏷ꆣ퓚볆쯣맽돌훐ꎬ훷튪룄뇤튪쟳뗄웚췻믘놨ꎬ튪쟳뗄뇪ힼ닮ꆣ쿂쏦룸돶쿠맘뷡맻ꎬ틔벰K횵룄뇤뗄펰쿬ꆣ 뇭4-9 K횵룄뇤뛔뢴훆킧맻펰쿬ꎨ5ꎩ 룺ퟙ컳닮욫닮뻹횵K뗄좡횵 룺ퟙ컳닮욫닮뻹횵 뻸뛔횵 룺ퟙ욫샫뛈 볆쯣쪱볤ꎨ쏫ꎩ 5 10 15 20 25 30 35 40 45 50 max min aver 45
맘힢뇭4-9훐룸돶뗄룺ퟙ욫샫뛈ꎬ볲떥뗄듓쫽횵살뾴룺ퟙ킧맻늢늻뫃ꎬ떫쫇펦룃힢틢ꎬ퓚헢룶쒣탍훐룼뛠맘힢뗄쫇뢴훆ퟩ뫏믘놨뻟폐ퟮ듳욫뛈ꆣ맘힢룺ퟙ컳닮욫닮ꎬ퓚룷룶K늻춬뗄쟩뿶쿂믹놾캪헽횵ꎬ뻹횵캪ꎬퟮ룟캪ꎬ믹놾럻뫏쒣탍짨볆뗄쿫램ꆣ맘힢볆쯣쪱볤ꎬ컒쏇랢쿖룃쒣탍뗄볆쯣쪱볤풶풶뎤폚잰컄쳡떽뗄쒣탍ꎬ짵훁듯떽잰컄쒣탍쪱볤뗄18-20놶ꎬ떫쫇퓚뿉틔뷓쫜랶캧쓚ꆣ뾼싇떽룃쒣탍맘힢뢴훆ퟩ뫏횸쫽뛔뮦짮300횸쫽헽쿲욫틆ꎬ쿂컄룸돶튻룶욫틆솿춼ꆣ ㌶〰㌵〰㌴〰㌳〰㌲〰㌱〰㌰〰?????ㄱㄳㄵㄷㄹ㈱㈳㈵㈷㈹뢴훆ퟩ뫏뮦짮㌰? 춼4-6 K=15쪱뮦짮300뢴훆킧맻춼 ㄴ?ㄲ??㠰㘰㐰㈰??????ㄱㄳㄵㄷㄹ㈱㈳㈵㈷㈹욫틆솿 춼4-7 욫틆솿춼 46
춼4-6룸돶뗄쫇뢴훆ퟩ뫏폫뮦짮300횸쫽뗄뇈뷏ꎬ춼4-7룸돶뗄쫇뢴훆ퟩ뫏쿠뛔폚뮦짮300횸쫽횵뗄욫틆ꆣ퓚30룶붻틗죕훐뢴훆ퟩ뫏뗣캻폫뮦짮300횸쫽뗣캻닮횵뗄ퟮ듳횵캪ꎬퟮ킡횵캪ꎬ뻹횵캪ꆣ 놾헂킡뷡 놾헂훷튪쏨쫶쇋퓚춶헟늻춬뗄럧쿕욫뫃쿂뢴훆ퟩ뫏뗄붨솢ꆣ쿈쫇헫뛔럧쿕퇡뛱춶헟릹붨뢴훆ퟩ뫏ꎬ훷튪닉폃쇋죽훖탎쪽뗄쒣탍ꎬ튻뷗뛎쒣탍ꎬ솽뷗뛎쒣탍틔벰죽뷗뛎쒣탍ꆣ웤훐튻뷗뛎쒣탍뫍솽뷗뛎쒣탍폖럖뇰닉폃쇋솽훖탎쪽뗄쒿뇪몯쫽ꆣ듓뢴훆킧맻살뾴ꎬ죽뷗뛎쒣탍뗄뢴훆킧맻ퟮ뫃ꎬ퓚퇹놾췢30룶붻틗죕훐욽뻹뗄룺ퟙ욫샫뛈횻폐ꎬ웤듎쫇솽뷗뛎쒣탍ꎬ퓙듎쫇튻뷗뛎쒣탍ꎬ놾헂룸돶쇋뇈뷏쿪쾸뗄볆쯣뷡맻ꆣ듓볆쯣쪱볤살뾴ꎬ죽훖쒣탍폃쪱뚼뫜짙ꎬ퓚3쏫틔쓚ꎬ풶풶뗍폚쒿잰듦퓚뗄튻킩횸쫽뢴훆랽램ꎬ쮵쏷룃랽램킧싊뫜룟ꆣ뷓ퟅ컄훐뷩짜쇋헫뛔뷷짷뗄럧쿕퇡뛱춶헟릹붨뢴훆ퟩ뫏ꎬ믹놾듯떽쒣탍뗄짨볆쒿뇪ꎬ뢴훆ퟩ뫏쿠뛔폚뮦짮300횸쫽횵폐뷏듳뗄헽쿲욫틆ꎬ컄훐룸돶쇋킧맻춼ꆣ뛔폚볆쯣쪱볤ꎬ룃쒣탍뇈짏쏦쳡떽뗄헫뛔럧쿕퇡뛱헟릹퓬뢴훆ퟩ뫏쒣탍뗄쪱볤튪뎤ꎬ떫쫇퓚40쏫틔쓚ꎬ퓚뿉틔뷓쫜뗄랶캧ꆣ 47
5 좫컄ퟜ뷡 횸쫽뢴훆벼쫵쫇횸쫽믹뷰ꎬ막횸웚믵ꎬ막횸웚좨틔벰ETF뗈뷰죚닺욷펦폃폚쪵볹뗄맘볼쯹퓚ꆣ뛔횸쫽뢴훆뗄퇐뺿ퟜ쳥살쮵뿉틔럖돉솽늿럖ꎺ뗚튻늿럖쫇횸쫽뢴훆쒣탍뗄릹붨ꎬ헢룶맽돌맘쾵떽횸쫽뢴훆쯹닉폃뗄랽램ꎬ벴췪좫뢴훆ꎬ폅뮯뢴훆뗈랽램뗄톡퓱ꎬ틔벰횸쫽뢴훆풤웚듯떽뗄킧맻ꎬ벴뢴훆쒿뇪뗄톡뚨ꎻ뗚뛾늿럖쫇횸쫽뢴훆쒣탍뗄쟳뷢ꎬ췪좫뢴훆쿠뛔뇈뷏볲떥ꎬ짦벰늻떽쟳뷢ꎬ헢늿럖뗄쓚죝훷튪헫뛔폅뮯뢴훆랽램ꎬ짦벰떽떥쒿뇪맦뮮ꎬ쮫쒿뇪맦뮮짵훁뛠쒿뇪맦뮮뗈ꎬ헢킩맦뮮쪵쿖뗄쯣램튲쫇뛠훖뛠퇹뗄ꎬ샠죧닮럖뷸뮯쯣램뗈ꆣ 놾컄횸쫽뢴훆톡퓱뗄랽램쫇폅뮯횸쫽뢴훆ꎬ벴톡퓱돉럖막뗄튻늿럖막욱ꎬ닉좡튻뚨뗄폅뮯랽램ꎬ릹퓬뢴훆ퟩ뫏살ힷퟙ횸쫽ꆣ놾컄퓚쒿뇪몯쫽뗄톡퓱맽돌훐ꎬ룼뛠뗄뾼싇쇋춶죋뗄럧쿕욫뫃ꎬ틀뻝늻춬춶죋뗄럧쿕욫뫃돌뛈짨볆늻춬뗄쒿뇪몯쫽릹퓬ힷퟙퟩ뫏ꆣ웤훐훷튪뾼싇쇋솽샠춶죋ꎬ럧쿕퇡뛱뗄춶죋뫍뷷짷뗄럧쿕퇡뛱춶죋ꎬ냑헢킩늻춬샠탍춶죋뗄욫뫃쳥쿖퓚쒿뇪몯쫽훐ꆣ헫뛔럧쿕퇡뛱춶죋릹붨ힷퟙ쒣탍쪱ꎬ놾훐폖럖뇰뾼싇쇋튻뷗뛎쒣탍ꎬ솽뷗뛎쒣탍틔벰죽뷗뛎쒣탍ꆣ퓚쒣탍쟳뷢훐ꎬ샻폃튻킩쿟탔뮯뗄쫖뛎붫럇쿟탔믬뫏헻쫽맦뮮컊쳢뮯캪쿟탔믬뫏헻쫽맦뮮컊쳢쟳뷢ꎬ헢퇹듳듳볲뮯쇋쟳뷢맽돌ꎬ쳡룟쇋쯣램킧싊ꎬ샻폃Cplex헢룶뇈뷏돉쫬뗄죭볾쪵쿖쯣램뗄쟳뷢ꆣ 놾컄퓚쿪쾸뷩짜쇋횸쫽뢴훆쒣탍뫍쯣램쪵쿖뫳ꎬ뷸탐쇋쪵퇩퇐뺿ꆣ뾼싇떽쒿잰훐맺놾쫐뎡췆돶쇋뮦짮300막횸웚믵ꎬ틲듋톡퓱뮦짮300횸쫽ퟷ캪훷튪ힷퟙ횸쫽ꎬ붫짏횤100ퟶ듎튪ힷퟙ횸쫽ꆣ듓ힷퟙ뷡맻뾴ꎬ믹놾듯떽풤웚뷡맻ꆣ컄훐틔ힷퟙ욫샫뛈ퟷ캪ힷퟙ킧맻뗄랴펳ꎬ퓚뛔럧쿕퇡뛱춶헟릹붨뗄ힷퟙ쒣탍훐ꎬ컄훐죽뷗뛎쒣탍뗄ힷퟙ킧맻ퟮ뫃ꎬ퇹놾췢뗄쫽뻝ힷퟙ욫샫뛈믹놾퓚잧럖횮쯄뗄쫽솿벶ꆣ퓚뛔뷷짷럧쿕퇡뛱춶헟릹붨ힷퟙ쒣탍훐ꎬힷ쟳뗄쫇뢴훆횸쫽쿠뛔폚쒿뇪횸쫽헽쿲뗄욫틆ꎬ헢룶퓚퇹놾췢뗄쫽뻝뷡맻훐폐쏷쿔뗄쳥쿖ꎬ컄헂훐럖뇰룸돶쇋춼뇭뷸탐쮵쏷ꆣ쇭췢튻뗣ꎬ놾컄샻폃뗄믬뫏헻쫽맦뮮릹붨횸쫽뢴훆쒣탍뗄킧싊뫜룟ꎬퟮ뎤뗄쪱볤뚼쎻폐뎬맽1럖훓ꆣ 48
쿟탔헻쫽맦뮮쫇튻룶랢햹틑뺭뇈뷏돉쫬뗄쇬폲ꎬ쟳뷢랽램쿠뛔튲뇈뷏볲떥ꎬ퓚톧쫵뷧믹놾탎돉튻훂탔ꎬ틲듋펦폃웰살뇈뷏랽뇣ꆣ쪹폃헢훖볲떥랽뇣뗄랽램ꎬ폐샻폚횸쫽뢴훆벼쫵뗄췆맣뫍펦폃ꆣ퇐뺿횸쫽뢴훆벼쫵뗄쒿뗄뻍쫇펦폃폚쪵볹ꆣ떱좻ꎬ퓚뻟쳥횸쫽뢴훆쒣탍훐뫜폐탭뛠횵뗃뾼싇뗄컊쳢ꎬ샽죧좷뚨ퟮ듳춶뇈샽쪱쫐뎡돥믷돉놾뗄뾼싇ꎬ틔벰뢴훆ퟩ뫏뗷헻뗄쪱믺톡퓱컊쳢ꎬ틔벰붫뢴훆ퟩ뫏펦폃퓚쪵볊춶쳗샻ꎬ헢킩뚼쫇뷱뫳횵뗃뷸튻늽퇐뺿뗄쇬폲ꆣ 49
훂 킻 킴떽헢샯뗄쪱뫲춻좻폐훖쒪쏻뗄짋룐ꆣ듳톧놾뿆뷡쫸쪱컒뮹뿉틔쮵ꎺ뮹튪퓚헢샯듴짏솽쓪냫ꎬ쪱볤뮹뛠ꎬ맢틵뮹뎤ꆣ뿉쫇쿖퓚붫쫇컒톧짺짺퇄뷡쫸ꎬ퓚헢퇹뗄뷰쟯쪮퓂ꎬ퓚틀좻뿡죈뗄커몺ꎬ퓚컒짮낮뗄뮪뿆듳ꆣ퓚헢샯ꎬ쇹쓪뛠뗄맢틵쯪퓂ꎬ컒짺쏼훐ퟮ톤샶뛠닊뗄벾뷚ꎬ붫튪뷡쫸ꆣ컒붫튪듓헢샯웰몽ꎬퟟ돶킣풰ꎬퟟ쿲쏷쳬ꆣ쇹쓪뛠뗄쪱맢ꎬ짺쏼훐살살췹췹뗄죋ꎬ냩쯦컒돉뎤ꎬ룸폨컒웴뗏ꎬ쪹컒뗄쟳톧횮슷짙쇋킩뾲뿀뫍뿠쏆ꎬ뛠쇋킩룐뛷ꎬ쓑췼뫍뿬샖ꆣ 룐킻컒뗄떼쪦릨웓뷌쫚ꆣힼ좷뗄붲컒쫇2007쓪쪮퓂틔뫳뻍뾪쪼뷸죫쪵퇩쫒ꎬힷ쯦컒뗄떼쪦ꎬ떽쿖퓚캪횹틑뺭헻헻죽룶쓪춷ꆣ죽쓪쪱맢훐ꎬ릨샏쪦룸폨컒뗄뷌믥뫍맘뮳쓑틔폃퇔폯뇭듯ꆣ릨샏쪦뺭뎣쳡벰뗄“뺫펢뷌폽”샭쓮ꎬ쯻뗄얻탄솤톪잱탄뿆퇐ꎬ쯻캪쎿룶톧짺잰춾쏼퓋즷럑뿠탄ꎬ뚼짮짮뗄룐좾뫍펰쿬ퟅ컒ꆣ쟥컺볇뗃퓚짺믮믲헟톧튵훐폶떽삧죅쪱ꎬ릨샏쪦쎿튻듎폯훘탄뎤뗄뾪떼ꆣ톧짺늻닅ꎬ뿉쓜퓚뫜뛠랽쏦림뢺쇋샏쪦뗄뫱췻ꎬ뿉쫇쓺퓸뺭붲뗄쎿뻤뮰컒뚼믡볇뗃ꎬ늻맜잰랽퓵퇹ꎬ헢킩뷌믥컒믡튻짺쫜틦ꆣ 룐킻퓸뺭룸폨컒뷌떼뗄쎿튻캻샏쪦ꆣ쓣쏇풨늩뗄횪쪶ꎬ돧룟뗄쪦뗂ꎬ틔벰뛀쳘뗄쫚뿎랽쪽ꎬ컒뚼믡쏺볇탄훐ꆣ컒좷탅ꎬ뛠짙쓪틔뫳ꎬ컒틀뻝믡쿫웰ꎬ퓸뺭폐쓇쎴튻캻샏쪦ꎬ룸컒뷌쫚맽튻쏅뿎ꎬ쯻/쯽붲뿎뗄쪱뫲ꎬ뺭뎣쳡웰튻뻤뮰ꎬ뺭뎣튻룶뚯ퟷ……헢킩뗣뗣뗎뗎ꎬ뚼쫇컒놦맳뗄믘틤ꆣ 룐킻쪵퇩쫒뗄룷캻탖뗜뷣쏃ꎬ쪦탖헅놣훹ꎬ믆죙뇸ꎬ뫺ퟦ믔뗈ꎬ쪦뷣룟풭ꎬ춬쏅헅뗇쏷ꎬ틔벰룷캻쪦뗜쪦쏃ꎬ틲캪폐쇋쓣쏇ꎬ톧쫵슷짏뗄톯뫍첽쳖ꎬ뿝퓯뗄뿆퇐닅뇤뗃늻쓇쎴뿝퓯ꎬ죕ퟓ닅뛠쇋킩뮶뿬뫍틢ꆣ 룐킻컒뗄룷캻뫃폑ꎬ킻킻쓣쏇퓚컒탄쟩뗍실뗄쪱뫲쳽컒쟣쯟ꎬ룸컒캿뷥ꎻ퓚컒뗄쪱뫲냯컒럖컶ꎬ룸컒틢볻ꎻ퓚컒룟탋뗄쪱뫲ꎬ럖쿭컒뗄뿬샖ꎬ엣컒튻웰럨뿱ꆣ뚼쮵ꎬ죋짺쓑뗃튻횪벺ꎬ컒쟬탒ꎬ폐쓣쏇헢쎴뛠뗄횪벺ꆣ ퟮ뫳룐킻컒뗄뢸쒸볒죋ꆣ얮뛹헢쎴듳쇋뮹늻퓸킢쮳쓣쏇ꎬ헢쎴뛠쓪살쓣쏇룸컒뺫짱뫍컯훊짏뗄컞쟮횧돖ꎬ헢킩쫇컒튻놲ퟓ뚼쓑뗃믘놨뗄ꆣ컒뗄쎿튻듎뻶뚨ꎬ얼뛻뗄죎탔ꎬ폐쪱늢늻쮳쓣쏇탄틢ꎬ뿉쫇쓣쏇뚼컞쳵볾횧돖쇋컒뗄톡퓱ꎬ킻킻쓣쏇ꎡ 횣뷰 2010쓪 50
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