ყ ҩ,୍ֻ3௹股票价格成份指数编制方法研究ྋ, ႃᆽ, ٚᅸЧ(中国科学技术大学管理学院,安徽合肥230026)ᅋ ေ:本文运用决策树和Logistic回归将基本面因素引入股价指数成份股的选择和权重的确定,编制引导基本面投资理念的基本面股价成份指数(JOYFI300),并论证了该指数在超额收益方面表现出良好特性b首先通过决策树引入净利润和成交金额变量作为成份股的选样标准,选择成份股初始样本;建立Logistic模型分析基本面变量对成份股权重的影响,通过数据分析客观确定指数成份股及权重;实证检验JOYFI300指数各项性质,与沪深300a中信标普300的比较表明该指数具有更优的超额收益bܱՍ:决策树;Logistic回归;超额收益;基本面指数ᇏٳোݼ: ໓ངѓ്:A ໓ᅣщݼ:1003-5192(2009)03-0057-04ResearchonConstructingStockPriceConstituentIndexWANGXin,YINLiu-zh,iFANGZhao-ben(SchoolofManagement,USTC,Hefei230026,China)Abstract:BasedondecisiontreesandLogisticregression,(JOYFI300),createdasaguidancetofundamentalin-vestment,,twoselectionmeasures,netprofitandtradingvalue,arechosenbyusingdecisiontrees,,,aftertestingandcomparingwefindthatJOYFI300IndexisbetteronexcessreturnthanShangha-iShenzhen300andCITIC/S&:decisiontrees;Logisticregression;excessreturn;fundamentalindexᄴӮٺܢѩಒקಃᇗ,ࡎᆴ֮ܙ֥ܢௐିࠆ֤۷1 ႄކ֥ಃᇗ,ՖطႪ߄ᆷඔ֥ڄག൬ၭหᆘ[1];ູଢభੀྛ֥ܢௐࡎ۬ᆷඔ๙ӈࣇၛܢௐ൧ᆴ൧ӆิ܂၂ᇕॖࢌၞ֥ਅݺࠎሙ[2],ႄ֝ࠎႿࠎቔູࡆಃၹሰ,طܢௐࠎЧ૫ၹᄝथקᆷඔӮٺЧ૫ሧ֥;ູቆކሧᆀิ܂၂ᇕܒࡹሧܢܒӮൈ,ෙಖ္Ⴕ෮ॉ੮,ᄝथקಃᇗൈಏໃቆކ֥ྍٚم[3~5],ၛิۚሧӁᇂི֥ݔ,՜ࣉିऎุุགྷᆃུၹbਸ਼၂ٚ૫,ഒඔᆷඔෙಖၘࣁವ۽ӱඌ֥ႋႨbϜࠎЧ૫ၹቔູࡆಃၹሰ,ҐႨਔᇶܴ֥֩حקಃٚم,ग़ܴ၇ऌ҂ቀ2 ሸඍ,ၛ۳ԛކ֥ࣜ࠶ࢳbࠎႿᆃ၂གྷሑ,Ч໓ᄎႨथҦඎඌಒקࠎЧ ܢௐࡎ۬Ӯٺᆷඔщᇅགྷሑࠣቋྍࣉᅚ૫ᆷඔ࿊ܢჰᄵބӮٺܢԚဢЧ;ᆭުᄜၛࠎЧགྷႵܢࡎӮٺᆷඔ࿊ဢѓሙݖႿࡥֆ,ն؟ᆺ૫эਈቔູࡆಃၹሰࡹ৫Logisticଆ,๙ݖଆॉ੮൧ᆴܿଆބੀྟၹ;Ֆקಃٚمഈ,ݓଽކٳ۲ၹሰؓဢЧܢࣉೆᆷඔ֥႕ཙӱ؇,ࣉ෮ႵܢࡎӮٺᆷඔनҐႨੀ๙൧ᆴࡆಃ,ߎીႵᆷطಒקӮٺܢܒӮࠣ۲ሱಃᇗbЧ໓ࡼႋႨഈඍඔҐႨࠎЧ૫ၹקಃb൧ᆴࡆಃ֥Ⴊׄ൞ಃᇗٚم࿊ᄴ300ࡅӮٺܢщᇅࠎЧ૫300ᆷඔ(ࡥӫၞႿಒק,ିܔ۳Ⴭᆰܴ֥ࢳ;ಌׄ൞ෛሢܢௐ/JOYFI3000)bࡎ֥۬э߄,۲Ӯٺܢ෮ᅝಃᇗෛᆭэ߄,ൈޓЧ໓࣮֥ၩၬᄝႿ,๙ݖႄೆࠎЧ૫ၹ࿊ഡ࠹ԛטᆜࠏᇅಃᇗ߭֞ކൡ֥ඣbطࠎ൬۠ರ௹:2008-01-07#57#
,ყ ҩ2009୍ֻ3௹Ч૫ၹࡆಃಏॖࣜႮᄜޙ(Rebalance)ࠏᇅሱഈൗࡀ70୍սၛটLogistic݂߭ଆ֥ಃᇗ߭֞Ԛ֥ඣ,ࠧ๙ݖࡨഒѯږौభܢௐ֥࣮ᇯ֤҄֞ധೆ[10],֥Ⴊׄ൞:(1)ൡႨႿၹэб২,ᄹࡆѯږઋުܢௐ֥б২,Ӯٺܢಃᇗྍਈ൞ٳোэਈ(ॖၛ൞ؽٳোࠇ؟ٳো)֥ඔऌԩ߭֞௹Ԛඣ,ၛ࣯ᆞሧொҵb;(2)ؓႿሱэਈ֥ٳ҃ીႵᆞࡌഡ่ࡱ,ඔݓ࠽ഈၘႵഒਈᆷඔҐႨࠎЧ૫ၹࡆಃ,ऌো࠻ॖၛ൞৵࿃эਈaэਈa္ॖၛ൞קಃٚمࢠູᇶܴ,ग़ܴ၇ऌ҂ቀ,ၛ۳ԛކэਈ(DummyVariable);(3)ໃቔٚҵఊྟࡌഡ;֥ࣜ࠶ࢳbଢభ܄षؿ҃ॉ੮ࠎЧ૫ၹ֥ᆷ(4)ေၹэਈაሱэਈᆭࡗ൞٤ཌྟܱ༢(SඔႵ[6]:(1)֡౪ථܢࡎᆷඔุ༢ᇏ֡౪ථಆ౯a౷ཌ),ࡌഡڛՖLogisticٳ҃bࡌഡڛՖѓሙྛြބᇝפࡕ50ᆷඔ۱ڄ۬ᆷඔ൞οᅶሱᆞٳ,҃ᄵູProbitଆbܴ֒ҩඔऌແ҆ࢠႮੀ๙൧ᆴaཧ൲/൬ၭ(S/E)a࣪০ࣉྛሸކஆ,ިࠇሱэਈູ৵࿃эਈൈ,ҐႨLogisticଆ۷ູ,ಃᇗٳљູ60%,20%,20%,ቋᇔӮٺܢಃൡ֒bᇗಯಖҐႨሱႮੀ๙൧ᆴbᆃੀ๙൧ᆴಯФቔ࠺۳קሱэਈ౼ᆴxkiൈ൙ࡱؿള่֥ࡱۀູቋᇗေ֥࿊ܢѓሙ,2۱ࠎЧ૫эਈ္ࣇο֩ಃੱູࣉྛԩb(2)ڶൈܢࡎᆷඔุ༢ᇏRAFI༢ਙᆷP(yi=1|x1i,x2i,,,xmi)=piඔ,ࠎႿR[7,8]obert֥࣮ॿࡏ,ၛཧ൲൬ೆaགྷࣁ֤֞Logistic݂߭ଆ(1)ൔ,AaBkٳљіൕLogisticੀaܢ༏aᅬ૫ࡎᆴູᆷඔ࿊ܢѓሙ,4۱эਈଆ֥ࢩएཛބ۲ሱэਈ݂߭༢ඔbဢο֩ಃࣉྛ࠹ෘbn(3)ѓሙ௴غܢࡎᆷඔุ༢ᇏӮӉࡎᆴڄ۬༢ਙᆷඔ္োරֹ࿊ᄴӮӉބexp(A+EBkxk)ik=1ࡎᆴэਈ܋7۱эਈቔູࡆಃၹሰ,ऎุקಃٚpi=n(1)1+exp(A+مໃ܄षbEBkxki)k= थҦඎބLogistic݂߭ഈൔॖሇߐູpiLogitྙൔ:ln()=A+थҦඎ1-p[9]൞ႨႿٳোބყҩ֥ყҩࡹଆٚinمb֥Ⴊׄ൞ٳোקٚمࡥֆۚ,ིളӮ֥ܿEBkxkibೂݔၹэਈބሱэਈ֥ܴҩᆴၘᆩ,ࣼᄵၞႿࢳބࢳ,ൡႿٳোэਈ֥ඔऌԩ;k=1҂ၞႿԩ৵࿃ඔऌbቔູඔऌٳো֥၂ᇕႵॖܙ࠹ԛଆ۲ཛ༢ඔ,ᆃུ༢ඔܙ࠹ᆴॖၛࢳ৯۽ऎູ۲ሱэਈᄝଆᇏ෮ఏ֥ቔႨb,थҦඎᄝܵaࣁವaള࠹֩ਵთ֤֞ਔܼٗႋႨbࡥֆটඪ,ᄎႨथҦඎࣉྛඔऌٳো3 JOYFI300ᆷඔ֥щᇅ၂Ϯٳູਆ۱҄ᇧ:(1)थҦඎ݂ବ,ࠧ০ႨඔऌܒࡹथҦඎ,ളӮٳোܿᄵb(2)ႋႨथҦඎၛૄ୍4ᄅ30ರູࠎሙ,ࡼھರധਆ൧෮ყҩဒඔऌ,ಒקඔऌোљbֻ2҄थҦඎ֥ႋႵၘഈ൧AܢቔູဢЧ,ླัԢ:(1)STa*STܢႨཌྷؓࡥֆbֻ1҄थҦඎࢲܒ֥ކ൞ླေᇗބᄠ๔ഈ൧ܢௐ;(2)ቋ࣍၂୍ؿളᇗնິمິܿׄॉ੮൙ࡱ;(3)ቋ࣍၂୍ҍༀБۡໃࠣൈࠇႵᇗն,֥҂֥थҦඎॖିӁള҂֥ٳোࢲݔb໙ี;(4)ഈ൧҂ડ11۱ࢌၞರ֥܄ඳb෮ႵඔᄝܒࡹथҦඎࣉྛඔऌٳোބყҩభ,ླؓඔऌन౼ሱwindࣁವඔऌ९bऌࣉྛၛ༯ყԩ थҦඎٳোэਈ:(1)ඔऌౢ(DataCleaning)bЇওಌാᆴ֥ԩބඔऌᄮല֥ཨࡨЧ໓࿊ᄴ13۱эਈቔູथҦඎٳোэਈ(;(2)ཌྷܱྟٳ༅і1)bުোࠎЧ૫ᆷѓᄝࣉྛथҦඎٳোభन(CorrelationAnalysis)bဢЧ֥ଖུඔऌඋྟॖି൞Ⴥ֥,აٳোѩ҂ཌྷܱ,๙ݖཌྷܱྟࣉྛਔࡆಃѓሙ߄b༵ࠧؓඔऌࣉྛ൧ᆴטᆜ,ၛٳ༅ࡼᆃུ؟Ⴥ֥උྟԢ;(3)ඔऌэߐఃᅝಆุဢЧ౼ᆴሹބ֥б২ቔູቋᇔ౼ᆴb൧(DataTransformation)b২ೂᆴטᆜၛ܄ඳൌ࠽ੀ๙൧ᆴᅝ܄ඳሹ൧ᆴ֥б২:ࡼ৵࿃ඔऌ๙ݖऊোٳ༅ࠇۀ߄ٳҪሇߐູٳোඔऌູಃᇗbູิۚथҦඎٳোིݔ,ᄎႨऊোٳ༅ࡼ;ؓඔऌࣉྛѓሙ߄ުੂো৵࿃эਈࣉ၂҄߄ູٳোэਈb,ඔऌ౼ᆴࣉೆᆷקࡗ,ೂ(0,1)֩b#58#
ྋ,:֩ܢௐࡎ۬Ӯٺᆷඔщᇅٚم࣮і1 थҦඎٳোэਈݼэਈսэਈӫэਈඋྟݼэਈսэਈӫэਈඋྟ1zcczሧӁᇗቆؽٳো8gsgrowཧ൲ᄹӉਈ৵࿃2cgjzdӻܢࠢᇏ؇ؽٳো9bvᅬ૫ࡎᆴ৵࿃3zrzᄜವሧؽٳো10np࣪০৵࿃4hydwྛြֹ໊ٳো11gsཧ൲൬ೆ৵࿃5hydbxྛြսіྟٳো12gdܢ༏ሹح৵࿃6cjjeӮࢌࣁحؽٳো13ygrsჴ۽ದඔ৵࿃7gdgqxzܢתܢಃྟᇉඹٳো थҦඎဢЧࠣٳোэਈཌྷܱྟٳ༅Ԛ࿊ဢЧ֥ٳॖႮ(2)ൔ֤,֞scoreiࣼ൞ֻiᆺՖ4۱োර֥300ᆷඔ(ധ300aᇏྐѓ௴Ԛ࿊ဢЧܢௐ֥ࠎЧ૫֤ٳb۴ऌٳնཬ࿊ԛభ300aണຣ300ބऍӖ300)ᇏ࿊౼ཌྷᇗކ֥Ӯٺܢቔ300ࡅܢௐቔູᆷඔӮٺܢb۲ӮٺܢቋᇔಃᇗႮູथҦඎ/ၒࣉೆᆷඔ0֥ဢЧ;ࡼ6۱৵࿃э܄ൔweighti=scorei/ਈο౼ᆴնཬஆ,ࡼᇀഒႵ5۱эਈஆᄝ༯Escorei࠹ෘbi1/2ٳ໊֥ܢௐቓູ/҂ၒࣉೆᆷඔscorei=B^1@bvi+B^2@npi+B^3@gdi+B^4@gsgrowi0֥ဢЧb۴ऌဢЧඔऌ,ؓഈඍэਈٳљაၹэਈ(2)(൞ڎࣉೆᆷඔ2)ቔpearsonVဒbᄝ95%ᇂྐඣ༯नऋधჰࡌഡ,ࠧૌაၹэਈࡗթᄝཁᇷ֥ཌྷܱྟܱ༢ Ӯٺܢ֥࿊ᄴაקಃҐႨRეކथҦඎ,ඎࢲܒ1bnpބcjjeਆ۱эਈࣼथקਔඎ֥ࢲܒ,ඪૼࣇܢௐြࠛބੀྟ൞JOYFI300Ӯٺܢ֥࿊ဢѓሙbЧ໓๙ݖؓඔऌ֥ࡆಃѓሙ߄ࡼ൧ᆴၹႄೆࠎЧ૫эਈ,ᄝࠎЧ૫эਈᇏࡗࢤّ႘܄ඳ൧ᆴնཬ,ၹՎJOYFI300აఃӮٺᆷඔ࿊ဢѓሙ֥ҵၳᆞ൞ุགྷᄝࣜ൧ᆴטᆜ֥࣪০ᆷѓഈb۴ऌඎࢲܒ1 थҦඎࢲܒؓఃჅဢЧࣉྛٳো,࿊ԛژކٳোѓሙ֥ܢௐ,ა/ၒࣉೆᆷඔ0֥ဢЧ܋ܒӮ JOYFI300ᆷඔဢЧ௹ࡗࠣ࠹ෘJOYFI300ӮٺܢԚ࿊ဢЧbၛ2005୍4ᄅ30ರູࠎ௹,ࠎׄ1000ׄ,ଆі2࠹ෘ2005୍5ᄅᇀ2007୍10ᄅJOYFI300ᆷ Logisticଆэਈ࿊ᄴࢲݔ (A=)эਈ༢ඔܙ࠹ᆴWaldᇂྐࡗWඔb۴ऌ۲Ӯٺܢࡆಃ൬ၭੱ࠹ෘૄರᆷඔ൬ၭaldV2Pᆴੱ֥э,ᄜߐෘӮૄರᆷඔэᆴbӮٺܢٳbvB^1=(B^,B^1+)<གྷࣁޣ০߶ੀ๙൧ᆴؿളэ,JOYFI300ؓՎnpB^2=(B^,B^2+)<֥ԩ൞ॉҳ௹ଽົӻఃಃᇗ҂э,ᆃཌྷ֒Ⴟᄝ۵gdB^=(B^,B^+)ሶJOYFI300ࣉྛᆷඔ߄ሧൈ,ޣ০ࠧൈᄜሧႿgsgrowB^4=(B^,B^4+)ھܢb ࠺ӮٺܢԚ࿊ဢЧၹэਈyູ1,ڎᄵູ0bᄎႨᇯ҄࿊ᄴم4 JOYFI300ᆷඔ֥ࡎაбࢠ(Stepwise)ؓ6۱৵࿃эਈࣉྛэਈ࿊ᄴ,ҐႨSAS֥[11]ProcLogisticӱ࠹ෘ,༢ඔܙ ڄག൬ၭหᆘ࠹ᆴཁᇷྟဒ(Waldဒ)֥ࢲݔі2bᅬ૫ᄜޙࠏᇅିܔಃᇗ߭֞ކൡ֥ඣ,္ࡎᆴa࣪০aܢ༏ሹحaཧ൲ᄹӉਈ4۱эਈPᆴ߶ิۚᆷඔ֥ᇛሇੱ,ᄹࡆࢌၞӮЧ,ၹՎླေॉཁᇷཬႿA=,ܣऋधჰࡌഡ(Hਈᄜޙ֥טᆜੱb๙ݖбࢠဢЧ௹ଽ۲ᆷඔ0:Bk=0)b۲#59#
,ყ ҩ2009୍ֻ3௹֥ሹ൬ၭੱ(і3),ૄ϶୍ބ҂ࣉྛᄜޙႮႿ൬ᇛሇൈ֥ࢌၞӮЧ,ཁಖૄ࠱ᄜޙሹ൬ၭੱ۷ၭหᆘໃіགྷԛཁᇷҵၳФ൮༵ڎק,ૄᄅᄜޙႪbު໓ᄝࣉྛᆷඔࡎൈनҐႨο࠱ᄜޙ֥ሹ൬ၭੱෙбૄ࠱ᄜޙۚ,൞ॉ੮ӮٺܢJOYFI300ᆷඔbі3 ۲োᆷඔሹ൬ၭੱбࢠ(2005୍5ᄅ~2007୍10ᄅ)JOYFI300JOYFI300JOYFI300JOYFI300(ૄᄅᄜޙ)(ૄ࠱ᄜޙ)(ૄ϶୍ᄜޙᇏѓ300)(ໃᄜޙധ300)ሹ൬ၭੱ587%582%532%453%500%510%і4 ۲ᆷඔ൬ၭหᆘбࢠᆷඔቋնᄅቋཬᄅࠫޅनࠫޅन୍ӑح൬ၭ൬ၭੱ൬ၭੱᄅ൬ၭੱ୍൬ၭੱ(ҕᅶധ୍ѯੱொ؇ڂ؇300)%%%%%%ᇏѓ%%%%%%ധ%%%%% JOYFI300ᄝ۲ཛ൬ၭੱᆷѓ(і4)ഈۚႿކ֥B༢ඔбധ300֮,აᇏѓ300նุཌྷਆбࢠᆷඔ;୍ѯੱაᇏѓ300aധ300ཌྷб;֒ࣜڄགטᆜު֥ሧቆކӑح൬ၭ(Jensen)္ٳљᄹࡆ%%,୍न൬ၭੱᄹږჹіགྷູJOYFI300۷Ⴊbჹӑݖ୍ѯੱ֥ᄹږ,ٳљ֞ղ%aі5 ࠎႿCAPM֥ڄག൬ၭหᆘ(ҕᅶധ300οᄅ൬9ၭੱ࠹ෘ).44%bொ؇ູᆞնඪૼ൬ၭੱ֥ٳ҃ࢠఃᆷඔӯགྷ۷ૼཁ֥Ⴗொ,ࠧᄝJOYFI300൬ၭੱᆷඔPearsonӑحBٳ֥҃Ⴗҧթᄝ۷؟֥ࠞ؊ᆴbڂ؇ۚіૼࡕཌྷܱ༢ඔ൬ၭIRJensenڂިແหᆘ۷ູཁᇷbڂ؇ொ؇ඔऌౢ༉ֹཁൕ%%ᇏѓ%%൬ၭੱٳ҃бఃᆷඔऎႵ۷Ⴊਅ֥ྟᇉ,֥Ⴗແ҆(ᆞ൬ၭੱ)Ⴕ۷؟۷ն֥ඔऌׄ ᆷඔ໗קྟٳ,҃ॖିऎႵ۷֥ۚनᆴඣbҕᅶఃਆᇕᆷJOYFI300֥ࢲܒטᆜЇওਆ۱ٚ૫:ӮٺܢඔؓJOYFI300ᄅӑح൬ၭࣉྛनᆴဒ(H0:ᄅק௹ބ҂ק௹֥טᆜaᆷඔಃᇗᄜޙbі6ᇏӑح൬ၭ[0),PᆴཁᇷཬႿ,ඪૼनᇛሇੱ֥࠹ෘሸކॉ੮ਔᆃਆٚ૫֥ၹbᆷJOYFI300ᄅӑح൬ၭཁᇷ҂ູਬ,ᄅ൬ၭੱनᆴඣбఃඔࢲܒטᆜ֥ӮЧ္টሱਆ۱ٚ૫:ࢌၞٮႨބᆳਆᇕᆷඔ۷ۚbྛӮЧbЧ໓ࣇॉ੮ࢌၞٮႨջট֥ӮЧbႮႿࠎႿሧЧሧӁקࡎં֥ٳ༅ॿࡏࠏܒሧᆀ๙ӈླࠇ҆ٳᆦڱࢌၞႛࣁ,෮ၛٳ,Ֆሧቆކ֥࢘؇ॉҳ۲ᆷඔ֥ڄག൬ၭหᆘљ࠹ෘࣇᆦڱႆඥ(ࢌၞӮЧ=3j)ބ҆ٳᆦ(і5),ڱࢌၞႛࣁ(ࢌၞӮЧ=5j)ਆᇕ౦ঃbJOYFI300ಯಖіགྷԛਅݺ֥หྟbࠎЧ૫ᆷඔቆі6 JOYFI300ᆷඔᇛሇੱაࢌၞӮЧ(ҕᅶധ300)ᆷඔनᄅӑࢌၞӮЧ=3jࢌၞӮЧ=5jቋնࢌၞӮЧᇛሇੱح൬ၭᄅӑح൬ၭӑح൬ၭാੱᄅӑح൬ၭӑح൬ၭാੱ(ӑح൬ၭ=0)%%%%%%%ඍٚمщᇅ֥JOYFI300ࠆ֤ਔཁᇷႪႿധ3005 ࢲ ંބᇏѓ300֥ӑح൬ၭ,ဢЧ௹ଽJOYFI300ᆷඔᄎႨथҦඎބLogistic݂߭ࡼࠎЧ૫ၹႄೆቆކ୍न൬ၭੱٳљۚԛ%ބ%bܢࡎӮٺᆷඔ֥щᇅ,Ӯٺܢ֥࿊ဢѓሙაקಃJOYFI300֥ڄག൬ၭหᆘіૼҐႨࠎЧ૫ၹࡆٚم۷ູކग़,ܴൈᄜޙࠏᇅԚಃᇗ֤ಃܒᄯ֥ᆷඔቆކ൞б൧ᆴࡆಃᆷඔቆކ۷ູႵၛЌӻ,ᆷඔ֥൬ၭྟᇉ֤֞ޓն֥ڿbҐႨഈ(下转第64页)#60#
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