ᇏݓܢௐ൧ӆሧӁקࡎଆ֥ྍဒ New Test of Asset Pricing Models in China 12ਟ ݚ ޠႥᨡ 1ࣜ࠶࿐Ѱൖa༰ն࿐ࣁವ༢ࢃഽ ༰ն࿐ࣁವ༢đ༰đ361005 cfc@ 2ࣜ࠶࿐Ѱൖaूମغն࿐ࣜ࠶࿐༢࢝൱aౢն࿐ࣜ࠶ܵ࿐ჽหௗ࢝൱ ूମغն࿐ࣜ࠶࿐༢ބ࠹॓࿐༢đ୧ჿđ14850 ౢն࿐ࣜ࠶ܵ࿐ჽđКࣘđ100084 yh20@ ๙ቔᆀ (Correspondent Author)ğޠႥᨡ Department of Economics, 424 Uris Hallđ Cornell University, Ithaca, NY 14853, ଽಸࡥࢺğሧӁקࡎ൞ࣁವ൧ӆؿᅚაປ֥၂۱ނྏ໙ีđ္၂ᆰ൞ࣁವਵთ֥၂۱ࠎԤྟ࣮໙ีbЧ໓০Ⴈᇏݓ1997Ē2004୍֥ܢௐࡎ۬ඔऌؓଢభᄝሧӁקࡎਵთቋູੀྛ֥ֆၹଆބၹଆࣉྛਔൌᆣٳ༅ބဒđ෮ဒ֥ଆഡקЇওીႵࢩइཛaЇݣࢩइཛၛࠣॉ੮๋ᄁၹሰbູਔؓ۲۱ଆ֥ഡקࣉྛဒაбࢠđૌႨਔHong & Lee (2005a, 2005b) ྍ࣍ิԛ֥ܼၬ௶֝ඔٳ༅ٚمbဒࢲݔཁൕğෙಖࢩइཛଆഡקمཁᇷֹิۚଆ֥ކӱ؇ބࢳି৯đ൞ಏॖၛႵֹིࢆ֮ଆ֥ഡק༂ҵđ൞ᆞಒଆഡק҂ॖಌഒ֥҆ٳbطᅫ૫൧ᆴб (BM)đ܄ඳܿଆ (SIZE) ၛ๋ࠣᄁၹሰෙಖॖၛิۚሧӁקࡎଆ֥ކӱ؇ބࢳି৯đಏمႵֹིڿଆ֥ഡק༂ҵbၹՎđᇏݓܢௐቆކ൬ၭੱᇏಯಖթᄝሢ၂ུمࢳ֥҆ٳđླေႄೆྍ֥ڄགၹࠇᆀॉ੮٤ཌྟܱ༢Ҍି֤ၛࢳथb ܱՍğሧӁקࡎđֆၹଆđၹଆđ๋ᄁđቋնරಖܙ࠹đܼၬ௶֝ඔٳ༅đഡקဒ JELٳোݼğE4,G0,G12 Abstract: Asset Pricing is a key problem for the development of financial research and has always been a basic research project in finance. This paper empirically tested and evaluated both one factor (CAPM) model and Fama-French three factor model by Chinese data from 1997-2004. The model specifications include without constant, with constant and with jump effect. To test different models’ specification, we used the spectral test proposed by Hong (1999), Hong & Lee (2004a, 2004b). The test results showed that although the intercept had no help on improving the fitting degree and explanation power of different models, it significantly reduced the models’ specification error. This implies that intercept is important for correct model specification. However, although BM, SIZE and jump factor could improve the fitting degree and explanation power of asset pricing models a lot, it had little effect on reducing the specification errors. There are still some unexplainable parts in stock return. This implies that we should consider some other risk factors or nonlinear return relationship in China Key Words: asset pricing, one factor model, three factor model, jump, maximum log likelihood estimation (MLE), spectral test, specification test. JEL classification: E4, G0, G12
1ēభ ሧӁקࡎčasset pricingĎ൞ࣁವ൧ӆؿᅚაປ֥၂۱ނྏ໙ีđ္၂ᆰ൞ࣁವਵთ֥၂۱ࠎԤྟ࣮໙ีb൮༵đؓሧӁקࡎ໙ี֥࣮ႵᇹႿิۚؓڄག֥ಪ്đՖطູሧथҦބส௹Ќᆴิ܂൙ൌ၇ऌĠఃՑđ๙ݖؓሧӁקࡎଆ֥࣮đॖၛड൧ӆഈФհ༂קࡎ֥ሧӁđѩҐ౼၂ק֥ٚൔܒᄯส০ቆކđࠆ౼ڄགส০ࠏ߶Ġֻđᆟکࡓܵ҆ॖၛ๙ݖཌྷܱ֥ሧӁקࡎଆ؎൧ӆ֥ࡎ۬ඣ൞ڎކđՖطູࣁವ൧ӆ֥ࡓܵิ܂్ൌॖྛ֥ંᆷ֝b ႮႿሧӁקࡎᄝࣁವਵთᇏ֥ᇗေቔႨđӉ௹ၛট၂ᆰ൞ࣁವ࣮֥၂۱ނྏ໙ีbSharpe (1964)aLintner (1965) ᄝMarkowitz (1952) Ⴕིቆކં֥ଆॿࡏ༯đၛܢௐሧӁቆކ֥ѓሙҵቔູھቆކڄག֥ޙਈԄ؇đ֝ԛሧЧሧӁקࡎଆ (CAPM)bھଆಪູđܢௐሧӁ֥ყ௹൬ၭੱᆺބ༢ྟڄགႵܱđطაھሧӁሱദหᆘ֩٤༢ྟڄགܱbᄝھଆᇏđᆺႵ၂۱ڄགၹi൧ӆڄགbھ൧ӆڄག֥նཬႨᆣಊ൬ၭэބଖ۱൧ӆቆކ (market portfolio) ൬ၭэ֥ླྀٚҵԢၛ൧ӆቆކ֥ٚҵ (ࠧ෮໌֥βၹሰ) ޙਈb Jensen (1968) ൮ՑႨൈࡗਙ݂߭ؓCAPMࣉྛਔဒđؿགྷൈࡗਙ݂߭෮֤֥֞ࢩइཛҕඔնႿ CAPMં֥ڄག൬ၭੱđ֤βၹሰᆴބყ௹൬ၭᆭࡗ֥ཌྷܱܱ༢ݖႿฌđࠧ۲ܢௐቆކ֥ყ௹൬ၭੱބβၹሰᆴޘࢩ૫ོ݂֥߭ੱཬႿCAPMં෮ࢣൕོ֥ੱbᆃ۱གྷའᄝFriend & Blume (1970) ބStambaugh (1982) ֥࣮ᇏ္֤֞ਔဒᆣbBlack (1972) ิԛਔթᄝࢹվཋᇅ֥CAPMđ٢ॺਔؓࢩइཛҕඔ֥ཋᇅđ֤ھଆॖၛࢳᄪ௹ൌᆣ࣮෮݂ବ֥CAPM҂ކགྷའb ಖطđᄀটᄀ؟֥ൌᆣ္࣮षؓBlack (1972) ิԛၐ໙ބ็ᅞđቋູԛ֥൞ؿགྷܢௐ൬ၭੱ֥ޓ؟э߄҂൞Ⴎ൧ӆڄགႄఏđطაഈ൧܄ඳ֥ཌྷܱหᆘđೂܿଆ (SIZE) (Banz, 1981)aᅫ૫൧ᆴб (BM) (Rosenberg֩, 1985)a൬ၭࡎ۬б (E/P) (Basu, 1977) ֩Ⴕܱbᆃུགྷའ္Фӫູܢௐ൧ӆo֥ၳའ (abnormalities)pbChan֩ (1991), Capaul֩ (1993) ၛࠣFama & French (1998) ߎؿགྷᄝఃݓࡅ֥ሧЧ൧ӆᇏ္թᄝোරၳའb ູਔࢳᆃུၳའđޓ؟࿐ᆀิԛਔ҂֥ંܴׄbֻ၂ো൞ྛູࣁವܴ ׄ(Lakonishok֩, 1994ĠFama & French, 1995ĠDebondt & Thaler, 1987ĠDaniel & Titman, 1997)bھંಪູđSIZEބBM҂൞ڄགၹđط൞սіഈ൧܄ඳ֥หᆘđّ႘ਔఒြ֥ଖᇕࠎЧ૫ၹbۚBM֥ఒြ൞ष༯߁֥ఒြ (ӫູoࡎᆴఒြp)đط֮BMᄵᇶေ൞ᄹӉఒြbႮႿሧᆀؓఒြൎіགྷ֥ݖ؇ّႋđ֤֮BM (ᄹӉॹđൎіགྷਅݺ)֥܄ඳܢௐࡎ۬ۚđطۚBM (ᄹӉતđൎіགྷҵ) ֥܄ඳܢௐࡎ֮۬bᆃ۱ݖ؇ّႋቋު߶࣯ᆞđՖط֝ᇁۚBMܢௐ֥ۚ൬ၭބ֮BMܢௐ֥֮൬ၭbਸ਼၂োંᄵᄝྟקࡎ֥ଆॿࡏ༯đಪູCAPM֥ࡌഡ่ࡱݖႿ۬aࡥֆđླေॉ੮۷ູگᄖ֥ሧӁקࡎଆđೂ Merton (1973) ิԛ֥ॴ௹CAPM (ICAPM)đLucas (1978), Breeden (1979), Hansen & Singleton (1982, 1983) ބJagannathan (1985)֩ࠎႿཨٮ֥ሧӁקࡎଆ (CCAPM), Ryder & Heal (1973), Becker & Murhpy (1988), Constantinides (1990), Campbell & Cochrane (1999), Normandin & Pascal (1998), ބBrandt & Wang (2001)֩ॉ੮༝ܸொݺؓCCAPM֥ຉᅚđၛࠣCochrane (2000) ބCampbell (2000) ০Ⴈෛࠏ์གྷၹሰ (SDF) ଆॿࡏؓሧӁקࡎଆ֥ሹࢲbਸ਼ຓđ۷؟֥ڄགၹ္ၹՎФႄೆ֞ሧӁקࡎଆᇏđႨႿࢳܢௐሧӁ൬ၭ֥эbఃᇏቋऎսіྟ֥ࣼ൞Fama & French (1993,1996) ิԛ֥oၹଆpbૌᄝ൧ӆڄགၹ֥ࠎԤഈႄೆਔਸ਼ຓਆ۱ڄགၹiSIZEၹބBMၹ,ѩٳљႨཬSIZEቆކ (S) ބնSIZEቆކ (B) ֥൬ၭੱҵ (SMB) ၛࠣۚBMቆކ (H) ބ֮BMቆކ (L) ֥൬ၭੱҵ (HML) іൕᆃਆᇕڄགၮԏbᄝ၂ק่ࡱ༯đؓڄགၮԏটჷ֥ಪ്ҵၳѩ҂߶႕ཙ֞ၹଆ֥ႋႨ (Fama & French, 2004)b
Hansen (1982), Hansen & Singleton (1982), Brown & Gibbons (1985) ֩ҐႨܼၬइٚم (General Method of Moments, GMM)đၛEulerٚӱ֥ᆞࢌྟ่ࡱູࠎԤࢳथਔ၂ུگᄖሧӁקࡎଆ֥ҕඔܙ࠹໙ีbਸ਼ຓ၂ུ࣮đᄵิԛྍ֥࠹ਈٚمؓഈඍሧӁקࡎଆࣉྛଆ֥ഡקဒđၛဒᆣሧӁקࡎଆ൞ڎթᄝ༂ҵbShiller (1979), Singleton (1980), Leroy & Porter (1981) ࣮ਔଆᆞಒഡק่ࡱ༯ཌྷܱѯੱ֥шࢸbHansan & Jagannathan (1991,1997) ᄵࡼᆃ۱ѯੱшࢸ (H-Jшࢸ) ቔູ၂Ϯ֥ᆐ؎۽ऎটؓሧӁקࡎଆࣉྛഡקဒđѩܒᄯԛཌྷႋ֥࠹ਈbሱՎđH-JшࢸٚمᇯࡶӮູሧӁקࡎଆቋູੀྛ֥ଆഡקဒ۽ऎ, Burnside (1994), Cecchetti, Lam & Mark (1994), Hansen, Peter & Luttmer (1995) ֩ؓՎࣉྛਔ࣮b൞đH-Jшࢸٚمթᄝࠫ۱ಌཊđཋᇅਔᄝଆഡקဒٚ૫֥ൌႨྟb൮༵đھٚمႨ֥൞่ࡱइط҂൞่ࡱइđޭਔקࡎҗҵॖିթᄝ֥٤ཌྟܱ༢֩ᇗေྐ༏đՖط֤ဒ҂ಸၞ֝ᇁऋधհ༂ଆbၹູᄝ٤ཌྟ่֥ࡱ༯đקࡎҗҵ่֥ࡱ௹ຬޓॖି҂֩Ⴟ0đࠧھਙ෮Ⴕ่֥ࡱླྀٚҵູ0bఃՑđھဒᆺॉ੮эਈᆭࡗ֥ؽࢨཌྷܱྟđીႵॉ੮קࡎҗҵਙᇏॖିթᄝ֥ۚࢨཌྷܱྟđೂڂ؇aொ؇֩ཌྷܱؓ൬ၭ֥႕ཙĠֻđھဒᆺႨਔѯੱ (ؽࢨइ) ؓሧӁקࡎଆࣉྛഡקဒđޭਔۚࢨइ (Snow, 1991)b ޓ؟ંބൌᆣ࣮іૼđሧӁ֥൬ၭੱਙޓॖିթᄝ٤ཌྟਙ၇ঠ (nonlinear serial dependence)b൮༵đՖ၂Ϯ֥नޙקࡎંٳ༅đሧᆀ֥ڄགညذӱ؇߶ෛሢ൬ၭੱ֥эطэđՖطؓሧӁࡎ֥۬ໃটэӁള٤ཌྟ႕ཙb֒൧ӆ൬ၭੱࠤख༯יൈđႮႿ൳֞છॢཋᇅaੀྟၛࠣҍༀາࠏ֥႕ཙđ൧ӆ֥ᆜุڄགညذӱ؇ࣼ߶ഈശđ൧ӆໃট֥ყ௹൬ၭੱࣼ߶ഈശbՎຓđBlack (1988) ิԛ֥नᆴ݂߭ყ௹ંၛࠣؓሧᆀྛູொҵ (behavior biases)֥ٳ༅đCampbell & Cochrane (1999) ॉ੮༝ܸ֥ཨٮሧӁקࡎଆđၛࠣChan & Kogan (2002) ॉ੮ၳᇉ (heterogeneous) ሧᆀ֥৵࿃ൈࡗሧӁקࡎଆđՖ҂֥ં࢘؇ંᆣਔሧӁ൬ၭੱॖିթᄝ٤ཌྟܱ༢bఃՑđՖྛູࣁವ֥࢘؇ٳ༅đࣁವ൧ӆ֥ሧҦॖၛٳູࡎᆴሧބඌሧbࡎᆴሧᇶေ৫ቀؓ܄ඳࠎЧࡎᆴ֥ٳ༅đطඌሧᄵᇶေ۴ऌܢௐࡎ֥۬ൎྐ༏b҂֥ሧҦ৫ቀႿ҂֥ྐ༏đؓ൧ӆሱಖࣼ߶Ӂള҂֥႕ཙb۷ູᇗေ֥൞đ҂ࣇᆜุሧᆀ֥ڄགညذඣ߶ෛሢ൬ၭੱ֥эطэđᆜุሧᆀᇏ҂ሧҦ෮ᅝб২္߶ෛሢ൧ӆߌ֥э߄طэ߄đ෮ၛఃؓ൧ӆ֥႕ཙ္ࣼ߶ෛሢൈࡗ֥э߄طэ߄đՖط൬ၭุགྷԛ٤ཌྟ֥หᆘb ၹՎđෙಖH-Jшࢸٚم൞ሧӁקࡎଆഡקဒࣜӈႨ֥ٚمđॖି҂൞၂۱ቋݺ֥ٚمđႭః൞ॖିޭཌྷܱэਈᆭࡗ֥٤ཌྟܱ༢bHong & Lee (2005a, 2005b) ྍ࣍ิԛ֥ܼၬ௶֝ඔٳ༅ٚمđᄵॖၛႵֹིࢳथᆃུ໙ีbॖၛဒޅྙൔ֥ਙཌྷܱđЇওनᆴਙ၇ঠބۚࢨइਙ၇ঠ (ೂѯྟਙ၇ঠđொ؇ਙ၇ঠބڂ؇ਙ၇ঠ) ؓܢௐ൬ၭੱ่ࡱनᆴ֥႕ཙbطđᆃᇕਙ၇ঠॖၛ൞ཌྟ֥đ္ॖၛ൞٤ཌྟ֥bᄝЧ໓֥ሧӁקࡎଆഡקဒᇏđૌࡼႨHong & Lee (2005a, b) ဒb ᄝݓଽሧӁקࡎ࣮ٚ૫đລބᇛდ (2002) ၛࠣᇫЏཉބޅᇍݓ (2002) ٳљؓᇏݓܢௐ൧ӆ֥SIZEིႋބBMིႋࣉྛਔൌᆣဒđ֤ԛਔड़ק֥ࢲંđࠧᇏݓܢௐ൧ӆթᄝSIZEིႋބBMིႋđᆃਆ۱ၹႵᇹႿࢳᇏݓܢௐ൬ၭੱ֥ൎэbӧྐჭ֩ (2001) ๙ݖ݂߭ٳ༅đಪູSIZEބBMؓܢௐ൬ၭੱऎႵཁᇷ֥ࢳି৯bဗ㬕ބӧᅚߩ (2003)đൗ୪ބྸ୍ྛ (2004) ֥ൌᆣࢲݔनᆦӻਔၹଆbफބྷྐᇑ (2004) ᄝၹଆࠎԤഈႄೆਔਆຓਆ۱ၹሰĒླྀொ؇ބླྀڂ؇bઅਟ (2003)đٓᆒބݚม (2003)đਾਡބౕມඨ (2004) ๙ݖ၂ק֥ൌᆣٳ༅ಪູ႕ཙᇏݓܢௐ൧ӆ൬ၭੱ֥ၹ҂ᆺ۱đсྶᄝၹଆࠎԤഈႄೆః֥ڄགၹሰb ཌྷбݓຓؓሧӁקࡎ໙ี֥ൌᆣ࣮đݓݓଽᄝຉᅚCAPMaဒሧӁקࡎଆഈ
֥࣮ߎթᄝޓ؟֥҂ቀđऎุіགྷᄝğն҆ٳᆺᆌؓଖ۱ଆࣉྛҕඔܙ࠹đીႵؓ҂ଆࣉྛಆ૫֥ሸކбࢠđࠧႵбࢠđ္ᆺ൞ࡥֆҰҕඔ֥࠹ཁᇷྟđીႵҐ౼۷ູࣈ֥࠹ਈٚمĠఃՑđીႵဒ۲۱ሧӁקࡎଆ֥ഡק൞ڎᆞಒbဒଆഡקᆞಒაڎؓ؎൞ڎߎթᄝఃڄགၹሰࠇᆀ൞ڎթᄝ٤ཌྟ൬ၭܱ༢ٳᇗေb൙ൌഈđଆഡקᆞಒაڎ္႕ཙ֞ؓଆҕඔ֥၂ᇁܙ࠹ބႵི֥ࣜ࠶ݣၬࢳbቋުđն҆ٳ࣮෮ҐႨ֥ඔऌൈࡗԳ१؋đ֤࣮ࢲંॖିݖႿோ૫b Ч໓Ⴈ1997-2004୍Ӊղ8୍֥ඔऌᄝॉ੮۲ᇕଆഡק֥౦ྙ༯ؓֆၹଆބၹଆࣉྛಆ૫֥бࢠđѩ๙ݖHong & Lee (2005a, 2005b) ဒؓ۲ᇕଆഡקࣉྛ۬ҩđၛဒᆣ۲ڄགၹބఃଆഡק൞ڎิۚଆࢳି৯đၛࠣ؎൞ڎթᄝఃڄགၹࠇ٤ཌྟ൬ၭܱ༢bᄝֻ2ࢫđૌࡼབྷ༥ࢺകૌေбࢠބဒ֥ሧӁקࡎଆĠᄝֻ3ࢫđૌࡼࢺകHong & Lee (2005a, 2005b) ֥ܼၬ௶֝ඔٚمĠᄝֻ4ࢫᇏđૌབྷ༥ٳ༅ބбࢠ۲۱ଆ֥ҕඔܙ࠹ࢲݔĠֻ5ࢫ০Ⴈܼၬ௶֝ඔٳ༅ٚمؓ۲۱ଆࣉྛഡקဒĠֻ6҆ٳᄵ൞ࡥ؋֥ࢲંb 2ēሧӁקࡎଆ Ч໓ᇶေଢ֥൞ؓਆ۱ଢభቋູੀྛ֥ሧӁקࡎଆğֆၹ (CAPM) ଆބၹଆࣉྛಆ૫֥бࢠbૌٳљᄝਆ۱ଆᇏॉ੮ਔ҂֥ଆഡק౦ঃbі1ਙԛਔૌေဒ֥ଆၛࠣ۲ᇕഡקđ༯૫ૌ၇Ցࢺകb (1) ֆၹଆ ഡrսіଖᆺܢௐࠇᆀቆކᄝൈ௹t֥൬ၭੱđrսі൧ӆڄག؋௹൧ӆ০ੱđptftr−rսі൧ӆቆކ֥ڄགၮԏđֆၹሧӁקࡎଆ๙ӈіൕູğ mtft2 đ č1Ď ε~σ r=..(0,)r+β(r−r)+εptftmttfttᆃӈඔβսіܢௐࠇᆀቆކ֥༢ྟڄགđطε൞קࡎҗҵbֆၹCAPM္ॖၛ֩tࡎіඍູğ 2 đ č2Ď r−r=βr−r+ε~...(0,σ εiid)()ptftmtfttt္ࣼ൞ඪđೂݔֆၹ (CAPM) ଆᆞಒđr−rਙބr−rਙڛՖࢩइཛູ0 ֥ptftmtftཌྟܱ༢đطקࡎҗҵεᇏ҂ЇݣႵޅॖၛႨটࢳܢௐࠇᆀቆކ൬ၭੱ֥ႵႨྐt༏b ൞ޓ؟ൌᆣ࣮іૼđܢௐ֥൬ၭੱթᄝޓ؟ၳའ (abnormalities)đمႨֆၹଆࢳbູਔဒᆣᆃུགྷའ൞ڎ္ᄝᇏݓሧЧ൧ӆթᄝđૌᄝ݂߭ᇏࡆೆਔࢩइཛğ 2 đ č3Ď r−r=α+β(r−r)+εε~.(0,σ)ptftmtfttt ଆഡק (3) ॖၛႨႿဒޓ؟ܢௐ൧ӆ֥ၳའbೂ֒ܢௐ൧ӆթᄝSIZEིႋൈđؓႿնSIZEቆކđఃα<0đطؓႿཬSIZEቆކđఃα>0Ġ֒ܢௐ൧ӆթᄝBMིႋൈđؓႿۚBM֥ቆކđఃα>0ĠؓႿ֮BMቆކđఃα<0bၹՎđ๙ݖؓ҂ܢௐቆކ֥൬ၭਙࣉྛ݂߭ٳ༅đဒࢩइཛαܙ࠹ᆴ֥࠹ཁᇷྟၛࠣଆ֥ކӱ؇đૌॖၛ؎ᇏݓܢௐ൧ӆ൞ڎթᄝၳའbଢభđݓଽն؟ඔؓܢௐ൧ӆၳའ֥ൌᆣ࣮
ᆺ൞ࡥֆֹбࢠ҂ቆކ֥൬ၭੱҵၳ൞ڎཁᇷ (ລބᇛდ (2002), ᇫЏཉބޅᇍݓ (2002), ൗ୪ބྸ୍ྛ (2004)֩)đطીႵऎุٳ༅ھҵၳ൞Ⴎ༢ྟڄགႄఏߎ൞ᆇᆞֹႮ༢ྟڄགᆭຓ֥܄ඳหᆘႄఏbႨଆഡק (3) ᄵॖၛႵֹིࡼ༢ྟڄགႄఏ֥ܢௐ൬ၭੱ҆ٳัԢđՖط۷ሙಒֹဒܢௐ൧ӆ֥ၳའb ਸ਼ຓđ۲ᇕᇗնࣜ࠶ྐ༏֥܄҃ބ൧ӆۄყ߶ؓ൧ӆଖᇕো֥ܢௐބ؋௹০ੱӁള๋ᄁྟ֥႕ཙ (Ball & Torous (1983), Das (2001))bᆃᄝᇏݓܢௐ൧ӆႭູԛđၹູᇏݓܢ൧֥၂۱ཁᇷหׄ൞൳ᆟکᆟҦ֥႕ཙޓնbႮႿሧᆀᄝն؟ඔ౦ঃ༯ѩ҂ିყҩᆟҦԛ֥ൈࡗၛࠣᆟҦ֥৯؇đᆟҦؓܢ൧֥႕ཙॖႮ๋ᄁၹሰট૭ඍbູਔॉ੮ᆃᇕ๋ᄁؓሧӁקࡎଆ֥႕ཙđૌᄝ݂߭ଆᇏ္ࡆೆਔ๋ᄁၹሰğ r−r=α+β(r−r)+J⋅D+ε,⎧ptftmtfttt⎪D~(q), č4Ď ⎪t⎨2J~N(ψ,γ)⎪2⎪ε~.(0,σ)⎩t ఘࣂູᆸđᄝᇏݓሧӁקࡎଆ֥ᇙ؟࣮ᇏႵഉໃႄೆ๋ᄁၹሰ֥࣮b๋ᄁၹሰ֥ႄೆԢਔॖၛख़߂ᇗնࣜ࠶ᆟҦؓܢௐ൧ӆ֥႕ཙᆭຓđՖ࠹ਈࣜ࠶࿐࢘؇ुđ္൞ٳсေ֥bૌॖၛ֤֞бࢠ໗ࡲ֥αބβҕඔ֥ܙ࠹ᆴđၹູαބβ֥ܙ࠹ؓ෮໌֥outliersޓૹۋb๋ᄁၹሰ֥ႄೆđᄵॖၛႵֹིౢԢoutliers෮ॖିջট֥႕ཙb (2) ၹଆ ູਔॉҳਸ਼ຓਆ۱ၹĒSIZEၹބBMၹᄝࢳܢௐ൬ၭੱэٚ૫֥ି৯đૌ္ॉ੮ᇏݓܢௐ൧ӆ֥ၹଆğ 2 đč5Ď r−r=β(r−r)+βSMB+βHML+ε~.(0,σ)εpttftmmtftSMBtHMLttဢֹđູਔࣉ၂࣮҄ᄝၹଆ༯ᇏݓܢௐ൧ӆॖିթᄝ֥ၳའđૌᄝ (6) ᇏࡆೆਔࢩइཛğ 2đ č6Ď r−r=α+β(r−r)+βSMB+βHML+εε~.(0,σ)ptftmmtftSMBtHMLtttՎຓđູਔ࣮ၹଆ༯ᇏݓܢௐ൬ၭੱ֥ಖэđૌߎႄೆ๋ᄁၹሰğ r−r=α+β(r−r)+βSMB+βHML+J⋅D+ε,⎧ptftmtftSMBtHMLttt⎪D~(q),⎪t č7Ď ⎨2J~N(ψ,γ)⎪2⎪ε~.(0,σ)⎩tဗ㬕ބӧᅚߩ (2003)đൗ୪ބྸ୍ྛ (2004) ࣮ਔၹଆ (7), ࡆೆ๋ᄁၹሰ֥ၹଆഉໃႵದ࣮b і1ğֆၹଆބၹଆ ଆ ଆഡק ֆၹଆ r−r=β(r−r)+ε҂ॉ੮ࢩइཛ֥ֆၹଆ ptftmtftt r−r=α+(r−r)+ॉ੮ࢩइཛ֥ֆၹଆ ptftmtftt
2 r−r=α+β(r−r)+J⋅D+ε,dD~iidBernoulli(q),J~N(ψ,γ)ॉ੮๋ᄁ֥ֆၹଆ ptftmtfttttၹଆ r−r=β(r−r)+βSMB+βHML+ε҂ॉ੮ࢩइཛ֥ၹଆ ptftmmtftSMBtHMLtt r−r=α+β(r−r)+βSMB+βHML+εॉ੮ࢩइཛ֥ၹଆ ptftmmtftSMBtHMLttr−r=α+(r−r)+SMB+βHML+J⋅D+,ॉ੮๋ᄁ֥ၹଆ ptftmmtftSMBtHMLttt 2dD~iidBernoulliq,J~N(ψ,γ)t2ᇿğіᇏε֥ഡקູğb ε~.(0,σ)tt 3ēܼၬ௶֝ඔဒٚم Ч໓֥ᇶေଢ֥൞ဒഈඍሧӁקࡎଆ൞ڎቀၛࢳᇏݓሧЧ൧ӆ֥൬ၭੱđหљ൞ဒ൞ڎթᄝః֥ڄགၹࠇᆀ٤ཌྟ൬ၭܱ༢bູՎđᄝᆃ၂ࢫᇏđૌࢺക၂ᇕྍ࣍ิԛ֥࠹ਈଆဒٚمb ࠎЧ࠹ਈଆ ഡൈࡗਙູđఃൈࡗਙଆູğđఃᇏіൕൈख़t-1֥{y}y=g(I,θ)+εIttt−1tt−1ሧᆀྐ༏ࠢކđ ൞่ࡱ௹ຬEđطθ∈Θսі၂۱Ⴕཋົҕඔ(Y|I֥ҕඔଆ)g(I,θ)t−1tt−1ࠢކᇏ֥၂۱ҕඔᆴbᄝૌ֥ႋႨᇏđyࡼ൞ܢௐቆކ֥ӑح൬ၭੱđࠧđy=r−rttptftࣼ൞ૌ෮ေဒ֥ሧӁקࡎଆb২ೂđ֒ሧӁקࡎଆູЇݣࢩइཛ֥ֆၹg(I,θ)t−1CAPMଆൈđૌႵೂݔሧӁקࡎଆg(I,θ)=α+βđ(r−r)θ=(αb,β)g(I,θ)t−1mtftt−1ഡקᆞಒđᄵթᄝθ∈Θ֤ 0Ηğ g(I,θ)=E(y|I)đ 0t−10t−1ೂݔଆഡקႵ༂đᄵؓႿၩ֥θ∈ΘđૌႵ Ηğ g(I,θ)≠E(y|I) 1t−1tt−1 ೂݔଆg(I,θ)ഡקᆞಒđᄵg(I,θ)෮Їݣ֥ڄགၹॖၛປಆࢳܢௐቆކ֥t−1t−1൬ၭੱbೂݔଆg(I,θ)ഡקհ༂đᄵၩሢေહթᄝఃڄགၹđေહ൬ၭੱթᄝt−1٤ཌྟܱ༢b ૌགྷᄝࢺകHong & Lee (2005a, 2005b)֥ଆഡקဒٚمbקၬଆ༂ҵε≡Y−g(I,θ)đθ∈Θbᄵೂݔଆഡקᆞಒđթᄝθ∈Θ֤ ttt−10E[ε(θ)|I]=0 t0t−1
εεᆃၩሢE[ε(θ)|I]=0đఃᇏI≡{ε(θ),ε(θ),...}bߐᆭđ֒ଆഡקᆞtt−1t−1t−10t−20ಒൈđࡎ۬༂ҵ{ε(θ)}൞၂۱᷉ҵٳਙđః่ࡱनᆴ҂թᄝޅਙ၇ঠb t0ູਔཿٚьđૌקၬε=ε(θ)bೂݔ{ε}ູ၂۱۬໗ݖӱđఃш࠽หᆘݦtttiuε+ivεiuεtt−|j|tඔູϕ(u)=E(e)đ৳ކหᆘݦඔϕ(u,v)≡E(e)đi=−1đu,v∈Rđjj=...,−1,0,+1,...bູਔٳ༅٤ཌྟൈࡗਙđHong (1999) ิԛਔܼၬ௶ݦඔbఃࠎЧනiuεtਫ਼൞ğקၬਙ{e}֥௶ݦඔູ ∞1−ijω,ω∈[−π,π], f(ω,u,v)≡σ(u,v)e∑j2πj=−∞ivεiuεiuεt−|j|ttఃᇏđωіൕੱđσ(u,v)=cov(e,e)іൕਙ{e}֥ླྀٚҵbھݦඔॖၛႨjႿဒ{ε}ޅྙൔ֥ཌྟބ٤ཌྟਙ၇ঠđЇও၂ࢨइਙ၇ঠ (नᆴਙ၇ঠ) ބtۚࢨइਙ၇ঠ (ೂѯྟਙ၇ঠ (ARCH)đொ؇ਙ၇ঠބڂ؇ਙ၇ঠ)bᆃ൞ၹູσ(u,v)=0֒ࣇ֒εބεཌྷ৫bطđھݦඔ֥թᄝѩ҂ླေ{ε}֥ޅइ่jtt−jt2ࡱbೂݔؽࢨइE(ε)թᄝđૌ๙ݖؓഈඍ௶ݦඔf(ω,u,v)ᄝ(u,v)=(0,0)ԩொ֝tඔࣼॖၛ֤֞{ε}֥ૢ௶ (power spectrum)ğ t2∞∂1−ijϖđb ω∈[−π,π]f(ω,u,v)|=−cov(ε,ε)e=h(ω)(u,v)=(0,0)∑tt−|j|∂u∂v2πj=−∞ૢ௶൞ཌྟൈࡗਙ٤ӈੀྛ֥ࠎЧٳ༅۽ऎđॖၛख़߂ཌྟਙཌྷܱb෮ၛđૌӫf(ω,u,v)ູ{ε}֥ܼၬ௶ (Generalized Spectrum)b tᄝࣜ࠶࿐ᇏđૢ௶ݦඔh(ω)ӈႨটٳ༅ࣜ࠶ѯ֥ᇛ௹ (Sargent, 1987)b൞ႮႿh(ω)ᆺିख़߂ཌྟܱ༢đؓሱཌྷູܱ0֥٤ཌྟܱ༢ᄵିູ৯đၹՎॖିޭ၂ུᇗေ֥ࣜ࠶ܱ༢bܼၬ௶ٳ༅ٚم൞ᄵൈࡗਙ၂ᇕྍ֥ٳ༅۽ऎđॖၛႨႿҩൈࡗਙၩइ֥ཌྟބ٤ཌྟ֥ਙཌྷܱđѩିܔख़߂Ⴎཌྟބ٤ཌྟਙཌྷܱ෮֝ᇁ֥{ε}่tࡱٳ֥҃ᇛ௹эđЇও่ࡱѯੱa่ࡱொ؇ބބ่ࡱڂ؇֥ᇛ௹эbၹՎбh(ω)۷ିѽሚބख़߂گᄖ֥ࣜ࠶ܱ༢đหљ൞٤ཌྟܱ༢b ൞ܼၬ௶ٳ༅ٚمЧദمႨႿဒሧӁקࡎଆđၹູဒ֥൞εބε൞ڎtt−jཌྷ৫đࠧ{ε}൞ڎູ৫ٳ҃ਙ (.)bطᄝဒሧӁקࡎଆഡקᆞಒაڎൈđt
ૌᆺླေဒࡎ۬༂ҵε่֥ࡱनᆴ൞ڎթᄝਙ၇ঠbؽᆀᆭࡗթᄝҵၳbࡌೂεູtt၂۱᷉ҵٳਙ (.)đࠧE(ε|I)=0đ൞ࡎ۬༂ҵթᄝѯऊোགྷའđࠧtt−122cov(ε,ε)≠0đᄵሧӁקࡎଆ൞ᆞಒ֥đ൞ܼၬ௶ݦඔf(ω,u,v)ࡼಪູሧӁקࡎtt−jଆ൞հ༂֥đၹູ{ε}҂൞৫ٳ֥҃bູਔࢳथᆃ၂đHong & Lee (2005a, 2005b) tิԛႨܼၬ௶ݦඔ֥ொ֝ඔ (Generalized Spectral Partial Derivatives)đၹູொ֝ඔᆺܱᇿ่ࡱनᆴᇏ֥ਙ၇ঠđ҂൳൞ڎթᄝۚࢨइਙ၇ঠ֥႕ཙbקၬğ ∞1(1,0)(0,1,0)−ijωđđω∈[−π−∞<v<∞đ ,π]f(ω,u,v)≡σ(u,v)e∑j2πj=−∞∂ivε(1,0)t−|j|ఃᇏđσ(0,v)=σ(u,v)|=cov(iε,e)đᆃ۱֝ඔॖၛҩjࢨሱ݂߭ݦඔjiju=0t∂uE(ε|ε)=0đၹՎൡކႿဒE(ε|I)=0đࠧൡކႿဒሧӁקࡎଆഡקᆞಒtt−jtt−1აڎbطđ҂ࣇॖၛဒקࡎ༂ҵε่ࡱनᆴ֥ཌྟཌྷܱđߎॖၛဒקࡎ༂ҵε่ttࡱनᆴ֥٤ཌྟ၇ঠđࠧᆃུਙ֥ሱཌྷܱ༢ඔູ0bೂ٤ཌྟ၍नݖӱ2ε=αzz+zđ{z}~.(0,σ)bᆃ۱ݖӱ֥ሱཌྷܱ༢ඔູ0đ൞၂۱Ϣᄮၻđtt−1t−2tt(1,0)൞E(ε|ε)≠0bᄝ၂ק่ࡱ༯đE(ε|ε)=0֩ࡎႿσ(0,v)=0đ∀v∈Rb෮tt−jtt−jjၛೂݔሧӁקࡎଆഡקᆞಒđ҂ܵקࡎҗҵ{ε}൞ڎթᄝѯऊোࠇᆀۚࢨइਙ၇t(0,1,0)ঠđݦඔf(ω,0,v)ࣼ߶эູ၂۱ඣ௶ (flat spectrum)ğ 1(0,1,0)(0,1,0)(1,0)đđω∈−∞<v<∞ [−π,π]f(ω,0,v)=f(ω,0,v)=σ(0,v)002π(0,1,0)ၹՎૌॖၛܙ࠹f(ω,0,v)đಖު؎൞ڎູ၂۱ඣ௶bೂݔ൞đሧӁקࡎଆᆞಒĠّᆭđᄵଆഡקհ༂b ဒ࠹ਈ ˆ ࡌഡθ ൞Ⴈඔऌ๙ݖ၂קٚم (ೂቋཬؽӰمaቋնරಖم) ܙ࠹ԛট֥ҕඔᆴđᄵˆሧӁקࡎଆg(I,θ)֥קࡎҗҵູˆε≡Y−g(I,θ)đt=1,2,...,TđIіൕൈख़t−1t−1ttt−1t−1(0,1,0)֥ྐ༏ࠢކbܼၬ௶֝ඔf(ω,0,v)ॖၛႨ၂۱߁֥ނܙ࠹ٚم (smoothed kernek method) ܙ࠹ğ T−11(0,1,0)1/2(1,0)−ijωˆđ−∞<v<∞ (8) f(ω,0,v)≡(1−ˆ|j|/T)k(j/p)σ(0,v)e,ω∈[−π,π]∑j2πj=1−T
ఃᇏp≡p(T)іൕջॺđk:(−∞,∞)→[−1,1]ູ၂۱ؓӫ֥ނݦඔđk(0)=1bނݦඔk(.)֥၂۱২ሰ൞Barlettނݦඔđࠧk(z)=(1−|z|)Ι(|z|≤1)đᆃΙ(.)൞ൕྟݦඔ (indicator function)đࠧೂݔ|z|≤1đΙ(|z|≤1)=1 đڎᄵః౼ᆴູ0b ᄝ (8) ᇏđૌߎקၬ T(1,0)−1ˆđ σˆˆ(0,v)=(T−|j|)εh(v),j=1−T,...−1,0,1,...,T−1j∑tt−|j|t=|j|+1∂'ˆˆˆˆˆđˆˆđ h(v)=ϕ(v)−Gβ(v)G=g(I,θ)t−|j|t−|j|t|j|tt−1∂θTT'−1ˆˆˆˆ ˆβ(v)=(GG)Gϕ(v)j∑tt∑tt−|j|t=1t=|j|+11(0,1,0)(1,0)ˆૌߎࣉ၂҄ܙ࠹ඣ௶fωv=σˆ(,0,)(0,v),ω∈[−π,π],−∞<v<∞bೂ002π(0,1,0)(0,1,0)ݔሧӁקࡎଆഡקᆞಒđf(ω,0,v)=f(ω,0,v)bၹՎૌॖၛყ࠹đ֒ଆ0(0,1,0)(0,1,0)ˆˆഡקᆞಒൈđਆ۱ܙ࠹ݦඔf(ω,0,v)ބf(ω,0,v)ࡼޓࢤ࣍b֒ؽᆀᆭࡗթᄝޓ0նҵљൈđᄵіૼଆഡקհ༂bູਔ۬бࢠᆃਆ۱൞ڎཌྷ࣍đHong & Lee (2005ađ2005b) ܒࡹဒ࠹ਈM(p)ğ T−12(1,0)2ˆˆ Mp=ˆ()[k(j/p)(T−j)|σ|dW(v)−C(p)]/D(p)∑j11∫j=1T−1T1222ˆˆ Cˆ(p)=k(j/p)ε|h(v)|dW(v)1∑∑tt−j∫T−jj=t=j+1T−2T−2T12222ˆˆˆ Dˆ(p)=2k(j/p)k(l/p)|εh(v)h(v')|dW(v)dW(v')1∑∑∑tt−jt−l∫∫T−max(j,l)j=1l1t=j1ᆃW(.)൞၂۱൙༵۳ק֥৵࿃࠹ٳ҃ݦඔđೂѓሙᆞٳ҃ݦඔbᄝ၂ק่֥ܿٓࡱ༯đ֒ሧӁקࡎଆഡקᆞಒđ࠹ਈM(p)ࡶࣉڛՖႿѓሙᆞٳ҃bೂݔ࠹(0,1,0)(0,1,0)ˆˆဒਈM(p)նႿଖ၂ཁᇷඣ֥N(0,1) ֥ਢࢸᆴൈđіൕf(ω,0,v)ބf(ω,0,v)0ཌྷҵޓնđሧӁקࡎଆհ༂bّᆭđೂݔM(p)ཬႿN(0,1) ֥ਢࢸᆴđᄵіൕਆᆀཌྷ࣍đሧӁקࡎଆᆞಒb ሹࢲഈ૫֥ٳ༅đࠎႿܼၬ௶֝ඔ֥ሧӁקࡎଆഡקဒ҄ᇧູ𠈈č1Ď۳קሧӁקࡎଆg(I,θ)đܙ࠹ଆҕඔθđࠆ֤קࡎ༂ҵ{ε}≡−b yg(I,θ)t−1ttt−1∂ˆčˆ2Ď࠹ෘˆđೂݔሧӁקࡎଆູཌྟଆg(I,θ)=XđᄵG=Xb 'θG=g(I,θ)t−1ttttt−1∂θˆˆčˆ3Ďϕ(v)ؓGࣉྛቋཬؽӰ݂߭đ࠹ෘҗҵh(v)b t−|j|tt−|j|
č4Ď࠹ෘ࠹ਈM(p)b č5Ďࡼ࠹ਈM(p)ބѓሙᆞٳ҃N (0,1) ֥ਢࢸᆴ (ೂ5%ཁᇷඣ֥ਢࢸᆴູ, 1%ཁᇷඣ֥ਢࢸᆴູ) бࢠđ؎ଆ൞ڎթᄝഡק༂ҵbೂݔ࠹ਈնႿਢࢸᆴđіૼଆഡקФऋधđଆഡקթᄝ༂ҵbླေᆷԛ֥൞đႨܼၬ௶֝ඔဒđ҂ေޅห൹֥ҕඔܙ࠹ٚمđᆺေିࡼᆇൌҕඔᆴθ၂ᇁܙ࠹ԛࠧॖbᆃࣼննٚьਔᆜ۱ଆ0ഡקဒݖӱđѩิۚਔھဒݖӱࢲં֥ॖौྟb 4ēඔऌ ဢЧ࿊ᄴაቆކܒᄯ Ч໓෮ҐႨ֥ඔऌູᇏݓܢௐ൧ӆ (Їও൧ބധ൧) 1997Ē2004୍ഈ൧܄ඳܢௐࡎ֥۬ᇛଌඔऌbູਔஆԢ၂ུห൹ܢௐ֥႕ཙđဢЧᇏัԢਔSTބPT܄ඳbቆކ֥ܒᄯᄵခႨFama-Frenchၹሰଆ֥ܒᄯٚمđᄝૄ୍6ᄅָࡼဢЧ܄ඳοᅶఃSIZEࣉྛஆđᆷѓ࿊ᄴੀྟܢௐ൧ᆴđοᅶSIZE֥նཬࡼܢௐٳູཬ (S)a2a3a4aն (B)ቆĠಖުૄቆܢௐᄜοᅶఃBMٳູቆđٳљ࠹ູۚ (H)a2a3a4a֮ (L)b෮ၛᆜ۱ܢௐဢЧФٳӮ25۱ቆކbቆކ൬ၭੱ֥࠹ෘҐႨSIZEࡆಃनٚمb࠹ෘൈࡗԳ१ູھ୍؇7ᄅᇀ༯۱୍؇6ᄅb൧ӆ൬ၭੱႨഈᆣᆷඔ൬ၭੱսіb ູਔ࠹ෘSMBބHMLđૌᄝૄ୍6ᄅָοᅶSIZEնཬࡼဢЧٳູն (B)aཬ (S)ਆቆđૄቆᄜοᅶBMٳູۚ (H)aᇏ (M)a֮ (L) ቆđࢌҭྙӮ6۱ቆކSL, SM, SH, BL, BM, BHb࠹ෘૄ۱ቆކھ୍7ᄅ֞༯୍6ᄅૄ۱ቆކᇛ൬ၭੱbSMB=(SL+SM+SH-BL-BM-BH)/3, HML=(SH+BH-SL-BL)/2b і2ਙԛਔဢЧ࿊ᄴ֥၂ུऎุඔऌbՖі2ᇏॖၛुԛđෛሢൈࡗ֥၍đݓഈ൧܄ඳ֥ඔਈᄹࡆđૄ۱ቆކ֥ܢௐඔਈ္ഈശđֆ۱ܢௐ֥٤༢ྟ႕ཙࠎЧഈॖၛФཨԢđ࣮ࢲݔ۷ିّ႘ᆜ۱൧ӆ֥༢ྟหᆘb і2ğဢЧ࿊ᄴაቆކܒᄯ 1997 1998 1999 2000 2001 2002 2003 2004 ܢௐඔਈ 292 537 654 736 827 963 1019 1089 ᇛඔ 50 50 50 50 49 49 49 50 ࠹หᆘ і3ਙԛਔቆކ֥၂ུ࠹หᆘbՖіᇏૌॖၛؿགྷᆃུቆކ֥၂ུ܋หᆘğ൮༵ቆކ൬ၭੱթᄝૼཁ֥٤ᆞྟđఃᇏࡕڂགྷའႭູԛĠఃՑđ۲۱ဢЧቆކمཁᇷֹၳႿ0đᆃіૼᆃུቆކمࠆ֤ध֥ؓ൬ၭđᆃোරႿဗ㬕ބӧᅚߩ (2003)ĠֻđෙಖH-LބS-Bቆކ֥൬ၭੱູᆞđ൞္൞҂ཁᇷ֥đіૼᆃུቆކ္مࠆ֤ध֥ؓ൬ၭđᆃაٓᆒބݚม (2003) োරđطაൗ୪ބྸ୍ྛ (2004) ০Ⴈᄅ؇ඔऌ֤ԛ൬ၭੱཁᇷնႿ0թᄝҵၳb 5ēൌᆣဒ
5ē1 ҕඔܙ࠹ ૌ࿊ᄴ֥ҕඔܙ࠹ٚمູቋնරಖᆴم (MLE)b ᄝܙ࠹ݖӱᇏđ࿊ᄴ֥ෘمູBHHHđӱᄎྛ๙ݖGAUSS Windows і4ਙԛਔ۲۱ֆၹଆ֥ܙ࠹ࢲݔđҕඔܙ࠹֥ѓሙ༂ၛࠣ۲۱ଆ֥ቋնරಖᆴbॉ੮ࢩइཛ֥ֆၹଆა҂ॉ੮ࢩइཛ֥ֆၹଆᆭࡗ֥රಖᆴࠫެીႵҵၳđіૼႄೆࢩइཛѩીႵཁᇷྟֹิۚଆ֥ކӱ؇đቆކ֥α္धն҆ٳ൞҂ཁᇷ֥bᆃ҂Ⴟൗ୪ބྸ୍ྛ (2004) ᇏն҆ٳαཁᇷ֥ࢲંbն҆ٳ҂ቆކ֥ᄝ1ቐβႷđіૼᇏݓܢௐ൧ӆऎႵޓ఼֥༢ྟྛູหᆘbఃᇏཬܿଆቆކ (S) ֥նႿնܿଆβቆކ (B)đіૼཬܿଆቆކ֥ڄག۷նbؓႿཌྷҪՑ֥SIZEඣđBMᄀۚđᄀնb βႄೆ๋ᄁၹሰᆭުđଆ֥රಖᆴิۚđၩሢ๋ᄁၹሰ֥ႄೆॖၛཁᇷֹڿଆ֥ކིݔb۷ູᇗေ֥൞đؓႿཬSIZE֥ܢௐቆކđఃαᆴཁᇷ֥նႿ0đطնSIZEܢௐቆކն҆ٳनཁᇷ֥ཬႿ0đіૼݓܢௐ൧ӆթᄝཁᇷ֥SIZEིႋđՖطᆣൌਔބᇛდ (2002)đൗ୪ބྸ୍ྛč2004Ďđဗ㬕ބӧᅚߩ (2003)đٓᆒބݚม (2003) ֩ದ֥ࢲંbൌᆣࢲݔіૼđ๋ᄁၹሰؓႿิۚݓֆၹሰଆ֥ࢳି৯൞٤ӈᇗေ֥đᆃ္൞ଢభݓଽ࣮෮ޭ֥၂۱ၹbᄝᇏݓܢௐ൧ӆ֥ؿᅚݖӱᇏđᆟک֥ᆟҦྛູϲဆਔᇗေ֥࢘bૄ֒၂۱ྍ֥ᆟҦྛູԛđܢௐ൧ӆ൳֞ᆟکᆟҦ֥႕ཙđࣼ߶ؿളಖྟ֥նږѯbᆃᇕնږѯႮႿᆟҦ֥҂ॖყҩྟࣜӈุགྷԛಖ๋ᄁ֥หᆘb๋ᄁၹሰᄵᆞݺॖၛѽሚ֞ᆃᇕಖ๋ᄁ֥ᇗေ൧ӆྐ༏đ෮ၛ൞࣮ݓܢௐ൧ӆࡎ۬эྛູหᆘ၂ᇕ٤ӈᇗေ֥ၹb҂ቆކ๋֥ᄁ఼؇թᄝбࢠն֥ҵၳđቋնູ֥đіૼन၂۱ᄅࣼ߶ؿള၂Ց๋ᄁĠቋཬູ֥đन7۱ᄅቐႷҌ߶ؿള၂Ց๋ᄁbሹุطđնSIZEቆކ๋֥ᄁ఼؇նႿཬSIZEቆކđ֮BMቆކ๋֥ᄁ఼؇նႿۚBMቆކđඪૼնSIZEቆކބ֮BMቆކؿള๋ᄁ֥ॖିྟ۷նbԢਔཬቆކ๋֥ᄁनᆴཁᇷູڵᆭຓđఃჅն҆ٳቆކ๋֥ᄁनᆴ҂ཁᇷđᆃၩሢཬቆކ෮ؿള֥ಖྟ๋ᄁࣜӈ൞նږ༯יđطఃቆކ๋֥ᄁ൞ؓӫ֥b҂ቆކ๋֥ᄁږ؇ᄵҵљ҂նđն҆ٳᄝ5%-11%ᆭࡗđఃᇏۚBMቆކ๋֥ᄁږ؇նႿ֮BMቆކđඪૼۚBMቆކ๋ᄁ֥หᆘ൞҂َđ൞๋ᄁږ؇նĠط֮BMቆކᄵ൞َ֥ཬږ๋ᄁb ૌགྷᄝሇཟ࣮ၹଆbі5ਙԛਔ۲ᇕၹଆ֥ܙ࠹ࢲݔđҕඔܙ࠹֥ѓሙ༂ၛࠣ۲۱ଆ֥ቋնරಖᆴbॖၛૼཁֹुԛđႄೆਸ਼ຓਆ۱ၹሰॖၛննֹิۚଆ֥රಖᆴބކӱ؇đᆃඪૼᆃਆ۱ၹሰ֥ಒႵᇹႿࢳܢௐ൬ၭ֥҆ٳэđᆃაݓଽն҆ٳؓၹଆ֥ൌᆣ࣮෮֤ԛ֥ࢲં၂ᇁbఃᇏཬSIZEቆކරಖᆴ֥ิۚږ؇ӑݖնSIZEቆކđඪૼਆ۱ڄགၹሰ۷ႵᇹႿࢳཬSIZE֥൬ၭੱэbაֆၹଆ֥ࢲંোරđႄೆࢩइཛࠫެمิۚଆ֥රಖᆴބކӱ؇đն؟ඔα္൞҂ཁᇷ֥đՖطᆣൌਔဗ㬕ބӧᅚߩ (2003)đൗ୪ބྸ୍ྛ (2004) ֥ࢲંb൞ૌ္҂ିࡥֆֹڎקၹଆđطླေ๙ݖଆഡקဒ֤ԛ۷ູކ֥ࢲંb ႄೆਸ਼ຓਆ۱ڄགၹሰᆭުđ۲۱ܢௐቆކ֥ᆭࡗ֥ҵए෪ཬđᄝ1ቐႷbᆃඪβmૼđัԢוSIZEၹაBMၹᆭުđ۲۱ܢௐቆކࠎЧഈބ൧ӆቆކ҄эbࠎβSMBЧഈෛሢSIZE֥ᄹնطᇯࡶࢆ֮đطބဗ㬕ބӧᅚߩ (2003) ֥ൌᆣࢲݔোරđཬSIZEቆކ֥նႿ0đն҆ٳնSIZE֥ཬႿ0đඪૼཬSIZEቆކؓSMB൬ၭੱ֥ββSMBSMBૹۋྟູᆞđSMB൬ၭഈശđཬSIZEܢௐቆކ֥ყ௹൬ၭੱ္ഈശđSMB൬ၭ༯יđཬ
SIZEܢௐቆކ֥ყ௹൬ၭੱ္ෛᆭ༯ࢆĠնSIZEቆކᄵაՎېݺཌྷّb֮BMቆކ֥βHMLཬႿ0đۚBMቆކ֥βնႿ0đඪૼ֮BMቆކؓHML൬ၭੱ֥ૹۋྟູڵđHMLHML൬ၭഈശđ֮BMቆކ֥ყ௹൬ၭੱ༯יđHML൬ၭ༯יđ֮BMቆކ֥ყ௹൬ၭੱᄵഈശĠۚBMቆކᄵཌྷّb൞҂Ⴟဗ㬕ބӧᅚߩ (2003)đቆކૹۋྟ֥նཬ߶൳֞SIZEၹ֥႕ཙđSIZEᄀնđૹۋྟᄀ఼đβ֥धؓඔᆴࣼᄀնbဢ൞֮BMđHMLնSIZEܢௐቆކčBLĎ֥βնჿູđطཬSIZEܢௐቆކčSLĎᆺႵჿĠHMLဢ൞ۚBMđնSIZEܢௐቆކčBHĎ֥βնჿູđطཬSIZEܢௐቆކčSHĎHMLᆺႵჿ ᄝၹଆᇏႄೆ๋ᄁၹሰᆭުđଆ֥රಖᆴᄹࡆđᆃඪૼđ๋ᄁၹሰ֥ಒႵᇹႿࢳᇏݓܢௐ൧ӆ൬ၭੱ֥၂ུၳӈགྷའbβββ֥ҕඔ࠹หᆘބ҂ॉ੮,,SMBHML๋ᄁၹሰીႵૼཁ֥ҵၳb๋ᄁ఼؇q෮Ⴕ֥ҕඔܙ࠹ࢲݔٳཁᇷđіૼᇏݓܢௐ൧ӆթᄝཁᇷ๋֥ᄁིႋbधն҆ٳ๋֥ᄁनᆴψ൞҂ཁᇷ֥đᆃაֆၹሰ๋ᄁଆᇏཬSIZEቆކ๋֥ᄁनᆴཁᇷ҂bᆃඪૼđᄝֆၹሰଆ่ࡱ༯مࢳaФಪק๋ູᄁ֥ࡎ۬э (ᇶေ൞ཬSIZEቆކࡎ۬༯י)ॖၛФਸ਼ຓਆ۱ڄགၹሰ෮ࢳđ҂ᄜФಪק๋ູᄁb҂ቆކ๋֥ᄁږ؇γҵए҂նđնᄝ5%ቐႷđቋնູ֥%đቋཬ֥ᄵູ%b 5ē2 ଆഡקဒ ႋھᆷԛ֥൞đ۲ሧӁקࡎଆᇏܙ࠹ҕඔᄝ࠹ဒഈཁᇷ҂ູ0đѩ٤іൕھଆഡקၘࣜᆞಒđطႵॖିޭః༢ڄགၹሰࠇᆀ٤ཌྟܱ༢b൙ൌഈđೂݔଆഡקհ༂đೂޭః༢ڄགၹሰ (ؓႋ࠹ਈࣜ࠶࿐෮ඪ֥omitted variables)đᄵҕඔܙ࠹ॖିႵொbೂݔթᄝ٤ཌྟܱ༢đପહβᆴࣼ҂൞၂۱ӈඔđၹՎ֒ޭ٤ཌྟܱ༢ൈđ෮֤֥ҕඔܙ࠹ᆴ҂Ⴕொđط҂ିࢳູڄགࡎ۬bູਔ؎൞ڎޭః༢ڄβགၹሰࠇᆀ٤ཌྟܱ༢đсྶࣉྛଆഡקဒbЧ໓࿊ᄴHong & Lee (2005a, 2005b) ิԛ֥ܼၬ௶֝ඔဒؓഈඍଆࣉྛഡקဒđᇶေଢ֥൞ဒଆ൞ڎթᄝഡק༂ҵđࠧଆҗҵਙ{ε}൞ڎᆇ֥൞᷉ҵٺਙ ()b࠹ෘဒᆷѓ෮࿊ᄴ֥ނݦඔູtBartlettނݦඔaParzenނݦඔaDanielނݦඔၛࠣQSނݦඔ (ҕुPriestley, 1981, p. 442)bඹᇕނݦඔ֥࠹ෘࢲݔٳࢤ࣍đູࢫസږđૌᆺਙԛBartlettނݦඔ֥࠹ෘࢲݔđᇌުൈ௹࿊ᄴ5ބ10b і6 (1) ਙԛਔֆၹଆބၹଆ֥ଆഡקဒᆷѓ࠹ෘࢲݔbࡼᆃུ࠹ෘࢲݔ5%ᇂྐඣ֥ਢࢸᆴбࢠđॖၛؿགྷޓ؟ቆކФཁᇷֹऋधਔđіૼᆃུቆކଆ֥ഡקթᄝ༂ҵđଆ֥җҵਙѩ҂൞đҗҵᇏಯಖЇݣ၂ུႵႨ֥ྐ༏đॖၛႨটࢳቆކ൬ၭbᆴ֤ᇿၩ֥൞đႄೆࢩइཛᆭުđଆ֥ഡק༂ҵննࢠഒđ၂ུ҂ݣࢩइཛൈФऋध֥ቆކᄝႄೆࢩइཛᆭުمФऋधđᆃіૼࢩइཛෙಖمཁᇷֹิۚଆܙ࠹֥රಖᆴđ൞ಏ൞ࡨഒଆഡק༂ҵ҂ॖഒ֥၂۱ၹሰbᆃൌ࠽ഈّ
႘ਔܢௐ൬ၭੱ҂۵༢ڄགႵܱđطഈ൧܄ඳႵܱđطᆃུაഈ൧܄ඳႵܱ֥ၹᇀഒॖၛ҆ٳֹႮࢩइཛख़߂ԛটbᆴ֤ᆷԛ֥൞đ๋ᄁၹሰ֥ႄೆෙಖॖၛཁᇷֹิۚଆҕඔܙ࠹֥රಖᆴđ൞ಏمႵི֥ڿଆ֥ഡק༂ҵđ๙ݖဒ֥ቆކބݣႵࢩइཛ֥ଆഡקીႵն֥љb і6 (2) ᄵਙԛਔ۲ᇕၹଆ֥ଆഡקဒ࠹ෘࢲݔbॖၛؿགྷđෙಖၹଆॖၛཁᇷֹิۚଆ֥රಖᆴބކӱ؇đ൞ಏمႵֹིࢆ֮ଆ֥ഡק༂ҵbႄೆਸ਼ຓਆ۱ڄགၹᆭުđଆ֥ഡק༂ҵѩીႵႵֹི༯ࢆđႵུቆކّطഈശਔbᆃіૼđਸ਼ຓਆ۱ڄགၹᄝࢳܢௐ൬ၭੱ҆ٳэ֥ൈջটਔ၂ུྍ֥ଆഡקհ༂bᄝࢩइཛ֥ଆഡקᇏđधն҆ٳቆކم๙ݖဒđіૼᆃུቆކଆ֥ഡקಯಖթᄝ༂ҵđଆ֥җҵਙѩ҂൞.đҗҵᇏಯಖЇݣ၂ུႵႨ֥ྐ༏đॖၛႨটࢳቆކ൬ၭbֆၹሰଆোරđႄೆࢩइཛᆭުđଆ֥ഡק༂ҵնږ༯ࢆđޓ؟ᄝჰ༵ીႵࢩइཛ่ࡱ༯م๙ݖဒ֥ቆކᄝࢩइཛ่ࡱ༯๙ݖਔଆഡקဒbᆃіૼđܢௐ൬ၭੱა൧ӆڄགބഈ൧܄ඳหᆘႵܱđطഈ൧܄ඳ႕ཙܢௐ൬ၭੱ֥หᆘၹѩ҂ࣇࣇ൞SIZEބBMطၘbࢩइཛॖၛख़߂SIZEބBMၛຓ֥܄ඳหᆘđၹطॖၛڿࣉଆb๋ᄁၹሰ֥ႄೆෙಖॖၛཁᇷֹิۚଆܙ࠹֥රಖᆴđ൞مႵֹིࢆ֮ଆഡק༂ҵđ๙ݖဒ֥ቆކ۱ඔބݣႵࢩइཛ֥ଆഡקીႵն֥љbഡקဒࢲݔіૼđࢩइཛ֥ଆഡקෙಖمཁᇷֹڿଆ֥ކིݔđ൞ಏॖၛཁᇷֹࢆ֮ଆഡק༂ҵĠაՎཌྷّđ๋ᄁၹሰෙಖॖၛཁᇷֹڿଆ֥ކӱ؇đ൞مཁᇷֹࢆ֮ଆഡק༂ҵb ଆഡקհ༂֥টჷႵਆ۱ॖିྟğ(1) թᄝః֥༢ڄགၹሰđHMLބSMBᆺି҆ٳֹսіܢௐቆކԢ൧ӆڄགຓ֥ఃڄགၹđܢௐቆކ൬ၭੱᇏಯಖթᄝሢ၂ུمࢳ֥҆ٳđсྶႨః֥ڄགၹࣉྛࢳđՖطᆣൌਔઅਟ (2003)đٓᆒބݚม (2003)đਾਡބౕມඨ (2004) ֥ࢲંĠč2Ďթᄝܢௐ൬ၭੱ֥٤ཌྟܱ༢đᆃᇕ٤ཌྟܱ༢مႨཌྟഡקᆞಒֹіൕԛটb၂ᇕॖିྟ൞βᆴऎႵൈэྟ (ઔ༟֣aᆢᆒބЌކ (2003))đбೂॖିෛሧᆀொݺ֥ڿэࠇᆀࣜ࠶ᇛ௹֥эطؿളэbᄝᆃᇕ౦ঃ༯đܢௐ൬ၭੱьӯགྷԛ٤ཌྟܱ༢bၹՎđᄝ࣮ᇏݓሧӁקࡎൈđԢਔॉ੮ఃڄགၹຓđૌ္ႋھဢᇗေֹॉ੮ॖିթᄝ֥٤ཌྟܱ༢bޓཁಖđ٤ཌྟሧӁקࡎࡹଆေбႄೆఃڄགၹሰ֤؟đၹູࣜ࠶ંીି۳ԛॖି֥٤ཌྟܱ༢bႋھ൞ࣂު࣮֥၂۱ٚཟb 6ēࢲંބࣂު࣮ٚཟ ሹࢲഈ૫֥ൌᆣٳ༅ࢲݔđૌॖၛ֤֞၂ུႵܱᇏݓܢௐ൧ӆሧӁקࡎଆ֥ࠎЧࢲંğ č1Ďᇏݓܢௐ൧ӆऎႵޓ఼֥༢ྟྛູหᆘđ۲۱ဢЧቆކ֥βཌྷҵږ؇бࢠཬđࠎЧഈބ൧ӆቆކ҄эb č2Ďᄝၹଆᇏࡆೆࢩइؓଆ֥ҕඔܙ࠹ીႵૼཁ֥႕ཙđරಖᆴ֥э္ޓཬb൞đಏॖၛႵֹིࢆ֮ଆ֥ഡק༂ҵb č3ĎᄝֆၹଆࠎԤഈࡆೆਸ਼ຓਆ۱ڄགၹiiSIZEၹაBMၹॖၛཁᇷֹิۚଆ֥රಖᆴބކӱ؇đ൞ಏمႵֹིࢆ֮ଆ֥ഡק༂ҵbଆഡקհ༂֥টჷႵਆ۱ॖିྟğ၂൞թᄝః֥༢ڄགၹሰĠؽ൞թᄝ٤ཌྟܱ༢b č4Ďႄೆ๋ᄁၹሰဢॖၛཁᇷֹิۚଆ֥රಖᆴބކӱ؇đ๋ᄁၹሰႵᇹႿࢳܢௐቆކ൬ၭੱ֥၂ུၳӈэbᄝֆၹଆᇏႄೆ๋ᄁၹሰުđॖၛૼཁֹुԛđૌܢௐ൧ӆթᄝSIZEིႋb൞đ๋ᄁၹሰ֥ႄೆဢمႵֹིࢆ֮ଆֹഡק༂ҵbಯಖթᄝྸ؟֥ܢௐቆކđః࠹ᆴӑݖਔ5%֥ਢࢸᆴb
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࣮vֻ12௹đ137Ē141b ᇫЏཉaޅᇍݓđ2002đoβᆴބᅫ૫/൧ᆴбაܢௐ൬ၭܱ༢֥ൌᆣ࣮pđuࣁವ࣮vֻ4௹đ71Ē79b і3: 25۱ቆކ֥࠹หᆘ οᅶBMٳቆ ቆљ H 2 3 4 L H-M SIZE čaĎğनᆴ S 2 3 -5 4 B S-B ѓሙҵ S 2 3 4 B S-B SIZE ொ؇ S 2 3 4 B S-B SIZE ڂ؇ S 2 3 4 B S-B
і4ğֆၹଆ֥ҕඔܙ࠹ࢲݔ (a) ҂ݣࢩइཛ BMH 2 3 4 L β***************S () () () () () ***************2 () () () () () ***************3 () () () () () ***************4 () () () () () ***************5 () () () () () රಖᆴ S 2 3 4 B (b) Їݣࢩइཛ αSIZE H 2 3 4 L S () () () () () 2 () () () () () 3 () () () () () *4 () () () () () *B () () () () () β***************S () () () () () ***************2 () () () () () ***************3 () () () () () ***************4 () () () () () ***************B () () () () () රಖᆴ S 2 3 4 B (c) ॉ੮๋ᄁၹሰ α SIZE H 2 3 4 L ***************S () () () () () ********2 () () () () ()
*3 () () () () () ***4 () () () () () ***********B () () () () () β***************S () () () () () ***************2 () () () () () ***************3 () () () () () ***************4 () () () () () ***************B () () () () () q ***************S () () () () () ***************2 () () () () () ***********3 () () () () () ***************4 () () () () () ***************B () () () () () ψ*************S () () () () () ***2 () () () () () *3 () () () () () 4 () () () () () B () () () () () γ ***************S () () () () () ***************2 () () () () () ***************3 () () () () () ***************4 () () () () () ***************B () () () () () රಖᆴ S 2 3 4 B 2ᇿğ҂ݣࢩइཛ֥ֆၹଆഡקູğ,ĠЇݣࢩइཛ֥ֆၹଆഡקູğr−r=β(r−r)+εε~.(0,σ)ptftmtfttt2,; ॉ੮๋ᄁၹሰ֥ֆၹଆഡקູğđr−r=α+β(r−r)+εε~.(0,σ)r−r=α+β(r−r)+J⋅D+εptftmtftttptftmtfttt22,,bі۬ᇏওݼຓ֥ඔᆴ൞۲ҕඔ֥ܙ࠹ᆴđওݼᇏ֥ඔᆴູھdD~iidBernoulli(qJ~N(ψ,γ)ε~.(0,σ)ttҕඔܙ࠹֥ѓሙ༂b*,**,***ٳљսі10%,5%ބ1%֥ཁᇷྟඣb
і5ğၹଆ֥ҕඔܙ࠹ࢲݔ (a) ҂ݣࢩइཛ BM βmSIZE H 2 3 4 L ***************S () () () () () ***************2 () () () () () ***************3 () () () () () ***************4 () () () () () ***************B () () () () () βSMB***************S () () () () () ***************2 () () () () () ***************3 () () () () () *********4 () () () () () **********B () () () () () βHML************S () () () () () *************2 () () () () () *************3 () () () () () ************4 () () () () () ***************B () () () () () රಖᆴ S 2 3 4 B (b) ݣႵࢩइཛ α SIZE H 2 3 4 L S () () () () () 2 () () () () () 3 () () () () () 4 () () () () () B () () () () () βm***************S () () () () () ***************2 () () () () () ***************3 () () () () () ***************4 () () () () () ***************B () () () () () βSMB
***************S () () () () () ***************2 () () () () () ***************3 () () () () () ********4 () () () () () **********B () () () () () βHML************S () () () () () **************2 () () () () () *************3 () () () () () ************4 () () () () () ***************B () () () () () රಖᆴ S 2 3 4 B (c) ॉ੮๋ᄁၹሰ α SIZE H 2 3 4 L *S () () () () () **2 () () () () () ****3 () () () () () ********4 () () () () () *****B () () () () () βm***************S () () () () () ***************2 () () () () () ***************3 () () () () () ***************4 () () () () () ***************B () () () () () βSMB***************S () () () () () ***************2 () () () () () ***************3 () () () () () ***************4 () () () () () ***************B () () () () () βHML************S () () () () () *************2 () () () () () ************3 () () () () () ***************4 () () () () ()
**************B () () () () () q ***************S () () () () () ***************2 () () () () () ***************3 () () () () () ***************4 () () () () () ***************B () () () () () ψS () () () () () 2 () () () () () *3 () () () () () 4 () () () () () B () () () () () γ ***************S () () () () () ***************2 () () () () () ***************3 () () () () () ***************4 () () () () () ***************B () () () () () රಖᆴ S 2 B 2ᇿğ҂ݣࢩइཛ֥ၹଆഡקູ,ĠЇݣࢩइr−r=β(r−r)+βSMB+βHML+εε~.(0,σ)pttftmmtftSMBtHMLtt2ཛ֥ၹଆഡקູğ,Ġॉ੮๋ᄁၹሰ֥r−r=α+β(r−r)+βSMB+βHML+εε~.(0,σ)ptftmmtftSMBtHMLttt2ၹଆഡקູğ,,, r−r=α+β(r−r)+βSMB+βHML+J⋅D+εε~.(0,σ)D~iidBern()ptftmmtftSMBtHMLttttt2bі۬ᇏওݼຓ֥ඔᆴ൞۲ҕඔ֥ܙ࠹ᆴđওݼᇏ֥ඔᆴູھҕඔܙ࠹֥ѓሙ༂b*,**,***ٳљսі10%,5%ބJ~N(ψ,γ)1%֥ཁᇷྟඣb
і6ğֆၹଆބၹଆഡקဒ (1) ֆၹଆ(2)ၹଆ (a) ҂ݣࢩइཛ Lag=5SIZE H 2 3 4 L H 2 3 4 L * *********S ** * * ***********2 *** ************3 * **** ************4 ** * ** ***********B Lag=10 SIZE H 2 3 4 L H 2 3 4 L ******************S ****************2 *********************3 ******************4 *******************B (b) ݣႵࢩइཛ Lag=5SIZE H 2 3 4 L H 2 3 4 L ***S **********2 ********3 *******4 ************B Lag=10 SIZE H 2 3 4 L H 2 3 4 L ****S ***********2 ********3 ********4 ************B (c) ๋ᄁଆ Lag=5SIZE H 2 3 4 L H 2 3 4 L ******S ********2 *******3 *************4 ********B Lag=10 SIZE H 2 3 4 L H 2 3 4 L *****S
*******2 ***********3 **********4 ***********B ᇿğі۬ᇏ֥ඔᆴູ۲ᇕଆ֥Hong & Lee (2005a,2005b) ဒ࠹ਈ,࿊ᄴ5ބ10bܙ࠹࠹ਈ෮Ⴈ֥ނݦඔູM(p)pBarlettނݦඔđࠧđᆃ൞ൕྟݦඔ (indicator function)đࠧೂݔđ đk(z)=(1−|z|)Ι(|z≤1Ι(|z|≤1)=|1)|z|≤1Ι(.)ڎᄵః౼ᆴູ0b*,**,***ٳљսі10%,5%ބ1%֥ཁᇷྟඣb
