资产定价模型

WhatisAnefficientcapitalmarketisoneinwhichstockpricesinstantaneouslyandfullyreflectallavailableModernVersionoftheIfwedef heintrinsicvalueofafirmasthepresentvalueofitsfuturepayoffsV

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Then,operationally,theEMHisofteninterpretedtomeanpricereflectsastock'sintrinsicvalue((PVtt3“ThePriceisTheimplicationofSixMarketsHaveNoIfthereisanynewinformation,TrustMarketThereAreNoFinancialIllusionsforAccountingChanges,StockSplitsandStockFirmsreceivethefairvalueforsecuritiesthattheysell.TheimplicationofReadingTheSeenOneStock,SeenThemInvestorsshouldonlyexpecttoobtainanormalrateofreturn t-YourselfAnexampleofIninventsanewtechnology,whichistobring$10dollarspershareThepriceofInAsaninvestor,youdonotneedtoknowwhatthenewsis…HowdomarketpricesreflectallMilton(bornJuly31,DifferentopinionscancelDifferenttypesofWeakformSemi-strongform(publicStrongform(allP(t)=P(t-1)+expectedreturn+randomerror(randomwalk)WEMHmeans ysisisRandomWalkRandomWalk兩張由BrealeyandMyers所提第一張圖是1980 S&PIndexAllpublicinformationisEarnings,accountingmethods,dividends,SomeThemarketreactionstostocksplitsareprettyquickTherecordofmutual“orangejuiceandweather”(Roll,ImplicationsforThedisclosurematters,buttheformatdoesFullNaïveinvestorsAccountingservesasatypeofFor–Information;measureofinformation•Event•Association StrongformInsiderInsider*InsiderCAPM:ValuationModelinFinance/AccountingRationalandRisk-AversePrice-takingandHomogeneousExpectationInvestorExistenceof AssumptionsofFixedtiesofFrictionlessMarket(Marketable,Divisible,NoShort-sellRestriction,NoTaxes,NoInformationallyEfficientFundamentalsforTwodimensionsofstock:expectedreturnandvariancePortfolio’srisk&Optimal ProposedbyJohn^DiedandWilliamSharpe*1990NobelpriceMarketTestsof(Fama&Macbeth1973,Fama&FrenchTestofempiricalmarketR

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R CAPM 0 (RmtRftbeta以外的其他因素（如P/E、sizeJanuaryeffect）Theestimationperiod:Estimatasusingmonthlydatafromyeart-5tot-1(60monthswithatleast24months)Testperiodforyeart(12 ˆ

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0,(thereturn-betarelationis0,(betaistheonlyrisktoexin 0,k4,...,n.(CharkisPagePracticalProblemsandExcessivetrading inthetraditionalmodel,thereshouldbelittleornotradingofindividualstocksExcessvolatilityinreturnsaretoovolatiletobeexBetasdonotexinfactorloadingshavelittlepowertoexross-sectionalvariationinstockreturnsRealizedreturnsareapoor expectedreturnsThenoisynatureofrealizedreturnsExante JointtestsofAjointtestsofmarketefficiencyandsomepricingmodels…(Roll’scritic)Isitgoodtohavean“Ifinformationiscostly,pricescannotperfectlyreflecttheinformationwhichisavailable;becauseifitdid,thosewhospendresourcestoobtainitwouldreceivenocompensation.” (SanfordGrossmanandJosephStiglitz1980AER)*2001NobelprizewinnerEarningsB/Meffect(Valuestockvs.GrowthAccrualsEffect(BuyLow,SellOthercorporateevents:splits,ValuestrategyandGrowthTheFama-FrenchTest(1992,Testthefollowingmodelusingindividual1<0,(thelargerfirmsize,thesmaller2>0,(thehigherBM(valuestock),thehigher3=0.(irrelevantwithpreviousSizeandbook-to-marketequitycapturethecross-sectionalvariationinaveragestockreturns.=>ValuestocksoutperformgrowthstocksTherelationbetweenbetaandaveragereturnisRptR pp,Mkt Rft)p,HMLp,SMB ept,pNullhypothesis(Actuallythisis Result:Reject

0,Chan,HamaoandLakonishok(1991,Stockreturnsarepositivelyrelatedtobook-to-marketequityandcashflowyieldandnegativelyrelatedtofirmsize.Daniel,Titman,andWei(2001, Stockreturnsarepositivelyrelatedtobook-to-marketequityandnegativelyrelatedtofirmsize.Book-to-marketequityhasthemostsignificantimpactonexpectedChuiandWei(1998,PACAP):Exam hecross-sectionalstockreturnsin,Korea,Malaysia,,andThailandTherelation agestockreturnandmarketbetaisThissavaluepremiumin,KoreaandThereissizeeffectinallmarkets,exceptBillings,BruceK.andRichardM.Morton(2001,TheyextendBeaverandRyan(1996,2000)by posingbook-to-marketintoamorepersistent(bias)componentandadelayedrecognition(lag)component.Thelagcomponentexinmostoftheinverserelationbetweenbook-to-marketandfuturestockreturns elagisconstructedbyregressingbook-to-marketonlaggedpricechanges,theresultsareconsistentwiththelagcomponentcapturingsystematicstockpricereversal(contrarian).Piotroski(2000,JAR):Theuseofhistoricalfinancialstatementinformationtoseparatewinnersfromlosersforhighbook-to-marketfirmsF_Score=F_ROA+F_ROA+F_CFO+F_Accrual+F_MarginF_Turn+F_Lever+F_LiquidThemeanreturnearnedbyhighbook-to-marketinvestorcanbereasedbyatleast7.5%annuallythroughtheselectionoffinancialstronghighBMAninvestmentstrategythatbuy pectedwinners(F_score=8or9)and pectedlosers(F_score=0or1)generatea23%annualreturns.WithintheportfolioofhighBMfirms,thebenefitstofinancialstatementysisareconcentratedinsmallandmedium-sizedfirms,companieswithlowshareturnover,andfirmswithnoysisfollowing.ValueExMkt(Market)SMB(Small(bottom50%)MinusBig(top50%))SZHML(High(top30%)MinusLow(bottom30%))BMFamaandFrenchTestportfolios:5×5size-BMResults:TheFFthreefactorscanexinthesizeandBMFamaandFrenchResults:TheFFthreefactorscanexinalltheanomalie ceptmediumtermmomentum=>LongMarketSmallSIZEHighBE/MEShort BigLow t* t*value-weightedmarket one-monthbillstockprice*sharesinJuneofyearmarketvaluationofequityatofDecemberofyeart-firmsmusthavestockpriceforDecemberofyeart-1andforJuneofyearBV(bookvalueofcommonequityforthefiscalyear alendaryeart-1bookvalueofstockholders’+balance-sheetdeferred+investmenttaxbookvalue（redemption,liquidation,parvalue）ofpreferredfirmmusthavebookvalueforyeart-BV(bookcommonequityforthefiscalyear alendaryeart-1bookvalueofstockholders’ SIZE(2groups–S/L+S/M+S/Hvs.BV/MV(3groups--30%,40%,--S/H+B/Hvs.PortfolioreturnsfromJulyofyearttoJuneof--reformedinJuneof12returnOnCOMPUSTATfortwoyears已上市櫃滿一年ThreeFactorsModelPanelARM(t):themarketindexbsThreeFactorsModelPanelARM(t):themarketindexh Risk-basedexFamaandFrench(1996,JF):3factorscanexinLiewandVassalou(2000,JFE):BMcanpredictGNPExpectationbiasorextrapolationexInvestorsaretoooptimisticaboutglamourstocksthathavehadgoodperformanceintherecentpastandtoopessimisticaboutvaluestocksthathaveperformedpoorlyLakonishok,Sheifer,andVishny(1994,JF):Doukas,Kim,andPantzalis(2002,JF):Atestoftheerrors-in-expectationsexnationofthevalue/glamourstockreturnsperformance:Evidencefromysts’forecasts(no)BanzandBreen(1986)andKothari,Shanken,andSloanLakonishok,Shleifer,andVishnyValuestrategiesthatinvolvebuyingout-of-favor(value)stocks(i.e.lowstockpricesrelativetoearnings,dividends,bookassets,orothermeasureoffundamentalvalue)haveoutperformedglamourThesevaluestrategiesworkbecausetheactualfuturegrowthratesofearnings,cashflow,etc.ofglamourstocksrelativetovaluestocksturnedouttobemuchlowerthantheywereinthepast.=>Marketparticipantsappeartohaveconsistentlyoverestimatedfuturegrowthratesofglamourstocksrelativetovaluestocks(Extrapolationorerror-ValuestrategiesappeartobenoriskierthanglamourDoukas,Kim,andPantzalis(2002,JF):Atestoftheerrors-in-expectationnationofthevalue/glamourstockreturnsperformance:Evidencefromysts’forecastsTheresultsfailtosupporttheextrapolationhypothesisthatpositsthatthesuperiorperformanceofvaluestocksisbecauseinvestorsmakesystematicerrorsinpredictingfuturegrowthinearningsofout-of-favorstocks.Buythepastwinnersandsimultaneouslysellthepastlosersbasedonthepast3-12monthreturns(formationperiod)Andthenholdfor3-12months(holdingSkiponemonthbetweenformationandholdingIntheUS:Profitonthemomentumportfolioformedonthebasisofbuyingthetopdecileandsellingthebottomdecilerankedonthepast6-monthreturnsisabout1%permonthIntheEuropeandevelopedmarkets,themomentumprofitisaboutthesameasintheUSInemergingmarkets,themomentumprofitismuchweaker(Rouwenhorst(1989,JF),Chui,Titman,andWei(2002))Industrymomentum(MoskowitzandGrinblatt(1999,JF),GrundyandMartin(2001,RFS),andLiuandWei(2002))Rpt pHML,pRHML,tSMB,pMkt,p(RMkt,tRft)PR1YRRPR1YR,t whereRPR1YRisthemomentumfactorbasedonfindingbyJegadeeshandTitman(1993,JF),whichisthereturndifferencebetweenwinners(top50%)andlosers(bottom50%)basedonpastone-yearreturnsskippedbyonemonth.Chui,Titman,andWei(2003,REE):Examhepre-andpost-1990periods,sethestructurechangeoftheREITaround1990.Novaluepremium(Nobook-to-marketThedeterminantsofexpectedreturnsdifferbetweenthetwoInthepre-1990subperiod,momentum,size,turnoverandystcoveragepredictREITreturns.Inthepost-1990period,momentumisthedominantpredictorofREITMomentumisstrongerforthelargerREITsratherthanforthesmallerMomentumeffectsarestrongerformoreliquidLeeandSwaminatahn(2000,JF):Tradingvolumeprovidesanimportantlinkbetween“momentum”and“value”strategiesFirmswithhigh(low)pastturnoverratio hibitmanyglamour(value)characteristics,earnlower(higher)futurereturns,andhaveconsistentlymorenegative(positive)earningssurprisesoverthenexteightquarters.Pasttradingvolumealsopredictsboththemagnitudeandpersistenceofpricemomentum.Specifically,pricemomentumeffectsreverseoverthenextfiveyearsHigh(low)volumewinners(losers)experiencefasterMomentumlifecycle:Buyinglowvolume(early)winnersandsellinghighvolume(early)loserscangeneratemuchhigherandlongerlastingreturnsthanasimplemomentumstrategyGlamour(negativeValueDebondtandThaler(1985,Buythepastlosersandsimultaneouslysellthepastwinnersbasedonthepast3-5yearreturns(formationperiod)Andthenholdfor1-3years(holdingIntheUS:ProfitonthecontrarianisSameinotherJapanesemarket:Contrarianforshort-,medium-,andlong-terms:Chou,Wei,andChung(2004)ExnationsforA“conservatismbias”canleadinvestorstounderreactorunderweightnewInthecasewithapureconservatismbias,oncetheinformationisfullyorporatedinprices,thereisnopredictabilityinstockreturns.Inthiscase,thepost-holdingperiodreturnswouldbezero.ThereisadelayedoverreactiontoThe“representativeheuristic,”whichsuggeststhatinvestorsmayoverlyextrapolateafirm’spastextraordinaryearninggrowthsintothefutureandhenceoverreacttopositive(ornegative)informationthatisprecededbypositive(ornegative)informationDelayedoverreactioncanarisebecauseof“self-attribution(orcognitive)bias.”Thatis,investorstendto emoreoverconfidentwhentheirstock ewinnersandtakemoreaggressivepositionsthatpushupthepricesofwinnersabovetheirfundamentalvalues.HongandStein(1999,Modeltwogroupsofinvestors:informedinvestorsandtechnicaltraders,whodonotfullytakeintoaccounttheactionsofeachother.Asaresult,informationis orporatedslowlyintostockprices,providingapotentialprofitopportunityfortechnicaltraders.Thesetraders,however,tendtopushpricesofpastwinnersabovetheirfundamentalvalues.Ineachofthesebehavioralmodels,pricestendtoeventuallyoverreacttoinformationandthenreversewhenpriceseventuallyreverttotheirfundamentals.EmpiricalHong,Lim,andStein(2002,DanielandTitman(1998,JegadeeshandTitman(2001,JF),Chui,Titman,andWei(2003,ConradandKaul(1998,RFS):Thisisconsistentwithanefficientmarketwherestockshavedifferentexpectedratesofreturnbecauseofdifferentriskexposures.Theyemphasizethattherewouldbesomeevidenceofmomentumeveniftherewerenotime-seriesvariationinexpectedreturnss estockswithhigh(low)expectedreturnswouldbeexpectedtohavethehighest(lowest)returnsinadjacentperiods.Thinationsuggeststhattheprofitsfromamomentumstrategyshouldbethesameinanypost-rankingperiod.JegadeeshandTitman(2002,RFS):CumulativeCumulativeHolding Event Post-holdingYear-EndWeekendIntradayValueLineInvestorSizeE/PCriticsofTradingcosts,arbitragecostandInformationcosts,modelMarketBehavioralFromEfficientMarket FromEfficientMarket證券商的角色撮合制度(Quotevs.(Callvs.Cont.) vs.揭示制度(HiddenOrder,資訊透明FromEfficientMarketProspectDispositionFramingMentalSelfMoods(Cloudy,Cold,Q&假设一个月前以每股50元买进某，目前该市价为40元，如果未来价格不是上涨10元，就是下跌10元，机率一样。那么究竟会卖出或继续持有该？假设一个月前以每股50元买进某，目前该市价为60元，如果未来价格不是上涨10元，就是下跌10元，机率一样。那么究竟会卖出或继续持有该？OtherC-CAPM,I-CAPM,…APT, (beta,size,B/M)(beta,size,B/M,E(Ri) i[E(Rm)RZwhereRf<RZ=returnonthezero-betaAssumptions:SameasthoseAPMand(5)noexistenceofrisk-rateTheArbitragePricingTheory(APT)[Ross(1976,Stockreturnsareassumedtobegeneratedbykfactors ibi1f1bi2f2... f eiwhereiistheexpectedreturnforsecurityi,=0,forallj,E(ei|f)=b’sarecalledfactorloadingsorfactorIfthereisnoarbitrageopportunity,thenwewhere’sarefactorriskInvestorsinvestnotonlyone-period.Theycanconstructportfolioundercontinuoustime.investorsaresolvinglifetimeconsumptiondecisionswhenfacedwithmorethanoneuncertainty.TheinterpretationforthismodelissimilartothatfortheAPT,exceptthatthefactorportfoliosherearethehedgeportfoliosthatareusedtomimictheinvestmentopportunity.E(R) c[E(R)R whereRcisthemimickingportfoliothathasthe correlationwithconsumption.ItisderivedfromMerton’sICAPM.Investorsuseconsumptionandmacroeconomicinformation.Investorstakeconsumptionriskintoaccount. E(Ri)R i[E(Rm)Rf] iwherei=(1–qi)i,qiisthepercentofinvestorswhocomple yknowsecurityi(qi=1=>allinvestorsknowsecurityi)andi=xii2/qi,whereisriskaversemeasureandxiistheweightofsecurityiinthemarketportfolio.ThismodelisrelatedtoLevy’s(1978,AER)model.Peopleusethismodeltotestthevisibilityhypothesisortheinvestorrecognitionhypothesis=>dlog|E(Ri)Rf|/dlog(qi)iOtherimplications:higheridiosyncraticvolatilityhashigherexpectedreturn.(Becauseinformationiscostly,investorsmustpaytogaininformationaboutastock.Theseinformationcostsshouldbecompensatedbystockreturns.)iPage dlog|

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CAPMwithIlliquidity[AmihudandMendelson(1986,E(Ri)Rfi[E(Rm)Rf]whereSpreadiisbid-askspreadornegativetradingvolume(turnover)andisameasureofilliquidity. pectedtobeCarrollandWei(1988,JB)testthefollowing

0

pk

ˆ2pk

k

wheredkisadummyvariablerepresentingsizegroupwiththesmallestsizegroupandd5asthelargestMerton’s(1987,JF)orLevy’s(1978,AER) informationmodelpredicts:1>2>3>4>5.Empiricalresults:Supporttheprediction.Thatis,theunsystematicriskismoreimportantforsmallsizefirmsthanlargesizefirmsAmihudandMendelson(1989,JF):Stockreturnspositivelycorrelatedwithbid-askDatar,Naik,andRadcliffe(1998,JFM):StockreturnsnegativelyassociatedwithBrennan,Chordia,andSubrahmanyam(1998,JFE):Stockreturnsarenegativelyrelatedtodollartradingvolume.Sloan(1996,JAR):examinewhetherstockpricesreflectinformationaboutfutureearningscontainedintheaccrualandcashflowcomponentsofcurrentearningsCurrentearningsperformancepersistingintothefuturedependsontherelativemagnitudesofthecashflowandaccrualcomponentsofcurrentearnings.Stockpricesarefoundto ifinvestors“fixate”onFirmswithloweraccrualsoutperformfirmswithhigherFirmswithhighercashflowsoutperformfirmswithlowercash Gompers,Ishii,andMetrick(2003,QJE):Exam relationshipbetweenthegoodcorporate ernanceindexandseveralforward-lookingperformancemeasuresduringthe1990s.Firmsinthehighestdecileofthegoodcorporate ernanceindexoutperformfirmsinthelowestdecileofthegoodcorporate indexby8.5%peryear.Ahighergoodcorporate ernanceindexisassociatedwithahigherfirmvalueFirmswithalowergoodcorporate ernanceindexareassociatedwithlowerprofits,lowersalesgrowth,highercapitalexpenditures,andhigheracquisition tradesofmutualChen,Jegadeesh,andWermers(2000,StockswidelyheldbyfundsdonotoutperformotherStockspurchasedbyfundshavesignificantlyhigherreturnsthanstockstheysellThisistrueforlargestocksaswellassmallstocks,forvaluestocksaswellasforgrowthstocks.BreadthofChen,HongandStein(2002,Themodelpredictsthatwhenbreadthislow(Breadth=#offundsholdthestock/total#offunds)–i.e.,whenfewinvestorshavelongpositions–thissignalsthatshort-salesconstraintisbindingtightly,andpricesarehighrelativetofundamental.ThissuggeststhatreductionsinbreadthshouldforecastlowerStockswhosechangeinbreadthinthepriorquarterisinthelowestdecileofthesampleunderperformthoseinthetopdecileby6.38%inthe12monthsafterformation.Severalstudiessuggestthatafirmdistressriskfactorcouldbebehindthesizeandbook-to-marketeffects.A forfirmdistressisbankruptcyIfbankruptcyriskissystematic,onewouldexpectapositiverelationbetweenbankruptcyriskandsubsequentrealizedreturns.Firmswithhighbankruptcyriskearnlowertha agereturnsseBankruptcyriskisnotawardedbyhighAmongfirmswiththehighestdistressriskasproxiedbyOhlson’s(1980)O-score,thedifferenceinreturnsbetweenthehighandlowbook-to-marketstocksismorethantwiceaslargeasthatinotherThislargereturnsdifferentialcannotbeexinedbytheFFthreefactorsorbydifferencesineconomicfundamentals.Consistentwithmispricingarguments,firmswithhighdistressriskexhibitthelargestreturnreversalaroundearningsannouncement,andthebook-to-marketeffectislargestinsmallfirmswithlow Bhandri(1988,JF)testthefollowing

Results:2>0.Thatis,higherdebttoequityratios,highexpectedreturnsLamont,Polk,andSaa-Requejo(2001,Financiallyconstrainedfirms’stockreturnsmovetogetherovertime,suggestingthatconstrainedfirmsaresubjecttocommonshocksConstrainedfirmsasproxiedbyKanandZingales(1997,QJE)KZindexhaveloweraveragestockreturns.Theisnoevidencethattherelativeperformanceofconstrainedfirmsreflectsm ary,creditconditions,orbusinesscycle Perez-QuirosandTimmermann(2000,Economictheorysuggeststhatthepresenceofasymmetriesinthevariationofsmallandlargefirms’riskovertheeconomicSmallfirmswithlittlecollalshouldbemorestronglyaffectedbytightercreditmarketconditionsinrecessionstatethanlarge,bettercollalisedones.Results:Smallfirmsdisythehighestdegreeofasymmetryintheirriskacrossrecessionandexpansionstates,whichtranslatesintohighersensitivitiesoftheirexpectedstockreturnswithrespecttovariablesthatmeasurecreditmarketconditionsDiether,Malloy,andScherbina(2002,JF):dispersionandStockswithhigherdispersionin ysts’earningsforecastsearnlowerfuturereturnsthanotherwisesimilarfirmsThiseffectismostprofoundinsmallstocksandstocksthathaveperformedpoorlyoverthepastyearsTheevidenceisconsistentwiththehypothesisthatpriceswillreflecttheoptimisticviewwheninvestorswithlowestvaluationdonottrade,whenweinterpretdispersionasa differencesinopinionaboutastockTheevidenceisnotconsistentwithaviewthatdispersioninysts’forecastsproxiesforriskShortDesai,Ramesh,Thiagarajan,andBalachandran(2002,JF):Exam herelationshipintheNasdaqmarket.Ahigherlevelofshort-saleinterestisastrongerbearishHeavilyshortedfirm periencesignificantnegativeabnormalreturnsrangingfrom–0.l76to–1.13%permonthaftercontrollingforthemarket,size,book-to-market,andmomentumHeavilyshortedfirmsaremorelikelytobedelistedcomparedtotheirsize,book-to-market,andmomentummatchedcontrolGervais,Kaniel,andMingelgrin,(2001,JF):TestthevisibilityhypothesisorrecognitionhypothesisofMerton periencingunusuallyhigh(low)tradingvolumeoveradayoraweektendtoappreciate(depreciate)overthecourseoffollowingmonth.Thishigh-volumereturnpremiumisconsistentwiththeideathatshocksinthetradingactivityofastockaffectitsvisibility,andinturnthesubsequentdemandandpriceforthatstock.CapitalTitman,Wei,andXie(2004,Firmsthatsubstantiallyreasecapitalinvestmentssubsequentlyachievenegativebenark-adjustedreturns.Thenegativeinvestment-returnrelationisshowntobestrongerforfirmsthathavegreaterinvestmentdiscretion,i.e.,firmswithhighercashflowsandlowerdebtratios.Consistentwiththehypothesisthatinvestorstendtounderreacttotheempirebuildingimplicationsofreasedinvestmentexpenditures.Thenegativecapitalinvestment/returnrelationistofthe edlong-termreturnreversalandsecondaryequityissueanomalies.Chan,Lakonishok,andSougiannis(2001,UndercurrentU.S.accountingstandards,R&Dspendingisexpensed.TheaveragehistoricalstockreturnsoffirmsngR&DmatchthereturnsoffirmswithoutCompanieswithhighR&Dtoequitymarketvalue(whichtendtohavepoorpastreturns)earnlargeexcessreturns.AsimilarrelationexistsbetweenadvertisingandstockInthepast20years,financialeconomistshavebeensearchingfortheoriesoranomaliestoexinthecross-sectionalvariationofexpectedstockreturnswithsomesuccess.Sofar,wehaveidentifiedthevariablesthatcanexinthecross-sectionofexpectedstockreturnsBid-askMedium-term(6-12months)tradingUnusualshort-term(onedaytooneweek)tradingMomentum:medium-term(3-12months)pastContrarian:long-term(3-5years)past TradesofmutualChangesinbreadthofinstitutionalBankruptcyDebt-to-equityFinancialDifferencesofShortCapitalR&DexpendituresandadvertisementTheoriestoexintheInctionofbusinesscycle,creditcondition,consumption,wealth,etc.withfirmfinancinginexiningtheasymmetriccross-sectionofexpectedstockreturnsSpecificformarkets:HAVEAPRODUCTIVEAmihud,Yakov,andHaimMendelson,1986,“Assetpricingandthebid-askspread,”JournalofFinancialEconomics,17,223-249.Black,Fisher,1972,Capitalmarketequilibriumwithrestrictedborrowing,JournalofBusiness45,Breeden,D.T.,1979,“Anintertemporalassetpricingmodelwithstochasticconsumptionandinvestmentopportunities,”JournalofFinancialEconomics17,265-296.Levy,H.,1978,Equilibriumin pletemarket:Aconstraintonthenumberofsecuritiesintheportfolio,AmericanEconomicReview68,643-658.Merton,R.C.,1987,Asimplemodelofcapitalmarketequilibrium pleteRoss,S.,1976“Thearbitragetheoryofcapitalassetpricing,”JournalofEconomicTheory13,Sharpe,W.,1964,“Capitalassetprices:AtheoryofmarketequilibriumunderconditionsofWei,K.C.,1988,“Anasset-pricingtheoryunifyingtheCAPMandAPT,”JournalofFinance44,Amihud,YakovandHaimMendelson,1989,“Theeffectsofbeta,bid-askspread,residualrisk,andsizeonstockreturns,”JournalofFinance44,479-486.Carroll,Carolyn,PaulD.Thistle,andK.C.JohnWei,1992,“Therobustnessofrisk-returnnonlinearitiestothenormalityassumption,”JournalofFinancialandtative 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