第七章效率市场证券投资学北大,杨云红

第七章效率市场主要内容效率市场的定义效率市场的实证结果证券市场中的几种反常现象行为金融MauriceKendall,Theanalysisofeconomictimeseries,PartI:Prices,JournaloftheRoyalstatisticalsociety96,1953.Hecouldidentifynopredictablepatternsinstockprices.1.Whyarenotstockpricespredictable?例子：一种模型预测股票价格三天后将从20元/股涨至23元/股Theforecastofafuturepriceincreasewillleadinsteadtoanimmediatepriceincreasethestockpricewillimmediatelyreflectthegoodnewsimplicitinthemodel’sforecast.例子：2001年10月21日晚，证监会宣布暂停国有股减持例子：2002年4月5日宣布，从5月1日起交易佣金使用0.3%上限向下浮动制。例子：中国人民银行决定，从2004年10月29日起上调金融机构存贷款基准利率并放宽人民币贷款利率浮动区间和允许人民币存款利率下浮。金融机构一年期存款基准利率上调0.27个百分点，由现行的1.98%提高到2.25%，一年期贷款基准利率上调0.27个百分点，由现行的5.31%提高到5.58%。由于存在聪明的投资者的原因，任何能够用来对股票价格作预测的信息已经反映在股票的价格中。任何新信息，如果是可以预测的，则已经反映在价格中；如果是不可预测的，则导致的股票价格变动也是不可预测的，即随机的信息导致随机的股票价格变化。2.股票价格的随机游走(randomwalk)股票价格的变动服从随机游走的形式。随机游走的形式并不是说明市场是非理性的，而恰恰表明这是投资者真相寻求相关信息，以使得自己在别的投资者获得这种信息之前买或者卖股票而获得利润的结果。反之，如果股票价格不是随机变动而是可以预测的，则表明所有的相关信息并没有完全反映在价格中，这表明市场是非有效的。股票价格反映了所有可得信息称为有效性市场假设。有效资本市场指的是现时市场价格能够反映可得信息的资本市场，在这个市场中，不存在利用可得信息获得超额利润的机会。资本市场的有效性这一概念对于金融投资者而言具有非常重要的意义。因为市场的有效性消除了许多可以提高收益的策略。MarketefficiencymeansPricesarecorrectTheyfullyreflectallavailableinformationPeopleuseallavailableinformationinformingexpectationsaboutfuturecashflows.Thediscountrateisrightfortherisknessofthecashflows.PricesreacttonewinformationquicklyandtotherightextentThereisnofreelunchTheonlywayyoucangethigherreturnsisbytakingonmoreriskThereisnoinformationouttherethatcanbeusedtoconstructstrategiesthatearnreturnshigherthanrequiredfortheirrisk.Whenwesay‘pricesarecorrect’,weareimplicitlystatementwhat‘correct’is(i.e.,weareassuminganassetpricingmodel)3.有效资本市场的描述例子：F-stopCameraCorporationisattemptingtodevelopacamerathatwilldoublethespeedoftheauto--focusingsystemnowavailable.在特定的价格下，持有股票的原因著名的光学专家加盟股价是否上涨股价上涨的原因股价上涨的时间一个市场对于一个信息集来说称为有效的，如果不存在利用该信息获得超额利润的机会。有效和非有效市场中价格对新信息的反应股票价格

0宣布前（-）或者后（+）的天数过激反应和回归延迟反应有效市场对新信息的反应三种有效市场(efficientcapitalmarket)不同的信息集对证券价格产生影响的速度不一样。为了处理不同的反应速度，把信息集分成不同的类别。最常用的一种分类方法：过去价格的信息，可得的公共信息，所有信息。针对这三种信息集，有三种形式的有效市场的定义弱有效市场(theweakform)半强有效市场(thesemistrongform)强有效市场(strongform)弱有效市场定义：一个资本市场称为弱有效的或者满足弱有效形式，如果证券价格充分反应了包含在历史价格中的信息。弱形式有效通常表示成下面的数学形式

+Expectedreturn+Randomerror这里随机误差项的均值为0，且不同时间的随机误差项是不相关的。弱形式有效性是最弱类型的有效性。股票价格的历史数据是可以免费得到的，如果这些数据里包含有用的数据，则所有的投资者都会利用它，导致价格调整，最后，这些数据失去价值。‘technical’analysisusingpastpricepatternswillnotproduceprofits.如果一个市场是弱有效的，考虑一个交易策略如果某股票的价格连续涨三天，就买进该股票；如果股票的价格连续降三天，就卖出股票。问题：这个策略能否赚钱。FairlyconvincedthatmarketsareweakformefficientBut,newevidence(i.e.,momentum)haschallengedthis.半强形式有效市场定义：一个市场是半强形式有效的，如果价格反应了所有公共可得的信息。这些信息包括：历史价格数据、与公司生产有关的基本数据、管理的质量、资产负债表、专利情况、收益预测、会计处理‘fundamental’analysis(e.g.sortingthroughincomestatements)willnotproduceprofits.Ex.Formingportfoliosonaccountingratios,balancesheet,orincomestatementinformationwillnotgenerateabnormalprofits.NoevidenceofabnormalreturnsafterapublicannouncementProfessionalmoneymanagersdonotoutperformthemarketMarketseemtobesemi-strongefficientBut,B/MandE/Pstrategiesstillchallengethis.(mayberisk,maybenot)强形式有效市场定义：一个市场是强有效的，如果价格反应了所有的信息，不管是公共的还是私有的。InsidertradingwillnotproduceprofitsEx.Knowingamergerisgoingtotakeplacebeforeitisannouncedpublicly.Althoughillegal,thereisevidencethatpricesmovebeforeannouncements,suggestinginsidertradestakeplaceInsidertradingappearsprofitable,indicatingmarketsarenotstrongformefficient.But,theseprofitsareshortlived,suggestingthemarketmaybeclosetoefficient.强形式有效性半强形式有效性弱形式有效性说明三种有效性的例子：总是在股价上涨后卖出股票，能赚到钱投资者在一家公司宣布增加收益后买该公司股票，能赚到钱知道采矿公司是否开采到了金子的内部消息后买该公司股票，能赚到钱4.Howcanwetellifmarketsareinefficient?Lookforstock-pickingstrategiesbasedonsomepastinformationwhichhaveearnedhighreturnswithlittlerisk.Unfortunately,wecanneverbesureofinefficiency.Itisalwayspossiblethatwearenotmeasuringriskproperly,i.e.,wedonotknowwhattherightdiscountrateisThisisthe‘Jointhypothesisproblem’5.Whywouldweexpectmarketstobeefficient?theforcesofarbitragesmartinvestorsexploitthemispricinginsecuritiesuntilitdisappearsToshowthatmarketsareineffcient,needtoshowthatpeoplemakeerrorsinsettingpricesthatarbitragefailstoeliminatetheseerrors一些例子GrossmanandStiglitz的结果不同市场的有效性不同：中国和美国的股市小股票和大股票的有效性不同RandomWalksandEfficientMarketsitisoftenthoughtthatefficientmarketspricesmoverandomlythisisnotnecessarilytrueStrictlyspeaking,weshouldcharacterizestockpriceasfollowingasubmartingale,meainngthattheexpectedchangeinthepricecanbepositive,presumablyascompensationforthetimevalueofthemoneyandsystematicrisk.Moreover,theexpectedreturnmaychangeovertimeasriskfactorschange.returnsaremean-revertingifthediscountrateforanassetdoesnotchangeovertime,thenitistruethatefficientmarketsrandomwalke.g.overshorttimeframes,returnsshouldlookrandom6.Evidenceformarketefficiencystockpricesappeartomoverandomlynewinformationappearstobequicklyincorporatedintopricese.g.announcementofatakeoverdoan‘eventstudy’tolookatthestockpricereactiontothenewsaverageovermanycompaniesProfessionalmoneymanagersdonotclearlybeatthemarketonaverage.7.EvidenceagainstmarketefficiencydidthevalueoftheU.S.economyreallydrop20%inOctober1987?thevolumeoftradingonstockexchangesistoohightobeconsistentwithrationalinvestorsthevolatilityofthemarketistoohigh(Shiller,1982).why?whyaretheresomanymutualfunds?thereareinvestmentstrategieswhichappeartohaveearnedhigheraveragereturnsthanisconsistentwiththeirriskThesearesocalled‘marketanomalies’suggeststhatnewinformationisnotalwaysimmediatelyincorporatedintopricesThisevidencereferstoweak/semi-strongversionsofmarketefficiencyHowaboutstrong-formefficiency?canyoumakemoneyusinginside,non-publicinformation?YES!stockpricesoftenmoveinadvanceofimportantcompanyannouncementsfromrecordsofinsidertrades,wefindthattheymakemoneyonaverageBUT:it'sillegalforcompanyinsiders(orpeopletippedbythem)totransactbasedonmaterialnon-publicinformationHowaboutinstitutionalinvestors?Wementionedmoneymanagersdonotexhibitabnormalperformanceonaverage,butmaybesomelocaladvantage.8.ThemarketanomaliesAnomaliescanbethoughtofasinvestmentstrategieswhichseemtoearnhighreturnswithoutbeingveryriskyThestrategiesarenormallybasedonsomefirmcharacteristic:sizeofthefirmitsprice-earningsratioRecipe:formaportfoliobasedonobservablecharacteristics,andmeasureitsreturnsovertimedoesthestrategygivehighreturnsonaverage?Whylookataveragereturns?IFYES:thestrategymayberiskyandthehighaveragereturnsarejustfaircompensationforthatriskhowdowemeasurerisk?(seebelow)ifriskdoesnotexplainthehighreturns,isitevidenceofmarketinefficiency?itmaybespurious,theresultofdata-miningifyoutrymanystrategies,someofthemwilldogreatinhistoricaldatadoesn'ttellyouanythingaboutfutureperformancepoorriskmeasurementfrictionstotradingandexploitingtheanomaly(bid-askspread,transactionscosts,liquidity,taxes,etc.)Measuringtheriskofastrategystandarddeviationdownsideriskdoesthestrategysometimesperformverypoorly?betalooksatstrategy'spayoffrelativetothemarket'spayoffahighcovarianceisunattractive(risky)lookatcovarianceofstrategy'spayoffwithvariableslikeGNPgrowth(factormodels)astrategywhichdoeswellingoodstatesoftheworldandpoorlyinbadstatesisriskyNote:evenifnoneoftheaboveturnupameasureofrisk,efficientmarketsenthusiastswillsay:theriskispresent,butjusthasn'tsurfacedwithinthesampleanalyzedOR:we'rejustnotlookingattherightmeasureofriskSmallvs.LargestocksSmallstockshaveoutperformedlargestocksbyabout12%ayearover1929-1979timeperiodShouldwebuylotsofsmallstocks?DependsonwhethertheyareriskiersmallstockshavehigherstandarddeviationsandbetasbutnothighenoughtoexplaintheirreturnsSo,smallstocksmaybemispricedBUT:althoughsmallstockreturnsarehigh,thismayonlybebasedonafewextraordinaryyearsWemaybemissingsomedimensionofriskTheJanuaryEffectMuchofthesmallfirmeffectseemstooccurinJanuaryMuchofsmallfirmpremiumoccursinfirstfivedaysofJanuaryoftenexplainedbytax-losssellinghowever,effectiswidespreadininternationalmarketsalso,evenwhenthere'snocapitalgainstaxand,therestillseemstobeasizeeffectaftercontrollingforthis.IfthepositiveJanuaryeffectisamanifestationofbuyingpressure,itshouldbematchedbyasymmetricnegativeDecembereffect.maynotaccordwithefficientmarketswhydon'tpeoplebuyinDecemberinanticipation?andthepredictableJanuaryeffectfliesinthefaceofefficientmarkettheory.‘Windowdressing'byinstitutionalinvestorsinfusionofcapitalatbeginningofyearOverreactionstudiessomestudiessuggestthatthereareinefficienciesduetopeopleoverreactingtoinformation（1）LosersandWinners----Longtermreversal

takeathreeyearperiodandrankstocksonthebasisoftheirperformanceoverthatperiodforma‘winner"portfolioofthetop10%best-performingstocksforma‘loser"portfolioofthebottom10%worst-performingstocksthisiscalledacontrarianstrategylookattheirreturnsoverthenextfewyearstheloserportfolioseemstooutperformthewinnerportfolio(DeBondtandThaler(1985))Twoexplanations:overreaction:thewinnersarefirmsthatpeoplehavebecometooexcitedaboutsubsequently,theyrealizethattheyweretoooptimisticpricefallsandreturnsarelowrisk:thelosersareriskierfirmstheirhigherreturnsarejustcompensationforriskbutlosersdonotappearriskieronstandardmeasuresofriskHowdoweaccountforrisk?VarianceUseregressionanalysisandapricingmodelCAPMFF3-factormodelExaminewhenthestrategyexhibitsthehighestandlowestpayoffs(i.e.,doesthestrategydowellwhenthemarketdoes?whenweareinthepeakofabusinesscycle?arecession?,etc.)Catastropherisk（2）ValueandGrowthformportfoliosofvaluestocksavaluestockisonewithlowpricerelativetosomemeasureoffundamentals,i.e.highbooktomarket(B/M)ratioscashflowtoprice(C/P)ratiosearningstoprice(E/P)ratiosalsoformportfoliosofgrowthstocks,i.e.withlowvaluesoftheseratiosWhygrowthvs.value?findthatvaluestocksdramaticallyoutperformgrowthstocksWhy?rational:Representsadistressfactorintheeconomy.Valuestocksaremorepronetothissourceofriskthangrowthstocks.higheraveragereturns.Valuestocksaretypically`fallenangels'irrational:Growthstocksare`glamorous'.Peopletendtowanttobuytheseandstampedetowardsthem,pushinguptheprice,anddepressingfuturereturns.Valuestockshavebeenneglected,causingtheirpricetofall,andexpectedreturnstorise.Thisisanoverreactionstory.Also,valuestocksdonotappearriskier,however.theydon'thavehighervariancetheydon'thavehighdownsiderisk(i.e.,donotunderperformoftenorbythatmuch)theydon'thavehigherbetastheydon'tunderperforminbadstatesoftheworldLakonishok,Shleifer,andVishny(1994)somaybeit'saninefficiency,drivenagainbyoverreactionPsychologicalfoundationsforoverreaction:representativenessheuristicsmallsamplebiasbutofcourse,itcouldstillberisk!TheFama-FrenchdebatesmallstocksandhighB/Mstocksearnreturnsthatarehigherthanisrequiredfortheirrisk,accordingtotheCAPMmeasureofrisktwopossibilities:smallstocksandhighB/MstocksaremispricedOR:theCAPMisn'tmeasuringriskproperlyFamaandFrench(1993)constructanewasset-pricingmodel,the‘’3-factormodel"whichmakessmallandhighB/Mstockslookriskierstartwiththemarketfactor,andaddtwonewfactors,F(small)(=SMB)andF(B/M)(=HML)theysupposedlytrackgoodandbadstatesoftheworldsmallstockshavehighcovariancewithF(small)highB/MstockshavehighcovariancewithF(B/M)theyareriskier!EvidenceinfavorofFF:Adjustingthelong-runcontrarianprofitsfoundbyDeBondtandThaler(1985)usingthe3-factormodel,theprofitsdisappear(i.e.,alpha=0.).pastlong-termlosersloadhigheronSMBandHMLthanpastwinners,eventhoughtheyhavethesamemarketbeta.long-termlosersmoreriskythanlong-termwinners.The3-factormodelcapturesahostofotheranomaliesaswell!EvidenceagainstFF:LSV(1994):HMLandotherbook-to-priceratiosperformwellinpoortimes.DanielandTitman(1997):characteristicsratherthanfactorloadingspriceassetsbettercontrolforsizeandB/Mcharacteristics,SMBandHMLnolongerexplainaveragereturnsex:twostockswithsamesizebutdifferentbetasonSMBhavethesameaveragereturn.twostockswithsamebetaonSMBbutdifferentsizeshavedifferentaveragereturns.DoesthisnecessarilyimplysizeandBE/MEareirrationalanomalies?No,couldproxyforsometrueunknownfactor,bettercapturedbythecharacteristic.Measurementofbetasarepronetoestimationerror,whichincreasesnoiseintherelationbetweenthebetasandaveragereturns.Underreactionstudiesotherstudiessuggestthatthereareinefficienciesduetopeopleunderreactingtoinformation（1）Momentumformportfoliosofstocksthatperformedverywellinrecentpast(`winners')i.e.overthepast3monthstooneyearsimilarly,formaportfolioof`loser'stocksthewinnersoutperformtheloserse.g.buythewinnersandselltheloserse.g.azero-costportfoliowhichbuyswinnersandsellslosersfromthepast6monthsearns12%(annually)overthenext6months!contrasttothemean-reversionresultsourceofinefficiency:underreactiontoinformation?Or,isitrisk?（2）EarningsAnnouncementsslowpriceresponsetoearningsannouncements(post-earningsannouncementdrift)eachquarter,rankstocksonthesizeofthesurpriseintheirearningsannouncement(surprise=actual-expected)formaportfolioofstockswithlargestpositivesurprises(portfolioA)andaportfolioofstockswiththelargestnegativesurprises(portfolioB)AoutperformsBisitrisk?beta,factormodeltypechecksdon'tfindanyover50quartersfrom1974-1986,strategyearnedpositiveabnormalreturns46timesManyexamplesofunderreactiontoinformation:tochangesindividendpolicystrategy:buycompaniesthathavejustannouncedadividendincrease;sellthosethathavejustannouncedacutindividendstorepurchasesofsharesstrategy:buycompaniesthathavejustannouncedasharerepurchasePsychologicalFoundationsforUnderreaction:conservatism,pessimismOtheranomaliesThenewissuespuzzleHotoffering

Iftheseanomaliesareinefficiencies,whydoesn'tarbitrageeliminatethem?inpractice,arbitrageislimiteddonothaveinfinitenumberofstocks,thereforethereissomerisksometimesthestrategycandoverypoorly,andyoulosealotofmoneymoneymanagersandindividualsmayhaveshorthorizons(duetoregularevaluationsorpsychologicalpreferences)amispricingcantakeawhiletocloseinfactitmaynotclosewithintheinvestor'shorizoninvestorwillrestrictthesizeofpositiontakentherecanbehightransactionsandtradingcostsduetoturnoverinthesestrategiesliquiditycanbelowattimeswhenyouneeditmostmonitoringcanbehighthereareshortsalesconstraintsMeasurementissues:Theseanomaliesaremarket-basedmeasurese.g.,theyincludepricesize,BE/ME,pastreturns(contrarianandmomentum),E/P,etc.,allcontainpriceinthem.soanythingmissedbythepricingmodelwillshowupinoneofthesevariablese.g.,appearsonbothsidesoftheregressionequationthiswasnotedbyBall(1978)andformalizedinBerk(1995)wemayneverknowifpickingupmispricingorinadequacyofpricingmodel.Dataminingtechniquesoffindinganomaliesareoftensubjecttothedataminingcritiqueifyoutryenoughvariables,somethingwilleventuallyappeartopredictreturnsbut,theforecastpowerofthisvariable

willbecompletelyspurious(i.e.,itwon'tworkoutofsample)e.g.,generate100differentdataseriesofcompletelyrandomnumbersrunaregressionofactualstockreturnsoneachofthe100randomdataseries.someoftheregressionswillproducesignificantresults:doesthismeanyoucanmakemoney?NO!thedataminingcritiqueisverypowerful:bearitinmindwhenpeopletrytoimpressyouwithstrategiesthatworkedgreatinthepast.theyprobablywon'tworkinthefuture!ResponsetoDataMiningCritique:Manyoftheseanomaliesappearinother(international)markets(seeHawa