Arbitrage Trading

60 Pages·2017·1 MB·English

Arbitrage Trading: The Long and the Short
of It
D
o
YongChen w
n
TexasA&MUniversity lo
a
d
e
d
ZhiDa fro
UniversityofNotreDame m
h
ttp
DayongHuang s://a
UniversityofNorthCarolinaatGreensboro c
a
d
e
m
ic
Weexaminenetarbitragetrading(NAT)measuredbythedifferencebetweenquarterly .o
u
abnormalhedgefundholdingsandabnormalshortinterest.NATstronglypredictsstock p
.c
returnsinthecross-section.Acrosstenwell-knownstockanomalies,abnormalreturnsare o
m
rfaecailliizteadtedonslhyoartmsoelnlgingstofocrkasreaxnpdeorimengcrionugplaorfgsetoNckAsT,.wEexpprleositeinntgcRauesgaulleavtiiodnenScHeOth,awtNhAicTh /rfs/a
hasstrongerreturnpredictabilityamongstocksfacinggreaterlimitstoarbitrage.Wealso d
v
findlargereturnsforanomaliesthatarbitrageurschosetoexploitdespitecapitalconstraints an
c
duringthe2007–09financialcrisis.Weconfirmourfindingsusingdailydata. (JELG11, e
G23) -artic
le
ReceivedSeptember1,2016;editorialdecisionMay28,2018byEditorAndrewKarolyi. -ab
s
AuthorshavefurnishedanInternetAppendix,whichisavailableontheOxfordUniversity tra
PressWebsitenexttothelinktothefinalpublishedpaperonline. c
t/d
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i/1
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WearegratefultoAndrewKarolyi(theExecutiveEditor)andananonymousrefereeforvaluableadvice.We y0
thankCharlesCao,RogerEdelen,SamuelHanson,JohanHombert(Parisconferencediscussant),Byoung- 97
HyounHwang(AFAdiscussant),HagenKim,WeikaiLi(CICFdiscussant),BingLiang,JeffreyPontiff,Marco /5
Rossi,KalleRinne(Luxembourgconferencediscussant),ThomasRuf(EFAdiscussant),ClemensSialm,Sorin 08
Sorescu,ZhengSun,RobertStambaugh,WeiWu,JianfengYu,andseminarandconferenceparticipantsat 63
McMasterUniversity,MiamiUniversity,TexasA&MUniversity,UniversityofHawaii,UniversityofNotre 2
1
Dame,the2015EuropeanFinanceAssociationMeetinginVienna,the4thLuxembourgAssetManagement b
Summit,2015MacquarieGlobalQuantitativeResearchConferenceinHongKong,the2016AmericanFinance y K
AssociationAnnualMeetinginSanFrancisco,the8thAnnualHedgeFundResearchConferenceinParis,the re
2016ChinaInternationalConferenceinFinanceinXiamen,andthe2016FinancialManagementAssociation s
MeetinginLasVegasforhelpfuldiscussionsandcomments.Chenacknowledgesfinancialsupportfromthe ge
RepublicBankResearchFellowshipatTexasA&MUniversity.Daacknowledgesfinancialsupportfromthe L
ZychFamilyFellowshipattheNotreDameInstituteforGlobalInvesting.Weareresponsibleforallremaining aw
errors.SupplementarydatacanbefoundonTheReviewofFinancialStudiesWebsite.Sendcorrespondence L
toYongChen,DepartmentofFinance,MaysBusinessSchool,TexasA&MUniversity,CollegeStation,TX ib
77843–4218;telephone:[phone].E-mail:[email protected]. ra
ry
u
s
©TheAuthor(s)2018.PublishedbyOxfordUniversityPressonbehalfofTheSocietyforFinancialStudies. e
Allrightsreserved.Forpermissions,pleasee-mail:[email protected]. r o
doi:10.1093/rfs/hhy097 n 2
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[08:3212/9/2018RFS-OP-REVF180097.tex] Page:1 1–39
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Arbitrageurs play a crucial role in modern finance. Textbooks describe
arbitrageursasentitiesthat,bysimultaneouslytakinglongandshortpositions
in different assets, help eliminate mispricing and restore market efficiency.
As a result, their trading pins down the expected return on these assets,
accordingtothearbitragepricingtheory(APT)ofRoss(1976).Ontheother D
o
hand,investors’behavioralbiasesandagencyfrictionsmayleadtopersistent w
n
mispricingwhenarbitrageursfacelimitstoarbitrage(e.g.,DeLongetal.1990; lo
a
ShleiferandVishny1997).1Relativetotheoreticaldevelopment,however,our de
d
understanding about arbitrage activity from empirical research is still rather fro
limited. m
h
One major challenge in studying arbitrage activity empirically has been ttp
the lack of data on arbitrageurs.2 However, as hedge funds emerged as s://a
institutionalized arbitrageurs and the data of their stock holdings became c
a
d
availableinrecentyears,aseriesofpapershasinferredthelongsideofarbitrage e
m
trading by investigating hedge fund stock holdings (e.g., Brunnermeier and ic
.o
Nagel 2004; Griffin and Xu 2009; Cao et al. 2018). Meanwhile, since short u
p
positionsareinvolvedinarbitragetrades,severalstudiestracktheshortsideof .c
o
m
aJorbnietrsa,gaendtraZdhinagngby20ex0a8m; Hinainngsosnhoarnt-dseSlluinndgearcatmivi2ty01o4n;sHtowckasng(e,.gL.i,uB,oaenhdmXeru, /rfs/a
d
forthcoming). v
a
Inthispaper,weproposeameasureofnetarbitragetradingagainstastockby nc
e
combininghedgefundholdingsastheproxyforthelongsidewithshortinterest -a
astheproxyfortheshortside.Intuitively,combiningthetwosidesprovidesa rtic
le
completeviewaboutarbitragetradingthatusuallyinvolvesbothlongandshort -a
b
positions.Theadvantageofourmeasure,however,goesbeyondaddingupthe stra
effectsfromthetwosides.Arbitrageursmaydisagreeonthevalueofastock, c
t/d
sothatthesamestockisboughtbysomearbitrageursandsoldshortbyothers. o
i/1
Moreover, a correctly priced stock may be purchased by some arbitrageurs 0
whilesoldshortbyothersforhedgingpurposes.3Thus,aslongasthecorrelation .10
9
boeutrwmeeenastuhreetwbaosseiddeosnisthneotn–e1t(pwohsiitcihonis—cothnafitrmis,edthienoduifrfeermenpcireicbaeltawneaelynsitsh)e, 3/rfs/h
h
two sides—differs from the summation of the effects from the two sides and y
0
representsamoreaccurateproxyforarbitragetrading.4Basedonthismeasure, 97
/5
0
8
6
3
1 SeeGrombandVayanos(2010)forasurveyoftheoreticaldevelopmentintheliteratureonlimitstoarbitrage. 21
b
2 Thetypeofarbitrageursweareinterestedinisthose,asdescribedintheAPT,whotakelongandshortpositions y
ianrbwiterallg-de,ivienrwsifihiecdhpaosrsteftosliionslownigthasnidmsilhaorrrtispkoseixtipoonssuhreasvebuidtedniftifcearelnctasehxpfleocwtesd.returns.Itisdifferentfrompure Kres
g
3 Forexample,acorrectlypricedvaluestockwithpoorrecentreturnsmaybeboughtbyavaluetraderand e L
simultaneouslyshortedbyamomentumtradertohedgehisrespectivelong-shortstrategies.Similarly,astock a
w
maybesoldshorttohedgeagainstaconvertiblebondpurchase.Insuchcases,simultaneousincreasesinboth L
longandshortsidesdonotnecessarilyindicatedisagreement(i.e.,differencesofopinion)amongarbitrageurs ib
aboutthevalueofthestockasdescribedinMiller(1977).Ourmeasure,however,capturesnetarbitragetrading ra
onthestock. ry
u
4 OuranalysisalsohelpsexplainthepuzzlingrelationdocumentedinBoehmer,Huszar,andJordan(2010)that se
heavilytradedstockswithlowshortinterestsubsequentlyexperiencesignificantlypositiveabnormalreturns. r o
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[08:3212/9/2018RFS-OP-REVF180097.tex] Page:2 1–39
ArbitrageTrading:TheLongandtheShortofIt
weattempttobetterunderstandtheinformationcontentofarbitrageactivity,in
particular,theinteractionbetweenarbitragetrading,stockanomalies,andthe
roleoflimitstoarbitrage.Wediscussthisinteractionindetailintheformof
hypothesisdevelopmentinSection1,andthosehypothesesguideourempirical
analysis. D
o
Fortheempiricalanalysis,wefirstcombinehedgefundholdingsandshort w
n
interest at the stock level over the period 1990–2015. To capture quarterly lo
a
variationsinarbitrageactivityrelativetothetrend,wedefineabnormalhedge de
d
fund holdings (AHF) and abnormal short interest (ASI) as their values in a fro
quarterminustheirmovingaveragesinthepastfourquarters.Then,wemeasure m
h
netarbitragetrading,denotedNAT,asthedifferencebetweenAHFandASIto ttp
s
capturethetradeimbalanceofarbitrageurs.Forexample,anNATof1%ona ://a
stockmeansthatarbitrageurs,asagroup,havepurchasedanadditional1%of c
a
d
thestock(asthepercentageoftotalnumberofsharesoutstanding)duringthe e
m
quarterrelativetotheirpastaverage. ic
.o
Ouranalysisprovidessixsetsofresults.First,weshowthatNATsignificantly u
p
predicts future stock returns. Stocks in the highest NAT quintile outperform .c
o
qthuoasreteirn. Tthheelroewtuersntsqpurienatidledbecyli0n.e7s3%oveprertimmeontoth0(.t4-0v%alupee=r m8.o5n6t)hin(t-tvhaeluneex=t m/rfs/a
4.43)inthesecondquarter,furtherdownto0.17%permonth(t-value=1.90) dv
a
inthethirdquarter,andthenbecomesinsignificantinthesubsequentquarters nc
e
withintwoyears.ThereturnpredictabilityofNATremainssignificantinthefirst -a
twoquartersevenonarisk-adjustedbasis,suggestingthatNATisinformative rtic
le
about mispricing. This return predictability holds in a battery of robustness -a
b
checks, including Fama-MacBeth cross-sectional regressions controlling for stra
otherreturnpredictorsanddoublesortingonAHFandASI.Importantly,this c
t/d
returnpredictabilitydoesnotreverseinthelongrun,suggestingthatitisnot o
i/1
duetotemporarypricepressurecausedbyarbitragetrading. 0
.1
Second, we examine the relation between NAT and stock anomalies. Our 0
9
toepsetsractoinvgertpernofiwte,llr-ektnuorwnnmanoommeanltiuems:,bomoakr-ktoe-tmcaarpkiettalriaztaioti,ognr,osasspsreotfigtarboiwlitthy,, 3/rfs/h
h
investment growth, net stock issues, accrual, and net operating assets. We y
0
9
find striking evidence that abnormal returns are driven by anomaly stocks 7
/5
tradedbyarbitrageurs.Specifically,wedefineananomalystocktobetradedby 0
8
arbitrageursifitisinthelongportfolioandrecentlyboughtbyarbitrageurs(i.e., 63
2
itsNATbelongstothetop30%),orifitisintheshortportfolioandrecentlysold 1
b
shortbyarbitrageurs(i.e.,itsNATbelongstothebottom30%).Onaverage,this y K
subsetofanomalystocksexhibitssignificantreturnspreads(betweenthelong re
s
and the short leg) of 0.88% (t-value = 7.95), 0.60% (t-value = 5.46), 0.41% ge
(t-value=4.04),and0.32%(t-value=3.25)permonthduringthefirst,second, La
w
L
ib
ra
ry
Theirfindingisnotsurprisingifwefocusonnetarbitragetradingbecausestockswithlowshortinterest,on u
average,experiencenetpurchasesfromarbitrageurs.Hence,combiningthetwosidesofarbitrageactivityprovides se
insightsthatcannotbeobtainedfromeithersidealone. r o
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TheReviewofFinancialStudies/v00n002018
third,andfourthquarters,respectively.Insharpcontrast,therestoftheanomaly
stocksearnreturnspreadslessthan0.15%permonthoverthesamequarters.We
confirmthispatternusingasinglecomprehensivemispricingmeasure(MISP)
constructedbyStambaugh,Yu,andYuan(2015).Among“mispriced”stocks,
thosetradedbyarbitrageursearnmuchhigherreturnsthantherestinthenext D
o
fourquarters.ThestrongreturnpredictabilityofNATinboththeentirecross- w
n
section and anomaly stocks suggests that the market is not always efficient lo
a
and the arbitrageurs are indeed effective in detecting mispricing. The fact de
d
thatNATpredictsreturnbeyondaquartersuggeststhatarbitragetradingdoes fro
not eliminate mispricing completely and instantaneously, consistent with the m
h
existenceoflimitstoarbitrage(ShleiferandVishny1997). ttp
s
Ourthirdsetofresultsdescribestwochannelsthroughwhichmispricingis ://a
eliminated and arbitrage profit is realized. One is the release of fundamental c
a
d
information,andtheotherisrelatedto“copycattrading.”Specifically,wefind e
m
that a disproportionately large portion of arbitrage profit takes place around ic
.o
earningsannouncementsinthenexttwoquarterswhenfundamentalcashflow u
p
information is released to the public. In addition, other types of institutional .c
o
m
iinnvtehsetosrasm(ee.gd.,irmecuttiuoanlafusnadrsb,ibtraangkesu,risn,sfuurratnhceer cfaocmilpitaantiinegs)psruibcseeqcounevnetlrygetrnacdee. /rfs/a
d
Interestingly, other institutional investors trade in the opposite direction to v
a
arbitrageurs in the contemporaneous quarter and start to follow arbitrageurs nc
e
withalagofatleastonequarter,consistentwithapatternofcopycattrading. -a
Fourth, NAT allows us to directly test an important implication of limits rtic
le
to arbitrage: when arbitrage is more difficult, arbitrage trading should reveal -a
b
more severe mispricing, all else being equal. We adopt Regulation SHO as stra
an instrument for limits to arbitrage in the cross-section, following Chu, c
t/d
Hirshleifer,andMa(2017).DuringtheperiodfromMay2005toAugust2007, o
i/1
RegulationSHOrelaxedshort-saleconstraintsforarandomlyselectedgroupof 0
“pilot”stocks.5Assuch,pilotstocksfacereducedlimitstoarbitragerelativeto .10
9
nefofne-cptioloftlsimtoictksst.oBayrbmiteraagsueroinngaarrbbiittrraaggeeatcratidviintyg,dwirheiccthlyi,nwteuernxaamffiencetsthaenocamuaslayl 3/rfs/h
h
returnsandmarketefficiency.BasedonNAT,weconfirmthatpilotstocksare y
0
9
soldshortmoreoftenthannon-pilotstocksinthepilotperiod,eventhoughthese 7
/5
stocksareotherwiseindistinguishableintermsofstockcharacteristics.More 0
8
importantly, we show that NAT identifies more mispriced stocks among the 63
2
non-pilotstocksamplethanamongthepilotstocksample,andthedifference 1
b
isconcentratedontheshortlegandduringthepilotperiod. y K
Fifth, we link aggregate limits to arbitrage to NAT and stock anomalies. re
s
g
Examining the NAT of anomaly stocks, we find significant withdrawal of e
L
a
w
L
5 FromtheRussell3000index,RegulationSHOremovedshort-salepricetests(i.e.,uptickruleforNYSE/AMEX ibra
andbidpricetestforNasdaq)forarandomsetofabout1,000pilotstocksthatwereincludedaseverythirdstock ry
rankedbytradingvolume.Thisexemptionoftheshort-salepricetestsforpilotstockslastedfromMay2,2005, u
toAugust6,2007.SeeDiether,Lee,andWerner(2009)foradetaileddescriptionofRegulationSHOandthe se
pilotprogram. r o
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ArbitrageTrading:TheLongandtheShortofIt
arbitrage capital during the financial crisis of 2007–09, consistent with Ben-
David,Franzoni,andMoussawi(2012)andNagel(2012).Asanovelresult,we
showthatduringthecrisiswhenarbitragecapitalwasconstrainedingeneral,
those anomalies to which arbitrageurs chose to allocate their scarce capital
realizedhighfutureabnormalreturns. D
o
Finally,weconfirmourmainresultsusingdailydataduringtheperiodfrom w
n
June2006toMarch2011.WeestimateNATatadailyfrequencybycombining lo
a
dailysecuritylendingdatawithdailytradingrecordsofasubsetofhedgefunds. de
d
The daily frequency of data provides statistical power even though the tests fro
areperformedoverarelativelyshortsampleperiod.WeshowthatdailyNAT m
h
significantlypredictsstockreturnsbothinthefullsampleandamonganomaly ttp
s
stocksuptoamonth.Inaddition,dailyNATpredictsmoreoverpricingamong ://a
non-pilotstocksduringthepilotperiod. c
a
d
Ourpapercontributestoagrowingliteraturethatexaminesarbitrageactivity e
m
byhedgefundholdingsandshort-sellingactivity.6 Usingdataonhedgefund ic
.o
holdings,BrunnermeierandNagel(2004)andGriffinetal.(2011)showthat, u
p
duringthetechbubbleperiod,hedgefundsrodewiththebubbleanddestabilized .c
o
m
cthheanmgeasrkient.hFeudrgtheefr,unGdrioffiwnnearnsdhipXufo(r2f0u0t9u)refisntdocwkeraektuprnresd,iwcthivielepAowgaerrwoafl /rfs/a
d
etal.(2013)documentstrongreturnpredictabilityofhedgefund“confidential v
a
holdings.” Sias, Turtle, and Zykaj (2016) show that shocks to hedge fund nc
e
demand can predict stock returns. Cao et al. (2018) find that, compared with -a
other types of institutional investors, hedge funds tend to hold and purchase rtic
le
undervaluedstocks,andundervaluedstockswithlargerhedgefundownership -a
b
realizehigherreturnssubsequently. stra
Focusingontheshortside,severalpapersdocumentthatstockswithhigher c
t/d
short-sellingactivityrealizelowerreturns(e.g.,AsquithandMeulbroek1995; o
Desai et al. 2002; Boehmer, Jones, and Zhang 2008).7 Using institutional i/10
.1
ownershiptoproxyforstockloansupply,Asquith,Pathak,andRitter(2005) 0
9
fiasnsdocthiaatte,dfowristmhanlelgsatoticvkesrwetiutrhnhs,igrehvsehaolirntginttheereesftf,elcotwofinsshtoitrut-tsioanleacloonwsntrearisnhtispoins 3/rfs/h
h
stockprices.Nagel(2005)findsthatshort-saleconstraintshelpexplaincross- y
0
9
sectionalstockreturnanomalies.DrechslerandDrechsler(2016)findthatthe 7
/5
short-rebatefeeisinformativeaboutoverpricingandarbitragetrades. 0
8
Tothebestofourknowledge,ourpaperisthefirsttocombineinformation 63
2
on both long and short sides to study the relation between arbitrage trading, 1
b
anomalies,andlimitstoarbitrage.Ourmeasureofnetarbitragetradingprovides y K
re
s
g
e
6 Thereexistotherproxiesforarbitragetradingintheliterature.Forexample,LouandPolk(2015)inferarbitrage La
w
activityfromthecomovementofstockreturns. L
7 Therearetheoreticalargumentsaboutwhyshortsalesorshort-saleconstraintsshouldberelatedtostockreturns. ibra
Miller(1977)arguesthat,inthepresenceofheterogeneousbeliefs,bindingshort-saleconstraintspreventstock ry
pricesfromfullyreflectingnegativeopinionsofpessimistictraders,leadingtooverpricingandlowsubsequent u
returns.DiamondandVerrecchia(1987)showthatgiventheirhighcosts(e.g.,noaccesstoproceeds),shortsales se
aremorelikelytobeinformative. r o
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TheReviewofFinancialStudies/v00n002018
substantialvalueoverexaminingeitherhedgefundholdingsorshortinterest
aloneandpresentsamorecompleteviewabouttheeffectofarbitrageactivity
on the returns on stocks, especially anomaly stocks.8 Indeed, NAT not only
predictsstockreturnsbutfacilitatesourinvestigationofthesourceofarbitrage
profit.Mostimportantly,whenusingthismeasuretostudystockanomalies,we D
o
findstrongevidencesupportingthenotionthatarbitragetradingisinformative w
n
aboutmispricing.Therefore,ouranalysisshedsnewlightonhowarbitrageurs lo
a
operateinstockmarketsandhowtheirtradingaffectsstockprices. de
d
Recently,exploitingregulatorychangestoshortselling,Chu,Hirshleifer,and fro
Ma(2017)showthatlimitstoarbitrageaffectthecorrectionofmispricing.To m
h
theextentthatarbitrageursarecrucialincorrectingmispricing,ourpaperfills ttp
s
intheimportantelementbyexaminingarbitragetradingdirectly.Forexample, ://a
onenovelhypothesisandfindingofourpaperisthat,inthepresenceoflimits c
a
d
toarbitrage,alargerNATrevealsmoreseveremispricing.Inaddition,Hwang, e
m
Liu,andXu(forthcoming)findthatrelaxationofshort-saleconstraintsinHong ic
.o
Kongisassociatedwithincreasedhedgefundpurchasesofunderpricedstocks, u
p
which highlights the important role of short positions in hedging arbitrage .c
o
m
rbiestkws.eIennothuerploanpgers,itdheeaNnAdTthmeesahsourrtesiisddeeosfiganrbeditrtaogceaapctutirveittyh.etradeimbalance /rfs/a
d
v
a
n
1. HypothesisDevelopment ce
-a
Inthissection,wedevelopourmainhypothesesforempiricalanalysis.Through rtic
le
testing these hypotheses based on the measure of net arbitrage trading, we -a
b
attempt to better understand the interaction between arbitrage trading, stock s
tra
anomalies,andtheroleoflimitstoarbitrageinthestockmarket. c
First, it is well known that if the stock market is efficient and information t/do
is fully and instantaneously incorporated into stock prices, arbitrageurs’ i/10
trades should not be systematically related to future stock returns (Fama .10
9
1970). Similarly, even if the market is not efficient but arbitrageurs are 3
uninformed about stock mispricing, arbitrage trading still does not predict /rfs/h
h
futurestockreturns.Thus,inthescenarioofanefficientmarketoruninformed y
0
arbitrageurs,theNATmeasureshouldnotberelatedtofuturestockreturnsin 97
thecross-section. /50
8
However,ifthemarkethasinefficienciesandarbitrageurspossessskillsto 63
2
correctlyidentifymispricing,thenarbitragetradingwillbeinformativeabout 1
b
futurestockreturns.Morespecifically,stocksheavilyboughtbyarbitrageursare y K
expectedtooutperformthoseheavilyshortedbyarbitrageursonarisk-adjusted re
s
basis in the future. Since such return difference is not caused by temporary ge
L
pricepressure,thisreturnpredictabilityarisingfromsuperiorinformationwill a
w
L
ib
ra
8 Jiao,Massa,andZhang(2016)findthatoppositechangesinhedgefundholdingsandshortinterestpredictstock ry u
returns.Differentfromtheirpaper,wefocusontheinteractionbetweenarbitragetrading,stockanomalies,and se
limitstoarbitrage. r o
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ArbitrageTrading:TheLongandtheShortofIt
not reverse and arbitrage trading should have a permanent price impact. As
such,weformourfirsthypothesisaboutthereturnpredictabilitywithinformed
arbitrageurs.
Hypothesis1(Informedarbitrageurs). NAT should positively predict
D
future stock returns above and beyond temporary price pressure, if the stock o
w
markethasinefficienciesandarbitrageursareinformedaboutmispricing. nlo
a
d
e
Next, we argue that an investigation of anomaly stocks can shed light on d
what stock-level information arbitrageurs may use to detect mispricing. If fro
m
arbitrageurs simply rely on the same set of anomaly stock characteristics h
(e.g., book-to-market ratio, operating profit), then arbitrage trading should ttps
have no additional return predictability among stocks with similar anomaly ://a
c
characteristics.9 Otherwise, return predictability of arbitrage trading among ad
e
stockswithsimilaranomalycharacteristicssuggeststhatnotallanomalystocks m
ic
are“createdequal”andthatarbitrageursuseinformationotherthancommon .o
u
stock characteristics to detect mispricing. This rationale leads to our second p
.c
hypothesis. om
/rfs
Hypothesis2(Arbitrageinanomalies). Within the set of stocks that have /ad
v
similar anomaly characteristics, NAT should positively predict future stock an
c
returns above and beyond temporary price pressure if arbitrageurs use e
-a
informationotherthancommonstockcharacteristics. rtic
le
-a
Since collecting and processing information in financial markets involves bs
costs for arbitrageurs (Grossman and Stiglitz 1980), the return predictability tra
c
of arbitrage trading should also reflect arbitrage costs. If arbitrage costs t/d
o
are negligible, informed arbitrageurs will trade quickly against mispricing i/1
0
until mispricing is eliminated almost instantaneously. In reality, however, .1
0
arbitrageursoftenfacesubstantialcostsintheformsoftransactioncosts,short- 93
saleconstraints,limitedarbitragecapital,noisetraderrisk,andsynchronization /rfs
/h
risk(e.g.,DeLongetal.1990;Pontiff1996;ShleiferandVishny1997;Abreu h
y
and Brunnermeier 2002). These frictions, which impose limits to arbitrage, 09
7
impede arbitrageurs from quickly correcting mispricing. As a result, the /5
0
correction to mispricing will occur with a delay as fundamental information 86
3
is released to the market gradually or during specific information events 2
1
(such as earnings announcements), or when other investors start to trade by
K
in the same direction as arbitrageurs perhaps after learning about arbitrage re
trading. Considering the existence of limits to arbitrage and the consequent sg
e
delay in the correction to mispricing, we develop our third hypothesis L
a
asfollows. w
L
ib
ra
ry
u
9 Section2.3andtheAppendixcontaindetaileddiscussionsofthesestockanomaliesthatthepreviousliterature se
hasdocumentedtopredictfuturereturnsinthecross-section. r o
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TheReviewofFinancialStudies/v00n002018
Hypothesis3(Presenceoflimitstoarbitrage). The predictive power of
NATforfuturestockreturnsshouldbe“longlasting”inthepresenceoflimits
toarbitrage.
Finally,limitstoarbitragevaryacrossstocksandovertime,andsuchvariation
D
isexpectedtorevealtheextentofmispricing.Mispricedstockswithsmalllimits o
w
toarbitragearerelativelyeasyforarbitrageurstotradeandwillthusyieldless nlo
a
abnormalprofit,sinceevensmallpricedeviationfromfundamentalvalueswill d
e
beexploitedbyarbitrageurs.Indoingso,arbitragetradingcorrectsmispricing. d fro
On the other hand, large frictions impose substantial costs to arbitrageurs m
and deter arbitrage trading. Hence, we hypothesize that, when a stock faces http
great limits to arbitrage yet arbitrageurs, as a group, still choose to trade it s
heavily,thestockislikelytobeseverelymispricedandthepotentialarbitrage ://ac
a
profitoutweighsthearbitragecosts.Thisintuitionleadstothefollowingnovel d
e
m
hypothesis. ic
.o
u
Hypothesis4(Limitstoarbitrageinthecross-sectionandovertime). All p
.c
elsebeingequal,thepredictivepowerofNATforfuturestockreturnsshould om
be stronger among mispriced stocks that face greater limits to arbitrage, and /rfs
duringtimeswhenarbitragecapitalismoreconstrained. /ad
v
a
n
Testing Hypothesis 4 in the cross-section requires a stock-level measure ce
omfislpimricitisngto.Itairsbeitmrapgierictahlalyt ddieftfiecrualtr,bhitorwageevetrr,atdoisnegpabruattedloimnitosttoafafrebcittreaxgeaanntde -article
exantemispricing,sincebothofthemareoftenproxiedinpreviousresearch -ab
s
by the same stock characteristics, such as size and volatility. In our paper, tra
c
we use Regulation SHO as an instrument of limits to arbitrage at the stock t/d
level,followingChu,Hirshleifer,andMa(2017).DuringtheperiodfromMay oi/1
2005 to August 2007, Regulation SHO reduced short-sale constraints for a 0.1
randomlyselectedgroupofpilotstocks.Asaresult,fortwoequallyoverpriced 09
3
stocks,thenon-pilotstockfacesgreaterlimitstoarbitragethanthepilotstock, /rfs
whilethesestockscouldotherwisebeidenticalduetotherandomnatureofthe /h
h
pilotstockassignment.Hypothesis4predictsthatoverpricednon-pilotstocks y0
9
soldshortbyarbitrageurswillexperiencelargerunderperformancethansimilar 7/5
overpricedpilotstocksduringthepilotperiod.Forunderpricedstocks,however, 08
6
nosignificantdifferenceshouldbeobservedbetweenpilotandnon-pilotstocks 3
2
1
duringthepilotperiod.Similarly,nosignificantdifferenceshouldbeobserved b
y
betweenthetwogroupsofstocksoutsidethepilotperiod. K
Limitstoarbitragealsovaryovertime.Forexample,Ben-David,Franzoni, res
g
and Moussawi (2012) and Nagel (2012) provide evidence that arbitrage e L
capitalwasseverelyconstrainedduringthe2007–09financialcrisis.OurNAT aw
measureallowsustodirectlyexaminehowsuchimportantlimitstoarbitrage Lib
affect various anomalies differently. Specifically, Hypothesis 4 predicts that ra
ry
anomalies exploited by arbitrageurs during the crisis, despite their capital u
s
e
constraints,shouldperformparticularlywellinthenearfuture. r o
n
2
2
O
c
8 to
b
e
r 2
0
1
8
[08:3212/9/2018RFS-OP-REVF180097.tex] Page:8 1–39
ArbitrageTrading:TheLongandtheShortofIt
2. DataandSampleConstruction
2.1 Hedgefundholdings
Forthelongside,weemploythedataonhedgefundstockholdingsfollowing
Caoetal.(2018).ThedataareconstructedbymanuallymatchingtheThomson
D
Reuters 13F institutional holdings data with a comprehensive list of hedge o
w
fund company names. The list of hedge fund company names is compiled n
lo
from six hedge fund databases, namely TASS, HFR, CISDM, Bloomberg, a
d
e
BarclayHedge,andMorningstar.UndertheSecuritiesExchangeActof1934, d
allinstitutionalinvestors,includinghedgefundmanagementcompanies,with fro
m
investment discretion over $100 million are required to report their stock h
holdingstotheSecuritiesandExchangeCommission(SEC)throughquarterly ttps
Form 13F filings in which stock positions greater than 10,000 shares or ://a
c
$200,000inmarketvaluearesubjecttodisclosure. ad
e
Since the 13F holdings data do not indicate which institutions are hedge m
ic
fund companies, we identify hedge fund companies through the following .o
u
three steps. First, 13F institutions are matched with the list of hedge fund p
.c
companynames.Second,amongthematchedinstitutions,weassesswhether om
hedgefundmanagementisindeedtheirprimarybusiness.Wecheckwhether /rfs
theyareregisteredwiththeSEC.BeforetheDodd-FrankAct,registeringwith /ad
v
theSECwasnotrequiredforhedgefundcompaniesunlesstheysimultaneously a
n
c
conducted non-hedge-fund businesses such as mutual fund management. e
-a
Following Brunnermeier and Nagel (2004), we include those unregistered rtic
with the SEC as pure-play hedge funds in our sample. If the adviser was le
-a
registered with the SEC and filed Form ADV, we follow Brunnermeier and b
s
Nagel (2004) and Griffin and Xu (2009) to include it in our sample only tra
c
if the following two criteria are both satisfied: over 50% of its investment t/d
o
is listed as “other pooled investment vehicle” (including private investment i/1
0
companies, private equity, and hedge funds) or over 50% of its clients are .1
0
high-net-worth individuals, and the adviser charges performance-based fees. 9
3
Finally, to address the concern that some hedge fund companies may not /rfs
report to a database because of the voluntary nature, we manually check /hh
y
the company website and other online sources for each of the unmatched 09
7
13F institutions to decide whether it is a hedge fund company. Over the /5
0
sampleperiod1990–2015,oursamplecovers1,494hedgefundmanagement 8
6
3
companies. 2
1
Foreachstockinoursample,wecomputeitsquarterlyhedgefundholdings b
y
(HF)astheratiobetweenthenumberofsharesheldbyallhedgefundcompanies K
re
attheendofthequarterandthetotalnumberofsharesoutstanding.Ifthestock sg
e
isnotheldbyanyhedgefundcompany,itsHFissettozero.Wedefineabnormal L
a
hedgefundholdings(AHF)asthecurrentquarterHFminustheaverageHFin w
L
the past four quarters. Though AHF is correlated with change in hedge fund ib
ra
ownershipfromtheonequartertothenext,itbettercapturesquarterlyvariations ry
inarbitrageactivityrelativetothetrend. us
e
r o
n
2
2
O
c
9 to
b
e
r 2
0
1
8
[08:3212/9/2018RFS-OP-REVF180097.tex] Page:9 1–39
TheReviewofFinancialStudies/v00n002018
2.2 Shortinterest
For the short side, short interest data, as a commonly used proxy for short-
selling activity, are obtained from the Compustat Short Interest file, which
reports monthly short interest for stocks listed on the NYSE, AMEX, and
NASDAQ.BecausetheCompustatShortInterestfileonlystartedcoverageon D
o
NASDAQstocksfrom2003,wefollowtheliteraturetosupplementoursample w
n
withshortinterestdataonNASDAQpriorto2003obtainedfromtheexchange. lo
a
Thedatahavebeenusedinseveralpreviousstudiestoexaminetheimpactsof de
d
shortinterestonstockprices(e.g.,Asquith,Pathak,andRitter2005;Hanson fro
andSunderam2014). m
h
Foreachstockinoursample,wecomputeitsquarterlyshortinterest(SI)as ttp
s
theratiobetweenthenumberofsharessoldshortattheendofthequarterand ://a
thetotalnumberofsharesoutstanding.Ifthestockisnotcoveredbyourshort c
a
d
interest files, its SI is set to zero. Similar to AHF, we define abnormal short e
m
interest(ASI)asSIinthecurrentquarterminustheaverageSIinthepastfour ic
.o
quarters. u
p
.c
o
m
2.3 Stockanomalies /rfs
Whenexaminingtherelationbetweenarbitragetradingandstockanomalies,we /a
d
considertenwell-knownreturnanomalieslargelyfollowingFamaandFrench va
n
(2008)andStambaugh,Yu,andYuan(2012). ce
(19T8h5e)fiarnsdt aFnaommaaalyndisFbroenockh-to(-1m99a3rk)edtorcautimo.eRntostheantbestrogc,kRsewidi,thanhdigLhanbsotoekin- -article
to-market ratio on average have high future returns, even after adjusting for -ab
s
marketriskbasedonthecapitalassetpricingmodel(CAPM)(Sharpe1964). tra
c
The second anomaly is operating profit. Fama and French (2015) show that t/d
firms’operatingprofitsarepositivelyrelatedtotheirfuturestockreturns.The oi/1
thirdanomalyisgrossprofitability.Novy-Marx(2013)showsthatfirmswith 0.1
higher gross profit have higher future returns. The fourth anomaly is return 09
3
momentum (Jegadeesh and Titman 1993). In our setting, at the end of each /rfs
quarter, we compute stock returns in the past twelve months by skipping the /h
h
immediatemonthpriortotheendofthequarter,dividethestocksintowinners y0
9
andlosers,andthenholdtheminthenextquarter.Thefifthanomalyismarket 7/5
capitalization. Banz (1981) and Fama and French (1993) show a negative 08
6
relation between firm size and expected stock return even after adjusting for 3
2
1
market risk. The sixth anomaly is asset growth. Cooper, Gulen, and Schill b
y
(2008),FamaandFrench(2015),andHou,Xue,andZhang(2015)showthat K
firmswithhighergrowthratesofassetshavelowerfuturereturns.Theseventh res
g
anomalyisinvestmentgrowth.Xing(2008)findsanegativerelationbetween e L
firm investment and expected stock return. The eighth anomaly is net stock aw
issues.Ritter(1991),LoughranandRitter(1995),andFamaandFrench(2008) Lib
find that larger net stock issues are associated with lower future returns. The ra
ry
ninth anomaly is accrual. Sloan (1996) and Fama and French (2008) find a u
s
e
negative association of accrual with future stock returns. Finally, the tenth r o
n
2
2
O
c
10 to
b
e
r 2
0
1
8
[08:3212/9/2018RFS-OP-REVF180097.tex] Page:10 1–39