1 Is Market Impact a Measure of the Information Value of Trades?Market Response to Liquidity vs Informed Trades1 C. Gomes and H. Waelbroeck Portware LLC Abstract Weexamineinformation,marketimpactandtradesizesusingadatasetofinstitutionaltradeswhere approximately 1/4 of the orders are labeled as having been created for cash flow purposes. We find that duringtheexecutionthefunctionalformandscaleofmarketimpactaresimilarforcashflowsasfor othertrades.Afterthetradeiscompleted,theimpactofcashflowsrevertsalmostcompletelyon averageintwotofivedays.Fortradesexcludingcashflowspricereversionisonlyafractionoftotal impact:foreverysize,thepriceafterreversionis,onaverage,equaltotheaverageexecutionprice, leavingnoimmediateprofitsafteraccountingfortradingcosts.Observedmark-to-marketprofitson merged orders from multiple portfolio managers and Nasdaq-listed stocks suggest that these trades are moreinformed than theaverage. Mark-to-market losses on cash flows,trades that follow momentum andadditionstoapriorpositionseekingtotakeadvantageofanimprovedpricerevealthelow information content of these trades. The complete price reversion for uninformed trades suggests that pricescannotbemanipulatedasassumedinno-quasi-arbitrageargumentsforthelinearityof permanent impact. There is no permanent impact, only information that causes trades.Keywords:ImplementationShortfall,MarketImpact,SunshineTrading,FairPrice,MarketEfficiency, Market Microstructure, Active Fund Management, Permanent Impact.

1 We thank N. Bershova, J. D. Farmer, J. Gatheral, E. Goldberg, D. Rahklin and S. Vilming for their insightful comments. The views expressed here are not necessarily those of Portware, LLC. 2 1.Introduction and Theoretical Background It is widely recognized that indirect trading costs cause a significant drag on fund performance, leading 80%ofactivelymanagedfundstounderperformthemarketindex(Forbes,2012).Institutionsare aware of this problem and, in spite of the potential timing costs associated with the loss of informational advantage, they choose to split their large trades into numerous slices and execute them incrementally overtimetotrytoreducemarketimpact(Chan &Lakonishok, 1995;Keim&Madhavan,1995).Asthe execution progresses there is a direct impact on price through the mechanical effect of the order on the orderbook(Hopman,2007;Bouchaudetal.2004,2009).Buttheremaybealsoanindirectimpact originated from the effect of the execution on expectations of market participants. It is generally agreed thatalthoughwidermarketinformationcancomethroughmanychannels,indirectimpactisthe mechanismwherebyinformationisconveyedtothemarketthroughtradeexecution(GrossmanandStiglitz 1980; Grosman 1989).In this paper we aim to test some of the predictions of models that explore the roles of information and mechanical effects on market impact. We use a dataset of 129,944 trades from 112 portfolio managers orstrategiestomeasurepricereversionafteratradeiscompleted.Wefindthattheprocessofpost tradereversioncontinuesforanamountoftimeisapproximatelyequaltotheexecutiontime.The expectedreturnafterreversion,orpermanentimpact,issuchthatinstitutionalordersbreakeven afterreversion.Cashflowtradesrevertmuchmorestrongly,morethancompensatingforthe implementationshortfallandquiteoftenrevertingcompletely.Thisevidencesuggeststhatmarket impact costs measure the short-term information value of a trade. Understandingthemechanismsthatshapemarketimpactisimportanttodevelopoptimalexecution schedules(Alfonsietal.,2010;AlmgrenandChriss99,2001;Almgrenetal.2005;BertismasandLo, 1998;Bouchaudetal.2009;ObizhaevaandWang,2013;Hasbrouck,2007;CriscuoloandWaelbroeck 2012,2013)andforportfoliooptimizationtodeterminetheoptimalscaleandturnoverratioforan activelymanagedfund(BerkandGreen,2004;SchwartzkopfandFarmer,2010).Thecurrentbodyof literaturecomprisestwoschoolsofthoughtregardingtherelationshipbetweenmarketimpactand information.One school of thoughtrefers to market impact as the market's attempt at pricing the expected value of theinformationthatledtothecreationofanorder.Ifthemarketweretoknowthatatradeis 3 uninformed,accordingtothisschoolitshouldbepossibletoexecuteitwithoutimpact2.Atthe microstructurelevel,theofferpriceistheexpectedfuturepriceconditionedonlyontheinformation thatthenextorderarrivalwillbeabuy,whereasthebidistheexpectedfuturepriceconditionedthe nextorderbeingasell.InHasbrouck'swords,"ordersdonotimpactprices,itismoreaccuratetosay that orders forecast prices" (J. Hasbrouck, 2007). Extending this view to the incremental execution of a hiddenorderovertime,marketimpactcorrespondstotheexpectedfuturepriceconditionedonthe existenceofthisorder,whichisonlyrevealedincrementallyaseachsliceisdeliveredtothemarket. Differentmodelspresentdistinctassumptionsonhoweachsliceispriced.Theinsidertradingmodel considers the case where an investor has exclusive access to information (the insider knows the closing priceofthesecurityinadvance).Kyle(1985)showsthatsuchaninsiderwillmaximizeherprofitby executingataconstantspeeduntilpricereachestheinformedpriceattheendofthesession;atthat point everyone discovers the final price and there is no reversion. Fair pricing theory (Farmer et al. 2013) (FGLW) considers the opposite case, where instead of having a single informed insider, a largenumber ofinvestorsreceivethesameinformationsignal.Theirordersareaggregatedintoalargermetaorder which is executed over time. Once filled shares are allocated to the investors at the average price. FGLW showthattheseassumptionsleadtoaNashequilibriumwheremetaordersizesaresuchthattheir impact matches the amount of information. This result is called "fair pricing" because the average price paidtoexecuteatradeisonaverageequaltothepost-reversionprice,soboththeinstitutionand liquidityprovidersbreakeven.Weusetheterminformationinthisarticletomeanshort-term information only, i.e., the information associated with the event or signal that led a portfolio manager to placeanorderonthisparticulardayandtimeratherthanafewdaysearlierorlater.Aportfolio manager may be contemplating an idea for some time before acting on it and typically aims to hold the positionovermonthsoryears.Eveniffairpricingisrightandtradingcannotbeexpectedtoproduce short-termreturnsafterreversion,aportfoliomanagerstradesmaywellbeprofitableoveralonger horizon.Theotherschoolofthoughtassumesthatagents,ratherthanbeingpurelyrational,simplyadoptthe current price as a reference point and randomly place buy or sell orders. Slices from institutional orders interact with the order book and cause impact according to the mechanics of a double auction market. Intheabsenceofreliableinformationonfairprices,themarketadoptsthenewpriceasreferencein

2 "Sunshine trading" aims to take advantage of this view by pre-announcing a trade so its execution can proceed without further impact (Anat R. et al. 1991). 4 pricingfurtherorders,andsopartoftheimpactbecomespermanent.Inaslightlydifferentversionof this model impact is amplified by herding behavior (Froot et al 1992, Cont and Bouchaud, 2000, Lillo et al2008):tradersrespondtoacommonsignalandcausemechanicalimpactregardlessofinformation. Theendresultintermsofpermanentimpactdependsonwhethertherearetradesmadeinthe oppositedirectiontoundothemechanicalimpactoftheoriginaltrades.Themostbasicwithinthe mechanicalimpactcategoryarezerointelligencemodels,whichaimtoexplainpricedynamicsatthe microstructurelevelassumingonlyrandomorderflowsandadoubleauctionprocess(Farmeretal. 2005).Remarkably,zero-intelligencemodelscorrectlypredictimportantstatisticalpropertiesofthe order book (Hopman, 2007). More recently, Bouchaud, Gefen, Potters and Wyart (Bouchaud et al. 2004) haveshowedthatmarketdataismoreconsistentwithan-intelligenceviewpointwhereaverysmall fraction of the orders are informed. This viewpoint is corroborated and made more concrete in a model we will refer to here as the -intelligence model (Toth et al. 2011), where the order book is formed from a random statistical stream of limit orders and market orders.. The market orders consume limit orders nearthecurrentmarketprice.Astheauthorsshow,overtimethisresultsinaV-shapeoftheorder book,i.e.thedepthoftheorderbookgrowslinearlywiththedistancefromthemidpointprice.It followsthattheimpactofimmediatemarketordersgrowsasasquarerootoftradesize.Theauthors usenumericalsimulationstostudytheimpactofmetaordersthatareexecutedalgorithmicallyover time.Tothetalshowthatthemarketoperatesatacriticalpointbetweenasub-diffusiveworld dominatedbymarketmakerswherepricefluctuationsaremeanrevertingandasuper-diffusivemode wheredirectionaltradersdrivepricetrends.Therecentphenomenonofmicro-crisesinmarket microstructure (the largest of which was the flash crash in US markets in May 2010) can be compared to other critical phenomena such as avalanches or forest fires.The two schools of thought lead to slightly different predictions about the shape of the impact function andabouttheamountofreversionafteratradeiscompleted.Accordingtothe-intelligencemodel, impactscalesasapoweroftradesizerangingfrom=0.55forveryrapidexecutions(30% participation)to=2/3forslowerones(5%participation).Intheslowercasepeakimpactwillbe +1 = 5/3oftheshortfall,afterwhichpricerevertsby25%.Thisimpliesthattradesareprofitable afterreversion. In contrast, fair pricing theoryderives theimpact exponent from the tail exponent ofthecumulativedistributionofmetaorders,whichitselffollowsfromthetailexponent

of informationshocksas 211=

+1(Farmeretal.2013).For

= 3(Plerouetal.1999),thisimplies that = 1.5; fair pricing theory predicts that should be equal to the tail exponent of the metaorder 5 sizedistributionminus1,i.e. = 1 =12.Theseresultsareconsistentwiththefindingsfromorder splitting models that show how the metaorder size distribution creates order flow auto-correlation with a tail exponent = 1 (Lillo et al. 2005); so the impact scaling exponent is predicted to be the same as the auto-correlation exponent. Various studies have reported different values of the auto-correlation exponents depending on the stock and listing market. Lillo et al. (2005) find = 0.53 for Shell; Toth et al. (2012) find an exponent close to 0.5 for a set of liquid stocks from the London Stock Exchange; Eisler et al. (2012) find = 0.7; Farmer et al. (2006) and Bouchaud et al. (2004) find the exponent to be in the ranges of 0.52-0.57 and 0.2-0.7, respectively.Order size distributions have been found to have power-law tails with exponents consistent with = 1: 1.56 for a buyside firm (Bershova and Rakhlin, 2013) or 1.7 for brokerages in the Spanish stock exchange (Vaglica et al. 2008). Taking = 1.5 as an example, FGLW show that impactgrows as a square root of tradesize, reachesa peak of 1.5 times the shortfall, then reverts by 1/3 back to the shortfall.Empirical observations of the shape of the impact function have been discussed elsewhere (Almgren et al. 2005, Engle et al. 2008) and generally confirm a power law with exponent in the range [0.4, 0.7]. Our ownestimatesindicatethatimpactscalesasasquarerootoftradesizeoverall.Wealsofindthatthe scaleofmarketimpactduringtheexecutionisnotsignificantlydifferentforcashflowtradesversus other trades.Our results on reversion are consistent with fair pricing for all order sizes excluding cash trades, with 1/3 reversion from peak impact. We also cannot reject the slightly lower prediction of 25% reversion in the -intelligence model. As noted previously cash flow trades are not consistent with fair pricing: reversion is much stronger and essentially eliminates impact completely.These results suggest that both schools of thought on the nature of market impact are essentially right: marketimpactisprimarilymechanicalduringtheexecutionprocessinthesensethatitdoesnot differentiateinformedfromuninformedtradesuntilimpacthasbecomequitelarge,butalso,the observationthatreversionfornoncash-flowtradesisconsistentwithfairpricingshowsthatimpact reflects the average information content of trades.Wehadtomakesomeassumptionsinpreparingthedatabeforederivingtheseresults.Wemerged overlappingtradesandnear-overlappingtradesfromthesamefirmonthesamesideintoasingle metaorder and only considered for analysis those metaorders above 1% of the average daily volume in thesecurity.Additionaltradesinthesamesecuritythatareclearlyseparatedfromtheinitialone,but 6 still within the window used to observe reversion, cause a bias in post-execution returns. To address this issue, we used an impact model to estimate the incremental impact of subsequent trading and adjusted prices by removing this impact from observed prices. The cash flow label is not available for all portfolio managers in our dataset, therefore the subset of trades that are not labeled as cash flow trades may or may not be originated for cash flow reasons.Ourmethodologyformergingordershasalotofcommonalitieswithotherempiricalstudiesof metaordersthatalsocombinemultipletrades.ChanandLakonishok(1995)introducedthisconceptin anempiricalstudybytreatinganentiresequenceoftradesfromthesamemanagerspanningover multipledays,albeitwithsomeintervals,astheirbasicunitofanalysisofmarketimpact.Keimand Madhavan(1997),Torre(1997)andAlmgrenetal.(2005)areotherexamplesofanumberofstudies that attempt to link sequences of trades that are part of the same transaction.Moro et al. (2009) take a slightly different approach by inferring hidden institutional orders from the analysis of rates of execution from different brokers. Bershova and Rakhlin (2013) looked at single-day trades from AllianceBernstein andathird-partydatasetthatstitchedtogethermulti-dayorderswherethenetaccumulationwasat least 5% of median daily volume in each day.Our handling of the data differs to some extent from thesestudiessincewemayaggregatetradesacrossmanagerswithinthesamefirmandconsidermaximum time gap of 60 minutes between trades that are aggregated across managers.Theresponsetotradeswithvariousinformationcontentsisofcrucialimportancetothemarket microstructureliteraturebut,empirically,theroleofinformationonpermanentimpacthasbeen difficulttostudyduetolackofdata.Llorenteetal(2002)haveemphasizedthedifferentialimpactof informed and liquidity trades but are only able to identify these trades separately by proxy (spread and market capitalization). Obizhaeva (2007) finds that in the context of portfolio transitions, buys are more oftendrivenbyinformationandhavepermanentimpactwhilesellsareusuallytriggeredbyliquidity needs and suffer more pronounced reversion. Other examples include Alexander et al. (2007), Coval and Stafford(2007),andDaetal.(2007)whoanalyzepriceresponsestoliquidity-motivatedand information-motivated trades of mutual funds, the information content of which is determined by fund inflows and outflows. The authors have to use proxies for actual inflows, outflows and transitions, which theyconstructfromfundholdingsandreturns.Anothersetofstudiesinvestigatespecifictradesof marketparticipantsthat aremostlikelynotdrivenbyprivateinformationas,forinstance,firesalesof fund managers (Coval and Stafford, 2007), merger-induced trading of arbitrageurs (Mitchell, Pulvino and Stafford, 2004), or changes in number of shares in margin accounts (Andrade et al. 2008). Although the 7 majorityofstudiesfindthateventuallyinitialpricedeviationsarefollowedbypartialorcomplete reversion, cases of permanent price changes or even continuations are documented as well. Our empirical analysis adds to this literature by testing the predictions of competing models on the role of information. We consider the mark-to-market P&L of trades at the reversion price by comparing the price paid for the position to the price after reversion is complete. Fair pricing is the condition that the P&Lshouldbeequaltozeroonaverageforeverytradesize.Asmentionedpreviously,ourresults suggest that the fair pricing condition holds, confirming the evidence recently provided by Bershova and Rakhlin(2013).But,formosttrades,thepointestimatesofreversionarealsoconsistentwithpure mechanicaleffectsalongsimilarlinesasthe-intelligencemodel.Theobservationofamuchstronger reversion in cash flows is the most difficult to reconcile with mechanical impact and gives more support to the theory that the information content of trades determines their permanent impact. If this is true, then it would follow that larger metaorders must be more informed on average than small ones. We explore further the role of information by looking for significant factors that would cause deviations from fair pricing in a regression analysis. A positive P&L is characteristic of metaorders that are too small relativetotheinformation,whereasanegativeP&Lrepresentsovertrading.Wefindthattradesthat followintradaymomentum,tradeinlargecapstocksandadditionstoapriorpositionseekingtotake advantage of an improved price are more likely to incur excessive implementation shortfalls relative to theirshort-terminformation.Onthecontrary,Nasdaqstocksandmetaordersthataggregateorders frommultiplemanagerstendtobeprofitablefortheportfolioonamark-to-marketbasisafter reversion,asdonewtradesinastockwheretheportfoliomanagerhasnotbeenactiveinthelast3 months. Inthenextsectionwewillexplainthedatapreparationinmoredetailandpresentthesummary statistics.In section 3 we provide formal testing of breakeven, efficiency and fair pricing. In section 4 we exploredeviationsfromthefairpricingcondition.Insection5wecomparethepredictionsofthefair pricing theory and the epsilon-intelligence model. We conclude in section 6 discussing the significance of our findings. 2. Data and Summary Statistics8 Our proprietary dataset comprises129,944 metaorders larger than 1% of daily volume originatedby a total of 112 portfolio managers across several large institutional asset managers between July 2009 and March 2012. Pre-processed data was extracted from OMS files and includes comprehensive information ontradecreation(timeofordercreation,portfoliomanagerandtradepurpose)anddetailson individual executions.Themetaordersresultfrommergingoverlappingtradesandnear-overlappingtradesinorderto replicatewhatmarketparticipantscanobservethroughouttheoverallexecutiontime.Someportfolio managerssendordersinmultipleblocks,preferringtoseetheresultofthefirstblockbeforesending the next. In other instances, a single research result from the firm can trigger order creations by multiple portfolio managers. In these cases, each block is assigned a different order ID at creation time, but once ordersreach thetrading deskthey are usually mergedintoa singletrade to be executed as a unit; the fills are then allocated to portfolio managersatthe averageprice. Even if the deskchoosesto execute multipleblocksseparatelyinsteadofmergingthemintoasingleunitthereisnowayformarket participants to distinguish different blocks from the sameportfolio manager or from different portfolio managerssinceordersaresenttothemarketanonymously.Hence,theimpactofthemultipleorders will be the same as for a merged metaorder.We merge orders on consecutive days in the same symbol and side by the same portfolio manager, and mergetradesegmentsoriginatedfromadifferentportfoliomanageratthesamefirmonthesame security and side that were either contemporaneous or less than 60 minutes apart, counting only open-market-hourstime.Approximately25%ofthetradesinthesamplearelabeledascashflowtrades, indicating they were created by a portfolio manager to invest inflows or fund outflows rather than being triggered from any information signal. These trades are analyzed separately from the other trades; cash flowtradescanbemergedwithothercashflowtradesbutarenotmergedwithtradesthatwerenot labeled as cash flows. For each merged trade, we then compute the average realized price per share and the final impact measured as the return from the mid-quote at the beginning of the first segment to the mid-quote at the end of the last segment. We also consider returns to the same-day market close and to the market close 1, 2, 5, 10, 20 and 60 days later, measured from the mid-quote at the beginning of the first segment. Reversion after trade completion is estimated as the symmetric return from mid-quote at the beginning of the first segment to the mid-quote at the time of the last fill.Returnsaftertradecompletionmaybesignificantlyaffectedbytheoccurrenceofadditionaltradesin the same security, which are clearly separated from the initial one or on the opposite side of the market.9 In order to address this bias, we take the cumulative sum of all subsequent trades from the desk on the sametickeroneithersideofthemarketexecutedwithinthetimewindowuntileachmarketclose benchmark.Wethenestimatethenetimpactoftheadditionalpositionswithasimpleandrobust impactmodel[(Torre,Moroetal.2009,Engleetal.2008)whichincludesasmainargumentsthe annualizeddailyvolatilityofthestockinpercentandthesquarerootoftradesizeasapercentageof averagedaily volume.Themodeliscalibratedbysettingthescalefactorso thattheaverageexpected impact is equal to the mean realized shortfall in our sample:() = 2.6 (1) Theunbiasedestimate of reversionuntildaytisderivedfromthe observedstockreturnsfromlastfill (

) tothemarketcloseatthetthdayaftertheendofthetrade( ,),netoftheestimated impactsoftheadditionalbuyandselltrades , untilthattime.Weconsiderupto20days after the trade ends. Using logarithmic returns expressed in basis points,

= 10,000 ln

,+

= +0, 1, 2, 5, 10, 20, 60 (2) Webelievethismethodtobeasuperioralternativetorestrictingtheanalysistometaorderswithout subsequent add-ons since additional positions on the same stock are very common and the sample size wouldbereducedconsiderably.Forexample,inourdataonly20%ofthetradeswouldmeetthis criterion.Furthermore,additionalpositionsonthesamestockareverylikelytobenon-randomand relatedmarketconditionssothatrestrictingtheanalysistothesubsetoftradeswithnotrade continuation would create selection bias. Fromtheoriginaldatasetof129,944metaorderslargerthan1%oftheaveragedailyvolume,we considerthe subset withduration ofatleast5 minutesandaparticipationratebelow50%in orderto drop trades that are likely to be dominated by a block execution. We also drop trades with price below $1andvolatilityabove200%.Table1includesdescriptivestatisticsoftheremaining27,581cashflow trades and 87,658 other trades. The results show that cash flow trades are smaller with a median size of 2.2%ofaveragedailyvolumeascomparedto5.1%forothertrades;theyarealsoexecutedmore patiently with an average participation rate of 6% versus 13% for other trades. 10 Cash Flow TradesOther Trades MedianMeanStddevMedianMeanStddev Average Daily Volume285K933K2.78M984K3.01M8.9M Volatility [%]34.6339.6120.932.9735.8416.14 Spread [bps]12.0422.6638.486.6513.1525.88 Shares Executed8,16726,55077,37761,100188,080551,800 Size [% ADV]2.2%4.7%9.4%5.1%15.1%38.3% Participation Rate [%]3%6%10.4%4.9%13%36.4% Trade Duration [hrs]3.28 4.415.254.386.0111.2 Observations27,59187,658 Table 1. Descriptive statistics of metaorders. The medianmetaorder size is 2.2% of average daily volume for cash flowtradesand5.1%forothertrades.Cashflowsalsotendtobeexecutedmoreslowlywithanaverage participation rate of 6% versus 13% for other trades.3. Breakeven, Efficiency and Fair Pricing3.1 Breakeven and Efficiency InTable2aweshowtheaveragesforseveralrelevantreturns.Shortfallisthedifferencebetweenthe average execution price and the mid-quote at arrival, expressed in basis points, signed by the side of the trade. Impact is measured from mid-quote at arrival to mid-quote at the time of the last fill, also signed by the side of the trade. Close is the signed return from order arrival to the market close of the day the tradewascompleted.Close+1,2,5and10daysarethesignedreturnsfromarrivaluntilthemarket closeonthenextdayandthenext2,5and10daysaftercompletion,respectively.Thedifference betweeneachreturnandtheshortfallrepresentsthemark-to-marketP&Lattherespectivemarket close. The results show that the P&L is always statistically significant and negative for cash flow trades, whereas it becomes insignificant after 2 days for other trades.InTable2bthereturnsarebeta-adjustedtoremovethesystematiccomponentfrom marketdrift. We define beta-adjusted shortfall as the shortfall minus one half of the stock's beta times the change in the S&P500 index from the start to the end of the trade, signed by the side of the trade. The factor of one half reflects the assumption that the execution takes place uniformly from the beginning to the end of the trade and the marketdriftis linear over that period. For thebeta-adjusted impactwesubtract the 11 full S&P500 return from start to end of trading. Similarly, the beta-adjusted returns to each market close subtract the full S&P500 return throughout the respective time window.(returns)Cash Flow tradesOther Trades ReturnReturn-ShortfallReturnReturn-Shortfall MeanMeanS.e.MeanMeanS.e. Shortfall27.22---33.24--- Impact33.666.44*(0.69) 44.9511.71*(0.44)Close21.01-6.21* (1.04)40.657.41* (0.6) Close+1 Day16.35-10.87* (1.79)38.174.93* (1.04) Close+2 Days13.9-13.32* (2.37)32.96-0.28 (1.28) Close+5 Days-4.99-32.21* (3.61)33.19-0.05 (1.88) Close+10 Days-9.33-36.55*(5.05)35.512.27(2.54) Observations27,59187,658 ()Cash Flow tradesOther Trades ReturnReturn-ShortfallReturnReturn-Shortfall MeanMeanS.e.MeanMeanS.e. Shortfall24.01---34.85--- Impact27.263.25*(0.61)48.1813.33*(0.40) Close15.35-8.66*(0.98641.927.07*(0.53) Close+1 Day10-14.01*(1.57)38.163.31*(0.9) Close+2 Days7.85-16.16*(2.04)34.49-0.36(1.12) Close+5 Days0.89-23.12*(3.09)32.22-2.62(1.56) Close+10 Days-13.43-37.44*(4.27)33.02-1.83(2.09) Observations27,59187,658 Table 2a, b: Average returns from arrivaland average by trade purpose (bps). Shortfall, impact and returns to themarketcloseafterthetradeiscompletedareshownbothintermsofabsolutereturns(top)andintermsof beta-adjusted returns (bottom). Standard errors are in parenthesis. Results marked with * are statistically different 12 from0ata5%significancelevel.Theresultsshowthatcashflowtradesareprofitableforliquidity providers;for the other trade (and the overall set) the results are consistent with breakeven on average. Theaveragebeta-adjustedshortfallforcashflowtradesis24basispointsandthetotalimpactatthe end of these trades is 27.3 bps. After the trade is finished, price reverts completely retracing the impact by T+5. The other trades have an adjusted shortfall of 34.9 bps and a peak impact of 48.2 bps. Reversion bringstheadjustedreturnfromarrivalto34.5bpsatT+2,within0.4bps oftheshortfall.Thus, with or withoutbetaadjustment,thepost-reversionpricesforalltradesexcludingcashflowtradesatthe market close on T+2, T+5 and T+10 are not statistically different from the average execution price - i.e., these trades break even on average. Breakevenonaverageshouldnotbeconfusedwithfairpricing,whichstatesthattradesmustbreak even for every trade size - a much stronger condition. As explained in more detail in [FGLW], breakeven averagedoveralltradesizesfollowsfromtheassumptionthatliquidityprovidersareefficient:if metaordersmademoneyonaveragetherewouldbenoliquidityproviders.Iftheylostaconsiderable amountofmoneytoliquidityprovidersthesewouldcompetemoreaggressivelyandinsodoingdrive impact costs lower.Ourfindingssuggestthatcashflowtradesareprofitablefortheliquidityprovider.Atfirstglancethis would seem to violate market efficiency. However, when liquidity providers compete to interact with a metaorderonthemarket,theyhavenowaytoknowwhetheratradeisacashflowtradeoran investmentdecision.Ifweblendresultsfromcashflowtradesandothertrades,thevalue-weighted average P&L of liquidity providers at T+2 is indistinguishable from zero at -0.19bps. 3.2 Fair Pricing Efficientcompetitionbetweenliquidityprovidersimpliesthattheirprofitsshouldbevanishinglysmall whenaveraged overallmetaordersizes. Doesthesameargumentalsoenforcefairpricing?Ifliquidity providers were able to know the size of a metaorder before providing liquidity, they would compete to fillmetaordersattheexpectedpost-reversionpriceforthegivensizeandcompetitionwouldenforce thefairpricingcondition.Butthisisnothowthemarketswork3:liquidityprovidersgenerallyinteract with child orders sliced from a metaorder without knowing the parents true size. The liquidity provider

3 The exception would be cash desks, which quote a price for the entire trade. Even here, cash desks will generally exit positions over time using algorithms so ultimately the fair price is that which can be realized through an extended execution process in a continuous market. 13 must set a price for each slice without knowing whether it will be the last. Let's imagine for example that providing liquidity to fill small metaorders were profitable. The average over all sizes breaks even, so it would be rational for a liquidity provider to provide capital to fill the first slice, hoping to make a profit if the metaorder is small. If the metaorder turns out to be large, the liquidity provider will come to realize that providing liquidity early on was an unlucky choice, but the marginal capital commitment required to continuefromthatpointforwardcanstillbeeconomicallyrational.Sotheefficientcompetitionof liquidity providers doesn't provide a mechanism to avoid cross-subsidization across sizes: losses on large tradesandcompensatingprofitsonsmallones.Efficientcompetitionbetweenliquidityproviders enforces that each slice is priced at the expected reversion price given the information at that point; this guarantees breakeven on average but not for every trade size.FGLWshowthatmetaordersbreakevenforeverysizewhenmultipleinvestorscompetetoexploita sharedinformationsignalinaNashequilibriumwheretheinformationiscompletelyconsumedby market impact.Each portfolio manager does not knowhow much sizetheotherswill placeand must learn to find the optimal sizes through experience. If the aggregate size were consistently too large for a certaintypeofinformationsignal,investorswouldexperienceanaveragelossafterreversionand reduce their order sizes. Vice-versa if the aggregate size were systematically too small there would be a mark-to-marketprofitandeachinvestorwouldhaveanincentivetoplacealargerorder.Atthe equilibrium, the realized price to execute the entire trade is equal to the expected price after reversion. Inotherwords,implementationshortfallequalspermanentimpactforeachmetaordersize.This propertyiscalled"fairpricing"becauseboththeinvestorandtheliquidityproviderbreakevenwhen theirpositionsaremarkedtomarketatthereversionprice.FGLWarguethatfairpricingmustbe enforcedbyportfoliomanagers,sincetheyaretheoneswhochooseordersizes.Largerorderscause more impact and, as our results on cash flows illustrate, if the impact is not matched by information this resultsinmark-to-marketAUMlossesafterreversion.Soaportfoliomanagerwouldavoidplacinga largeorderwhenshehaslessconfidenceinthedecisionorexpectsothermanagerstoovertradethe samesignal.Theaggregatedmetaorderswouldthenrepresenttheportfoliomanagerscollectivevote on the information of the signal. Fair pricing claims that this vote is accurate on average. Beforetesting the fair pricing condition, we need a methodology for measuring the reversion price for eachordersize.Figure1showsthebeta-adjustedreturnsasafunctionoftimegroupedbytrade duration and purpose. For all tradesexcludingcash flowtrades wefindthat trades that take longer to execute also require a greater amount of time for reversion. Reversion is complete by the market close 14 for trades execute in a half day or less; for trades between 1/2 day and 2 days, reversion is complete at theendoftheseconddayaftertheclose;fortradesthatrequirebetween2and5daystoexecute, reversion continues for 5 days; for the largest trades which execute for more than 5 days, reversion also takes at last 5 days to complete.Figure1alsoshowsthattheshapeandscaleofmarketimpactissimilarduringtheexecutionofcash flowtradesasforinformedtrades.Theshortfallandtotalimpactattheend ofcashflowtradesisthe sameastheaverageofothertrades.Afterthetradeiscompleted,thedifferencebecomesclearly apparent with cash flow trades post-reversion prices lower than the average execution price by the end of the day of trade completion. By five days after trade completion, cash flow trades have experienced full reversion, i.e. the impact has been completely erased and the realized shortfall stands as a mark-to-marketportfolioloss.Thisresultissurprisingsinceitsuggestssuboptimaltradesizeswerechosenfor cashflowtrades;therearepotentialsavingsfromspreadingliquiditytradesacrosstheassetsinthe portfolio in such a manner that no individual cash trade is a large percentage of daily volume.Theseresultssupporttheviewpointadoptedbyzeroand-intelligencemodelsthatduringthe execution process the marketis primarily concerned with digesting an order flowimbalancethat looks the same for cash flow trades as for other trades. But the observation of fair pricing for informed trades oncetheprocessofreversioniscompletedandcompletepricereversionforuninformedtradesgive strong support to the theory about the role of information on permanent market impact. -40 -20 0 20 40 60 80 100 120 140 160 StartAverageEndClose1 Day2 Days5 Days10 Days Return vs Trade Arrival [bps] Beta-Adjusted Returns vs Time by Trade Duration and Purpose < 1/2 day1/2 to 2 days2-5 days5+ daysCash Trades 15 Figure1:Beta-adjustedreturns)fromarrivalbytradedurationandpurpose.Reversiontimetakesthesame number of days to complete as the duration of themetaorder. The average shortfall and end impact of cash flow tradesaresimilartotheaveragefornon-cash-flowtrades,butthereturnsaftertradecompletionaremarkedly different. Cash flow trades revert completely, whereas each other group only reverts back to a level similar to the shortfall (first point from the left), consistent with the fair pricing concept.In Table 3, weprovide a more formal testing of the fair pricing condition for the four duration bins for alltradesexcludingcashflowtrades,overalongertimescaleupto60tradingdaysfromorder completion.Theresultsshowthatforthesmallesttradesfairpricingthatequatesaverageexecution price and post-reversion price cannotberejected at the nextday market close. For tradesthat take at leasthalfadaytocompletewecantrejectthenulloffairpricingatthecloseont+2orhigher.For tradeslongerthan2daysreturnstot+5stillexceedtheshortfallbymorethan7basispointsbutthis differenceisnotstatisticallysignificantduetothesmallersamplesizeandlargerstandarderror. Similarly,fortradeslongerthan5daysreturnstoT+2andT+5exceedshortfallby18.4and8.3bps, respectively,butthedifferencesarenotstatisticallysignificant.Ourresultsonreversionsupportfair pricing for all trade durations, but we also cannot reject the -intelligence prediction of 25% reversion. 16 1% ADV filter. We find that trade durations are consistent with a Pareto distribution with a tail exponent

= 1.8 for durations of at least onewholeday(Figure12).Thisishigherthantheexponent1.3foundbyVaglicaetal.(2008)who considerpatchesofdirectionaltradingbybrokersonthreestocksinSpain'sBMEandlowerthanthe exponent 3 predicted by Gabaix et al. (2006).44 Figure 12:Distribution of trade durations. The probability density function of trade durations in minutes falls off asapowerlawwithexponent2.8(exponent1.8forthecumulativedistribution).Spikesatmultiplesof390 minutes reflects a preference by trading desks to start at the market open and end trades at the market close. Toanalyzethedistributionoftradesize,wenormalizedtradedquantitybytheaveragedailyvolume (ADV)toenablecomparisonacrossstockswithverydifferenttradedvolumes.TheaverageADVis definedasthe30-daytrailingaverageofregularmarkethours volume.Wefindthesizedistributionis consistent with a tail exponent = 1.5 (Figure13). In Figure 14 we show the distribution of trade sizes for cash flows only. Cash flow trades are not well modeled by the Pareto distribution with exponent 1.5; the distribution is consistent with a log-normal overall. 45 Figure 13: Trade size distribution. The distribution of trade sizes normalized to Average Daily Volume (ADV) fits a power-law decay with = 1.5, extending up to metaorders of 5-10 x daily volume. Figure 14: Trade size distribution for cash flows. The size distribution of cash flow trades does not support the tail exponent1.5foundformetaordersoverall;cashflowsarewell-modeledbyalog-normaldistributionoverthe entire range of sizes in our sample. 46 ThedistributionoftradesizesinsharesisshowninFigure15.Thetailexponentislowerthanthatof normalized trade sizes due to the larger number of stocks with a low ADV. Figure15:Tradesizedistributioninsharesfilled.Thedistributionoftradesizesinsharesisdistortedbythe samplingacrossstockswithverydifferentdailyvolumes.Neitherthelog-normalorParetodistributionprovidea good fit; we show a slope -2 (Cauchy distribution) for illustration purposes. There are several prior results in the literature regarding the tail exponent of the order distribution. The signs of order flow in equity markets have a long memory so that their auto-correlation function decays slowly as where 0.5(Lillo et al. 2005). As noted in Lillo et al., under a simple theory of ordersplitting,theauto-correlationinorderflowcanbeshowntofollowfromafat-tailedmetaorder distributionwithtailexponent = +1.Gabaixetal.(2006)haveatheoreticalpredictionof3/2 consistenttoourresult.Vaglicaetal.(2008)findanexponent1.7usingbrokeragedata.Theyshowed that the size distribution of metaorders from a single source should be expected to be log-normal (once sizesarenormalizedbydailyvolumetoenablecomparisonacrossstocks)andthatthefat-tailedsize distribution in brokerage data is an effect of the aggregation of data from many firms of different sizes. The size of banks(Pushkin and Aref,2004) and mutual funds(Gabaix et al., 2006) followZipf's law, i.e. the cumulative probability that assets under management be greater than decays as 1/. Our data is dominated by a few very large firms.47 Our sample of portfolio managers certainly does not represent an unbiased sampling of firm sizes. And indeed, the data shown in Figure 15 is not sufficient to affirm that the distribution is better modeled by a power-law tail than a log-normal. However, we find that the slope of the PDF distribution in logs does appeartobeapproximately-2.5forlargetrades.BershovaandRakhlin(2013)alsofoundthatalog-normal size distribution improves on the Pareto distribution..