Arbitrage and Liquidity: Evidence from a Panel of Exchange Traded Funds

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Arbitrage and Liquidity: Evidence from a Panel of Exchange Traded Funds David E. Rappoport W. and Tugkan Tuzun 2020-097 Please cite this paper as: Rappoport W., David E., and Tugkan Tuzun (2020). “Arbitrage and Liquidity: Evidence from a Panel of Exchange Traded Funds,” Finance and Economics Discussion Series 2020-097. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2020.097. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Arbitrage and Liquidity: Evidence from a Panel 1 of Exchange Traded Funds David E. Rappoport W. Tugkan Tuzun FederalReserveBoard FederalReserveBoard November24,2020 Abstract Market liquidity is expected to facilitate arbitrage, which in turn should affect the liquidity of the assets traded by arbitrageurs. We study this relationship using a uniquedatasetofequityandbondETFscompiledfrombigtrade-leveldata. Wefind that liquidity is an important determinant of the efficacy of the ETF arbitrage. For less liquid bond ETFs, Granger-causality tests and impulse responses suggest that thisrelationshipisstrongerandmorepersistent,andliquidityspilloversareobserved from portfolio constituents to ETF shares. Our results inform the design of synthetic securities,especiallywhenderivedfromlessliquidinstruments. Keywords: Exchangetradedfunds,ETF,marketliquidity,lawofone-price,arbitrage,ETF premium. JELclassification: G12,G14. 1We thank Terry Hendershott and seminar participants at CFE, IFABS (Chile), DC Juniors, and the Federal Reserve Board for their comments. We especially acknowledge valuable discussions with Stefan Lewellen during early stages of this project. Tejas Dave, Zach Fernandes, Shannon Nitroy, Tyler Wake, andMaggieYellenprovidedexcellentresearchassistance. Allerrorshereinareours. Theviewsexpressed in this paper are those of the authors and do not necessarily represent those of Federal Reserve Board of GovernorsoranyoneintheFederalReserveSystem. Emails: david.e.rappoport@frb.gov,tugkan.tuzun@frb.gov. 1

1 Introduction Liquidityisanimportanttopicforregulators,academicsandpractitionersalike. Absence of arbitrage, on the other hand, is at the hart of our modern understanding of financial markets. Scholarsrecognizethattradingfrictions,likethoseassociatedwiththepresence of positive bid-ask spread, are related to deviation from the no arbitrage benchmark. Recent papers have found that arbitrage, in turn, affects market liquidity of stocks and currencies (Roll, Schwartz and Subrahmanyam 2007, Foucalt, Kozhan and Tham 2016, Rösch2018). Buttherelationshipbetweenliquidityandarbitrageinvolvingfixedincome securities remains largely unexplored. Our paper aims to fill this gap in the literature, presenting new evidence about the relationship between arbitrage and liquidity from a panel of Exchange Traded Funds (ETFs), spanning funds that invest in stocks and corporatebonds. Scholarsareinterestedinunderstandingtherelationshipbetweenarbitrageandliquidityinfixed-incomemarkets. Infact,intheseminalpaperinthisliterature,Roll,Schwartz and Subrahmanyam (2007) suggested this extension to the literature. Moreover, this extension of the literature is relevant for practitioners given the prominence of derivative and structured products involving government bonds, corporate bonds, and mortgagebackedsecurities,amongothers. Furthermore,theroleofthesestructuresinthefinancial crisis of 2007-08 has renewed the attention of academics and policy makers about their roleinfinancialmarkets. Furthermore, ETFs have attracted the interest of economists as they represent one of themostimportantfinancialinnovationsindecades(LettauandMadhavan2018). Infact, fromthebeginningof2000totheendof2017,assetsundermanagementofdomesticETFs have increased from $26 billions to $3.5 trillions, according to data from Morningstar. ETFs offer a proportional share in a portfolio like mutual funds, but their shares trade in exchanges, where their price and liquidity are determined. These institutional features naturally give rise to the following questions: how well do ETFs track their underlying portfolio?, what are the determinants of the liquidity of ETF shares?, does ETF arbitrage linkstheliquidityofETFsharesandETFconstituents? ThestructureofETFsisparticularlysuitableforouranalysis. First,ETFsinvestinboth relatively liquid equity securities and relatively illiquid fixed income securities, allowing us to compare these two asset classes under the same institutional setting. Second, the ETF arbitrage mechanism allows arbitrageurs to do in-kind conversions between ETF 2

shares and ETF portfolio constituents. As we describe in section 2, in-kind conversions allow arbitrageurs to close their positions, attenuating the concern that our results are confoundedbyomittedvariablesassociatedwiththerisksofmaintainingopenarbitrage positions. Finally, ETFs issue and withdraw shares typically in response to arbitrage activity, allowing us to empirically validate the use of ETF mispricing as a proxy for arbitrageactivity. Inthispaper,wecompileauniquedatabaseofequityandbondETFsusingbigtradelevel data on both stocks and bonds. Liquidity of ETF shares and ETF constituents, at dailyfrequency,isproxiedwitheffectivespreads. Wecalculateeffectivespreadsforstocks usingDailyNYSETradeandQuotes(DTAQ)andforbondsusingFINRATradeReporting andComplianceEngine(TRACE).Inthisway,weobtaineffectivespreadsforETFshares, whichtradeasstocksintheU.S.Inaddition,weuseETFportfoliocompositionfilesfrom Markit North America, Inc. to compute portfolio-level effective spreads from portfolio constituentsspreadscalculatedfromDTAQandTRACE.Wesupplementthisinformation with data on the ETF premium—the difference between the ETF price and its net-asset value (NAV). Since arbitrageurs can profit from large ETF premia and discounts, we consider the absolute value of the premium, which we refer to as ETF mispricing. Our final sample contains over 400,000 observations from February 1, 2012 to December 28, 2017for584domesticETFs: 509domesticequityETFsand75domesticbondETFs. Usingthisinformation,wefirstexaminetherelationshipbetweentheliquidityofETF shares and ETF constituents and the efficacy of the ETF arbitrage mechanism, measured by the speed of adjustment of mispricing. We find that ETF mispricing reverts to zero relatively fast, with the average speed of mean-reversion implying a mispricing half-life of 0.44 days. This result is consistent with previous work that argues for the efficacy of the ETF arbitrage mechanism given the small and transient nature of ETF mispricing (Engle and Sarkar 2006). Moreover, we document that the average speed of adjustment of mispricing is slower for bond ETFs, relative to equity ETFs, with half-lives of 1.36 and 0.37 days, respectively. The fact that bond ETFs, which invest in more illiquid corporate bonds, exhibit a slower speed of adjustment illustrates that constituents’ liquidity is an importantconsiderationforarbitrageurswhosetradesextinguishthemispricing. Infact, at the ETF level we find a strong negative correlation between the mispricing speed of adjustment and average ETF portfolio spreads. The illiquidity of ETF shares also is negatively correlated with the speed of adjustment when we consider only equity ETFs. Togethertheseresultsshowthatliquidityaffectstheefficacyofarbitrage. 3

Next, we study the joint dynamics of ETF mispricing and liquidity in our sample of 584 ETFs, relating these variables in panel vector autoregressions (PVARs) for equity and bond ETFs separately. Our endogenous variables are ETF spreads, ETF portfolio spreads, and ETF mispricing. To avoid the possibility of spurious results these series are expunged of trends and calendar regularities. Our PVAR approach builds on Roll, SchwartzandSubrahmanyam(2007),whousedaVARtorelatethedynamicsofarbitrage and liquidity, using the NYSE composite index and future contracts on this index. By contrast, we consider a panel of ETFs. As these authors, we consider mispricing as a proxy for arbitrage activity and measure the illiquidity of the portfolio associated with a derivative asset—ETF shares in our case—using bid-ask spreads. Relative to these authors, we expand the analysis to also consider the liquidity of the derivative, allowing ustoanalyzethejointdynamicofarbitrageandtheliquidityofthederivative,inaddition to the liquidity of the associated portfolio as previously done. ETFs are a relatively new product, so the time series dimension of our sample is relatively shorter, but the panel dimensionincreasesthepowerofthestatisticalanalysesallowingusforthepossibilityof reliableconclusions. Ouranalysisyieldsthefollowingresults. First,liquidityandarbitragedisplayastatisticallysignificanttwo-wayrelation,bothin thecaseofequityandbondETFs. Infact,forbothassetclassesthereistwo-wayGranger causality between ETF mispricing and the effective spreads of both ETF shares and ETF portfolios. Second,theeffectofarbitrageonliquidity,andofliquidityonarbitrage,islarger andmorepersistentinthecaseofbondETFs. Infact,inthecaseofbondETFs,ashockto the ETF or portfolio spread predicts larger and more persistent responses of mispricing, and similarly, a shock to mispricing predicts larger and more persistent responses of spreads. Finally,liquidityspilloversarestatisticallysignificantinsomecases,withshocks tobondportfoliospreadspredictingfuturespreadstobondETFshares. We contribute new evidence from a panel of ETFs to the literature that analyzes the relationshipbetweenarbitrageandliquidity. Thetheoreticalliteratureproposesdifferent mechanism through which arbitrage can affect liquidity. Holden (1995) presents a model where arbitrageurs equate net order imbalances across markets, acting as cross-sectional market makers. Kummar and Seppi (1994) present a model where trades by informed cross-market arbitrageurs can have nonmonotone effects on liquidity. Foucalt, Kozhan andTham(2016)arguethatarbitragecanbe“toxic”asitcanleadmarketmakerstocharge higher bid-ask spread to compensate for the expected losses from trades with informed arbitrageurs. 4

Empiricalstudieshavescrutinizedtherelationshipbetweenarbitrageandliquidityin equity and currency markets. Our paper builds on Roll, Schwartz and Subrahmanyam (2007),whostudythisrelationship,usingtheNYSEcompositeindexandfuturecontracts on this index. Deville and Riva (2007) study arbitrage and liquidity using data from the French index options market. Rösch (2018) investigate the relationship between arbitrage and liquidity using American Depositary Receipts of stocks traded in foreign markets. Foucalt, Kozhan and Tham (2016) document the presence of toxic arbitrage at intraday frequency in currency markets. Our paper present new evidence about the relationshipbetweenarbitrageandliquidityforapanelofETFspanningbothequityand bondsecurities. ThegrowthofETFsledtoimportantquestionsabouttheirimpactonfinancialmarkets. Theevidenceontheirimpactonstockmarketliquidityismixed. Hamm(2014)andIsraeli, LeeandSridharan(2017)arguethattheyreducetheliquidityofstocks. Ontheotherhand, Sag˘lam,TuzunandWermers(2018)provideevidenceforETFsimprovingtheliquidityof stocks. There is also an important debate on the impact of ETFs on the informativeness of stock prices. Israeli, Lee and Sridharan (2017) argue that ETFs reduce the sensitivity of stocks to their earnings news. On the other hand, Glosten, Nallareddy and Zou (2016) suggestthatETFsincreasetheinformationalefficiencyofstockswithrespecttosystematic componentoftheirearningsnews. Hasbrouck(2003)andMadhavanandSobczyk(2016) showed that ETFs play an important role in price discovery. In addition, many studies (such as Da and Shive (2012) and Israeli, Lee and Sridharan (2017)) find evidence that ETFs increase the correlation of returns between their underlying assets. Bhattacharya and O’Hara (2017) argues that ETFs could distort the pricing efficiency of underlying securities, because market makers in individual securities learn from ETF prices, which include idiosyncratic information of other securities. In addition, ETFs can attract shorthorizon uninformed traders, which increases the non-fundamental price volatility of the underlyingstocks(Ben-David,FranzoniandMoussawi2018). Danhauser(2017)findsthat ETFs lead to long-term positive valuations for their underlying corporate bonds. Finally, Pan and Zeng (2017) show that the creation and redemption of ETF shares is affected by bond-dealer inventories. The difference between these recent papers on ETFs and ours is thatweanalyzethejointliquiditydynamicsofETFsandtheirportfolios. The rest of the paper is organized as follows. Section 2 presents some background on the ETF arbitrage mechanism that are relevant for our analysis. Section 3 describes the data and the calculations of our arbitrage and liquidity measures. Section 4 analyzes the 5

relationship of liquidity and the speed of adjustment of mispricing. Section 5 presents our PVAR analysis relating liquidity and arbitrage. Section 6 offer some conclusions. Appendicesprovideadditionaldetailaboutthecalculationofourvariables. 2 Background: ETF Arbitrage Mechanism Exchange-tradedfunds(ETFs)arepooledinvestmentvehicles,whichofferaproportional share in a portfolio like mutual funds.1 Similar to close-end funds, ETFs and their constituentsarelistedonexchangesandtradeatpricesdeterminedinmarkets. Marketprices for ETF shares and constituents determine the ETF premium: the difference between the ETF share price and its net-asset value (NAV), i.e., the per share market value of the ETF portfolio. Although there are similarities with close-end funds, ETFs are different because they allow shares to be created and redeemed through the ETF arbitrage mechanism.2 This mechanism allows arbitrageurs to close their positions, facilitating the arbitrage of ETF mispricings. Infact,EngleandSarkar(2006)findthatthearbitragemechanismlimitsthe sizeandpersistenceofETFpremia,relativetoclose-endfunds. Inanutshell,theETFarbitragemechanismworksasfollows. Arbitrageurscreateand redeem ETF shares in exchange for pre-specified baskets of constituent securities. Each ETFestablishescontractualrelationshipswithasetoftradingfirms,knownasAuthorized Participants (APs), specifying the process for creating and redeeming ETF shares. But, any interested arbitrageur, like broker/dealers or trading firms, can place creation and redemption orders through APs, so in our analysis we consider that these creation and redemptionordersareplacedbygenericarbitrageurs,asopposedtosolelybyAPs. SomeaspectsofthisprocessarecommonacrossETFs. Forinstance,ETFsarerequired, before each trading day, to make available a portfolio composition file that describes the makeup of the creation and redemption baskets during the trading day. So, the compositionofthecreationandredemptionbasketsisknowninadvancetoarbitrageurs.3 By contrast, other aspects of the creation and redemption process are ETF specific. For 1Most domestic ETFs are registered as investment companies under the Investment Company Act of 1940andregulatedbytheSecuritiesExchangeCommission(SEC). 2Foramorecomprehensivedescriptionofthearbitragemechanismsee,forinstance,LettauandMadhavan(2018)andAntoniewiczandHeinrichs(2014). 3Theportfoliocompositionfileistransmittedthepreviousday,butrevisionscantakeplaceuntilnoon ofagiventradingday(seeAntoniewiczandHeinrichs2014). 6

example,whenmostconstituentsecuritiesareeligibletosettlethroughNationalSecurities ClearingCorporation(NSCC),creationsandredemptionsaresettledthroughNSCC,who acts as the central counterparty. Alternatively, creation and redemption orders can be settled directly between APs and ETFs, in which case APs may be required to pledge collateralwhiletheorderisbeingsettled. Ouruseoftrade-leveldatatocomputeeffectivespreadsforETFconstituentsnaturally makesmostoftheconstituentsfortheETFsinoursampletobeNSCCeligible,sowefocus ontherulesthatapplyinthiscase. Severaloftheserulesarerelevantforouranalysis. First,APscanconvertcreationandredemptionbasketsforETFsharesaspre-specified intheportfoliocompositionfile.4 Theseconversionstakeplaceattheendofthetradingsessionin-kindallowingarbitrageurstolock-inprofitsbeforetheactualcreation/redemption takesplaceattheendofthetradingday. Toillustratethis,considerthecaseofthecreation order depicted in Figure 1. The figure shows that at 10:00 am ETF shares were valued at 100, while the ETF NAV was 98. At that point an arbitrageur buys the creation basket for 98 and shorts the ETF shares at 100, earning the ETF premium of 2 per share. The arbitrageur’s position is exposed to market risk, as its mark-to-market value fluctuates. But, once the arbitrageur has bought the creation basket and shorted the ETF shares, the arbitrageurcanputacreationorderthatwillallowhertoexchangethecreationbasket inkindforthecorrespondingETFshares. Thisclosesthearbitrageurpositionasshetransfers her long ETF portfolio position and obtains the ETF shares to deliver on her short sale. If the ETF premium was negative (ETF was trading at a discount), then the arbitrageur can trade in the opposite direction, redeeming ETF shares. Therefore, the absolute value of ETFpremium—orETFmispricing—shouldbeagoodproxyforarbitragetradesbetween theETFsharesandtheETFconstituents. TheabilitytoconvertETFsharestoredemptionbasketsandtoconvertcreationbaskets to ETF shares makes ETFs a good laboratory to study the relationship between arbitrage and liquidity. In fact, previous and contemporary investigations of this relationship considersimilarsettings. Rösch(2018)considersAmericanDepositaryReceipts,orADRs, which typically can be converted to shares in the home country, and vice versa. Roll, Schwartz and Subrahmanyam (2007) study this relationship considering future contracts on the NYSE composite index. In the case of future contracts, arbitrageurs can only lock-in profits at the expiration of the future contract. By contrast, the ETF arbitrage 4APshavetheoptiontoaccumulatecreationandredemptionordersduringthedayandcanuseopposing orderstooffsetthem. 7

mechanismgrantarbitrageurstheoptiontoexchangeETFsharesandETFconstituentsat anypointafterthearbitragepositionistaken. Thus,forthesameconstituentportfoliothe ETF arbitrage is expected to carry lower costs and risks relative to index arbitrage, using futures. Second,transactioncostareborebyarbitrageursaffectingtheirprofitsandincentives.5 For example, Flannery, Nimalendran, Ray, and Yousefi (2017) use ETF premia to get a measure of corporate bond liquidity. To illustrate the impact of trading costs consider the previous example, but where arbitrageurs can trade at the prevailing bid and ask quotes. Figure 2 depicts this case. If arbitrageurs were to purchase the ETF portfolio at the prevailing ask quote, and short the ETF shares at the prevailing bid quote, then their profits will be equal to the ETF portfolio ask quote minus the ETF share bid quote. That is, ceteris paribus, transaction costs lower the profits earned from ETF arbitrage. In practice,arbitrageurscanobtainmorefavorablepricesbutwewillstillexpectthathigher trading costs would reduce arbitrage incentives, as trading costs may be related to the price impact of trades, influencing the effective prices at which securities are traded, or mayberelatedtothedifficultyoflocatingthinlytradedsecurities. It is worth noting that the arbitrage of ETF mispricing involves additional risks and costs. Arbitrageurs are exposed to liquidity risk given uncertainty about their price impacts, availability of securities for shorting, and adverse price movements before all trades are completed. In addition, arbitrageurs may have to pay fees associated with the creation/redemptionprocesstotheETFmanagerortheAP. Third, APs and arbitrageurs are not required to create or redeem shares, but they do so when it is in their own interest. For example, an arbitrageur interested in profiting from the discrepancy between the prices of an ETF and its constituents may place a creation/redemptionorderthroughanAP.Alternatively,APsmayusethecreation/redemption mechanismtofulfilllargeordersfortheirinstitutionalclients. Finally, the creation and redemption basket need not be “equal” to the ETF portfolio. That is, the creation or redemption baskets may not be proportional to the ETF portfolio, or tracking basket.6 In choosing securities for creation and redemption baskets, ETF managers have the flexibility to deviate from the ETF tracking basket. For instance, 5Aconsequenceofthedesignofthearbitragemechanismisthattradingcostsareexternalizedfromthe ETF investors perspective. In fact, the creation and redemption of ETF shares are recorded by the ETF at NAV(andtakeplacein-kind). 6TrackingbasketisnotthesamethingastheindextrackedbytheETF.Trackingbasketisthebasketof securitiesfromwhichNAViscalculatedtotrackthevalueoftheETFportfolio. 8

managersmightsubstituteilliquidorhardtofindsecuritieswithmoreliquidalternatives including cash in order to facilitate the creation and redemption process; or they might wanttousedifferentbasketstorebalancetheirportfolioholdings. This practice of using different baskets is more common in fixed income ETFs in our data. Using Markit data (described in the next section), we compute for each ETF the fractionofdayswherethecreation,redemption,andtrackingbasketareequal. Considering the 527 domestic equity ETFs in the data we calculate the distribution of the fraction of days that all three baskets are equal. Figure 3a shows that for 97 percent of domestic equity ETFs these baskets are equal at least 9 out of 10 days, i.e., the fraction of days is at least 0.9. In fact, for 57 percent of ETF these three baskets are equal, i.e., the fraction of days is 1. By contrast, considering the 76 bond ETFs in the data we observe a different pattern(Figure 3b). Only54percentofbondETFshaveallthreebasketsthesameatleast 9 out of 10 days, and there is a 25 percent of bond ETFs that have these baskets being differentatleaston1outof10days. Figure3alsodepictinredthefractionoftimeswithin each fraction-of-days bin when only the creation and redemption baskets are equal. For domestic equity ETFs, the creation and redemption baskets are almost always the same, soredbarsareofthesameheightasthebluebars. Bycontrast,forbondETFs,weseethat even in the cases that the three baskets are different most days, more than 30 percent of timesthecreationandredemptionbasketswerethesame. Wewillusethisfacttomotivate ourdefinitionoftheETFportfolioeffectivespread,describedinthenextsection. 3 Data Description We combine information from four main sources for trading days between 02/01/2012 and 12/31/2017. First, we use data from Markit North America, Inc. for daily portfolio composition files that are used to link portfolio constituents to ETFs. In addition, we use two sources of transaction level data to compute security-level effective spreads. For domestic stocks—including ETF shares—we use New York Stock Exchange, Daily TAQ (DTAQ); and for domestic corporate bonds we use FINRA Trade Reporting and Compliance Engine (TRACE). Finally, we use Morningstar to supplement our data with fundlevelinformation. We use Morningstar data to classify ETFs in two major asset classes: domestic equity anddomesticcorporatebonds,seeAppendix A fordetails. 9

3.1 ETF Premium From Morningstar, we obtain daily ETFs’ closing prices and net asset values (NAV). The NAV corresponds to the per share value of the ETF tracking portfolio. Markit ETF data allows us to compute NAV from constituent-level information. But this alternative is less reliable compared to NAV information from Morningstar, which is reported by ETF sponsorsasarequirementtogetexemptionreliefbytheSEC. For ETF i on day t, we denote by p the log of the ETF closing price and n the log of it it theNAVcomputedusingclosingprices. WecomputetheETFpremiumasthedifference between the ETF price and its NAV; and the ETF mispricing as the absolute value of this difference. Thatis, Premium = (p n ) 104 and Mispricing = p n 104 , (1) it it − it × it | it − it |× wherethefactor104 expressesthepremiuminbasispointsoftheNAV. Since arbitrageurs are incentivized by both large premia or discounts, i.e., negative premia,inmostofouranalysisweconsiderthe Mispricing,whichisequaltotheabsolute value of the ETF premium (equation (1)). Roll, Schwartz and Subrahmanyam (2007) interpret mispricing as a proxy for arbitrage activity. By contrast, Rösch (2018) interprets mispricing as a proxy for impediments to arbitrage. Both interpretations are testable in the context of the ETF arbitrage mechanism, as arbitrage activity expands and contracts thenumberofETFsharesoutstanding. Undertheformeralargepremiumshouldpredict ETF share creations, whereas under the latter a large premium should not be associated with ETF share creation. The same being true for ETF discounts and ETF share redemptions. Unreported results show that the ETF premium predicts ETF share creation and redemptionactivity,sowefollowRoll,SchwartzandSubrahmanyam(2007)andinterpret mispricingasaproxyforarbitrageactivity.7 InthecaseofinternationalsecuritiesorsecuritiesthathavenottradedrecentlythecalculationofNAVmayconsiderstaleprices,orpricesinferredfromcomparablesecurities, so the premium will not reflect arbitrage incentives so accurately. This concern is largely absentfordomesticequitiesbutcouldinfluenceourpremiummeasureforbondETFs. 7Specifically, we relate the ETF premium and arbitrage activity in a panel vector-autoregression, with arbitrage activity computed as the ratio of the value of the change in outstanding shares and the fund’s lagged netassets. Both for equity and bond ETFs, Granger-causality tests reject that the ETF premium do notGranger-causearbitrageactivity. 10

3.2 ETF and Portfolio Effective spread We calculate the effective spreads of ETFs and their stocks constituents from the DTAQ, whichcoverstheintradaytransactionsandquotesofU.S.stocksandU.S.ETFs. Similarto LeeandReady(1991),weclassifyeachtradeasbuyorsellbycomparingittotheprevailing quotes. We compare each transaction price with the midpoint of one millisecond prior best bid and ask quotes to determine whether a transaction is a buy or sell. The effective spreadsforETFsandstockconstituentsarecalculatedastwicethedifferencebetweenthe execution price and the midpoint of the best bid and ask as a fraction of the midpoint. Daily effective spread corresponds to the volume-weighted average of effective spreads in that day. On day t, we denote with ETFSpread the effective spread of ETF i and it withConstituentSpread theeffectivespreadofstockconstituent j. (SeeAppendixC.1for jt details.) Forcorporatebondconstituents,weuseTRACEdatatocomputetheeffectivespread. TRACEreportscorporatebondtransactionsdealer-to-dealerandcostumer-to-dealer. We useonlythecustomer-to-dealertrades,i.e.,whenthebuyerorsellerhasbeenidentifiedas acustomer.8 Effectivespreadsofcorporatebondsarecalculatedasthedifferencebetween the volume-weighted buy prices and the volume-weighted sell prices as a fraction of the volume-weightedprices. Wedenotewith ConstituentSpread theeffectivespreadofbond jt constituent j onday t. (SeeAppendix C.2 fordetails.) Markit ETF contains cusips for ETF shares and ETF constituents. We use this data to create daily links between ETF cusips and the cusips of its constituents. These links are used to merge fund-level information with constituents’ information. We use the constituent information to calculate the effective spread of a portfolio corresponding to a singleshareofanETFbasket. Todescribetheweightsusedtoaggregateconstituentspreads,itisusefultointroduce the following notation. Let b index the three ETF baskets, C,R,T , let be the set of ibt { } J constituents of basket b of ETF i on day t, let p be the close price of constituent j on day jt t, let u be constituent j units in basket b of ETF i on day t, and x be the number of ibjt ibt ETF shares in basket b of ETF i on day t. The latter is sometimes referred to as the size of thecreation-redemptionbasketandtypicallyequals50,000shares. TheidentitythatNAV 8TRACEdataispre-filteredfollowingtheproceduredevelopedinDick-Nielsen(2012). 11

equalsthepersharevalueofaportfoliomotivatesthefollowingconstituentweights u p ibjt j,t 1 w = − . (2) ibjt x n ibt i,t 1 − In fact, the NAV identity implies that n x = p u , that is the value of the conit ibt j ∈Jibt jt ibjt stituentsofbasketbofETFiondatetequalstheNAVofbasketb. Weusetheonedaylagof P constituentpricesandNAVtoavoidintroducingspuriousdependencebetweenportfolio spreadsthatwillbecomputedwiththeseweightsandpremiathatdependsnegativelyon NAV. We construct effective spread measure for each ETF basket portfolio as the weighted sumoftheirconstituents’effectivespreads. Thatis,forbasket b ofETF i onday t,9 PortfolioSpread = ω ConstituentSpread . (3) ibt ibjt jt j X∈Jibt In practice, basket weights could be unavailable reflecting that constituent price information is unavailable from TAQ or TRACE (equation (2)). Thus, the calculation of portfolio spreads for each basket assumes that the effective spread of constituents for which the portfolio weights are missing equal the average effective spread for the constituentswithavailableweights. Thisassumptionshouldbiasourcalculatedbasket-level effective spreads down, if price information is less likely to be obtained for more illiquid securities. Thiscouldbethecaseif,forinstance,lessliquidsecuritiestradelessfrequently, explaining the missing price information. This feature of the data should bias our results towards not being able to elicit a relationship between (il)liquidity and mispricing, as we arenotbeabletomeasuretheilliquidityofsecuritiesthatdonottradeonagivenday. As described in section 2, for arbitrageurs the relevant portfolio spreads are for the creation and redemption baskets when the ETF premium is positive and negative, respectively. In order to account for this institutional aspects and based on the evidence about the relationship of the creation and redemption portfolios presented in section 2, wedefinetheETFportfolioeffectivespreadastheaverageofthecreationandredemption basketspreads. Thatis, PortfolioSpread +PortfolioSpread PortfolioSpread = iCt iRt . (4) it 2 9In order to have reliable liquidity measures for ETF baskets we only consider basket-level effective spreadswhenourbasketweightsω adduptoatleast0.5andtoatmost1.25(seeAppendixB). ibjt 12

Analternativetoequation(4)wouldhavebeentodefineportfoliospreadastheportfolio spreadofthecreationbasketwhenthepremiumispositiveandastheportfoliospreadof theredemptionbasketwhenthepremiumisnegative. Butthisalternativecouldintroduce amechanicalrelationshipbetweenpremiumandportfoliospread. Wenotethatinlightofthefactthatwithindomesticequitythecreationandredemption baskets are identical on almost all days, our definition only affects portfolio spreads for bondETFs. Ourfinalsamplefiltersobservationsaccordingtodataavailabilityandtoensureaccuracyofourportfoliospreadmeasures(seeAppendixB).Moreover,toreducetheinfluence of outliers in our analysis we winsorize ETF mispricing, and ETF and portfolio effective spreadsatthe1stand99thpercentiles. Ourfinalsamplecontainsover400,000observations for584domesticETFs: 509domesticequityETFsand75domesticbondETFs. Table 1 presents descriptive statistics for Mispricing, ETFSpread, and PortfolioSpread computedaccordingtotheaforementionedconventionsoverourfinalsample. Considering all ETFs, average portfolio spreads are 16 basis points, whereas average ETF spreads are12basispoints,andaveragemispricingis11basispoints. Bothportfoliospreadsandmispricingarehigheronaverageforbondrelativetoequity ETFs. Considering only domestic equity ETFs, we observe tighter portfolio spreads with an average of 11 basis points. In contrast, for domestic bond ETFs, portfolio spreads are almost 60 basis points, reflecting the illiquidity of corporate bonds. Average mispricing displays a similar pattern with an average of 8 and 31 for equity and bond ETFs, respectively. Higher mispricing of bond ETFs may not be surprising if high portfolio spreads impede arbitrage. However, it is interesting to note that despite these facts, average ETF spreadsforbothequityandbondETFsaresimilartakingvaluesof12and14basispoints, respectively. Figures 4 and 5 presents the median, 25th and 75th percentiles of the distribution of daily values for ETF mispricing, and ETF and portfolio spreads in our sample of equity andbondETFs,respectively. Weseethatoveroursampletheseseriesexhibitmildtrends andsomedeterministicpatterns,somethingthatwefurtherinvestigatebelow. 4 Liquidity and the Speed of Adjustment of Mispricing We begin our analysis inspecting the relationship between the speed of adjustment of mispricing and the market liquidity of both ETF shares and ETF constituents. Our null 13

hypothesis is that the speed of adjustment is independent of market liquidity. This couldbethecase,becauseeithermispricingdoesnotincentivizearbitrage,sothespeedof adjustmentisindependentofthemispricing. Orthiscouldbethecase,becauseliquidityis notanimportantconsiderationforarbitrageurs,sothespeedofadjustmentisindependent ofliquidity. Ouralternativehypothesisisthatthespeedofadjustmentdependsonmarketliquidity. This could be the case if ETF mispricing gives arbitrageurs an incentive to take offsetting positionsinETFsharesandETFconstituentstoearnthepricedifferential. Asarbitrageurs take these positions, ETF mispricing should shrink. And given that market liquidity facilitatesarbitrageurs’trades,thespeedofadjustmentofETFmispricingshoulddepend onmarketliquidity. In order to measure how fast ETF mispricing mean revert, we calculate a measure of the speed of adjustment of ETF mispricing by running the following regression for each ofthe584ETFsinoursample,separately: ΔMispricing = α +μ Mispricing +(cid:15) , (5) it i i i,t 1 it − whereMispricing istheabsolutevalueofthelogdifferencebetweentheETFi’spriceand it itsNAV,α andμ arecoefficientstobeestimated,and(cid:15) arezeromeandisturbances. The i i it coefficientμ characterizesthespeedofmean-reversionofETFmispricing. Infact,ignoring i theconstant,itiseasytoshowthatthehalf-lifeofmispricingisgivenby ln(2)/ln(1+μ). i − Panel A of Table 2 reports the average and standard deviation of the estimates for μ i acrossoursampleof584ETFs. FortheentiresampleofETFs,theaveragemean-reversion coefficientis-0.79,orahalf-lifeof0.44days. OnceweseparatetheequityandbondETFs, a clear distinction appears. The mean-reversion coefficient for domestic equity ETFs is -0.85 whereas it is -0.40 for bond ETFs, i.e., a half-life of 0.37 and 1.36 days, respectively. Thelargerabsolutevalueofthemean-reversioncoefficientindicatesthatthemispricingof equity ETFs disappears faster, likely reflecting a more effective ETF arbitrage activity. By contrast, the mispricing of bond ETFs disappears slower. The fact that bond ETFs, which invest in more illiquid corporate bonds, exhibit a slower speed of adjustment suggests that constituents’ liquidity is an important consideration for arbitrageurs whose trades extinguishthemispricing. WefurtherinvestigatetheroleofETFshares’orETFconstituents’liquidityplayinthe effectiveness of arbitrage by computing the correlation of the speed of adjustment and liquidity at the ETF level. Panel B of table 2 report the correlation of our estimates for 14

μ with ETF and portfolio spreads across ETFs. Considering all ETFs, these correlation i coefficients are both positive and statistically significant, rejecting our null hypothesis in favorofouralternativehypothesis. ThefactthatthecorrelationislargerforETFportfolio spreads is consistent with the view that liquid ETF constituents enable more effective arbitrageandafasterspeedofadjustmentofETFmispricing. Thefactthatthecorrelation is positive and statistically significant for the spread of ETF shares, indicates that ETF liquidity also enables arbitrage. But the small correlation suggests a lesser role for ETF shares’liquidityinexplainingthecrosssectionalvariationinarbitrageeffectiveness,likely reflectingthesmallerdispersionofETFspreadsinourdata. The correlation coefficients when we consider only equity and bond ETFs are different. Considering equity ETFs, the correlation coefficient with the ETF spread is positive whereas the correlation coefficient with portfolio spread is not statistically significant. In contrast, for bond ETFs, the correlation coefficient with portfolio spread is positive, whereas it is not statistically significant for ETF spread. These findings suggest that with respect to the effectiveness of arbitrage, there are important differences between equity andbondETFs. ForequityETFs,theeffectivenessofarbitrageislinkedtotheliquidityof ETFswhereasforbondETFs,itisrelatedtotheportfolioliquidity. Together these results show that liquidity affects the efficacy of arbitrage. Yet, it is importanttopointoutthatarbitragemayalsofeedbackintomarketliquidity. Inthenext section, we analyze the joint dynamics of liquidity and arbitrage activity in our panel of ETFs. 5 Joint Dynamics of Arbitrage and Liquidity We continue our analysis studying the joint dynamics of mispricing and the liquidity of ETF shares and ETF constituents. Before analyzing this joint dynamics, we expunge our variables of common regularities and trends to minimize the possibility of spurious conclusions. Then, we related the adjusted variables in a panel vector autoregression (PVAR)analysis. 5.1 Adjustment Regressions Before we estimate the PVAR, we aim to remove the common regularities and trends from the variables to avoid the possibility of spurious results. We follow Roll, Schwartz 15

and Subrahmanyam (2007) and use adjustment regressions to remove the deterministic components in ETF spread, portfolio spread and mispricing. We run these regressions separately for equity and bond ETFs to account for possible differences between these asset classes. The rationale for removing deterministic components in these series comes from previous research that have found that spreads exhibit time trends and calendar regularities (see Chordia, Roll and Subrahmanyam 2001). This, in turn, suggests that mispricing might also exhibit these deterministic components. In fact, Roll, Schwartz andSubrahmanyam(2007)findtimetrendsandcalendarregularitiesforthefutures-cash basis, i.e., the difference between the NYSE composite index and the price for this index implied by futures contract associated with it. Since trends and calendar regularities of ETF premia and spreads have largely been unexplored, our analysis is of independent interest. We regress the raw spreads for ETF shares and ETF portfolios on the following variables: (i) time trend and square of the time trend; (ii) day-of-the-week dummies; (iii) pre-holidaydummywhichindicatesadaybeforeaholiday;10 (iv)monthlydummies;and (v) ETF fixed effects. We regress the raw ETF mispricing on the same set of variables, butconsideronlyaFridaydummy,insteadoftheday-of-the-weekdummies. TheFriday dummy is expected to account for the increased cost of holding arbitrage inventory over theweekend. Table3presentstheresultsoftheseadjustmentregressionsforequityETFs. Largemajorityoftheestimatedcoefficientsarestatisticallysignificant,confirmingthedeterministic variation in ETF spread, portfolio spread, and mispricing. For the ETF spread, the estimatedcoefficientsfortrendandtrend2 arenegativeandimplyadecreasingtrajectoryfor thespreadoveroursampleperiod. ThiscouldreflectaseculardeclineinETFspreadsdue to survivorship bias—only ETFs that attract more investors interest are likely to remain inbusiness. Inthecaseofportfoliospread,theestimatedcoefficientsfortrendandtrend2 are positive and statistically significant. Together they imply a non-monotone trend over our sample period, with average portfolio spreads decreasing mildly in the first quarter of our sample and increasing thereafter. For the mispricing regression, trend and trend2 coefficients are statistically significant and imply a decreasing trend for mispricing over oursample. Monthly dummies, which omit January, are negative. That is, ETF spreads are gener- 10We consider holidays that did not fall on a Monday from the list maintained by SIFMA, https: //www.sifma.org/resources/general/us-holiday-archive/. 16

ally higher in January. Similarly, mispricing and portfolio spreads also display a January effect, but on average they are higher in December. The presence of a January effect for spreads is largely consistent with the evidence of Roll, Schwartz and Subrahmanyam (2007),whoconsidertheweightedaveragequotedandeffectivespreadfortheconstituents oftheNYSEcompositeindex. For all of the three regressions, the pre-holiday dummy is positive and significant, suggestingthatETFsandtheirconstituentsarelessliquid,andmispricingishigher,prior to a holiday. Friday dummy is positive and significant for the ETF mispricing. This is consistent with the idea that arbitrageurs may require additional compensation if they willhavetoholdtheirpositionsovertheweekend. Portfoliospreadstendtobehigheston Fridays,whichcouldberelatedtothepreviousfinding. However,ETFspreadstendtobe highestonMondays,asimpliedbythenegativecoefficientsontheday-of-weekdummies inthiscase. Table 4 summarizes the results of the adjustment regressions for bond ETFs. Similar to equity ETFs, for ETF spread trend and trend2 coefficients are negative and statistically significant. However, in this case, the estimated coefficients imply an inverted U-shape trend: mildlyincreasinginthefirstquarterofthesampleanddecreasingthereafter. Both in the case of portfolio spread and mispricing the coefficients are statistically significant and their values imply a decreasing and convex trend over our sample period. Unlike equity ETFs, spreads of bond ETFs do not seem to display a January effect. The monthly dummiesdonotlendthemselvestoaclearinterpretation: onaverage,bond-ETFspreads arehighestinJuly,portfoliospreadsarehighestinDecember,andmisprincingsarehighest inFebruary. InthecaseofbondETFs,spreadsforbothETFsharesandETFconstituentsarehigher in the days preceding a holiday, but for mispricing the positive estimated pre-holiday effectcannotberejectedtobedifferentthanzero. Also,Fridaydummyinthemispricing regression is positive, but not significant, which suggests that the forced holding of bond positions over the weekend is not a major consideration for bond arbitrageurs. As with equity ETFs, for bond ETFs the spread of ETF shares appears higher on Monday. By contrast, for portfolio spreads we see a different pattern between equity and bond ETFs. ForbondETFsportfoliospreadsarelowerinthelaterdaysoftheweek,whereasforequity ETFsportfoliospreadswerehighestonFriday. BeforeturningtoourPVARanalysisweanalyzethestationarityandcorrelationofour adjusted series, i.e., the residuals from the regressions presented in Tables 3 and 4. We 17

denotetheadjustedseriesby ETFSpread∗ ,PortfolioSpread∗ ,and Mispricing∗ . Toassessthestationarityoftheresidualsfromtheadjustmentregressions,weperform apanelunitroottestbasedonPhillip-Perronfortheseadjustedseries. Thesetestsstrongly rejecttheexistenceofunitrootforallthreepaneltimeseriesatp-valueslessthan0.001. Table 5 report the cross correlations of our adjusted series. All pairwise correlations are statistically significant at the 1 percent level. For both asset classes the correlation betweenETFspreadsandmispricingisthehighestwithvaluesabove0.4. Thiscorrelation isfollowedinmagnitudebythecorrelationofETFandportfoliospreadsforequityETFs, with a value of 0.22, and portfolio spread and mispricing for bond ETFs, with a value of 0.28. Finally, the lowest correlation for equity ETFs is between portfolio spread and mispricing, with a value of 0.16, whereas for bond ETFs it is between ETF spread and portfolio spread, with a value of 0.11. These correlations and their statistical significance suggestthepresenceofmultivariatecausalityamongmispricingandtheliquidityofboth ETFsharesandETFportfolioconstituents. 5.2 PVAR Analysis WeexaminethejointdynamicsofETFmispricingandliquidityinoursampleof584ETFs, relatingthesevariablesinseparatePVARsforequityandbondETFsrespectively. Ourinputvariablesaretheresidualsfromtheadjustmentregressions: Mispricing∗ ,ETFSpread∗ , it it andPortfolioSpread∗ . OuruseofaPVARapproachismotivatedbythemultivariatecausalit ity among these variables suggested by the statistically significant cross-correlations reported in Table 5. Intuitively, when financial markets are illiquid, it could be harder to arbitrage mispricings away. Conversely, arbitrage may create imbalances in order flows and market makers’ inventories increasing illiquidity in both the market for ETF shares and ETF constituents. This feedback loop between ETF shares’ and ETF constituents’ liquidity, or the participation of the same investors or market-markers in the markets for ETFsharesandETFconstituents,canintroducebivariatecausalityamongthesesecurities’ liquidity. Our PVAR approach builds on Roll, Schwartz and Subrahmanyam (2007), who used a VAR to relate the dynamics of arbitrage and liquidity, using the NYSE composite index and future contracts on this index. By contrast, we consider a panel of ETFs. As these authors, we consider mispricing as a proxy for arbitrage activity and the spread of the portfolio associated with a derivative asset. But, we expand the analysis to also consider 18

the liquidity of the derivative—ETF shares in our case. This allows us to analyze the join dynamicofarbitrageandtheliquidityofthederivative,inadditiontotheliquidityofthe associated portfolio as previously done. ETFs are a relatively new product, so the time series dimension of our sample is relatively short, but the panel dimension increases the powerofthestatisticalanalysesallowingusforthepossibilityofreliableconclusions. Weexaminethejointdynamicsofourvariablesofinterest,stackingtheminthevector Y it = (Mispricing∗ it ,ETFSpread∗ it ,PortfolioSpread∗ it ), where i index the different ETFs and t T indextradingdayswhereETF i isobservedinourunbalancedpanel. i ∈ Morespecifically,wemodelthisrelationshipas: Y = Y A +...+Y A +e , (6) it it 1 1 it p p it − − p where A are 3-by-3-coefficient matrices to be estimated and e are 3-dimensional { j }j=1 it vectorswithzeromean. ThePVARisspecifiedwith5autoregressiveterms. Table 6 reports the results of the PVAR for equity ETFs. The estimated coefficients of all variables on their own lags are positive, statistically significant, and decay over time almost monotonically. The latter confirms the absence of unit roots, as indicated by the Phillip-Perron tests reported in subsection 5.1, and it suggests some persistence of these variables. The cross-effects between these variables are generally positive and statistically significant, suggesting that all variables are interrelated. That is, there are liquidityspilloversfromETFsharestoportfolioconstituents,andviceversa;andthereis abivariatecausalitybetweenmispricing,representingarbitrageactivity,andtheliquidity ofbothETFsharesandETFportfolios. Moreover,therelativemagnitudeoftheestimated coefficients and t-statistics suggests a stronger relationship between mispricing and ETF shares’spread. Theseresultsareinlinewiththevaluesforthecross-correlationsreported intheprevioussubsection. Table7reportsthePVARresultsforbondETFs. SimilartoequityETFs,forallvariables theestimatedcoefficientsontheirownlagsarepositive,statisticallysignificant,anddecay overtime. Inthiscase,thecross-effectsaregenerallypositivebutmostarenotstatistically significant. Lagged ETF spreads do not seem to affect current portfolio spreads, but the statistical significance of the cross-effects for the other pairs of variables suggest the presence of liquidity spillovers from bond portfolios into bond ETF spreads, and a bivariatecausalitybetweenmispricingandbothliquiditymeasures. Table 8 reports the correlations of innovations, i.e., residuals, from the three PVAR 19

equationsforourtwoassetclasses. Asitwasthecasefortheadjustedseries,thecorrelation fortheinnovationsishighestbetweenthemispricingandETFspreadforbothequityand bond ETFs, with values of 0.08 and 0.09, respectively. Also in line with the previous evidence, for equity ETFs, the second largest correlation is between both spreads, with a valueof0.03,followedbythecorrelationofportfoliospreadandmispricing,withavalue of 0.01. For bond ETFs, the correlation of portfolio spread with both mispricing and ETF spread is 0.01. This contrast with the evidence for the adjusted series, where portfolio spreadsandmispricingexhibitedahighercorrelation. Next,weperformGranger-causalitytestsfortheseparatelyestimatedPVARsforequity andbondETFs. PanelAofTable9reportsthechi-squarestatisticsandp-valuesforequity ETFs and Panel B reports the same statistics for bond ETFs. The null hypothesis is that thevariableslistedintherowsdonotGranger-causethevariableslistedinthecolumns. ForequityETFs,allthreevariablesGranger-causeoneanother. Inallcasesthetestthat row variables do not Granger-cause column variables is rejected at the 1 percent level. This is consistent with liquidity influencing arbitrage and arbitrage, in turn, influencing liquidity for both ETF shares and ETF constituents. The Granger-causality relationship betweenETFspreadandmispricingappearstobethestrongest,inlinewiththeevidence from the correlations of adjusted series and PVAR innovations presented above. This finding is interesting as the previous study by Roll, Schwartz and Subrahmanyam (2007) didnotprovideevidenceontherelationshipofarbitrageandtheliquidityofthederivative. In our case, the ETF share corresponds to the the derivative, and it exhibits the strongest relationwitharbitrage. For bond ETFs, mispricing and ETF spread are Granger-caused by the other two variablesinoursystem. However,inthecaseofportfoliospread,onlymispricingGrangercauses it. In other words, the mispricing provides information about the future portfolio spreads,butthetestcannotrejectthattheETFspreaddoesnotGranger-causetheportfolio spread. The latter suggests that there are no direct liquidity spillovers from bond ETF sharesintobondETFconstituents. ButitdoesnotruleoutthatETFspreadscanindirectly affectthespreadsofbondETFconstituents,asETFspreadsinfluencemispricingwhichin turninfluencesportfoliospreads. To analyze the impact of a shock to one variable on the other variables in the system, wecomputetheimpulseresponsefunctions(IRF)impliedbyourPVAR.TheIRFsaccount for both the direct and indirect effects from the shock to an individual variable. In order to isolate the effect of a shock to a single variable, we orthogonalize the residuals from 20

the PVAR using the inverse of the Cholesky decomposition of the residual covariance matrix. Unlike the PVAR estimated coefficients and, thus, the Granger-casuality test, the IRFs depend on the ordering of the endogenous variables used for the Cholesky decomposition. Wereporttheresultswhenthevariableorderingis: Mispricing∗ ,ETFSpread∗ and PortfolioSpread∗ .11 Ourconclusionsarelargelyrobusttotheorderingofthesevariables. Figure 6 plots the impulse response functions for equity ETFs with 95 percent confidencebandsusing1,000MonteCarloreplications. Allofthethreevariablesdisplaysome persistence, so a shock to a given variable provide information about the future value of thesamevariable,especiallyoverthenextfewtradingdays. Next, we inspect the interrelation between portfolio spread and mispricing, which we can compare to the evidence presented in Roll, Schwartz and Subrahmanyam (2007). As these authors we find that shocks to the mispricing help to predict portfolio spreads over the next couple of days. That is, the ETF arbitrage affects the liquidity of the ETF portfolioconstituents. Roll,SchwartzandSubrahmanyam(2007)findweakpredictability, in the reverse direction, from the average spread of NYSE composite index constituents to mispricing. By contrast, we find that shocks to the ETF portfolio spread seem to have explanatory power on ETF mispricing over the next two weeks, with the effect of portfolio spread on mispricing manifesting after a couple of days. We note that the two set of results are not expected to coincide. First, the two studies use different constituent samples. Roll,SchwartzandSubrahmanyam(2007)considertheconstituentsoftheNYSE compositeindexfrom1988to2002,whereasweconsidertheportfolioconstituentsof509 domestic equity ETFs from 2012 to 2017. Second, our study includes the liquidity of the derivativesecurityinthePVARsystem,sothepredictabilityofmispricingfromshocksto portfolio spreads could reflect the indirect effects through the ETF spread. We continue theinspectionoftheIRFsbylookingattheeffectofETFspreadshocksonmispricingand viceversa. Studyingthisrelationshipisinterestingbecause,forone,littleisknownabout the effect of arbitrage on derivates’ liquidity. For another, this relationship appeared empirically relevant based on the inference from the correlations of adjusted variables and PVAR innovations and the Granger-causality tests. The IRFs confirm the empirical relevance of the relation between ETF spread and mispricing. Mispricing shocks have a relativelylargeandpersistenteffectontheETFspread(bottomleftpanel),andthesameis trueinthereversedirection(toprightpanel). Theseresultssuggestthatilliquidityshocks 11We order mispricing first to facilitate comparisons with the reported results in Roll, Schwartz and Subrahmanyam(2007). 21

especially in ETF shares reduce arbitrage incentives in equity ETFs. Hence, ETF spreads areimportantforthelawofoneprice. The aforementioned results are insensitive to the relative ordering of spreads and mispricing, but the relative ordering of ETF spread and portfolio spread affects the IRF fromETFspreadshocksonportfoliospreads,andviceversa. ThereportedIRFsexhibitaa significantalbeitshort-livedeffectfromETFspreadsshocksonportfoliospreads,whereas theeffectofportfoliospreadshocksappearsstatisticallyinsignificantonETFshares. These IRFs,togetherwiththecorrelationanalysisandGranger-causalitytests,suggeststhatETF andportfoliospreadsarejointlydeterminedforequityETFs. Littleisknownabouttherelationshipbetweenarbitrageandliquidityforfixedincome securities, so the IRFs for bond ETFs are of special interest. Figure 7 plots the IRFs for bond ETFs with 95 percent confidence bands using 1,000 Monte Carlo replications. It should be noted that these IRFs are plotted over a much larger time range, considering 100 trading days, instead of 20 as for equity ETFs. This fact underscores the richer and morepersistentdynamicsamongourvariablesofinterestforbondsETFs. Aswithequity ETFs, shocks to a bond ETF variable are informative in predicting the future values of the same variable, with shocks to bond portfolio spreads and mispricing being relatively more persistent. The latter is consistent with the results of section 4 that showed that for bondETFsmispricingismorepersistent. WeproceedtoinspecttheseIRFsinthesameorderasforequityETFs,beginningwith therelationshipbetweenportfoliospreadandmispricing. Wefindapositive, significant, and very persistent effect of shocks to mispricing on bond portfolio spreads, and we find thesamepropertiesintheresponseofmispricingtoportfoliospreadshocks. Theseresults arestrikingcomparedtothepreviousevidenceforequityETFs,wheretheseIRFsreflected smaller and shorter lived responses. In the case of bond ETFs, the effect of a shock to portfoliospreadormispricinghelpspredictthevalueoftheothervariableevenafter100 trading days after the shock! These more persistent dynamics suggests the presence of a reinforcing feedback between portfolio spreads and mispricing. As portfolio spreads widen arbitrage incentives decrease making mispricing more persistent, as suggested by the analysis of section 4. Larger mispricing appears to feed back into wider portfolio spreads. Thisfeedbacklikelyreflecttheactionofdealers,whomakemarketsforthebond constituents. Basedonourevidence,wecanonlyspeculateovertheeconomicincentives driving the response of dealers. One explanation could be that dealers set larger bid-ask spreads in response to order imbalances caused by arbitrage activity incentivized by a 22

wider mispricing. But this explanation seems at odds with the fact that arbitrage for bond ETFs appeared less effective (section 4), if the effectiveness of arbitrage is related to the number of arbitrage trades. Another explanation is simply that dealers have market power and are able to extract arbitrage rents by widening bond bid-ask spreads. Additional research should further scrutinize dealers’ economic incentives in the context ofETFarbitrageforbondETFs. WecontinueinspectingIRFsforbondETFs,lookingattheeffectofETFspreadshocks on mispricing and vice versa. Inference from Granger-causality tests and correlations reported in Tables 5 and 8 make us expect a strong relationship between these variables. Infact,mispricingshockshaveasignificantandpersistenteffectontheETFspread(bottom leftpanel),thesamebeingtrueinthereversedirection(toprightpanel). Theseresults,in line with the results for equity ETFs, suggest that ETF shares’ liquidity is important for arbitrage incentives in bond ETFs. We conclude that ETF spreads (in both asset classes) areimportantfortheefficacyoftheETFarbitragemechanism. Finally we inspect the relationship between the liquidity of bond ETFs and their constituents. Inference from previous results suggested the absence of a direct effect of ETFspreadsonbond-ETFportfolioconstituents. TheIRFinthetopmiddlepanelofFigure 7 supports the absence of both a direct and an indirect effect of shocks to ETF spreads on thespreadbondconstituents. Thatis,wedonotfindliquidityspilloversfrombondETFs intotheirconstituentbonds. Bycontrast,liquidityshockstobondETFportfoliosdoaffect thesubsequentliquidityofbondETFshares(leftmiddlepanel). InthecaseofbondETFs allresultsareinsensitivetotheorderingofvariablesassumedtocomputetheIRFs. Differences in our results for equity and bond ETFs are interesting, as they shed light on the role of the liquidity of the portfolio constituents on the dynamic relation between arbitrage and liquidity. Figure 8 compares the IRFs for both equity and bond ETFs, considering 25-basis-point shocks to our three endogenous variables. This comparison shows that, generally, the response of our endogenous variables for the same shock is largerandmorepersistentforbondETFs. Thediscrepancyisstarkwhenweconsiderthe relationship between portfolio spread and arbitrage, with the IRFs for bond ETFs being larger and more persistent. When we consider the relationship between mispricing and ETF spread, we see also larger and more persistent effects for shocks to ETF spread on mispricing; however, for shocks of mispricing on ETF spread the effects upon impact is larger for equity ETFs, with the effect still being more persistent for bond ETFs. Together theevidenceleadustoconcludethatthemoreilliquiditytheconstituentsthestrongerand 23

more persistent is the relationship between arbitrage and liquidity. Finally, we compare the IRFs that capture the liquidity spillovers between ETF shares and ETF constituents. Asdiscussedabove,forequityETFsthedirectionforliquidityspilloverswassensitiveto the assumed ordering of the variables in the PVAR. By contrast, for bond ETFs the IRFs suggestedthatthereareliquidityspilloversfrombondportfoliostobondETFshares,but nottheotherwayaround. TheseresultssuggeststhatliquidityspilloversfromETFshares toETFconstituentsareweakerwhenconstituentsarelessliquid. 6 Conclusions In this paper, we present new evidence about the relationship between arbitrage and liquidity using a panel of ETFs, spanning both domestic equities and bonds. To study the relationship between arbitrage and liquidity, we compile a unique ETF dataset from big trade-level data. To the best of our knowledge, our paper is the first to dynamically relatemispricingtoendogenousliquiditymeasures,suchaseffectivespreads,whenfixedincomesecuritiesareinvolved. Our results indicate that the liquidity of ETF shares and ETF constituents promotes the efficacy of the ETF arbitrage mechanism. For equity ETFs, the average speed of adjustment implies an ETF mispricing half-life of 0.37 days. The fast speed of reversion tozerosuggestsaneffectiveETFarbitragemechanism(EngleandSarkar2006). Forbond ETFs, the average speed of convergence implies an ETF mispricing half-life of 1.36 days. The less effective arbitrage of bond ETF mispricing is associated to the lower liquidity, on average, of bond ETF constituents. Liquidity of ETF shares is also associated to the efficacyofarbitrage,butonlywithinequityETFs. OuranalysisfindsweakliquidityspilloversbetweenETFsharesandETFconstituents. In most cases, Granger-causality tests indicate that one effective spread have predictive power over the other spread. But, only shocks to bond portfolio spreads have predictive poweroverfuturebondETFspreads. Ourfindingssupportthepresenceofarobustinterrelationshipbetweenliquidityand arbitrage, when the securities involved are either equities or bonds. These findings, on the one hand, provide additional supporting evidence for this interrelationship when equitiesareinvolved(Roll,SchwartzandSubrahmanyam2007,Rösch2018). Ontheother hand, these findings suggests that the effect of arbitrage on liquidity, and of liquidity on arbitrage,islargerandmorepersistentwhenlessliquidbondsecuritiesareinvolved. 24

Our results also give insights about some important aspects of synthetic securities derived from illiquid assets. The liquidity of these synthetic securities seems sensitive to the liquidity shocks to their underlying investments. Hence, the liquidity of synthetic securities are not independent of their illiquid investments. If the liquidity of their investments becomes more illiquid, the liquidity of the synthetic security may also dry up. On the other hand, we cannot find evidence suggesting that the liquidity of underlying illiquidinvestmentsdriesupwhenthesyntheticsecuritybecomesmoreilliquid. References Antoniewicz, Rochelle, and Jane Heinrichs. 2014. “Understanding Exchange-Traded Funds: HowETFsWork.” ICIResearchPerspective,20(5):1–39. Ben-David, Itzhak, Francesco Franzoni, and Rabih Moussawi. 2018. “Do ETFs Increase Volatility?” TheJournalofFinance. Bhattacharya, Ayan, and Maureen O’Hara. 2017. “Can ETFs increase market fragility? EffectofinformationlinkagesinETFmarkets.” AvailableatSSRN. Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam. 2001. “Market liquidity andtradingactivity.” Thejournaloffinance,56(2):501–530. Dannhauser, Caitlin D. 2017. “The impact of innovation: Evidence from corporate bond exchange-tradedfunds(ETFs).” JournalofFinancialEconomics,125(3):537–560. Da,Zhi,andSophieShive. 2012.“Exchangetradedfundsandassetreturncorrelations.” EuropeanFinancialManagement. Deville, Laurent, and Fabrice Riva. 2007. “Liquidity and Arbitrage in Options Markets: ASurvivalAnalysisApproach.” ReviewofFinance,11(3):497–525. Dick-Nielsen,Jens.2012.“HowtocleanEnhancedTRACEData.”WorkingPaper,CopenhagenBusinessSchool. Engle,RobertF,andDebojyotiSarkar.2006.“Premiums-DiscountsandExchangeTraded Funds.” TheJournalofDerivatives,13(4):27–45. 25

Flannery, Mark, Mahendrarajah Nimalendran, Sugata Ray, and Amir Yousefi. 2017. “UsingETFPremiatoMeasureCorporateBondLiquidity.” Foucault, Thierry, Roman Kozhan, and Wing Wah Tham. 2017. “Toxic arbitrage.” The ReviewofFinancialStudies,30(4):1053–1094. Glosten,Lawrence,SureshNallareddy,andYuanZou. 2016.“ETFactivityandinformationalefficiencyofunderlyingsecurities.” Hamm,SophiaJW. 2014.“TheeffectofETFsonstockliquidity.” Hasbrouck,Joel.2003.“IntradaypriceformationinUSequityindexmarkets.”TheJournal ofFinance,58(6):2375–2400. Holden, Craig W. 1995. “Index arbitrage as cross-sectional market making.” Journal of FuturesMarkets,15(4):423–455. Israeli, Doron, Charles MC Lee, and Suhas A Sridharan. 2017. “Is there a dark side to exchange traded funds? An information perspective.” Review of Accounting Studies, 22(3):1048–1083. Kumar,Praveen,andDuaneJSeppi.1994.“InformationandIndexArbitrage.”TheJournal ofBusiness,67(4):481–509. Lee, Chales M. C., and Mark J. Ready. 1991. “Inferring Trade Direction from Intraday Data.” JournalofFinance,46(2):733–746. Lettau, Martin, and Ananth Madhavan. 2018. “Exchange-Traded Funds 101 for Economists.” JournalofEconomicPerspectives,32(1):135–54. Madhavan, Ananth, and Sobczyk Aleksander. 2016. “Price Dynamics and Liquidity of Exchange-tradedFunds.” JournalofInvestmentManagement,14(2):1–17. Markit North America, Inc. n.d.. “Exchange Traded Product (ETP) Encyclopedia and TradeData(viaSOLAplatform).” http://www.markit.com/Product/SOLA. New York Stock Exchange. n.d.. “Daily TAQ (Historical Trades & Quotes), Wharton ResearchDataServices.” http://wrds-web.wharton.upenn.edu/wrds/. Pan,Kevin,andYaoZeng. 2017.“ETFarbitrageunderliquiditymismatch.” 26

Roll,Richard,EduardoSchwartz,andAvanidharSubrahmanyam. 2007.“Liquidityand the law of one price: the case of the futures-cash basis.” The Journal of Finance, 62(5):2201–2234. Rösch,Dominik. 2018.“Theimpactofarbitrageonmarketliquidity.”mimeo. Sag˘lam, Mehmet, Tugkan Tuzun, and Russ Wermers. 2018. “Do ETFs Increase Liquidity?” 27

Appendix A ETF Categories Thisappendixdescribesthedefinitionofour2ETFassetclassesusingMorningstarinformation. Fundsclassifiedindomesticequitiescorrespondtoequityfundsthatarenotinternationalfunds. Equityfundscorrespondtofundswherevariable‘globalbroadcategorygroup’equals‘Equity’or wherevariable‘morningstarcategory’equals‘PreferredStock’. Weconsiderequityfundstoinvest internationally if ‘group US category’ equal ‘International Equity’, or if ‘category morningstar’ containsanyofthefollowingstrings: ‘USFundChina’,‘USFundDiversifiedEmergingMarkets’, orif‘categorymorningstarinstitutional’containsanyofthefollowingstrings: ‘EmergingEurope’, ‘LatinAmerica’,‘Pacific/Asia’,‘India’,‘DiversifiedEmergingMarkets,’‘World’,‘Foreign’. Domesticbondfundsarecomprisedofinvestmentgradeandhighyieldbondfunds. Theformer we identify with the funds where variable ‘category Morningstar’ contains any of the following strings: ‘US Fund Short-Term Bond’, ‘US Fund Ultrashort Bond’, ‘US Fund Intermediate-Term Bond’, ‘US Fund Long-Term Bond’, ‘US Fund Corporate Bond’. The latter corresponds to funds with‘categoryMorningstar’equalto‘USFundHighYieldBond’. B Calculation of Basket-level Effective Spreads WeuseMarkitETFdatatolinkportfolioconstituentsandETFs. FromMarkitETFweobtaindaily portfolio composition files that, for each ETF, list the units of each security in basket b = T,C,R. Consideringhenotationintroducedinthepaperweintroducethefollowingfilterstoensurethat effective spreads for each basket and ultimately our ETF portfolio measure are good proxies of the actual effective spreads that prevailed on a given day. Let Ω = ω , i.e., the sum of ibt j ∈Jibt ibjt portfolioweightsdefinedinequation(2). Missingweightsareignoredortreatedaszeroes. Missing P weightsmayreflectthatconstituentpriceinformationisunavailablefromTAQorTRACE,orthat wecannotcomputeNAVastheratioofassetsundermanagementandsharesoutstandingusing MarkitETFinformation. Ourfirstfilteristhatwedropbasket-leveleffectivespreadsif Ω < 0.5 ibt orΩ > 1.25. Inaddition,letΩ = (Ω +Ω )/2,i.e.,theaveragesumofweightsforthecreation ibt it iCt iRt and redemption baskets. Then, our second filter is that we drop observations were this average sumofweightsΩ < 0.75orΩ > 1.25. it it In addition, we filter ETFs with less than 35 days in our sample after filtering on Ω and it requiringthatinformationisavailablefortheETFpremium,theETFeffectivespread,andtheETF portfoliospread. C Calculation of Securities’ Effective Spreads Thisappendixprovidesadditionaldetailsabouthoweffectivespreadsarecalculatedforindividual securities: ETFsharesandETFconstituents. 28

C.1 Effective Spread of ETFs and Stock Constituents WetreatbothETFandstockconstituentsasstockstocomputetheireffectivespreads. Information on secondary market stock transactions is from DTAQ. First, we sign each trade aggressive and passivebasedontheLeeandReady(1991)algorithmbychoosingcontemporaneousbestbidand bestaskpricesonemillisecondprior. Second,wecomputetheeffectivehalf spreadasthedifference between the transaction price and the mid-point of the best bid and ask prices as a ratio of the mid-pointofthebestbidandaskprices: TransactionPrice MidPointPrice BuySideHalfSpread = − (C.7) MidpointPrice MidPointPrice TransactionPrice SellSideHalfSpread = − (C.8) MidpointPrice Ourstockeffectivespreadmeasureistwicethedailyvolume-weightedaverageoftheseeffectivehalf spreads. nSize HalfSpread Ef fectiveSpread = 2 i i × i (C.9) Stock ∗ Volume P whereSize isthesizeofthetransaction iandvolumeisthesumofalldailytransactionvolume. i C.2 Effective Spread of Bond Constituents Information of corporate bond transactions is from the Enhanced TRACE. After we clean the Enhanced Trace following Dick-Nielsen (2012), we select the customers-to-dealer and dealer-todealer trades. First, we compute the dollar effective spreads as daily volume-weighted prices of customer buy and customer sell transactions. Second, we compute the inter-dealer transaction pricesasdailyaveragepriceofdealer-to-dealertransactions. Ourcorporatebondeffectivespread measureistheratioofdollareffectivespreadstotheinter-dealertransactionprices. CustomerBuyPrice CustomerSellPrice Ef fectiveSpread = − (C.10) Bond InterDealerTransactionPrice 29

Tables and Figures Table1: SummaryStatistics Mean Std Min Max ETFs Obs ALL PortfolioSpread 15.57 18.84 1.41 165.38 584 408,960 ETFSpread 12.28 13.26 1.08 111.11 584 408,960 Mispricing 10.84 14.96 0.00 141.08 584 408,960 DomesticEquity PortfolioSpread 10.72 7.46 2.86 43.98 509 366,069 ETFSpread 12.07 12.83 1.22 89.17 509 366,069 Mispricing 8.44 10.47 0.00 58.34 509 366,069 BondETFs PortfolioSpread 56.96 31.55 1.41 165.38 75 42,891 ETFSpread 14.04 16.37 1.08 111.11 75 42,891 Mispricing 31.26 27.05 0.00 141.08 75 42,891 The table reports the summary statistics of ETF spread, portfolio spread and mispricing for U.S. ETFs. As defined in equation 2, portfolio spread is the weightedeffectivespreadsofETFconstituents. Forbondconstituents,FINRA TRACEisusedtocalculatetheeffectivespreads. Effectivespreadofbondsare simple the volume-weighted difference of customer buy and sell transactions asapercentofinter-dealertransactionprices. ForstocksconstituentsandETF Spreads, NYSE DTAQ is used to calculate the effective spreads by following Lee-Ready algorithm. ETF mispricing is the absolute value of the difference between ETF market price and ETF netasset value from Morningstar Direct. Allvariablesareinbasispoints. Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 30

Table2: Mean-reversionofETFMispricing PanelA:Basic Statistics μ i AllETFs EquityETFs Bond ETFs Mean -0.79 -0.85 -0.40 Std 0.19 0.11 0.19 ETFs 584 509 75 PanelB:Correlationof μ with Illiquidity i AllETFs EquityETFs Bond ETFs ETFSpread 0.08 0.13 -0.09 (0.07) (0.00) (0.45) PortfolioSpread 0.63 -0.03 0.22 (0.00) (0.48) (0.05) We estimate the mean-reversion coefficient, μ, of ETF Mispricing from the i belowregressionforeachETF: ΔMispricing = α +μ Mispricing +(cid:15) it i i i,t 1 it − whereMispricing istheabsolutevalueofthelogdifferencebetweenpriceand it NAV of ETF i. Number in parenthesis report the significance level of each correlationcoefficient. Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 31

Table3: Pre-FilteringRegressions: EquityETFs ETFSpread PortfolioSpread Mispricing Coeff. t-statistic Coeff. t-statistic Coeff. t-statistic Trend -0.71 -23.62 0.05 3.60 -2.32 -83.96 Trend2 -0.20 -5.44 0.05 2.92 0.34 9.94 Pre-holidayDummy 1.11 8.56 1.60 25.65 0.65 5.45 Tuesday -0.85 -17.01 0.10 4.17 Wednesday -0.71 -14.32 0.15 6.09 Thursday -0.77 -15.37 0.12 4.91 Friday -0.55 -10.97 1.97 81.87 0.15 4.31 February -0.28 -3.27 -0.77 -18.88 -0.38 -4.83 March -0.72 -9.00 -0.90 -23.48 -0.55 -7.40 April -0.61 -7.23 -0.74 -18.47 -0.36 -4.68 May -0.80 -9.74 -0.70 -17.81 -0.31 -4.12 June -0.43 -5.18 -0.71 -17.99 0.49 6.46 July -0.61 -7.43 -0.63 -16.06 -0.78 -10.36 August -0.75 -9.03 -0.70 -17.55 -0.57 -7.45 September -0.90 -11.01 -0.94 -24.01 -0.12 -1.54 October -0.51 -6.23 -0.58 -14.66 -0.07 -0.94 November -0.30 -3.49 -0.01 -0.27 -0.26 -3.33 December -0.25 -3.05 0.26 6.67 0.31 4.09 ETFFixedEffects Yes Yes Yes #ofETFs 509 509 509 #ofobs 366,069 366,069 366,069 AdjR-squared 0.46 0.63 0.31 The table reports the regression results of the filtering regressions on the variables for equity ETFs. Trend is a time-trend variable going from -1 at the beginningofthesampleto1attheendofthesampleandquadratictimetrend variable is equal to (Trend2 1)/2. Pre-holiday is a dummy variable, taking − a value of 1 if it is one business day before a holiday. Tuesday, Wednesday, Thursday,Friday,February,March,April,May,June,July,August,September, October,November,Decemberaredayandmonthdummyvariables. Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 32

Table4: Pre-FilteringRegressions: BondETFs ETFSpread PortfolioSpread Mispricing Coeff. t-statistic Coeff. t-statistic Coeff. t-statistic Trend -3.57 -29.04 -16.98 -96.15 -12.76 -51.99 Trend2 -3.38 -25.07 5.94 30.67 3.09 11.46 Pre-holidayDummy 1.22 2.75 2.19 3.44 0.89 1.01 Tuesday -0.54 -3.12 0.42 1.70 Wednesday -0.29 -1.69 -1.09 -4.41 Thursday -0.21 -1.20 -1.63 -6.57 Friday 0.03 0.16 -1.46 -5.88 0.18 0.66 February 0.98 3.14 2.89 6.43 2.44 3.92 March 0.11 0.39 1.96 4.66 2.13 3.65 April -0.63 -2.08 -0.68 -1.56 -0.41 -0.67 May -0.41 -1.40 -0.42 -1.01 -1.97 -3.39 June 1.60 5.44 3.36 7.92 0.60 1.02 July 1.82 6.20 2.50 5.91 1.52 2.59 August 0.43 1.47 3.42 8.07 0.30 0.52 September 0.77 2.57 0.82 1.90 0.42 0.70 October 0.77 2.57 1.00 2.31 -0.43 -0.71 November 0.54 1.70 1.49 3.27 -1.63 -2.59 December 1.59 5.20 4.12 9.39 -0.28 -0.46 ETFFixedEffects Yes Yes Yes #ofETFs 75 75 75 #ofobs 42,891 42,891 42,891 AdjR-squared 0.54 0.74 0.32 The table reports the regression results of the filtering regressions on the variables for bond ETFs. Trend is a time-trend variable going from -1 at the beginningofthesampleto1attheendofthesampleandquadratictimetrend variable is equal to (Trend2 1)/2. Pre-holiday is a dummy variable, taking − a value of 1 if it is one business day before a holiday. Tuesday, Wednesday, Thursday,Friday,February,March,April,May,June,July,August,September, October,November,Decemberaredayandmonthdummyvariables. Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 33

Table5: CorrelationCoefficientsofAdjustedVariables Equity ETFs Mispricing∗ PortfolioSpread∗ ETFSpread∗ Mispricing∗ 1.00 PortfolioSpread∗ 0.16 1.00 ETFSpread∗ 0.45 0.22 1.00 Bond ETFs Mispricing∗ PortfolioSpread∗ ETFSpread∗ Mispricing∗ 1.00 PortfolioSpread∗ 0.28 1.00 ETFSpread∗ 0.41 0.11 1.00 The table reports the correlation coefficients of the ETF variables after the filteringregressions. Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 34

Table6: PVAR:DomesticEquityETFs DomesticEquity Mispricing∗ PortfolioSpread∗ ETFSpread∗ Coeff. t-stat Coeff. t-stat Coeff. t-stat Mispricing∗ L1. 0.10 32.66 0.00 2.24 0.04 14.81 L2. 0.08 25.80 0.00 1.28 0.03 9.17 L3. 0.07 23.17 0.00 1.09 0.02 8.32 L4. 0.07 23.93 0.00 -3.31 0.02 6.05 L5. 0.07 22.37 0.00 -3.18 0.02 6.90 PortfolioSpread∗ L1. 0.00 0.25 0.27 79.59 0.01 1.53 L2. 0.00 0.23 0.18 57.06 0.00 0.59 L3. 0.01 2.18 0.15 51.56 0.00 -0.37 L4. 0.00 0.89 0.14 50.71 -0.02 -3.33 L5. 0.01 2.23 0.10 33.92 -0.01 -1.06 ETFSpread∗ L1. 0.03 11.94 0.00 1.15 0.12 34.33 L2. 0.03 12.89 0.00 2.06 0.10 30.65 L3. 0.03 11.42 0.00 -3.13 0.09 25.41 L4. 0.02 8.50 0.00 -3.49 0.08 24.30 L5. 0.03 10.17 0.00 0.39 0.08 25.04 #obs 366,069 ETFs 509 Average#ofdaysforanETF 719.19 ThetablereportstheestimationresultsforequityETFsfromthePVARanalysis describedinequation 6. Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 35

Table7: PVAR:BondETFs BondETFs Mispricing∗ PortfolioSpread∗ ETFSpread∗ Coeff. t-stat Coeff. t-stat Coeff. t-stat Mispricing∗ L1. 0.36 43.08 0.02 3.62 0.02 3.97 L2. 0.20 24.27 0.00 0.92 0.01 1.16 L3. 0.13 15.70 0.00 0.41 0.01 1.31 L4. 0.08 9.96 0.00 0.06 0.00 0.41 L5. 0.09 11.47 0.01 1.96 0.00 -0.25 PortfolioSpread∗ L1. 0.02 2.86 0.28 33.65 0.01 2.07 L2. 0.00 -0.58 0.19 24.70 0.00 1.02 L3. 0.00 0.48 0.16 20.48 0.00 0.67 L4. 0.01 1.24 0.13 17.52 0.00 -0.50 L5. 0.01 1.94 0.17 22.06 0.00 0.93 ETFSpread∗ L1. 0.05 3.78 0.01 1.01 0.25 21.97 L2. 0.01 0.82 -0.01 -0.79 0.15 13.32 L3. 0.03 2.02 0.00 -0.72 0.11 10.78 L4. 0.00 0.27 0.01 1.12 0.09 9.12 L5. 0.00 0.08 -0.01 -1.57 0.09 8.59 #obs 42,891 ETFs 75 Average#ofdaysforanETF 571.88 ThetablereportstheestimationresultsforbondETFsfromthePVARanalysis describedinequation 6. Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 36

Table8: CorrelationCoefficientsofInnovationsfromPVAR Equity ETFs Mispricing∗ PortfolioSpread∗ ETFSpread∗ Mispricing∗ 1.00 PortfolioSpread∗ 0.01 1.00 ETFSpread∗ 0.08 0.03 1.00 Bond ETFs Mispricing∗ PortfolioSpread∗ ETFSpread∗ Mispricing∗ 1.00 PortfolioSpread∗ 0.01 1.00 ETFSpread∗ 0.09 0.01 1.00 Thetablereportsthecorrelationcoefficientsfortheorthogonalizedinnovations fromthePVARanalysisdescribedinequation 6. Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 37

ytilasuaCregnarG :9elbaT sFTE ytiuqEcitsemoD:AlenaP ∗daerpSFTE ∗daerpSoiloftroP ∗gnicirpsiM eulav-p erauqSihC eulav-p erauqSihC eulav-p erauqSihC 10.0 72.61 10.0 15.51 ∗daerpSoiloftroP 00.0 04.03 00.0 18.064 ∗daerpSFTE 00.0 55.024 00.0 74.03 ∗gnicirpsiM 00.0 82.654 00.0 14.26 00.0 76.274 LLA sFTE dnoB:BlenaP ∗daerpSFTE ∗daerpSoiloftroP ∗gnicirpsiM eulav-p erauqSihC eulav-p erauqSihC eulav-p erauqSihC 00.0 48.91 00.0 89.72 ∗daerpSoiloftroP 63.0 74.5 00.0 33.91 ∗daerpSFTE 00.0 15.66 00.0 41.55 ∗gnicirpsiM 00.0 46.901 00.0 62.26 00.0 88.64 LLA ehT .6 noitauqe ni debircsed sisylana RAVP eht morf stluser tset ytilasuac-regnarG eht stroper elbat ehT .elbairavnmulocehtesuac-regnarGtonseodelbairavworehttahtsisisehtopyhllun .ratsgninroMdna,ECART,QATD,.cnI,aciremAhtroNtikraMnodesabnoitarobalenwO :ecruoS 38

Figure1: ETFArbitragewithoutTransactionCosts. p creationorder in-kindexchange arbitrage 100 profits ETF 99 holdings 98 0 10:00am 4:30pm t Figure2: ETFArbitragewithTransactionCosts. p creationorder in-kindexchange arbitrage profits 100 constituents’ask ETFask 99 ETFbid constituents’bid 98 0 10:00am 4:30pm t 39

Figure3: DistributionofFractionofDayswithEqualBaskets (a)EquityETFs Fraction of Days by ETF ytisneD 0.0 0.2 0.4 0.6 0.8 1.0 8.0 4.0 0.0 (b)BondETFs T==C==R fraction C==R Fraction of Days by ETF ytisneD 0.0 0.2 0.4 0.6 0.8 1.0 8.0 4.0 0.0 T==C==R fraction C==R Blue bars denote the distribution of the fraction of days the creation (C), redemption (R), and tracking (T) baskets are all equal. Red bars represent the fractionoftheseobservationswheretheCandRbasketsareequal. Source: OwnelaborationbasedonMarkitNorthAmerica,Inc. 40

Figure4: DomesticEquity: DistributionofETFPremium,andETFandPortfolioSpreads (a)ETFMispricing (b)ETFSpread (c)PortfolioSpread Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 41

Figure5: DomesticBonds: DistributionofETFPremium,andETFandPortfolioSpreads (a)ETFMispricing (b)ETFSpread (c)PortfolioSpread Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 42

Figure 6: Equity ETFs: Impulse Response Functions ETF Spread* : ETF Spread* ETF Spread* : Portfolio Spread* ETF Spread* : Mispricing* 10 .6 .1 .4 5 .05 .2 0 0 0 Portfolio Spread* : ETF Spread* Portfolio Spread* : Portfolio Spread* Portfolio Spread* : Mispricing* .1 .05 3 .05 0 2 -.05 1 0 -.1 0 -.05 Mispricing* : ETF Spread* Mispricing* : Portfolio Spread* Mispricing* : Mispricing* .8 .04 8 .6 .02 6 .4 4 0 .2 2 -.02 0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 step 95% CI Orthogonalized IRF impulse : response The figure reports the orthogonalized impulse-response functions for equity ETFsfromthePVARanalysisdescribedinequation 6. Shadedareasrepresent the95percentconfidencebandsusing1,000MonteCarloreplications. Source: Own elaboration based on IHS Markit ETF, TAQ, TRACE, and Morningstar. 43

Figure 7: Bond ETFs: Impulse Response Functions ETF Spread* : ETF Spread* ETF Spread* : Portfolio Spread* ETF Spread* : Mispricing* 10 .4 1 .2 5 .5 0 0 -.2 0 Portfolio Spread* : ETF Spread* Portfolio Spread* : Portfolio Spread* Portfolio Spread* : Mispricing* 15 1.5 .3 10 1 .2 .1 5 .5 0 0 0 Mispricing* : ETF Spread* Mispricing* : Portfolio Spread* Mispricing* : Mispricing* 1 1 15 10 .5 .5 5 0 0 0 0 50 100 0 50 100 0 50 100 step 95% CI Orthogonalized IRF impulse : response The figure reports the orthogonalized impulse-response functions for bond ETFs from the PVAR analysis described in equation 6. The shaded areas representthe95percentconfidencebandsusing1,000MonteCarloreplications. Source: Own elaboration based on IHS Markit ETF, TAQ, TRACE, and Morningstar. 44

Figure8: IRF:ComparisonofEquityandBondETFs ETF Spread* : ETF Spread* ETF Spread* : Portfolio Spread* ETF Spread* : Mispricing* 30 0.4 2 0.3 1.5 20 0.2 1 10 0.1 0.5 0 0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Portfolio Spread* : ETF Spread* Portfolio Spread* : Portfolio Spread* Portfolio Spread* : Mispricing* 0.6 30 1.8 0.4 20 1.2 0.2 0 10 0.6 -0.2 -0.4 0 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 Mispricing* : ETF Spread* Mispricing* : Portfolio Spread* Mispricing* : Mispricing* 1.4 30 2 1 20 0.6 1 10 0.2 0 -0.2 0 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 IMPULSE : RESPONSE EQUITY BOND The figure reports the orthogonalized impulse-response functions for equity (blue)andbond(red)ETFsfromthePVARanalysisdescribedinequation 6. Source: OwnelaborationbasedonMarkitNorthAmerica,Inc.,DTAQ,TRACE, andMorningstar. 45