Trading Costs v. Indicative Liquidity in the Off-the-Run Treasury Market

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Trading Costs v. Indicative Liquidity in the Off-the-Run Treasury Market Oleg Sokolinskiy 2025-049 Please cite this paper as: Sokolinskiy, Oleg (2025). “Trading Costs v. Indicative Liquidity in the Off-the-Run Treasury Market,” Finance and Economics Discussion Series 2025-049. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2025.049. 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.

Trading Costs v. Indicative Liquidity in the Off-the-Run Treasury Market * OlegSokolinskiy† July7,2025 Abstract Thispaperestimatestradingcostsintheoff-the-runTreasurymarketusingcomprehensivetransactionsdataandmachinelearningtechniques.Theanalysisrevealsseveral keyfindingsthatenhancetheunderstandingoftheoff-the-runTreasurymarketliquidity.First,theindicativebid-askspreadisshowntobeabiasedmeasureofliquidity,even when not considering transaction volume. Specifically, bid-ask spreads systematically overstatetradingcostsofmoreseasonedTreasuries,andtheliquidityofbenchmark,onthe-runsecuritiesaffectshowoff-the-runbid-askspreadsmaptotradingcosts. Second, thepaperdemonstratesthattradingcostsmayscalenon-monotonicallywithtransaction volume,whichsuggestsselective,opportunisticliquidity-taking. Additionally,transactionsizehasgreatereffectonoff-the-runsecurities’tradingcostswhenbenchmark,onthe-runliquidityislower.Finally,indicativebid-askspreadsmaynotablyoverstatetrading costs for larger orders of relatively less liquid securities. These findings contribute toourunderstandingofactualliquidityintheoff-the-runTreasurymarket,whilehighlightingthelimitationsofatraditionalliquiditymeasure. Byprovidingamorenuanced view of trading costs, this study contributes valuable insights for supporting financial stabilityandoptimalassetallocation. Keywords: liquidity,Treasurymarket,off-the-run,effectivebid-askspread JELcodes: G10,G12 *This article represents the views of the author, and should not be interpreted as reflecting the views of theBoardofGovernorsoftheFederalReserveSystemorothermembersofitsstaff. Iamgratefulforhelpful commentsfromanddiscussionswithDavidBowman,DobrislavDobrev,MaximilianDunn,SebastianInfante Bilbao,PeterJohansson,DonKim,EdithLiu,AndrewMeldrum,MariusRodriguez,andMinWei. †BoardofGovernorsoftheFederalReserveSystem.Email:oleg.v.sokolinskiy@frb.gov 1

1 Introduction TheU.S.Treasurymarketisthedeepestfixedincomemarketintheworld. Marketliquidity –abilitytotransactsignificantamountswithouttemporarilydislocatingprices–allowsthe Treasurymarkettoserveasabenchmarkforvaluationandasourceofnearrisk-freecollateral. However,TreasurymarketfunctioningbecameaconcernattheheightoftheCOVID-19 crisis(e.g., see Logan,2020;FlemingandRuela,2020;Duffieetal.,2023).1 TheMarch2023 SVBcollapseandtheApril2025tradetensionsledtotwomoreepisodesofseverelystrained Treasurymarketliquidity. Furthermore,thesupplyofTreasurysecuritieshasbeenincreasing relative to the primary dealers’ ability to intermediate in this market (see Duffie, 2023, 2025). Asaresult,thefunctioningoftheTreasurymarketislikelytoremainakeyfocusfor bothregulatorsandinvestors. TheTreasurymarkethastwomajorsegmentsthatdifferintheirmicrostructureand,consequently, liquidity. First, there are on-the-run Treasuries – most recently-issued securities for a given maturity date. On-the-run Treasuries have much higher trading volumes than other Treasuries, with a significant proportion of trades being on centralized markets with firmquotes.2 However,on-the-runTreasuriesareonlyasmallfractionofthenotionalofall outstanding marketable Treasury debt. Second, there are off-the-run Treasuries – all Treasurysecuritiesthatarenoton-the-run. Incontrasttoon-the-runsecurities,off-the-runTreasuries trade infrequently in a decentralized, bilateral market providing indicative quotes.3 Due to this microstructure of the off-the-run Treasury market, its liquidity is difficult to gauge. Inthispaper,Isuggestanestimateoftheeffectivethebid-askspreadmeasure(seeDem- 1Adrianetal.(2025)considersTreasurymarketliquidityoveralongertimelinestartingfromtheGFC. 2A firm quote with an associated volume is a commitment of a liquidity provider to trade in that size if requestedtodoso. 3Indicativequotesarenotfirmcommitmentstotrade,andthepriceofapotentialtradeismaybesetupon furthernegotiations. 2

setz, 1968) for the off-the-run Treasury market liquidity largely based on actual trades.4 The core components of the suggested method for the assessment of actual trading costs intheoff-the-runTreasurymarketare(i)relianceonoff-the-runTreasuries’transactiondata along with firm quotes for on-the-run Treasuries and (ii) state-of-the-art machine learning approach to fitting the term structure of benchmark, on-the-run rates. The method relies ontheon-the-runTreasuries’quotesasthesourceofmostrecentinformationonchangesin thebenchmarkinterestratetermstructure. Inturn,periodicsnapshotsofindicativequotes enabletheestimationofidiosyncraticpricecomponentsofparticularoff-the-runsecurities. Themachinelearning-basedmethodofFilipovic´ etal.(2022)forfittingthetermstructureof interest rates – the second critical component of the suggested method – delivers sufficient accuracyandstabilitytoestimatethetermstructureofbenchmark,on-the-runratesateach momentwhenatradeinanoff-the-runsecurityoccurs.5 Havingconstructedameasureoftradingcostsforoff-the-runTreasuries,Iexplorehowit deviatesfromindicativeliquidity. First,Idocumentbiasesinindicativebid-askspreadsthat are unconditional on transaction volume. In particular, indicative bid-ask spreads tend to systemicallyoverstatetradingcostsformoreseasonedsecurities. Anotherbiasofindicative bid-askspreadsresultsfromtheirfailuretoreflectbenchmark, on-the-runTreasurymarket liquidity. When benchmark, on-the-run liquidity is degraded, indicative bid-ask spreads foroff-the-runsecuritiestranslateintogreatertradingcosts. Thisbiasisofparticularsignificanceforassessingfinancialstability–amarketdysfunctionresultingfromprohibitivetrading costs in the off-the-run Treasury market may occur at lower off-the-run bid-ask spread levelsthanasimplerlinearregressionmodelmaysuggest. Second, overcoming the inherent limitation of indicative quotes, I explore the effect of transaction size on price. While indicative bid-ask spreads do not provide information on 4Bid-askspreadisthedifferencebetweenthelowestpriceatwhichasecuritymaybeboughtandthehighest priceatwhichthesecuritymaybesold. 5SubjecttoconsideringtradesthatoccurduringtheBrokerTecplatform’sactivehours. 3

how trading costs scale with the size of an order, effective bid-ask spreads are associated withparticulartransactionvolumes. Withinanon-parametricframeworkformodelinghow tradingcostsvarywithtransactionvolume,Iestimatethecorrespondingscalinglawsconditionaloneitherbenchmarkliquidityorrelativeliquidityofthespecificoff-the-runsecurity. I show how the effect of volume on trading costs in the off-the-run market varies with the liquidity conditions in the benchmark, on-the-run Treasury market: worse benchmark liquiditytranslatesintohighertradingcostsintheoff-the-runmarket,evencontrollingforthe correspondingly wider off-the-run securities’ indicative bid-ask spreads. Finally, I demonstratethatindicativebid-askspreadsmaynotablyoverstateexpectedtradingcostsforlarger transaction volumes of relatively less liquid off-the-run securities. More generally, I obtain evidenceinfavorofselectiveliquiditytaking–endogeneityoftradinginresponsetoavailableliquidity. Literature In the remainder of this section, I place this paper within the framework of the existent research. In particular, there are three strands of research that this paper contributes to: (i) liquidity measurement in the decentralized, bilateral Treasury off-the-run market; (ii) differences between indicative and actual liquidity; and (iii) scaling of trading costs with transactionvolume. First,thesuggestedmethodforthecalculationoftheeffectivebid-askspreadcontributes to the literature on liquidity measurement in the off-the-run Treasury market. The opacity of the off-the-run Treasury market shifted research focus to the liquidity in the on-the-run Treasurymarket,forwhichthereisampleexcellentresearchbyFleming(2001)amongothers. Incontrast,liquidityintheoff-the-runmarketisthesubjectoffarfewerstudies. Dueto sparsenessoftradesinspecificoff-the-runTreasuries,theindicativebid-askspread(orsome transform thereof) is a prominent measure of Treasury market liquidity, as in Pasquariello 4

and Vega (2009) and Goyenko et al. (2011). Another strand of literature relies on liquidity measuresthataremoresimilartopriceimpact. Amongthesepapers, Babbeletal.(2004)is conceptually closest to the approach I adopt in this paper. Babbel et al. introduces a price pressuremeasureintheoff-the-runTreasurymarket,whichisthedifferencebetweenasynthetic‘on-the-runprice’–priceofthesecurityobtainedbydiscountingcashflowsusingthe interestratetermstructurefromon-the-runTreasuries–andtheactualtradepriceforrelatively low volume transactions. Similar to Babbel et al., I also use on-the-run Treasuries as thebenchmarkformostup-to-datepricing,butfitthetermstructureusingthemoreflexible model of Filipovic´ et al. (2022) instead of the Nelson and Siegel (1987) parametric model.6 The approach of Babbel et al. also relies on the identification of whether the trade was initiated by the buy or sell side based on the assumption that $1mm trades have a negligible effective bid-ask spread. In contrast, using indicative quotes I circumvent the necessity to identify the trade-initiating side and, instead, directly estimate the spread between cash flow equivalent on- and off-the-run securities. Among other papers in the strand of literaturegoingbeyondindicativebid-askspreadsareFurfineandRemolona(2002)andDiazand Escribano (2017). Furfine and Remolona uses the Hasbrouck (1991) price impact measure toestimateliquidityoverlongerperiodsbasedondailyreturns. DiazandEscribanousesa setofmeasuresincludingtheAmihud(2002)measureandtheirversionoftheJankowitsch etal.(2011)dispersionmeasure. Finally,thespreadbetweenon-andoff-the-runTreasuries iscommonlyreferredtoastheliquiditypremium,asinDiazandEscribano. However,this spreadcapturesnotonlyliquiditybutdifferingfinancingcostsofon-andoff-the-runsecurities,(Krishnamurthy,2002),aswellasrepocounterpartyrisk,(LiuandWu,2017). Second,thispapercontributestotheliteratureondifferencesinindicativeandactualliquidity. Inequitymarkets,BlumeandGoldstein(1992)demonstratesnotabledifferencesbetweentheeffectiveanddisplayedspread,withthedifferencesbeingaffectedbytheposted 6Andersen(2007)arguesthatparametricmodelsdonotallowforsufficientflexibilityandarenotincommon usebymarketmakers–acriticalrequirementforobtainingabenchmark,on-the-runinterestratetermstructure. 5

volume available at the quotes. In the market for collateralized loan obligations, Hendershott et al. (2024) shows that indicative quotes in over-the-counter markets may lead to an overestimate of available liquidity when failed attempts to trade are ignored. In this paper, I uncover several biases in indicative bid-ask spreads. In particular, indicative bid-ask spreads overestimate trading costs for seasoned and relatively less liquid securities. Moreover, I show that reliance on the regular relationship between indicative and effective bidask spreads leads to an underestimate of the liquidity deterioration in the off-the-run Treasury market during periods of low benchmark, on-the-run Treasury market liquidity. This evidence augments the results in Furfine and Remolona (2002) that off-the-run securities’ liquidity – as measured by price impact – deteriorates proportionately more than on-therunsecurities’liquidityduringperiodsofmarketstress. Finally, this paper contributes to research on how trading costs scale with transacted volume in decentralized, bilateral markets. The majority of existent empirical results are for CLOB-driven markets, with the notable exception of Babbel et al. (2004). Bouchaud et al. (2009), Farmer et al. (2006), and Lillo and Farmer (2004) among others find that trading costs are non-linear in transaction volume. A notable distinction of this paper from most empirical studies in the field is that I allow for the scaling law to vary with market conditions and relative liquidity of the security. Therefore, I consider conditional scaling laws. Furthermore, I find evidence in support of selective liquidity taking – large trades get executedwhenliquidityishigh. ThisfindingcomplementsHendershottetal.(2024)thatdraws attentiontounobservedfailedtradeswhenavailableliquidityislow. The rest of the paper is organized as follows. In Section 2, I suggest a method for calculating the effective bid-ask spread for off-the-run Treasuries. In Section 3, I explore the relationshipbetweenactualandindicativeliquiditybycomparingthestatisticalproperties of effective bid-ask spreads and price improvements relative to indicative bid-ask spreads. 6

In conclusion of that section, I identify various biases in indicative bid-ask spreads using thelinearmixedeffectsmodelingframework. InSection4,Iextendthelinearmixedeffects modeltoobtainscalinglawsfortheconditionaldependenceoftheeffectivebid-askspread ontransactedvolume. Iallowthescalingwithvolumetodependonbenchmark,on-the-run TreasurymarketliquidityinSection4.1andonrelativeliquiditycharacteristicsofsecurities in Section 4.2. In Section 5, I reiterate the main results of the paper and suggest topics for further research. Finally, in a series of appendices, I provide some background details, as well as explore the robustness and extensions of results to various closely related Treasury marketsegments. InAppendixAIprovideabriefoverviewofon-andoff-the-runTreasury market microstructure. Then, I consider (i) the effect of Alternative Trading Systems (ATS) intermediationonliquidityinAppendixB,(ii)interconnectednessofliquidityinthedealerto-client and dealer-to-dealer segments in Appendix C, and (iii) execution quality of retail clients’tradesinAppendixD. 2 Effective Bid-Ask Spread for Off-the-Run Treasuries Themethodologicalframeworkofthispaperhastwocomponents–(i)analgorithmforcalculatingtheeffectivebid-askspreadforoff-the-runTreasuries,and(ii)alinearmixedmodel frameworkthatallowsforrandomeffectsassociatedwitheachsecurity,whileenablingnonparametricexplorationofhowtheeffectivebid-askspreadscaleswithordersize. Icoverthe firstcomponentinthissectionanddeferthedescriptionofthemixedmodelingframework untilthetimeitisappliedinSection3.3. 2.1 AdvantagesoverCompetingMeasureofLiquidity Theeffectivebid-askspread(seeDemsetz,1968)isthedifferencebetweenthetradepriceof anassetanditsfairvalue. Thewidertheabsolutevalueoftheeffectivebid-askspread,the 7

greater the trading costs are.7 The effective bid-ask spread is a measure of actual, experienced liquidity for each individual transaction. Consequently, transaction characteristics – liketradedvolume–arelinkedtoeachobservationoftheeffectivebid-askspread. Theeffectivebid-askspreadhasthreemainadvantagesoverindicativebid-askspreads. First,theeffectivebid-askspreadisbasedonactualtransactionsandnotmereindicationsof whereagenerictradecouldoccur(absentpossiblenegotiations). Second, theeffectivebidaskspreadallowstheexplorationofhowtradingcostsscalewithvolume,whichisentirely latent in indicative bid-ask spreads. There may not be a precise order size associated with the quote. This is particularly the case for streamed quotes.8 In general, a ‘normal market size’mayserveastheimpliedpotentialtransactionvolume. However,whatis‘normal’may changedependingonmarketconditions. Finally,duetothebilateralnatureoftradinginthe off-the-runTreasurymarketandmultiplecompetingintermediaries,obtainingreliablebest indicative bid and ask prices for all off-the-run Treasuries may be prohibitively expensive evenforsomemarketparticipants. Insummary,marketmicrostructureconsiderationsfavor the effective bid-ask spread over the indicative bid-ask spread as a measure of liquidity in theoff-the-runTreasurymarket. The effective bid-ask spread is also a more fitting measure for off-the-run Treasury liquiditythanpriceimpact. Priceimpact–howmuchtradeororderflowofagivenmagnitude overasetexecutionhorizonaffectsthemarketprice–isaprominentmetricinCentralLimit Order Book (CLOB) markets.9 On CLOB-based platforms, market participants split their totaldesiredtransactionintomultiplesmallerchildordersthattheysubmitovertimewhile targetingaparticularaverageexecutionprice,withpossibleopportunisticdeviationsinresponse to the CLOB dynamics. This manner of execution is supported, if not required, by 7Undertheassumptionthatpositive(negative)differencebetweenthetradepriceofanassetanditsfundamentalvaluecorrespondstobuyer-initiated(seller-initiated)transactions. 8Asnotedabove,marketmakersmaystreamquotestoclientsviatheirin-houseplatformsorexternalAlternativeTradingSystems(ATS).Incontrasttotherequestforquote(RFQ)protocol,clientsdonotcontactdealers toobtainquotesand,thus,hidetheirinterestinapotentialtrade. 9BrokerTecplatformisaprominentexampleofaCLOB-basedmarketforon-the-runTreasuries. 8

the limited immediately available liquidity on the CLOB. In stark contrast, such execution would be considered a breach of expected behavior in the bilateral market for off-the-run Treasuries (see Wood, 2018). If a client splits a large order among multiple market makers, thepriceoftheassetislikelytomoveagainstthemarketmakersastheinformationsubsequentlysipsintothemarket. Ifaclientweretoengageinsuchordersplitting,itmayexpect toreceiveconsiderablylessfavorablequotesinitsfutureinteractionswithmarketmakers.10 Thus,theatomicnatureoftheeffectivebid-askspreadthatdoesnotincorporateflowsover aperiodoftimeismoresuitablefortheoff-the-runTreasuriesmarket. Inaddition,asnoted inHendershottetal.(2024),accurateestimationofpriceimpactatadailyfrequencyrequires moretransactionsthancommonlyoccurinmanyindividualoff-the-runTreasuries. 2.2 EstimationAlgorithm Theanalyticaldefinitionoftheeffectivebid-askspread,adaptedfromHagströmer(2021),is: (cid:16) (cid:17) 2D Ptrade−P fair , (1) i i,t i,t where Ptrade is the transaction price and P fair is the fair value of security i at time t; D is i,t i,t i equal to 1 for buyer-initiated and −1 for seller-initiated trades. The scaling by 2 expresses theeffectivebid-askspreadonthesamescaleastheindicativebid-askspread. Fortransaction prices I rely on the comprehensive Treasury Trade Reporting and Compliance Engine (TRACE) data from the Financial Industry Regulatory Authority (FINRA). Since Treasury TRACE data do not contain an explicit identifier of the side initiating a transaction, I make theassumptionthataggressivebuying(selling)leadstopositive(negative)deviationsofthe 10Thesamelogicdoesnotapplyincentralized,CLOB-basedmarkets. Whilethegradualexecutionofalarge orderwouldalsomovethepriceagainstmarketmakersthatprovidedliquidityfortheearlierchildorders,the anonymityonCLOB-basedmarketsdoesnotallowmarketmakerstoretaliateagainstclientsinfutureinteractionsbasedontheirpastbehavior. 9

tradepricefromthefairvalue,thatis,Iset: (cid:16) (cid:17) D := sign Ptrade−P fair . i i,t i,t In order to make the effective bid-ask spread comparable for securities of different maturities,Iintroducetheduration-normalizedeffectivebid-askspread: (cid:12) (cid:12) (cid:12)Ptrade−P fair(cid:12) (cid:12) i,t i,t (cid:12) EBA = 2· , (2) i,t duration i,t whereduration measuresthesensitivityofsecurityi’spricetochangesininterestratesat i,t time t (its modified duration multiplied by its price). Normalization by duration expresses the effective bid-ask spread in the yield space, rather than in the price space – durationnormalizedeffectivebid-askspreadistheparallelshiftoftheinterestratetermstructurethat wouldcausetwicethedollardifferencebetweenthetransactionpriceandthefairpriceofa security. Suchnormalizationoftheeffectivebid-askspreadbydurationenablescomparison and unified modeling of liquidity across the curve. For brevity, I henceforth refer to the duration-normalizedeffectivebid-askspreadinEq. (2)astheeffectivebid-askspread. While the definition of the effective bid-ask spread is straightforward, its estimation is complex. Thetradepriceisobserved,butthefairvaluehastobeestimated. Themostcommon estimate of the fair value is the mid-point between the best bid and ask quotes at the timeofthetrade. However,Hagströmer(2021)showsthatthisfairvalueestimatebiasesthe effective bid-ask spread measure. Moreover, unlike in the equity market, best bid and ask pricesareopaqueforoff-the-runTreasurysecurities. Tradinginoff-the-runTreasuriesisbilateralandrelativelyreliablequotesfromaspecificdealerareavailableonlyviatherequest forquoteprotocol;streamedquotestendtobeanotablyrougherindicationofprice.11 Thus, 11Clientscannotroutinelyrequestquotesfromtheentireuniverseofdealerstoassessthetruebestbidandask quotes. Requestingquoteswithoutacertainamountoftradingwouldviolatethemarketetiquette–inmany cases,generationofoff-the-runTreasuryquotesisnotfullyautomatedandis,thus,costlytothedealer. 10

some indicative quotes may differ from the best available bids and offers. Also, conversationswithmarketparticipantsindicatethatmarketmakersdifferintherelativefirmnessof their indicative quotes – with some being more reliable indications of the price at which a trade can occur. Furthermore, in bilateral relationships the identities of counterparties are known and market makers may shade their quotes based on their assessment of how informed the client is (see Wood, 2018). Consequently, there is no single price that would be availabletoallmarketparticipants. GuidedbytheTreasurymarketmicrostructure,Iestimateoff-the-runTreasuries’fairvalues based on transparent firm quotes for on-the-run Treasuries from the leading BrokerTec ATS and indicative NPQS quotes from the Federal Reserve Bank of New York. In greater fair detail, to calculate the fair value of an off-the-run Treasury, P , I deconstruct it into the i,t benchmarkandidiosyncraticpricecomponents,asfollows. Thebenchmarkcomponentoftheoff-the-runTreasury’spriceisthepriceofthehypothetical on-the-run security with equivalent cash flows – it reflects the interest rate term structure under conditions of high liquidity and low financing costs. An idiosyncratic component of the off-the-run Treasury’s price captures the effects of lower liquidity and less favorable financing of a specific security relative to the on-the-run benchmark. The benchmark componentreflectstheinformationinnewsannouncementsandflowsoffunds. Consequently, the benchmark component may be highly variable intraday. In contrast, the financing cost and liquidity premia are relatively stable intraday – these premia primarily depend on the financingandliquidityconditionsovertheremaininglifeofthebond.12 Duetohigherliquidityandtradingvolumesintheon-the-runTreasurymarket,itisthe locus of Treasury price discovery. Thus, to estimate the benchmark price component I use 12Cheap financing and high liquidity benefit the investor over the holding period, and their values over the remaining life of the security will likewise affect future holders of the security. Consequently, financing andliquiditycharacteristicsovertheremaininglifeofthesecuritydeterminethecorrespondingpremia. That said,valueofliquiditycanspikeduringmarketstress. InSection3.1,Iintroduceaforecastaccuracyfilterthat mitigatestheeffectofsuchspikesonliquiditymeasurement,albeitatthecostofretainingfewerobservations. 11

firm on-the-run Treasuries’ quotes from one of the leading inter-dealer broker (IDB) BrokerTecAlternativeTradingSystem(ATS).13Crucially,firmon-the-runTreasuries’quotesare available at a high frequency, which precludes pricing based on stale information.Another argument in favor of the on-the-run Treasury market as the source of the benchmark price componentisthatoff-the-runTreasuriescanbequotedbydealersintermsoftheirspreads to the corresponding on-the-run securities. Dealers also engage in swap box trading where theyeffectivelyhedgetheiroff-the-runTreasurieswithon-the-runsecuritieswithinasingle transaction. Finally, the differences between NPQS and BrokerTec ATS quotes for on-therun securities are generally negligible, suggesting that market makers refer to prominent CLOB-drivenATSwhenquotingpricesforon-the-runsecuritiestoreducetheprobabilityof beingexploitedbyarbitrageurs. A term structure model ingests firm on-the-run Treasury quotes to generate the benchmarkpricecomponentforanyTreasurycharacterizedbyitsremainingcashflows. Ateach trade time t in Treasury TRACE data, I fit the state-of-the-art machine learning term structure model of Filipovic´ et al. (2022).14 To reiterate, the benchmark price component is the value of a security’s cash flows when discounted using time t fitted on-the-run term structure. Next, to estimate the idiosyncratic price component – capturing the security’s financing and liquidity premia – I use indicative NPQS quotes at 08:40am, 11:30am, 2:15pm, and 3:30pm. ForeachNPQSquotesnapshot,IfitaFilipovic´ etal.(2022)termstructuremodelto the NPQS quotes for on-the-run Treasuries. For each off-the-run Treasury security, the differencebetweentheNPQSquoteandthevalueofitscashflowswhendiscountedusingthe 13OtherprominentATSincludeDealerwebandFenicsUST.Duetoprincipaltradingfirmsbeingactiveon allmajorATS,themidpointsbetweenbestbidandaskquotesoneachmajorATSmustbesufficientlycloseto preventstraightforwardarbitrage. 14The term structure is fitted with the smoothness parameter λ = 1 (before scale normalization), maturity weight of α = 0.05, and tension parameter δ = 0.001 (see Filipovic´ et al., 2022, for details). I found that the methodofFilipovic´ etal.(2022)deliverssuperiorbondyieldforecastingaccuracyrelativetopopularalternatives,includingFamaandBliss(1987),NelsonandSiegel(1987),Tanggaard(1997)andAndersen(2007). 12

fitted on-the-run term structure is the idiosyncratic price component. I take these idiosyncratic price components to be constant between consecutive NPQS quote snapshots within thetradingday. fair Finally,thefairvalueofanoff-the-runTreasuryiattimet, P ,isthetimetbenchmark i,t pricecomponentadjustedforthesecurity’sidiosyncraticpricecomponentestimatedatthe latestNPQSquotesnapshottimethatprecedestimet. 3 Actual v. Indicative Liquidity 3.1 SampleConstruction The sample comprises dealer-to-client trades in nominal Treasury Notes and Bonds, coveringtheperiodfromJanuary2018toJune2024. ATS-intermediateddealer-to-clienttrades anddirectdealer-to-dealertradesarethesubjectsofAppendicesBandC,respectively. Ialso remove likely retail trades by considering transactions of at least $10mm in notional value; IconsiderretailtradesinAppendixD.15 Only transactions during the active trading hours between 8:40am and 5:00pm are retained, which tempers the liquidity seasonality at the market opening. With most of the repo trades done early in the trading day, the financing conditions are largely determined before 8:40am. Thus, the assumption of stable intraday financing premiums in Section 2 is morelikelytoholdfortransactionsthatoccurpost8:40am. Since an accurate determination of the fair value is critical to the measurement of the effective bid-ask spread, I retain transactions in securities for which the model achieves accurateforecasts. Specifically,Iconsiderintradayforecastsofmid-quotesatthreesnapshot times–11:30am, 2:15pm, and3:30pm.16 Iretainsecurity i onday d inthesamplewhenthe 15Thisthresholdissomewhatdiscretionary–itmayalsoleadtotheomissionofverysmallinstitutionaltrades. Also,wealthyindividualsmaytransactinmorethan$10mmnotionalamountofTreasuries,butsuchtradesare likelytoberelativelyrare. 16The price forecasts are model estimates of fair values based on the most recent benchmark, on-the-run 13

maximum absolute value of the forecast error normalized by the indicative bid-ask spread forsecurityiondaydislessthanonehalf. Analyticexpressionforthisrequirementis: (cid:12) (cid:12)   (cid:12) (cid:12)P fair− P i a ,t sk+P i b ,t id(cid:12) (cid:12)  (cid:12) i,t 2 (cid:12) 1 max < ,  Pask−Pbid  2   i,t i,t   t∈T whereT = {d11 : 30am,d2 : 15pm,d3 : 30pm}areindicativequotesnapshottimesonday d. As many off-the-run Treasuries trade rather infrequently, making it difficult to reliably isolate the security-level effect from that of explanatory variables, I construct a sample of actively traded securities. First, I select 250 off-the-run Treasury securities with the largest number of trades in the full sample. Second, on any given trading day, I retain trades in a security only if it traded at least 50 times during that day. These sample selection criteria justify a caveat that the current analysis applies to the more liquid segment of the off-therun Treasury market. However, it is important to note that the sample is not dominated by cheapest-to-deliver securities – securities that market participants prefer to deliver into Treasuryfutures. Finally,tofurtherreducetheeffectofoutliersandnon-obviousdata-entryerrorsinTreasuryTRACEdata,Iaggregateeffectivebid-askspreadsoverasetofvolumebinsthatreflect common trade sizes. Specifically, the effective bid-ask spread measure is set to its median within each aggregation group defined by the tuple of the security identifier, trading day, andvolumebin,{i,d,v}: (cid:16) (cid:17) EBAmed := med {EBA } , (3) i,d,v i,t t∈d,v∈V where i is the security index, t is the time of the trade, d is the trading day (t ∈ d), med quotesandpriorestimatesofidiosyncraticcomponents. Oneachtradingday,thequotesnapshotat08:40amis necessaryforestimatinginitialidiosyncraticpricecomponentsand,thus,belongstothein-sampleperiod. 14

is the median operator, and V is the set of volume bins defined by the cutoff values of {10,15,...,50,60,...,100,125,...250},inmillionsofdollars. Duetotheirrarity,Iexcludetrades withnotionalsgreaterthan$250mm. In summary, such filtering and aggregation of Treasury TRACE data results in a sample of 101,978 observations of trades in 118 different Treasury securities over 1,589 trading days. Other data sources include BrokerTec inter-dealer-broker ATS for on-the-run TreasuryquotesandtheFederalReserveBankofNewYorkNPQSforlower-frequencyintraday snapshotsofallTreasurysecurities’quotes. 3.2 DistributionsofEffectiveBid-AskSpreadsandPriceImprovements In this section, I describe the empirical distributions of the effective and indicative bid-ask spreads. Panel A of Figure 1 depicts the empirical density of the effective bid-ask spread. Whilethemajorityoftheeffectivebid-askspreadsfallinthezerototwobasispointsrange, the heavy right tail is evident even when the graph is truncated at 10 basis points. The natural conjecture is that market participants obtain good execution for most transactions, while paying substantially larger trading costs for a not insignificant number of transactions. PanelAofTable1containssummarystatisticsfortheeffectiveandindicativebid-ask spreads. The median of the effective bid-ask spread is below that of the indicative bidask spread – suggesting better-than-expected execution for most trades. On the contrary, the right tail is notably more pronounced for the effective relative to the indicative bid-ask spread, as evidenced by the comparison of their 95th percentiles. Kurtosis of the indicative bid-ask spread is above 21, while that of the effective bid-ask spread is an order of magnitude larger still. The positive skew of the effective bid-ask spread distribution also far exceedsthestillnotableskewoftheindicativebid-askspread. To quantify the deviation between actual and expected execution quality, I suggest a 15

priceimprovementmetric: (cid:32) (cid:33) (cid:26) (cid:27) EBA IMPRVT = 1−med i,t , (4) i,d,v IBA i,t− t∈d,v∈V where EBA is the effective and IBA is the indicative bid-ask spread for security i, i,t i,t− expressed in basis points, at times t and t− := max(s ∈ {quote snapshot times} : s ≤ t), respectively. Thus, the price improvement is measured relative to the indicative bid-ask spread – it is positive only when the effective bid-ask spread is less than the indicative bid-ask spread, with the maximal improvement being unity. Negative price improvement values correspond to trades where the effective bid-ask spread exceeds the corresponding indicativebid-askspread. PanelBofFigure1depictstheempiricalprobabilitydensityofpriceimprovements. The shape of the distribution validates the above conjecture that the majority of trades occur at pricesthataremorefavorabletotheinitiatingsidethanindicativebid-askspreadssuggest. One explanation for the apparent ubiquity of price improvements is that clients conduct mini-auctionsamongmarketmakers–aclientobtainsquotesfrommultiplemarketmakers andselectsthequotecorrespondingtothesmallesteffectivebid-askspread. Anotherpossibilityisthatmarketmakersseetheirquotesasafirststepinnegotiationsandwanttohave some leeway to provide their clients with a ‘good deal’ relative to their initial indication. Finally,indicativequotesmayreflectquotesavailableforagenericclient,whileactualclient relationships allow for better prices available to preferred and less informed clients. Since the majority of clients likely fall into the category of less informed market participants – participantsthatdonothavesuperiorabilitytoforecastTreasuryyields–weobserveprice improvementsforthemajorityoftrades. Therearealsomanytradesthatoccuratpricesthat are significantly worse to the initiating side than indicative bid-ask spreads suggest. This may reflect either trading by informed clients or larger transaction volumes – I discuss the latterpossibilitynext. 16

Figure2depictsempiricalprobabilitydensitiesofeffectivebid-askspreadsandpriceimprovementsseparatelyfortradesoflessthanandgreaterthan$50mminnotionalvalue. The probabilityofalowereffectivebid-askspreadandacorrespondingpriceimprovementare considerablyhigherforlowervolumetransactions. PanelsBandCofTable1containsummary statistics for effective bid-ask spreads and price improvements conditional on transaction volume of below and above $50mm, respectively. For smaller-volume transactions, the 95th percentiles of the effective and indicative bid-ask spreads are nearly identical. On the other hand, the right tail of the effective bid-ask spread, as measured by its 95th percentile, isconsiderablygreaterforlarger-volumetransactions. Finally, themedianeffective andindicativebid-askspreadsarenearlyidenticalforlarger-volumetransactions,withthe correspondingpriceimprovementsbeingrathermodestforhalfthetradesinthiscategory. 3.3 BiasesinIndicativeBid-AskSpreads In this section, I construct a series of linear mixed models to document biases in indicative bid-ask spreads. The linear mixed model framework naturally fits the data structure – as thesamesecuritymaybetradedmultipletimesduringagivenday,thereisnaturalvariance error clustering associated with the grouping of observations by traded security. A linear mixedmodelallowsforrandomeffectsassociatedwitheachsecurity: EBA = α +α ·IBA +X γ+Z β+ϵ, (5) i 0 1 i i i i where i is the trade index, EBA and IBA are the effective and indicative bid-ask spreads, respectively; X is a vector of variables that may help detect biases in indicative bid-ask i spreads; {α ,α ,γ} are fixed effect coefficients; Z is the ith row of the n×s random-effects 0 1 i model matrix – a sparse indicator matrix that captures the grouping of n observations by s tradedsecurities; βisthevectorofrandomeffectsthathaveamultivariatenormaldistribution,N (0, Σ);ϵ isthenoiseterm. i 17

Todetectpotentialbiasesinindicativebid-askspreads, Iconsiderfourmodelspecificationsthatdifferinexplanatoryvariables,X. WithinthespecificationofEq. (5),thehypothi esis of unbiased indicative bid-ask spreads corresponds to the joint restriction of α = 0, 0 α = 1, and γ = 0. Table 2 contains maximum likelihood parameter estimates of these 1 models.17 Model I is the benchmark specification corresponding to an empty set of control variables, X. The intercept is positive and significant, suggesting a constant bid-ask spread component that is not represented by the variation in indicative bid-ask spreads. At the same time, the coefficient in front of the indicative bid-ask spread is significantly below unity,whichalignswellwithcommonlyobservedpriceimprovementsnotedinSection3.2. Thus, already a simple benchmark model suggests that indicative bid-ask spreads do not translatenearlyone-to-onetoeffectivebid-askspreads. Model II introduces an interaction term between the indicative bid-ask spread and security’s relative age, IBA·RA. I define a security’s relative age as the ratio of the remaining time to maturity to its original time to maturity. The significant negative coefficient in frontof IBA·RAsuggeststhatmarketmakerstendtoquoteoverlyconservativeindicative spreads for more seasoned securities. Consequently, measures of off-the-run v. on-the-run liquidity premiums are inflated if they are based on indicative bid-ask spreads, especially for more seasoned securities. In Model II, the coefficient in front of the indicative bid-ask spread is notably higher than in Model I, suggesting a closer correspondence between indicative and effective bid-ask spreads for more recently issued securities; however, it still remainssignificantlybelowunity. Forasecuritythathasjustbecomeoff-the-run,aonebasispointchangeinitsindicativebid-askspreadtranslatesintoanexpected0.73basispoints changeinitseffectivebid-askspread. Asaresult,awideningofindicativebid-askspreads 17MaximumlikelihoodestimationfollowsBatesetal.(2015)–itinvolvesrepeatedapplicationsofpenalized leastsquares, whichallowsforexpressionsofvariousprobabilitydensitiesrequiredforthecalculationofthe log-likelihood. 18

mayexaggeratethemagnitudeofanactualliquiditydeterioration. Model III extends Model II by introducing an interaction term between the indicative bid-askspreadandanindicatorofwhetherthesecurityisthecheapest-to-deliver(CTD)into aTreasuryfuturescontract, IBA·CTD.18 CTDsecuritiesareTreasurysecuritiesthatparties holding short Treasury futures positions find most profitable to deliver into the futures, if they were to make a delivery. Given the demand for CTD securities from the Treasury futuresmarketparticipants(e.g.,fromTreasurycash-futuresbasistraders),CTDsecuritiesare more likely to trade special in the repo market (resulting in cheaper financing) and exhibit greaterliquidity. Thecoefficientinfrontoftheinteractionterm, IBA·CTD,isinsignificant. Thus, indicative bid-ask spreads properly reflect any effects induced by the CTD status of Treasuries. Model IV extends Model III by introducing an interaction term between the indicative bid-ask spread in the off-the-run market and a measure of liquidity in the corresponding maturity sector of the benchmark, on-the-run Treasury market. To some extent, Model IV complementstheconditionalvolumescalinganalysisofSection4.1,butinasimplerframework. Next, I describe the construction of control variables for the on-the-run Treasury marketliquidity,whichmustbetailoredtocorrespondingoff-the-runsecurities. Liquidityconditionscandiffernotablywithasecurity’smaturity,asexemplifiedbynotably worse deterioration in the liquidity of shorter maturity Treasuries during the most recent monetary policy tightening cycle. Recognizing maturity-dependent liquidity conditions, I assign off-the-run Treasury securities to a set of duration groups.19 Then, I assess benchmark,on-the-runTreasurymarketliquidityconditionsseparatelyforeachconsidered durationgroup. Specifically,Ifirstmatcheachdurationgrouptoanappropriateon-the-run 18CTDsecurities’CUSIPsareidentifiedbasedondatafromJ.P.MorganChase&Co., MorganMarketsand DataQuery,https://markets.jpmorgan.com. 19Durationisameasureofinterestsensitivitythatdependsonthesecurity’sremainingtimetomaturity. I considerfourdurationgroups{(1,2],(2,5],(5,10],(10,30]}. 19

Treasurysecurity.20 Combiningtheabovetwomaps,eachoff-the-runsecurity,smaybeassociated with an on-the-run security ξ(s). Then, for each trading day, I use a transform of the time-weighted average bid-ask spread from the BrokerTec ATS as a measure of overall benchmark, on-the-run market liquidity in the corresponding sector of the curve.21 A bidaskspreadontheBrokerTecATSisboundedfrombelowbythecorrespondingticksize–the minimalpricechangeincrement–prescribedbythetradingplatform. Ingeneral,ticksizes differforon-the-runTreasurysecuritiesofdifferentmaturities. Tocapturetheliquidityconditions in different sectors of the market on a common scale, I consider a security-specific empirical cumulative probability of the bid-ask spread as the measure of the benchmark, on-the-runTreasurymarketliquidityinadurationsector: (cid:16) (cid:17) θ = ecdf BBA ξ(s) , (6) i ξ(s) d wherei isthetransactionindexforatradeinsecurity s,belongingtoadurationgroupthat maps to the on-the-run security ξ(s), during trading day d; BBA ξ(s) is the time-weighted d average – with weights corresponding to lengths of time during which each spread level prevailed–bid-askspreadoftheon-the-runbenchmark, on-the-runTreasurysecurity ξ(s) during trading day d; ecdf is the empirical cumulative distribution function of the bid- ξ(s) ask spread for on-the-run security ξ(s). High values of θ correspond to higher bid-ask spreadsforbenchmark,on-the-runsecuritiesand,thus,lowerbenchmarkliquidity. Estimates of Model IV suggest that benchmark, on-the-run Treasury market liquidity is a significant scaling factor for indicative bid-ask spreads. When benchmark, on-the-run liquidity is low – θ is high – changes in indicative bid-ask spreads have a greater impact on the corresponding effective bid-ask spreads. This effect is sufficiently strong to make 20Indetail,Iusethe2-,5-,10-,and30-yearon-the-runTreasurysecuritiesasthecorrespondingbenchmarks for{(1,2],(2,5],(5,10],(10,30]}durationgroups. 21Time-weightedaveragebid-askspreadondaydistheweightedaverageofbid-askspreadswhereweights reflectthelengthsoftimethatagivenspreadwasobservedduringtheactivehoursoftradingdayd. 20

the coefficient in front of the unscaled indicative bid-ask spread, IBA, insignificant. Thus, i the relationship between indicative and effective bid-ask spreads for off-the-run Treasuries depends on liquidity in the benchmark, on-the-run Treasuries market. Section 4 develops theseinsightsfurtherbyconditioningthedependencebetweentheeffectivebid-askspread andtransactionvolumeonliquidityintheon-the-runTreasuriesmarket. Since clients in the off-the-run Treasuries market do not commonly split their volumes among multiple dealers to obtain their best prices, transaction volume is particularly relevantfortheeffectivebid-askspread. Modelsofthissectionservedtodocumentbiasesinthe simplestframework,withthenon-lineareffectsofvolumeleftforexplorationinthefollowingsection. InSection4,Ifocusontherelationshipbetweentheeffectivebid-askspreadand transactionvolume. However,alreadyatthisstage,Inotethatthebiasofindicativebid-ask spreadsagainstmoreseasonedTreasurysecuritiesremainssignificantwhencontrollingfor volume. Furthermore, Section 4.1 extends the results on the effect of benchmark, on-therun Treasury market liquidity. Beyond illuminating the dependence between the effective bid-ask spread and order volume, Section 4.1 may be seen as an extension of Model II that controlsforordervolumewithinaflexible,non-parametricspecification. 4 Scaling of Trading Costs with Order Volume Severalchannelsexistforwhytransactionvolumeaffectsthetradepriceand,thus,theeffectivebid-askspread. First,theinformationalcontentofatrademayvarywithvolume,asin BarclayandWarner(1993). Second,tosupportlargertransactionsizes,marketmakersneed to either carry a larger inventory on their balance sheet – the channel explored in Cohen et al. (2023) – or be able to source a large amount of the security in the inter-dealer market. Thethirdchannelistheendogeneityinliquidity-taking–largetradesareenteredintowhen 21

there is sufficient liquidity.22 Thus, selective liquidity-taking would suggest that clients in the off-the-run Treasury market are sufficiently sophisticated and opportunistic to seek to avoid large price dislocations. Either one or, more likely, a combination of these channels givesrisetocomplexscalingoftheeffectivebid-askspreadwithtransactionvolume. Power law scaling is a common choice for modeling priceimpact’s dependence on volume (see Plerou et al., 2004; Zhang, 1999, among others). In this section I find that onedimensional power law models are overly restrictive for two reasons. First, selective liquiditytakingmaycauseanon-monotonerelationshipbetweentheeffectivebid-askspread and transaction volume. Second, other explanatory variables – like benchmark, on-the-run Treasury liquidity – can affect the dependence of the effective bid-ask spread on volume. Ignoring suchexplanatory variables istantamount to estimatingan average scalinglaw, as opposedtothescalinglawconditionalonrelevantmarketandsecurity-specificvariables. Thelinearmixedmodelframeworkiswell-suitedformodelinghowtheeffectivebid-ask spread scales with transaction volume. First, the task requires retention of multiple transactions for each security on any given trading day. Such data structure is supported by a linear mixed model that accounts for random effects associated with each security. Second, the shape of the relationship between trading costs and transaction volume may be too complex for a simple polynomial model. The linear mixed model framework has the advantageofallowingfornon-parametricmodelsofmultivariatesurfacesthroughthetensor spline methodology of Wood et al. (2013). In particular, bivariate tensor splines enable therelationshipbetweentradingcostsandtransactionvolumetobeconditionalonanother variable. I identify two conditioning variables that significantly affect the scaling relationship–benchmark,on-the-runTreasurymarketliquidityconditionsandtherelativeliquidity oftheoff-the-runsecurity. Toaccommodatethedependenceofthescalinglawonanothermarketorsecurity-specific 22Farmeretal.(2004)suggeststhatlargepricemovesoccurduetomarketparticipantstakingliquiditywhen itisscarce. 22

variable, I model the effect of volume via the two-dimensional tensor product smoothing method of Wood et al. (2013). Following the results of Section 3.3, in all model specifications, I control for the indicative bid-ask spread and its interaction with the relative age of thesecurity. So,IextendthemodelspecificationinEq.(5)tothenon-parametricframework ofWoodetal.(2013): (cid:34) (cid:35) ∑ EBA = α +α ·IBA +α ·IBA ×RA +Z β+ L T (V,θ ) +ϵ, (7) i 0 0 i 1 i i i ij j i i i j where EBA and IBA are the effective and indicative bid-ask spreads for transaction i in i i security s, IBA ×RA is the interaction term between the indicative bid-ask spread and i i security’s s relative age. T (V,θ ) are unknown smooth functions of transaction volume, j i i V, and of the explanatory variable, θ , that affects the scaling relationship. The degree of i i smoothnessoffunctionsT (V,θ )isnotknowninadvancebutthereisanassociatedpenalty j i i functional, J (T ),foreachfunction. L are,ingeneral,knownlinearfunctionals. j ij In Section 4.1, I show how the effective bid-ask spread scales with volume under different benchmark, on-the-run Treasury market liquidity conditions. Then, in Section 4.2, I explorewhetherthescalingisdifferentforrelativelylessliquidsecuritiesamongtheoff-theruns. 4.1 ScalingLawConditionalonBenchmark,On-the-RunTreasuryLiquidity In this section, I consider how the effective bid-ask spread scales with transaction volume underdifferentbenchmark,on-the-runTreasurymarketliquidityconditions. Theconstruction of a maturity sector-specific measure of benchmark liquidity conditions follows the approach in Section 3.3 – specifically, I set θ in Eq. (7) in accordance with the definition in i Eq. (6). Figure3showstheconditionaleffectofvolumeontheexpectedeffectivebid-askspread, 23

as well as the associated 95 percent confidence intervals. I consider the scaling law conditionaloneithermedianorbadbenchmark,on-the-runTreasuryliquidityconditions,corresponding to θ = 0.5 and θ = 0.75, respectively. Controlling for indicative bid-ask spreads, whenbenchmarkliquidityislow,transactionvolumehasauniformlygreaterpositiveeffect on the effective bid-ask spread – indicating higher trading costs. This finding extends the resultsofModelIVfromSection3.3–indicativebid-askspreadsdonotadequatelycapture how off-the-run Treasury market liquidity changes with benchmark, on-the-run Treasury liquidityconditions. Therelationshipbetweentheeffectivebid-askspreadandtransactionvolumeisconcave, irrespectiveofbenchmark,on-the-runliquidityconditions. Anovelempiricalfindingisthat theeffectofselectiveliquidity-taking–clientstransactinginlargevolumesonlywhenmarketmakersoffersufficientlyattractivequotes–canmakeincrementalordervolumedecrease the expected effective bid-ask spread for sufficiently large transactions. The resulting nonmonotonedependencecannotbeadequatelydescribedbyclassicpowerlaws. Thepointat whichtheeffectofincrementalvolumeontheeffectivebid-askspreadbecomesnegativeis atalowervolumelevelunderbadbenchmark,on-the-runliquidityconditions. Thisobservationsuggeststhatselectiveliquidity-takingmotiveisstrongerwhenbenchmarkliquidity islower. 4.2 ScalingLawforSecuritiesofVaryingLiquidity In this section, I consider whether relatively less liquid securities exhibit different dependence of the effective bid-ask spread on transaction volume. To determine the relative liquidity of securities on a specific trading day, I rank securities within their duration groups in accordance with their indicative bid-ask spreads. Then, I measure the relative liquidity of the security by an empirical cumulative probability of the indicative bid-ask spread – a fraction of securities with lower indicative bid-ask spreads within the duration group on a 24

given day. The greater the measure, the less the relative liquidity of the security. Since the ranking of securities is specific to both trading day and duration group, overall Treasury marketliquiditydoesnotaffectthismeasureofrelativeliquidity. Analytically,therelativeliquidityvariable,θ is: i θ = ecdf (IBAs), (8) i ψ,d d where i is the transaction index for a trade in security s, belonging to duration group ψ, during trading day d; IBAs is the simple average indicative bid-ask spread of security s d during trading day d, estimated by an average of the corresponding bid-ask spreads over NPQS quote snapshots on day d; ecdf is the empirical cumulative distribution function ψ,d of average indicative bid-ask spreads on day d for the duration group ψ. High values of θ correspond to comparatively less liquid securities within their duration groups for the particulartradingday. Figure4depictstheconditionaleffectofvolumeontheexpectedeffectivebid-askspread, aswellasassociated95percentconfidenceintervals. Iconsiderscalinglawsconditionalon median and lower liquidity securities, corresponding to θ = 0.5 and θ = 0.75, respectively. Thelevelandshapeofthescalinglawformedianliquiditysecuritiesisessentiallysimilarto thescalinglawobtainedwhenconditioningonbenchmark,on-the-runmarketliquidity(see Section 4.1 above). For less liquid securities, the effect of volume is somewhat lessened for transactionsofmodestvolumes. Theresultsarenotablymorepronouncedforlargertransaction volumes, albeit confidence intervals are also wider: indicative bid-ask spreads may notably overstate trading costs for larger volumes of relatively less liquid off-the-run securities. Moreover, thethresholddefiningtheregionwhereselectiveliquiditytakingprevails occurs for notably smaller volumes. These results suggest that higher indicative bid-ask spreads tend to be overly conservative relative to the median indicative bid-ask spreads. In other words, indicative bid-ask spreads tend to present a somewhat distorted picture of 25

relative liquidity across different off-the-run Treasuries. One explanation is that relatively higher indicative bid-ask spreads may be biased by some dealers that prefer not to trade in the particular security, while clients can still locate dealers that have no such preference againstthepotentialtrade. 5 Conclusion Actualliquidityexperiencedbyclientsintheoff-the-runTreasurymarketcandiffersystemically and notably from the levels reflected in indicative bid-ask spreads. In particular, I showthatindicativebid-askspreadsarebiasedforseasonedTreasurysecurities,Moreover, indicative bid-ask spreads have a greater effect on actual trading costs when benchmark, on-the-runTreasurymarketliquidityislow. Whilebetter-then-indicatedexecutioniscommonformoderatetransactionvolumes,the effective bid-ask spread of large trades can be substantially wider. Large order sizes incur notabletradingcoststhatareoftenfarinexcessofwhatindicativebid-askspreadssuggest. And it is the capacity to transact in significant volume without causing price dislocations that is necessary for securities to act as benchmarks and near risk-free collateral. Thus, the dependence of the effective bid-ask spread on transaction volume – the scaling law – is criticalforassessingactualliquidity. In agreement with earlier studies, I also find a non-linear relationship between trading costs and transaction volume. In this paper, I introduce two key features that sharpen the results. First, I consider the relationship between the effective bid-ask spread and transaction volume conditional on either benchmark, on-the-run Treasury market liquidity or the relative liquidity of a particular security – this is in contrast to unconditional modeling that is prevalent in the existent literature. I find that both conditioning variables have notableeffectsontherelationshipbetweentheeffectivebid-askspreadandtransactionvolume. Second,Iobtainevidenceofselectiveliquidity-taking–marketparticipantstimetheir 26

large trades to coincide with the willingness of market makers to quote large volumes at favorable prices. The inflection point where the effective bid-ask spread starts to decrease with marginal transaction volume marks the start of the region where selective liquiditytakingbecomesthedominantfactor. Theresultantnon-monotonicityoftheeffectivebid-ask spread’sdependenceontransactionvolumecannotbecapturedbypowerlaws. The empirical framework of this paper can support a number of directions for future research into the off-the-run Treasury market liquidity. First, future research can model liquidityheterogeneity–marketmakersmayofferdifferentqualityofexecutionundervariousmarketconditions. Ifclientshavestrongtiestospecificmarketmakers–perhaps,due to other lines of business – clients will be exposed to heterogeneous liquidity conditions in the market. Furthermore, clients vary in their information advantage and negotiating power. Resultant price discrimination by market makers may lead to vastly different liquidityconditionsfordifferentclients. Second,futureresearchcaninvestigatethetimeseries aspectsofaggregateliquidityintheoff-the-runTreasurymarket. Specifically,itcanexplore the association between aggregate liquidity in the off-the-run Treasury market and interest rateuncertaintyundervariousmarketconditions(possibly,alongthelinesof Meldrumand Sokolinskiy,2025). Theoff-the-runmarketliquidity’ssensitivitytointerestrateuncertainty mayincreasewiththelevelofmarketstress. Suchnon-linearitymayhavenotablefinancial stabilityimplicationsasitwouldmagnifytheprobabilityofamarketdysfunction. References Adrian, Tobias, Michael J Fleming, and Kleopatra Nikolaou, “US Treasury Market FunctioningfromtheGFCtothePandemic,”FRBofNewYorkStaffReport,2025,(1146). Amihud, Yakov, “Illiquidity and Stock Returns: Cross-Section and Time-Series Effects,” Journaloffinancialmarkets,2002,5(1),31–56. 27

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Table1: BiasesinIndicativeBid-AskSpreads PanelA.Entiresample EBA IBA IMPRVT 5%quantile 0.03 0.18 -6.57 10%quantile 0.07 0.23 -1.65 50%quantile 0.37 0.68 0.50 90%quantile 2.79 2.72 0.90 95%quantile 6.22 4.16 0.95 mean 1.51 1.22 -1.30 sd 6.74 1.53 13.10 skew 36.93 3.53 -50.10 kurt 2188.18 21.40 4803.63 PanelB.Tradesinlessthan$50mmnotional EBA IBA IMPRVT 5%quantile 0.03 0.19 -2.60 10%quantile 0.06 0.24 -0.71 50%quantile 0.32 0.71 0.55 90%quantile 2.09 2.75 0.91 95%quantile 4.29 4.16 0.95 mean 1.16 1.24 -0.50 sd 5.90 1.52 10.05 skew 49.79 3.44 -56.67 kurt 3704.79 20.77 4939.37 PanelC.Tradesinmorethan$50mmnotional EBA IBA IMPRVT 5%quantile 0.05 0.18 -24.14 10%quantile 0.09 0.21 -8.80 50%quantile 0.62 0.62 0.20 90%quantile 6.27 2.62 0.85 95%quantile 12.41 4.15 0.93 mean 2.59 1.17 -3.76 sd 8.77 1.58 19.57 skew 21.53 3.79 -37.59 kurt 773.63 23.08 2879.57 Notes: Thistablereportsthesummarystatisticsfortheeffectivebid-askspreads, EBAdefinedinEq. (3), NPQSindicativebid-askspreadsIBA,andthepriceimprovement,IMPRVT,definedinEq.(5).Thesample consistsofdirectdealer-to-clienttradesfromJanuary2018toJune2024,filteredandaggregatedasdescribed inSection3.1. Datasources: FinancialIndustryRegulatoryAuthority(FINRA),BondTradeDissemination System(BTDS)andTradeReportingandComplianceEngine(TRACE);informationobtainedfromtherepo InterDealerBrokercommunity;FederalReserveBankofNewYork,NPQS. 32

Table2: BiasesinQuotedBid-AskSpreads ModelI ModelII ModelIII ModelIV α 0.91∗∗∗ 0.81∗∗∗ 0.81∗∗∗ 0.99∗∗∗ 0 (0.04) (0.05) (0.05) (0.05) IBA 0.48∗∗∗ 0.73∗∗∗ 0.73∗∗∗ −0.07 (0.01) (0.03) (0.03) (0.07) IBA·RA −0.51∗∗∗ −0.51∗∗∗ −0.15∗ (0.05) (0.05) (0.06) IBA·CTD −0.04 −0.02 (0.10) (0.10) IBA·θ 0.80∗∗∗ (0.07) BIC 677253.40 677180.44 677194.64 677073.21 Num. obs. 101,978 Num. cusips 118 Randomeffectsvariance 0.13 0.13 0.13 0.14 Notes: This table reports estimates of linear mixed models following the general specification in Eq. (5), reproducedhereforconvenience: EBA =α +α ·IBA +Xγ+Zβ+ϵ, i 0 1 i i i i whereEBAistheeffectivebid-askspreadsfortradei; IBA istheindicativebidaskspread; X isavector i i ofcontrolvariablesthatidentifiespotentialbiases;{α ,α ,γ}arefixedeffectcoefficients;Z istheithrowof 0 1 i then×srandom-effectsmodelmatrix–asparseindicatormatrixthatcapturesthegroupingofnobservationsbystradedsecurities; βisthevectorofrandomeffectsthathaveamultivariatenormaldistribution, N (0,Σ); ϵ isthenoiseterm. Controlvariablesincludetheinteractionsofindicativebid-askspreadswith i thefollowingvariables. RAistherelativeageofthesecurity,definedastheratioofremainingtimetomaturitytotheoriginaltimetomaturity. CTDisanindicatorofwhetherthesecurityischeapest-to-deliverinto afront-monthTreasuryfutures. θasecurity-specificempiricalcumulativeprobabilityofthebid-askspread intheon-the-runTreasurymarket.Thesampleconsistsofdirectdealer-to-clienttradesfromJanuary2018to June2024,filteredandaggregatedasdescribedinSection3.1. ∗∗∗;∗∗;∗ denotesignificanceatthe0.1,1and 5percentlevelsrespectively. Datasources: FinancialIndustryRegulatoryAuthority(FINRA),BondTrade DisseminationSystem(BTDS)andTradeReportingandComplianceEngine(TRACE);informationobtained fromtherepoInterDealerBrokercommunity;FederalReserveBankofNewYork,NPQS;J.P.MorganChase &Co.,MorganMarketsandDataQuery,https://markets.jpmorgan.com. 33

Figure1: DistributionsofEffectiveLiquidityandExecutionQuality (a)EffectiveBid-AskSpread (b)PriceImprovement NOTE:theeffectivebid-askspreads,EBA,isdefinedinEq.(3)andthepriceimprovementisdefinedinEq.(4);thegraphistruncated at10basispoints. Thesampleconsistsofdirectdealer-to-clienttradesfromJanuary2018toJune2024,filteredandaggregatedas describedinSection3.1. Datasources:FinancialIndustryRegulatoryAuthority(FINRA),BondTradeDisseminationSystem(BTDS) andTradeReportingandComplianceEngine(TRACE);informationobtainedfromtherepoInterDealerBrokercommunity;Federal ReserveBankofNewYork,NPQS. Figure2: DistributionsofEffectiveLiquidityandExecutionQuality ConditionalonVolume (a)EffectiveBid-AskSpreadby (b)PriceImprovementby VolumeGroup VolumeGroup NOTE:theeffectivebid-askspreads,EBA,isdefinedinEq.(3)andthepriceimprovementisdefinedinEq.(4);thegraphistruncated at10basispoints. Thedistributionsareconditionalontransactionvolume: tradesoflessthan$50mm–blue-shadeddistribution, tradesof$50mmormore–red-shadeddistribution. Thesampleconsistsofdirectdealer-to-clienttradesfromJanuary2018toJune 2024, filtered and aggregated as described in Section 3.1. Data sources: Financial Industry Regulatory Authority (FINRA), Bond TradeDisseminationSystem(BTDS)andTradeReportingandComplianceEngine(TRACE);informationobtainedfromtherepoInter DealerBrokercommunity;FederalReserveBankofNewYork,NPQS. 34

Figure3: EffectofVolumeonEffectiveBid-AskSpread ConditionalonBenchmark,On-the-RunLiquidity NOTE: Theexpectedeffectsofvolumeontheeffectivebid-askspreadconditionalonbenchmark,on-the-runliquidity,asestimated basedonspecificationinEq.(7),reproducedhereforconvenience: (cid:34) (cid:35) EBAi =α0 +α0 ·IBAi +α1 ·IBAi ×RAi +Ziβ+ ∑ Lij T j (Vi,θi ) +ϵi, j whereEBAiandIBAiaretheeffectiveandindicativebid-askspreadsfortransactioniinsecuritys,IBAi ×RAiistheinteractionterm betweentheindicativebid-askspreadandsecuritysrelativeage;{α0,α1,γ}arefixedeffectcoefficients;Ziistheithrowofthen×s random-effectsmodelmatrix–asparseindicatormatrixthatcapturesthegroupingofnobservationsbystradedsecurities;βisthe vectorofrandomeffectsthathaveamultivariatenormaldistribution,N(0,Σ);ϵiisthenoiseterm;T j (Vi,θi )areunknownsmooth functionsofvolume,Vi,andoftheexplanatoryvariable. θi isthesecurity-specificempiricalcumulativeprobabilityofthebid-ask spread,BBA,asthemeasureofbenchmark,on-the-runTreasurymarketliquidityinadurationsector: θi =ecdf ξ(s) (cid:16) BBAξ d (s)(cid:17) , whereiisthetransactionindexforatradeinsecuritys,belongingtoadurationgroupthatmapstotheon-the-runsecurityξ(s), duringtradingday d; BBAξ(s) isthetime-weightedaverage –withweightscorrespondingtolengthsof time duringwhicheach d spreadlevelprevailed–bid-askspreadoftheon-the-runbenchmark,on-the-runTreasurysecurityξ(s)duringtradingdayd;ecdf ξ(s) istheempiricalcumulativedistributionfunctionofthebid-askspreadforon-the-runsecurityξ(s). Highvaluesofθcorrespondto higherbid-askspreadsforbenchmark,on-the-runsecuritiesand,thus,lowerbenchmarkliquidity. Thescalinglawconditionalonmedianbenchmark, on-the-runTreasuryliquidityconditions, θ = 0.5, isinblue. Thescalinglaw conditionalonbadbenchmark,on-the-runTreasuryliquidityconditions,θ = 0.75,isinred. Theshadedregionscorrespondtothe 95percentconfidenceintervals. Thedashedverticallinesmarkthelocalmaximaoftheexpectedeffectsofvolumeontheeffective bid-askspread. Datasources:FinancialIndustryRegulatoryAuthority(FINRA),BondTradeDisseminationSystem(BTDS)andTradeReportingand ComplianceEngine(TRACE);informationobtainedfromtherepoInterDealerBrokercommunity;FederalReserveBankofNewYork, NPQS. 35

Figure4: EffectofVolumeonEffectiveBid-AskSpread ConditionalontheSecurity’sRelativeLiquidity NOTE: Theexpectedeffectsofvolumeontheeffectivebid-askspreadconditionalonthesecurity’srelativeliquidity,asestimated basedonspecification7,reproducedhereforconvenience: (cid:34) (cid:35) EBAi =α0 +α0 ·IBAi +α1 ·IBAi ×RAi +Ziβ+ ∑ Lij T j (Vi,θi ) +ϵi, j whereEBAiandIBAiaretheeffectiveandindicativebid-askspreadsfortransactioniinsecuritys,IBAi ×RAiistheinteractionterm betweentheindicativebid-askspreadandsecuritysrelativeage;{α0,α1,γ}arefixedeffectcoefficients;Ziistheithrowofthen×s random-effectsmodelmatrix–asparseindicatormatrixthatcapturesthegroupingofnobservationsbystradedsecurities;βisthe vectorofrandomeffectsthathaveamultivariatenormaldistribution,N(0,Σ);ϵi isthenoiseterm;T j (Vi,θi )areunknownsmooth functionsofvolume,Vi,andoftheexplanatoryvariable.θiisthesecurity-andtradingday-specificempiricalcumulativeprobability ofindicativebid-askspreads: θi =ecdf ψ,d (IBAs d ), whereiisthetransactionindexforatradeinsecuritys,belongingtodurationgroupψ,duringtradingdayd; IBAs isthesimple d averageindicativebid-askspreadofsecuritysduringtradingdayd,estimatedbyanaverageofthecorrespondingbid-askspreads overNPQSquotesnapshotsondayd;ecdf ψ,distheempiricalcumulativedistributionfunctionofaverageindicativebid-askspreads ondaydforthedurationgroupψ. Highvaluesofθcorrespondtocomparativelylessliquidsecuritieswithintheirdurationgroups fortheparticulartradingday. Thescalinglawforamedianliquiditysecurity,θ = 0.5,isinblue. Thescalinglawforarelativelyilliquidsecurity,θ = 0.75,isin red. Theshadedregionscorrespondtothe95percentconfidenceintervals. Thedashedverticallinesmarkthelocalmaximaofthe expectedeffectsofvolumeontheeffectivebid-askspread. Datasources:FinancialIndustryRegulatoryAuthority(FINRA),BondTradeDisseminationSystem(BTDS)andTradeReportingand ComplianceEngine(TRACE);informationobtainedfromtherepoInterDealerBrokercommunity;FederalReserveBankofNewYork, NPQS. 36

Appendices A Treasury Market Microstructure – On- v. Off-the-Run With existent ample research into on-the-run Treasury market liquidity, it is important todetailthecausesmakingon-the-runandoff-the-runTreasurymarketliquiditynotably different,and,thus,requiringaseparatestudyoftheoff-the-runTreasurymarket. Most trades in on-the-run Treasuries occur on alternative trading systems (ATS) that offer the central limit order book (CLOB) protocol for matching buy and sell orders. The CLOBcontainstime-prioritizedqueuesofbuyandsellordersatvariouspricelevelsthat may be observed by all market participants. Thus, the CLOB provides a good indication ofimmediatelyavailableliquidity.23 Incontrast, off-the-runTreasurymarketliquidityismoreopaquebecausetradingoccurs bilaterally, even when intermediated by an ATS. A client willing to trade can ask severalmarketmakersforquotesforaspecifictransactionvolumeandreceivenon-firm, indicative quotes that could form the basis of further negotiations. Alternatively, some market makers stream quotes to clients via their in-house platforms or external ATS allowing potential clients to hide their intention to trade. Generally available streamed quotesare,however,evenlessreliableindicatorsofwhereactualtradescanoccur.24 Complete anonymity of participants in CLOB-based markets is another key difference between trading benchmark, on-the-run Treasuries via an inter-dealer broker ATS and trading off-the-run Treasuries in the dealer-to-client Treasury market segment. Lack of anonymity in direct bilateral trading allows market makers to discriminate against ‘toxicflow’–tradesbywell-informedclientswithatrackrecordofeitherpredictingprice changes or executing in a manner that would move the price against the market maker (seeWood,2018). In summary, on-the-run and off-the-run Treasury markets have vastly different mi- 23Whileimmediatelyavailableliquidityatthebestpricesisrelativelymodestandorderstradingthrough multiplelevelsofthebookarerareundernormalmarketconditions, marketparticipantsmayobservethe CLOB’sresponsetotradestoinferthewillingnessofmarketmakerstoreplenishtheCLOB. 24This is natural given that market makers would prefer to discriminate among clients based on their perceivedabilitytoforecastfutureprices. 37

crostructurethatmakesliquidityofevensimilarsecuritiesnotablydifferent. Besides the economic importance of the off-the-run Treasury market, one more argument that recommends research into its liquidity is the opportunity to study a critical decentralized market where bilateral relationships and search costs matter. While onthe-run Treasuries often serve as barometers of liquidity, there is no simple relationship betweenliquidityofon-the-runandoff-the-runsecurities. Particularlyduringperiodsof market stress, when there is a flight to quality, off-the-run Treasuries’ liquidity tends to suffermorethanon-the-runTreasuries’liquidity(seeFurfineandRemolona,2002).25 B Trades Intermediated by Alternative Trading Systems MarketmicrostructureintheAlternativeTradingSystem(ATS)intermediatedsectordiffers from that of the direct dealer-to-client sector. Crucially, ATS may offer anonymity to their participants, thereby removing the possibility of price discrimination by market makersbasedonaclient’sperceivedsophistication. Thatsaid,curatedmarketsthatseek toexclude‘toxic’flowsfrommostinformedparticipantshavebeenapopularinnovation. Inaddition,anonymityremovestheconsiderationofaclient-dealerrelationship. Finally, ATS may offer a variety of trading protocols that suit different groups of market participants.26 In this section, I show how the effective-bid ask spread depends on transaction volume in the ATS-intermediated sector of the dealer-to-client market. First, I consider the model specification in Eq. (7) with θ of Eq. (6) to allow for the effect of benchmark, on-the-runTreasurymarketliquidity. Panel(A)ofFigureA-1depictstheimpactoftransaction volume on the expected effective bid-ask spread for client trades intermediated by ATS, conditional on median and poor benchmark, on-the-run Treasury market liquidity. Relative to the direct dealer-to-client trades, the dependence of the effective-bid ask spread on transaction volume has a more complex shape for the ATS-intermediated 25The spreads between off-the-run and on-the-run Treasury yields compensate for liquidity differential betweenthetwotypesofsecurities. Thesespreadstendtowidennotablyduringperiodsofmarketstress (seeWarga,1992;FurfineandRemolona,2002). 26AsingleATSmayoffermultipletradingprotocols.Unfortunately,TreasuryTRACEdatadonotcontaina variableindicatingtheprotocol.Ileavelessdirectwaysofidentifyingthetradingprotocolforfutureresearch. 38

trades – the mean effects function has both convex and concave regions. Similar to the direct dealer-to-client market, I obtain evidence for selective liquidity taking – a region where the expected effective bid-ask spread decreases with incremental volume. However, in the ATS-intermediated market, for even greater transaction volumes, selective liquidity-takinglosesitsdominance. Thismaybeanindicationthatorderswhereclients do not have time discretion are more likely to be executed via an ATS. As in the case of thedirectdealer-to-clientmarket,theeffectoftransactionvolumeontheeffectivebid-ask spreadisgreaterwhenoverallTreasurymarketliquidityislow. Second,IconsiderthemodelspecificationinEq. (7)with θ ofEq. (8)toallowforsystemic differences between securities of varying liquidity. Panel (B) of Figure A-1 depicts theimpactoftransactionvolumeontheexpectedeffectivebid-askspreadforclienttrades intermediatedbyATS,forsecuritiesofmedianandlowrelativeliquiditylevels. Relative to the direct dealer-to-client trades, the differences in the scaling laws for securities of varyingrelativeliquidityaremuchmoremodest. Onenotableattributeofthescalinglaw forATS-intermediatedtradesisagreaterregionofconvexity,especiallyforlowerrelative liquidity securities. Once again, this is evidence that selective liquidity-taking is more prevalentinthedirectdealer-to-clientsegment. C Liquidity in the Dealer-to-Dealer Market Dealer-to-dealeroff-the-runTreasurymarketisalsoadecentralized,bilateralmarket–just like the dealer-to-client market. However, there are important differences. First, trading norms differ with respect to typical counterparty search patterns; in particular, explicit mini-auctionsmaybelesslikely. Second,thereis,arguably,lessinformationheterogeneity amongleadingdealersrelativetothatamongclients. Whilethemicrostructuredifferencesbetweenthedealer-to-dealeranddealer-to-client marketsareimportant,thetwomarketsarecloselytied. First,whenamarketmakerdoes not have the security requested by a client in its inventory, it can act as a (i) broker – sourcingthesecurityintheinter-dealermarketonanagencybasis,or(ii)dealer–selling the security that it does not possess with the intention of obtaining it in the inter-dealer 39

market later that business day – all done on a principal basis.27 In summary, there are apparent differences in the relationships between the participants in the dealer-to-client anddealer-to-dealermarkets,butalsocloselinksbetweenthetwoexist. Panels A and B of Figure A-2 depict the probability density plots of the effective bidask spreads and price improvements, respectively, for transactions in the dealer-to-client anddealer-to-dealersegments. Thecloselinksbetweenthedealer-to-clientanddealer-todealer segments make the distributions of effective bid-ask spreads and price improvementsnearidenticalinthetwosegments. D Retail Trades Retail investors are active in the Treasury market, likely constituting the majority of the trade count, but not volume. Systemic differences in trading costs of retail and institutionalinvestorsisduetoinformationandrelationshipeffects. First,retailclientsarecommonlyseenasless‘toxic’,thatis,lessinformed.28 Second,thereistheoffsettingfactorin theformoflessvalueassignedtoeachretailclient-dealerrelationship. Third,dealersmay seetheirretailclientsaslesslikelytoshoparoundforbetterexecution,asretailinvestors areunlikelytobeabletoaccuratelyassessexecutionquality. WhileretailtradesarenotexplicitlyidentifiedinTreasuryTRACEdata,transactionsof lessthan$1mminnotionalmayonlybereasonablyattributedtoretailinvestors.29 When suchsmallnotionaltransactionsoccurbetweenlargedealers,itmustmeanthatonedealer soldTreasuriestoaretailinvestorthatthedealerdidnothaveatthemomentofreceiving theclient’sorderandhadtoimmediatelysourcethesecuritiesfromanotherdealer. Panels A and B of Figure A-3 depict the probability density plots of the effective bid- 27Thus,adealeriseffectivelyabroker-dealer,butthecommonpracticeistorefertothemarketsegment as‘dealer-to-dealer’–andnot‘broker-dealer-to-broker-dealer’–forbrevity. Amarketparticipantcansella securitythatitdoesnotpossessatthemomentthetransactionisenteredinto,withtheintentionofsourcing itlater,becauseTreasurymarketssettleonthenextbusinessday. Thesecuritycanalsobeborrowedinthe specials repo market where a specific security is used as collateral. Finally, if a dealer cannot source the securityintime,afailoccursandcorrespondingpenaltiesarelevied. 28Principaltradingfirmsintheequitymarketareenteringinspecialarrangementswithbrokeragestogain accesstosuchless-toxictradeflows. 29Retailinvestorsmayalsotradeinlargernotionalamounts,butthiswouldlikelyconstituteanegligible fractionofalltrades. 40

ask spreads and price improvements, respectively, for transactions of retail vis-à-vis institutional investors. There is clear evidence that retail investors get worse execution – theypayhighereffectivebid-askspreadsanddonotexperiencethesamedegreeofprice improvement as institutional investors.30 Thus, retail investors do not benefit from their crediblenon-toxicity,whiletheirinabilitytoassessexecutionqualityandthelackofsufficientclient-dealerrelationshipvalueresultinwidereffectivebid-askspreads. 30Sinceretailtradesareallinsmallvolumes,analysisofthedependenceoftheeffectivebid-askspreadon transactionvolumeisirrelevantforthismarketsegment.Accountingfortheeffectofvolumeontheeffective bid-askspreadofinstitutionalinvestors’tradeswouldmaketheresultsevenmorepronounced. 41

Appendix Figures FigureA-1: ConditionalEffectofVolumeonEffectiveBid-AskSpreadforClient TradesIntermediatedbyanATS (a)ConditionalonBenchmark, (b)ConditionalonRelativeLiquidity On-the-RunLiquidity NOTE: Theexpectedeffectsofvolumeontheeffectivebid-askspread,asestimatedbasedonspecificationinEq. (7),reproducedherefor convenience: (cid:34) (cid:35) EBAi =α0 +α0 ·IBAi +α1 ·IBAi ×RAi +Ziβ+ ∑ Lij T j (Vi,θi ) +ϵi, j whereEBAiandIBAiaretheeffectiveandindicativebid-askspreadsfortransactioniinsecuritys,IBAi ×RAiistheinteractiontermbetween theindicativebid-askspreadandsecuritysrelativeage;{α0,α1,γ}arefixedeffectcoefficients;Zi istheithrowofthen×srandom-effects modelmatrix–asparseindicatormatrixthatcapturesthegroupingofnobservationsbystradedsecurities;βisthevectorofrandomeffects thathaveamultivariatenormaldistribution,N(0,Σ);ϵiisthenoiseterm;T j (Vi,θi )areunknownsmoothfunctionsofvolume,Vi,andofthe explanatoryvariable. InPanel(A),Iconditionthedependencebetweentheeffectivebid-askspreadandordervolumeonthebenchmark,on-the-runTreasurymarket liquidityinadurationsector,withθi–thesecurity-specificempiricalcumulativeprobabilityofthebid-askspread: θi =ecdf ξ(s) (cid:16) BBAξ d (s)(cid:17) , whereiisthetransactionindexforatradeinsecuritys,belongingtoadurationgroupthatmapstotheon-the-runsecurityξ(s),during tradingdayd;BBAξ(s) isthetime-weightedaverage–withweightscorrespondingtolengthsoftimeduringwhicheachspreadlevelprevailed d –bid-askspreadoftheon-the-runbenchmarkTreasurysecurityξ(s)duringtradingdayd;ecdf ξ(s)istheempiricalcumulativedistribution functionofthebid-askspreadforon-the-runsecurityξ(s).Highvaluesofθcorrespondtohigherbid-askspreadsforbenchmark,on-the-run securitiesand,thus,lowerbenchmarkliquidity. InPanel(B),Iconditionthedependencebetweentheeffectivebid-askspreadandordervolumeontherelativeliquidityofasecuritywithin itsdurationgrouponthecorrespondingday,withθi –thesecurity-andtradingday-specificempiricalcumulativeprobabilityofindicative bid-askspreads: θi =ecdfψ,d (IBAs d ), whereiisthetransactionindexforatradeinsecuritys,belongingtodurationgroupψ,duringtradingdayd;IBAs isthesimpleaverage d indicativebid-askspreadofsecuritysduringtradingdayd,estimatedbyanaverageofthecorrespondingbid-askspreadsoverNPQSquote snapshotsondayd;ecdfψ,distheempiricalcumulativedistributionfunctionofaverageindicativebid-askspreadsondaydfortheduration groupψ.Highvaluesofθcorrespondtocomparativelylessliquidsecuritieswithintheirdurationgroupsfortheparticulartradingday. Panel(A)depictsthescalinglawconditionalonmedianbenchmark,on-the-runTreasuryliquidityconditions,θ=0.5,inblue,andthescaling lawconditionalonbadbenchmark,on-the-runTreasuryliquidityconditions,θ =0.75,inred. Panel(B)depictsthescalinglawforamedian liquiditysecurity,θ=0.5,inblue,andthescalinglawforarelativelyilliquidsecurity,θ=0.75,inred.Theshadedregionscorrespondtothe95 percentconfidenceintervals.Thedashedverticallinesmarkthelocalmaximaoftheexpectedeffectsofvolumeontheeffectivebid-askspread. Datasources:FinancialIndustryRegulatoryAuthority(FINRA),BondTradeDisseminationSystem(BTDS)andTradeReportingandComplianceEngine(TRACE);informationobtainedfromtherepoInterDealerBrokercommunity;FederalReserveBankofNewYork,NPQS. 42

FigureA-2: Dealer-to-DealerTrades: DistributionsofEffectiveLiquidityand ExecutionQuality (a)EffectiveBid-AskSpread (b)PriceImprovement NOTE:theeffectivebid-askspreads,EBA,isdefinedinEq.(3)andthepriceimprovementisdefinedinEq.(4).Thesampleconsistsofdirect dealer-to-dealertradesanddealer-to-clienttradesfromJanuary2018toJune2024,filteredandaggregatedasdescribedinSection3.1. The empiricalprobabilitydensitiesofmetricsfordealer-to-dealertradesareinblue,whiletheempiricalprobabilitydensitiesofmetricsfordealerto-clienttradesareinred.Theempiricalprobabilitydensitiesfordealer-to-dealertradesanddealer-to-clienttradesarenearlyidentical.Data sources:FinancialIndustryRegulatoryAuthority(FINRA),BondTradeDisseminationSystem(BTDS)andTradeReportingandCompliance Engine(TRACE);informationobtainedfromtherepoInterDealerBrokercommunity;FederalReserveBankofNewYork,NPQS. FigureA-3: RetailTrades: DistributionsofEffectiveLiquidityandExecutionQuality (a)EffectiveBid-AskSpread (b)PriceImprovement NOTE:theeffectivebid-askspreads,EBA,isdefinedinEq. (3)andthepriceimprovementisdefinedinEq. (4). Thesampleconsistsofretail dealer-to-clienttrades,identifiedastradesoflessthan$10mmnotional,anddirectinstitutionaldealer-to-clienttrades,identifiedastradesof $10mmnotionalorgreater,fromJanuary2018toJune2024,filteredandaggregatedasdescribedinSection3.1. Theempiricalprobability densitiesofmetricsforinstitutionaltradesareinblue,whiletheempiricalprobabilitydensitiesofmetricsforretailtradesareinred. Data sources:FinancialIndustryRegulatoryAuthority(FINRA),BondTradeDisseminationSystem(BTDS)andTradeReportingandCompliance Engine(TRACE);informationobtainedfromtherepoInterDealerBrokercommunity;FederalReserveBankofNewYork,NPQS. 43