Reaching for Duration and Leverage in the Treasury Market

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Reaching for Duration and Leverage in the Treasury Market Daniel Barth, R. Jay Kahn, Phillip Monin and Oleg Sokolinskiy 2024-039 Please cite this paper as: Barth, Daniel, R. Jay Kahn, Phillip Monin, and Oleg Sokolinskiy (2024). “Reaching for Duration and Leverage in the Treasury Market,” Finance and Economics Discussion Series 2024-039. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2024.039. 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.

Reaching for Duration and Leverage in the Treasury Market* DanielBarth,R.JayKahn,PhillipMonin,andOlegSokolinskiy BoardofGovernorsoftheFederalReserveSystem May23,2024 Abstract We show substantial variation in mutual funds’ use of Treasury futures, both over time and across funds. This variation from mutual funds drives much of the time series variation inaggregateTreasuryfuturesopeninterest, includingover60%oftherecentriseinTreasury futurespositions.WeprovideevidencetheseTreasuryfuturespositionsarelargelyattributable tomutualfunds“reachingforduration”inordertotrackthedurationofabenchmarkindex with high cash Treasury exposure. Specifically, we show mutual funds use futures to fill the gapbetweentheirportfolioandtheindexthatresultswhentheytilttheircashpositionstoward higherreturnbutlowerdurationassets,suchasmortgage-backedsecuritiesandequities,and away from cash Treasuries. Treasury futures positions are more common in mutual funds which indicate a focus on dual objectives of duration management and total return whose style has a higher allocation to Treasuries. Reaching for duration allows funds to track their indexbetteratlowercost,butincreasesleverageintheTreasurymarketboththroughmutual fundslongTreasuryfuturespositionsandthroughtheleverageofhedgefundswhotakethe correspondingshortpositionsinTreasuryfutures. Keywords: Treasury markets, mutual funds, duration, indexing, futures, mortgage-backed securities JELCodes: G11,G12,G13,G23 *Daniel Barth (daniel.j.barth@frb.gov), R. Jay Kahn (jay.kahn@frb.gov), Phillip Monin (phillip.monin@frb.gov), Oleg Sokolinskiy (oleg.v.sokolinskiy@frb.gov). Views and opinions are those of the authors and do not necessarily representtheviewsoftheBoardofGovernorsoftheFederalReserveSystem. WethankDouglasDiamond,Anthony LeeZhangandparticipantsattheUniversityofChicagoBoothBankingSeminarforhelpfulcommentsandAudrey SelleyandMelindaWangforexcellentresearchassistance.

1 Introduction Recenteventshaveillustratedtherisksofnon-bankleverageinTreasurymarkets. InMarch2020, large sales by a variety of Treasury investors placed pressure on levered actors in the Treasury market that may have exacerbated a general dash for cash and thereby contributed to a burst of illiquidity.1 Similarly, leverage among Liability Driven Investment companies contributed to the 2022giltmarketcrisis.2 Historically,leveredbetsinTreasurymarketsalsocontributedtoTreasury market instability in the 1950s and 1960s.3 The risks posed by outsized leverage in the Treasury marketmakeunderstandingtheincentivestoleverTreasurypositionsanimportantareaoffocus for regulators and policymakers. Yet, because of the difficulty in observing the activities of most non-bankactors,therehavebeenrelativelyfewstudiesofthedeterminantsofcross-sectionaland time-seriesvariationinleverageinTreasurymarkets. In this paper, we examine mutual fund leverage in the Treasury market resulting from long Treasury futures positions. We form a unique dataset by merging information on mutual funds andtheircashandderivativesinvestmentsfrommultiplesources, includingregulatorydataand fundprospectuses. Usingthisdata,weshowthatmutualfunds’demandforlongTreasuryfutures is substantial: mutual funds make up roughly 53% of all asset manager long Treasury futures positions,whichstoodat$579billioninnotionaloutstandinginJune2023,and31%oflongopen interestinTreasuryfutures. Moreover,thereissubstantialtimeseriesandcross-sectionalvariation in the use of Treasury futures by mutual funds. Futures use by mutual funds exhibits a strong procyclical pattern, falling by almost 25% between December 2019 and June 2021 before rising by 65% between June 2021 and June 2023. Between 2021 and 2023, mutual funds made up 62% of the increase in total open interest in long Treasury futures. Further, while Treasury futures positions are concentrated in a few mutual fund strategies, even within these strategies there are largecross-sectionaldifferencesinTreasuryfuturesholdings. Weprovideevidencethatthisvariationisdrivenbyfunds’incentivesto“reachforduration,” usingTreasuryfuturestolengthenthedurationoftheirportfoliotomatchtheinterestrateriskof their benchmark indexes while reducing their cash Treasury positions and investing in other se- 1See Duffie (2020) He et al. (2020), Schrimpf et al. (2020), Vissing-Jorgensen (2021), Barth and Kahn (2021) and Kruttlietal.(2021)amongothersforadiscussion. 2SeePinter(2023)andAlfaroetal.(2024). 3SeeGarbade(2021),KahnandNguyen(2022)andMenandandYounger(2023). 1

curitieswithhigherexpectedreturns. Specifically,whenfixed-incomemutualfundsincreasetheir longTreasuryfuturespositions,theysimultaneouslydecreasetheirholdingsof(longer-duration) Treasury securities and increase their holdings of (shorter-duration) mortgage-backed securities (MBS). We find that funds with broader objectives also increase their holdings of equities. This suggests that by using Treasury futures, mutual funds can track their benchmark indexes while holdinglesscashTreasuriesandmorehigher-yieldingassets. Reachingfordurationresultsfromatensionbetweenthedurationoftheindexthatfundsare benchmarkedagainst(often,forfuturesusers,theBloombergU.S.AggregateIndex)andtheneed togeneratereturns. Treasuryholdingstendtobeboththehighestdurationandoneoftheloweryielding assets in fixed-income fund portfolios. The share of Treasuries in the Aggregate Index is both large and has grown over time, rising from 35% in 2011 to almost 45% in 2023 as Treasuryissuancehasexpanded. Inadditiontobeinglow-yielding,theseTreasuriesarealsoprimarily off-the-run, making them costly to hold relative to other more liquid and higher-yielding assets. ActivefundsthereforehaveanincentivetoallocateawayfromtheseTreasuriesandtowardsother assets. Indeed, wefindthatingeneralactivefundstrackingtheAggregateIndexhavelowerdurationthantheindexbuthigherreturns. Byusingfutures,fundscanobtainasimilardurationto theAggregateIndexusingfewercashTreasuries. WefindthatthemutualfundsthatuseTreasury futures track their benchmark index better overall, even though the duration of their cash holdings tends to differ more from the duration of the cash holdings in the index when their futures holdingsarehigh. Weshowthatthesefunds’futuresholdingsclosethegapbetweentheduration oftheircashpositionsandthedurationofthebenchmarkindex. Theincentivetoreachfordurationisdriveninlargepartbytheopportunitycostofinvestingin higher-durationassets: foregonepositionsinlow-durationassets. Overrecentquarters,weshow muchofthevariationinreachingfordurationisdrivenbychangesinreturnstoinvestinginlowdurationmortgage-backedsecuritiesrelativetoTreasuries. WefindthatTreasuryfuturesholdings arelargerwhentheexpectedreturnsonmortgage-backedsecuritiesarehigher,measuredbothin terms of option-adjusted spreads and dollar roll specialness. The increased allocation towards mortgage-backed securities and away from Treasuries that results drives most of the changes in the durationof cashassets for futuresusers relativeto the indexthat futuresusers thenmake up withtheirderivativesholdings. 2

Inthecross-sectionoffunds,wefindthattheuseoffuturesishighlypersistent,andthelargest futures users tend to be the same funds over time. There is little difference in performance between futures users and non-users, but the flow-performance relationship is weaker for futures users, which may be due to demand for the duration exposure these funds provide. Among Treasury futures users, the use of derivatives is often specifically mentioned in their prospectuses’ sections on principal risks and strategies and is significantly less commonly mentioned by non-users, providing an important bar to short-term entry. We find futures use is more common amongfundsthathaveagreaterincentivetoreachfordurationalongtwodimensions. First,they are more likely to track their benchmark indexes more closely, and their prospectuses may state explicitgoalstomatchtheirbenchmarkindexduration. Second,theyappeartobemorelikelyto take on active positions that count on the appreciation of securities. In particular, evidence from fundprospectusesindicatesthatfundswithhigherfuturespositionstendtohavehigherturnover, objectives focused on total return rather than income, and higher fees. Taken together, this constitutes strong evidence that mutual fund leverage in Treasury futures is driven by incentives to reachfordurationthatvaryoverthecycle. Our results show that mutual funds use Treasury futures to match their benchmark index returnwhiletiltingtowardshigher-yieldingassetswiththeircashportfolio. Thisstandsincontrast torecentresearchonmutualfunduseofderivativesincludingKanielandWang(2022)andChoi etal.(2023). Inbothcases,theauthorsfindthatmutualfundsusederivativesprimarilyasameans of amplifying returns and taking on additional risk. While we find that funds that use Treasury futures are increasing the duration of their overall portfolio, we show that these funds generally remain below the duration of the index they track. Funds with high use of futures are therefore closer to the performance of the index than those without. Meanwhile, both high futures users and funds that do not use futures tilt away from the index in different ways. The closest comparable paper to our own is Choi et al. (2023), which examines the use of interest-rate derivatives bymutualfunds. WhiletheirsampleincludesusersofTreasuryfutures,itisdominatedbyusers of interest-rate swaps. They find that funds are often using interest-rate derivatives for speculation and that derivative portfolios and cash portfolios are often unrelated. In contrast, we find that funds use Treasury futures specifically to match their index duration while tilting towards higher-yielding assets with their cash portfolio. Rather than suggesting that mutual funds are 3

using Treasury futures for independent speculation or to amplify returns, we show that mutual funds are using Treasury futures to reach for yield in a way that is consistent with their overall investment objectives and the structure of their benchmark indexes. Therefore, in the case of Treasuryfutures,wefindthatcashpositionsandfuturespositionsareintimatelyrelated. Indemonstratingthetilttowardsriskiermortgage-backedandasset-backedsecuritiesbymutualfundsthatuseTreasuryfutures,ourpaperalsocontributestoalargeliteratureonrisk-taking andreachingforyieldinmutualfundsandotherassetmanagers,includingKacperczykandSchnabl (2013), Becker and Ivashina (2015), Di Maggio and Kacperczyk (2017), Choi and Kronlund (2018)andChenandChoi(2023). Reaching-for-yieldbehaviorissimilartothereach-for-duration behaviorwedemonstrateinthispaperinthatinbothcasesthefunds’portfolioistiltedawayfrom theindexandtowardshigheryieldassets. Thetwobehaviorsthereforebothresultfromatension between the need to generate returns and the need to match an index or benchmark. However, thereach-for-durationbehaviorweexamineinvolvesweightingtheportfolioofthefundtowards one higher-yielding asset class away from another given an overall objective to match duration. Ontheotherhand,reachingforyieldinvolvestiltingtowardshigher-yieldingassetswithinaclass or rating, given an objective to maintain a certain share in each rating or asset class. In the case of reaching for duration, we show that the tension between returns and benchmarking can ultimately have consequences for financial stability through driving large mutual fund positions in Treasuryfutures. By examining long positions in Treasury futures, we also contribute to the literature on the cash-futures basis trade.4 This literature has generally discussed short positions in Treasury futures, which as discussed by Schrimpf et al. (2020), Barth and Kahn (2021), Kruttli et al. (2021), Banegas et al. (2021), Barth et al. (2023) and Glicoes et al. (2024) are often taken by hedge funds toexploitapositivebasisbetweencashandfuturesmarkets. Theexistenceofapositivebasishas often been explained as a result of the costs of holding cash Treasuries for dealers, as in FleckensteinandLongstaff(2020)andDuetal.(2023). Thisleavesopenthequestionofwhyotheractors wouldbewillingtotakethelongfuturesposition. Ourresultssuggestthatmutualfundstakethe 4Cash-futuresbasesexistinmanymarketsoutsideofU.S.Treasuries. Forinstance,Hazelkornetal.(2023)studies thecash-futuresbasisinequitymarkets.Theyfindthatflowstomutualfundstrackinganindexareanimportantdriver ofdemandforthatindex’sequityfutures,butintheircasetherelationshipappearstobefrommutualfunds’demand forthecashindexratherthanfutures. 4

longsideoffuturespositionstoshifttheircashholdingsawayfromTreasuriesandtowardhigheryieldingcashassets. Apositivebasismeansthatthisleveragecouldtheoreticallybeaccomplished morecheaplyusingTreasurycashsecuritiesborrowedintherepomarket. However, weprovide evidence that most mutual funds are severely limited in their ability to use repo leverage by the terms of their prospectuses and by the costs of transacting in the repo and cash Treasury market. Moreover, consistent with the model in Barth and Kahn (2021), our results suggest that mutual funddemandforTreasuryfutures,drivenbyanincentivetoreachforduration,maybeacontributor to the overall demand for Treasury futures, and therefore to the positive basis distinct from thebalancesheetcostsofdealers. Finally, our results have implications for the literature on Treasury inconvenience. Results in Duffie(2020),Heetal.(2020),andDuetal.(2023)suggestthatasTreasuryissuancecontinues,the costofholdingTreasurieshasrisensubstantially. However,thefocusofthesepapershasgenerally beenonregulatorycoststolargeTreasuryexposuresondealerbalancesheets. Ourresultspointto substantialimplicitcostsofholdingcashTreasuries,andespeciallyoff-the-runcashTreasuries,for mutualfunds—coststhatareavoidedbythesefundsholdingfuturesinstead. Thegeneralrisein outstandingTreasurieshasledtoariseintheshareofTreasuriesintheindexfundsmanymutual funds track and thereby may have increased the need for mutual funds to allay these costs. We alsoshowthatthedemandfrommutualfundsforTreasuryfuturestoreplaceTreasurysecurities depends on the returns to MBS, which provides an important link from Treasury inconvenience tootherassetmarketsand,implicitly,therealsideoftheeconomy. 2 Data For aggregate futures data, we use the Commodity Futures Trading Commission’s Traders in Financial Futures data, which provides weekly information on long and short positions for broad categories of investors — dealers, asset managers, leveraged investors (primarily hedge funds), andothers,andforawiderangeofcontracts,includingTreasuryfutures. We rely on three principal micro-level data sources: the CRSP Survivor-Bias-Free US Mutual Fund Data, the SEC’s Form N-PORT, and a hand-collected dataset formed by scraping mutual fundprospectuses. 5

TheSEC’sFormN-PORTprovidesdetailedportfolioholdingsformutualfundsonaquarterly basis,aswellasfund-levelinformationincludingassetsandliabilities,certainriskexposures,and returns. Funds that together with other funds under the same parent investment company have net assets of $1 billion or more were required to begin reporting Form N-PORT for the period ending March 31, 2019, but filings only became public starting September 30, 2019. Smaller fund groupsbeganreportingfortheperiodendingMarch31,2020. We scrape the universe of N-PORT filings from 2019 to 2023 from the SEC’s website. This resultsin208,579filingsintotal. Forourpurposes,thekeyadvantageoftheN-PORTdataisthatit hasdetailsonfunds’holdingsofderivatives. Importantly,N-PORTidentifiesfutures,swaps,forwards,andoptionpositionsseparately,whichallowsustofocusontheTreasuryfuturesholdings of mutual funds. We therefore primarily use the N-PORT data to identify futures positions. We verify the validity of both data sources by comparing fields where the N-PORT data and CRSP dataoverlapandfindtheyprovidesimilarresults. WeusekeywordstoextracttheTreasuryfuturespositionsfromN-PORT.Forinstance,futures derivativepositionscontainingthestrings“2y,”“5y”and“10y”arelikelytobe2-year,5-yearand 10-year Treasury futures positions. However, we are careful to exclude words suggesting that these may be non-U.S. futures positions, such as “EUREX,” “JPN” or “gilt.” Similarly, positions labeled “TU”, “FV” or “TY” are likely to be 2-year, 5-year and 10-year Treasury futures because thesestringscorrespondtothetickerslistedonBloomberg. Finally, wespot-checkthisclassification against a sample of funds to ensure that the procedure is accurate. In all, we identify 96,227 uniqueTreasuryfuturespositionsacrossfundsandovertime. In addition to the data on futures positions, we also use the N-PORT data for detailed information on holdings of cash assets. N-PORT provides some general classifications of investments basedontheirassettypeandissuer. Mostoftheseclassificationsarestraightforward. Weclassify investments as Treasuries whenever their issuer is identified as the Treasury Department, which can include certain bills otherwise classified on N-PORT as cash assets. Investments in MBS are classified as agency MBS when they are recorded as MBS and their issuer is a U.S. government agencyorgovernment-sponsoredenterprise,andasprivate-labelMBSiftheirissueriscorporate. To provide more detail on fixed-income instruments, we use ICE pricing and valuation data. This data covers a wide range of fixed-income securities, including corporate debt, ABS, MBS, 6

Treasuries, and non-U.S. sovereign debt. It contains two key features for our analysis. The first isthedurationofcashinvestments, whichweusetostudytheoveralldurationofmutualfunds’ cashportfolios. ThesecondisratingsforcorporatedebtbyFitch,Moody’s,andS&P,whichweuse toclassifycorporatedebtsecuritiesintoinvestment-gradeandspeculative-gradedebt. Weclassify investments as speculative grade whenever at least one of these three rating agencies rates it as speculativegrade. WematchthisdatatoN-PORTinvestmentsbasedontheCUSIPofthesecurity andthedateofthefiling. While ICE covers a broad range of instruments, we do not have access to details on duration for the to-be-announced (TBA) MBS market. As we describe below, the TBA market is a popular investment for certain mutual funds heavily invested in Treasury futures. We use data from JP Morgan Markets to provide an estimate of the duration of these instruments. We also use JP Morgan data on spreads, duration, convexity, and dollar roll specialness for aggregate analysis, and for the duration of Treasury futures contracts. This sample covers the period from 2012 to 2023. WeusetheSEC’sMutualFundProspectusRiskReturndatasetandscrapeadditionaldatafrom theSEC’swebsitecoveringtheuniverseofmutualfundprospectuses. Weusethisdatatoidentify thestatedobjectives,strategies,andrisksoffunds,theirbenchmarkindexes,andtoidentifyfunds that have stated objectives to use derivatives. We merge based on funds’ SEC-assigned series identifier. Forasubsetoffixedincomefundsweareinterestedintheirbenchmarkindex. Asubset offundsliststhisbenchmarkdirectlyintheirN-PORTfilings,inwhichcaseweusethisasthefund benchmark. For the remaining funds, the benchmark is determined by matching key phrases in the fund prospectus to a list of common fixed-income benchmarks, such as the Bloomberg U.S. Aggregate Index, the Bloomberg U.S. Universal Index, or the Bloomberg Credit Index. First, we search the principal strategy section of the prospectus to find a match. If we cannot find a match inthissection,wethensearchtheremainderoftheprospectus. We then merge the N-PORT data with the CRSP Survivor-Bias-Free US Mutual Fund data to obtainacomprehensivedatasetofmutualfundholdings,returns,fundcharacteristics,andfutures positions. TheCRSPdataprovidesmonthlyholdingsanddailyreturnsformutualfunds. Weuse databeginningin2015forthepurposesofthisstudy. CRSPidentifiersdonotoverlapwiththeN- PORTdata. Weperformamatchbetweendatasetsfirstusingfundtickerswherepossibletomatch 7

betweenthetwosets,thenusingfundnameswheretickersarenotavailable. Whenmatchingon fundnames,wefirstlookforwhethertheCRSPnamecontainsboththeseriesnamefromN-PORT and the regulatory name from N-PORT, since often the CRSP name is a concatenation of these two names with additional characters describing the share class. In the case that this procedure producesmultiplematches,wethenhand-selectbetweenthematches. Foraselectgroupoffunds that weare unableto matchusing this procedure, we thenhand-match the funds. We are able to match13,481fundsbetweenthetwodatasetsfortheperiod2019through2023. 3 Aggregate Treasury futures positions of mutual funds One of the more dramatic changes in Treasury market activity over the past decade is the significant rise in Treasury futures volumes. Aggregate positions in Treasury futures have risen from roughly $500 billion in notional exposure in 2010 to over $2 trillion in 2024. This growth has receivedattentionprimarilyduetoworriesaboutthegrowthinhedgefunds’shortTreasuryfutures positions, which seem to primarily support their activity in the cash-futures basis trade.5 Yet, much less is known about the incentives for investors to take long positions in Treasury futures. Below, we describe the essential features of the U.S. Treasury futures market. We then show that the primary investors in long Treasury futures are asset managers, with the majority of positions accounted for by mutual funds. We demonstrate these positions show substantial variation over time and across funds, though it is usually the same funds holding the largest futures positions across time. The rest of the paper then focuses on what drives both the time-series and crosssectionalvariationinmutualfundholdingsofTreasuryfutures,tounderstandthedriversofthis majorconcentrationofleverageintheTreasurymarket. 3.1 Structureofthefuturesmarket TheTreasuryfuturesmarkethasbeencoveredelsewhereingreatdetail,forinstanceinBurghardt and Belton (2005) and Barth and Kahn (2021). Here, we provide a brief overview of some salient featuresofthemarketstructureandtheroleofassetmanagersinthismarket. 5SeeSchrimpfetal.(2020),BarthandKahn(2021),Kruttlietal.(2021),Banegasetal.(2021),Barthetal.(2023)and Glicoesetal.(2024). 8

Treasury futures are offered at a variety of different maturity points. The most common contracts are the 2-year, 5-year, 10-year, and 30-year Treasury futures. Each contract is settled via physical delivery. The CBOT allows for several different Treasuries in a specified range of maturitiestobedeliveredintoeachcontract. Allowingthedeliveryofmultiplesecuritiesiscommonly thought to afford additional liquidity to the Treasury futures market, and the Treasury futures marketisgenerallythoughttobemoreliquidthanTreasurycashsecurities,providedthosesecuritiesarenoton-the-run(seeBakeretal.(2020)). Theprice,duration,andyieldofaTreasuryfuturescontractarerelatedtotheunderlyingTreasuries because of the option to physically deliver Treasuries into the contract at expiration. This near-arbitragerelationshipisenforcedbytheTreasurycash-futuresbasistrade,whichisdiscussed at length in Burghardt and Belton (2005), Fleckenstein and Longstaff (2020) and Barth and Kahn (2021). As a result of this trade, the price and risk attributes of a Treasury futures contract will closely replicate a Treasury cash security, the difference being that the futures contract does not requirethefullnotionalamounttobepostedupfront. Theonlycashrequirementattheinitiation of a futures contract is the initial margin. Variation margin may also be called if the position depreciates(orappreciatesfortheshortposition)enough. Thisallowsfortheuseofleverageinthe Treasuryfuturesmarket,whichwediscussbelowasakeyfeatureoftheattractivenessofTreasury futurestoassetmanagers. 3.2 AssetmanagerTreasuryfuturespositions AsdiscussedinBarthandKahn(2021), assetmanagersmakeupthemajorsourceofdemandfor long Treasury futures positions. Figure 1 shows the growth in aggregate short and long futures positionsseparatelyforthreeentitytypes: hedgefunds,assetmanagers(includingmutualfunds), andothertypes. AsshowninFigure1,themajorityoflongTreasuryfuturespositionsareheldby assetmanagers. AsofJanuary2024,assetmanagersaccountedfor58%ofthe$2.04trillionintotal open interest. Figure 1 also shows that asset managers are always net long Treasury futures and that their long futures positions are always significantly larger than their short futures positions. Finally, the figure also illustrates that hedge funds in general take up the opposite side of asset managers’futurespositions. 9

Perhapsmoreimportantly, assetmanagersaccountforasubstantialproportionofthechanges in aggregate long futures positions over time. Figure 2 plots the cumulative change in aggregate long futures positions against the cumulative change in asset managers’ long futures positions between January 2018 and March 2024. On average over this period, asset managers account for 83%ofthecumulativevariationinaggregatelongfuturespositions. While it has been documented previously that asset managers drive a substantial share of the variation in Treasury futures open interest, much less is known about which types of asset managers are responsible for this activity. The asset manager category in CFTC futures data is broad,comprisingmutualfunds,pensionfunds,endowments,sovereignwealthfunds,andother entitytypes. UsingdatafromFormN-PORT,weshowthatmutualfundsaccountforalargeproportionof the variation in total long asset manager futures positions. Figure 3 plots the cumulative change inlongTreasuryfuturespositionsfromN-PORTdataagainstthecumulativechangeinassetmanager futures positions from CFTC futures data between January 2020 and September 2023. A significant portion of the decline in aggregate futures following the stress in Treasury markets in early2020,aswellasasignificantportionoftheriseinlongassetmanagerTreasuryfuturesbeginning in late 2021, are due to changes in mutual fund Treasury futures positions. In total, mutual funds accounted for 53% of asset manager long Treasury futures positions in June 2023. The significant overlap between asset manager and mutual fund Treasury futures is notable given that thesedataoriginatefromdifferentsources. Table 1 shows the long futures positions of asset managers and mutual funds for three dates: December 2019, June 2021, and June 2023, roughly corresponding to the dates of the pre-COVID peak, most recent trough, and most recent peak (as of the writing of this paper and available N-PORT data). The table shows that throughout the period, mutual funds’ share of total asset manager futures has stayed relatively constant at just about 50%. Mutual funds also accounted foramajorityofthedeclinefromDecember2019toJune2021,andthesubsequentrisefromJune 2021toJune2023. Mutual funds appear to have disproportionately large positions in the shorter-maturity Treasuryfuturescontracts,whicharealsothecontractsmostheavilyassociatedwithhedge-fundbasis trading. Table 1 shows these positions segmented by contract. Mutual fund holdings are partic- 10

ularly high in the 2-year and 5-year contracts, which Barth and Kahn (2021) argue have been the focusofbasistraders. WhereasmutualfundlongfuturesfromN-PORTdataaccountforjustover 50%oftotalassetmanagerlongfuturesfromCFTCdata, theyaccountforover70%ofthe2-year and5-yearnotionalamounts. And,mutualfundsaccountfor80%ofthegrowthinassetmanager longTreasuryfuturesbetweenJune2021andJune2023inthe2-yearand5-yearcontracts. Mutualfunds’substantialportionsofthelevelandcumulativechangeinaggregatelongTreasury futures positions make their motives for holding Treasury futures important for recent developmentsinTreasurymarkets,especiallyintheleverageandTreasuryholdingsofhedgefunds. However, mutual funds are also important to study in this context because their motivations for using leverage in the Treasury market may help shed light on the motivations of other, more opaque asset management structures such as separately managed accounts, liability-driven investment funds, endowments, or sovereign wealth funds. Further, mutual funds’ incentives to vary their use of Treasury futures over time may be a hint as to the motivations of other asset managementtypesthatholdfutures. Whilenostatisticsarecurrentlyavailablefortheother47% ofassetmanagerpositions,anecdotalevidencesuggeststhatmuchoftheremainingnotionaloutstandingisheldbyseparatelymanagedaccounts,whichoftenhavesimilarinvestmentobjectives andrestrictionsasmutualfunds. For these reasons, this paper explores mutual funds’ significant use of long Treasury futures positions,withaneyetowardunderstandingbothtime-seriesandcross-sectionalvariation. 3.3 MutualfundstylesandTreasuryfutures The use of long Treasury futures by mutual funds is concentrated in a few specific investment styles. Table2showsthetotalassetsandlongTreasuryfuturesnotionalamounts, alongwiththe share of all mutual fund long Treasury futures positions accounted for, by Lipper objective code (representing the fund’s investment style) for three different dates. The Intermediate Investment Grade Debt style (“IID”) accounts for roughly one-third of the total long Treasury futures held by mutual funds. Short Investment Grade Debt funds (“SID”), Balanced funds (“B”), and Short Intermediate Investment Grade Debt funds (“SII”) account for another 19%. IID funds not only account for a large share of the total long Treasury futures positions but also a large share of the 11

totaldecreasefrom2019to2021(59%)andincreasefrom2021to2023(32%). Intermediateinvestmentgradedebtfundsare,accordingtoLipper,definedas“[F]undsinvest primarilyininvestmentgradedebtissues(ratedintopfourgrades)withdollar-weightedaverage maturities of five to ten years.” This objective code contains funds that are sometimes called “Core” or “Core Plus” Bond Funds in the industry. These funds are usually benchmarked to the Bloomberg U.S. Aggregate Bond Index (formerly the Barclay’s U.S. Aggregate Bond Index), or less commonly the U.S. Universal Bond Index. The Aggregate Bond Index is a broad index of U.S.fixed-incomesecurities,includinginvestment-gradeTreasuries,agencyMBS,corporatedebt, andABS,butnotablyexcludingfloatingratesecuritiesandsub-investmentgradedebt. Treasuries makeupnearly45%oftheindex. Figure 4 examines the holdings of IID funds over time, both in notional amounts and as a weightedaverageshareoftotalassets. Ascanbeseen,notionalamountsofIIDfundsfollowtotal mutualfundlongTreasuryholdingsclosely. Moreover,theshareofthesepositionsintotalassets displays the same pattern. This implies that the use of Treasury futures by these funds is not driven by changes in the size of the IID sector, but actually represents higher relative allocation towardsTreasuryfutures. BecauseIIDfundsrepresentsuchalargeshareofthefuturesmarkets,andbecauseitisuseful to make a comparison between funds that are similar in their investment objectives, we focus on IID funds in many of the later analyses. However, we note that there are many similarities between IID funds and SID and SII funds. All three categories invest in investment-grade debt issues and maintain relatively short dollar-weighted average maturities. The main difference is that SID funds invest in debt with average maturities of less than three years, while SII funds invest in debt with average maturities of three to five years. Finally, while balanced funds invest in a mix of equities and fixed-income securities (usually on a 60/40 basis) their debt portion is oftenindexedtotheAggregateBondIndexorasimilarlybroadindex. Evenwithinafundinvestmentstyle, thereissubstantialvariationintheuseoflongTreasury futures. Table3showsthedistributionofnotionalamountsofTreasuryfuturesonJune23rd,2023, for the subset of investment styles shown in Table 2, as well as the percentage of funds within that style that hold a positive amount of long Treasury futures. For IID-style funds, 54% report holding some long Treasury futures. The median amount held is $3 million, the 75th percentile 12

is $140 million, and the 99th percentile is $15.18 billion. SID-style funds had 50% long Treasury futures ownership, with similar percentiles of notional amounts other than the 99th percentile, which held only $3.13 billion. SII-style funds also demonstrate significant long Treasury futures ownership,witha75thpercentileof$70million,anda99thpercentileof$7.28billion. The high concentration of long Treasury futures among certain investment styles suggests these fund types have particular incentives to hold Treasury futures. It also makes comparisons withinfundstylesparticularlyconvenient. However,theheterogeneitywithinfundsofthesame stylealsosuggeststhatotherfactorsaredrivingthecross-sectionalvariationintheuseofTreasury futuresbeyondthebroadstyleofinvesting. Wewillreturntotheseissuesbelow. 3.4 NetTreasuryfuturesholdingsandduration MutualfundsholdshortaswellaslongTreasuryfutures. However,themajorityofmutualfunds’ Treasury futures positions are long, especially during times of high overall futures use such as 2019 and 2023. The top panel of Figure 5 shows gross long, gross short, and net long Treasury futures positions of mutual funds in notional billions. Short positions are relatively low in 2019, peak in early 2022, and decline through 2024. They therefore follow the opposite pattern as the long positions, and as a result, the U-shaped pattern of long positions over this period is even strongerfornetpositions. One concern with this pattern of futures holdings might be that funds are actually using futures to place direct bets on the shape of the yield curve, for instance through steepeners or flatteners. If this represents the usual use case for Treasury futures, we would expect the duration of mutual funds’ futures portfolios to be roughly flat over time. However, the bottom panel of Figure5showsthatthedurationofmutualfunds’futuresholdingsactuallythetotalnetnotional pattern. This suggests that futures are not being used primarily for yield curve bets. A more detailed comparison is provided in A.1, which shows that this inverse-U-shaped pattern generally holdsacrossthedifferentmaturitiesofTreasuryfutures,againsuggestingthatfundsarenotusing futurestomakebetsontheshapeoftheyieldcurve. 13

3.5 Persistenceinmutualfunds’Treasuryfuturespositions ThesetoffundsholdinglongTreasuryfuturesappearspersistentovertime. Figure6plotsaggregatelongTreasuryfuturespositionsforfourgroupsofmutualfunds,basedonfuturesholdingsas ofJune2023: fundswithnolongTreasuryfuturespositions,fundsinthebottomone-thirdoflong Treasury futures positions (by notional amount), funds in the middle-third of long Treasury futurespositions,andfundsinthetopone-thirdoflongTreasuryfuturespositions. Asshowninthe figure, the substantial majority of total long Treasury futures positions are held by mutual funds inthetopone-thirdofpositions. ThispatterndatesbacktoJanuary2020;thatis,themutualfunds that hold the most long Treasury futures in June 2023 comprise the significant majority of long Treasury futures positions across the entire sample period for which N-PORT data are available. This suggests that it is predominately the same funds that increase and decrease the intensity of longTreasuryfuturesovertime,ratherthanthesetoflargefuturesusersshiftingovertime. Lookingatthelargestfuturesholdersbroadlysupportsthisview. Table4showstheidentities ofthetop10fundsbylongTreasuryfuturespositions,theirnetassets,andcomparisonsofnotional amounts held on December 2019, June 2021, and June 2023, both in dollars and as a percentage of assets. Overall, the largest holders of long Treasury futures in June 2023 also held significant positions in December 2019. Moreover, many of the largest holders of long Treasury futures are IIDfunds. Notably,thelargestTreasuryfuturesuserasof2023wastheAmericanBalancedFund, whichheld$34billionoflongTreasuryfuturesinJune2023,or77%ofallfuturesholdingsofbalancedfunds. Sixofthesetenfundsalsosharethesamemanager: AmericanBalancedFund,Bond FundofAmerica,AmericanFundsStrategicBondFund,IntermediateBondFundofAmerica,the U.S.GovernmentSecuritiesFund,andAmericanFundsInflationLinkedBondFundareallmanaged by Capital Research & Management. This suggests an important role for the fund manager indeterminingthestanceoffundstowardsTreasuryfutures. Resultsfromasimplelinearprobabilitymodelalsosupporttheviewthatfuturespositionsare persistent within funds. A regression of an indicator for whether the fund holds long Treasury futures in June 2023 on an indicator for whether the fund held long Treasury futures in January 2020 delivers a coefficient of 0.73 with a t-statistic of 104. The R2 from this regression is nearly 50%. Prior long futures positions appear to be a strong predictor of future long Treasury futures 14

positions, indicating this is a persistent feature of certain mutual funds portfolio choices across changinginterestrateandinvestmentopportunityenvironments. The persistence in these futures positions suggests that funds that hold long Treasury futures can betreated as asomewhat distinct category from thosethat do not, andone thatpersists over time. It also underscores that the decision to hold futures is a persistent feature of certain funds’ investment strategies, rather than a response to short-term changes in the investment environment,eveniftheleveloffuturesholdingsvariesmoresubstantiallyovertime. Wethereforebegin byexaminingthetime-seriesvariationinfundfuturespositions,especiallyhowfuturespositions co-movewithotherinvestmentsintheirportfolio,beforereturningtothecross-sectionalvariation infuturespositionsandtheincentivesthatdrivethatvariation. 4 Futures positions and portfolio choices of mutual funds Inthissection,weexaminetheportfoliochoicesoffuturesusersandnon-users. Weconcentrateon IIDfundssincetheyhavebothhighfuturesholdingsandhighvarianceofholdingsacrossfunds, but relatively similar investment objectives. We show that funds that hold long Treasury futures makedifferentportfoliochoicesthanthosethatdonot,andthendiscusshowthesechoicescreate demandforTreasuryfutures. 4.1 Treasuryfuturesandportfoliochoices We begin by focusing on IID funds. We make additional restrictions on the sample of funds to make portfolio choices more comparable. First, we include only funds that list the Bloomberg AggregateIndexastheirtargetindex. Second,weexcludefundsthathavemorethan90%oftheir assetsinequitiesorregisteredinvestmentcompanies—thisdropsafewfeederfundsthatreport investments almost exclusively in their respective master funds. Finally, we drop any exchangetradedfunds. Table 5 reports the percentage of total assets of IID funds held in various asset classes as of three dates: December 2019, June 2021, and June 2023. The investment allocations of three types of funds are examined: index funds, active fund non-futures holders, and active fund futures holders. Sorting into active fund futures holders and non-futures holders is done by holdings 15

as of June 2023, so that we are comparing the same funds over time. The dates chosen again correspondtothepre-Covidpeakinfuturesuse,themostrecenttrough,andthepost-Covidpeak. Therefore,assetsthatdecreaseinthefirstperiodandincreaseinthesecondperiodaremorelikely to berelated to theincrease in futurespositions. By comparing thesechanges to indexfunds, we isolatetheactivecomponentoffuturesholders’assetmanagementdecisions. Bycomparingthem tonon-indexfunds,wecanisolatethecomponentsofthesedecisionsthatarerelatedtotheuseof futures. ThefirstassetclasscoveredinthetableiscashTreasurysecurities. Itisimmediatelyclearthat both types of active funds hold fewer Treasury securities than index funds, at a little more than half of the allocation to Treasuries of these funds. Similarly, the allocation of the Bloomberg Aggregate Index to Treasuries was roughly 40-45% throughout this period, a little less than double the allocations of active funds. The difference is particularly notable for shorter maturity Treasuries. This already suggests that allocation away from Treasuries is a popular strategy among activefunds. Table5providesevidencethatTreasuryfuturesserveasasubstituteforholdingsofcashTreasuriesforfuturesusers. Asabenchmark,indexfundsreducedtheircashTreasuryholdingsby2% between December 2019 and June 2021, then increased their holdings by 3% between June 2021 and June 2023. Between December 2019 and June 2021, non-futures holders followed a similar path, reducing their cash Treasury positions by 3%. Similarly, non-futures holders exhibited a slight decrease in their holdings of cash Treasuries (as a percentage of assets) between June 2021 and June 2023. This stands in stark contrast to futures holders. Futures holders increased their allocationtocashTreasurysecuritiesby6%ofassetsbetweenDecember2019andJune2021,then reduced these holdings by 5% of assets between June 2021 and June 2023. Recall that mutual fundsreducedtheirlongTreasuryfuturespositionsbetweenDecember2019andJune2021, then increased these positions between June 2021 and June 2023. This suggests that, for Treasury futuresholders,cashTreasuriesandTreasuryfuturesaresubstitutes. One potential objection to this evidence would be that the short time series afforded by the N-PORT data is not enough to make inferences about the substitutability between Treasury cash andfutures. Toextendthesample,weexamineholdingsof2023futuresholdersandindexfunds 16

over time using the CRSP mutual funds monthly holdings data.6 Figure 7 shows visually the contrast in cash Treasury positions between Treasury futures holders and non-futures holders. Thelight-bluelineplotsaggregatefuturespositionsbyassetmanagersfromCFTCdata,thesame datareportedinFigure1. Ingreen,weplotthetotalcashTreasuryinvestmentsofIIDindexfunds, andindarkblueweplotthetotalcashTreasuryinvestmentsofIIDfuturesholders. Thegreenline shows a steady, upward path, driven primarily by the increase in assets under management of IID funds over this period. The green line shows little resemblance to aggregate asset manager Treasury futures positions. The dark blue line, on the other hand, remains roughly flat between 2015andlate2020—whilenon-futuresusersweregrowingtheircashTreasurypositions,futures userswerekeepingthemconstant. Onlyinlate2020,onceaggregateassetmanagers’futuresfell, did futures users begin to grow their cash Treasury holdings. This pattern swiftly reversed in early 2022, as cash Treasuries fell substantially amid a new wave of rising long Treasury futures positions. Table 5 also shows ways in which both futures-holders and non-futures-holder active funds tilt away from the index. For instance, index funds have negligible allocations to CDOs, ABS contracts other than agency MBS, and speculative-grade corporate debt. This largely follows the constructionoftheBloombergAggregateIndex,whichexcludesspeculative-gradedebtandmost CDOs and other ABS. Additionally, both non-futures holders and futures holders have higher allocations to corporate debt than index funds, with non-futures holders having an even higher allocation than futures holders. Especially, for corporate debt positions and private-label MBS, thesepositionsmayinvolveadditionalexposuretocreditrisknotpresentinthebenchmarkindex. However, exposures to these instruments do not appear to be related to the aggregate pattern of Treasuryfuturesholdingsamongmutualfunds,withallcategoriesbeingfairlyconstantasashare offuturesholderassetsoverthethreeperiods. Alternatively,TreasuryfuturesholdershavemuchhigherallocationstoMBS,andparticularly agency MBS, than either index funds or non-futures holders. The allocation to MBS for index fundsisalittleunderaquarterofassets,andthisallocationisrelativelyconstantovertime. Nonfuturesholdershaveahigherandmorevariableallocation,between23and30percentagepointsof 6Weareunabletoobservefuturesholdingsofthesefundspriorto2019,soouranalysisherereliesontheassumptionthatfuturesholdingswerealsoquitepersistentpriorto2019.Withoutanysourceofdataonfutures,itisimpossible toexternallyvalidatethisassumption,butgivenourresultsonholdings,itappearsreasonable. 17

assets,withadeclineof6percentagepointsbetween2019and2021andanincreaseof3percentage points between 2021 and 2023. However, the allocation of futures holders is as high as 43% of assets in December 2019, with a decline of nearly 16 percentage points between December 2019 andJune2021,andasubsequentincreaseofroughly11percentagepointsbetweenJune2021and June2023. That the increase in MBS for futures holders is not only coincident with the pattern of usage offuturespositionsbutalsothatthischangeisnotpresentintheindexallocationprovidesstrong evidencethatthischangeisassociatedwithfuturesuse. Buildingonthisintuition,Figure7plots the difference in the cumulative change in asset class investments since 2015 for futures holders andnon-futuresholders(hereincludingbothindexandactivefunds). Themeasureshowninthe figureis:     (cid:88) (cid:88) m i,t =  w j F ,t ×holding i,j,t −w j F ,T ×holding i,j,T − w j N ,t ×holding i,j,t −w j N ,T ×holding i,j,T  j∈F j∈/F where F is the set of futures holders, wF is the share of assets for fund j in all futures holders at j,t timet,wN istheshareofassetsforfundjinallnon-futuresholdersattimet,andholding isthe j,t i,j,t holdingofassetclassibyfundj attimet. Thismeasureisessentiallyadifference-in-differences, with similar advantages because it partials out the time-invariant differences between funds and thetime-varyingdifferencesbetweenfundsthatarenotrelatedtofuturesholdings. However,we donotintenditasacausalmeasure,butratherasawayofexploringassociationsbetweenfutures useandportfoliochoices. Figure 7 reinforces that changes in Treasury holdings and mortgage-backed securities for futuresholdersarebothcoincidentwithperiodsofhigherfuturesholdingsandlargerthanchanges for non-futures holders. In Figure 9, we show the raw cumulative changes further subdivided intoindexfundsandfuturesholders. TheseillustratethatindexfundallocationstoMBSandcash Treasuriesareessentiallyconstantovertime,whilefuturesholderstilttowardsMBS.Theevidence inthesetwofiguresshowsthatshiftsintheportfoliosfromTreasuriestoMBSareprimarilytheresultofreallocationfromfuturesfundsnotpresent(ormoremuted)inindexfundsandnon-futures holders. 18

Thesefiguresdonotallowustoexaminetheintensivemarginoffuturesuseortomakestatisticalcomparisons. InTable6,weevaluatetheportfoliochoicesoffundsformally. Table6regresses thepercentageofthefund’sAUMheldindifferentassetclassesontheratioofafund’slongTreasury futures notional value to AUM. The left-hand side variable is not exactly a portfolio weight becauseweareusingnotionalvalues,whileportfolioweightswoulddependonthemarketvalue of the derivatives contract. As a result, without fixed effects, the sum of coefficients across asset classes should be nearly zero, since asset shares must sum to one and the cash outlay to open a futures position is relatively small.7 To account for attributes of the fund’s overall strategy that maybecorrelatedwithfundsthatusefutures,weincludefundfixedeffects,whiletoaccountfor time variation in the attractiveness of investments that do not vary with futures use, we include time fixed effects. Notably, the fund fixed effect will essentially exclude all funds that never use futures,sothattheseeffectswillbeidentifiedontheintensivemargin. Column (1) in Panel A shows that, as a percentage of assets under management, Treasury futures and cash Treasury securities are strongly negatively correlated. A one percentage point higherallocationto(notional)longTreasuryfuturesisassociatedwitha0.125%higherallocation to cash Treasury securities, with a t-statistic on the coefficient above 10. The benefit of investing inTreasuryfuturesoverTreasurycashpositionsisthatanequivalentexposuretoTreasuryyields requires much less cash upfront. Column (2) of Panel A provides evidence of how this extra cashisbeingdeployedbylongTreasuryfuturesholders. Aonepercentagepointincreaseinlong Treasury futures is associated with an increase of 0.047% in MBS. This relationship is also highly statistically significant, with a t-statistic of around four. Investments in ABS also increase, with a similarmagnitudeandahighert-statisticofabove6, thoughthischangeismoreconcentratedin smaller funds and so does not show up to the same degree in the aggregate. In Table A.2 in the Appendix,weexaminetheseshiftsinmoredetail,findingthattheincreaseinMBSisroughlysplit betweenagencyandprivate-labelMBS.OnepossibilityisthattheseMBSpositionsareassociated withdollarrolls(seeSongandZhu(2019)). Weconstructanestimateofdollarrollactivityfromthe minimumofshortandlongTBApositionsandshowthisisnotthedriveroftheoverallresponse. 7ThecashrequirementstoopenaTreasuryfuturespositionistheinitialmargin,whichvariesbycontract,butwas $1,150forthe2-yearcontract, $1,400forthe5-yearcontract, and$2,125forthe10-yearcontractasofApril1st, 2024 (recallthateach2-yearcontractrepresents$200,000notional,andthe5-yearand10-yearcontractsrepresent$100,000 notional). 19

Meanwhile, for other ABS investments, the increase is driven by a rise in CDOs, with a smaller butstillsignificantcontributionfromothernon-MBSclassesofABS. Incolumn(3),PanelAofTable6,wefindnostatisticallysignificantassociationbetweenlong Treasury futures and broad corporate debt. Table A.3 in the Appendix provides a breakdown of corporate debt investments to examine whether the lack of an overall effect masks a transition towards riskier debt. Instead, we find that there is a shift from speculative-grade to investmentgradedebt,aswellasfromU.S.tonon-U.S.debt. Thissuggeststhatthereisnotasignificantshift of futures holders into more credit-sensitive instruments that are not present in the Aggregate Index. Incolumn(5)ofTable6,wedofindevidencethatasTreasuryfuturesincrease,sotoodoes theamountofcashheld, possiblyinanticipationoffuturemarginrequirementsontheincreased futures positions, although this result is weaker than for cash Treasuries, MBS and ABS (with a t-statisticjustbelow1.6). Panel B of Table 6 repeats the regressions in Panel A, but includes all fund strategies. As in Panel A, long Treasury futures positions are strongly negatively related to cash Treasury positions. Also, similar Panel A, column (2) shows that MBS is positively related to Treasury futures use. However, unlike Panel A, allocations to corporate debt are negatively related to long Treasuryfutures,andthereisastrongpositiverelationshipwithequityinvestments. Therelationship here is driven primarily by balanced funds, for whom corporate debt and Treasuries are closer substitutes,andequityisanallowableinvestmentwithhigherreturns. Overall,PanelBprovides furthersupportforareach-for-durationmotive: fundswithhigherTreasuryfuturespositionsreducetheirlower-yieldingTreasuryandcorporatebondholdingswhileincreasingtheirallocations toMBSandequities. Ontheotherhand,wedofindthatthereisashiftoffutures-holderstowardsfloatingratedebt, a category also excluded from the index. Table 7 shows the portfolio shifts associated with long Treasury futures also correspond to a shift from fixed to floating-rate debt. Column (1) of Table 7showsthatahigherallocationtoTreasuryfuturesisassociatedwithalowervalueoffixed-rate debt;aonepercentagepointincreaseinlongTreasuryfuturesrelativetoassetsisassociatedwitha 0.089%decreaseinfixed-ratedebtholdings. Conversely,asshownincolumn(2),thesamechange inlongTreasuryfuturescorrespondstoa0.047%increaseinfloatingratedebt. Similarly,column (3)showsthatholdingsofvariableratedebt,atypeofdebtsecuritywheretheinterestrateresets 20

periodically, also increases as long Treasury futures increase. This is consistent with the overall shifttowardsMBSandCDOsinceamongfloating-ratesecuritiesinthedata,28%areMBS,19%are collateralizeddebtobligations(CDO),and32%areloans,withanother10%inotherasset-backed securities. Meanwhile, the top panel of Table 8 shows that futures use is associated with a decrease in fundinvestmentsinshorter-maturitydebt. ThiseffectismostpronouncedforcashTreasuries,as shown in the bottom panel, with more than half of the total association coming from Treasuries due in less than five years. This is consistent with the aggregated evidence in 5 that funds that hold long Treasury futures have a lower allocation to shorter maturity Treasuries. As we shall see it also has important implications due to the relatively long maturity of Treasury securities comparedtootherinvestmentsforIIDfunds. TheresultsinthissectionstronglyimplythatTreasuryfuturesuseisassociatedwithchanges in the cash portfolios of the mutual funds that take on futures positions. The changes in investmentsthatweobserveareconsistentwithfundsmovingfromlower-yieldingTreasuriestohigheryieldingassets,though,notably,thesefundsdonottakeoncreditrisk,anditisunclearwhythese funds choose to conduct this reallocation when they do. Additionally, in contrast to previous results established by examining other derivatives contracts used by mutual funds such as Choi etal.(2023),thisimpliesthatthecashportfolioandTreasuryfuturesportfolioarestronglyrelated. However,therelationshipbetweentheseinvestmentsisunclear. Whyshouldfundsincreasetheir holdings of Treasury futures when they decrease their holdings of Treasuries and increase their holdingsofMBS?Weexplorethisquestioninthenextsection,providingevidencethattheuseof Treasury futures is related to an attempt to match the duration of the overall index while tilting towardsMBS.Inthefollowingsection,wethenexaminethecyclicalincentivesforfundstoinvest inagencyMBS,andhowtheseincentivesarerelatedtotheuseofTreasuryfutures. 4.2 AggregateTreasuryfuturesandmortgage-backedsecurities The prior section documented a significant shift from cash Treasury securities to MBS associated with an increased allocation to long Treasury futures. This suggests the relative attractiveness of MBSisanimportantfactorinthetime-seriesvariationofmutualfunds’useofTreasuryfutures. 21

Totestthishypothesismoreformally,wefocusontheto-be-announced(TBA)segmentofthe residentialMBSmarket(RMBS),whichareoftentheinstrumentsofchoiceforassetmanagersdue to their superior liquidity (see Vickery and Wright (2013)). A TBA trade is essentially a forward contract on a generic pool that satisfies certain specified characteristics, including the GSE program, original loan maturity, and coupon. Specifically, we focus on the front, nearest-maturity TBAtradesforcurrentcouponFNMA30-yearinstruments.8 WeprovideresultsbasedonalternativeunderlyingsecuritiesinAppendixA.1.3. WeuseavarietyofmeasurestoproxyfortheattractivenessofRMBSpositions. Weuseoptionadjusted spreads (OAS) as a measure of the current attractiveness of RMBS securities, and the specialness of the current dollar roll to proxy for expected RMBS returns.9 Song and Zhu (2019) showthatdollarrollspecialnessisnegativelyassociatedwithexpectedTBAreturns. FigureA.13 depictsthetimeseriesoftheconsideredRMBSvariables. RMBS have other features that are relevant for Treasury futures holdings. Specifically, effects related to option-adjusted duration and convexity. While underlying mortgages typically have originalmaturitiesof30-years,theoption-adjusteddurationsofRMBStendtobemuchlowerdue toprepayments. ThetopleftpanelofFigureA.13plotsthedurationofthebellwetherTBAFNMA 30-year current coupon: since 2016 its duration has been lower than 6 and even below 4 after 2022.10 Duration of the bellwether TBA trended downward between 2013 and March 2020, and then again during the recent period of high interest rates. This suggests that funds substituting out of cash Treasuries and into MBS may be lowering overall portfolio duration. Further, MBS have negative convexity, while Treasury securities have positive convexity. While convexity is a second-order sensitivity, it becomes crucial when interest rate volatility increases and duration matchingresultsininsufficienthedgingprecision. Consequently,assetmanagerswhotilttoward RMBSmayalsoneedtousevariousTreasuryfuturestomatchtheconvexityofthebenchmarkas well. Our RMBS variables are observed at the daily frequency. For comparability to weekly aggre- 8CurrentcouponisthehighestcouponthatmakestheTBAtradeatorbelowtheparvalue. 9AdollarrollisessentiallyacalendarspreadinTBAs. Dollarrollspecialnessisthedifferencebetweenthecorrespondingfinancingreporateandthedollarrollimplied(break-even)financingrate(seetheonlineappendixtoKandrac (2018)andSongandZhu(2019)fordetails). 10Asdurationisameasureofsensitivitytorates(andnotofmaturity),weavoidsuggestingthatitismeasuredin years;albeit,ingeneral,itisausefulheuristic. 22

gateTreasuryfuturesdata,weaggregatethemtoweeklyfrequencybyaveragingoverthetrading daysbetweentwoconsecutiveobservationsoftheweeklyfuturesdata(includingtherightboundaryofthetimeinterval).11 WetesttheextenttowhichRMBScharacteristicsexplainassetmanagers’longTreasuryfutures positionsbyestimatingthefollowingspecification: 12 (cid:88) ω = α +X β+roll.eff + γ Month i +ϵ . (1) t 0 t t i t t i=2 ω is the fraction of all long Treasury futures positions (aggregate or in a specific group of fut turescontracts)heldbyassetmanagers;X isasubsetofconsideredRMBSexplanatoryvariables; t roll.eff is an indicator for a futures roll date (when dominant open interest shifts from one cont i tract to another), and Month are calendar month fixed effects to capture any seasonality. In the t Appendix, we discuss how we address issues related to cointegration and other time-series concerns. Table 15 contains estimates of specification (1) for asset managers’ aggregate positions, normalized by aggregate open interest, and various sets of explanatory variables. All variables are scaledtogeneratecoefficientestimatesofthesameordersofmagnitude;spreadsareexpressedin basispointswhiledurationandconvexityarescaledby100. ModelIexaminestheyield-chasingresponseofassetmanagers. Thecoefficientontheoptionadjusted spread (OAS) is positive and significant at the 1% level, consistent with current MBS returns motivating asset managers to shift their portfolios into RMBS when RMBS returns are attractive. Thecoefficientondollarrollspecialnessisnegativebutstatisticallyinsignificant. Recall that Song and Zhu (2019) show find a negative relationship between dollar roll specialness and expectedRMBSreturns. Therefore,thenegativecoefficientondollarrollspecialnessisconsistent with higher expected returns being associated with additional positions in RMBS. A comparison of the goodness of fit measures for Models I and II indicates that both models have significant explanatorypower. ModelIIcombinesbothchannels,andwefindqualitativelysimilar. 11Alternativeapproachesinclude(i)retainingonlythemostrecentlyavailableend-of-dayvariablesforeachweekly observationand(ii)fittingaMIDASspecificationofGhyselsetal.(2004).DuetopersistenceinthetimeseriesofRMBS variables, theseapproachesyieldqualitativelysimilarresults. Moreover, thepersistenceofcovariateslikelyinduces largestandarderrorsoftheparametriclagweightintheMIDASspecification. 23

Finally,wehypothesizethatthedecisiontorotateintoRMBSwouldlikelydependonahistory of returns and expectations, requiring a period of attractive returns and heightened expectations to motivate meaningful portfolio shifts. Model III relies on 8-week moving averages of OAS and dollar roll specialness, and obtains greater significance for MBS-return related covariates, along withaslightlyimprovedfit. Figure11depictstheactualandfittedtime-seriesofassetmanagers’ aggregatepositions(asfractionsofopeninterest),basedonmodelIII. 5 Duration Why do Treasury futures appear to serve as complements to MBS and ABS investments but as substitutes to cash Treasuries? In this section, we provide evidence that IID funds use Treasury futures to manage their duration. This dovetails with results in later sections that show that one predictoroffuturesuseinthebroadercross-sectionoffundsistheextenttowhichtheirprospectuses mention duration in their principal strategies. This is particularly common for IID debt funds. For instance, the summary prospectus of the Western Asset Core Plus Bond Fund states thattheobjectiveofthefundsisto: “Maximizetotalreturn,consistentwithprudentinvestmentmanagementandliquidity needs,byinvestingtoobtaintheaveragedurationspecifiedbelow.” In turn, this duration target is specified as being “within 30% of the average duration of the domesticbondmarketasawhole.” OtherIIDfundswilloftenstaterangesofdurationrelativetothe AggregateBondIndexorsimilarbenchmarks. ToexaminetherelationshipbetweenTreasuryfuturesandthedurationofthesefunds,webeginbylookingattheextenttowhichIIDfundfuturesholdersandnon-holdersmatchtheduration oftheAggregateBondIndexusingtheoverallempiricaldurationoftheirportfolioasameasure. WeshowthatIIDfundsareusuallywellbelowthedurationoftheAggregateBondIndex,butthat futuresholderstendtobecloserthanotherfunds,andareespeciallyclosewhenTreasuryfutures positionsarelarge,asduringtheseperiodstheiroverallempiricaldurationincreases. Wethenexaminethedurationoftheunderlyingcashportfolioofthefundsandshowthatwhenfuturesare morepopularthedurationoftheircashportfoliodecreases,implyingawideninggapbetweenthe 24

overall duration of the portfolio and the duration of the cash assets. Indeed, we show this gap is matched by the duration of the futures portfolio. We then provide evidence that the decrease indurationofthecashportfolioisprimarilyduetochangesintheallocationsofthefundsacross assetclasses,inturn,attributablelargelytotransitionsfromTreasuriestoMBSandABS.Takentogether,thissuggeststhatlongTreasuryfuturesarebeingusedtofillthegapbetweentheduration of the cash portfolio and the duration of the Aggregate Bond Index created by reallocating from cashTreasuriestoagencyMBSandABS. 5.1 Empiricalduration TodeterminehowwelldifferentIIDfundstrackthedurationofthebenchmark,webeginbyconstructing an empirical measure of duration using fund returns. Using the daily portfolio returns from CRSP, we form a balanced panel of the daily returns of IID funds from 2015 to 2023. We restrict the sample to active funds that list the U.S. Aggregate Index as their benchmark to focus onfundsthathavethesametargetbutalsohaveatleastsomeincentivetodeviatefromtheallocationoftheindex. Foreachfund,wethenrundailyregressionsoffundreturnsonchangesinthe 10-year Treasury yield and take the coefficient on the 10-year Treasury yield to be the empirical duration of the fund. We perform the same regression for the Bloomberg Aggregate Index and takethecoefficientonthe10-yearTreasuryyieldtobetheempiricaldurationoftheindex. ThefirstpanelofTable10showsstatisticsoftheresultingempiricaldurationestimatesforthe fullsample, splitinto thebottomthirdoffuturesholders (conditional onfuturesownership), the middle third, and the top third. The table reports the average empirical duration of funds in the sample, the difference between the average duration of the fund and the average duration of the index, theaverage absolute trackingerror (thepercentage differencebetween theduration ofthe fundandoftheindex), andtheshareoffundswithin1-yearoftheindex. Additionally, weshow standarderrorsfortheaveragedurationofthefundinclusiveofthefirst-stageestimationerrorof the regressions. Finally, we show the difference between high futures holders and funds that do not hold futures, along with the stars denoting the significance of a t-test that the means of the twogroupsarethesame. For the full sample, duration is generally increasing from funds that use no futures to funds 25

that use high futures. Almost half a year separates the low futures users from the high futures users, and the difference is statistically significant. However, notably at 5.15 years, the duration of the Aggregate Index is higher than the average in any of the groups of funds, for which the highestvalueis4.87yearsforhighfuturesusers. Fundsthatusemorefuturesarethereforebetter matchedtotheindexonaverage. Moreover,theyhavelowerabsolutetrackingerrorandsharesof fundswithinoneyearoftheindex. Thissuggeststhatfundsthatusefuturesarebetteratmatching thedurationoftheindexoverall. We next show that during periods with high use of Treasury futures, high futures users track the index better than in periods with low futures use. In the second to fourth panels of Table 10, we estimate the same statistics as in the first panel, but for the years 2019, 2021, and 2023 separately. In2021,whenTreasuryfuturesusewaslow,absolutetrackingerrorsforfuturesuserswere significantlyhigherandtheshareoffundswithempiricaldurationwithinoneyearofthebenchmarkdurationwassignificantlylower. Thedifferenceinaveragedurationbetweenlow,medium, and high futures users was also small and non-monotonic. In 2023, however, high futures users hadnotablyhigheraverageduration,asignificantlysmallerdifferencefrombenchmarkduration, andasignificantlylowertrackingerror. Similarly,duringtheperiodofhighusagein2019,thedifference in average duration from the index was also lower for high Treasury users, and absolute trackingerrorsandshareswithin1-yearoftheindexwerealsocloser. These findings suggest that during periods of high aggregate long Treasury futures holdings, mutual funds that extensively use futures deviate much less from the target benchmark, both in termsofdurationandaggregatereturns. Theseportfolio-leveldurationsareinclusiveoftheeffects of futures. We next examine the duration of the underlying cash portfolio of the funds, as a way ofinferringthecontributionoffuturestotheoveralldurationofthefund. 5.2 Cashportfolioduration To examine the duration of the underlying cash portfolio of the funds, we again return to the N- PORT data. We obtain CUSIP-level duration data from ICE for a wide range of debt instruments toconstructameasureofthedurationofthecashportfolio,calculatedastheweightedaverageof the duration of each cash security. Note that these durations differ from the empirical durations 26

in the previous section since they are based on ICE calculations of the theoretical sensitivity to a parallelshiftintheyieldcurve,ratherthantheactualreturnsoftheassets.12 Therefore,whilethe direction of relative changes in duration is likely to be comparable with results in the previous section,theactuallevelsarenot. In Table 11 we show the weighted-average duration of IID index funds, active funds that do notusefutures,andactivefundsthatdousefutures,aswellastheaveragedurationsandweights oftheindividualassetclassesinthecategory’saggregatecashportfolio. Weshowthesestatistics forthesamedatesasabove: December2019,June2021,andJune2023. Aswithempiricaldurations,thedurationofthecashsecuritiesintheindex(asproxiedbythe durationofindexfundsreplicatingtheindex)ishigherthantheaveragedurationofbothfutures usersandnon-futuresusersthroughoutthesampleperiod. However,unlikeempiricaldurations, theaveragedurationofthecashportfoliooffundsthatusefuturesfallsbelowthedurationofthe cashportfoliooffundsthatdonotusefuturesinperiodsofhighfuturesuse,specificallyDecember 2019andJune2023. Asaresult,betweenDecember2019andJune2021,thegapbetweenthecash durationoffuturesusersandtheindexfallsfromalmostayear(0.97)toroughlyfourmonths(0.34) andthenrisesagaintoroughly10months(0.80)byJune2023. Thissuggeststhathighfuturesuse in2019and2023wasassociatedwithadecreaseinthedurationofthecashportfoliooffundsthat usefutures,andthatfuturesmayhavefilledthegap. In order to explore the extent to which futures fill a duration gap further, we calculate the durationofthefunds’cashportfolioalongwiththeirfuturesposition. Whilethefuturesposition addslittletothedurationofindexfundsornon-futuresholders,itaddsoverayeartotheduration offuturesholdersin2019andabout10monthsin2023. Asaresult, thefuturesportfolioofthese fundsnearlyperfectlyfillsthegapbetweenthedurationsofthefundandoftheindexthroughout theseperiods. Thefulltime-seriesofthesetwomeasuresforIIDfutures-usersisshowninFigure 10, where we can see that in the aggregate the rise in duration from futures coincides with the declineincashduration,andfillsthegapbetweencashdurationoffutures-usersandindexfunds. In Table 12, we examine cash duration and futures duration in the panel of IID funds. We 12Ideallywewouldusethesamemeasureforboththecashandtheempiricalduration,butconstructingameasure oftheempiricaldurationofthecashportfolioisdifficultduebothtothedifficultyofassemblingdailyreturnsandthe questionofhowtodealwiththeneedtorollovermaturingsecuritiesonanintra-quarterbasiswhenconstructingdaily returnswithonlyquarterlydataonholdings.Withoutthisability,wewouldbelimitedtoquarterlydurationestimates thatwouldnotbereliablegiventheshortperiodforwhichwehaveN-PORTdata. 27

regress the change in the duration of their cash portfolio on the change in the duration of their futures. If IID funds were perfectly filling the gap between cash and futures we would expect a coefficient of -1, since the change in the duration of the cash portfolio would be exactly offset by the change in the duration of the futures portfolio. Across specifications, including both time and fund fixed effects, we find a coefficient of roughly -0.4. While not perfectly offsetting, this strongly suggests a gap-filling motive to futures use, but leaves open the question of where the gapbetweenthedurationofthefundsandtheirindexcomesfrom. Tobeginexplainingtheemergenceofthisdurationgap,wenotethatforfuturesholders(and active non-futures holders), the highest duration asset class is U.S. Treasuries. The duration of U.S. Treasuries held by these funds is also higher than the duration of U.S. Treasuries held by the index funds, consistent with the lower allocation towards short-maturity Treasuries noted above.13 Meanwhile,ABSandMBSassetshavethelowestdurationsofanyassetclassforfutures holders. Therefore, the reallocation from cash Treasuries to ABS and MBS is likely associated withadecreaseintheoveralldurationofthecashportfolio. Additionally,thedurationofthecash portfoliocouldchangebecauseofchangesinthedurationoftheunderlyingassets,duetochanges inaggregateinterestrates,orfromchangesinthecompositionoftheindividualsecuritieswithin theassetclass. To separate these effects, we perform a partial decomposition of the change in the duration of the cash portfolio of each fund class into a component due to changes in the duration of the underlyingassetsandacomponentduetochangesintheallocationofcapitalacrossassetclasses. More specifically, the average weighted average duration of each group of funds can be written as:   (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) (cid:88) ∆ p i,t w i,j,t D i,j,t = p i,t ∆w i,j,t D i,j,t + p i,t w i,j,t ∆D i,j,t + p i,t D i,j,t w i,j,t D i,j,t , i j i i j i j where i denotes the fund, j denotes the asset class, p is the share of the fund in all IID assets, i,t w is the weight of asset class j in fund i’s portfolio as of time t, and D is the duration of i,j,t i,j,t 13Anecdotally,longmaturityU.S.Treasuriesareoftenusedbythesefundstogaindurationexposure,becausesimilar maturitycorporatesecuritiesarehardertofindandbecausethedurationofMBSisusuallyquiteshorterduetothe prepaymentoption. LongermaturityTreasuriesinthiscasemaystayonfuturesholderbalancesheetssincetheyare themostdifficulttoreplicateeitherwithotherholdingsorwithfutures. 28

assetclassj infundi’sportfolioasoftimet. Thefirsttermontheright-handsideisthechangein thedurationofthecashportfolioduetochangesintheallocationofthefundacrossassetclasses; thesecondtermisthechangeinthedurationofthecashportfolioduetochangesintheduration of the underlying assets; and, the third term is the level of the duration of the cash portfolio. We calculate these changes keeping the 2021 portfolio as a baseline and show the results in Table 13. Therowlabeled“2021allocations”correspondstochangesduetothedurationoftheunderlying assets, whereas “2021 durations” correspond to changes due to the allocation of the funds across assetclasses. We find that the change in the duration of the cash portfolio of funds that use futures is primarilyduetochangesintheallocationofcapitalacrossassetclasses. Thisisincontrasttochanges in the duration of the index, which are driven almost entirely by changes in the duration of the underlying holdings. To further investigate the drivers of this shift we construct a hypothetical change in duration from only the changes in the allocation of funds from agency MBS to U.S. Treasuriesas: (cid:88) p ×∆w ×(D −D ). i,t i,MBS,t i,MBS,t i,UST,t i These results are reported in the row “Agency MBS only”. While index funds have virtually no changeinthismeasure,futuresholdershavethelargestchangesoutofallthreefunds,accounting formorethan100%ofthetotalchangesindurationduetoallocationchanges. Thissuggeststhat thereallocationfromMBStoU.S.Treasuriesistheprimarydriverofthedecreaseintheduration ofthecashportfoliooffundsthatusefutures. Next, we decompose changes in cash duration into asset-class level effects in Table 14. Each dependentvariableisconstructedas: (cid:88) ∆w ×(D −D˜ ). i,j,t i,j,t i,t i whereD˜ istheweightedaveragedurationoffundiattimet. Thiseffectivelymeasuresacouni,t terfactual change in duration that would result if duration within the asset class had remained constantandcapitalwasdrawnequallyfromallassetclassesintoclassj. Asbefore,theindependentvariableistheratiooflongTreasuryfuturesnotionalvaluetoAUM,withbothfundandtime 29

fixedeffectsandonlyforactivefunds,asintheprevioussection. Table14showsthatreallocationsawayfromTreasuriesandtowardsagency,private-labeldebt and CDOs contributed substantially towards the overall decrease in durations due to changes in asset allocation. Meanwhile, allocations to corporate debt actually increased the duration of thefunds. InAppendixTableA.4,wefindaninsignificantrelationshipbetweenTreasuryfutures allocationsandtheoveralldurationofthefund. However,whenonlythechangesindurationdue to changes in portfolio allocations across asset classes are considered, the relationship becomes largeandstatisticallysignificant. Taken together, the evidenceinthis sectionis consistentwith fundsusing futuresto filla gap betweenthedurationoftheircashportfoliosandthedurationoftheindextheytrack,createdby reallocatingfromcashTreasuriesintoMBSandABS.However,thisdoesnotestablishwhyfunds wouldwanttomakethisreallocationatcertaintimes. Inthenextsection,weexaminethecyclical incentivesforfundstoinvestinMBS. 6 Alternative explanations The preceding sections have presented evidence consistent with the following: (1) funds use futures to target duration when the gaps between their benchmark and the duration of their cash portfoliosarelarge,(2)thatthesegapsarecommonlycausedbytheirreallocationfromTreasuries to MBS, and (3) that this reallocation, in turn, may be due to cyclical variation in the attractiveness of MBS relative to Treasuries. This channel is what we refer to as “reaching for duration,” with funds chasing higher returns on MBS by tilting away from their index but using futures to maintaintheirdurationtarget. ItisworthconsideringafewalternativeexplanationsforthevariationinTreasuryfuturesand whether we can reject them based on these results. One possibility is that funds are using Treasury futures to hedge against interest rate risk. However, Treasury futures appear to be actually increasing their duration and therefore boosting the variance of their fund returns rather than reducing them. Therefore, while the behavior of these futures users does bring them into closer alignmentwiththeirtargetindex,itdoesnotreducetheoverallriskoftheirportfolioaswouldbe expectedwithconventionalhedging. 30

Another possibility is that funds use Treasury futures to generally increase the risk of their portfolio for speculative purposes. While this cannot be eliminated, we note that these funds, in general, are less volatile than their target benchmark, which suggests that their risk-taking is not excessiverelativetowhattheypromiseinvestors. Moreover,wefindnoevidencethatthesefunds are tilting towards conventional risky assets such as speculative-grade debt. While the funds do takeonmorerepaymentriskthantheirbenchmark,theyarethereforenottakingongreatercredit risk. Arelatedpossibilityisthatfundsusefuturestobetonthelevelofinterestratesorchangesin the slope of the yield curve. Again, this is difficult to eliminate, and the incentives to tilt toward MBSwillberelatedtothelevelandslopeoftheyieldcurvethroughtheprepaymentoptiongiven toborrowers. However,itseemsunlikelythatfundsareusingfuturesalonetoconstructartificial steepeners or flatteners. As discussed above, the d futures positions that funds hold are largely one-sided,evenwhenadjustedforduration. Therefore,thesepositionscannotbepureyield-curve bets constructed using futures since the funds are substantially net long in all contracts. On the otherhand,yield-curvetradescouldbeconstructedusingcashsecuritiesandfuturesofdifferent maturities. This can also be eliminated for the majority of futures positions since we find that futuresusersaresellingshort-maturityTreasurypositions,whichwouldthenmatchtheduration of the predominately 2-year and 5-year futures positions they are being replaced with. If funds were instead speculating on changes in the yield curve, we would instead see that the duration of the cash positions being sold would be longer than the duration of the futures positions being bought. Lastly, funds may increase their futures use to save cash to meet potential redemptions while tracking their benchmark index. This explanation would be closely related to reaching for duration since it would represent a shift from high-duration to low-duration cash assets, but distinct in that cash assets are generally lower-yield than Treasuries. We do see a slight increase in cash holdingsinthefinalcolumnofTable6,butitisnotsignificant. Thepriorsectionshaveexaminedthetime-seriesvariationinTreasuryfuturespositionsofmutual funds. Next, we explore cross-sectional heterogeneity and offer some preliminary evidence foritssource. 31

7 Cross-sectional heterogeneity A natural question arises from the preceding sections. Why do some funds use Treasury futures while others do not? In this section, we examine the cross-sectional variation in Treasury futures use among intermediate investment-grade debt funds. We find that funds that use Treasury futures appear to be differentiated from other funds. There is little difference in returns between futures holders and non-holders. However, flows of futures holders are less sensitive to performancethantheirotheractivepeers,suggestinginvestorsmaybeattractedtotheirabilitytotrack theirdurationbenchmarks. Manyofthesefundsalsohavespecificwordingintheirprospectuses mentioningtheirabilitytousederivatives. Meanwhile, consistent with the above discussion of reaching for duration, futures users are morelikelytobeinLipperobjectivecodeswheretheindexfundsinthesamecodehaveahigher allocationtoTreasuries. Theyalsotendtomentiondurationandwordsassociatedwithmortgagebacked securities in their prospectuses. Finally, futures users are also more likely to state “total return”astheirobjectiveandhavesignificantlyhigherturnoverratios. 7.1 FlowsandPerformance Next, we turn to the incentives faced by fund managers. Mutual funds earn fees based on assets under management, and managers are incentivized to maximize assets under management in order to maximize fee income. A rich literature examines the relationship between flows and performance (Berk and Green (2004), Coval and Stafford (2007)). In this section, we examine whethertheassociationbetweenflowsandperformancediffersbetweenfundsthatholdTreasury futuresandthosethatdonot. First, we discuss the performance of these funds. Table 16 shows that there is little difference intheaverageperformanceoffundsthatholdTreasuryfuturesandthosethatdonot,noramong fundsthatholddifferentamountsofTreasuryfutures. However,allfundsoutperformtheAggregateBondIndex,whichisconsistentwiththelowerallocationtoTreasuriesofbothfutures-users and non-futures-users. This pattern continues when we examine portfolio alpha in the third column. Thatfundsthatusederivativesdonotoutperformfundsusingderivativesisconsistentwith previousresultsinKoskiandPontiff(1999),Fongetal.(2005),andCaoetal.(2011). 32

Meanwhile,thefourthcolumnshowsthathigherfuturesholdersaregenerallymoreriskythan lower futures holders, as measured by the standard deviation of their returns. This is accounted forbythehigherdurationoffuturesholders,asshownintheprevioussection. Thefinalcolumnof thistableshowsthisconcretelyusingthestandarddeviationofthefittedreturnsfromtheregressionoffundreturnsonthe10-yearTreasuryyieldasameasureoftheraw“durationcomponent” ofrisk. Thatfuturesholderscontinuetooperatewithsimilarreturns,buthigherrisk,ispuzzling,we show that it is explained by a different flow-performance relationship for futures holders and non-holders. Table 21 regresses quarterly percentage fund flows on one-quarter lagged returns, indicatorsforTreasuryfuturesownership,andtheirinteraction,alongwithothercontrols. Flows (cid:2) (cid:3) are calculated as AUM − (1 + R ) × AUM /AUM , where AUM is assets under i,q i,q i,q−1 i,q−1 i,q management for fund i in quarter q and R is the quarterly return for fund i earned between i,q quarters q − 1 and q. Controls include the log of total AUM, sales restrictions (as reported in CRSP),andindicatorsforwhetherthefundiscurrentlyopentoinvestorsandwhetherthefundis aretailfund. Column(1)ofTable21showstheresultsofquarterlypercentageflowsregressedfuturesownership, the one-quarter lagged (quarterly) return, and their interactions. Log (lagged) net assets undermanagementareincludedasacontrol. Asexpected,thelaggedquarterlyreturnisstrongly related to flows. A one percentage point higher return in the previous quarter is associated with a0.58greaterpercentagepointinflowinthatquarter. Further, allthreecategoriesofTreasuryfuturesinvestors(bottomthird—“Lowfutures”;middlethird—“Mediumfutures”;andtopthird — “High futures”) show a negative interaction coefficient, with the coefficient on high-futures being statistically significant at the 5% level. In columns (2) and (3), we find similar quantitative results when controls, time fixed effects, and fund fixed effects are included. In each case, funds that are the heaviest users of Treasury futures display a weaker flow-performance relationship thanfundsthatdon’tuseTreasuryfuturesatall. ThefindingsinTable21makesenseifinvestorschoosetoinvestinfundsthatusederivatives because they can more closely adhere to the aggregate benchmark return. Table 10 showed that futures holders do indeed demonstrate smaller tracking errors and a closer connection to benchmark duration. In this case, investors in funds with greater futures holdings (and in turn better 33

indextracking)respondlesstoperformancebecauseagreaterportionofthefund’sreturnistied totheperformanceofthebenchmark,whichisoutofthefund’scontrolandultimatelytheexposure investors presumably want in the first place. Said differently, the value of funds investing in futures is that during periods of attractive near-substitutes for Treasuries, such as MBS, these funds can shift into such assets while maintaining a tighter link to the aggregate bond market index. 7.2 Investmentpoliciesandderivativesconstraints Onepossibleexplanationforthecross-sectionaldifferenceinTreasuryfuturesuseamongIIDmutualfundsisexplicitconstraintsthatprohibit,orstronglyrestrict,theabilityofsomefundstouse derivatives. Below, we provide evidence in support of such constraints being binding for some funds. Then,weshowthatparticularfundcharacteristics,independentofinformationfromfund prospectuses,canexplainvariationinTreasuryfuturesusage. First,wesortfundsintofourgroupsasofJune2023: fundsthatinvestinbothTreasuryfutures and other derivatives, funds that invest in Treasury futures but not other derivatives, funds that invest in other derivatives and not Treasury futures, and funds that invest in neither Treasury futures nor other derivatives. We find that among funds that hold no Treasury futures, 73% also hold no other derivatives. This is strong evidence in support of implicit or explicit constraints on derivatives usage. Seemingly, many funds simply do not invest in derivatives of any type. Such a restriction will likely be explicated in the fund’s prospectus, and we discuss suggestive evidence from these prospectuses below. Further, among Treasury futures holders, 73% invest in other derivatives, further supporting the hypothesis that funds to a large degree segment into thosethatmay(andoftenwill)usederivativesandthosethatwillnot. Acrossallfunds,37%hold someformofderivatives. Next, we turn to fund prospectuses. One source of explicit fund constraints on the ability to usederivativescomesfromfunds’statedinvestmentstrategyviatheirprospectusestoinvestors. Prospectusesarelegallybindingdocuments,andfundsmustadheretothepoliciessetoutintheir offering documents. In their prospectuses, funds generally describe their investment mandate along with tools for achieving that mandate, including the extent to which they will employ tra- 34

ditionalleverage(e.g. borrowingonmarginorinrepomarkets)orwillusederivatives. The first two columns of Table 17 report the percentage of funds that discuss derivatives in the “Principal Strategies” section of their prospectuses. Across all fund types, only 36% of funds that don’t hold any Treasury futures as June 2023 mention “derivatives”. Comparatively, this percentage is near or above 80% for funds that hold Treasury futures. Restricting the sample to IID funds, Table 17 shows that around half of non-futures users mention derivatives, but 95% of high futures users mention derivatives. p-values are reported for null that there is no difference betweennon-futuresholdersandthelargestfuturesholdersandareminuscule. Columns(3)and (4)ofTable17conductasimilaranalysisforthe“PrincipalRisks”sectionoftheprospectus. Asin columns(1)and(2),“derivatives”arementionednearlytwiceasoftenforTreasuryfuturesholders asnon-futuresholders. Table 18 offers an alternative view of mutual fund strategies outlined in their prospectuses. Table18showsthetwentywordsmostpredictiveofpositiveTreasuryfuturespositions. Themost commonwordsreportedforfuturesusersare“mortgage”,“backed”,and“debt.” Thecommonality of MBS-related words within fund prospectuses is strongly supportive of our earlier findings that funds that use Treasury futures shift out of cash Treasuries and into MBS when the relative attractivenessofMBSspreadsishigh. TheexplicitmentionofMBS-relatedtermsfurthersuggests thesefundsviewMBSasclosesubstitutesofcashTreasuriesandintendforMBStobeaconsistent partoftheirinvestmentstrategy. Otherwordsassociatedwithinterestrateriskarealsocommon: “duration”,“swaps”,“dollar”,and“inflation”. ThesecommonwordsofferfurthersupportiveevidenceofthehypothesisthatmutualfundsthatuseTreasuryfuturesdosototargetinterestrisks whileshiftingassetsawayfromcashTreasurysecuritiesandintohigher-yieldingassets. 7.3 FundCharacteristics Funds’ descriptions of derivatives use in their prospectuses effectively tie the hands of mutual fundmanagers. Anopenquestionremains,however,whysomefundswouldrestrictthemselves insuchamanner. Or,whywouldn’tallfundsrestrictthemselvesinsuchamanner? Inthissection, weexaminewhetherparticularfundcharacteristicsareassociatedwithvariationinlongTreasury futuresuse,independentofrestrictionsinfundprospectuses. 35

Table 19 regresses an indicator for whether the fund holds long Treasury futures on a set of fund characteristics.14 The first column conducts this regression for only IID funds, while the remainingthreecolumnsincludeallfunds,regardlessofinvestmentstyle. Inthesecondcolumn, one of the most important predictors of Treasury futures investments across fund styles is the index Treasury share, which is the share of Treasuries in all index funds in the same fund style. We use this as an indicator of the likely allocation of Treasuries for the funds’ benchmark index. In terms of magnitude, a 1 percentage point increase in this Treasury share is associated with a 26%increaseinthelikelihoodofthefundusinglongTreasuries. Similarly,TableA.6showsthata 1percentagepointincreaseintheTreasurysharecorrespondstoan8percentagepointincreasein Treasuryfuturesnotionaltoassets. Thisagainillustratesthekeyimportanceofthelargeallocation ofthebenchmarkindrivingmutualfunds’Treasuryfuturesuse. Additionally, the second column of Table 19 finds that funds that mention either “mortgage” or“duration”intheprincipalstrategiessectionoftheirprospectusesaremorelikelytoownTreasury futures across styles. The importance of duration in the funds’ strategy statement is consistent with the incentive to match the duration of an index, while mortgage-backed securities use as we have shown is a key alternative to Treasury holdings for these funds. Collectively, these variables explain much of the variation across fund styles, as adding fund style dummies in the thirdcolumnonlyaddsroughly8%totheR2 oftheregression. Otherfundfeatureshavestrongexplanatorypowerbothinandacrossfunds. Fundsthattrade more, as measured by their turnover ratio, or that have a total return objective are more likely to hold long Treasury futures. A focus on total return may mean the fund is more likely to take on positions in response to temporary market conditions, such as if MBS are attractive relative to Treasuries. Trading frequently would be consistent with this strategy as well, and would also meanthatdealingwithoff-the-runTreasuriescouldbecostlyforthefund. Thisstandsincontrast to index funds, which may be better able to hold positions including off-the-run Treasuries for the long term. Funds that use Treasuries are more likely to mention leverage as a risk in their prospectus,againpointingtowardsthesalienceoffuturesuseforinvestors. Finally,largefundsaremorelikelytousefutures,whichmaypointtoeconomiesofscale. This 14In the appendix, Table A.6 conducts a similar exercise for futures as a percent of total assets, with very similar results. 36

isreinforcedbythefactthatadvisorfixedeffectsaddsignificantlytotheexplanatorypowerofthe regression in the fourth column. This is consistent with the prevalence of long futures positions amongthefundsofcertainassetmanagers. Inbothcases,itmaysuggesttheimportanceofhaving managers with experience with futures markets who are able to use derivatives effectively to manageduration. 7.4 Flowsandfuturesuse Table 19 showed that certain fund characteristics are associated with the decision to invest in Treasury futures. Next, we examine whether Treasury futures holdings are associated with fund flows. Here, we focus on characteristics of flows independent of their association with returns, andstudytheflow-performancerelationshipanditsassociationwithflowsinalatersection. We hypothesizethreeseparatemechanismsthatmaylinkflowstoTreasuryfuturespositions. First,it may be funds that have greater flow volatility are more likely to hold Treasury futures. Because Treasury futures tend to be more liquid than cash Treasuries, particularly off-the-run Treasuries, fundswithgreaterflowvolatilitymayusefuturesasawaytomanageliquiditycostsinresponse unexpectedly large inflows our outflows. Second, funds that experienced particularly large outflowsduringtheCovidpandemicmayhavegreaterincentivestooutperformthebenchmarkand “reachforyield”,leadingsuchfundstouseTreasuryfuturesasleveragetomagnifyperformance. Lastly, large inflows during the Covid recovery period may force funds to tilt away from cash TreasuriesandtowardTreasuryfuturesifthecostofholdinglargeramountsofTreasuriesaresufficientlyhigh,orconversely,ifweakerinflowsduringtherecoveryperiodmayfurtherincentivize reachingforyield. Table 20 investigates each of these possibilities. We find no evidence that any of the three mechanisms are important factors for the growth or size of Treasury futures positions. We focus on“IID”fundsonlyforcomparabilityofestimates,thoughresultsaresimilarwhenweincludeall fundtypesandafixedeffectforfundtype. Columns(1)and(2)reportsresultsfromcross-sectionalregressionsofanindicatorforwhether the fund holds Treasury futures as of June 2023 on the volatility of fund flows prior to 2018. We restrict to observations prior to 2018 because 2018 is when the first build-up of long Treasury 37

futurespositionsbyassetmanagersbegan. Column(1)isanunconditionalregressionandcolumn (2) includes as controls the same covariates included in Table [17]. In each regression, we find a negative and statistically insignificant coefficient, suggesting higher flow volatility would be associatedwithalowerprobabilityofinvestingTreasuryfutures. Wefindsimilarresultswhenwe usethevolatilityofflowspriorto2023. In columns (3) and (4), we estimate panel regressions of long Treasury futures ownership in June2023ontheaveragepercentagefundflowbetweenJanuary2020andDecember2021,which we roughly identify as the Covid crisis period. The sign of the coefficient is negative in both specifications, consistent with a “reaching for yield” motive, however we note the coefficient is statistically insignificant. Similarly, in columns (5) and (6), we examine whether average flows during the Covid recovery period, which we define as the entirety of 2022, are associated with the probability of investing in Treasury futures. As with the other specifications, we again find no statistically significant association between average flows in 2022 and the likelihood of holding Treasury futures, though we note that as in columns (3) and (4), the coefficient estimates are negative,consistentwithpotentialreachingforyield. Intotal,whilecoefficientsignsmaysuggest someincentivetoholdTreasuryfuturesinresponsetolargeroutflowsorweakerinflows,wefind nostatisticalevidenceofaneffectofthelevelorvolatilityofflowsonthelikelihoodofinvestment inTreasuryfuturespositions. 8 Discussion 8.1 AlternativemeansofTreasuryleverage In this section, we answer another related question: given that funds want to pursue higher returns by tilting towards MBS, why do they use Treasury futures to do so, as opposed to other meansofsecuringlevereddurationsuchasrepoorswaps? One way to replicate a Treasury without using a futures contract or significant balance sheet space is to borrow against the Treasury in the repo market. These two strategies (long futures versus cash Treasury borrowed in the repo market) are not perfect substitutes, but they do make up the two legs of the cash-futures basis trade. In fact, as shown in Barth and Kahn (2021), the recent periods where asset managers have been most active in the Treasury futures market have 38

been associated with a relatively high cash-futures basis. This suggests that it would be cheaper formutualfundstosecuretheirTreasuryleveragebybuyingtheTreasuryandborrowingthrough repo than it is to use futures. Moreover, while funds use of Treasury repo was previously separately limited, under SEC rule 18f-4, which was adopted in 2020, repo and futures are subject to thesameVaR-basedleveragelimit,meaningthatthereisnoadditionalregulatorylimitappliedto repo. It is therefore somewhat surprising that, as Table 22 shows, while 9% of all funds and 51% of IIDfundshavelongTreasuryfuturespositions,onlyabout0.5%ofallfundsand1%ofIIDfunds userepo. Toshedsomelightonwhy,inTable22,wesplitbothIIDfundsandallfundsintothose thatdidanddidnotuseTreasuryfuturesasofJune2023,andthosethatdidordidnotborrowin therepomarket. Wenotethat,althoughrepoistreatedsimilarlybyregulators,itisoftendisclosed separatelyintherisksandstrategiessection. Moreover,whilesomefundsthatusefuturesdonot mentionleverageasarisk,nearlyallfundsthatuserepomentionleverageasarisk. Thissuggests thatrepomayhaveastigmaattachedtoitthatfuturesdonot. Giventhat18f-4wasonlyadopted recently, and that it takes time for new rules to percolate through the industry, it is possible that repousewillincreaseandfuturesusedecreaseastimegoeson. Anotherfactoristhatfuturesaresimplerthanrepos. Dealer-to-customerrepotransactionslack transparency,makingitdifficulttonegotiateafairpriceandmeaningthatrepomarketpricingis oftendependentonrelationships.15 Incontrast,Treasuryfuturesaretradedelectronicallyontransparent screens with very low transaction costs. Similarly, central clearing for dealer-to-customer repotrades,whilegrowing,isalsolimited. AsdiscussedinKahnandOlson(2021),nearlyallthe volume from customers borrowing in the cleared markets is from hedge funds. This means that repo borrowing by mutual funds would have to take place through non-centrally cleared repo, andpotentiallyinvolvecounterpartyrisknotpresentinthecentrally-clearedfuturesmarket. Finally,weconsidertheuseofswaps. Swapsareanotherwaytosecureleveredduration,and they are often used by funds that want to take on interest rate risk. In Table A.13, we consider a similar split to the split for repo borrowing on the use of interest-rate swaps. Interest-rate swaps 15SeeClarketal.(2021)andKahnetal.(2023)fordiscussionsoftransparencyandtransactioncostsinthedealerto-customer market. For the value of relationships see Han et al. (2022). Several studies, such as Anbil et al. (2021) andEisenschmidtetal.(2024)pointtodispersioninthesemarketsthatmayberelatedtothislackoftransparencyand relianceonrelationships. 39

are much more popular than repo borrowing, with 3% of all funds and 23% of IID funds using swaps. They also appear to be considered comparably risky to futures based on their mentions in the risks and strategies sections of the prospectuses of swaps users. However, the notional amounts involved for IID funds, while large relative to the total assets of the fund are not nearly aslargewhenconsideredinthecontextoftheaverageswapuseroverall. Therefore,eitherthebespokenatureoftheOTCswapsmarketortherelativelyhightransactioncostsofswapscompared tofuturesmaybelimitingtheirusebyfundsthataremoreactiveinTreasuryfutures. 8.2 Treasuryinconvenience The results above suggest that mutual funds use Treasury futures to replicate the duration exposuresofTreasurieswhileusingtheirbalancesheettoholdotherassets. Whyshouldmutualfunds want to avoid holding cash Treasuries? One key reason suggested above is the relatively low yields offered by Treasuries. However, there may be additional costs from the type of Treasuries in the index. Table 23 shows the holdings of IID index funds, non-futures holders, and futures holders by run-status of the Treasury. The vast majority (85% as of June 2021) of Treasuries held byindexfundsweclassifyas“deepoff-the-run”,meaningTreasuriesthatwerefirstissuedovera yearago,andhaveusuallybeenheldforasubstantiallengthoftime. Incontrastwithindexfunds,butconsistentwiththeapparentfocusoffuturesholdersonhighturnoverinvestments,muchoftheTreasuryholdingsoffuturesholders(55%asofJune2021)are either highly liquid on-the-run securities or relatively recent off-the-run securities issued within the last year to year-and-a-half. This suggests that funds that use futures may face higher costs, broadly defined, to transact in the off-the-run market, and therefore may not be able to easily securetheTreasuryneededtouserepotoreplicatetheindex. Replicatinganindexwithdeepoffthe-runTreasuriesisespeciallyexpensiveforfundsthattraderegularlyaspartoftheirinvestment strategy, and therefore may have to buy or sell these Treasuries as part of their regular business. ThismaybeanotherreasonwhyturnoverisassociatedwithhigherTreasuryfuturesuse. Meanwhile,muchoftheMBSinvestmentsoffuturesholdersareinrelativelyliquidTBAcontracts (roughly 50% as of June 2021). Again this is consistent with the high-turnover nature of futuresholders. ButitalsomayprovideanotherreasonwhyTreasuryfuturesareattractive. One 40

ofthekeydifficultiesinusingTreasuryfuturesisthecomplicatednatureofthedeliveryprocess.16 Whiletheprocessmaybeopaquetosomeinvestors,insomeways,itisverysimilartothedelivery processfortheTBAmarket,sothismaymakefuturesrelativelyeasierforthesefundstouse. Regardless of whether the cost is solely due to the low yield on Treasuries or due to the difficultyoftradingoff-the-runTreasuries,itislikelythiscostriseswiththeshareofTreasuriesinthe index. WiththelightbluelineinFigure12weshowthattheshareofTreasuriesintheBloomberg Aggregate Index has been increasing over time, using the iShares Core US Aggregate ETF as a proxy. Theindexhasrisenfromroughly35%inearly2010toalmost45%in2023,eventhoughas weshowmostofthefundstargetingthisindexhaveremainedwellbelowthisallocationtoTreasuries. ThisinturnincreasesthetensionbetweentheAggregateIndexdurationandtheduration ofthefundsthatleadstotheuseoffuturestoreachforduration. TheAggregateIndexinturnhasanimportantrelationshiptooutstandingTreasurydebt. The allocation of the index to Treasuries is largely determined by the share of total Treasuries, less FederalReserveholdingsofTreasuries,intotaldebt. WeshowthisinthedarkbluelineinFigure 12, using data from the financial accounts and monthly statements of the public debt.17 As this figure shows, issuance since the 2008 financial crisis increased the share of Treasury debt in the Aggregate Index, while Federal Reserve purchases of Treasury debt in 2020 more than offset the effect of the increases in Treasury debt since the COVID crisis into 2022, tightening has begun to increase the share in the Aggregate Index again. Going forward increases in Treasury debt may lead to increases in the Aggregate Index allocation to Treasuries, with the consequence of higher mutualfundholdingsofTreasuryfutures. 9 Conclusion We show that the substantial magnitudes and time-series variation in long Treasury futures positions are driven in large part by asset manager positions. Mutual funds in particular appear to bea significantsourceof thisvariation. We showfurtherthat Treasuryfuturespositions aresubstitutesforcashTreasuries,ratherthancomplements,andfreeupcashformutualfundstoinvest 16SeeBurghardtandBelton(2005)fordetails. 17Specifically,weusetotalmarketableTreasurydebtheldbythepubliclessSOMATreasuryholdingsoverthesum ofcorporatedebt,agencydebtandTreasurydebt. 41

in other assets. In particular, we show that when Treasury futures positions of mutual funds are high, mutualfundsshiftawayfromcashTreasuriesandintoMBSandotherasset-backedsecurities, specifically CDOs. This shift pushes funds away from their duration targets, and funds use Treasury futures to maintain these targets during times when other assets — MBS and CDOs — areparticularlyattractive. Indoingso,fundsmanagetheirdualobjectivesofachievinghightotal returnswhilestayingnearthedurationoftheaggregatebondmarket. Treasuryfuturesreducethecostofmeetingbenchmarkindexdurationsformutualfunds. By allowingthesefundstoholdfewerTreasuriesandmoremortgage-backedsecurities,mutualfunds canprovidebetterreturnstoinvestors. Theyalsoenablefundstoindirectlyprovidefundingand liquiditytothemortgagemarket. Thisrolehasbecomemoreimportantastheindexesthatfixedincome funds are benchmarked against have become more heavily allocated towards Treasuries and may become even more important in the future if Treasury borrowing continues at the same pace. Whiletheseservicesarebeneficial,theuseofTreasuryfuturesbymutualfundsalsointroduces leverageintoTreasurymarkets,bothdirectlyandindirectly. First,mutualfundsthatreducepositionsincashTreasuriesandreallocatetowardMBSandABSmaytakeonadditionalsourcesofrisk in their cash portfolios. MBS and ABS are, in general, lower duration, but they have additional prepayment risk. Moreover, because Treasury futures require less cash up front they constitute a leveraged position in Treasuries. This introduces funds to cash flow risk through the threat of margincallsthatarenotpresentwhenfundsholdcashTreasuriesratherthanfutures,whichmay magnifyinstabilityinTreasurymarketsifthesefundsareforcedtoreducetheirpositionsquickly. Additionally, hedge funds are the primary traders opposite mutual funds in Treasury futures markets, taking the short positions that prior research suggests are in service of the cash-futures basis trade. The basis trade pairs a short Treasury futures contract with a long cash Treasury position, financed in repo. The trade is relatively low return, however, and hedge funds correspondingly apply significant leverage. Because this leveraged trade results from mutual funds’ demand for long Treasury futures, an indirect consequence of mutual funds’ demand for futures positions is the associated Treasury market leverage introduced through hedge funds. Both of thesesourcesofleveragemaypresentincreasedriskstoTreasurymarkets,asmaterializedduring March2020. 42

This paper documents a novel channel through which asset managers may affect core bond markets. In managing their dual objectives of generating returns for investors while matching a benchmark index duration, mutual funds’ reach-for-duration incentive drives greater leverage in the Treasury market. Though we have already seen important consequences of large Treasury futures holdings in the events leading up to March 2020, this activity may become increasingly importantfordynamicsinTreasurymarketsintheyearstocome. 43

Dec2019 Jun2021 Dec2019 Jun2021 Jun2023 toJun2021 toJun2023 Total Allassetmanagers 888 682 1087 -206 405 Mutualfunds 503 362 583 -141 221 2-year Allassetmanagers 347 166 346 -181 180 Mutualfunds 190 122 259 -68 137 5-year Allassetmanagers 221 187 250 -34 63 Mutualfunds 172 108 163 -64 55 10-year Allassetmanagers 162 159 252 -3 93 Mutualfunds 77 72 92 -5 20 10-yearUltra Allassetmanagers 31 47 82 16 35 Mutualfunds 16 9 21 -7 12 30-year Allassetmanagers 51 56 69 5 13 Mutualfunds 15 25 17 10 -8 30-yearUltra Allassetmanagers 73 64 86 -9 22 Mutualfunds 30 23 28 -7 5 Table1: NotionallongTreasuryfuturesofallassetmanagersandmutualfunds: Thetableshows the notional amount of Treasury futures held by all asset managers (from the CFTC’s Traders in FinancialFuturesdata)andmutualfunds(fromFormN-PORT)attheendofDecember2019,June 2021, and June 2023. The last two columns show the change in notional amount from December 2019toJune2021andfromJune2021toJune2023. 44

Dec2019 Jun2021 Dec2019 Jun2021 Jun2023 toJun2021 toJun2023 Totalassets: 25,048 31,834 29,611 6,785 -2,222 Totallongfutures: 503 362 583 -140 221 IntermediateInvestmentGradeDebt Totalassets 1,677 2,088 1,931 410 -156 Longfutures 191 118 190 -72 71 Shareofallfutures 38 32 32 -5 0 ShortInvestmentGradeDebtFunds Totalassets 347 422 354 74 -67 Longfutures 28 51 48 22 -2 Shareofallfutures 5 14 8 8 -5 Balanced Totalassets 857 978 486 120 -491 Longfutures 23 14 44 -9 30 Shareofallfutures 4 3 7 0 3 ShortIntermediateInvestmentGradeDebt Totalassets 149 233 206 84 -26 Longfutures 17 9 25 -8 16 Shareofallfutures 3 2 4 -1 1 GrowthandIncome Totalassets 3,540 4,509 6,243 969 1,733 Longfutures 7 8 23 1 15 Shareofallfutures 1 2 4 0 1 Table 2: Notional long Treasury futures of mutual funds by Lipper objective codes: The table shows the total assets and notional amount of Treasury futures held by mutual funds at the end of December 2019, June 2021 by Lipper objective code along with the share of the code in total mutual fund Treasury futures. The last two columns show the change from June 2021 to June 2023. 45

Percentiles %positive 1% 10% 25% 50% 75% 90% 99% $billions Total 10 0.0 0.0 0.0 0.0 0.0 0.002 0.81 IntermediateInvestment 54 0.0 0.0 0.0 0.003 0.144 0.587 15.086 GradeDebt ShortInvestmentGradeDebt 50 0.0 0.0 0.0 0.002 0.144 0.502 3.126 Funds Balanced 24 0.0 0.0 0.0 0.0 0.0 0.063 1.979 ShortIntermediate 39 0.0 0.0 0.0 0.0 0.068 0.361 7.277 InvestmentGradeDebt GrowthandIncome 6 0.0 0.0 0.0 0.0 0.0 0.0 0.144 %ofnetassets Total 10 0.0 0.0 0.0 0.0 0.0 0.915 41.366 IntermediateInvestment 54 0.0 0.0 0.0 2.473 19.515 32.056 125.441 GradeDebt ShortInvestmentGradeDebt 50 0.0 0.0 0.0 0.902 23.951 47.335 74.464 Funds Balanced 24 0.0 0.0 0.0 0.0 0.0 6.978 18.476 ShortIntermediate 39 0.0 0.0 0.0 0.0 18.59 29.084 61.774 InvestmentGradeDebt GrowthandIncome 6 0.0 0.0 0.0 0.0 0.0 0.0 6.886 Table3: VariationinnotionallongTreasuryfuturesofmutualfundsbyLipperobjectivecodes: The table shows percentiles of the notional amount of Treasury futures held by mutual funds at theendofJune2023byLipperobjectivecodealongwiththeshareoffundsineachobjectivecode with positive long Treasury futures holdings. Results are shown for the top five codes. The first set of rows show the percentiles for billions of notional dollars, while the final set of rows show thepercentilesforpercentofnetassets. 46

Longfuturespositions $billions %assets Jun Jun Dec Jun Jun Dec Fundname Netassets 2023 2021 2019 2023 2021 2019 AmericanBalanced 202 34 7 17 16 3 10 BondFundofAmerica⋆ 75 31 9 18 41 13 38 AmericanFundsStrategicBond⋆ 17 28 0 0 158 0 27 MetropolitanWestTotalReturnBond⋆ 62 23 2 12 37 2 15 LordAbbettShortDurationIncome 46 22 21 5 47 35 9 WesternAssetCorePlusBond⋆ 24 17 13 29 72 31 94 IntermediateBondFundofAmerica 24 17 2 7 71 9 33 U.S.GovernmentSecurities 19 14 0 7 74 2 46 AmericanFundsInflationLinkedBond 13 11 1 1 84 9 27 PGIMTotalReturnBond⋆ 40 8 18 28 21 30 57 Table4: Top10holdersoflongnotionalTreasuryfuturesinJune2023: Thetableshowsthetotal assets, notional amount of Treasury futures at the end of December 2019, June 2021, and share of Treasury futures in total net assets for the top 10 holders as of June 2023. Stars denote funds classifiedashavinganintermediateinvestmentgradedebtobjectivebyLipper. Percentoftotalassets Indexfunds Non-futuresholders Futuresholders Dec Jun Jun Dec Jun Jun Dec Jun Jun Assetclass 2019 2021 2023 2019 2021 2023 2019 2021 2023 Treasuries 42 40 43 24 22 21 22 28 23 < 5YTM 25 23 25 10 9 7 11 16 9 5-10YTM 9 9 10 8 7 5 5 5 6 >10YTM 8 8 8 7 6 9 6 8 8 MBS 25 23 23 29 23 27 44 27 39 Agency 25 22 22 24 18 22 34 19 32 Privatelabel 0 1 1 4 5 5 10 8 8 Corporatedebt 28 31 29 33 39 37 31 32 31 Investment-grade 27 30 28 28 32 34 25 25 25 Speculative-grade 1 1 1 5 7 4 6 7 6 U.S.borrower 22 25 23 25 30 29 22 24 23 Non-U.S.borrower 6 6 6 8 9 9 9 8 7 CDO 0 0 0 2 2 3 4 5 5 OtherABS 0 0 0 5 7 5 3 3 4 Non-USsovereigndebt 2 2 2 1 2 1 4 3 2 Other 3 3 3 6 6 6 -8 2 -3 Table 5: Holdings of intermediate investment grade debt funds: The table shows the share of each asset class in the total assets of intermediate investment grade debt funds as classified by Lipper in December 2019, June 2021 and June 2023. The sample is split into index funds and activefundsthatholdlongfuturesandthosethatdonot. 47

PanelA:IIDFunds Treasuries MBS Corporate Other Cash (cash) Debt ABS Treasuryfuturestoassets −0.125∗∗∗ 0.047∗∗∗ 0.008 0.040∗∗∗ 0.014 (0.015) (0.013) (0.009) (0.008) (0.014) Fundfixedeffect X X X X X Timefixedeffect X X X X X R2 0.811 0.867 0.858 0.873 0.65 Observations 4,402 4,402 4,402 4,402 4,402 PanelB:Allfunds Treasuries MBS Corporate Other Equity (cash) Debt ABS Treasuryfuturestoassets −0.053∗∗∗ 0.004∗∗∗ −0.005∗∗∗ 0.004∗∗∗ 0.028∗∗∗ (0.007) (0.003) (0.002) (0.002) (0.008) Fundfixedeffect X X X X X Time×objectivefixedeffect X X X X X R2 0.93 0.956 0.982 0.931 0.976 Observations 183,594 183,594 183,594 183,594 183,594 Table6: RegressionofportfolioshareincashassetsonTreasuryfuturesshare. Thetableshows results of quarterly regressions of holdings of certain asset classes on Treasury futures notional positions. All variables are normalized by fund assets. Panel A shows results for intermediate investment-grade debt (IID) funds and Panel B shows results for all funds. Results use N-PORT datafromDecember2019toSeptember2023. ABSincludescollateralizeddebtobligations,assetbacked commercial paper and other ABS, but excludes MBS. All regressions include fund and time fixed effects. Standard errors are in parentheses. * indicates significance at the 10% level, ** atthe5%level,and***atthe1%level. Fixed Floating Variable Treasuryfuturestoassets −0.090∗∗∗ 0.047∗∗∗ 0.018∗∗∗ (0.017) (0.008) (0.004) Fundfixedeffect X X X Timefixedeffect X X X R2 0.763 0.821 0.91 Observations 4,402 4,402 4,402 Table 7: Regression of portfolio share in debt type on Treasury futures share. The table shows resultsofquartelyregressionsofintermediateinvestment-gradedebtfundholdingsoffixed,floating and variable debt on Treasury futures notional amounts to total assets. Results use N-PORT datafromDecember2019toSeptember2023. Allregressionsincludefundandtimefixedeffects. *indicatessignificanceatthe10%level,**atthe5%level,and***atthe1%level. 48

<5years 5-10years 10-20years >20years Allsecurities Treasuryfuturestoassets −0.022∗ −0.004 −0.008 0.012 (0.013) (0.01) (0.006) (0.014) Fundfixedeffect X X X X Timefixedeffect X X X X R2 0.8 0.784 0.797 0.842 Observations 4,402 4,402 4,402 4,402 U.S.Treasuriesonly Treasuryfuturestoassets −0.064∗∗∗ −0.028∗∗∗ −0.008∗∗∗ −0.024∗∗∗ (0.011) (0.009) (0.003) (0.004) Fundfixedeffect X X X X Timefixedeffect X X X X R2 0.773 0.715 0.71 0.725 Observations 4,402 4,402 4,402 4,402 Table 8: Regression of portfolio share in debt maturity on Treasury futures share. The table shows results of quartely regressions of intermediate investment-grade debt fund holdings by years to maturity on Treasury futures notional amounts to total assets. Results use N-PORT data from December 2019 to September 2023. All regressions include fund and time fixed effects. * indicatessignificanceatthe10%level,**atthe5%level,and***atthe1%level. Treasuries MBS Corporate Other Equty Debt ABS Treasuryfuturestoassets −0.053∗∗∗ 0.004∗∗∗ −0.005∗∗∗ 0.004∗∗∗ 0.028∗∗∗ (0.007) (0.003) (0.002) (0.002) (0.008) Fundfixedeffect X X X X X Time×objectivefixedeffect X X X X X R2 0.93 0.956 0.982 0.931 0.976 Observations 183,594 183,594 183,594 183,594 183,594 Table 9: Regression of portfolio share in cash assets on Treasury futures share (all funds). The table shows results of quartely regressions of holdings of particular asset classes on Treasury futuresnotionalamountstototalassets. ResultsuseN-PORTdatafromDecember2019toSeptember 2023. All regressions include fund and time by Lipper objective fixed effects. * indicates significanceatthe10%level,**atthe5%level,and***atthe1%level. 49

Average Difference Standard Averageabsolute Sharewithin duration fromindex error trackingerror 1-yearofindex Fullsample Nofutures 4.51 −0.64 0.009 13.06 87.27 Lowfutures 4.72 −0.43 0.014 8.48 95.24 Mediumfutures 4.77 −0.38 0.013 10.8 90.91 Highfutures 4.86 −0.29 0.01 7.18 95.65 Highminusno 0.35∗∗∗ 0.35∗∗∗ 8.38 2019 Nofutures 4.13 −0.56 0.016 15.26 81.82 Lowfutures 4.28 −0.4 0.028 12.36 85.71 Mediumfutures 4.42 −0.27 0.023 14.32 87.88 Highfutures 4.5 −0.18 0.019 7.08 93.48 Highminusno 0.37∗∗∗ 0.37∗∗∗ 11.66∗ 2021 Nofutures 4.17 −0.78 0.02 17.13 74.55 Lowfutures 4.57 −0.38 0.029 9.65 80.95 Mediumfutures 4.47 −0.48 0.024 11.72 87.88 Highfutures 4.5 −0.45 0.019 12.47 80.43 Highminusno 0.34∗∗∗ 0.34∗∗∗ 5.89 2023 Nofutures 5.37 −0.59 0.019 10.83 83.64 Lowfutures 5.65 −0.32 0.032 6.79 90.48 Mediumfutures 5.72 −0.24 0.026 6.19 100.0 Highfutures 5.93 −0.04 0.022 5.43 97.83 Highminusno 0.56∗∗∗ 0.56∗∗∗ 14.19∗∗ Table10: Empiricaldurationsofintermediateinvestment-gradedebtfundsbyfuturesuse. The table shows details of the distribution of empirical durations of intermediate investment-grade debt funds split into subsamples by futures use and by year. For each sub-sample, average duration reports the average estimated empirical duration, estimated by regression daily returns within the subsample on the change in 10-year Treasury yields. Difference from index is the differencebetweenthisaverageandtheBloombergAggregateIndex. Standarderroristhestandard erroroftheaverage,takingintoaccounttheunderlyingestimationerrorfromtheregression. Average absolute tracking error is the average across funds of the absolute percentage difference between the estimated duration of the fund and the index. Share within 1-year of the index is theshareoffundswithdurationwithin1-yearoftheindex. The“highminusno”rowsshowthe difference between high futures users and funds that do not use futures. Stars denote the significance of this difference, with * denoting significance at the 10% level, ** denoting significance at the5%level,and***atthe1%level. 50

Dec2019 Jun2021 Jun2023 Share Duration Share Duration Share Duration Indexfunds U.S.Treasuries 42.99 6.4 41.51 6.79 45.07 6.04 AgencyMBS 24.98 3.33 22.83 3.85 22.71 5.17 Private-labelMBS 0.31 1.27 1.2 5.03 0.93 3.87 Corporatedebt 22.21 8.23 24.61 9.02 22.39 7.4 CDO 0.04 0.42 0.32 1.57 0.43 2.01 OtherABS 0.05 0.13 0.01 0.06 0.01 0.04 Other 9.42 6.39 9.53 6.68 8.46 5.64 Totalduration Cashonly 6.03 6.62 6.08 Cash+Futures 6.03 6.62 6.08 2023Non-futuresholders U.S.Treasuries 19.25 8.71 18.08 8.18 23.63 9.19 AgencyMBS 32.58 3.38 27.04 4.3 33.17 4.24 Private-labelMBS 6.45 2.4 4.65 3.22 3.15 2.4 Corporatedebt 22.76 6.64 28.44 7.86 23.09 6.94 CDO 0.68 0.09 1.46 0.14 0.87 0.29 OtherABS 6.92 1.67 5.85 2.18 8.93 2.04 Other 11.36 6.51 14.48 7.02 7.16 6.26 Totalduration Cashonly 5.35 6.05 5.83 Cash+Futures 5.50 6.17 5.83 2023Futuresholders U.S.Treasuries 21.62 9.3 29.71 9.41 21.52 9.3 AgencyMBS 30.93 3.53 19.7 4.25 33.12 3.78 Private-labelMBS 8.15 2.5 6.75 2.78 6.63 2.76 Corporatedebt 21.76 5.56 25.24 7.38 22.81 5.95 CDO 2.21 0.78 1.85 0.83 1.68 1.01 OtherABS 2.28 1.7 2.83 2.04 3.24 1.86 Other 13.06 4.77 13.93 5.66 11.0 4.73 Totalduration Cashonly 5.06 6.28 5.28 Cash+Futures 6.11 6.76 6.08 Table 11: Weighted average duration of intermediate investment-grade debt funds by investment. Thistableshowsthedurationofcashholdingsofintermediateinvestment-gradedebtfunds by asset category, along with the weight of each category in total net assets of the funds, and the totalweighted-averagedurationofthefunds. Resultsaresplitbyindexfunds,non-futuresholdersandfuturesholders. 51

∆Treasuryfuturesduration (1) (2) (3) ∆Cashduration −0.360∗∗∗ −0.358∗∗∗ −0.417∗∗∗ (0.059) (0.059) (0.065) Fundfixedeffect X X Timefixedeffect X R2 0.070 0.100 0.149 Observations 1,051 1,051 1,051 Table 12: Regression of change in Treasury futures duration on change in cash duration. The tableshowsresultsofquartelyregressionsofchangesinthedurationofafund’sTreasuryfutures positionagainstthedurationofthecashportfolio. ResultsuseN-PORTdatafromDecember2019 to September 2023. * indicates significance at the 10% level, ** at the 5% level, and *** at the 1% level. Levels Differences Dec2019 Jun2021 Jun2023 2021–2019 2023–2021 Indexfunds Totalduration 6.03 6.62 6.08 0.59 -0.54 2021allocations 6.07 6.62 6.10 0.55 -0.52 2021durations 6.54 6.62 6.57 0.08 -0.05 AgencyMBSonly 6.56 6.62 6.61 0.06 -0.01 2023Non-futuresholders Totalduration 5.35 6.05 5.83 0.70 -0.22 2021allocations 5.61 6.05 6.02 0.44 -0.03 2021durations 5.74 6.05 5.95 0.31 -0.10 AgencyMBSonly 5.52 6.05 5.69 0.53 -0.36 2023Futuresholders Totalduration 5.06 6.28 5.28 1.22 -1.00 2021allocations 5.55 6.28 5.81 0.73 -0.47 2021durations 5.76 6.28 5.98 0.52 -0.30 AgencyMBSonly 5.25 6.28 5.38 1.03 -0.90 Table 13: Decomposition of changes in weighted average cash duration of intermediate investment-grade debt funds. This table shows a decomposition of the changes in weighted averagedurationforthecashinvestmentsofintermediateinvestment-gradedebtfunds. Thefirst three columns show the level of duration under different alternatives. In the row labelled “2021 allocations”,weightsonassetclassesareheldfixedatlevelsinJuneof2021,butdurationswithin theclassesvarythroughtime. Inthe“2021durations”rows,durationswithintheclassesareheld fixed, butweightsareallowedtovary. Inthe“AgencyMBSonly”row, weonlyallowtheinvestmentinagencyMBStovary,andassumethatanadditionaldollarinvestedinagencyMBScomes fromadecreaseofadollarininvestmentintoU.S.Treasuries. 52

Treasury Agency Private-label Corporate CDO Other MBS MBS Debt ABS Treasuryfutures −0.186∗∗ −0.179∗∗ −0.112∗∗∗ 0.059∗∗∗ −0.078∗∗∗ 0.002 toassets (0.092) (0.072) (0.028) (0.021) (0.027) (0.037) Fundfixedeffect X X X X X X Timefixedeffect X X X X X X R2 0.499 0.629 0.43 0.405 0.278 0.304 Observations 1,122 1,122 1,122 1,122 1,122 1,122 Table14: RegressionofcontributionofassetstochangesindurationonTreasuryfuturesshare. Thetableshowsresultsofquartelyregressionsofthecontributiontototalchangesindurationof differentcashsecuritiesforintermediateinvestment-gradedebtfundholdingsonTreasuryfutures notional amounts to total assets. Results use N-PORT data from December 2019 to September 2023. Thedependentvariableinthe first columnistheactualduration, thesecondcolumnisthe durationthatwouldresultwith2021allocations,thethirdcolumnisthedurationthatwouldresult with 2021 asset-level durations. All regressions include fund and time fixed effects. * indicates significanceatthe10%level,**atthe5%level,and***atthe1%level. 53

Table15: ImpactofMBSonAggregateAssetManagers’LongFuturesPositions ModelI ModelII ModelIII MBSreturns TBAOAS 23.14∗∗∗ 12.62∗∗ (8.45) (5.63) DollarRollSpec −61.30 −28.07 (45.24) (19.97) TBAOAS(MA) 13.39∗∗ (5.58) DollarRollSpec(MA) −52.49∗∗ MBSsensitivities TBADuration −2.17∗∗∗ −2.10∗∗∗ (0.59) (0.57) TBAConvexity −3.37∗∗∗ −3.39∗∗∗ (0.83) (0.85) (23.86) Controls Rolleffect −0.03∗∗∗ −0.03∗∗∗ −0.02∗∗∗ (0.00) (0.00) (0.00) Monthindicators X X X R2 0.33 0.79 0.80 Adj. R2 0.31 0.78 0.79 ∗∗∗p<0.01;∗∗p<0.05;∗p<0.1 Assetmanagers’longTreasuryfuturespositionsarenormalizedbytotalopeninterest. AllRMBScovariatesareforFNMA30-year currentcouponTBAtradesanddollarrolls.DynamicsOLSestimateswithp=2.Newey-Westrobuststandarderrorswithalagof52 weeksarereportedinparenthesis.Datasources:J.P.MorganChase&Co. ReturnrelativetoAggregateIndex Duration Averageexcess Beta Alpha Std. Dev component Nofutures 0.28 0.88 0.32 0.45 0.37 Lowfutures 0.34 0.93 0.38 0.45 0.39 Mediumfutures 0.46 0.94 0.49 0.47 0.39 Highfutures 0.34 0.96 0.36 0.47 0.40 Table 16: Performance of intermediate investment-grade debt funds by futures use. The table shows statistics on the performance of IID funds grouped into no long Treasury futures use, and lowmediumandhighTreasuryfuturesuse. Statisticsincludeexcessreturnrelativetotheaggregateindex,thebetaofthefundrelativetotheaggregateindex,thealphaofthefundrelativetothe aggregateindex,thestandarddeviationofthefunds’return,andthecomponentofthatstandard deviationduetodurationaccordingtoasimplelinearregression. 54

Mentionsderivatives... inPrincipalStrategies inPrincipalRisks Allfunds IIDfunds Allfunds IIDfunds Nofutures 36% 47% 49% 57% Lowfutures 85% 84% 85% 74% Mediumfutures 78% 85% 83% 87% Highfutures 79% 95% 83% 93% χ2 1069.82 65.2 726.04 51.4 p-value 1.3×10−231 4.5×10−14 4.7×10−157 4.0×10−11 Table 17: Prospectus mentions of derivatives by notional futures holdiings. The table shows share of all funds and intermediate investment-grade debt (IID) funds with mentions of derivativesinprincipalstrategiesandprincipalriskssectionsoftheprospectusforfundswithnoholdings of Treasury futures in June 2023, low holdings (bottom-third of positive holdings), medium holdings (middle-third of positive futures holdings), and high holdings (upper-third of positive futuresholdings). StatisticsareforthelatestprosectusavaiablepriortoJune2023foreachfund. Allfuturesusers Highfuturesusers Rank Word χ2 Word χ2 1 mortgage 239.97 mortgage 134.67 2 backed 183.06 backed 95.42 3 debt 137.58 debt 65.4 4 duration 114.27 duration 54.3 5 fixed 104.15 dollar 53.26 6 swaps 97.73 swaps 44.92 7 credit 84.33 inflation 40.34 8 government 75.83 pgim 40.21 9 dollar 75.6 freedomincome 38.06 10 currency 71.69 credit 33.79 11 pimco 70.32 unrated 33.47 12 grade 68.64 rolls 33.13 13 tba 63.52 fixed 32.55 14 bonds 62.68 grade 32.4 15 default 61.62 linking 31.88 16 index 60.41 government 31.49 17 instruments 59.7 tba 30.39 18 derivatives 59.55 default 30.38 19 inflation 58.29 loan 29.79 20 rolls 56.7 guaranteed 29.57 Table18: Wordsinprincipalstrategysectionofprospectusmostpredictiveoffuturesuse. The tableshowsthetwentywordsmostpredictiveoffuturesusein2023acrossallfundsaccordingto theχ2 statisticoftheirfrequencywithintheprincipalstrategysectionofthefunds’prospectuses. StatisticsareforthelatestprosectusavaiablepriortoJune2023foreachfund. Thelefttwocolumns showthewordsmostpredictiveofanyfuturesuse,whiletherighttwocolumnsshowthewords mostpredictiveofhighfuturesuse(upper-thirdpositivefuturesholdings). 55

Dependentvariable: HaslongTreasuryfutures Allfunds IIDfunds (1) (2) (3) IndexTreasuryshare 25.50∗∗∗ (5.926) Turnoverratio 0.063∗∗∗ 0.016∗∗∗ 0.008∗∗∗ 0.017∗∗∗ (3.143) (3.822) (2.675) (4.425) Risksmentionleverage 0.200∗∗ 0.067∗∗∗ 0.065∗∗∗ 0.084∗∗∗ (2.277) (8.637) (8.554) (8.359) Strategy: Duration −0.107 0.069∗∗∗ 0.015 0.013 (−1.179) (5.077) (1.009) (0.891) Strategy: Mortgage 0.343∗ 0.221∗∗∗ 0.125∗∗∗ 0.123∗∗∗ (1.767) (13.849) (7.399) (7.365) Objective: Totalreturn −0.033 0.079∗∗∗ 0.051∗∗∗ 0.060∗∗∗ (−0.366) (6.867) (4.487) (5.104) Objective: Income −0.137 0.013 0.005 0.019 (−1.558) (1.33) (0.453) (1.524) Indexfunddummy −0.102∗∗∗ −0.094∗∗∗ −0.134∗∗∗ (−9.454) (−6.649) (−7.371) Logoftotalnetassets 0.075∗∗∗ 0.023∗∗∗ 0.024∗∗∗ 0.010∗∗∗ (3.77) (13.286) (13.704) (4.943) Objectivefixedeffect X X Advisorfixedeffect X Observations 143 5,886 5,886 5,886 R-squared 0.232 0.254 0.337 0.488 Table 19: Explanatory regressions for Treasury futures holdings (indicator). The table shows regression results for cross-sectional regressions on IID funds and all fund types of whether the fund is a Treasury futures holder on dummies for whether the principal risk section mentions leverage, whether the principal strategies section mentions duration or mortgages, whether the objectivesectionmentionstotalreturn,andwhethertheobjectivesectionmentionsincome. Data is for the cross-section of funds as of Q2 2023. * denotes significance at the 10% level, ** denotes significanceatthe5%level,and***atthe1%level. 56

DependentVariable: HaslongTreasuryfutures (1) (2) (3) (4) (5) (6) FlowVolatilitypre-2018(%,monthly) -0.75 -0.44 (-0.49) (-0.36) Flow2020-2021(%,monthly) -0.89 -1.88 (-0.46) (-1.17) Flow2022(%,monthly) -0.46 -0.84 (-0.25) (-0.51) Controls X X X AdjustedR2 -0.01 0.17 -0.01 0.18 -0.01 0.16 N 128 128 138 138 142 142 Table 20: Fund flows and futures use for intermediate investment-grade debt funds. This table regresses an indicator for whether the fund holds Treasury futures in June 2023 on various measures of fund flows. Columns (1) and (2) include as the independent variable the standard deviation of monthly flows for flows occurring prior to January 2018. In columns (3) and (4), the independentvariableistheaverageofmonthlyflowsbetweenJanuary2020andDecember2021. In columns (5) and (6), the independent variable is the average flows occurring in 2022. In each specification, flowsarecalculatedasapercentageofnetassets. Robuststandarderrorsarecalculated in each specification and t-statistics are reported in parenthesis. Controls include turnover ratio,anindicatorforwhetherthe“Risks”sectionoftheprospectusmentionsleverage,indicators forwhetherthe“Strategy”sectionoftheprospectusmentions“Duration”or“Mortgage”,indicatorsforwhetherthe“Objectives”sectionoftheprospectusmentions“Income”or“TotalReturn”, and the log of net assets. * denotes significance at the 1% level, ** denotes significance at the 5% level,and***denotessignificanceatthe10%level. 57

Dependentvariable: Percentflows (1) (2) (3) Logoftotalnetassets 0.002∗∗∗ 0.003 0.003 (3.592) (1.23) (1.231) Quarterlyreturn 0.528∗∗∗ 0.454∗∗∗ 0.571∗∗∗ (3.453) (2.949) (2.979) Quarterlyreturn×Lowfutures −0.007 −0.012 −0.006 (−0.105) (−0.178) (−0.083) Quarterlyreturn×Mediumfutures −0.105 −0.107 −0.107 (−1.586) (−1.606) (−1.607) Quarterlyreturn×Highfutures −0.093∗ −0.091∗ −0.099∗ (−1.891) (−1.825) (−1.944) Salesrestriction 0.001 (0.828) Opentoinvestors 0.001 (0.165) Retailfund −0.001 (−0.614) Quarterlyreturn×Salesrestriction −0.168∗∗∗ (−2.971) Quarterlyreturn×Opentoinvestors −0.28∗∗ (−2.194) Quarterlyreturn×Retailfund −0.061 (−1.029) Timefixedeffects X X X Entityfixedeffects X X Observations 8,288 8,288 8,288 R-squared 0.019 0.019 0.019 Table 21: Flow-performance regressions for intermediate investment-grade debt funds. The table shows regression results for regressions of fund flows on quarterly returns interacted with low, medium and high holdings of futures as of 2023. t-statistics are in parentheses. Regressions are at a monthly frequency. The dependent variable is the percentage of net assets that flow into the fund. The sample is restricted to active intermediate investment-grade debt funds observed in all months using the Bloomberg Aggregate Index as benchmark. The first columns control for time fixed-effects but not fund fixed-effects, and we have excluded estimates for the dummy variables of futures-use categories for brevity. The second column includes both fund and tiime fixed-effects, andthethirdcolumnincludesadditionalcontrolsforsalesrestirctions, whetherthe fund is open to investors, and whether the fund is a retail fund. Standard errors are clustered at thefundlevel. ThesampleperiodisfromJanuary2015toDecember2020. *denotessignificance atthe10%level,**denotessignificanceatthe5%level,and***atthe1%level. 58

Haslong Has Average Strategiesmention Risksmention Treasury reverse reverse Leverage Repo Leverage Repo futures repo repo Leverage Repo Leverage Repo Intermediateinvestment-gradedebtfunds Treasuryfuturesuse No 0.00 1.25 0.01 61.25 16.25 17.50 10.00 Yes 100.00 1.47 0.20 80.88 16.18 11.03 11.76 Reverserepouse No 62.91 0.00 0.00 73.24 15.49 13.15 10.80 Yes 66.67 100.00 9.10 100.00 66.67 33.33 33.33 Overall 62.96 1.39 0.13 73.61 16.20 13.43 11.11 Allfunds Treasuryfuturesuse No 0.00 0.22 0.09 42.18 4.89 12.79 1.87 Yes 100.00 3.46 0.33 76.92 14.23 18.15 8.77 Reverserepouse No 10.82 0.00 0.00 45.75 5.49 13.29 2.41 Yes 66.18 100.00 19.84 97.06 80.88 30.88 41.18 Overall 11.14 0.58 0.12 46.05 5.93 13.39 2.64 Table 22: Treasury futures use and reverse-repo use. The table shows share of intermediate investment-grade debt (IID) funds and all funds with mentions of reverse repo or levereage in the principal risk of strategies section of the prospectus as well as the share of funds with long Treasuryfuturesholdings,thesharewithreverserepoborrowingandtheaverageofreverserepo borrowingtoassetsforfundswithandwithoutlongTreasuryfuturesholdingsandwithorwithout reverse repo borrowing. Data is for June 2023. Statistics are for the latest prosectus avaiable priortoJune2023foreachfund. 59

Percentoftotalassets Indexfunds Non-futuresholders Futuresholders Dec Jun Jun Dec Jun Jun Dec Jun Jun Assetclass 2019 2021 2023 2019 2021 2023 2019 2021 2023 TotalTreasuries 42 40 43 24 22 21 22 28 23 On-the-run 1 1 0 1 3 2 2 5 3 1-3Off-the-run 4 6 5 4 4 3 6 10 4 Deepoff-the-run 37 34 39 20 18 18 15 18 18 TotalagencyMBS 25 22 22 24 18 22 34 19 32 TBA 2 2 1 2 5 2 11 10 12 Allother 24 20 21 22 13 19 23 10 19 Dollarroll(est) 1 0 0 0 0 0 3 1 1 Table 23: Holdings of intermediate investment grade debt funds by liquidity categories: The table shows the share of Treasury and agency mortgage-backed securities in total assets of intermediate investment grade debt funds as classified by Lipper in December 2019, June 2021 and June 2023. Asset categories are further split into categories corresponding to liquidity. For Treasuries,webreakoutholdingsintoon-the-runTreasuries,first-throughthird-off-therunTreasuries and all “deep” off-the-run Treasuries that were issued prior to the third-off-the-run. For agency MBS, we divide the sample into to-be-announced (TBA) securites and all other holdings, as well asshowinganestimateofdollarrollactivitybasedontheminimumofshortandlongTBAholdings. The sample is split into index funds and active funds that hold long futures and those that donot. 60

Short Positions 3000 2500 Others 2000 Asset managers 1500 Hedge funds 1000 500 0 Long Positions 3000 2500 Others 2000 Asset managers 1500 Hedge funds 1000 500 0 2008 2010 2012 2014 2016 2018 2020 2022 2024 Figure1: Treasuryfuturespositionsbytypeoffund: Thisfigureshowsnotionalbillionsofdollars in long and short Treasury futures positions for asset managers, hedge funds and other traders across all Treasury futures contracts. Data are from the CFTC’s Commitment of Traders releases. ThisfigureupdatesasimilarfigureshowninBarthandKahn(2021). 61

1600 1400 1200 1000 800 600 400 200 0 2016 2017 2018 2019 2020 2021 2022 2023 2024 5102 ecnis egnahc evitalumuC )lanoiton snoillib $( Open interest Hedge fund short Asset manager long Figure2: CumulativeChangesinTreasuryFutures: Thisfigureshowsthecumulativechangein aggregatelongfuturesandaggregatelongassetmanagerfuturesovertime. 500 400 300 200 100 0 −100 2020-01 2020-07 2021-01 2021-07 2022-01 2022-07 2023-01 2023-07 1202 enuJ morf lanoiton ni egnahC )snoillib $( Asset manager long positions (TIFF) Mutual fund long positions (NPORT) Figure 3: Cumulative change in notional long Treasury futures positions of mutual funds and allassetmanagers: ThefigureshowsthecumulativechangerelativetoJune2023innotionallong Treasury futures positions of mutual funds, taken from N-PORT data, and all asset managers, takenfromTradersinFinancialFuturesdatafromthebeginningof2020to2023. Thepositionsare inbillionsoftotalnotionaldollars. 62

180 160 140 120 100 2020-01 2020-07 2021-01 2021-07 2022-01 2022-07 2023-01 2023-07 snoillib $ lanoitoN Long futures notional (left axis) 11 10 9 8 7 6 5 )%( stessa latot fo erahS Long futures as share of assets (right axis) Figure4: TotallongfuturespositionsofIIDmutualfundsThefigureshowsnotionallongpositions in Treasury futures in $ billions and as a share of assets for intermediate investment-grade debt(IID)funds. 600 400 200 2020-01 2020-07 2021-01 2021-07 2022-01 2022-07 2023-01 2023-07 snoillib $ lanoitoN Long Short Net 300 200 100 0 2020-01 2020-07 2021-01 2021-07 2022-01 2022-07 2023-01 2023-07 )snoillim $( 10VD Figure 5: Mutual fund goss and net positions in Treasury futures: The figure shows total long, shortandnetTreasuryfuturespositionsofmutualfundsindollars(toppanel)andDV01(bottom panel). 63

600 500 400 300 200 100 0 2020-01 2020-07 2021-01 2021-07 2022-01 2022-07 2023-01 2023-07 serutuf yrusaerT gnol lanoitoN )snoillib $( No long positions Middle third Total Bottom third Top third Figure6: TotallongTreasuryfuturesholdingsovertimebyholdingsasofJune2023: Thefigure showstotalholdingsoffuturesbymutualfundsforfundswithdifferentholdingsasofJune2023, in particular split into no futures holdings in June 2023, and then the bottom, middle and top thirdsofpositivelongfuturesholdingsinJune2023. 400 350 300 250 200 150 100 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 )snoillib $( seirusaerT hsac fo sgnidloH Left axis 1200 IID futures user funds IID index funds 1000 800 600 400 200 )snoillib $( tnuoma lanoitoN Right axis Asset manager long futures Figure7: CashTreasuryholdingsoffuturesholderandnon-futuresholderintermediateinvestment grade debt funds: The figure show total cash Treasury holdings of funds that held long Treasury futures in June 2023 and those that did not on the left axis. On the right axis, the figure showstotalassetmanagerfuturesholdingsfromtheCFTC’sTradersinFinancialFuturesdata. 64

10 5 0 −5 −10 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 stessa latot fo tnecreP Treasuries Corporate debt Mortgage-backed securities Asset-backed securities Figure 8: Relative change in positions for futures holder and non-futures holder intermediate investmentgradedebtfunds: ThefigureshowstheshareofcashTreasuriesandmortgage-backed securitiesintotalassetssince2015forfuturesholderandnon-futuresholderintermediateinvestmentgradedebtfunds. 60 40 20 0 stessa latot % Index funds Cash Treasuries MBS 60 40 20 0 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 stessa latot % Futures holders Figure 9: Share of Treasury cash and mortgage backed securities in total assets for futures holder and index fund intermediate investment grade debt funds: The figure show the differencebetweenthecumulativechangeinshareofdifferentassetclassesintotalassetssince2015 forfuturesholders(bottompanel)andindexfunds(toppanel)asofJune2023. 65

8 7 6 5 4 2020-01 2020-07 2021-01 2021-07 2022-01 2022-07 2023-01 2023-07 )sraey( noitaruD Index duration Cash duration Cash + futures Figure 10: Duration of cash and futures positions for intermediate investment-grade debt funds: The figure show the difference between the cumulative change in share of different assetclassesintotalassetssince2015forfuturesholders(bottompanel)andindexfunds(toppanel) asofJune2023. 0.6 0.5 0.4 0.3 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 carf ,snoitisop gnol MA Figure 11: Fraction of asset managers’ aggregate long positions and model fit The black line is the aggregate long Treasury futures positions of asset managers as a fraction of total long open interest,whilethebluelineisthefittedvaluesfromModelIVinTable15. 66

60 55 50 45 40 35 30 25 20 2006 2010 2014 2018 2022 latot ni erahs yrusaerT iShares Core US Agg ETF Financial accounts aggregate Figure 12: Share of Treasuries in index fund and aggregate debt The figure show the share of TreasuriesintheiSharesCoreUSAggregateETFandinaggregatedebtasreportedinthefinancial accountsaggregateanddefinedinthetextofthepaper. SeriesfortheiSharesCoreUSAggregate ETFbeginin2010withthebeginningofportfoliosharecoveragefromCRSP. 67

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A Appendix A.1 AdditionalMBSResultsandRobustness A.1.1 EstimationDetails Option-adjusted duration, convexity and asset managers’ long futures positions show considerablepersistence—fortheseseries,AugmentedDickey-Fullertests(DickeyandFuller(1979))cannotrejectthepresenceofunitrootsatthe10percentsignificancelevel. Thus,wefirstexcludethe possibilityofaspuriousregressionbyverifyingthattheresidualsfromallmodelsofspecification (1) (where potentially integrated, I(1), processes appear on both the left and right hand side of theequation)arenotthemselvesintegratedoforderunity,asverifiedbytheAugmentedDickey- Fullerunitroottestsatthe5percentsignificancelevel, usingthecut-offvaluesfromPhillipsand Ouliaris (1990). Our primary approach is to treat (1) as a cointegrating relationship and estimate it accordingly by dynamic OLS (DOLS).18 For all estimated models, we report Newey-West robust standard errors with a lag of 52 weeks.19 Finally, we note that in the case that none of the true data-generating processes are integrated of order unity, our parameter estimates and their standarddeviationsremainvalid.20 A.1.2 IndividualFuturesContracts We examine individual futures contracts. We consider the Model IV version of specification (1) for asset managers’ long Treasury futures positions in: (i) the 2-year contract (Model TU); (ii) the 5-year contract (Model FV), (iii) the 10-year contract (Model TY); (iv) the average of the 10year Ultra, 30-year, and 30-year Ultra contracts (Model Long Dur); and (iv) the average of 2-year and10-yearcontracts(ModelTY-TY).Alllongpositionsarenormalizedbythetotalopeninterest over all Treasury futures contracts. Table A.7 reports DOLS estimates of these models and the associatedNewey-Weststandarderrors. Asset managers’ long positions in the 2-year contract (Model TU) exhibit the qualitative responsesthatweidentifiedforaggregateholdingsand,inparticular,presentthestrongestsupport 18SeeStockandWatson(1993),aswellasHayashi(2011)andreferencestherein. 19Asafurtherrobustnesscheck(notreported),weconductedblockbootstrapstofurtherverifythesignificanceof ourresultswithlessrelianceontheasymptoticdistributionofcoefficientestimates. 20WeobtainqualitativelysimilarresultswhenestimatingmodelswithOLS,insteadofDOLS. 71

forthedurationhedgingmotiveofholdingTreasuryfutures. Also,longerdurationfutures(Model Long Dur) exhibit negative and significant, albeit less pronounced, dependence on RMBS duration. Notably,ModelFVsuggeststhatthe5-yearcontractmaybemoreactivelyusedforconvexity ratherthanfordurationhedging. TheRMBScovariatesexplainmorevariationforthe2-yearand longer duration futures relative to the 5-year and, especially, 10-year contracts. Interestingly, the average of 10-year Ultra, 30-year, and 30-year Ultra Treasury futures long positions is negatively affectedbyRMBSreturnproxies. A.1.3 RobustnesstoGSEpoolselection Inthissection,weestablishrobustnessofourresultswithrespecttothetypeofgenericGSEpools underlying the TBAs. Table A.8 reports the parameter estimates of model specification (1) for aggregateassetmanagers’longfuturespositionsandGNMA30-yearcurrentcouponcovariates. Table A.9 reports estimates for the effects of RMBS variables on asset managers’ long futures positionsbrokenoutbycontract. Onceagain,theroleof5-yearfuturesasconvexityhedgesclearly standsout. A.2 AlternativemodelspecificationforMBSeffects Instead of relying on Newey-West standard errors, we may also consider a specification with an autoregressivecomponent: 12 (cid:88) ω = α +α ω +X β+roll.eff + γ Month i +ϵ (2) t 0 1 t−1 t t i t t i=2 72

Dec2019 Jun2021 Dec2019 Jun2021 Jun2023 toJun2021 toJun2023 Total Allassetmanagers 410 493 439 83 -54 Mutualfunds 181 285 208 104 -77 2-year Allassetmanagers 176 104 101 -72 -3 Mutualfunds 46 61 29 15 -32 5-year Allassetmanagers 83 111 93 28 -18 Mutualfunds 39 46 31 7 -15 10-year Allassetmanagers 81 152 123 71 -29 Mutualfunds 40 83 59 43 -24 10-yearUltra Allassetmanagers 29 66 65 37 -1 Mutualfunds 26 50 47 24 -3 30-year Allassetmanagers 28 30 29 2 -1 Mutualfunds 21 19 17 -2 -2 30-yearUltra Allassetmanagers 10 28 27 18 -1 Mutualfunds 8 24 22 16 -2 Table A.1: Notional short Treasury futures of all asset managers and mutual funds: The table shows the notional amount of Treasury futures held by all asset managers (from the CFTC’s TradersinFinancialFuturesdata)andmutualfunds(fromFormN-PORT)attheendofDecember 2019, June 2021, and June 2023. The last two columns show the change in notional amount from December2019toJune2021andfromJune2021toJune2023. 73

MBS ABS Agency Private-label Roll(est) CDO Other Treasuryfuturestoassets 0.030∗∗ 0.017∗∗∗ 0.007∗∗ 0.030∗∗∗ 0.010∗∗ (0.014) (0.005) (0.003) (0.006) (0.004) Fundfixedeffect X X X X X Timefixedeffect X X X X X R2 0.839 0.915 0.481 0.838 0.915 Observations 4,402 4,402 4,402 4,402 4,402 Table A.2: Regression of detailed ABS shares on Treasury futures share. The table shows results of quartely regressions of intermediate investment-grade debt fund holdings of particular assetclassesonTreasuryfuturesnotionalamountstototalassets. ResultsuseN-PORTdatafrom December 2019 to September 2023. Roll indicates estimated mortgage dollar roll activity. All regressionsincludefundandtimefixedeffects. *indicatessignificanceatthe10%level,**atthe5% level,and***atthe1%level. Creditquality Borrowerdomicile Investment-grade Speculative-grade U.S. Non-U.S. Treasuryfuturestoassets 0.026∗∗∗ −0.016∗∗∗ −0.010 0.018∗∗∗ (0.008) (0.004) (0.007) (0.003) Fundfixedeffect X X X X Timefixedeffect X X X X R2 0.839 0.862 0.863 0.897 Observations 4,402 4,402 4,402 4,402 Table A.3: Regression of detailed corporate debt shares on Treasury futures share. The table showsresultsofquartelyregressionsofintermediateinvestment-gradedebtfundholdingsofparticularassetclassesonTreasuryfuturesnotionalamountstototalassets. ResultsuseN-PORTdata fromDecember2019toSeptember2023. Allregressionsincludefundandtimefixedeffects. *indicatessignificanceatthe10%level,**atthe5%level,and***atthe1%level. 74

Cashsecurityduration Actual 2021allocations 2021durations Treasuryfuturestoassets −0.487∗∗∗ 0.282 −0.519∗∗∗ (0.165) (0.231) (0.14) Fundfixedeffect X X X Timefixedeffect X X X R2 0.8 0.771 0.89 Observations 1,122 1,122 1,122 Table A.4: Regression of portfolio duration on Treasury futures share. The table shows results of quartely regressions of the duration of cash securities for intermediate investment-grade debt fund holdings on Treasury futures notional amounts to total assets. Results use N-PORT data from December 2019 to September 2023. The dependent variable in the first column is the actual duration, the second column is the duration that would result with 2021 allocations, the third column is the duration that would result with 2021 asset-level durations. All regressions include fund and time fixed effects. * indicates significance at the 10% level, ** at the 5% level, and *** at the1%level. 75

Allfuturesusers Highfuturesusers Rank Word χ2 Word χ2 1 backed 220.63 backed 95.75 2 mortgage 186.31 mortgage 89.45 3 debt 97.58 libor 42.8 4 libor 92.11 chance 39.66 5 loans 82.71 debt 36.59 6 credit 78.88 moderate 33.98 7 loan 62.13 loans 33.34 8 rate 58.31 credit 29.39 9 derivatives 56.07 loan 27.29 10 prepayment 50.46 mortgages 23.81 11 mortgages 47.82 rolls 21.43 12 rates 47.51 rate 21.09 13 companies 46.35 derivatives 19.56 14 quality 39.57 rates 18.87 15 pimco 39.11 refinance 17.91 16 sovereign 39.04 companies 16.97 17 extension 38.22 extension 16.72 18 obligations 38.05 prepayment 16.45 19 chance 37.47 tba 15.32 20 fixed 36.57 index 15.12 Table A.5: Words in principal risks section of prospectus most predictive of futures use. The table shows the twenty words most predictive of futures use in 2023 across all funds according to the χ2 statistic of their frequency within the principal risks section of the funds’ prospectuses. StatisticsareforthelatestprosectusavaiablepriortoJune2023foreachfund. Thelefttwocolumns showthewordsmostpredictiveofanyfuturesuse,whiletherighttwocolumnsshowthewords mostpredictiveofhighfuturesuse(upper-thirdpositivefuturesholdings). 76

Dependentvariable: LongTreasuryfuturestoassets Allfunds IIDfunds (1) (2) (3) IndexTreasuryshare 8.099∗∗∗ (5.809) Turnoverratio 0.016∗∗ 0.003∗∗∗ 0.002∗∗ 0.004∗∗∗ (2.456) (3.301) (2.363) (2.811) Risksmentionleverage 0.043 0.013∗∗∗ 0.015∗∗∗ 0.017∗∗∗ (1.186) (7.235) (7.898) (6.439) Strategy: Duration −0.058 0.016∗∗∗ 0.005 0.001 (−1.211) (4.231) (1.139) (0.163) Strategy: Mortgage 0.166∗∗∗ 0.046∗∗∗ 0.023∗∗∗ 0.022∗∗∗ (3.654) (9.924) (5.548) (4.508) Objective: Totalreturn −0.025 0.010∗∗∗ 0.007∗∗ 0.007∗∗ (−1.047) (3.191) (2.161) (1.976) Objective: Income −0.079∗∗ −0.007∗∗ −0.010∗∗∗ −0.008∗ (−2.083) (−2.534) (−2.628) (−1.934) Indexfunddummy −0.018∗∗∗ −0.017∗∗∗ −0.018∗∗∗ (−7.58) (−6.001) (−4.406) Logoftotalnetassets 0.029∗∗∗ 0.003∗∗∗ 0.003∗∗∗ 0.001 (2.876) (5.068) (5.242) (1.45) Objectivefixedeffect X X Advisorfixedeffect X Observations 143 5,886 5,886 5,886 R-squared 0.232 0.254 0.337 0.488 Table A.6: Explanatory regressions for Treasury futures holdings (percent of assets). The table showsregressionresultsforcross-sectionalregressionsonIIDfundsonlyandonallfundtypesof notionalTreasuryfuturesovertotalassetsondummiesforwhethertheprincipalrisksectionmentionsleverage,whethertheprincipalstrategiessectionmentionsdurationormortgages,whether the objective section mentions total return, and whether the objective section mentions income. Dataisforthecross-sectionoffundsinQ22023. *denotessignificanceatthe10%level,**denotes significanceatthe5%level,and***atthe1%level. 77

8 6 4 2 2013 2015 2017 2019 2021 2023 noitaruD AO −1 −2 −3 −4 2013 2015 2017 2019 2021 2023 ytixevnoC AO 90 60 30 0 2013 2015 2017 2019 2021 2023 daerpS AO 20 15 10 5 0 2013 2015 2017 2019 2021 2023 ssenlaicepS lloR ralloD Figure A.13: RMBS Rate Sensitivities and Return Proxies. The blue lines in the bottom panels are8-weeksmovingaveragesofthecorrespondingtimeseries. Datasource: J.P.MorganChase& Co. 78

ModelTU ModelFV ModelTY ModelLongDur ModelTU-TY MBSsensitivities TBADuration −1.01∗∗∗ 0.75 −0.22 −0.54∗∗∗ −0.61∗∗∗ (0.38) (0.70) (0.23) (0.09) (0.17) TBAConvexity −2.40∗∗∗ −1.90∗∗ 0.52 0.13 −0.94∗∗∗ (0.54) (0.76) (0.36) (0.13) (0.16) MBSreturns TBAOAS(MA) 6.78∗ 9.78∗ 2.51 −1.89∗∗∗ 4.64∗∗∗ (3.74) (5.60) (2.12) (0.68) (1.50) DollarRollSpec(MA) 12.61 −106.11∗∗∗ −14.26 18.43∗∗∗ −0.83 (18.96) (26.13) (10.71) (3.85) (9.30) Controls Rolleffect −0.00 −0.01∗∗∗ −0.01∗∗∗ −0.00∗∗ −0.00∗ (0.00) (0.00) (0.00) (0.00) (0.00) Monthindicators X X X X X R2 0.72 0.43 0.24 0.60 0.75 Adj. R2 0.71 0.40 0.20 0.58 0.74 ∗∗∗p<0.01;∗∗p<0.05;∗p<0.1 TableA.7: ImpactofMBSonAssetManagers’LongFuturesPositionsbyContract. Assetmanagers’ long Treasury futures positions are normalized by total open interest. All RMBS covariates are for FNMA 30-year current coupon TBA trades and dollar rolls. Dynamics OLS estimates with p = 2. Newey-Westrobuststandarderrorswithalagof52weeksarereportedinparenthesis. Datasources: J.P.MorganChase&Co. 79

ModelI ModelII ModelIII ModelIV MBSsensitivities TBADuration −5.82∗∗∗ −4.22∗∗∗ −4.24∗∗∗ (0.74) (0.86) (0.99) TBAConvexity 0.63 −2.75∗∗ −2.74∗∗ (1.49) (1.12) (1.20) MBSreturns TBAOAS 10.82∗∗∗ 7.67∗∗∗ (2.28) (2.20) DollarRollSpec −58.36 38.41∗∗ (40.77) (18.25) TBAOAS(MA) 7.86∗∗∗ (2.42) DollarRollSpec(MA) 37.15 (23.89) Controls Rolleffect −0.02∗∗∗ −0.03∗∗∗ −0.02∗∗∗ −0.02∗∗∗ (0.01) (0.01) (0.00) (0.00) R2 0.73 0.41 0.80 0.81 Adj. R2 0.71 0.39 0.79 0.79 Monthindicators X X X X ∗∗∗p<0.01;∗∗p<0.05;∗p<0.1 Table A.8: Impact of MBS on Aggregate Asset Managers’ Long Futures Positions: GNMA 30yearCCcovariatesAssetmanagers’longTreasuryfuturespositionsarenormalizedbytotalopen interest. AllRMBScovariatesareforGNMA30-yearcurrentcouponTBAtradesanddollarrolls. Dynamics OLS estimates with p = 2. Newey-West robust standard errors with a lag of 52 weeks arereportedinparenthesis. Datasources: J.P.MorganChase&Co. 80

ModelTU ModelFV ModelTY ModelLongDur ModelTU-TY MBSsensitivities TBADuration −3.55∗∗∗ 0.29 0.57 −0.52∗∗ −1.49∗∗∗ (1.14) (0.82) (0.66) (0.25) (0.54) TBAConvexity 0.32 −4.22∗∗∗ −0.76 0.64∗∗ −0.22 (1.26) (1.24) (0.73) (0.32) (0.60) MBSreturns TBAOAS(MA) 2.00 3.06∗ 2.27∗∗ 0.18 2.13∗ (2.03) (1.74) (1.02) (0.52) (1.09) DollarRollSpec(MA) 79.87∗∗∗ −51.84∗∗∗ −28.19 12.44∗∗ 25.84∗∗∗ (29.22) (16.34) (17.40) (5.28) (9.35) Controls Rolleffect 0.00 −0.01∗∗∗ −0.01∗∗∗ −0.00∗∗ −0.00 (0.00) (0.00) (0.00) (0.00) (0.00) Monthindicators X X X X X R2 0.60 0.66 0.21 0.49 0.69 Adj. R2 0.58 0.64 0.17 0.46 0.67 ∗∗∗p<0.01;∗∗p<0.05;∗p<0.1 TableA.9: ImpactofMBSonAssetManagers’LongFuturesPositionsbyContract: GNMA30yearCCcovariatesAssetmanagers’longTreasuryfuturespositionsarenormalizedbytotalopen interest. AllRMBScovariatesareforGNMA30-yearcurrentcouponTBAtradesanddollarrolls. Dynamics OLS estimates with p = 2. Newey-West robust standard errors with a lag of 52 weeks arereportedinparenthesis. Datasources: J.P.MorganChase&Co. 81

Table A.10: Impact of MBS on Aggregate Asset Managers’ Long Futures Positions: specificationwithanARterm ModelI ModelII ModelIII ModelIV MBSsensitivities TBAOAS 0.55∗∗ 0.91∗∗ (0.25) (0.41) DollarRollSpec −4.64∗∗ −4.96∗∗ (2.11) (2.03) MBSreturns TBAOAS(MA) 1.04∗∗ (0.43) DollarRollSpec(MA) −6.35∗∗ (2.95) TBADuration −0.27∗∗∗ −0.19∗∗∗ −0.19∗∗∗ (0.06) (0.07) (0.07) TBAConvexity −0.14∗∗∗ −0.25∗∗∗ −0.27∗∗∗ (0.04) (0.07) (0.07) Controls lagAMlongpos 0.93∗∗∗ 0.97∗∗∗ 0.92∗∗∗ 0.92∗∗∗ (0.01) (0.01) (0.01) (0.02) Rolleffect −0.01∗∗∗ −0.01∗∗∗ −0.01∗∗∗ −0.01∗∗∗ (0.00) (0.00) (0.00) (0.00) Monthindicators X X X X ∗∗∗p<0.01;∗∗p<0.05;∗p<0.1 Assetmanagers’longTreasuryfuturespositionsarenormalizedbytotalopeninterest.AllRMBScovariatesareforFNMA30-yearcurrentcouponTBAtradesanddollarrolls.DynamicsOLSestimates withp=2. Newey-Westrobuststandarderrorswithalagof52weeksarereportedinparenthesis. Datasources:J.P.MorganChase&Co. TableA.11: ImpactofMBSonAggregateAssetManagers’LongFutures Positions: specificationwithanARtermAssetmanagers’longTreasury futurespositionsarenormalizedbytotalopeninterest. AllRMBScovariates are for FNMA 30-year current coupon TBA trades and dollar rolls. DynamicsOLSestimateswithp = 2. Newey-Westrobuststandarderrors withalagof52weeksarereportedinparenthesis. Datasources: J.P.MorganChase&Co. 82

Strategiesmention Objectivesmention Averagereported Maturity Duration Total Current Turnover Expense bounds target return income ratio ratio Nofutures 25% 34% 54% 36% 1.14 0.0058 Lowfutures 28% 28% 71% 40% 2.05 0.0058 Mediumfutures 16% 38% 76% 28% 2.45 0.0059 Highfutures 18% 37% 67% 41% 2.64 0.0073 χ2 2.29 0.99 7.64 1.88 p-value 0.51 0.8 0.05 0.6 TableA.12: Prospectusmentionsofkeyphrasesbynotionalfuturesholdings. Thetableshows share of intermediate investment-grade debt (IID) funds with mentions of maturity bounds or duration targets in principal strategies and of total returns or income in the objectives section of the prospectus, as well as average turnover and expense ratios, for funds with no holdings of TreasuryfuturesinJune2023,lowholdings(bottom-thirdofpositiveholdings),mediumholdings (middle-third of positive futures holdings), and high holdings (upper-third of positive futures holdings). StatisticsareforthelatestprosectusavaiablepriortoJune2023foreachfund. 83

Haslong Has Average Strategiesmention Risksmention Treasury rate rate Leverage Swaps Leverage Swaps futures swaps swaps Leverage Swaps Leverage Swaps Intermediateinvestment-gradedebtfunds Treasuryfuturesuse No 0.00 8.75 4.22 61.25 30.00 17.50 43.75 Yes 100.00 41.18 110.36 80.88 44.12 11.03 82.35 Swapexposure No 52.29 0.00 0.00 69.28 30.72 12.42 58.82 Yes 88.89 100.00 243.61 84.13 58.73 15.87 90.48 Overall 62.96 29.17 71.05 73.61 38.89 13.43 68.06 Allfunds Treasuryfuturesuse No 0.00 1.46 77.09 42.18 18.47 12.79 24.36 Yes 100.00 28.69 401.10 76.92 46.00 18.15 68.31 Swapexposure No 8.32 0.00 0.00 44.05 19.78 12.86 26.29 Yes 71.18 100.00 2,520.21 88.74 58.97 24.62 92.37 Overall 11.14 4.49 113.19 46.05 21.54 13.39 29.25 Table A.13: Treasury futures use and interest-rate swap use. The table shows share of intermediateinvestment-gradedebt(IID)fundsandallfundswithmentionsofswapsorlevereageinthe principal risk of strategies section of the prospectus as well as the share of funds with long Treasuryfuturesholdings,thesharewithinterest-rateswapsexposureandtheaverageofinterest-rate swap notional to assets for funds with and without long Treasury futures holdings and with or without interest-rate swap exposure. Data is for June 2023. Statistics are for the latest prosectus avaiablepriortoJune2023foreachfund. 84