Interconnectedness in the Corporate Bond Market

Finance and Economics Discussion Series Federal Reserve Board, Washington, D.C. ISSN 1936-2854 (Print) ISSN 2767-3898 (Online) Interconnectedness in the Corporate Bond Market Celso Brunetti, Matthew Carl, Jacob Gerszten, Chiara Scotti, Chaehee Shin 2024-066 Please cite this paper as: Brunetti, Celso, Matthew Carl, Jacob Gerszten, Chiara Scotti, and Chaehee Shin (2024). “Interconnectedness in the Corporate Bond Market,” Finance and Economics Discussion Series 2024-066. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2024.066. 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.

Interconnectedness in the Corporate Bond Market CELSO BRUNETTI MATTHEW CARL JACOB GERSZTEN CHIARA SCOTTI CHAEHEE SHIN∗ April 2024 ABSTRACT Doesinterconnectednessimprovemarketquality? Yes. We develop an alternative network structure, the assets network: assets are connected iftheyareheldbythesameinvestors. Weuseseverallargedatasetstobuildtheassets networkforthecorporatebondmarket. Throughcarefulidentificationstrategiesbased on the COVID-19 shock and “fallen angels,” we find that interconnectedness improves market quality especially during stress periods. Our findings contribute to the debate on the role of interconnectedness in financial markets and show that highly interconnectedcorporatebondsallowforrisksharingandrequirealowercompensationforrisk. Keywords: financialstability,interconnectedness,institutionalinvestors,bigdata JELClassificationCodes: C13,C55,C58,G1 ∗CelsoBrunettiandChaeheeShinarewiththeFederalReserveBoard.ChiaraScottiisattheBankofItaly. MatthewCarlisaPh.D.studentattheUniversityofWisconsin-Madison. JacobGersztenisattheUniversity of Michigan Law School. The authors can be reached via email at celso.brunetti@frb.gov, mcarl@wisc.edu, gersztenj@umich.edu,chiara.scotti@bancaditalia.it,andchaehee.shin@frb.gov.WethankNathanFoley-Fisher andseminarandconferenceparticipantsattheFederalReserveBoard, QatarCenterforGlobalBankingand Finance,King’sCollegeLondon,UniversityofWisconsin,2022IAAEconference,2022EEA-ESEMconference, and2022InternationalRiskManagementConferenceforhelpfulcomments.Theviewsexpressedinthisarticle arethoseoftheauthorsandnotnecessarilyoftheFederalReserveSystem.WethankGeneKangforexcellent researchassistance.

1. Introduction Thenotionof“interconnectedness”becamepopularwiththeGreatFinancialCrisis(GFC). Linkages between markets and institutions as well as the ramifications of financial distress to the real economy put interconnectedness in the limelight. In fact, interconnectedness is now part of the regulatory framework.1 Interconnectedness is a sophisticated concept: too little interconnectedness (sparse network) may impede market functioning, and too much interconnectedness (dense network) may exacerbate the effects of a shock. The goal of this paperistostudythelinkagesbetweeninterconnectednessandmarketquality. We choose the corporate bond market as our sandbox. This market has grown substantially in recent years and represents an important source of funding for the corporate sector.2 It is dominated by institutional investors, which allows us to map linkages among the largest market players such as insurance companies and mutual funds. Compared to equity markets,itsliquidityandmarketfunctioninginthecorporatebondmarkethavebeenunder muchscrutiny,leadingtoarapiddevelopmentoftheliterature(see,Boyarchenkoetal.,2021; Dick-NielsenandRossi,2019;TrebbiandXiao,2019). Finally,thecorporatebondmarketexperienced significant disruptions in March 2020 because of the COVID-19 pandemic (see, HaddadandMuir,2021). Hence,studyinghowinterconnectednessrelatestomarketquality inbothtranquiltimesaswellasintimesofdistressisparticularlyinformative. In this paper, we develop an alternative and complementary network structure—the assets network—which mirrors the traditional notion of a portfolio similarity network. This new network construct is derived at the asset level and is based on the idea that assets are interconnectediftheyareheldbythesameinvestors. The more traditional portfolio similarity network captures spillover effects due to overlapping portfolios: two financial institutions with similar portfolios are linked because a shocktoonefinancialinstitutionhasrepercussionsontheotherfinancialinstitutionthrough 1InterconnectednessisoneofthecriteriausedbytheFinancialStabilityBoardtodesignateGlobalSystemicallyImportantBanks(G-SIBs).IntheU.S.,interconnectednessisalsousedbytheFinancialStabilityOversight Council(FSOC)todesignatenonbankSystemicallyImportantFinancialInstitutions(SIFIs). 2Ithasreachedover$15trillionasofQ42023–seeFinancialAccountoftheU.S. 1

their common asset holdings (see, Caccioli et al., 2015). In contrast, our network construct captures linkages among assets given that these assets are held by several financial institutions. The emphasis of our network is on the assets as opposed to financial institutions. Studyingthenetworkofassetsisfundamentallyimportantforseveralreasons. First,itallows ustoinvestigatehowinterconnectednessoffinancialassetsislinkedtoasset-specificcharacteristicssuchasliquidityandvolatilityand,moregenerally,tomarketquality. Second,there isagrowingliteratureoninstitutionalassetpricing;ournetworkstructureprovidesanother lens through which to study how assets held by several institutions—our assets network— impact the pricing process. This is particularly relevant in our framework which analyzes corporatebondholdingsbylargeinvestors. Third,assetsinterconnectednessprovidesanalternativeanduniqueperspectiveonhowfinancialassetsarelinkedincontrasttocorrelation analysis. Diebold and Yılmaz (2014) and Billio et al. (2012) construct assets networks based on the variance-covariance matrix of returns. Our network builds edges based on whether assets are held by common investors, and is, therefore, potentially more accurate because it doesnotrequireestimatinganymomentofthereturnsdistribution(see,Adamicetal.,2017). Finally,thetraditionaloverlappingportfolionetworkputsemphasisonfinancialinstitutions and is more suitedfor an entity-based supervisory approach, while our assets networkmay provideusefulforanactivity-basedapproachforregulation.3 We first focus on the interconnectedness of the corporate bond market, leveraging the rich information available in the Thomson Reuters eMAXX database, which contains data oncorporatebondholdingsattheinstitutionalinvestor-bond-year-quarterlevel. Webuilda networkofcorporatebondsandmeasuretheirinterconnectednessusingcosinesimilarity. As expected,wefindthatbondsissuedbylargefirmsarepartoftheportfolioofmanyinvestors and form the core of our networks, while smaller bond issuers comprise the periphery— implyingthatonlyafewinvestorsholdthesebonds. Wealsomatchtheinterconnectedness measures of corporate bonds with the TRACE database that has security-level data on corporatebondtradingvolume,liquidity,andvolatility. The new interconnectedness construct and the complexity of our data allow us to use a richpanelregressionanalysistoinvestigatethelinkbetweeninterconnectednessandspread, 3See,Borioetal.(2022). 2

liquidity, and volatility of corporate bonds. We find that the higher the interconnectedness of an asset—meaning that the asset is common to many investors’ portfolios—the lower its spread and the higher its liquidity. This result highlights that, as expected, corporate bonds thatareheldacrossseveralportfoliosrequirealowercompensationforriskandaremoreliquid. Thisrelationis,however,affectedbymarketconditions. Weexploretheheterogeneous effects of interconnectedness throughout the conditional distribution of the response variables(spreads,liquidity,andvolatility),whilecontrollingforbondcharacteristics,througha paneldataquantileregression. Wefindthattherelationwehavejusthighlightedisstronger whenafinancialassetisunderstress,i.e. thespreadandliquidityofanassetareintheupper tail of their conditional distributions. Altogether, higher interconnectedness is associated with lower spreads and volatility, and higher liquidity in normal market conditions (mean effect) and these results are stronger when markets are distressed (as shown by quantile regressions).4 Whiletheanalysisthusfardocumentslinkagesbetweeninterconnectednessandmarket quality measures, we are interested in determining causality. That is, we are interested in understanding whether higher interconnectedness reduces spreads, increases liquidity, and tamesvolatility. Thisisafundamentalissue. Ontheonehand,AllenandGale(2000)develops a model in which complete networks (high interconnectedness) help mitigate the effects of a shock through risk sharing and, therefore, are beneficial to financial stability. On the other, Acemoglu et al. (2015) shows that if the shock is too large, high interconnectedness propagates the shock leading to a more fragile financial system. The COVID-19 outbreak representsalargeexogenousshock. FollowingHassanetal.(2023),weseparatebondsissued by firms affected by the shock from bonds issued by firms not affected by the pandemic. We find that the effects of the shock are mitigated when bonds issued by firms exposed to thepandemicarehighlyinterconnectedtobondsissuedbyfirmsnot exposedtotheshock— spreaddecreasesandliquidityincreases. Ourresultsindicatethatinterconnectednessenables risksharingand,onnet,isbeneficialtothecorporatebondmarket. 4Our results are robust to different model specifications and to several controls that are known to affect corporatebondpricingdynamics,suchasinvestorconcentrationandthenumberofuniqueinvestors. 3

To corroborate these results we also look at “fallen angels:” bonds downgraded from investment grade to high yield. We select bonds with similar characteristics and a credit rating of BBB- (the lowest credit rating in the investment grade category). Only some of thesebondsaredowngradedinthenextperiod. Sincethebondsweconsiderinthisexercise have similar characteristics, the bifurcation between fallen angels and non-fallen angels is plausibly exogenous within the short time window we are considering—the analysis only considerstwoperiods,beforeandafterthedowngrade.5 Ourresultsshowthataonestandard deviationincreaseininterconnectednessofafallenangelsubstantiallydecreasesspreadsand increasesliquidity. Overall, our findings establish that higher levels of interconnectedness are positively linked to market quality. Moreover, the link between interconnectedness and market qualitychangesovertimewhenmarketconditionsalsochange. Importantly,thislinkisstronger duringperiodsofmarketdistress. Finally,interconnectednessisparticularlyimportantwhen large negative shocks hit financial markets (COVID-19) and when major corporate events occur (fallen angels). In these crisis situations, interconnectedness, through risk sharing, promotesmarketfunctioning. Our paper contributes to several strands of the literature. First, we contribute to the interconnectedness literature. Networks in finance have been mapped using three main techniques: (i) correlation networks, in which edges between financial institutions are based on estimates of the variance-covariance matrix of publicly available data, such as asset returns (see, Billio et al., 2012; Diebold and Yılmaz, 2014); (ii) physical networks, in which edges capture contractual agreements among counterparties, such as interbank transactions (see, Brunettietal.,2019);and(iii)commonholdingsnetworks,inwhichinvestorsareconnected if they hold similar portfolios (see, Caccioli et al., 2015; Greenwood et al., 2015; Cetorelli etal.,2023). Inthispaper,weproposeanewapproachofmappingfinancialnetworkswhich mirrors the notion of overlapping portfolios, and which we call the assets network or investor similarity network. Similar to our approach, Antón and Polk (2014) connect stocks commonly held by mutual funds. Their goal is to study how common ownership affects the 5Känzig (2021) proposes an identification strategy based on precisely selecting the time frame of specific events,whichforusisthedowngrade. 4

cross-sectional correlation in the rate of returns. Our focus is instead on the network structure and its properties. We are interested in fully understanding the interconnectedness of the new network and how it evolves both over time and in different market conditions. In fact,ourgoalistoprovideanewandalternativemappingforfinancialnetworks. Second,weconnecttotheemergingliteratureoninstitutionaldemand-basedassetpricing. Onestrandofthisliteraturestudiestheroleofintermediariesinassetpricing,suchasin Haddad and Muir (2021) and He et al. (2017). Another strand of the literature examines the roleofinstitutionalholdersinassetpricingand,inparticular,thecompositionofinstitutional investorsasapotentialstatevariableinthecorporatebondmarket. Forinstance,Ben-David etal.(2021)showhowtherisingconcentrationofholdingsbyinstitutionalinvestorsaffects stock volatility and price inefficiency, Li and Yu (2022) find that investor concentration is related to bond liquidity, and Li and Yu (2021) and Bretscher et al. (2022) analyze how the compositionofinstitutionalinvestorsrelatestocorporatebondmarketqualities. Corelletal. (2023) also look at European corporate bonds to find how convenience yields could vary by differingdemandsfromvariousinstitutionalinvestors. Overall,thisliteraturetracksbackto the demand-based asset pricing approach of Koijen and Yogo (2019). We contribute to this emerging area by showing that the interconnectedness of an asset plays an important role incorporatebondmarkets. Finally,werelatetotherecentfinancialstabilityliteraturethattriestodeterminewhether high interconnectedness is a vulnerability or a virtue of the financial system. Conflicting views exist in the literature, from Allen and Gale (2000), who find interconnectedness to be avirtue,tomorerecentempiricalworksfindingevidenceforfinanciallinkagesandoverlapping holdings of assets to be a contagion or fire sales mechanism (Allen et al., 2012; Duarte andEisenbach,2021;Falatoetal.,2021;Greenwoodetal.,2015,amongothers). Somewherein between these two conflicting views, many recent works study the non-monotonic tradeoff betweencontagionandrisksharing,socialoptimalityofinterconnectedness,andconditions for which one type of network is better than another (Acemoglu et al., 2015; Cabrales et al., 2017;Elliottetal.,2014,2021;Gofman,2017,amongothers). Ourresultsprovideevidenceof acausaleffect: interconnectednessimprovesmarketquality. 5

Thepaperisorganizedasfollows. Section2describesournovelnetworkapproach,illustrating the building blocks of the asset-based network of investor similarity. Section 3 summarizesthewealthofdatathatweuseintheempiricalinvestigation. Section4describesthe resultingmeasuresthatweuseintheanalysis. Section5explainstheregressionframework and its results, including those for the quantile regressions. Section 6 examines the causal linkagesbetweeninterconnectednessandmarketmarketquality. Section7concludes. 2. Network Approach There are several ways to construct networks in finance. The three main approaches can be briefly described as: (i) correlation networks, which are based on estimates of the variance-covariance matrix of publicly available data such as asset returns (see, Billio et al., 2012; Diebold and Yılmaz, 2014);6 (ii) physical networks, which reflect contractual agreementsbetweencounterpartiesandcaptureimportantaspectsofrisksuchasconterpartyrisk (see,Brunettietal.,2019);and(iii)overlappingportfoliosnetworks,whichconnectinvestors through their common holdings (see, Caccioli et al., 2015; Greenwood et al., 2015). In this paper,weproposeanewapproachofmappingfinancialnetworkswhichparallelsthenotion ofoverlappingportfolios,butthatdrawsedgesbetweenassetsratherthaninstitutions. Thestartingpointisabipartitenetworkwithtwosetsofnodes: financialinstitutionsor investors(𝐼s)andfinancialassets(𝐴s). AsshowninFigure1a,ifafinancialinstitutionholds an asset in its portfolio, there is an edge between that asset and that financial institution. For example, because investor 𝐼 holds asset 𝐴 , there is an edge between 𝐼 and 𝐴 . The 1 1 1 1 traditional network of overlapping portfolios, or common asset holdings, implies that since 𝐴 is held also by 𝐼 and 𝐼 , all three investors are interconnected through their common 1 2 3 holdings of 𝐴 . Similarly, because𝐴 is held by 𝐼 and 𝐼 , there is a link between these two 1 2 2 3 investors(seeBaruccaetal.,2021). Wederiveanalternativenovelnetworkstructureattheassetlevel,basedontheideathat twoassets,𝐴 and𝐴 ,areinterconnectediftheyareheldbythesameinvestor. InFigure1b, 1 2 6Arelatedapproachadoptsquantileregressionanalyses,seeAndoetal.(2021)andHärdleetal.(2016). 6

𝐴 and 𝐴 are interconnected because both assets are held in the portfolio of investor 𝐼 . 1 3 3 Similarly,𝐴 and𝐴 arealsointerconnectedsincetheyareheldbyinvestors𝐼 and𝐼 . Infact, 1 2 2 3 𝐴 and 𝐴 are interconnected to a higher extent than 𝐴 and 𝐴 because these assets share 1 2 1 3 twooverlappinginvestors. This asset-based network allows us to examine important effects of interconnectedness across financial assets. In Figure 1b, interconnectedness between 𝐴 and 𝐴 captures and 1 3 quantifies the following mechanism. Suppose a shock hits𝐴 (e.g., downgrade to junk) and 1 reduces its market value. This shock will then negatively impact the performance of the portfolios of all investors, 𝐼 , 𝐼 , and 𝐼 since they all hold 𝐴 . Investors will be forced to 1 2 3 1 re-balancetheirportfoliostoraisemorecapitalorliquidity(e.g.,inthecaseofmutualfunds, to meet redemptions) and the re-balancing will trigger a change in holdings of both𝐴 and 2 𝐴 becausethere-balancinginvestorsalsohold𝐴 (𝐼 and𝐼 )and𝐴 (𝐼 ). 3 2 2 3 3 1 InFigure1b,ourmeasureofinterconnectednessbetween𝐴 and𝐴 isstrongerthanthat 1 2 between𝐴 and𝐴 becausetwoinvestors(𝐼 and𝐼 )holdtheseassetsasopposedtojustone 1 3 2 3 investorfor𝐴 and𝐴 . Thisnetworkfeatureimpliesthatthesameinitialshockon𝐴 (and/or 1 3 1 𝐼 and/or𝐼 )willlikelyspilloverto𝐴 toagreaterextentthanitwillto𝐴 ,sinceboth𝐼 and 2 3 2 3 2 𝐼 willre-balancetheirportfoliosasopposedtojustoneinvestor(𝐼 )re-balancinginthecase 3 3 of𝐴 and𝐴 . 1 3 Noticethatthenotionofoverlappinginvestorsforabondis,however,differentthanthe sheernumberofinvestorsholdingthebond. InFigure1b,𝐴 isheldbythehighestnumberof 1 investors(𝐼 ,𝐼 ,and𝐼 ),followedby𝐴 ,whichisheldbytwoinvestors(𝐼 and𝐼 ). However, 1 2 3 2 2 3 𝐴 hasthesamenumberofoverlappinginvestors—anddegreeofinterconnectedness—as𝐴 . 1 2 This arises because out of the three investors holding 𝐴 , one investor (𝐼 ) does not invest 1 1 in any other assets, thereby eliminating its propensity to “overlap” with other investors. In general,aswehaveillustratedinthisexample,itispossiblethatassetswithfewerinvestors are more interconnected (have more overlapping investors) than other assets with more investors. In what follows, we describe our notion of the asset-based network in more detail and highlightthenetworkmeasureusedintheanalysis. 7

2.1. Network of Financial Assets and Institutions We start by denoting the network of financial assets and financial institutions as 𝑄 = (𝐴,𝐼,E),where𝐴 =𝐴 1 ,𝐴 2 ,...,𝐴 𝑆 isthesetofnodescorrespondingtofinancialassets(corporate bonds only, in our case), 𝐼 = 𝐼 1 ,𝐼 2 ,...,𝐼 𝑁 represents the set of financial institutions, and Eisa𝑆 ×𝑁 matrixrepresentingtheamount,𝐸 𝑖,𝑘,heldby𝐼 𝑘 in𝐴 𝑖: 𝐼 𝐼 ··· 𝐼 1 2 𝑁 𝐴 𝐸 𝐸 ··· 𝐸 𝑉𝐴 1 11 12 1𝑁 1 𝐴 𝐸 𝐸 ··· 𝐸 𝑉𝐴 E = . . . 2 . . . 21 . . . 22 ... 2 . . . 𝑁 . . . 2 . (1) 𝐴 𝐸 𝐸 ··· 𝐸 𝑉𝐴 𝑆 𝑆1 𝑆2 𝑆𝑁 𝑆 𝑉𝐼 𝑉𝐼 ··· 𝑉𝐼 1 2 𝑁 Summing across columns gives the total amount of security 𝑖 held by the system (investorsinourdata),𝑉𝐴 ,knownasthestrengthofthenetwork: 𝑖 𝑁 (cid:213) 𝑉 𝑖 𝐴 = 𝐸 𝑖,𝑘 , (2) 𝑘=1 andsummingacrossrowsproducesthetotalamountinvestedbyinvestor𝑘 inallassets,𝑉𝐼 . 𝑘 Dependingonthescopeoftheanalysis,𝐸 𝑖,𝑘 couldbenormalizedbythetotalissuedamount ofasset𝑖 outstandingorby𝑉𝐴 . 𝑖 ◦ WedefineasEthecorrespondingadjacencymatrix 8

𝐼 𝐼 ··· 𝐼 1 2 𝑁 ◦ ◦ ◦ 𝐴 𝐸 𝐸 ··· 𝐸 𝐷𝐴 1 11 12 1𝑁 1 ◦ ◦ ◦ E ◦ = 𝐴 . . . 2 𝐸 . . . 21 𝐸 . . . 22 · . · . · . 𝐸 2 . . . 𝑁 𝐷 . . . 2 𝐴 , (3) ◦ ◦ ◦ 𝐴 𝐸 𝐸 ··· 𝐸 𝐷𝐴 𝑆 𝑆1 𝑆2 𝑆𝑁 𝑆 𝐷𝐼 𝐷𝐼 ··· 𝐷𝐼 1 2 𝑁 ◦ where the generic element 𝐸 𝑖,𝑘 = 1 if 𝐸 𝑖,𝑘 > 𝑞 and zero otherwise. The parameter𝑞 denotes athresholdandintraditionalnetworkanalysis𝑞 = 0.7 Similartobefore,thesumacrosscolumnsgivesthetotalnumberoffinancialinstitutions holdingsecurity𝑖,𝐷𝐴 ,knownasnetworkdegree, 𝑖 𝑁 (cid:213) ◦ 𝐷 𝑖 𝐴 = 𝐸 𝑖,𝑘 , (4) 𝑘=1 andthesumacrossrowsgeneratesthetotalnumberofassetsinvestor𝑘 hasinvestedin,𝐷𝐼 . 𝑘 2.2. Asset-based Network of Investor Similarity Thenetworkwefocusoninthispaperisderivedfromthenetworkoffinancialassetsand financial institutions 𝑄 described in the previous section and captures interconnectedness amongassetsbasedonwhethertheassetsbelongtothesameportfolios. We define the network of financial assets as 𝑂𝐴 = (cid:0)𝐴,P 𝐴(cid:1) , where 𝐴 = {𝐴 1 ,𝐴 2 ,...,𝐴 𝑆 } 𝐴 represents the set of assets, and P is the matrix measuring similarities of assets in terms of investors. Several distance measures exist to quantify similarities (see, Newman, 2010; Delpinietal.,2013;Baruccaetal.,2021;Brunettietal.,2023). Inthispaper,weusethenotion 7Giventherichnessofourdata,wecouldalsoadopt𝑞 >0toselectthestrongestlinksamongnodes. 9

ofcosinesimilarity(ordistance)tomeasureinterconnectednessbetweenanypairofassets𝑖 and 𝑗 ∈ {1,...,𝑆}: 𝑁 ◦ ◦ (cid:205) 𝐸 𝐸 𝑖,𝑘 𝑗,𝑘 𝑃𝐴 = 𝑘=1 , (5) 𝑖,𝑗 (cid:13) ◦ (cid:13)(cid:13) ◦ (cid:13) 𝐸 𝐸 (cid:13) 𝑖·(cid:13)(cid:13) 𝑗·(cid:13) (cid:13)◦ (cid:13) where(cid:13) 𝐸 𝑖(cid:13)isthenormofthevectorofinvestorsholdingasset𝑖 (see,Getmanskyetal.,2016; Barucca et al., 2021) and 𝑃𝐴 , the cosine similarity, captures the distance between two non- 𝑖,𝑗 zerovectorsofaninner-productspace.8 Finally, for each asset 𝑖, we aggregate its pair-wise interconnectedness with all other assets 𝑗 in𝑆 where 𝑗 ≠ 𝑖 and𝑖, 𝑗 ∈ {1,...,𝑆} to produce an asset-level measure of interconnectednessinthisnetwork: 1 (cid:213) 𝐼𝐶𝐴 = 𝑃𝐴. (6) 𝑖 𝑁(𝑆 −1) 𝑖,𝑗 𝑗∈{1,...,𝑆}:𝑗≠𝑖 Wenormalizeasset-levelinterconnectednessby (𝑆 −1)∗𝑁,where𝑆 isthetotalnumber of assets and 𝑁 is the total number of investors, to account for the fact that the number of financialassetsandinstitutionschangeovertimeinourdata. 8There can be alternative definitions of similarity. One option is to use simple counts of the number of ◦ ◦ portfoliostwoassetsarepartofandhenceusethefollowingdefinitionfor𝑃𝐴 :𝑃𝐴 =𝐸(cid:0)𝐸(cid:1)(cid:62) . Anotheroptionis tocomputethesemeasuresusingtheparamountsheldbyinvestors𝑘 asafractionoftheamountoutstanding ofassets𝑘,therebycapturinganintensivemarginmeasureofinvestorsimilarity. Inthiscase,wedivideeach element 𝐸 𝑖,𝑘 from (3) by 𝐼𝑠𝑠𝑢𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑖, and use this new adjacency matrix directly to compute similaritymeasures𝑃𝐴 .Wetestedtheaforementionedtwoalternativemeasuresandfoundthattheresultswere similar to those using cosine similarity on the extensive margin of investors’ holdings. Yet another measure ofsimilarity(distance)canbederivedfromthenotionofEuclideandistance,namely,𝑃 𝑖 𝐴 ,𝑗 (cid:48) = 1 2 (cid:205) 𝑁 (cid:12) (cid:12) 𝐸 𝑖 ◦ ,𝑘 −𝐸 ◦ 𝑗,𝑘 (cid:12) (cid:12). 𝑘=1 However,wedidnotusethismeasureinouranalysisduetothesparsityofthenetworkinoursample. 10

2.3. An Example: How Shocks Propagate Through an Assets Network Anexamplemayhelptoexplaintheseconcepts. Considerthenetworkbelowconsisting of only three assets and three investors, where the entries in the left matrix represent the dollar amount of each asset held by each investor. This network can be represented by the ◦ adjacencymatrixE𝑒𝑥𝑎𝑚𝑝𝑙𝑒 ontheright: 𝐼 𝐼 𝐼 𝐼 𝐼 𝐼 1 2 3 1 2 3 𝐴 1 6 5 4 ◦ 𝐴 1 1 1 1 E𝑒𝑥𝑎𝑚𝑝𝑙𝑒 = E𝑒𝑥𝑎𝑚𝑝𝑙𝑒 = . 𝐴 0 3 2 𝐴 0 1 1 2 2 𝐴 0 0 1 𝐴 0 0 1 3 3 ◦ Thetop-leftcellofthematrixE𝑒𝑥𝑎𝑚𝑝𝑙𝑒 isequalto1becauseinvestor𝐼 1 hasasset𝐴 1 inher portfolio, while 0 in𝑐𝑒𝑙𝑙(2,1) indicates that investor 𝐼 has not invested in asset 𝐴 . Using 1 2 equation(5),wecanthencomputethecosinesimilaritymetricforanytwopairsofassets: 𝐴 𝐴 𝐴 1 2 3 𝐴 - 0.82 0.58 𝐴 1 P = 𝑒𝑥𝑎𝑚𝑝𝑙𝑒 𝐴 0.82 - 0.71 2 𝐴 0.58 0.71 - 3 Accordingly,followingequation(6),thevectorofinterconnectednessmeasurescorrespond- 𝐴 ingtoP is: 𝑒𝑥𝑎𝑚𝑝𝑙𝑒 (cid:104) (cid:105)(cid:48) 𝐼𝐶𝐴 = 0.230.250.21 𝑒𝑥𝑎𝑚𝑝𝑙𝑒 The magnitudes of asset-level interconnectedness shown in 𝐼𝐶𝐴 indicate that 𝐴 , 𝑒𝑥𝑎𝑚𝑝𝑙𝑒 2 has the highest level of interconnectedness in the network, followed by 𝐴 and 𝐴 , which 1 3 has the lowest interconnectedness. We highlight that that the interconnectedness measure capturesanon-linearaspectofthenetworkbeyondthesimplenumberoffirmsinvestingin 11

eachasset,i.e.,theassets’degreeinthebipartitegraph. Forexample,although𝐴 isheldby 1 allinvestorsand𝐴 isonlyheldbytwoinvestors,𝐴 isthemostcentralnodeinthisnetwork. 2 2 𝐴 ’scentralitygivesrisetoahigherasset-levelinterconnectednessrelativeto𝐴 . 2 1 Whichassetexperiencestheinitialshockplaysafundamentalroleindetermininghowa shockpropagatesthroughthisnetwork. Thatis,differentassetsembeddifferentmagnitudes of shock propagation. If a shock hits 𝐴 , reducing its market value and the performance 2 of portfolios held by both 𝐼 and 𝐼 , re-balancing responses by investors 𝐼 and 𝐼 create a 2 3 2 3 channelthroughwhichtheinitialshockon𝐴 couldpropagateto𝐴 because𝐴 and𝐴 are 2 1 1 2 commonly held by investors 𝐼 and 𝐼 . By contrast, an initial shock on 𝐴 could propagate 2 3 3 tootherassetsthroughthere-balancingbehaviorof𝐼 . Noticethatourmeasureofintercon- 3 nectedness,asshownin𝐼𝐶𝐴 ,convenientlyaggregatesandquantifiesthemagnitudesof 𝑒𝑥𝑎𝑚𝑝𝑙𝑒 shock propagation for each asset; the impacts are largest for𝐴 (0.25), followed by𝐴 (0.23) 2 1 and𝐴 (0.21)inourexample. 3 3. Data Ouranalysisreliesondatafromdifferentsources. Primarily,weusetheThomsonReuters eMAXX database and the Financial Industry Regulatory Authority (FINRA)’s fixed income market Trade Reporting and Compliance Engine (TRACE) database. We supplement these sources with additional data from S&P Global and the Mergent Fixed Income Securities Database(FISD). 3.1. eMAXX WeobtaininformationonU.S.institutionalinvestorsandtheir8-digitCUSIP-levelbond holdings from the Thomson Reuters eMAXX database, which draws from the quarterly N- CSR,N-CSRS,N-Q,andN-PORTfilingswiththeSecurityandExchangeCommission(SEC). The data runs from 1998:Q3 until 2021:Q3, and in each quarter we observe the full fixed- 12

income portfolios of all subaccounts belonging to an institutional investor and detailed informationoftheunderlyingsecuritiesincludingtheirratings,maturities,andcouponrates. We use several approaches to contain the dimensionality of the network computation. First, we aggregate across all sub-accounts of each institutional investor and also collapse the8-digitCUSIP-levelbondholdingsinformationtothe6-digitissuer-level. Inthisway,our datasetissimplifiedandeffectivelycaptureshowmucheachinstitutionalinvestorinvestsin eachissuer(e.g. FordorIBM).9Asidefromholdingsdatawhichissummed,most8-digitbond characteristics, such as coupon rates, are weighted-averaged to the 6-digit level. Second, we restrict the sample of institutional investors to the largest investors with assets under management (AUM) within the top 50th percentile of the AUM distribution each quarter, basedonlyoncorporatebondAUM. 3.2. TRACE Weobtainsecurity-leveldataoncorporatebondtradingvolume,liquidity,andvolatility fromtheintradaytradinginformationavailablefromtheTRACEdatabase. Weaggregatethe intradayTRACEdataatthequarterlyfrequencytomatchthequarterly-leveleMAXXdataset. Because trade frequencies are extremely sparse for some bonds, we check the robustness of our analyses by using alternate methods of quarterly aggregation, including the mean, median,andlastquarterlyobservationofeachvariable. For bond illiquidity, we use two proxies that are widely adopted in the literature: the Amihud measure and the interquartile range (IQR). Amihud (2002) price impact is defined as: 𝐷 𝑖,𝑡 𝑟 1 (cid:213) 𝑖,𝑙,𝑡 𝐴𝑚𝑖ℎ𝑢𝑑 𝑖,𝑡 = (7) 𝐷 𝑄 𝑖,𝑡 𝑖,𝑙,𝑡 𝑙=1 9SeeAppendixAfordetailsonidentifyinguniqueinstitutionalinvestors.UsingthefirstsixdigitsofCUSIP toidentifyissuersfollowsawell-usedpracticeinthecorporatebondliterature. 13

where 𝐷 𝑖,𝑡 is the total number of trades on bond𝑖 at time (day)𝑡, and𝑟 𝑖,𝑙,𝑡 and𝑄 𝑖,𝑙,𝑡 refer to the return and traded volume of the 𝑙th transaction of bond 𝑖 on day 𝑡, respectively. IQR of traded prices is defined and calculated as the difference between the 75th and the 25th percentiles of daily prices. Volatility of bond prices is measured as the quarterly standard deviation of traded prices of a bond and effectively measures realized volatility at quarterly frequency. As with variables from eMAXX, we collapse the 8-digit CUSIP-level information tothe6-digitissuer-levelusingoutstandingissueamountsasweights. 3.3. Other Data Sources Additional information for each bond issuance comes from the Mergent Fixed Income Securities Database (FISD). Data include issuer-specific, issue-specific, and transaction information. In addition to basic bond characteristics such as maturity, issuer identity, etc., the database includes pricing at issue (but no pricing information thereafter), ratings, sinkingfundandcallinformationincludinganestimateoftheamountoutstandingatanygiven time, covenants, defaults, and more. We obtain the total amount outstanding for each asset and take the mean amount outstanding for each quarter for each CUSIP. We then link this informationtotheeMAXXholdingsdataattheCUSIP-quarterlevel. SinceeMAXXdoesnot havecompletecoverageofbondratings,wesupplementthemissingobservationswithdata fromFISDthatcoverratingsfromS&P,Fitch,andMoody’s. WesupplementmissingratingsobservationsinbotheMAXXandFISDwithratingsdata from the S&P Global database. In the end, roughly 3 million rating observations have been filled in accordingly. The ratings from the three ratings agencies have been transformed into a numerical scale between 1 (lowest) and 21 (highest). We take the average of ratings from S&P, Fitch, and Moody’s whenever multiple ratings are available. On the numerical scale, investment-grade bonds are defined as bonds that have ratings equal to or above 12 andhigh-yieldbondsaredefinedasbondsthathaveratingsstrictlybelow12. 14

4. Network of Corporate Bonds and Interconnectedness In this section, we describe the structure of the network in the corporate bond market. Asmentionedabove,wecollapseall8-digitCUSIP-levelbondinformationtothe6-digit issuer-levelinallofourempiricalanalyses(issuershaveanaverageof38individualbonds). Throughouttherestofthepaper,weinterchangeablyusebondwithissuerandinthiscontext, bond,wheneverused,willbereferringtotherepresentativebondoftherespectiveissuer. 4.1. Network of Corporate Bonds Table1showsthesummarystatisticsofcorporatebondcharacteristics. Oursampleconsists of about 200,000 bonds with an average outstanding amount of about $2 billion, an average remaining maturity of 8 years, and an average coupon rate of 6 percent. Following our numerical conversion of ratings, with the scale of 1 to 21 corresponding to the S&P Global rating of D to AAA, the average rating of 12 in our sample corresponds to a rating of BBB-, which is the lowest rating in investment grade. Because many corporate bonds do not trade often, trade volumes and illiquidity measures show high standard deviations. For instance, an average bond has a median trade volume of about $113 million while minimum and maximum trading volumes each reach as small as $0.11 million and as large as $4.7billion. SummarystatisticsonIQRalsohighlightasparsenetworkwherecertainbonds trade more often than others; an average bond has a quarterly median IQR of 0.367 where thesmallestandlargestIQRscanrespectivelyreach0.005and4.124. Bondpricevolatilityis itselfvolatileaswell. Figure2,panel(a),plotstheuniverseoffinancialinstitutionsinvestingincorporatebonds as captured in our network. Following the process mentioned in Section 3, our sample contains 112 banks, 543 investment managers, 473 insurance companies, and 114 other funds— or, altogether, 1,242 unique institutional investor identifiers that uniquely appear across the panelinatleastonequarter. Thissub-sampleofthelargestinstitutionalinvestors(quarterly corporate bond AUM above the 50th percentile) represents the lion’s share of the total par amount outstanding, about 80% of the total par amount of corporate bonds held within the 15

eMAXX universe. Panel (b) of Figure 2 shows the number of unique corporate bonds in the portfolios of banks, insurance companies, investment managers, and other asset managers ascapturedinourdataset. Figure3illustratesthenetworkofcorporatebondsasdefinedbyourmethodology,with eachnodedenotingacorporatebondissuer,andeach(weighted)edgeconnectingtwonodes representing the cosine similarity of the overlapping investors holding corporate bonds of thetwoissuers. Becausewecomputethesenetworksineachyear-quarter,forsimplicity,we report the network based on the most recent holdings data, 2021:Q3. Figure 3a represents the full network, with 1,566 bond issuers and 1,020,826 total edges connecting the nodes.10 Here,theminimumandmaximumcosinesimilarityacrossallpairsofnodesis0.017and1.0, respectively with an average value of 0.331. The network exhibits a dense core, roughly in twotiers,andarelativelysparserperiphery. Figure 3b portrays a sub-network of the largest 20 corporate bond issuers based on the issuedamountoutstandingin2021:Q3. Here,thesizeofthenodesisscaledaccordingtothe total amount of corporate debt outstanding for each issuer. In our data, the corporate bond issuer with the largest amount of corporate debt outstanding is Verizon, with $110 billion. In this sub-network, the minimum and maximum cosine similarity between two corporate bondissuersare0.501(Pemex,aMexicanoilfirm,andGoldmanSachs)and0.895(AT&Tand Verizon), respectively. The average pair-wise cosine similarity in this sub-network of the largest corporate bond issuers is 0.751, more than twice as high as the average in the full network,implyingahighdegreeofinterconnectedness. 4.2. Interconnectedness in the Corporate Bond Market Panel A of Table 2 reports summary statistics for the corporate bond issuer-level (crosssection)interconnectednessandothernetworkmeasures. Becauseourmeasureofinterconnectedness,thecosinesimilarity,capturesanon-linearaspectofinterconnectedness,itssum- (cid:18) 1,566 (cid:19) 10Therearefewerthan edgesinthenetworkgiventhatsomepairsofnodeshavenooverlapping 2 investors. 16

marystatisticsreaddistinctlyfromthoseof,say,degree. Normalizedtobeintheunitinterval [0,1] and by the number of investors and corporate bond issuers in each year-quarter, the averageinterconnectednessacrossbondsofthesameissuers(6-digitCUSIP)inoursampleis 0.034andthestandarddeviationisabouthalfofthat,suggestingsomewhatlessvariancethan linearmeasures. FigureB3intheappendix,showsthesameinformationasacross-sectional distribution,highlightingbi-modalityandsomewhatlightertailsthananormaldistribution. Thedegree,asdefinedinequation(4),relaysthatanaveragebondisintheportfolioof44 investors. Itfeaturessignificantvariability,withhighstandarddeviation,andheterogeneity, lookingatitsminimumandmaximum. Thestrength,asdefinedinequation(2),referstothe totalamountofbondsofaspecificissuer(6-digitCUSIP)heldbythesystemanditsaverage is about $370 million in our sample. There are 7,350 corporate bond issuers that we follow throughtimeandonaverageanissuerisinthesamplefor19quarters,reflectingthesparsity (minimum2quarters,maximum19.25years,or77quarters)ofthenetwork. Looking at sub-samples in Panel B of Table 2, we find the investor similarity network changes over time. Its dynamics suggest that interconnectedness increased after the Great Financial Crisis (GFC).11 This is an interesting result. In physical networks, e.g. interbank market, we usually observe a jump-up in connections leading to the crisis, followed by a rapid decrease as a consequence of the increased uncertainty. Our results indicate that the crisis generated higher bond interconnectedness with more corporate bonds held in portfolios of institutional investors. A plausible explanation for this finding is that, after the GFC,institutionalinvestorstriedtodiversifytheirholdingsandmitigaterisk,followingtraditional finance theory. Various reforms could have also geared institutional investors to hold a similar set of assets that are deemed safer, which might have made corporate bonds moreinterconnectedonaverage. Theeffectofinterconnectednessonmarketqualityandthe volatilityofcorporatebondsisthesubjectofthenextsection. 11ThischangeisnotamechanicalresultduetocorporatefailurestriggeredintheaftermathofGFC.Inthe fewcasesofM&Asorcorporaterestructuresinoursample,6-digitCUSIPsdonotchange. 17

5. Interconnectedness and Market Quality Theadvantageofourmeasuresofinterconnectednessisthattheyarespecifictoagiven asset. Given the wealth of information contained in the eMAXX database about corporate bondholdings,wecancomputeinterconnectednessmeasuresaggregatedattheissuerlevel, and we can use those measures in a panel data setting to analyze the relation between the interconnectednessofabondanditsspread,liquidity,andvolatility. Wecanalsoinvestigate how this relation is affected during periods of stress with a quantile regression approach. Finally, we test the robustness of our findings by further controlling for other statistics that capturedifferentaspectsofthenetwork. 5.1. Mean Effects To understand the relation between interconnectedness and market quality, we start by investigating the contemporaneous correlation among our variables. In particular, we quantify the relation between interconnectedness and the first moments of an asset—such as spread and liquidity—or its second moments—such as volatility—after controlling for the usualcharacteristicsoftheassetincludingrating,couponrate,andoutstandingamount: 𝑆𝑝𝑟𝑒𝑎𝑑 𝑖,𝑡 = 𝛼 +𝛽 1 𝐼𝐶 𝑖,𝑡 +𝜸 (cid:48) X𝑖,𝑡 +𝐹𝐸 𝑖 +𝐹𝐸 𝑡 +𝜖 𝑖,𝑡 (8) 𝐼𝑙𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑖,𝑡 = 𝛼 +𝛽 1 𝐼𝐶 𝑖,𝑡 +𝜸 (cid:48) X𝑖,𝑡 +𝐹𝐸 𝑖 +𝐹𝐸 𝑡 +𝜖 𝑖,𝑡 (9) 𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦 𝑖,𝑡 = 𝛼 +𝛽𝐼𝐶 𝑖,𝑡 +𝜸 (cid:48) X𝑖,𝑡 +𝐹𝐸 𝑖 +𝐹𝐸 𝑡 +𝜖 𝑖,𝑡 (10) InEquation(8),thedependentvariableisthespreadofbond𝑖 attime𝑡,measuredasthe differencebetweentheaverageyieldforalltradesonthebondonagivendayandthecomparableTreasuryorinterpolatedmaturity-matchedswaprateonthesameday,aggregatedat 18

the quarterly level. In Equation (9), the dependent variable is illiquidity, computed as either the Amihud measure or the interquantile range (IQR) of traded prices. Finally, in Equation (10), realized volatility is thedependent variable, computed as the quarterly standarddeviationofthetradedpricesofabond. In all three equations, the main variable of interest is our measure of corporate bond interconnectedness based on investor similarity for each issuer 𝑖’s bond (aggregated at the issuer level) at time𝑡, 𝐼𝐶 𝑖,𝑡, which we measure according to Equation (6). X𝑖,𝑡 is a matrix of time-varying bond characteristics that includes credit rating, coupon rate, time to maturity, outstandingissuancesize,andtradingvolume. 𝐹𝐸 𝑖 referstoissuerfixedeffects. 𝐹𝐸 𝑡 controls fortimefixedeffects(currentyear-quarter). Table 3 presents the results. For ease of interpretation, all variables are standardized to unitsoftheirownstandarddeviation. First,column(1)showstheresultsofestimatingEquation(8). Ourmeasureofinterconnectednessisnegativelyassociatedwiththespread,meaning that an increase in interconnectedness is associated with a decrease in corporate bond spreads. Ifweinterpretspreadsasameasureofriskappetite,anincreaseininterconnectednessincreasestheappetiteforthesebonds. Boththestatisticalandeconomicmagnitudesof thiseffectaresubstantial. Thecoefficientissignificantatthe1%levelandaone-standarddeviationincreaseininterconnectednesslowersthespreadby44.9basispoints,corresponding to about one-sixth of a standard deviation, controlling for everything else. This magnitude is substantially larger than the effect of a one standard deviation change in most control variables including coupon rate, time to maturity, outstanding issuance amount, and trade volume, and is only smaller than that of credit ratings. This is consistent with the wellknown fact that a bond’s credit rating is the predominant factor in determining corporate bondinvestmentdemand. Columns (2) and (3) show the results of estimating Equation (9) using the two different measuresofilliquidity. Thecoefficientsforinterconnectednessaresignificantatthe1%level andcarrynegativesigns,meaningthatanincreaseininterconnectednessisassociatedwith a decrease (increase) in corporate bond illiquidity (liquidity). Specifically, a one-standard 19

deviationincreaseininterconnectednessisassociatedwitha0.15standarddeviationdecrease inAmihudilliquidityanda0.11standarddeviationdecreaseintheIQRmeasure. Finally,column(4)showstheresultsofestimationEquation(10). Interconnectednesshas anegativecoefficientoncorporatebondvolatility,implyingthathigherinterconnectedness is associated with lower volatility. A one standard deviation increase in interconnectedness isassociatedwitha0.07standarddeviationdecreaseinrealizedvolatility. Theeffectis,again, statisticallysignificantatthe1%level. Itisalsonoteworthythatallofourestimatedcoefficientsforinterconnectednessremain significantevenaftercontrollingforthe“size”ofthebond,measuredbyoutstandingissuance amountandtradevolume. Itimpliesthatthisnonlinearmeasureofcorporatebondcentrality doesnotsimplycapturethelinearsizeaspectsofthecorporatebondnetwork(e.g.,numberof investors)andthatassetswhicharecommontomanyportfoliosaremoreliquid,lessvolatile, andhavelowerspreads. More specifically, the role of interconnectedness seems to be more important for highyield bonds, as opposed to investment-grade bonds. Table 4 shows the results of running the same estimation equations as before on sub-samples of investment grade (in Panel A) and high-yield bonds (in Panel B), respectively. In column (1), the magnitude of the slope coefficientoninterconnectednessissmallerforinvestment-gradebonds(-0.158)comparedto high-yieldbonds(-0.545). Botharestatisticallysignificantatthe1-percentlevel. Incontrast, the association of interconnectedness with illiquidity seems to be stronger for investmentgrade bonds, as shown in column (2). Interconnectedness, again, has a stronger negative coefficient for volatility for high-yield bonds, as shown in column (4). We examine the full distributionalquantileeffectsofinterconnectednessinthenextsection. 5.2. Quantile Regression Analysis Measuresofconditionalcentraltendencydonotalwaysadequatelycharacterizethestatisticalrelationsamongvariables. Infact,wethinkitisparticularlyinterestingtoestimatethe conditionalquantilesofspread,illiquidity,andvolatilityasafunctionofinterconnectedness 20

andavectorofcovariates. Inotherwords,whenwethinkaboutfinancialstabilityconsiderations,weareactuallyinterestedinthetailsofthedistributions. Inparticular,wecareabout the right tail, corresponding to stressful market situations when spreads and volatility are highandilliquidityishigh. Figure 4 illustrates the results of quantile regressions between interconnectedness and ourbondmarketqualitymeasures: spread,illiquidity,andrealizedvolatility. Whiletheoverallnegativelinkagesbetweeninterconnectednessandspread,illiquidity,andvolatilityisstill evident,theresultsfromthisanalysisshowtheestimatedcoefficientsaremuchlargerinthe righttail,whencorporatebondmarketsareunderstress. Forexample,lookingatspreadsin Figure 4a, a one standard deviation increase in interconnectedness has very small associationswithspreadbelowthemedian. Onlyabovethemediandoesinterconnectednessbegin to bear a negative association in large magnitudes, leading up to around 150 basis points in spreadreductionfromonestandarddeviationincreaseininterconnectedness. Resultsbased on illiquidity and realized volatility in Figure 4b and Figure 4c are similar. A one standard deviation increase in interconnectedness is associated with larger reductions in IQR as the quantileincreases,reachinguptonearlyonestandarddeviationreductioninIQRandabout halfofastandarddeviationinrealizedvolatility,inthehighestquantile. Overall, the quantile results show that when volatility and spreads are high, and liquidity is scarce, an increase in interconnectedness is associated with a larger improvement in marketconditions. Attheoppositeendofthespectrum,whenvolatilityandspreadsarelow, andliquidityisabundant,thelinkbetweeninterconnectednessandmarketconditionsisless important(estimatedparametersareclosetozero). 5.3. Robustness Any measure of interconnectedness could be, to some extent, endogenously correlated with conventional asset characteristics or other measures that capture different aspects of the network. For this reason, we check the robustness of our results in two ways: 1) exam- 21

ining the descriptive statistics of our control variables by interconnectedness decile and 2) controllingforadditionalnetworkstatisticsthatcaptureothercharacteristicsofthenetwork. We use five control variables in our regressions: credit rating, coupon rate, time to maturity, outstanding issuance size, and trading volume. Table 5 shows the summary statistics ofthesevariablesgroupedbydecilesofbondinterconnectedness. Importantly,creditrating, whichisthemostpredominantdeterminantofbondinvestment,doesnotvarysignificantly acrossbondswithdifferentlevelsofinterconnectedness. Sucharesultsuggeststhatourmeasure of interconnectedness, cosine similarity, is not picking up a correlated variation purely arisingfromdifferencesincreditratingcharacteristicsofthebondsinoursample. Timetomaturityalsodoesnotexhibitaclearcorrelationpatternwithinterconnectedness deciles, although extremely high levels of interconnnectedness seem to be associated with a lower time to maturity, highlighting investors’ preferences for shorter maturity bonds. Outstandingissuanceamountsandtradingvolumesinlowerinterconnectednessdecilesare alsolow,whichissimplybyconstruction: corporatebondswithlargeissuanceamountsand large trading volumes naturally imply that these bonds are likely to be in the portfolio of manyinvestors. Theonlyvariablethatseemstobemeaningfullyassociatedacrossdifferent deciles of interconnectedness is coupon rate. Higher coupon rates are observed in lower deciles of interconnectedness and the rates decline with interconnectedness deciles. This implies some comovement between coupon rates and interconnetedness such that bonds withhigherratesarenotcommonlyheldbymanyfinancialinvestors. Ifhighercouponrates are associated with a higher perceived risk by market participants, our results indicate that investorsprefertoinvestinlessriskyassets. Table 6 estimates Equations (8)-(10), additionally controlling for two new variables, investorconcentration,asmeasuredbytheHerfindahl-HirschmanIndex(HHI),anddegree,as defined in equation (4). There has been an emerging literature in asset pricing on how institutional investors can affect prices and qualities of various financial assets including corporate bonds (Bretscher et al., 2022; Coppola, 2021; Haddad and Muir, 2021, among others). Forinstance,LiandYu(2022)findanegativeassociationbetweeninvestorconcentrationand transactionturnoverandliquidity,andapositiveassociationbetweeninvestorconcentration 22

and spread. We measure investor concentration with the HHI and show results in Panel A ofTable6. WhiletheHHIissignificantacrossspecifications,coefficientsforinterconnectednessinallfourcolumnsremainstatisticallysignificantatthe1%levelandalsoeconomically significant,thoughthemagnitudesareslightlysmallerthaninTable3. On the other hand, controlling for degree, which counts the number of unique financial institutions that hold each corporate bond, can allow us to examine whether our measure of interconnectedness is simply picking up the number of investors holding that corporate bond. Panel B in Table 6 shows the results of the regressions controlling for degree. All of the interconnectedness coefficients in the regressions for spread, illiquidity, and volatility remain negative and significant at the 1% level, with very small variation in the size of the coefficients compared to Table 3. Finally, Panel C controls for both HHI and degree and showssimilarresultstothosefromPanelsAandB. Therobustnessanalysesaboveofferuspreliminaryevidenceofuniquevariationsthatour measureofinterconnectednesscarriesaboveandbeyondwhatconventionalbondcharacteristicsandalternativestatisticsofnetworkscanoffer. Giventheeffectivenessofthismeasure, we now turn to investigating the mechanism linking interconnectedness with market characteristics. 6. Interconnectedness and Risk Sharing Doesinterconnectednessallowrisksharingandhencehelpmitigatetheeffectsofanegative shock to the financial system? Or does interconnectedness exacerbate the effects of a shock through contagion? This is a fundamental question in the network literature. The modelinAllenandGale(2000)suggeststhatacompletenetwork(whereeverynodeislinked toanother)isbeneficialinmitigatingtheeffectsofashockwhileAcemogluetal.(2015)show thattheoveralleffectdependsonthesizeoftheshock. WhileourempiricalanalysesinSection5providesevidenceofanetpositivelinkbetween interconnectedness and market quality, there may be times when risk sharing can play an 23

evenmoresignificantroleinimprovingmarketfunctioning. Inthissection,weproposetwo identification strategies to study the causal effect of interconnectedness on the corporate bondmarket. WelookattheCOVID-19outbreakandfallenangels. Throughthesetwospecificevents,weisolateshocksthataffectonlyasubsetofbondsinoursampleandanalyzethe impactofinterconnectednessacrossgroupsthatweredifferentiallyaffectedbytheshocks. 6.1. Evidence from COVID-19 Outbreak The outbreak of COVID-19 in March 2020 introduced a purely exogenous bifurcation of firms by adversely affecting those belonging to a certain set of industries, such as transportationandretail,andnotaffectingthosebelongingtootherindustries,suchashousehold goodsandutility. LetuscallthebondsissuedbyfirmsinCOVID-affectedindustries“COVIDexposed bonds" and those issued by firms in industries not affected “COVID-unexposed bonds."Thisbifurcationprovidesuswithanideallaboratorytoexaminewhethertheimpact of the initial shock on COVID-exposed bonds was mitigated by their interconnectedness to unexposedbonds,thatiswhetherinterconnectednessallowsrisksharingandthereforehelps absorbtheeffectofashockasimpliedbyAllenandGale(2000). We obtain data on each issuer’s exposure to COVID-19 using textual analysis of quarterly earnings call transcripts (Hassan et al., 2023). The exposure to COVID-19 is measured by counting the number of times the word “COVID” appears around a negative or positive sentiment word, normalized by the total number of words in the transcript (Loughran and McDonald,2011). Wefirstrankeachfirmbyitsnetsentimentscorein2020. Firmswithahigh scorearethefirmsmostexposedtotheCOVID-19shock. Hence,wedefineCOVID-exposed bonds as bonds issued by firms with sentiment score belonging to the top 25 percent of the distributionandCOVID-unexposedbondsasbondsissuedbyfirmswithsentimentscoresin themiddle25percent(betweenthe37.5and62.5percentiles).12 12Weusethemiddle25percentasourcontrolgroupinsteadofthebottomofthenetsentimentdistributionto avoidcapturinganyotherportfoliore-balancingeffectsduetobondsthatactuallybenefitedfromtheCOVID-19 outbreak,suchashealthcare. 24

Then, for the group of COVID-exposed bonds, we estimate the following equations for 𝑡 =2020:Q1and𝑡 −1 =2019:Q4: 𝑆𝑝𝑟𝑒𝑎𝑑 𝑖 𝑒 , 𝑥 𝑡 𝑝𝑜𝑠𝑒𝑑 = 𝛼 +𝛽 1 𝐼𝐶 𝑖 𝑢 ,𝑡 𝑛 − 𝑒𝑥 1 𝑝𝑜𝑠𝑒𝑑 +𝜸 (cid:48) X𝑖,𝑡 +𝐹𝐸 𝑖 +𝐹𝐸 𝑡 +𝜖 𝑖,𝑡 (11) 𝐼𝑙𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑖 𝑒 , 𝑥 𝑡 𝑝𝑜𝑠𝑒𝑑 = 𝛼 +𝛽 1 𝐼𝐶 𝑖 𝑢 ,𝑡 𝑛 − 𝑒𝑥 1 𝑝𝑜𝑠𝑒𝑑 +𝜸 (cid:48) X𝑖,𝑡 +𝐹𝐸 𝑖 +𝐹𝐸 𝑡 +𝜖 𝑖<𝑡 (12) 𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦 𝑖 𝑒 , 𝑥 𝑡 𝑝𝑜𝑠𝑒𝑑 = 𝛼 +𝛽𝐼𝐶 𝑖 𝑢 ,𝑡 𝑛 − 𝑒𝑥 1 𝑝𝑜𝑠𝑒𝑑 +𝜸 (cid:48) X𝑖,𝑡 +𝐹𝐸 𝑖 +𝐹𝐸 𝑡 +𝜖 𝑖,𝑡 , (13) 𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝑒𝑥𝑝𝑜𝑠𝑒𝑑 where 𝑆𝑝𝑟𝑒𝑎𝑑 , 𝐼𝑙𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 , and𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦 refer to spreads, illiquidity and 𝑖,𝑡 𝑖,𝑡 𝑖,𝑡 𝑢𝑛𝑒𝑥𝑝𝑜𝑠𝑒𝑑 volatilityofexposedbondsattime𝑡,while𝐼𝐶 indicatesthecosinesimilarityintercon- 𝑖,𝑡−1 nectednessmeasurebetweenexposedandunexposedbondsattime𝑡 −1. Theseregressions exploretherelationbetweentheinterconnectednessofCOVID-exposedbondstothebonds that would be eventually unexposed immediately before the COVID outbreak and the performanceofthesebondsinthequarterthatCOVIDbecamesalient. Importantly,computing interconnectedness at time 𝑡 − 1, before the shock which, by definition, is unpredictable, allowsustoaddressallpossibleendogeneityissues. Table 7 Panel A shows the results. Interconnectedness of COVID-exposed bonds to unexposed bonds matters for spread and the Amihud measure of illiquidity. A one standard deviationincreaseininterconnectednessofexposedbondstounexposedbondsisassociated with a 75.4 basis points decline in spread and a 0.4 standard deviation decline in Amihud illiquidity. Both effects are statistically significant at the 1% level. These magnitudes are substantially higher—2/3 larger for spread and more than two times as large for Amihud illiquidity—thanthosefromthemeaneffectsforthewholepanelinTable3. Thecoefficients of interconnectedness in the IQR and realized volatility regressions are not statistically significant. Overall, the results show that, for COVID-exposed bonds, being interconnected to unexposedbondsenabledrisksharingandhencewasbeneficial. 25

We can also investigate the opposite case to see how the unexposed bonds fared due to their interconnectedness to exposed bonds. To do so we run the same regressions as above butonthesampleofunexposedbonds: 𝑢𝑛𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝑆𝑝𝑟𝑒𝑎𝑑 𝑖,𝑡 = 𝛼 +𝛽 1 𝐼𝐶 𝑖,𝑡−1 +𝛾𝑋 𝑖,𝑡 +𝐹𝐸 𝑖 +𝐹𝐸 𝑡 +𝜖 𝑖,𝑡 (14) 𝑢𝑛𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝐼𝑙𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝑖,𝑡 = 𝛼 +𝛽 1 𝐼𝐶 𝑖,𝑡−1 +𝛾𝑋 𝑖,𝑡 +𝐹𝐸 𝑖 +𝐹𝐸 𝑡 +𝜖 𝑖,𝑡 (15) 𝑢𝑛𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝑒𝑥𝑝𝑜𝑠𝑒𝑑 𝑉𝑜𝑙𝑎𝑡𝑖𝑙𝑖𝑡𝑦 𝑖,𝑡 = 𝛼 +𝛽𝐼𝐶 𝑖,𝑡−1 +𝛾𝑋 𝑖,𝑡 +𝐹𝐸 𝑖 +𝐹𝐸 𝑡 +𝜖 𝑖,𝑡 (16) Table 7 Panel B shows the results. Contrary to the previous findings from COVIDexposed bonds, interconnectedness is not statistically significant for spread and both measures of illiquidity. However, interconnectedness of unexposed bonds to COVID-exposed bonds matters for the realized volatility of exposed bonds, as can be seen in column (4). Specifically, as the interconnectedness of unexposed bonds to COVID-exposed bonds increased by one standard deviation, the realized volatility of unexposed bonds increased by about a quarter of standard deviation. This effect is statistically significant at the 1% level. Overall, the results are also consistent with the risk sharing argument: bonds of firms not affected by COVID take up some of the risk of COVID-exposed bonds. InterconnectednessallowsrisksharingwithoutmaterialconsequencesonspreadsandliquidityofCOVIDunexposedbonds. 6.2. Evidence from Fallen Angels Creditratingsplayanintegralpartincorporatebondinvestment,andratingdowngrades are major events that affect the demand and market characteristics of the bond, such as liquidity. Downgrades are especially more significant events when the corporate bond is downgraded from the lowest credit rating in investment grade (BBB-) to high yield. These 26

bonds are called “fallen angels.” The change from investment grade to high yield involves an entire identity change in the bond’s membership, and many institutional investors such as insurers have investment mandates on how much exposure they can carry with regard to high-yield investment. Spreads widen, liquidity drops, and volatility increases for most fallenangels. Weareinterestedinstudyinginterconnectednessandmarketcharacteristicswhensome bonds become fallen angels. From our data, we sample corporate bonds with an average creditratingbetweenBBB-(thelowestinvestmentgrade)andBBB.Withinthissub-sample, weconsiderwhichbondisdowngradedinthenextperiod. Again,thebifurcationofwhether abondbecomesafallenangelornotisplausiblyexogenouswithinthisnarrowwindow. The idea isthat, byconsidering onlytwo time periods,𝑡 −1, beforethe downgrade,and𝑡, when thedowngradeoccurs,insulateouranalysisfromendogeneityconcerns. We measure interconnectedness of 580 fallen angels in our sample with respect to the bondsthatdidnotgetdowngradedandestimatethesamethreeEquations(11)-(13)totestif interconnectednesscontinuestoplayanimportantroleinthebond’smarketspreads,liquidity,andvolatility. Table8showstheresults. Interconnectednesscontinuestoreducespreads andimproveliquidityforthissub-sampleoffallenangels. Ourresultsshowthataonestandard deviation increase in interconnectedness of a fallen angel is associated with a 62 basis points decrease in its spread and about one third of a standard deviation of illiquidity measures; the effects are statistically significant at the 1% level. The economic magnitudes are, as with the case with COVID-related results from the Section 6.1, substantially higher than thosefromthemeaneffectsforthewholepanelinTable3,implyingaparticularlylargerole ofinterconnectednessinmarketqualityoffallenangels.13 Thefindingsevenaroundthesemajorcorporateeventssuggestthatinterconnectedness hasanexplanatorypowerovermarketcharacteristicsofcorporatebondsaboveandbeyond what can be conventionally measured through a standard set of market-based data such as creditrating,couponrate,andtimetomaturity. 13Resultsforthesub-sampleofcorporatebondsthatwerenotdowngradedarereportedinTableB1. 27

7. Conclusion In this paper, we develop an alternative and complementary network structure derived at the asset level and based on the idea that assets are interconnected if they are held by the same investors. We focus on the corporate bond market to investigate the link between interconnectedness and spread, liquidity, and volatility of corporate bonds. We find that the higher the interconnectedness—meaning that the asset is common to many investors’ portfolios—the lower its spread and the higher its liquidity. This result highlights that, as expected, corporate bonds that are held across several portfolios are those that require a lower compensation for risk and that are more liquid. This relation is, however, affected by market conditions. We explore the heterogeneous links of interconnectedness throughout the conditional distribution of the response variables (spreads, liquidity, and volatility), whilecontrollingforindividualandtime-specificbondcharacteristics,throughapaneldata quantile regression. We find that the relation we have just highlighted is stronger when a financialassetisunderstress,i.e.,whenthespreadandilliquidityofanassetareintheupper tailsoftheirconditionaldistributions. Importantly,interconnectednessmitigatestheeffects of negative shocks in the financial system through risk sharing. The COVID-19 and “fallen angels”analysesallowustoclaimacausaleffectinthesensethathigherinterconnectedness improvesmarketfunctioning. Our results shed light on the role of interconnectedness in financial markets. They provide an important contribution to the debate on whether a more connected network is beneficialtomarkets. Ourcontributionsarerelevanttoacademiaaswellastopolicymakers. In timesofdistress, anypolicyinterventionfacilitatingthe creationofedges—i.e. allowingthe network to be more dense—would improve market conditions. In fact, any policy intervention in crisis periods tends to restore confidence and, hence, facilitate market functioning, makingmarketsandinstitutionsmoreinterconnected. 28

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Tables and Figures Table1 BasicStatisticsonBondCharacteristicsintheNetwork Thistablepresentssummarystatisticsofbond-levelcharacteristicsinournetwork,aggregatedateachissuer level.SpreadiscalculatedasyieldminustheTreasuryrateofcomparablematurity.Ratingiscalculatedasthe averageratingofthreeratingagencies,S&P,Fitch,andMoody’s,wherethecategoricalratingsaretransformed intoanumericalscalebetween1(lowestrating)and21(highestrating).Volatilityiscalculatedasthestandard deviation of daily traded price during each quarter. We use two measures of bond illiquidity, the Amihud (2002)priceimpactmeasure(per$mil)andtheinterquartilerange("IQR")ofdailytradedprices. Allvariables arewinsorizedatthetopandbottom1percentiles.Source:eMAXX,FISD,S&PGlobal,andTRACE. Variable Obs Mean Std.Dev. Min Max Outstandingissueamount($bil) 192,399 1.961 3.669 0.035 23.72 Remainingmaturity(quarter) 191,016 33.24 24.08 3 119 Couponrate 189,699 6.188 2.101 1.516 11.601 Spread(quarterlymean) 192,399 3.150 3.278 -0.857 19.28 Spread(quarterlymedian) 192,399 3.116 3.251 -0.882 19.06 Spread(lastquarterlyobservation) 192,399 3.107 3.367 -1.200 19.86 Rating 185,036 12.02 3.987 4 21 Tradevolume(quarterlymean;$mil) 192,399 307.85 462.29 0.20 11,980 Tradevolume(quarterlymedian;$mil) 192,399 112.69 183.47 0.11 4,715 Tradevolume(lastquarterlyobservation;$mil) 192,399 248.91 1049.00 0.00 239,900 PriceVolatility 192,399 1.641 1.460 0.022 11.14 Illiquidity:Amihud(quarterlymean) 192,399 0.003 0.009 0 0.230 Illiquidity:Amihud(quarterlymedian) 192,399 0.001 0.002 0 0.035 Illiquidity:Amihud(lastquarterlyobservation) 144,758 0.002 0.005 0 0.032 Illiquidity:IQR(quarterlymean) 192,399 0.526 0.497 0.006 5.032 Illiquidity:IQR(quarterlymedian) 192,399 0.367 0.410 0.005 4.124 Illiquidity:IQR(lastquarterlyobservation) 142,341 0.626 0.756 0.012 4.348 32

Table2 CorporateBondInterconnectednessandOtherNetworkMeasures This table presents summary statistics for the interconnectedness and other network measures of corporate bonds used in this paper. Panel A reports the summary statistics for the cross-section of corporate bonds (aggregated at the issuer level). Specifically, for each bond, we take the arithmetic average of the variables acrossthetimeperiodinwhichthatbondappearsinthesample. TheNumberofQuartersvariablecaptures how many quarters a particular bond is in the sample. Panel B reports the summary statistics broken down intoseveraltimeperiodsduringoursampleperiod.Strengthisdefinedasinequation(2)andreferstothetotal amountofthecorporatebondofaspecificissuerheldbythesystem. Degreeisdefinedasinequation(4)and referstothetotalnumberofinvestorsinvestinginaspecificcorporatebond.Cosinesimilarityisdefinedasin Equation(6)andisinbasispoints.Source:eMAXXandauthors’calculations. PanelA:Cross-sectionofCorporateBonds Variables N Mean Median Std.Dev. Minimum Maximum Skew. Kurt. CosineSimilarity 7,350 0.034 0.033 0.015 0.0019 0.067 -01.30 208.2 Degree 7,350 44.37 32.78 40.46 1 294 2.04 8.71 Strength($mil) 7,350 369,524 178,285 625,914 512 6,458,448 4.51 29.35 NumberofQuarters 7,350 18.98 11 18.89 2 77 1.43 4.22 PanelB:Bond-QuarterPanel Variables N Mean Median Std.Dev. Minimum Maximum Skew. Kurt. 2002:Q3–2021:Q3 CosineSimilarity 192,242 0.0406 0.0413 0.0159 0 0.0794 -21.3 220.3 Degree 192,242 69.91 49 63.69 1 510 1.848 7.330 Strength($mil) 192,242 1.983e+06 377,254 7.005e+06 1 2.401e+08 12.26 234.1 2002:Q3–2008:Q4 CosineSimilarity 51,907 0.0278 0.0281 0.0104 0 0.0794 -18.6 253.6 Degree 51,907 53.32 35 55.01 1 510 2.562 12.11 Strength($mil) 51,907 476,083 196,299 868,356 1 3.510e+07 6.251 90.93 2009:Q1–2021:Q3 CosineSimilarity 140,335 0.0454 0.0479 0.0149 0.00000601 0.0776 -61.8 275.6 Degree 140,335 76.05 56 65.56 1 496 1.683 6.506 Strength($mil) 140,335 2.540e+06 516,578 8.111e+06 2 2.401e+08 10.61 175.4 33

Table3 AnalysisofCorporateBondInterconnectednessversusSpread,Liquidity,and Volatility Thistablepresentsresultsfromtheanalysisofinterconnectednessandspread,illiquidity,andrealizedvolatility usingEquations(8),(9),and(10),aggregatedattheissuerlevel.Incolumn(1),thedependentvariableisspread ofacorporatebondissuer𝑖’saveragebondattime𝑡,measuredastheyieldforalltradesforeachofissuer𝑖’s bondovercomparableTreasuryorinterpolatedmaturity-matchedswaprateonthesameday,andaggregated at the quarterly-level (median). In columns (2) and (3), the dependent variables are illiquidity of bond 𝑖 at time𝑡, measured following Amihud (2002) and interquartile range (IQR) of trade prices (quarterly medians), respectively. Incolumn(4),thedependentvariableisvolatilityofbond𝑖 attime(quarter)𝑡,measuredasthe standarddeviationoftradepricesofbond𝑖 duringeachquarter. Inallcolumns,themainvariableofinterest is“interconnectedness,"whichwemeasurebycosinesimilaritybasedonEquation(5). Creditratinghasbeen convertedfromtheaverageofthethreeratingagencies,S&P,Fitch,andMoody’stoanumericalscalebetween 1(lowest)and21(highest). Timetomaturityisinquarters. Outstandingissuanceamountandtradevolume (quarterlymedian)areinlog($thous). Foreaseofreading,mostvariableshavebeentransformedintounitsof standarddeviation.Source:eMAXX,FISD,S&PGlobal,TRACE,andauthors’calculation. (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized illiquidity) tradedprices) volatility) Std(Interconnectedness) -0.449*** -0.152*** -0.114*** -0.066*** (0.062) (0.018) (0.015) (0.016) Std(Rating) -2.431*** -0.205*** -0.317*** -0.373*** (0.143) (0.021) (0.022) (0.031) Std(Couponrate) 0.376*** -0.132*** -0.107*** -0.078*** (0.054) (0.016) (0.013) (0.015) Std(Timetomaturity) -0.021** 0.016*** 0.019** 0.018*** (0.010) (0.005) (0.008) (0.005) Std(Outstandingissueamount) 0.295*** 0.325*** 0.222*** 0.020 (0.056) (0.023) (0.019) (0.013) Std(Tradevolume) -0.264*** -0.464*** -0.281*** (0.025) (0.019) (0.016) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 182,607 182,607 182,607 182,607 R-squared 0.702 0.468 0.439 0.464 34

Table4 InterconnectednessofInvestmentGradeandHighYieldBonds Thistablepresentsresultsfromtheanalysisofinterconnectednessandspread,illiqudity,andrealizedvolatility using Equations (8), (9), and (10), aggregated at the issuer level, for the sub-sample of investment grade andhighyieldbondsinPanelsAandB,respectively. Incolumn(1),thedependentvariableisspreadofcorporatebondissuer𝑖’saveragebondattime𝑡, measuredastheyieldforalltradesforeachofissuer𝑖’sbond overcomparableTreasuryorinterpolatedmaturity-matchedswaprateonthesameday,andaggregatedatthe quarterly-level(median). Incolumns(2)and(3), thedependentvariablesaretheilliquidityofbond𝑖 attime 𝑡, measured following Amihud (2002) and the interquartile range (IQR) of traded prices (quarterly medians), respectively.Incolumn(4),thedependentvariableisthevolatilityofbond𝑖attime(quarter)𝑡,measuredasthe standarddeviationoftradedpricesofbond𝑖 duringeachquarter. Inallcolumns,themainvariableofinterest is“interconnectedness,"whichwemeasurebycosinesimilaritybasedonEquation(5). Creditratinghasbeen convertedfromtheaverageofthethreeratingagencies,S&P,Fitch,andMoody’stoanumericalscalebetween 1(lowest)and21(highest). Timetomaturityisinquarters. Outstandingissuanceamountandtradevolume (quarterlymedian)areinlog($thous). Foreaseofreading,mostvariableshavebeentransformedintounitsof standarddeviation.Source:eMAXX,FISD,S&PGlobal,TRACE,andauthors’calculation. (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized illiquidity) tradedprices) volatility) PanelA:Investment-gradebonds Std(Interconnectedness) -0.158*** -0.209*** -0.126*** -0.00762 (0.0270) (0.0251) (0.0194) (0.0149) Std(Rating) -0.839*** -0.113*** -0.149*** -0.124*** (0.0695) (0.0352) (0.0288) (0.0292) Std(Couponrate) 0.176*** -0.111*** -0.0418*** 0.0578*** (0.0248) (0.0253) (0.0152) (0.0130) Std(Timetomaturity) 0.114*** 0.165*** 0.223*** 0.259*** (0.0172) (0.0132) (0.0119) (0.0119) Std(Outstandingissueamount) 0.0567** 0.340*** 0.198*** -0.0462*** (0.0227) (0.0234) (0.0190) (0.0103) Std(Tradevolume) -0.119*** -0.432*** -0.263*** (0.0112) (0.0202) (0.0161) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 109,332 109,332 109,332 109,332 R-squared 0.669 0.480 0.468 0.547 PanelB:High-yieldbonds Std(Interconnectedness) -0.545*** -0.136*** -0.126*** -0.113*** (0.0759) (0.0208) (0.0200) (0.0222) Std(Rating) -3.400*** -0.336*** -0.489*** -0.642*** (0.157) (0.0342) (0.0338) (0.0465) Std(Couponrate) 0.546*** -0.126*** -0.141*** -0.148*** (0.0724) (0.0175) (0.0181) (0.0209) Std(Timetomaturity) -0.335*** 0.0955*** 0.155*** 0.192*** (0.0959) (0.0261) (0.0230) (0.0206) Std(Outstandingissueamount) 0.676*** 0.412*** 0.348*** 0.136*** (0.0739) (0.0326) (0.0287) (0.0203) Std(Tradevolume) -0.451*** -0.556*** -0.356*** (0.0370) (0.0240) (0.0236) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 73,243 73,243 73,243 73,243 R-squared 0.713 0.520 0.470 0.481 35

Table5 CorporateBondCharacteristicsbyInterconnectednessDecile Thistablepresentssummarystatisticsforcorporatebondcharacteristicsforeachdecileofinterconnectedness, as measured by the cosine similarity. These characteristics are averaged across the full sample time period, from2002:Q3to2021:Q3.Creditratinghasbeenconvertedfromtheaverageofthethreeratingagencies,S&P, Fitch,andMoody’stoanumericalscalebetween1(lowest)and21(highest). Timetomaturityisinquarters. Outstandingissuanceamountandtradevolume(quarterlymedian)arein$billion.Source:eMAXX,FISD,S&P Global,TRACE,andauthors’calculation. Decile Rating Couponrate Timetomaturity Outstandingissueamount($bil) Tradevolume($bil) 1 10.92 7.24 109.54 0.27 81.53 2 10.41 7.45 149.16 0.31 95.76 3 10.74 7.22 82.83 0.45 105.99 4 10.97 6.81 188.91 0.51 109.07 5 10.75 6.75 124.82 0.65 106.14 6 11.13 6.36 91.24 0.80 104.63 7 11.39 6.02 173.37 1.16 105.69 8 11.93 5.70 106.88 2.21 109.49 9 11.96 5.41 41.75 3.26 136.11 10 11.41 4.93 41.85 3.97 162.64 36

Table6 RobustnessUsingOtherNetworkMeasures This table presents results from running the same analysis of interconnectedness and spread, liquidity, and volatilityusingEquations(8),(9),and(10)andnowcontrollingfortwoadditionalvariables,investorconcentrationasmeasuredbyHerfindahl-HirschmanIndex(HHI)inPanelAanddegreeinPanelB.PanelCcontrols forbothHHIanddegree.Incolumn(1),thedependentvariableisspreadofacorporatebondissuer𝑖’saverage bond at time𝑡, measured as the yield for all trades for each of issuer𝑖’s bond over comparable Treasury or interpolatedmaturity-matchedswaprateonthesameday,andaggregatedatthequarterly-level(median). In columns (2) and (3), the dependent variables are illiquidity of bond𝑖 at time𝑡, measured following Amihud (2002) and interquartile range (IQR) of trade prices (quarterly medians), respectively. In column (4), the dependentvariableisvolatilityofbond𝑖 attime(quarter)𝑡,measuredasthestandarddeviationoftradeprices ofbond𝑖 duringeachquarter. Inallcolumns,themainvariableofinterestis“interconnectedness,"whichwe measurebycosinesimilaritybasedonEquation(5). Creditratinghasbeenconvertedfromtheaverageofthe threeratingagencies,S&P,Fitch,andMoody’stoanumericalscalebetween1(lowest)and21(highest).Timeto maturityisinquarters.Outstandingissuanceamountandtradevolume(quarterlymedian)areinlog($thous). Foreaseofreading,mostvariableshavebeentransformedintounitsofstandarddeviation. Resultsforrating, couponrate,timetomaturity,outstandingissueamount,andtradevolumeareshowninAppendixB.Source: eMAXX,FISD,S&PGlobal,TRACE,andauthors’calculation. PanelA:HHI (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized illiquidity) tradedprices) volatility) Std(Interconnectedness) -0.336*** -0.126*** -0.092*** -0.052*** (0.060) (0.018) (0.016) (0.017) Std(HHI) 0.150*** 0.034*** 0.029*** 0.018** (0.028) (0.011) (0.009) (0.007) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 182,607 182,607 182,607 182,607 R-squared 0.702 0.468 0.439 0.464 PanelB:Degree (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized illiquidity) tradedprices) volatility) Std(Interconnectedness) -0.449*** -0.186*** -0.130*** -0.0541*** (0.062) (0.019) (0.016) (0.016) Std(Degree) 0.002 0.129*** 0.062*** -0.044*** (0.042) (0.018) (0.016) (0.014) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 182,607 182,607 182,607 182,607 R-squared 0.702 0.470 0.440 0.464 37

Table6 RobustnessUsingOtherNetworkMeasuresCont’d PanelC:HHIandDegree (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized illiquidity) tradedprices) volatility) Std(Interconnectedness) -0.326*** -0.165*** -0.110*** -0.037** (0.062) (0.019) (0.017) (0.017) Std(HHI) 0.152*** 0.026** 0.025*** 0.022*** (0.028) (0.010) (0.009) (0.008) Std(Degree) -0.030 0.123*** 0.056*** -0.049*** (0.043) (0.018) (0.016) (0.014) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 182,607 182,607 182,607 182,607 R-squared 0.702 0.470 0.440 0.464 38

Table7 InterconnectednessofCOVID-exposedand-unexposedBonds Thistablepresentsresultsfromtheanalysisoneffectsofinterconnectednessforthesub-sampleofbondsthat wereseverelystressed(“exposed”)andnotstressed(“unexposed”)byCOVID-19outbreakrespectivelyinPanels AandB,usingEquations(11)–(16). Thedependentvariablesarespreadofacorporatebondissuer𝑖’saverage bond at time𝑡, measured as the yield for all trades for each of issuer𝑖’s bond over comparable Treasury or interpolated maturity-matched swap rate on the same day, and aggregated at the quarterly-level (median); illiquidityofbond𝑖 attime𝑡,measuredbasedonAmihud(2002)andusinginterquartilerange(IQR)oftrade prices(quarterlymedians); andvolatilityofbond𝑖 attime(quarter)𝑡, measuredasthestandarddeviationof tradepricesofbond𝑖duringeachquarter.ThemainvariableofinterestiscosinesimilarityofCOVID-exposed bondswithunexposedbonds,basedonEquation(5).Creditratinghasbeenconvertedfromtheaverageofthe threeratingagencies,S&P,Fitch,andMoody’stoanumericalscalebetween1(lowest)and21(highest).Timeto maturityisinquarters.Outstandingissuanceamountisinlog($thous).Foreaseofreading,mostvariableshave beentransformedintounitsofstandarddeviation. Source: eMAXX,FISD,S&PGlobal, TRACE,andauthors’ calculation. (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized t=2020Q1,t-1=2019Q4 illiquidity) tradedprices) volatility) PanelA:COVID-exposedbonds Std(ICtounexposedbonds𝑡−1 ) -0.754*** -0.394*** -0.293 0.006 (0.213) (0.080) (0.073) (0.091) Std(Rating𝑡) -1.743*** -0.350*** -0.340*** -0.305*** (0.154) (0.058) (0.053) (0.063) Std(Couponrate𝑡) 0.285* -0.158*** -0.022 0.159** (0.159) (0.060) (0.054) (0.067) Std(Timetomaturity𝑡) 0.285** 0.150*** 0.192*** 0.338*** (0.132) (0.050) (0.045) (0.055) Std(Outstandingissueamount𝑡) 0.508** 0.643*** 0.428*** 0.053 (0.249) (0.094) (0.086) (0.088) Std(Tradevolume𝑡) -0.053 -0.784*** -0.300*** (0.186) (0.070) (0.064) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 278 278 278 278 R-squared 0.451 0.385 0.204 0.207 PanelB:COVID-unexposedbonds Std(ICtoexposedbonds𝑡−1 ) -0.140 -0.119 -0.052 0.243*** (0.105) (0.083) (0.069) (0.087) Std(Rating𝑡) -0.890*** -0.289*** -0.192*** -0.240*** (0.078) (0.062) (0.052) (0.064) Std(Couponrate𝑡) 0.608*** -0.022 0.024 0.266*** (0.0822) (0.065) (0.055) (0.069) Std(Timetomaturity𝑡) 0.084 0.038 0.019 0.138*** (0.056) (0.045) (0.037) (0.047) Std(Outstandingissueamount𝑡) 0.137 0.535*** 0.105 0.020 (0.102) (0.081) (0.068) (0.075) Std(Tradevolume𝑡) 0.001 -0.713*** -0.187*** (0.078) (0.062) (0.052) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 322 322 322 322 R-squared 0.594 0.336 0.115 0.196 39

Table8 InterconnectednessofFallenAngels Thistablepresentsresultsfromtheanalysisoneffectsofinterconnectednessforthesub-sampleofbondswhose average credit rating from the three rating agencies was between BBB- (the lowest investment grade) and BBBinthepreviousperiodandbecamefallenangels,usingEquations(11)-(13). Thedependentvariablesare spread of a corporate bond issuer𝑖’s average bond at time𝑡, measured as the yield for all trades for each of issuer𝑖’s bond over comparable Treasury or interpolated maturity-matched swap rate on the same day, and aggregated at the quarterly-level (median); illiquidity of bond𝑖 at time𝑡, measured based on Amihud (2002) andusinginterquartilerange(IQR)oftradeprices(quarterlymedians);andvolatilityofbond𝑖attime(quarter) 𝑡,measuredasthestandarddeviationoftradepricesofbond𝑖 duringeachquarter. Inallcolumns,themain variableofinterestis“interconnectedness,"whichwemeasurebycosinesimilaritybasedonEquation(5).Credit ratinghasbeenconvertedfromtheaverageofthethreeratingagencies,S&P,Fitch,andMoody’stoanumerical scalebetween1(lowest)and21(highest). Timetomaturityisinquarters. Outstandingissuanceamountisin log($thous).Foreaseofreading,mostvariableshavebeentransformedintounitsofstandarddeviation.Source: eMAXX,FISD,S&PGlobal,TRACE,andauthors’calculation. (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized illiquidity) tradedprices) volatility) Std(Interconnectedness) -0.619*** -0.343*** -0.289*** -0.148 (0.214) (0.084) (0.099) (0.097) Std(Rating) -2.313*** -0.469*** -0.290* -0.314* (0.363) (0.142) (0.167) (0.165) Std(Couponrate) 0.518*** -0.103 0.082 -0.040 (0.192) (0.075) (0.088) (0.087) Std(Timetomaturity) -0.086 -0.028 -0.028 0.0006 (0.083) (0.033) (0.038) (0.038) Std(Outstandingissueamount) 0.390** 0.714*** 0.590*** 0.225*** (0.177) (0.069) (0.081) (0.076) Std(Tradevolume) 0.052 -0.770*** -0.558*** (0.121) (0.048) (0.056) FE Time Time Time Time Observations 580 580 580 580 R-squared 0.643 0.515 0.447 0.454 40

Figure1 IllustrationofNetworksBasedonOverlappingPortfoliosvs. Investors Sub-figure (a) illustrates the conventional network of financial institutions, or investors, constructed via their overlapping portfolios. In this example, Investor 1 holds positive amounts of Assets 1, Investor 2 holds positive amounts of Assets 1 and 2, and Investor 3 holds positive amounts of all three assets.TheresultingnetworkofoverlappingportfolioshasconnectionsbetweenallinvestorsthroughtheircommonholdingsofAsset1orAssets1and 2. Sub-figure(b)depictsournewnetworkoffinancialassetsconstructedviatheoverlappinginvestors. Noticethatthefocusisnowonassetsandthe arrowsareflipped,enablingtheinterpretationthatAsset1isheldbyallinvestors,Asset2isheldbyInvestors2and3,andAsset3isheldonlybyInvestor 3. Inthisnetworkofoverlappinginvestors,Assets1and2areconnectedviatheircommonexposuretoInvestors2and3,Assets1and3areconnected throughInvestor3,andAssets2and3areconnectedthroughInvestor3. (a)NetworkofOverlappingPortfolios (b)NetworkofOverlappingInvestors Investor1 Investor2 Investor3 Investor1 Investor2 Investor3 Asset1 Asset2 Asset3 Asset1 Asset2 Asset3 Investor1 Asset1 Investor2 Asset1 Investors2&3 Asset2 Asset1 Investor3 Assets1&2 Investor3 Asset3 Investor3 41

Figure2 NumberofFinancialInstitutionsandCorporateBondsintheNetwork Sub-figure(a)plotsthenumberofuniqueinvestorsinthenetworkoffinancialinvestors(institutions)andcorporatebonds.Investortypeswerecarefullyverifiedandassignedviaamanualauditingprocess;seeAppendix A for more details. Sub-figure (b) plots the number of unique corporate bonds held by these investors over time.Quarterlyfiguresareaveragedwithinayear.Sources:eMAXXandauthors’calculation. (a)NumberofUniqueInvestors srotsevnI fo rebmuN 004 003 002 001 0 2000 2005 2010 2015 2020 Year Banks Investment managers Insurance companies Other (b)NumberofUniqueCorporateBonds sPISUC fo rebmuN 0052 0002 0051 0001 005 2000 2005 2010 2015 2020 Year Banks Investment managers Insurance companies Other 42

Figure3 NetworkofCorporateBondsBasedonOverlappingInvestors Thisfigureshowsthenetworkofcorporatebondsbasedonoverlappinginvestors. Eachnodeisacorporate bond issuer, and the (weighted) edges between two nodes capture the cosine similarity of the overlapping investorsholdingthecorporatebondsofthetwoissuers. Sub-figure(a)showstheentirenetworkin2021:Q3; sub-figure (b) shows the sub-network of the largest 20 corporate bond issuers in 2021:Q3. Sources: eMAXX andauthors’calculation. (a)Fullnetwork (b)Networkofbondissuerswithlargestamountoutstanding 43

Figure4 QuantileRegressions Thisfigureillustratestheresultsofquantileregressionsbetweeninterconnectednessmeasuresandbondmarketqualitymeasures(spread,illiquidity,andrealizedvolatility.) Source: eMAXX,TRACE,andauthors’calculations. (a)Spread (b)Illiquidity(IQR) (c)RealizedVolatility 44

Appendix A Additional Details on Data A.1 Cleaning eMAXX • We drop observations for which the external manager is not disclosed (firmid = 0). Because we focus on institutional investors, we also drop observations relating to theholdingsofco-managedsubaccounts. • TherearesomeinstancesinwhichthemarketsectorofaCUSIPchangesovertime. To enforce consistency of this variable over time, we collapse the market sector variable toitsmodalvalueforeachCUSIP. • We supplement the eMAXX holdings data with further detail on the institutional investors, including the reported investor name, type, and headquarters location. All U.S.institutionalinvestors,withtheexceptionofpensionfunds,aremandatedtoreport theirentireportfolioeachquarter,arulethathasbeenineffectsinceMay2004.14 Thus, we focus on the set of investors domiciled in the United States (firm_domicile = “USA”). • Weinitiallysortinstitutionalinvestorsintofourtypesbasedonthefirm_codevariable. 1. Banks: BKM,BKT,BMS,BFM,BKP 2. Investmentmanagers: INM 3. Insurancecompanies: ILF,IMD,IND,IPC,REI 4. Pension/other firms: GPE, UPE, CPE; EQM, FEN, GVT, HGE, CRP, CRU, FCC, HLC,OTG,SVG,TRT,UIT • BecausetheeMAXXdatadistinguishbetweenthesubsidiariesofinstitutionalinvestors, for example, JP Morgan Chase (New York) and JP Morgan Chase (Los Angeles), some investorsbelongingtoasingleparentcompany(i.e.,JPMorganChase)arecodedwith different investor identifiers. This property of the data is inconvenient given our research objective of constructing networks that link assets together based on overlap- 14https://www.sec.gov/rules/final/33-8393.htm. 45

ping investors. We do not wish to differentiate between an institutional investor’s subsidiaries’bondportfolios, soweaggregatethese subsidiaries’bondholdingsintoa singleinstitutionalinvestorportfolio. Toidentifyandaggregateinformationattheparentlevel,weutilizeastringmatching algorithm on the reported institutional investor names to match investors that plausibly belong to the same parent company, but which potentially receive separate investor identifiers in eMAXX. Following the string matching algorithm, we then conduct a manual audit on the matches to ensure their validity. Ultimately, we obtain a dictionary mapping parent companies to their subsidiaries and use this dictionary to replace the subsidiaries’ identifiers with a new investor identifier. Finally, we aggregate the bond holdings data to the institutional investor level. Following the string matching algorithm, we identify 4,972 unique institutional investors. While eMAXX reportsatypeforeachinstitutionalinvestor(seeAppendixA.2),weuncoveredseveral discrepancies between the true type of an investor and the type reported by eMAXX (for example, JP Morgan Chase is classified as a mutual fund). We therefore further audit the investor type in the final set of institutional investors and categorize each investorasabank,investmentmanager,insurancecompany,orotherinvestortype. • Wefocusonthetopmarketplayersintermsofassetsundermanagement. Specifically, foreachquarter,weranktheassetmanagersintermsoftheirassetsundermanagement observedintheeMAXXuniverse,whichweconstructdirectlyfromtheholdingsdata. Next,wetakethedistributionoffirms’AUMbasedonthisranking,andselectthefirms whoseAUMfallswithinthetop50thpercentile(righttail)ofthedistributionoffirms’ AUM in that quarter. Finally, we select the median number of firms across the entire sampleperiodtoincludeinthenetworkanalysis. • The eMAXX data also has information on the market sector to which each security belongs: asset-backed securities, including collateralized debt obligations and covered bonds; corporate bonds, including high-yield and investment grade; government bonds, including sovereign and government agency; mortgage-backed securities, including agency and private label pass through, collateralized mortgage obligations, collateralizedmortgage-backedsecurities,andresidentialmortgage-backedsecurities; 46

regionalandmunicipalbonds,includingU.S.muniandinternationalcities,states,and provinces; private placements, including 144A and non-144A; and emerging markets. For the scope of this paper, we only use those securities that belong to the corporate bondmarketsector. 47

A.2 Institutional Investor and Subaccount Types in eMAXX ThistablereportstheinstitutionalinvestorandsubaccounttypesincludedintheeMAXXdata.Therearefour typesofinstitutionalinvestortypes—banks,investmentmanagers,insurancecompanies,andotherinvestors— andfourtypesofsubaccounttypes—insuranceinvestmentaccounts, mutualfunds, pensionfunds, andother funds. InstitutionalInvestorType SubaccountType Banks InsuranceInvestmentAccounts Bank-ManagementDivision InsuranceCo-Diversified Bank-Portfolio InsuranceCo-Life/Health Bank-Savings/BldgSociety InsuranceCo-Prop&Cas Bank-Trust MutualFunds Broker/Dealer-FundMgr MutFd-O/E/UnitTr/SICAV Broker/ManagementSub MutFd-C/E/InvstTr InvestmentManagers MutualFund-Equity InvestmentManager MutualFund-FundofFunds MutualFundManager PensionFunds InsuranceCompanies PensionFund-Corporate InsuranceCo-Diversified PensionFund-Government InsuranceCo-Life PensionFund-Union InsuranceCo-MgmtDiv OtherFunds InsuranceCo-Prop&Cas 401K ReinsuranceCompany Annuity/VariableAnnuity OtherInvestors Bank-Portfolio PensionFund-Government Bank-Trust PensionFund-Union Church/ReligiousOrg Corporation Corporation CreditUnion CreditUnion EquityManager FinanceCompany Finance/CreditCompany FondsCommundePlacement Foundation/Endowment Foundation/Endowment Government HealthCareSystems HealthCareSystems HedgeFund HedgeFund Hospital NuclearDe-CommTrust InvestmentManager Other-General NuclearDe-CommTrust PensionFund-Corporate Other TrustCompany SmallBusinessInvstCo UnitInvestmentTrust UnitInvestmentTrust 48

Appendix B Additional Tables and Figures TableB1 InterconnectednessofBondsThatDidNotBecomeFallenAngels Thistablepresentsresultsfromtheanalysisoneffectsofinterconnectednessforthesub-sampleofbondssubsampleofcorporatebondswhoseaveragecreditratingfromthethreeratingagencieswasbetweenBBB-and BBBinthepreviousperiodbutluckilydidnotbecomefallenangels,usingEquations(8)-(10). Thedependent variablesarespreadofacorporatebondissuer𝑖’saveragebondattime𝑡,measuredastheyieldforalltrades foreachofissuer𝑖’sbondovercomparableTreasuryorinterpolatedmaturity-matchedswaprateonthesame day,andaggregatedatthequarterly-level(median);illiquidityofbond𝑖 attime𝑡,measuredbasedonAmihud (2002)andusinginterquartilerange(IQR)oftradeprices(quarterlymedians);andvolatilityofbond𝑖 attime (quarter)𝑡, measuredasthestandarddeviationoftradepricesofbond𝑖 duringeachquarter. Inallcolumns, themainvariableofinterestis“interconnectedness,"whichwemeasurebycosinesimilaritybasedonEquation (5).Creditratinghasbeenconvertedfromtheaverageofthethreeratingagencies,S&P,FitchandMoody’sto anumericalscalebetween1(lowest)and21(highest). Timetomaturityisinquarters. Outstandingissuance amount is in log($thous). For ease of reading, most variables have been transformed into units of standard deviation.Source:eMAXX,FISD,S&PGlobal,TRACE,andauthors’calculation. (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized illiquidity) tradedprices) Volatility) Std(Interconnectedness) -0.379*** -0.306*** -0.275*** -0.064*** (0.0183) (0.013) (0.013) (0.011) Std(Rating) -1.471*** -0.202*** -0.422*** -0.263*** (0.089) (0.062) (0.065) (0.054) Std(Couponrate) 0.454*** -0.033*** 0.040*** 0.208*** (0.0147) (0.0102) (0.011) (0.009) Std(Timetomaturity) 0.017*** 0.011*** 0.019*** 0.0006 (0.005) (0.004) (0.004) (0.003) Std(Outstandingissueamount) 0.138*** 0.432*** 0.319*** 0.067*** (0.017) (0.012) (0.012) (0.009) Std(Tradevolume) -0.019* -0.452*** -0.304*** (0.011) (0.007) (0.008) FE Time Time Time Time Observations 16,570 16,570 16,570 16,570 R-squared 0.494 0.298 0.290 0.386 49

TableB2 RobustnessUsingOtherNetworkMeasures: FullResults Thistablepresentsthefullresultsfromrunningthesameanalysisofinterconnectednessandspread, liquidity,andvolatilityusingEquations(8),(9),and(10)andnowcontrollingfortwoadditionalvariables,investor concentrationasmeasuredbyHerfindahl-HirschmanIndex(HHI)inPanelAanddegreeinPanelB.PanelC controlsforbothHHIanddegree. Incolumn(1),thedependentvariableisspreadofacorporatebondissuer 𝑖’s average bond at time 𝑡, measured as the yield for all trades for each of issuer 𝑖’s bond over comparable Treasuryorinterpolatedmaturity-matchedswaprateonthesameday,andaggregatedatthequarterly-level (median).Incolumns(2)and(3),thedependentvariablesareilliquidityofbond𝑖attime𝑡,measuredfollowing Amihud(2002)andinterquartilerange(IQR)oftradeprices(quarterlymedians),respectively.Incolumn(4),the dependentvariableisvolatilityofbond𝑖 attime(quarter)𝑡,measuredasthestandarddeviationoftradeprices ofbond𝑖 duringeachquarter. Inallcolumns,themainvariableofinterestis“interconnectedness,"whichwe measurebycosinesimilaritybasedonEquation(5). Creditratinghasbeenconvertedfromtheaverageofthe threeratingagencies,S&P,FitchandMoody’stoanumericalscalebetween1(lowest)and21(highest).Timeto maturityisinquarters.Outstandingissuanceamountandtradevolume(quarterlymedian)areinlog($thous). Foreaseofreading,mostvariableshavebeentransformedintounitsofstandarddeviation. Source: eMAXX, FISD,S&PGlobal,TRACE,andauthors’calculation. PanelA:HHI (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized illiquidity) tradedprices) volatility) Std(Interconnectedness) -0.336*** -0.126*** -0.092*** -0.052*** (0.060) (0.018) (0.016) (0.017) Std(Rating) -2.407*** -0.199*** -0.312*** -0.370*** (0.142) (0.022) (0.022) (0.031) Std(Couponrate) 0.389*** -0.129*** -0.104*** -0.077*** (0.054) (0.016) (0.013) (0.015) Std(Timetomaturity) -0.021** 0.016*** 0.019** 0.018*** (0.010) (0.005) (0.008) (0.005) Std(Outstandingissueamount) 0.317*** 0.330*** 0.226*** 0.023* (0.056) (0.023) (0.019) (0.013) Std(Tradevolume) -0.268*** -0.465*** -0.281*** (0.025) (0.019) (0.016) Std(HHI) 0.150*** 0.034*** 0.029*** 0.018** (0.028) (0.011) (0.009) (0.007) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 182,607 182,607 182,607 182,607 R-squared 0.702 0.468 0.439 0.464 50

Table5 RobustnessUsingOtherNetworkMeasures(cont’d) PanelB:Degree (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized illiquidity) tradedprices) volatility) Std(Interconnectedness) -0.449*** -0.186*** -0.130*** -0.0541*** (0.062) (0.019) (0.016) (0.016) Std(Rating) -2.431*** -0.221*** -0.325*** -0.367*** (0.143) (0.021) (0.022) (0.030) Std(Couponrate) 0.376*** -0.127*** -0.104*** -0.080*** (0.054) (0.016) (0.013) (0.015) Std(Timetomaturity) -0.021** 0.019*** 0.020** 0.017*** (0.010) (0.005) (0.008) (0.006) Std(Outstandingissueamount) 0.293*** 0.256*** 0.189*** 0.044*** (0.060) (0.024) (0.020) (0.014) Std(Tradevolume) -0.264*** -0.465*** -0.281*** (0.025) (0.019) (0.016) Std(Degree) 0.002 0.129*** 0.062*** -0.044*** (0.042) (0.018) (0.016) (0.014) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 182,607 182,607 182,607 182,607 R-squared 0.702 0.470 0.440 0.464 PanelC:HHIandDegree (1)Spread (2)Std(Amihud (3)Std(IQRof (4)Std(Realized illiquidity) tradedprices) volatility) Std(Interconnectedness) -0.326*** -0.165*** -0.110*** -0.037** (0.062) (0.019) (0.017) (0.017) Std(Rating) -2.403*** -0.216*** -0.320*** -0.363*** (0.142) (0.022) (0.022) (0.031) Std(Couponrate) 0.388*** -0.125*** -0.102*** -0.075*** (0.054) (0.016) (0.013) (0.015) Std(Timetomaturity) -0.021** 0.019*** 0.020** 0.017*** (0.010) (0.005) (0.008) (0.006) Std(Outstandingissueamount) 0.333*** 0.263*** 0.195*** 0.049*** (0.062) (0.024) (0.021) (0.014) Std(Tradevolume) -0.267*** -0.466*** -0.282*** (0.025) (0.019) (0.016) Std(HHI) 0.152*** 0.026** 0.025*** 0.022*** (0.028) (0.010) (0.009) (0.008) Std(Degree) -0.030 0.123*** 0.056*** -0.049*** (0.043) (0.018) (0.016) (0.014) FE Issuer,time Issuer,time Issuer,time Issuer,time Observations 182,607 182,607 182,607 182,607 R-squared 0.702 0.470 0.440 0.464 51

FigureB1 SharesofCorporateBondHoldingsbyInvestorType This figure depicts how much each investor type holds out of the total outstanding amount of bonds in our final sample of bond holding data. Each point represents the sum of bond holdings by the investor type—as shownineMAXX—dividedbythesumofoutstandingamountofthebondsbasedonFISD.BondsineMAXX andFISDarematchedbasedonCUSIPs. Quarterlystatisticsareaveragedwithineachyear. Sources: eMAXX andFISD. gnidnatstuO tnuomA/dleH tnuomA raP 8. 6. 4. 2. 0 2000 2005 2010 2015 2020 Year Banks Investment managers Insurance companies Other 52

FigureB2 NumberofQuartersaBondAppearsinOurSample Thisfigureshowsthedistributionofthenumberofquartersabondappearsinourdata(bondisaggregated attheissuerlevel).Sources:eMAXX. ytisneD 1. 80. 60. 40. 20. 0 0 20 40 60 80 Number of Quarters in Sample 53

FigureB3 Cross-sectionalDistributionofInterconnectednessofCorporateBonds Thisfigureshowsthedistributionofinterconnectedness,asmeasuredbycosinesimilarity,inthecross-section of corporate bonds in our sample (aggregated at the issuer level). Specifically, for each bond, we take the arithmetic average of our interconnectedness measure across the time period in which that bond appears in thesample.Source:eMAXXandauthors’calculation. noitcarF 40. 30. 20. 10. 0 0 .0002 .0004 .0006 .0008 Cosine Similarity 54

FigureB4 Cross-SectionalDistributionsofOtherNetworkMeasures Thisfigureshowsthedistributionofothernetworkmeasuresinthecross-sectionofcorporatebondsinoursample(aggregatedattheissuerlevel). Specifically,foreachbond,wetakethearithmeticaverageofthevariables acrossthetimeperiodinwhichthatbondappearsinthesample.Sources:eMAXXandauthors’calculation. (a)Strength noitcarF 5. 4. 3. 2. 1. 0 (b)Degree 0 2000000 4000000 6000000 Strength (Company Level) noitcarF 80. 60. 40. 20. 0 0 100 200 300 Degree (Company Level) (c)NumberofOverlappingInvestors noitcarF 1. 80. 60. 40. 20. 0 0 .02 .04 .06 .08 .1 Number of Overlapping Investors (Company Level) 55