Equity Financing Risk

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Equity Financing Risk Mamdouh Medhat and Berardino Palazzo 2020-037 Please cite this paper as: Medhat, Mamdouh, and Berardino Palazzo (2020). “Equity Financing Risk,” Finance and Economics Discussion Series 2020-037. Washington: Board of Governors of the Federal Reserve System, https://doi.org/10.17016/FEDS.2020.037. 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.

∗ Equity financing risk Mamdouh Medhat† and Berardino Palazzo‡ Thisdraft: May19,2020 Abstract A risk factor linked to aggregate equity issuance conditions explains the empirical performance of investmentfactorsbasedontheassetgrowthanomalyofCooper, Gulen, andSchill(2008). Thisnew risk factor, dubbed equity financing risk (EFR) factor, subsumes investment factors in leading linear factor models. Most importantly, when substituted for investment factors, the EFR factor improves the overall pricing performance of linear factor models, delivering a significant reduction in absolute pricingerrorsandtheirassociatedt-statisticsforseveralanomalies,includingtheonesrelatedtoR&D expendituresandcash-basedoperatingprofitability. Keywords: Equityreturns,R&D,financingconstraints,equityissuances,factormodels JELClassification: G12,G31,G35 Firstdraft: November10,2017 ∗WethankRuiAlbuquerque,AndreaBuffa,HuiChen,ApoorvaJavadekar,XiaojiLin,EvgenyLyandres,Emilio Osambela, Valery Polkovnichenko, Lukas Schmid, Enrique Schroth, Neng Wang, Lucy White, Mindy Xiaolan, Fan Yang,FrancescaZucchi,andseminarparticipantsatBostonUniversity,the1st conferenceonCorporatePoliciesand AssetPrices(COAP),theNorthernFinanceAssociationmeeting,theFederalReserveBoard,CassBusinessSchool, GeorgetownUniversity,TexasA&M,UTDallasFinanceConference,LondonEmpiricalAssetPricing(LEAP)Workshop,andAmericanUniversityfortheircomments.Theviewsexpressedarethoseoftheauthorsanddonotnecessarily reflectthoseoftheFederalReserveBoardortheFederalReserveSystem. Allerrorsareourown. †CassBusinessSchool. Email: mamdouh.medhat@city.ac.uk. ‡FederalReserveBoard. Email: dino.palazzo@frb.gov.

1 Introduction We show that a risk factor linked to aggregate equity issuance conditions explains the empirical performance of investment factors based on the asset growth anomaly of Cooper, Gulen, and Schill(2008). Thisnewriskfactor,dubbedequityfinancingrisk(EFR)factor,subsumestheinvestment factors from the linear factor models of Fama and French (2015) and Hou, Xue, and Zhang (2015) infactor spanning tests. Most importantly, whenthe investment factorsare replaced bythe EFR factor, both mentioned factor models see a significant improvement in their overall pricing performanceacrossadiversesetofanomalies. Ouranalysisbuildsontheobservationthat,overtime,U.S.publiclylistedfirmshavedisplayed astrongermotiveforprecautionarysavingsduetotheentryintopublicequitymarketsoflowprofitability (i.e., weaker) firms, as documented by Fama and French (2004) and Denis and McKeon (2017), among others. A direct consequence is a secular increase in the propensity to save cash out of equity issuance proceeds (e.g., McLean, 2011), especially when equity issuance costs are assumed to be low. Given that the level of equity issuance costs depends on aggregate economic conditions, a firm that relies on cash savings out of equity issuances to support its growth is exposed to an additional source of risk, namely, equity financing risk. This source of risk consists in having states of the world during which a firm needs to replenish its cash reserves via equity issuancebutcanonlydosoataveryhighcostornotatallif,forexample,liquiditydriesup. There is ample evidence that supports the systematic nature of equity issuance costs. Choe, Masulis,andNanda(1993)showthatadverseselectioncostsassociatedwiththeofferingofequity shares are lower during economic expansions, while Eisfeldt and Muir (2016) show that the average cost per dollar of external financing raised displays a strong countercyclical behavior. Erel, Julio, Kim, and Weisbach (2012) show that macroeconomic conditions matter for capital raising, andespeciallysoforlowerrated,non-investmentgradefirms,whichexperienceareductionincapitalraisingduringeconomicdownturns. McLeanandZhao(2014)provideevidencethataggregate conditionsaffectthecostofissuingequitymorethanthecostofissuingdebt. CovasandDenHaan (2012) show how the addition of a countercyclical equity issuance cost greatly improves the qualitative performance of a real business cycle model in describing the cyclical behavior of debt and equity. More recently, Belo, Lin, and Yang (2019) identify a proxy for an aggregate issuance cost shockandshowthatitisapricedsourceofriskinthecrosssectionofequityreturns. 2

Differently from the papers discussed above, we focus our attention on the subset of R&Dintensive firms to better identify the exposure to equity financing risk. Because of the high adjustment costs and the intangible nature that characterize the R&D process, R&D-intensive firms rely heavily on precautionary savings to avoid disruptions in their investment activities. However, because R&D-intensive firms are on average unable to generate internal financing, they have to relyonseasonedequityofferingstobuildliquidityreserves. Duetotheirintangibilityandinability to service debt, R&D-intensive firms cannot readily substitute equity with debt and are thus more likelytobeexposedtothetime-varyingnatureofequityissuancecosts1. Toempiricallycapturefirm-levelconcernsaboutequityissuancecosts,wedefineafirm’sR&D coverage ratio as its liquid assets relative to its R&D expenditures. The R&D coverage ratio tells us how many quarters of R&D expenditures a firm can sustain with current liquid assets assuming future R&D expenditures remain unchanged. A firm with a high R&D coverage ratio is unlikely to issue equity for cash savings purposes given high equity issuance costs in the near future. Conversely,thisismuchmorelikelyforafirmwithalowR&Dcoverageratio. Having a high or low R&D coverage ratio clearly affects a firm’s exposure to EFR. However, thisexposurecanchangequitedramaticallydependingonafirm’sabilitytoengageinprecautionary equity issuances. A firm with very little R&D coverage can suddenly reduce its exposure to EFR if it has the opportunity, in a given quarter, to perform a large equity issuance and save the proceeds. For this reason, we explore the interplay between R&D coverage and equity issuance activitytoempiricallyidentifyfirmswithloworhighexposuretoEFR.2 We start our empirical analysis with Fama and MacBeth (1973) cross-sectional regressions of firms’ returns on R&D coverage, equity issuance, and standard firm-level return predictors. To mitigate overinfluence of small stocks, we estimate the regressions using weighted least squares (WLS) with firms’ market capitalizations as weights. We find that the R&D coverage ratio carries anegativeandsignificantriskpremium. Atthesametime,wefindthathigherequityissuancesare associatedwithsignificantlylowerfuturereturns,whichisconsistentwiththefindingsinprevious literature. Importantly, we find that the predictive power of R&D coverage and equity issuance is 1Brown and Petersen (2011) study the link between cash balances and the high adjustment costs of the R&D process,whileFalato,Kadyrzhanova,andSim(2013)explorehowthelackoftangibilityofR&Dinvestmentsincreases afirm’sprecautionarysavingmotive.Passov(2003)providesanecdotalevidenceontheimportanceofseasonedequity offeringstobuildcashreserves. 2In Appendix C, we show how exposure to equity financing risk naturally arises in a stylized model of a firm’s optimalcashmanagementinthepresenceofcostlyandriskyexternalfinancing. 3

substantiallyweakenedorcompletelydisappearsamongfirmswith(i)highprofitabilityand/or(ii) zero or missing R&D expenditures. These findings support the idea that equity issuance is particularly important in reducing the exposure to equity financing risk, and thus in lowering expected returns,forR&D-intensivefirmswhichhavelittleabilitytointernallyfinanceR&Dexpenditures. Next,weexploretheinterplaybetweenR&Dcoverageandequityissuanceforexpectedreturns ingreaterdetailusingportfoliosdoublesortedonthetwocharacteristics. Theuseofdouble-sorted portfolios allows us to separate firms with a very low R&D coverage that are not able to issue equity in a given quarter and firms with a very high R&D coverage that are also able to issue equity in a given quarter. The former firms are naturally more sensitive to future equity issuance conditions (i.e., more exposed to EFR), while the latter, having plenty of liquid reserves relative to their R&D expenditures, can afford to wait a long time before tapping external financing again. All our portfolio sorts employ NYSE breakpoints and value-weighted returns in order to mitigate overinfluenceofsmallstocks. We find that firms more exposed to EFR (i.e., those with low R&D coverage ratio and no equityissuance)generatesignificantlyhigheraveragereturnsthanfirmslessexposedtoEFR(i.e., firms with a high R&D coverage ratio and high equity issuance), with an economically sizeable spread of about 1% per month. Moreover, when we include an additional control for size in our portfolio sorts, we find that the spread is particularly pronounced for small firms, where those moreexposedtoEFRgeneratesignificantlyhigheraveragereturnswithaspreadofalmost2%per month. Among large firms, those more exposed to EFR also generate higher average returns with asignificantspreadofabout1%permonth. Motivatedbytheseresults,weconstructanempiricalassetpricingfactorthatplausiblycaptures the exposure to EFR. We construct our EFR factor using the same basic procedure employed by Fama and French (2015) and Hou, Xue, and Zhang (2015). Specifically, the EFR factor is an equal-weightedaverageofvalue-weightedlarge-capandsmall-capEFRstrategies. TheEFRfactor generatesalargeandhighlysignificantaveragereturnof1.45%permonthwithat-statisticof4.80. Importantly, this return is neither explained by Fama and French’s (2015) five-factor model, with orwithoutthemomentumfactor,norbyHou,Xue,andZhang’s(2015)q-factormodel. ConsistentwithourpriorthattheEFRfactorshouldproxyfortheexposuretoaggregateequity issuance conditions, we show that this factor is highly correlated with three commonly employed proxies for aggregate equity issuance conditions: the implied volatility index (VIX), Pa´stor and 4

Stambaugh’s (2003) aggregate liquidity measure, and the market excess return. Specifically, the EFR factor’s excess returns tends to be high when implied volatility is high, or when the market excess return is low, or when aggregate liquidity is low. Moreover, we show that a linear combination of the three proxies of aggregate equity issuance conditions fully explain the EFR factor’s averageexcessreturnandasubstantialfractionofitsvolatility. In the last part of the paper, we provide evidence in support of the inclusion of the EFR factor in the five-factor and q-factor models. First, we show in factor spanning tests that the EFR factor completely subsumes these models’ investment factors (CMA and I/A): either model’s investment factor is within the span of EFR, with or without controls for the other factors. The reason is that bothCMAandI/Aarehighlycorrelatedwithaggregateequityissuanceconditions. Specifically,we conductadetailedanalysisoftheinvestmentfactors’underlyingportfoliocharacteristicsandshow thatthelargeincreaseintotalassetsthatdifferentiatestheinvestmentfactors’shortportfoliosfrom their long portfolios are predominantly driven by large equity issuances and increases in liquid assetsratherthanincreasesinphysicalassets. Assuch,ourresultssuggestthatthese“investment” factors conflate variation in returns due to physical investments with variation in returns due to precautionarysavingsfromequityissuanceaimedatreducingtheexposuretoEFR. Then, we conclude our empirical analysis by comparing the pricing power of the EFR factor with that of the investment factors. To this end, we borrow a set of test assets from the list of 46 strategies in Hou, Xue, and Zhang (2018) that generate a significant average return as well as a significant q-factor abnormal return. We find that when an investment factor is replaced by the EFR factor in the factor models of Fama and French (2015) and Hou, Xue, and Zhang (2015), thereisasignificantreductioninabsolutepricingerrorsandtheirassociatedt-statisticsforseveral anomalies,includingtheonesrelatedtoR&Dexpendituresandcash-basedoperatingprofitability. LiteratureReview Ourpaperbelongstoarecentefforttounderstandthesourcesofrisk(ormispricing)thatdrive the asset growth anomaly of Cooper et al. (2008). Cooper, Gulen, and Ion (2017) challenge the ideathatfirm-levelinvestmentisthemaindriverbehindtheexplanatorypoweroftheassetgrowth factorsusedinthemultifactormodelsofFamaandFrench(2015)andHou,Xue,andZhang(2015). More recently, O’Donovan (2019) provides evidence that the asset growth anomaly was driven in the past by mispricing caused by earnings management. O’Donovan (2019) shows that in recent 5

years this source of mispricing has greatly reduced, thus causing a weakening of the asset growth anomaly. We contribute to this effort by offering an alternative and complementary interpretation basedonprecautionaryfinancingmotivesaimedatreducingexposuretoequityfinancingrisk3. We also provide a novel explanation for the observed negative relation between seasoned equityofferings(SEOs)andequityreturns.4 Weshowthatwhenfirmsissueequityforprecautionary savings, they reduce their exposure to equity financing risk and thus witness a reduction in expected equity returns. This channel complements explanations based on asymmetric information (e.g.,LelandandPyle1977;MyersandMajluf1984;MillerandRock1985;LucasandMcDonald 1990), exposure to inflation and default risk (e.g., Eckbo, Masulis, and Norli (2000)); heterogenous beliefs (e.g., Dittmar and Thakor, 2007), and investment activity (e.g., Carlson, Fisher, and Giammarino2006andLyandres,Sun,andZhang2008). Lastly, our paper contributes to a vast literature that tries to understand how firm-level characteristics shape the cross section of equity returns (e.g., Fama and French 1992 and more recently Hou, Xue, and Zhang 2018, among many others). We propose a new firm-level characteristic, the liquid assets-to-R&D ratio, that is linked to exposure to equity financing risk and is significantly priced in the cross section. In addition, we also contribute to the empirical asset pricing literature byintroducinganewriskfactor,namely,theequityfinancingrisk(EFR)factor. Thisfactoris(i)relatedtoaggregateequityissuanceconditions(ii)notsubsumedbythemultifactormodelsofFama and French (2015) and Hou, Xue, and Zhang (2015); and (iii) produces significant improvements inpricingperformancewhenusedinplaceofthesemodels’investmentfactors. The paper is organized as follows. Section 2 provides a description of the data and sample used in the empirical analysis. In Section 3, we run Fama and MacBeth (1973) cross-sectional regressions of firms’ returns on R&D coverage, equity issuances, and standard firm-level return predictors. Section 4 presents the portfolio analysis. Section 5 describes at length the equity financing risk (EFR) factor. We perform asset pricing tests using the EFR factor in Section 6. Section7concludes. 3Harford, Klasa, andMaxwell(2014)exploretheroleofcashholdingsinmitigatingdebtrefinancingrisk. They find that the importance of cash holdings in lowering refinancing risk is much higher for firms with more debt. In thispaper,wecomplementtheirstudybyfocusingonhowcashsavingsoutofequityissuanceproceedsaffectequity returnsbymitigatingequityfinancingrisk. 4The literature on the negative relation between SEOs and equity returns includes Asquith and Mullins (1986); MasulisandKorwar(1986);SpiessandAffleck-Graves(1995);Brav,Geczy,andGompers(2000);DanielandTitman (2006);PontiffandWoodgate(2008);FamaandFrench(2008);andmanyothers. 6

2 Data and sample Our sample consists of firms for which we could obtain quarterly accounting data from the S&P Global’s Compustat North America database (Compustat) and monthly security data from the Center for Research in Security Prices US Stock Database (CRSP) accessed via the Wharton ResearchDataServices(WRDS).Weusequarterlyaccountingdatainordertocapturehowwithinyear dynamics in R&D coverage and equity issuance affect subsequent returns. To be included in our main sample, firms must have ordinary common shares (SHRCD 10 and 11) traded on NYSE,Amex,orNasdaqaswellasstrictlypositiveR&Dexpenditures(XRDQ).5 FollowingHou, Xue, and Zhang (2015, 2018), we exclude financial firms (SIC codes 6000-6999) and firms with negative book equity, and we employ quarterly earnings (IBQ) in the months immediately after earningsannouncementdates(RDQ)butimposea4-monthlagbetweenotheraccountingdataand subsequent returns to ensure no look-ahead bias. Our sample covers January 1990 to December 2016,wherethestartdateisdeterminedbytheavailabilityofquarterlyR&Ddata.6 PrimarymeasuresofR&Dcoverageandequityissuances A firm’s exposure to equity financing risk should depend on the amount of liquid assets relative to R&D expenditures (i.e., the R&D coverage ratio). Our primary measure of a firm’s R&D coverage ratio in quarter t is its beginning-of-quarter near cash or “quick” assets relative to its end-of-quarter R&D expenditure, QA /R&D. Quick assets are current assets minus inventory t−1 t (ACTQ−INVTQ)or,equivalently,thesumofcash,marketablesecurities,andaccountsreceivable (CHEQ+RECTQ).7 Quickassetsarethemostliquidcurrentassets. Theyaretypicallyconvertible tocashatnearbookvalueandpledgeableasloancollateral. Equity issuances are also important in shaping the exposure to equity financing risk. This is becauseafirmcanradicallyincreaseitsR&Dcoveragebyissuingequityandsavingstheproceeds. 5R&Dexpendituresaresubjecttotwoaccountingrequirements. First,theymustbeexpensedanddeductedfrom earnings (IBQ) when incurred. Second, if the amount exceeds 1% of total revenue (REVTQ), it must be disclosed either as a separate line on the Income Statement or in the Notes to the Accounts. If not reported as a separate line on the Income Statement, R&D expenditures are typically included in selling, general, and administrative expenses (XSGAQ)andinveryfewcasesincostofgoodssold(COGSQ).SeeBall,Gerakos,Linnainmaa,andNikolaev(2015). 6Forthesamereason,Hou,Xue,andZhang(2015,2018)alsostarttheirportfoliosortsinvolvingquarterlyR&D datainJanuary1990. 7WemeasurequickassetsasACTQ−INVTQwhenavailable,orelseasCHEQ+RECTQ.Compustat’sCHEQis alsothesumofcashandshort-terminvestments(CHQ+IVSTQ).Quickassetsarecommonlyemployedtomeasure liquiditybalancesincorporatefinance,assetpricing,andcreditriskstudies(see,e.g.,AlmeidaandCampello(2007); HahnandLee(2009);Acharya,Davydenko,andStrebulaev(2012);andthereferencestherein). 7

To measure a firm’s equity issuance proceeds, we start with Fama and French’s (2005) marketbased “dSM” variable, which gives the net dollars issued or repurchased over the latest year. At theendofmonthm−1inquartert(forpredictingreturnsovermonthm),wemeasurenetissuance proceedsoverthelatestyear(4quarters)asthemonthlychangeinsplit-adjustedsharesoutstanding timesthemonthlyaveragesplit-adjustedsharepriceaccumulatedoverthelatest12months: dSM ≡ (cid:88)11 ∆(cid:0) SHROUT CFACSHR (cid:1) × 1 (cid:16) PRC(m−1)−n + PRC(m−1)−n−1 (cid:17) . (1) t−4,t (m−1)−n (m−1)−n 2 CFACPR(m−1)−n CFACPR(m−1)−n−1 n=0 The positive part, dSM + = max{0,dSM }, is then our measure of equity issuance proceeds t−4,t t−4,t over the latest year. Related measures are employed by Stephens and Weisbach (1998), Daniel and Titman (2006), Pontiff and Woodgate (2008), and Fama and French (2008). We accumulate monthly values because sampling prices at a higher frequency gives a more accurate estimate of issuance proceeds over time, although our results are insensitive to the sampling frequency. The one-year horizon is common and helps alleviate seasonalities in equity issuances. To alleviate the influence of outliers and errors in the split-adjustment factors, we trim them at the monthly 0.005 and0.995levelsbeforecomputingdSM.8 NotethatdSMdoesnotincludeIPOproceedsbecauseit requiresafirm’sshareprice,butthatitcapturesallotherissuances,includingthosenotpublicized. Summarystatistics Table 1 shows summary statistics for the main variable we employ in our tests as well asother key firm characteristics. When possible, the summary statistics are shown for the R&D sample (firm-quarters with strictly positive R&D expenditures) as well as the non-R&D sample (firmquarters with zero or missing R&D expenditures). To avoid undue influence from outliers, the shownstatisticsareforvariablestrimmedatthesamples’1stand99thpercentiles. Over our sample period, the R&D coverage ratio (QA /R&D) has a mean of 30.78 and a t−1 t medianof17.76. Thatis,thetypicalliquiditybalancecancoverR&Dexpendituresforaperiodof between 4.5 and 7.5 years. The mean quarterly R&D expenditure is 3% of assets. R&D-intensive firmshaveameanquickassets-to-assetsratioof47%,over1.6timeshigherthannon-R&Dfirms. Brown, Fazzari, and Petersen (2009) show that R&D-intensive firms tend to rely much more 8Forthesamereasons,FamaandFrench(2006)requirethatthesplit-adjustmentfactorsfromCRSPandCompustat match,whilePontiffandWoodgate(2008)correctfirms’split-adjustedsharesoutstandingiftheychangebymorethan 20%,andsubsequently95%ofthechangeisreversedwithinthreemonths. Ourapproachissimplerbutaseffective. 8

Table1. Summarystatistics.Thistableshowssummarystatisticsforthemainvariableweemployinourtestsaswell asotherkeyfirmcharacteristics.The“R&D”sampleconsistsoffirm-quarterswithstrictlypositiveR&Dexpenditures, whilethe“Non-R&D”sampleconsistsoffirm-quarterswithzeroormissingR&Dexpenditures. QA isquickassets t inquartert (ACTQ−INVTQorelseCHEQ+RECTQ),R&D isresearchanddevelopmentexpenditures(XRDQ), t + A istotalassets(ATQ),dSM isthepositivepartofthemonthlychangeinsplit-adjustedsharesoutstandingtimes t t−4,t + the monthly average split-adjusted share price accumulated over the latest 12 months, dD is the positive part of t−4,t the year-over-year change in interest-bearing debt (DLCQ + DLTTQ), COP is cash-based operating profits, ROE t t isreturn-on-equity(incomebeforeextraordinaryitems,IBQ,dividedbylaggedbookequity, B ),and M ismarket t−1 t equity(PRCCQ×CSHOQ).Theshownstatisticsareforvariablestrimmedatthesample’s1stand99thpercentiles. Thesampleexcludesfinancialfirmsandfirmswithnegativebookequity. Dataarequarterlyandcover1989to2016, wherethestartdateisdeterminedbytheavailabilityofquarterlydataonR&Dexpenditures. Percentile Variable Sample Mean Standard 1st 25th Median 75th 99th deviation R&Dcoverage R&Dcoverageratio(QAt−1/R&Dt) R&D 30.78 42.99 2.93 10.59 17.76 32.04 246.13 R&Dexpenditures(R&Dt/At−1) R&D 0.03 0.04 0.00 0.01 0.02 0.04 0.17 Quickassets(QAt−1/At−1) R&D 0.47 0.22 0.09 0.29 0.44 0.64 0.93 Non-R&D 0.29 0.19 0.03 0.14 0.25 0.39 0.85 Equityanddebtissuance Equityissuance(dSM+ t−4,t /At−4) R&D 0.24 0.56 0.00 0.00 0.02 0.16 3.03 Non-R&D 0.09 0.34 0.00 0.00 0.00 0.03 1.84 Debtissuance(dD+ t−4,t /At−4) R&D 0.04 0.11 0.00 0.00 0.00 0.02 0.60 Non-R&D 0.06 0.13 0.00 0.00 0.00 0.06 0.69 Profitability Cash-basedoperatingprofitability R&D −0.01 0.08 −0.27 −0.04 0.01 0.04 0.14 netofR&D((COPt −R&Dt)/At−1) Non-R&D 0.02 0.06 −0.18 0.00 0.03 0.05 0.16 Returnonequity(ROEt) R&D −0.03 0.13 −0.57 −0.06 0.01 0.04 0.18 Non-R&D 0.01 0.09 −0.42 0.00 0.02 0.04 0.19 Leverage Marketleverage(Dt/(Dt +Mt)) R&D 0.11 0.16 0.00 0.00 0.03 0.16 0.68 Non-R&D 0.25 0.23 0.00 0.05 0.20 0.40 0.82 Bookleverage(Dt/At) R&D 0.13 0.16 0.00 0.00 0.06 0.22 0.61 Non-R&D 0.24 0.19 0.00 0.07 0.23 0.37 0.68 heavily on equity issuances compared to debt issuances when tapping capital markets. The sum- + mary statistics confirm this. For R&D-intensive firms, equity issuance-to-assets (dSM /A ) t−4,t t−4 + has a mean of 24% and a median of 2%, while debt issuance-to-assets (dD /A ) has a mean t−4,t t−4 of 4% and a median of zero. For non-R&D firms, equity issuance-to-assets has a mean of 9% and a median of zero, while debt issuance-to-assets has a mean of 6% and a median of zero. Hence, while equity and debt issuances are of about the same size for non-R&D firms, R&D intensive firms’equityissuancesaretypicallymuchlargerthantheirdebtissuances. The large liquidity balances and the preference for equity issuances are consistent with R&Dintensive firms’ lower profitability and lower leverage. For instance, while cash-based operating 9

profitabilitynetofR&D((COP −R&D)/A )hasameanof−1%andamedianof1%forR&Dt t t−1 intensive firms, its mean and median are 2% and 3% for non-R&D firms.9 Similar statistics hold for return on equity (ROE ).10 Our data show that R&D-intensive firms are also less levered, a t fact in accordance with Hall and Lerner’s (2009) view that leverage is a poor substitute for equity financing and delivers small benefits for this kind of firm. For instance, while market leverage (D/(D +M))hasameanof11%andamedianofjust3%forR&D-intensivefirms,ithasamean t t t of25%andamedianof20%fornon-R&Dfirms. Similarstatisticsholdforbookleverage(D/A). t t 3 Fama and MacBeth regressions We start our exploration of the relation between the R&D coverage ratio and equity issuance ononehandandequityreturnsontheotherhandusingFamaandMacBeth(1973)cross-sectional predictive regressions. To mitigate the influence of small firms in OLS regressions, we estimate thecoefficientsviaweightedleastsquares(WLS)withmarketcapitalizationasweight. In addition to our primary measure of R&D coverage, QA /R&D, we employ two other t−1 t measures. Thefirstreplacesquickassetswithjustcashholdings(CHEQ).Forthesecondmeasure, we replace R&D expenditures with total operating costs which, following Novy-Marx (2011), are costsofgoodssoldplusselling,general,andadministrativeexpenses(COGSQ+XSGAQ). + In addition to our primary measure of equity issuance proceeds, dSM , which is over the t−4,t latest year, we also employ two measures over the latest quarter: the monthly change in splitadjustedsharesoutstandingtimesthemonthlyaveragesplit-adjustedstockpriceaccumulatedover the latest 3 months, dSM (see Eq. (1)), and the quarterly net sale of common and preferred t−1,t stock from Compustat, NSS (defined as quarterly SSTKY minus quarterly PRSTKCY). We take t 9WeuseaquarterlyversionofCOP definedsimilarlytotheannualversionemployedbyBall,Gerakos,Linnaint maa, and Nikolaev (2016). Specifically, it is total revenue minus the cost of goods sold minus selling, general, and administrativeexpensesplusR&Dexpenditures(zeroifmissing)minusaccountingaccrualsadjustments(REVTQ− COGSQ−XSGAQ+XRDQ−∆RECTQ−∆INVTQ+∆(DRCQ+DRLTQ)+∆APQ+∆XACCQ).Allchangesare quarterly differences, and missing changes are set to zero. We subtract R&D expenditures from COP in Table 1 to t makeitcomparableacrossthesubsamplesofR&D-intensiveandnon-R&Dfirms. 10WefollowHou,Xue,andZhang(2015)anddefinequarterlyreturnonequity,ROE,asthemostrecentlyavailable t quarterlyearnings(IBQ)dividedbyone-quarterlaggedbookequity,B .Quarterlybookequity,B,isdefinedsimilar t−1 t totheannualversionemployedbyFamaandFrench(1993,2015),Novy-Marx(2013),andothers,andisshareholder’s equityplusdeferredtaxesminuspreferredstock. Shareholder’sequityisSEQQ.IfSEQQismissing,wesubstituteit bycommonequity,CEQQ,pluspreferredstock(definedbelow),orelsebytotalassetsminustotalliabilities,ATQ− LTQ.Deferredtaxesisdeferredtaxesandinvestmenttaxcredits,TXDITCQ,orelsedeferredtaxes,TXDBQ.Preferred stockisredemptionvalue,PSTKRQ,orelsecarryingvalue,PSTKQ. 10

Table2.FamaandMacBethregressionsofreturnsonR&Dcoverageandequityissuance.ThistableshowsFama andMacBethcross-sectionalpredictiveregressionsoffirms’monthlyreturnsonmeasuresofR&Dcoverage(PanelA) andequityissuance(PanelB).InPanelA,QA isone-quarterlaggedquickassets(ACTQ−INVTQorelseCHEQ t−1 +RECTQ),R&D isresearchanddevelopmentexpenditure(XRDQ),C isone-quarterlaggedcashandequivalents t t−1 (CHEQ),andOC isoperatingcosts(COGSQ+XSGAQ).InPanelB,dSM anddSM arethemonthlychanges t t−4,t t−1,t insplit-adjustedsharesoutstandingtimesthemonthlyaveragesplit-adjustedsharepriceaccumulatedoverthelatest 12and3months,respectively;NSS isthequarterlynetsaleofcommonandpreferredstock(quarterlySSTKYminus t quarterly PRSTKCY); A is total assets (ATQ), and x+ = max{0,x} denotes the positive part of x. Regressions are t estimatedusingWLSwithmarkedcapitalizationasweight. Independentvariablesaretrimmedatthemonthly1stand 99thpercentilesandthenstandardizedbytheircross-sectionalmeansandstandarddeviations. ControlsareSize(log ofmarketcapitalization,M,forthepreviousmonth),book-to-marketequity(B/M,whereMisforthepreviousmonth), pastperformanceoverthepreviousmonth(r )andtheprevious12to2months(r ),returnonequity(ROE),asset 1,0 12,2 growth(dA /A ),andrepurchases(dSM− /A ,wheredSM− =max{0,−dSM }). Thesampleisrestricted t−4,t t−4 t−4,t t−4 t−4,t t−4,t to firm-quarters with strictly positive R&D expenditures and excludes financial firms and firms with negative book equity. DataaremonthlyandcoverJanuary1990toDecember2016. Slopes(×100)andtest-statistics(inparentheses) fromWLScross-sectionalregressionsoftheformrit =βββ(cid:48)Xit +(cid:15)it Independent (1) (2) (3) (4) (5) (6) (7) (8) variable PanelA:R&Dcoveragevariables log(QAt−1/R&Dt) −0.23 −0.24 −0.23 −0.31 −0.25 (−3.20) (−2.07) (−3.08) (−2.75) (−3.78) log(Ct−1/R&Dt) −0.09 0.06 −0.11 0.12 (−1.40) (0.51) (−1.66) (1.19) log(QAt−1/OCt) 0.02 0.00 0.07 −0.04 (0.22) (−0.01) (0.77) (−0.54) ROE 0.37 (3.43) dAt−4,t/At−4 −0.14 (−1.77) dSM− t−4,t /At−4 0.02 (0.46) log(B/M) 0.11 0.05 0.00 0.09 0.05 0.01 0.06 0.20 (1.11) (0.47) (0.01) (0.94) (0.54) (0.14) (0.56) (1.93) Size −0.08 −0.09 −0.07 −0.08 −0.10 −0.09 −0.10 −0.14 (−0.68) (−0.82) (−0.67) (−0.72) (−0.88) (−0.83) (−0.93) (−1.29) r1,0 −0.26 −0.26 −0.23 −0.27 −0.25 −0.23 −0.26 −0.27 (−2.15) (−2.15) (−1.90) (−2.37) (−2.13) (−1.93) (−2.25) (−2.31) r12,2 0.27 0.27 0.21 0.25 0.24 0.22 0.23 0.31 (1.72) (1.70) (1.31) (1.66) (1.54) (1.41) (1.52) (2.02) Avg.adj.R2 8.6% 8.5% 9.3% 9.8% 10.2% 10.0% 11.0% 10.8% Avg.N 1,146 1,157 998 1,132 983 978 970 1,099 PanelB:Equityissuancevariables dSM+ t−4,t /At−4 −0.30 −0.29 −0.33 −0.30 −0.20 (−3.76) (−3.26) (−3.94) (−3.36) (−2.55) dSM+ t−1,t /At−4 −0.20 −0.10 −0.21 −0.11 (−3.23) (−1.66) (−3.48) (−1.75) NSS+ t /At−1 −0.04 0.04 −0.03 0.03 (−0.60) (0.56) (−0.48) (0.42) ROE 0.25 (2.22) dAt−4,t/At−4 −0.12 (−1.65) dSM− t−4,t /At−4 0.02 (0.62) log(B/M) 0.03 0.03 0.06 0.02 0.02 0.02 0.02 0.08 (0.25) (0.26) (0.59) (0.20) (0.20) (0.19) (0.16) (0.77) Size −0.11 −0.09 −0.07 −0.12 −0.12 −0.09 −0.12 −0.15 (−1.07) (−0.78) (−0.64) (−1.09) (−1.12) (−0.85) (−1.13) (−1.42) r1,0 −0.28 −0.27 −0.26 −0.28 −0.28 −0.27 −0.28 −0.28 (−2.32) (−2.22) (−2.08) (−2.36) (−2.34) (−2.21) (−2.36) (−2.39) r12,2 0.32 0.30 0.26 0.33 0.31 0.29 0.32 0.30 (2.02) (1.91) (1.64) (2.12) (1.95) (1.84) (2.05) (1.94) Avg.adj.R2 8.6% 8.1% 8.0% 8.8% 8.7% 8.4% 9.0% 10.4% Avg.N 1,171 1,172 1,170 1,164 1,161 1,162 1,155 1,125 11

thepositivepartofbothvariablesandscalethembyone-quarterlaggedtotalassets, A . t−1 ThepredictivepowerofR&Dcoverageratioandequityissuance Table 2 reports the results from Fama and MacBeth (1973) regressions employing the R&D coverage and equity issuance variables. Because R&D coverage has a highly right-skewed distribution, we use a log-transformed version in the regressions (similar to market capitalization and book-to-marketequity),althoughtheresultsareinsensitivetothistransformation. Theregressions controlforSize,book-to-marketequity(B/M),pastperformanceoverthepreviousmonth(r )and 1,0 the previous 12 to 2 months (r ), return on equity (ROE), growth in total assets (dA /A ), 12,2 t−4,t t−4 and repurchases (dSM− /A , where dSM− = max{0,−dSM }).11 To mitigate the influence t−4,t t−4 t−4,t t−4,t outliers and aid interpretability, independent variables are trimmed at the monthly 1st and 99th percentilesandthenstandardizedbytheircross-sectionalmeansandstandarddeviations. Panel A shows the results for the regressions employing the R&D coverage variables. The first three specifications show that while quick assets relative to R&D expenditures has a negative and significant coefficient, neither cash relative to R&D expenditures nor quick assets relative to operating costs is significant. Specifications (4)-(7) show that the significance of the quick assetsto-R&D ratio does not disappear when we control for the two other measures, whether employed individuallyortogether. Theeighthspecificationshowsthattheeffectofthequickassets-to-R&D ratioisonlystrengthenedwhencontrollingforprofitability,assetgrowth,andrepurchases. PanelBshowstheresultsfortheregressionsemployingtheequityissuancevariables. Thefirst three specifications show that only the market-based measures of equity issuance are significant, both with a negative coefficient. Specifications (4) to (7) show that dSM + /A subsumes the t−4,t t−4 twootherequityissuancemeasures,whetheremployedindividuallyortogether. Finally,theeighth specification shows that while controlling for profitability and asset growth does reduce the pre- + dictivepowerofdSM /A ,itstillremainssignificant. Thefactthatcontrollingforprofitability t−4,t t−4 and asset growth diminishes the predictive power of equity issuance is consistent with the results ofHou,Xue,andZhang(2015)andFamaandFrench(2016).12 11WeusequarterlyversionsofSize,B/M,andassetgrowthdefinedsimilartothetheannualversionsemployedby FamaandFrench(2015). Sizeisthelogofequitymarketcapitalization, M,forthepreviousmonthfromCRSP.Asset growthistheyear-over-yearpercentagechangeintotalassets(i.e.,dA /A ≡ATQ/ATQ −1). Book-to-market t−4,t t−4 −4 equityisquarterlybookequity,B,dividedbymarketcapitalization,M,forthepreviousmonthfromCRSP. 12Inuntabulatedtests,wealsocontrolforfirm-levelfinancingconstraintsusingHadlockandPierce’s(2010)sizeageindex. Wefindthatthesize-ageindexhasnopredictivepowerincross-sectionalregressionsofreturnsandthat 12

Table 3. Fama and MacBeth regressions of returns on R&D coverage and equity issuance within subsamples. ThistableshowsFamaandMacBethcross-sectionalpredictiveregressionsoffirms’monthlyreturnsonR&D coverageandequityissuance. R&Dcoverageisone-quarterlaggedquickassetsrelativetocurrentR&Dexpenditures (QA /R&D).Equityissuanceisthepositivepartofthemonthlychangeinsplit-adjustedsharesoutstandingtimesthe t−1 t monthlyaveragesplit-adjustedsharepriceaccumulatedoverthelatest12monthsandscaledbybeginning-of-period + totalassets(dSM /A ). RegressionsareestimatedusingWLSwithmarkedcapitalizationasweight. Independent t−4,t t−4 variablesaretrimmedatthemonthly1stand99thpercentilesandthenstandardizedbytheircross-sectionalmeansand standard deviations. Controls are return on equity (ROE), asset growth (dA /A ), repurchases (dSM− /A ), t−4,t t−4 t−4,t t−4 book-to-market equity (B/M), Size, and past performance (r and r ). In specifications (1)-(5), the the sample is 1,0 12,2 restricted to firm-quarters with strictly positive R&D expenditures. In specifications (2)-(5), “low” and “high” are definedaccordingtothemonthly20thand80thpercentilesforNYSEstocks. Thesplittingvariableinspecifications (2)-(3) is lagged return on equity (ROE ) and in specifications (4)-(5) it is cash-based operating profits relative to t−1 R&Dexpenditures(COP/R&D). Inspecification(6),thesampleconsistsoffirm-quarterswithzeroormissingR&D t t expenditures. All specifications exclude financial firms and firms with negative book equity. Data are monthly and coverJanuary1990toDecember2016. Slopes(×100)andtest-statistics(inparentheses) fromWLScross-sectionalregressionsoftheformrit =βββ(cid:48)Xit +(cid:15)it R&Dsamplesplitinto R&Dsamplesplitinto ROEt−1quintiles COPt/R&Dtquintiles Independent FullR&Dsample Low High Low High ZeroormissingR&D variable (1) (2) (3) (4) (5) (6) log(QAt−1/R&Dt) −0.26 −0.54 −0.28 −0.44 −0.06 (−3.82) (−4.57) (−2.43) (−4.16) (−0.43) dSM+ t−4,t /At−4 −0.20 −0.24 −0.25 −0.46 −0.43 −0.08 (−2.50) (−2.12) (−0.95) (−3.01) (−0.34) (−1.46) ROE 0.34 0.40 0.29 0.38 0.15 0.34 (3.12) (3.90) (1.12) (2.64) (0.43) (4.56) dAt−4,t/At−4 −0.12 −0.23 0.09 −0.07 −0.26 −0.12 (−1.65) (−2.43) (0.49) (−0.61) (−0.55) (−2.35) dSM− t−4,t /At−4 0.01 −0.01 0.04 0.11 −0.05 0.03 (0.18) (−0.13) (0.62) (1.25) (−0.58) (1.11) log(B/M) 0.17 0.43 0.34 0.05 0.28 0.22 (1.65) (3.20) (1.53) (0.38) (1.26) (3.27) Size −0.16 −0.07 −0.06 −0.22 −0.11 −0.11 (−1.51) (−0.40) (−0.29) (−1.43) (−0.62) (−1.32) r1,0 −0.27 −0.54 −0.10 −0.22 −0.36 −0.22 (−2.29) (−4.47) (−0.61) (−1.90) (−1.81) (−2.28) r12,2 0.33 0.37 0.24 0.19 0.35 0.19 (2.10) (2.49) (1.16) (1.26) (1.48) (1.41) Avg.adj.R2 11.2% 11.3% 19.8% 13.7% 26.1% 8.9% Avg.N 1,094 488 128 455 78 1,786 The exposure to equity financing risk crucially depends on a firm’s ability to generate internal resources and to substitute equity financing with debt financing. For this reason, the power of R&D coverage and equity issuance in predicting returns should be stronger among firms with lower profitability, given their inability to generate internal financing. Similarly, the power of equity issuance in predicting returns should be stronger among R&D-intensive firms compared to non-R&Dfirms,givenR&D-intensivefirms’inabilitytosubstituteequitywithdebt. In Table 3 we test these predictions using subsamples defined according to firms’ profitability controllingforithasnoimpactonthepredictivepowerofR&Dcoverageorequityissuance. 13

and R&D intensity. All specifications control for profitability, asset growth, repurchases, bookto-market, size, and past performance. The first specification shows that, in our full sample of firm-quarters with positive R&D expenditures, R&D coverage ratio and equity issuance remain significant when employed together (t-statistics of −3.82 and −2.50, respectively). The second andthirdspecificationsrepeatthisregressionwithinthesubsamplesoflowandhighlaggedreturn on equity (ROE ), defined according to the monthly 20th and 80th percentiles for NYSE stocks. t−1 They show that the power of the R&D coverage ratio is much stronger for the low-profitability group and that equity issuance is only significant within this group. The fourth and fifth specifications show that the same results hold when ROE is replaced by cash-based operating profits t−1 (which are before R&D expenditures) relative to R&D expenditures (COP/R&D). The sixth t t and final specification shows that within the sample of firm-quarters with zero or missing R&D expenditures,therelationbetweenequityissuanceandreturnsisnolongersignificant. ThesefindingssupportourviewoftheR&Dcoverageratioasaproxyfortheexposuretoequity financing risk. Unprofitable, R&D-intensive firms are unable to fund their R&D investments with internally generated cash flows. Hence, the ones with lower R&D coverage are more exposed to equity financing risk and have higher expected returns. At the same time, equity issuance activity seemstomatterforfuturereturnsonlyforunprofitableR&D-intensivefirmsinvirtueofitsability toincreaseprecautionarysavingsandreducetheexposuretoequityfinancingrisk. Overall, Tables 2 and 3 show that R&D coverage and equity issuances are important determinants of equity returns, especially for unprofitable firms. In the next section, we use a portfolio approachtostudyhowthesetwocharacteristicsjointlyshapethecrosssectionofequityreturns. 4 Portfolio sorts The exposure to equity financing risk should be affected by a firm’s R&D coverage as well as its ability to engage in precautionary equity issuances. Fixing equity issuances, firms with higher R&D coverage should earn lower future returns. Conversely, fixing R&D coverage, firms that issuemoreequityshouldearnlowerfuturereturns. Inthissection,weprovideevidenceinsupport of these predictions using portfolios double sorted on R&D coverage (QA /R&D) and equity t−1 t issuance(dSM /A ). WeonlykeepfirmswithnonnegativedSM . t−4,t t−4 t−4,t Table4showstheresults. Theportfoliosarefromindependent3×3sorts,wherethebreakpoints 14

Table4.Double-sortsonR&Dcoverageandequityissuances. Thistableshowsresultsforportfoliosdouble-sorted onR&Dcoverage(QA /R&D)andequityissuance(dSM /A ). WeonlykeepfirmswithnonnegativedSM . t−1 t t−4,t t−4 t−4,t The portfolios are from from independent 3 × 3 sorts where the breakpoints are the 30th and 70th percentiles for NYSEstocksandarevalue-weightedandrebalancedattheendofeachmonth. PanelAshowstheportfolios’average monthly excess returns above the T-bill rate as well as their abnormal returns relative to Fama and French’s (2015) five-factormodel,includingthemomentumfactor,andHou,Xue,andZhang’s(2015)q-factormodel. Italsoshows time-seriesaveragesoftheportfolios’value-weightedcharacteristics[ROE iscurrentreturnonequity;dA isthe t t−4,t year-over-year change in total assets; dPI is the year-over-year change in gross property, plant, and equipment t−4,t plus inventory (PPEGTQ+INVTQ); dQA is the year-over-year change in quick assets; and B/M is the book-tot−4,t marketequityratio]aswellasequal-weightedaveragemarketcapitalization(M,in$millions)andnumberoffirms (n). Panel B shows summary statistics and performance measures for equity financing risk (EFR) trading strategies thatbuythelow/lowcornerandshort-sellthehigh/highcornerfromthedouble-sorts. Teststatistics(inparentheses) are adjusted for heteroscedasticity and autocorrelation. R2 is adjusted for degrees of freedom and given in %. The sample is restricted to firm-quarters with strictly positive R&D expenditures and excludes financial firms and firms withnegativebookequity. DataaremonthlyandcoverJanuary1990toDecember2016. PanelA:Portfolioexcessreturns,abnormalreturns,andcharacteristics dSMt−4,t/At−4tertiles dSMt−4,t/At−4tertiles dSMt−4,t/At−4tertiles Low 2 High Low 2 High Low 2 High QAt−1/R&Dttertiles Excessreturn FF5+MOMα q-factorα Low 1.13 1.27 0.81 0.49 0.77 0.38 0.62 0.81 0.39 (3.19) (3.76) (1.92) (1.83) (3.84) (2.12) (1.85) (3.70) (1.58) 2 0.61 1.06 0.49 0.07 0.57 0.28 0.19 0.59 0.31 (1.73) (3.47) (1.19) (0.35) (3.09) (1.32) (0.83) (3.13) (1.32) High 0.81 0.70 0.09 −0.08 −0.06 −0.44 −0.12 0.03 −0.46 (2.35) (2.06) (0.20) (−0.31) (−0.30) (−2.03) (−0.51) (0.13) (−2.07) QAt−1/R&Dt dSMt−4,t/At−4 ROEt Low 12.61 12.62 11.81 0.00 0.02 0.96 0.04 0.04 −0.01 2 28.39 27.50 27.14 0.00 0.02 0.60 0.03 0.04 0.04 High 142.93 155.64 190.56 0.00 0.02 1.04 0.05 0.04 0.03 dAt−4,t/At−4 dPIt−4,t/At−4 dQA t−4,t /At−4 Low 0.09 0.13 0.59 0.03 0.06 0.11 0.02 0.04 0.24 2 0.07 0.13 0.53 0.03 0.04 0.10 0.03 0.05 0.30 High 0.06 0.13 0.90 0.03 0.06 0.15 0.02 0.05 0.38 B/M AverageM Averagen Low 0.39 0.30 0.22 1,952 2,147 1,443 71 136 309 2 0.47 0.37 0.25 1,910 2,306 2,669 69 114 156 High 0.59 0.49 0.34 1,450 1,356 1,139 56 59 80 PanelB:Equityfinancingrisk(EFR)strategyperformance E[re] Volatility Sharpe Skewness Excess ratio kurtosis Summarystatistics 1.04 23.83 0.52 0.52 3.05 (2.79) α MKT SMB HML RMW CMA MOM R2 FF5+MOM 0.93 −0.24 −0.41 −0.38 0.29 1.28 0.01 23.9% (2.55) (−1.95) (−2.20) (−1.52) (0.93) (3.09) (0.10) α MKT ME ROE I/A R2 q-factor 1.08 −0.37 −0.36 0.09 0.84 21.1% (2.64) (−2.69) (−1.50) (0.28) (2.15) 15

are the 30th and 70th percentiles for NYSE stocks, and are value-weighted and rebalanced at the end of each month. Panel A shows average monthly excess returns above the T-bill rate as well as abnormal returns relative to Fama and French’s (2015) five-factor model augmented with the momentum factor (FF5+MOM) and Hou, Xue, and Zhang’s (2015) q-factor model. Panel A also shows time-series averages of the portfolios’ characteristics. Panel B shows the performance of a long-shortequityfinancerisk(EFR)strategythatbuysthelow/lowcornerportfolio(highexposure toEFR)andshortsellsthehigh/highcornerportfolio(lowexposuretoEFR). Theresultsarelargelyconsistentwithourpredictions. PanelAshowsthatwithinagivenR&Dcoveragetertile,averagereturnsdecreasewithequityissuances,andthesameistrueforabnormal returns. Similarly, within a given equity-issuance tertile, average returns and abnormal returns decrease with R&D coverage. Hence, both R&D coverage and equity issuances are negatively related to future returns when controlling for the other effect. However, the economic importance of R&D coverage for future returns depends crucially on how it is with coupled equity issuances, and vice versa. Indeed, as we move diagonally from the high-EFR portfolio (i.e., firms with a low R&Dcoverageratioandlowequityissuance)tothelow-EFRportfolio(i.e.,firmswithahighR&D coverage ratio and high equity issuance), average excess returns decrease monotonically from a highly significant 1.13% per month (t = 3.19) to an insignificant 0.09% per month (t = 0.20). Similarrelationsholdforabnormalreturns. Panel B sheds more light on this return spread by studying the performance of the long-short EFR strategy. The strategy earns a significant average excess return of 1.04% per month with a t-statistic of 2.79. When we risk-adjust using the FF5+MOM or q-factor models, the spread is largelyundiminished(0.93%and1.08%permonthwitht-statisticsof2.55and2.64,respectively) despitethelargeandpositiveloadingsontheassetgrowthfactors(1.28onCMAand0.84onI/A). TheEFRstrategy’slarge,positiveloadingsontheinvestmentfactorsareinlinewiththeportfolio characteristics in Panel A. They show that the strategy—like the asset growth factors—indeed tends to be long firms with low asset growth (9% on average) and short ones with high asset growth (90% on average). However, the remaining portfolio characteristics show that the higher asset growth in the EFR strategy’s short end (the low-EFR portfolio) is almost entirely driven by precautionary savings from equity issuances and not by physical investments. Firms in the low- EFR portfolio have large equity issuances (104% of book assets on average), but this is coupled with large increases in quick assets (38% of book assets on average) rather than gross property, 16

plant, and equipment plus inventory (15% of book assets on average). We will later explore the connectionbetweenprecautionaryequityissuancesandtheassetgrowthfactorsingreaterdetail. 4.1 Portfolio sorts controlling for size Despite being value-weighted and based on NYSE breakpoints, the double sorts in Table 4 do not explicitly control for size. This subsection alleviates concerns related to the large number of small-cap firms in our sample by using triple sorts on size (equity market capitalization from CRSP), R&D coverage (QA /R&D), and equity issuance (dSM /A ). The triple sorts show t−1 t t−4,t t−4 thatourresultsalsoholdamonglargecaps. Table5showstheresults. Theportfoliosarefrom2×3×3sortsbasedonNYSEbreakpointsand arevalue-weightedandrebalancedattheendofeachmonth. Thebreakpointforsizeisthemedian, while the breakpoints for R&D coverage and equity issuance are the 30th and 70th percentiles. Because the three sorting variables are correlated, independent 2 × 3 × 3 sorts based on NYSE breakpointscauseahighlyunevenallocationofstocksacrosstheportfolios. This,andthefactthat we restrict the sample to firm-quarters with strictly positive R&D expenditures, results in some portfolios being extremely thin or even empty. To allocate stocks more evenly, we follow Fama and French (2015) and use separate NYSE breakpoints for small and large stocks when we sort on R&D coverage and equity issuance. Panel A of the table shows the portfolios’ average excess returns, abnormal returns, and average characteristics. Panel B shows the performance of longshortequityfinancerisk(EFR)strategieswithinsmallandlargefirms. Panel A shows that, for both small and large caps, average excess returns are monotonically decreasing as we move diagonally from the low-EFR to the high-EFR portfolio (from 2.01% to 0.11% per month for small firms and from 1.12% to 0.11% per month for large firms). Similar, monotonicrelationsholdfortheabnormalreturns. Panel A also shows that small caps are on average less profitable, as measured by return on equity (ROE ), compared to large caps in the same category. Nonetheless, among both small t and large caps, the least profitable firms are in the highest equity-issuance tertile, as they are the ones that need liquid resources the most. The increase in quick assets for these firms following an equityissuanceisfivetotentimeshigherthantheirincreaseinphysicalassets. Theaveragemarket capitalizationsalsorevealaninterestingpattern. Amongsmallcaps,thehigh-EFRportfoliohas 17

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the lowest average market capitalization ($139 million). Among large caps, the opposite is true, as the high-EFR portfolio has the highest average market capitalization ($16.8 billion). This also explainswhytherearerelativelymanysmallhigh-EFRfirmsbutonlyafewlargehigh-EFRfirms. Thedifferentabilitytointernallygenerateliquidresourcesisalsoreflectedintheaveragereturn spreads between the low- and high EFR-portfolios among small and large caps. Among small caps, the spread reported in Panel B is a large 1.90% per month with a t-statistic of 5.07, and the corresponding abnormal returns are slightly larger with t-statistics exceeding 5.00. Among large caps, the spread is 1.01% per month with a t-statistic of 2.57, and the corresponding abnormal returns are about as large with t-statistics exceeding 2.40. At the same time, the strategy among smallcapshasalowervolatilitythatcausesatwiceashighSharperatio(1.00versus0.50). Hence, while we get qualitatively similar results among small and large caps, the average return spread andcorrespondingabnormalreturnsareconsiderablystrongeramongsmallerstocks. The portfolio analysis clearly shows that firms more likely to be exposed to equity financing risk earn a positive and significant excess return over firms less likely to be exposed to the same sourceofrisk. Inwhatfollows,weusethesetwogroupsoffirmstobuildariskfactorthatproxies forexposuretoequityfinancingrisk. 5 Equity financing risk (EFR) factor We construct an equity financing risk (EFR) factor as an equal-weighted average of the valueweighted small-cap and large-cap EFR strategies from Table 5. As such, the EFR factor is constructedusingthesamebasicprocedureemployedbyFamaandFrench(2015)andHou,Xue,and Zhang (2015) to construct their factors (i.e., with a control for size). As we detail below, the EFR factor generates a large and highly significant average return of 1.45% per month with a t-statistic of4.80overour1990-2016sampleperiod. Figure 1 shows the EFR factor’s post-formation and time-series performance. The left panel shows that the EFR factor’s positive average returns persist for more than 7 years after formation. Fortheunderlyingsmall-andlarge-capEFRstrategies,thepersistenceisover10yearsandaround 4 years, respectively. These findings show that the exposure to equity finance risk is a persistent phenomenon, especially for small caps, which, as we saw in Table 5, tend to be much less profitable. The right panel shows that the EFR factor has consistently delivered positive excess 20

Figure1. EFRfactor: Persistenceandtime-seriesperformance. 70 60 50 40 30 20 10 0 Months after portfolio formation )%( nruter ssecxe evitalumuc egarevA 200 EFRSmall EFRBig 100 EFRFactor 50 20 10 5 2 1 0 24 48 72 96 120 1990 1995 2000 2005 2010 2015 )gol( tnemtsevni fo eulav ralloD EFR $149.61 MKT I/A CMA $11.74 $4.95 $4.56 Thisfigureshowsthepersistenceandtime-seriesperformanceoftheEFRfactor.Theleftpanelshowsaveragesofcumulativesumsofexcess returnstotheEFRfactoraswellastheunderlyingsmall-andlarge-capEFRstrategies,alongwith95%confidencebands,asafunctionofmonths afterportfolioformation.Therightpanelshowsatime-seriesplotofthevalueofa$1investmentattheendofDecember1989intheEFRfactor, themarket(MKT),andtheinvestmentfactors(CMAandI/A),calculatedasinDanielandMoskowitz(2016).DataaremonthlyandcoverJanuary 1990toDecember2016. returns over time with no particular subsample driving its performance, and, moreover, that it has outperformedtheassetgrowthfactors(CMAandI/A)aswellasthemarketoveroursampleperiod. In the following subsections, we provide evidence that the EFR factor is linked to aggregate equityissuanceconditions. Inaddition,weshowthattheEFRfactor(i)generatesahigheraverage return and a higher Sharpe ratio than the FF5+MOM factors and the q-factors; (ii) is highly nonredundant in either factor model, even by the higher significance threshold advocated by Harvey, Liu, and Zhu (2016), and (iii) completely subsumes these models’ asset growth factors (CMA and I/A).Thelatterfindingsuggeststhatthese‘investment’factors,atleastoveroursampleperiod,conflatevariationinreturnsduetophysicalinvestmentswithvariationinreturnsduetoprecautionary savingsfromequityissuanceaimedatreducingtheexposuretoequityfinancingrisk. 5.1 EFR and aggregate equity issuance conditions The EFR factor should, in principle, capture the exposure to aggregate corporate financing conditions and, specifically, aggregate equity issuance conditions. We consider three measures of aggregate equity issuance conditions: the CBOE implied volatility of the S&P 500 index (VIX), theone-monthlaggedPa´storandStambaugh(2003)aggregateliquiditymeasure(AggLIQ ),and −1 theexcessreturnonthemarketfactor(MKT).HighervaluesfortheVIXindicateworseningequity 21

Table6. Correlationsbetweenmeasuresoffinancingconditions. Thistableshowspairwisecorrelationsbetween measures of financing conditions. We consider three measures of equity issuance conditions: the CBOE implied volatilityoftheS&P500index(VIX),theone-monthlaggedPa´storandStambaugh(2003)aggregateliquiditymeasure (AggLIQ ), andtheexcessreturnonthemarketfactor(MKT).PanelAshowspairwisecorrelationsatthemonthly −1 frequency between the three measures of equity market financing conditions and four financing conditions indexes: the Chicago Fed National Financial Conditions Index (NFCI), the Kansas City Financial Stress Index (KCFSI), the GoldmanSachsFinancialConditionsIndex(GSFCI),andtheBloombergFinancialConditionsIndex(BFCI).PanelB showspairwisecorrelationsattheannualfrequencybetween12-monthmovingaveragesofthethreeequityissuance measuresandEisfeldtandMuir’s(2016)estimatedaveragecostpaidperdollarofexternalfinancing(E&M,whichis onlyavailableannually). Teststatistics(inparentheses)areadjustedforheteroscedasticityandautocorrelation. PanelA:Equityissuanceconditionsandaggregatefinancingconditions(monthly) AggLIQ MKT NFCI KCFSI GSFCI BFCI −1 VIX −0.31 −0.38 0.76 0.81 0.41 −0.81 (−3.94) (−3.53) (14.61) (14.13) (1.69) (−13.03) AggLIQ 0.07 −0.26 −0.33 −0.13 0.34 −1 (0.90) (−7.41) (−8.06) (−1.66) (5.97) MKT −0.19 −0.19 −0.22 0.27 (−1.78) (−1.61) (−2.53) (3.16) NFCI 0.93 0.52 −0.89 (13.74) (1.92) (−9.43) KCFSI 0.47 −0.89 (1.56) (−11.72) GSFCI −0.43 (−2.98) PanelB:Equityissuanceconditionsandestimatedissuancecosts(annual) AggLIQ MKT E&M −1 VIX −0.58 −0.33 0.44 (−3.12) (−1.92) (1.73) AggLIQ 0.43 −0.22 −1 (3.10) (−1.11) MKT −0.53 (−2.78) issuance conditions, while higher values for either AggLIQ or MKT indicate improving equity −1 financingconditions.13 In Panel A of Table 6, we report the pairwise correlation at a monthly frequency between the three measures of equity market financing conditions and four financing conditions indexes: the Chicago Fed National Financial Conditions Index (NFCI), the Kansas City Financial Stress Index (KCFSI), the Goldman Sachs Financial Conditions Index (GSFCI), and the Bloomberg Financial ConditionsIndex(BFCI).14 Market volatility is negatively correlated with the market return and (lagged) aggregate liq- 13Schill(2004)showthatmarketvolatilitynegativelyaffectsfirm-levelequityissuanceactivity,especiallyforsmall or unseasoned firms. Butler, Grullon, and Weston (2005) and Hanselarr, Stulz, and Van Dijk (2019) document a positive correlation between aggregate market liquidity and the cost of issuing equity. Baker and Wurgler (2000), amongothers,showthatfirmstimethemarketandtendtoissueequitybeforeperiodsoflowmarketreturns. 14Inadditiontotheseproxies,theSt.LouisFedalsopublishesaFinancialStressIndex(STLFSI).However,because itisonlyavailablefromJanuary1994,weexcludeitfromourmainanalysistomaximizethenumberofobservations. Inuntabulatedtests,wefindverysimilarresultswhenweincludeSTLFSIintheanalysisfrom1994. 22

Table7. EFRandaggregateequityissuanceconditions. Thistableshowstime-seriesregressionsofthemonthly excessreturntotheequityfinancingrisk(EFR)factor. Theexplanatoryvariablesarethethreemeasuresofaggregate equityissuanceconditionsconsideredinTable6: theCBOEimpliedvolatilityoftheS&P500index(VIX),theonemonth lagged Pa´stor and Stambaugh (2003) aggregate liquidity measure (AggLIQ ), and the excess return on the −1 marketfactor(MKT).Inthefifthspecification,weexcludetheinterceptbutreporttheaverageresidual (cid:15) (in%per t month). Teststatistics(inparentheses)areadjustedforheteroscedasticityandautocorrelation. Dataaremonthlyand coverJanuary1990toDecember2016. Intercepts,slopes,andtest-statistics(inparantheses) fromtime-seriesregressionsoftheformEFRt =βββ(cid:48)Xt +(cid:15)t Independent (1) (2) (3) (4) (5) variable Intercept 1.68 −7.64 1.07 −1.33 (5.59) (−2.90) (3.53) (−0.49) MKT −0.37 −0.33 −0.34 (−4.32) (−3.78) (−4.14) VIX(log) 0.03 0.01 0.01 (3.31) (0.94) (4.24) AggLIQ −0.17 −0.14 −0.15 −1 (−2.53) (−2.33) (−2.57) Adj.R2 8.9% 3.7% 4.1% 12.2% 18.5% (cid:15)t (%) −0.01 (−0.05) uidity. At the same time, this variable is very highly correlated with all the financing conditions indexes in Table 6, with the exception of GSFCI. This is not surprising since all the indexes but GSFCI include aggregate volatility among their components. The aggregate market excess return show no correlation with (lagged) aggregate liquidity, however both measures are correlated with allofthefinancingconditionsindexeswithasignoppositetoaggregatevolatility. In Panel B of Table 6, we report the pairwise correlations at an annual frequency between 12-month moving averages of the three equity issuance measures and Eisfeldt and Muir’s (2016) estimated average cost paid per dollar of external financing (E&M, which is only available annually). This cost is significantly lower when aggregate market volatility is lower or when aggregate market return is higher. The correlation with aggregate liquidity is negative, as expected, but not significant15. Overall, the results in Table 6 make clear that the three measures of equity market financing conditions are correlated with widely used aggregate financing conditions indexes and withaggregateexternalfinancingcosts. Table 7 explores the connection between the monthly excess returns to the EFR factor and aggregate equity issuance conditions using time-series regressions. The first three specifications 15The lack of significance might be attributed to the fact that the estimated average cost of external financing in EisfeldtandMuir(2016)takesintoaccountbothdebtandequityissuancecosts. 23

Figure2. EFRandthefirstprinciplecomponentofaggregateequityissuanceconditions. 1.2 0.8 0.4 0.0 -0.4 -0.8 1995 2000 2005 2010 2015 snoitidnoc ecnaussi ytiuqE )esrow si rehgih ,egareva gnivom raey-3( 4 3 2 1 0 nruter ylhtnoM )% ,egareva gnivom raey-3( PC 1 (left) EFR (right) EFR (right) Thisfigureshowsatime-seriesplotof3-yearmovingaveragesthefirstprincipalcomponentofthethreemeasuresofequitymarketfinancing conditions(PC1,redsolidline,leftaxis),thepredictedexcessreturntotheEFRfactorbasedonspecification(5)inTable7(E(cid:100)FR,blacksolidline, rightaxis),andtherealizedexcessreturntotheEFRfactor(blackdashedline,rightaxis).PC1ispositivelycorrelatedwithaggregatevolatilitybut negativelycorrelatedwiththemarketreturnandaggregateliquidity.Hence,higherPC1valuesindicateworseaggregateequityissuance conditions.DataaremonthlyandcoverJanuary1990toDecember2016. showthatEFRissignificantlycorrelatedwithallthreemeasuresofequitymarketfinancingconditions. Specification(4)employsallthreevariablestogether. Here,themarketreturnandaggregate liquidity remain significant with essentially unchanged coefficients, while both market volatility and the intercept become insignificant. Hence, in specification (5), we re-estimate the model with azerointercept. Theresults inspecifications(5)showthat theaverageexcessreturn toEFRanda substantialfractionofitsvolatilitycanbeexplainedbyalinearcombinationsofthethreemeasures ofaggregateequityissuanceconditions.16 To conclude, Figure 2 shows 3-year moving averages of the first principal component of the three measures of equity market financing conditions (PC ), the predicted excess return to the 1 EFR factor based on specification (5) in Table 7 (E(cid:100)FR), and, finally, the realized excess return to the EFR factor. PC is positively correlated with aggregate volatility but negatively correlated 1 with the market return and aggregate liquidity. Hence, higher PC values indicate worse aggre- 1 16Itisworthnotingthat,overoursampleperiod(January1990toDecember2016),theEFRfactorhasanaverage excessreturnof1.45%permonthandavolatilityof5.37%permonth, whilethepredictedfactorfromspecification (5)inTable7hasanaverageexcessreturnof1.44%permonthandavolatilityof2.12%permonth. 24

gate equity issuance conditions.17 Both the predicted and the realized excess returns to the EFR factor closely follow the time-series behavior of PC . In particular, both the predicted and the 1 realized EFR returns peak around the burst of dot-com bubble in the early 2000s and around the great financial crises of the late 2000s and early 2010s. These periods are characterized by very unfavorable aggregate equity issuance conditions, as captured by the corresponding peaks in PC . 1 Conversely,boththepredictedandtherealizedEFRreturnsdipintheintermediateperiods,which arecharacterizedbymuchmorefavorableequityfinancingconditions.18 5.2 Spanning tests relative to the FF5+MOM factors Table 8 reports the performance of the EFR factor relative to the FF5+MOM factors. Panel A shows that over our 1990-2016 sample, EFR earned a highly significant average return of 1.45% permonthwithat-statisticof4.80andaSharperatioof0.97,allofwhicharemuchhigherthanthe ones for the FF5+MOM factors over our same period. It did so while exhibiting a slight positive skewnessof0.70andanonlymoderateexcesskurtosisof3.37. Panel B shows pairwise correlations between the factors. The EFR factor has a negative and significant correlation with the market (−0.30 with t = −4.32). This result suggests that increases inequityfinancingrisktendtocoincidewithmarketdownturns. Notsurprisingly,theEFRfactor’s correlation with CMA is positive and significant (0.37 with t = 4.81). The correlations with the remainingfactorsallaresmallandinsignificant. PanelCshowsfactorspanningtests,whicharetime-seriesregressionsofonefactoronasetof explanatory factors. A significant abnormal return suggests that the left-hand-side factor captures return variation not explained by the right-hand-side factors and is, as such, non-redundant in an asset pricing model that features the right-hand-side factors. An insignificant abnormal return, however,suggeststhattheleft-hand-sidefactorisredundantrelativetotheright-hand-sidefactors. A redundant factor adds no additional explanatory power to that of the right-hand-side factors regardlessofwhichassetsoneattemptstopricewiththesefactors. The first specification shows that EFR is highly non-redundant in the FF5+MOM model, as 17Thefirstprincipalcomponent(PC )explains47%ofthevolatilityinthemarketreturn,71%ofthevolatilityin 1 theVIX,and35%ofthevolatilityinaggregateliquidity. 18Inuntabulatedtests,wefindthattheEFRfactor’slonglegisresponsibleforthebulkofthefactor’sco-movement withPC . Intuitively,thefirmswithlowR&Dcoverageandlow(past)equityissuanceinthefactor’slonglegbecome 1 riskier when aggregate equity issuance conditions are less favorable, while the firms with high R&D coverage and high(past)equityissuanceinthefactor’sshortlegaremuchlessaffectedbyaggregateequityissuanceconditions. 25

Table 8. EFR factor spanning tests: Fama and French five-factor model. This table shows summary statistics (PanelA),pairwisecorrelations(PanelB),andtime-seriesregressions(PanelC)fortheequityfinancingrisk(EFR) factorandtheFamaandFrench(2015)factors,includingthemomentumfactor.TheEFRfactor,basedontheportfolios inTable5,isdefinedasanequal-weightedaverageofvalue-weighted,monthlyrebalanced,long-shortstrategieswithin smallandlargefirmsthatbuyfirmsinthelow/lowtertilesandsellfirmsinthehigh/hightertilesoffinancialslackand equity issuance. Test statistics (denoted by “t” in Panel A and given in parentheses in Panels B and C) are adjusted forheteroscedasticityandautocorrelation. R2isadjustedfordegreesoffreedom. DataaremonthlyandcoverJanuary 1990toDecember2016 PanelA:Factorsummarystatistics E[re] Volatility t Sharpe Skewness Excess ratio kurtosis EFR 1.45 18.03 4.80 0.97 0.70 3.37 MKT 0.62 14.88 2.50 0.50 −0.65 1.17 SMB 0.20 10.73 1.17 0.22 0.47 5.11 HML 0.25 10.48 1.29 0.29 0.16 2.56 RMW 0.34 9.50 1.98 0.43 −0.45 10.90 CMA 0.26 7.25 2.04 0.43 0.57 2.27 MOM 0.52 16.86 1.84 0.37 −1.52 10.88 PanelB:Factorcorrelations MKT SMB HML RMW CMA MOM EFR −0.30 −0.07 0.16 0.13 0.37 0.02 (−4.32) (−0.53) (1.20) (0.63) (4.81) (0.22) MKT 0.21 −0.17 −0.43 −0.37 −0.25 (3.01) (−1.58) (−3.61) (−5.87) (−3.07) SMB −0.13 −0.47 −0.04 0.02 (−0.82) (−3.41) (−0.78) (0.13) HML 0.38 0.65 −0.19 (3.32) (11.77) (−1.17) RMW 0.23 0.08 (1.84) (0.41) CMA 0.05 (0.38) PanelC:Spanningtests Independentfactors Dependentfactor α MKT SMB HML RMW CMA MOM EFR R2 (1) EFR 1.46 −0.23 −0.04 −0.24 0.00 0.97 −0.08 16.3% (4.74) (−2.86) (−0.31) (−1.62) (0.01) (3.73) (−0.81) (2) SMB 0.30 0.04 0.05 −0.55 0.08 0.05 22.4% (1.78) (0.69) (0.51) (−3.74) (0.51) (0.89) (3) SMB 0.32 0.03 0.05 −0.55 0.09 0.05 −0.01 22.2% (1.82) (0.65) (0.48) (−3.69) (0.62) (0.87) (−0.29) (4) HML −0.11 0.11 0.03 0.36 0.93 −0.13 55.0% (−0.73) (1.93) (0.49) (3.83) (9.60) (−4.09) (5) HML −0.05 0.09 0.03 0.36 0.97 −0.14 −0.04 55.4% (−0.33) (1.82) (0.47) (4.19) (9.86) (−4.39) (−1.46) (6) RMW 0.47 −0.21 −0.32 0.38 −0.24 0.05 42.6% (3.76) (−5.36) (−3.32) (3.14) (−1.51) (1.20) (7) RMW 0.47 −0.21 −0.32 0.38 −0.24 0.05 0.00 42.4% (3.43) (−5.24) (−3.26) (3.28) (−1.75) (1.17) (0.01) (8) CMA 0.24 −0.15 0.02 0.47 −0.12 0.05 52.2% (2.55) (−4.74) (0.53) (9.04) (−1.42) (1.58) (9) CMA 0.10 −0.11 0.02 0.46 −0.11 0.05 0.08 55.8% (1.07) (−3.83) (0.65) (11.45) (−1.75) (1.96) (3.51) (10) MOM 0.58 −0.22 0.13 −0.66 0.25 0.51 14.0% (1.93) (−2.16) (0.91) (−3.38) (1.15) (1.35) (11) MOM 0.68 −0.24 0.13 −0.67 0.25 0.57 −0.07 14.2% (2.24) (−2.34) (0.89) (−3.60) (1.14) (1.61) (−0.76) 26

its abnormal return is a highly significant 1.46% per month with a t-statistic of 4.74. The latter comfortably exceeds the higher t-statistic threshold of 3.00 advocated by Harvey et al. (2016). TheEFRfactorgeneratesthislargeabnormalreturndespitegarneringalarge,positive,andhighly significantloadingonCMA(0.97witht = 3.73). TheadjustedR2 ofjust16.3%suggeststhatEFR capturesreturnvariationthatisinherentlydistinctfromthatcapturedbytheFF5+MOM factors. The remainder of Panel C shows spanning tests for the other factors with and without EFR as anexplanatoryfactor. Specifications2and3showthatSMBisredundantintheFF5+MOM model and that adding the EFR has no effect on these results. Specifications 4 and 5 show that the same results hold for HML. The sixth specification shows that RMW’s abnormal return of 0.47% per month (t = 3.76) is larger and much stronger than its average return over the sample (0.34% with t = 1.98), mainly because of its negative loadings on MKT and SMB. The seventh specification showsthatcontrollingforEFRslightlyshrinksRMW’sabnormalreturnt-statisticto3.43. The eighth specification shows that CMA’s abnormal return of 0.24% per month (t = 2.55) is about as large as, but statistically stronger than, its average return over the sample (0.26% with t = 2.04). The ninth specification shows that this is no longer the case when controlling for EFR: With the addition of EFR, the abnormal return to CMA fades to an insignificant 0.10% per month (t = 1.07) because CMA garners a positive and highly significant loading on EFR. As a result, CMA is redundant relative to the model that includes EFR. In untabulated tests, we find that CMA iswithinthespanofEFRevenwithoutcontrollingfortheotherfactors(abnormalreturnof0.04% permonthwithat-statisticof0.35),whereasEFRisnotwithinthespanofCMA(abnormalreturn of 1.10% per month with a t-statistic of 4.15). These results suggest that the redundancy of CMA isentirelydrivenbyEFR,andnotacombinationofEFRandtheotherfactors. The last two specifications show that MOM’s abnormal return relative to the FF5 factors is 0.58% per month with a t-statistic of 1.93, which is similar to its average return over the sample (0.52%, t = 1.84). The addition of EFR increases this abnormal return to 0.68% per month with a t-statisticof2.24,mainlybecauseMOM hasanegative(albeitinsignificant)loadingonEFR. 5.3 Spanning tests relative to the q-factors Table 8 shows that EFR is non-redundant in the FF5+MOM model and that it subsumes the model’sassetgrowthfactor. Table9showsthatthesameresultsholdrelativetotheq-factormodel. 27

Before going into details, it is important to note that while this may seem unsurprising given themanysimilaritiesbetweentheFF5andq-factormodels,itisinfactremarkablegiventhesubtle but important differences between the two. Specifically, while both models feature a profitability and an asset growth factor, the factor construction differs across the two models. The factors from the FF5 model (RMW and CMA) are constructed from independent double sorts on size and either operating profitability or asset growth, where the sorts employ annual data and the portfolios are rebalanced annually. In contrast, the corresponding q-factors (ROE and I/A) are based on independent triple sorts on size, return on equity, and asset growth, where the ROE sorts employ quarterly data and monthly rebalancing, while the I/A sorts employ annual data and annual rebalancing. As such, RMW and CMA capture profitability and asset growth at a low (annual) frequency without controlling for the other effect. ROE and I/A, however, capture highfrequency (quarterly) profitability but low-frequency (annual) asset growth with a control for the othereffect. AsarguedbyNovy-Marx (2015a,b), thesesubtlebutimportant differencesmatterfor theq-factormodel’sabilitytopricestrategiesbasedonpricemomentum,earningsmomentum,and gross profitability. Nonetheless, we show in the following that EFR (i) performs better over our sample than the q-factors, (ii) is non-redundant in the q-factor model, and (iii) subsumes the I/A factordespitethefactthatI/Acontrolsforhigh-frequencyprofitability. Table9’sPanelAshowsthatEFRstronglyoutperformstheq-factorsoverour1990-2016sample in terms of its average return, the significance of its average return, and its Sharpe ratio. As expected, Panel B shows that EFR is positively correlated with I/A (0.30 with t = 3.46), but has otherwiseinsignificantcorrelationswithROE andtheq-factormodel’ssizefactor,ME. Panel C shows spanning tests employing the q-factors. The first specification shows that EFR isalsonon-redundantintheq-factormodel,asitgeneratesalargeandhighlysignificantabnormal returnof1.55%permonthwithat-statisticof4.59. ThelatteragainsatisfiesHarveyetal.’s(2016) higher threshold of 3.00. EFR generates this abnormal return despite its positive and significant loadingonI/A(0.59witht = 2.54). TheadjustedR2 isjust13.3%,similartoFF5+MOM. The remaining specifications in Panel C show spanning tests for the q-factors with and without EFR on the right-hand side. The second specification shows that ME, like its counterpart in the FF5+MOM model, is redundant. The third specification shows that controlling for EFR implies that ME’s abnormal return t-statistic increases to 2.03. Hence, controlling for the exposure to equity financing risk, the small-stock premium captured by the ME factor becomes significant 28

Table 9. EFR factor spanning tests: q-factor model. This table shows summary statistics (Panel A), pairwise correlations(PanelB),andtime-seriesregressions(PanelC)fortheequityfinancingrisk(EFR)factorandtheHou, Xue,andZhang(2015)factors.TheEFRfactorisbasedontheportfoliosinTable5andisdefinedasanequal-weighted averageofvalue-weighted,monthlyrebalanced,long-shortstrategieswithinsmallandlargefirmsthatbuyfirmsinthe low/lowtertilesandsellfirmsinthehigh/hightertilesoffinancialslackandequityissuance. Test-statistics(denoted by“t”inPanelAandgiveninparenthesesinPanelsBandC)areadjustedforheteroscedasticityandautocorrelation. R2isadjustedfordegreesoffreedom. DataaremonthlyandcoverJanuary1990toDecember2016. PanelA:Factorsummarystatistics E[re] Volatility t Sharpe Skewness Excess ratio kurtosis EFR 1.45 18.03 4.80 0.97 0.70 3.37 MKT 0.60 14.91 2.41 0.49 −0.70 1.45 ME 0.26 11.02 1.49 0.28 0.81 7.33 ROE 0.48 9.61 2.96 0.60 −0.74 4.57 I/A 0.28 6.92 2.43 0.49 0.31 1.96 PanelB:Factorcorrelations MKT ME ROE I/A EFR −0.31 −0.05 0.07 0.30 (−4.45) (−0.35) (0.52) (3.46) MKT 0.23 −0.44 −0.34 (3.00) (−7.06) (−5.29) ME −0.33 −0.13 (−2.65) (−1.46) ROE 0.18 (1.42) PanelC:Spanningtests Independentfactors Dependentfactor α MKT ME ROE I/A EFR R2 (1) EFR 1.55 −0.33 0.02 −0.15 0.59 13.3% (4.59) (−3.43) (0.12) (−0.86) (2.54) (2) ME 0.39 0.07 −0.33 −0.07 11.4% (1.68) (0.90) (−1.95) (−0.35) (3) ME 0.38 0.07 −0.32 −0.07 0.01 11.1% (2.03) (1.16) (−2.26) (−0.37) (0.12) (4) ROE 0.67 −0.24 −0.21 0.04 24.0% (6.04) (−3.88) (−2.87) (0.21) (5) ROE 0.72 −0.25 −0.21 0.06 −0.04 24.2% (5.69) (−3.96) (−3.03) (0.35) (−0.82) (6) I/A 0.37 −0.15 −0.03 0.02 11.1% (3.03) (−3.92) (−0.38) (0.20) (7) I/A 0.22 −0.11 −0.03 0.03 0.08 15.3% (1.56) (−3.17) (−0.40) (0.37) (2.08) at conventional levels, which is generally in line with our results from Table 5. The fourth specification shows that ROE’s abnormal return of 0.67% per month (t = 6.04) is considerably higher andtwiceasstrongasitsaveragereturnoveroursample(0.48%,t = 2.96). Thefifthspecification showsthatcontrollingforEFRreducesROE’sabnormalreturnt-statisticto5.69. TurningtothespanningtestsforI/A,thesixthspecificationsshowsthatitgeneratesanabnormal returnof0.37%permonthwithat-statisticof3.04,whichisonlyslightlyhigherbutconsiderably stronger than its average return over our sample (0.28%, t = 2.43). The seventh and final specifi- 29

Table 10. Factor spanning tests using EFR projected on equity issuance conditions. This table shows timeseries regressions of the monthly excess returns to the asset growth factors (CMA and I/A) from each of the Fama andFrench(2015)andHou, Xue, andZhang(2015)factormodels. Theexplanatoryvariablesarethepredictedand residual components of the EFR factor (E(cid:100)FR and EFR⊥) based on the regression of EFR on the three measures of aggregate equity issuance conditions in specification (5) of Table 7. Test statistics (in parentheses) are adjusted for heteroscedasticityandautocorrelation. DataaremonthlyandcoverJanuary1990toDecember2016. Intercepts,slopes,andtest-statistics(inparantheses) fromtime-seriesregressionsoftheformyt =α+βββ(cid:48)Xt +(cid:15)t Dependentfactor CMA I/A Independent (1) (2) (3) (4) (5) (6) factor Intercept 0.26 −0.35 −0.34 0.28 −0.26 −0.26 (2.04) (−1.95) (−2.20) (2.43) (−1.42) (−1.63) (cid:91) EFR 0.41 0.41 0.37 0.37 (3.25) (4.23) (2.91) (3.74) EFR⊥ 0.11 0.08 (3.56) (1.98) Adj.R2 13.0% 19.1% 11.4% 14.8% cationshowsthatI/Aisredundantintheq-factormodelwhencontrollingforEFR,asitsabnormal return is reduced to an insignificant 0.22% per month with a t-statistic of 1.56. The reason is I/A’s positiveandsignificantloadingonEFR. 5.4 Why does the EFR factor subsume asset growth factors? In this section, we shed more light on why the EFR factor subsumes asset growth factors. We dothisusingbothatimeseriesandacrosssectionalapproach. Table 10 shows time-series regressions of the asset growth factors (CMA and I/A) on each of the predicted and residual components of the EFR factor (E(cid:100)FR and EFR⊥). The latter are based on the regression of EFR on the three measures of aggregate equity issuance conditions in specification (5) of Table 7. The table shows that regressing the asset growth factors on the predictedcomponent(E(cid:100)FR)impliesthattheirpositiveandsignificantaveragereturnsturnnegative (marginally significant forCMA and insignificant for I/A) because both asset growth factors load positively and significantly on E(cid:100)FR. Furthermore, the regressions’ R2 values are 13% for CMA and 11% for I/A. In contrast, we do not find these result when we regress the asset growth factors on the residual component (EFR⊥): both CMA and I/A have a positive and significant abnormal return relative to EFR⊥ despite garnering positive and significant loadings on it. Furthermore, the regressions’ R2 values are at most 6%. That is, the ability of EFR to subsume the asset growth 30

factorsisentirelydrivenbythepartofEFRdirectlylinkedtoaggregateequityissuanceconditions. AnyresidualvariationinEFRcannotsubsumetheassetgrowthfactors. Table 11 shows portfolio characteristics for the long and short portfolios (within size groups) underlying each of EFR and CMA. We focus on CMA for simplicity and because its construction (beinglongandshortasingleportfoliowithinsizegroups)makesiteasiertocompareto EFR.19 Panel A shows the average overlap between the stocks held in the long and short portfolios underlying EFR and CMA. The two factors display substantial overlap in the stocks held in their long and short legs among both small- and large-caps. Among small-caps, the average overlap is over 50% for both legs, and the same is true for the short leg among large-caps. Only the long leg amonglarge-capsdisplaysasomewhatloweroverlap,althoughitisstillaconsiderable24%. Panel B shows time-series averages of the portfolios’ monthly value-weighted characteristics together with each factor’s long-short difference for each characteristic within size groups. Two results are worth highlighting. First, the two factors display a remarkable similarity across the six characteristics we consider: asset growth; equity issuances from CRSP and from Compustat; growth in net property, plant and equipment; growth in quick assets; and book-to-market equity. Second, for both factors, the difference in asset growth is predominantly driven by large changes inquickasset. Inparticular,thehigherassetgrowththatcharacterizestheCMAfactor’sshortlegis alsopredominantlydrivenbyhighersavingsfromprecautionaryequityissuances,notfromgreater investmentinphysicalassets. Panel B of Table 11 also shows a significant long-short difference in physical capital among both small- and large-caps portfolios used to build the EFR factor. As a consequence, a concern might be whether the EFR factor it is merely an investment-based factor in disguise. To alleviate such a concern, we consider the relation between the EFR factor and what is plausibly a more ‘pure’investmentfactor;namely,theLyandres,Sun,andZhang(2008)factor(LSZ).Weconstruct 19To construct the CMA portfolios, we follow Fama and French (2015) and use NYSE breakpoints to sort all commonsharesonNYSE,Amex,andNasdaqinto6portfoliosfrom2×3independentsortsonsizeandassetgrowth. The breakpoint for size is the median while the breakpoints for asset growth are the 30th and 70th percentiles. The portfoliosarevalue-weightedandrebalancedannuallyattheendofJune. Sizeisequitymarketcapitalizationatthe endofJunefromCRSPwhileassetgrowthistheyear-over-yearpercentagechangeintotalbookassets(AT/AT −1) −1 fromtheannualCompustatfile. AnnualaccountingdataforagivenfiscalyearisemployedstartingattheendofJune of the following calendar year. We exclude financial firms and firms with negative book equity. CMA is the equalweightedaverageofthevalue-weightedlarge-capandsmall-capstrategiesthatbuythelow-asset-growthportfolioand short the high-asset-growth portfolio. Over our sample period (January 1990 to December 2016) the original CMA (fromKenFrench’swebsite)yieldsanaverageexcessreturnof0.26%permonthwithat-statisticof2.04. TheCMA webuildyieldsanaverageexcessreturnof0.26%permonthwithat-statisticof2.28. Theircorrelationisover95%. 31

Table 11. Portfolio characteristics for EFR and CMA. This table shows portfolio characteristics for the long and short portfolios within size groups underlying each of EFR and CMA. Panel A shows time-series averages of the monthlyoverlapbetweenstocksintheportfolios,wherethe‘overlap’betweentwosets,XandY,ismeasuredas|X∩ Y|/min{|X|,|Y|}. PanelBshowstime-seriesaveragesoftheportfolios’monthlyvalue-weightedcharacteristicsaswell as the difference in averages. Test-statistics (in parentheses) are adjusted for heteroscedasticity and autocorrelation. A istotalassets;“dSM fromCRSP”isthemonthlychangeinsplit-adjustedsharesoutstandingtimesthemonthly t t−4,t averagesplit-adjustedsharepriceaccumulatedoverthelatest12months;“dSM fromCompustat”istheyear-overt−4,t year change in split-adjusted shares outstanding times the yearly average split-adjusted share price at the beginning and end of the year from Compustat (quarterly file for EFR, annual file for CMA); PI is gross property plant and t equipment plus inventory; QA is quick assets (current assets minus inventories, or else cash and equivalents plus t receivables); B/M is the book-to-market equity ratio. The sample excludes financial firms and firms with negative bookequity. ThesampleusedtoconstructEFRisrestrictedtofirm-quarterswithstrictlypositiveR&Dexpenditures. DataaremonthlyandcoverJanuary1990toDecember2016. PanelA:Portfoliooverlap Small Big Long Short Long Short Overlapbetweenstocks 53.9% 56.2% 24.0% 59.0% inEFRandCMAportfolios (30.24) (37.61) (11.65) (17.53) PanelB:Portfoliocharacteristics Small Big Characteristic Factor Long Short Diff Long Short Diff dAt−4,t/At−4 CMA −0.06 1.08 −1.14 −0.04 0.46 −0.51 (−6.81) (3.88) (−4.15) (−6.84) (5.04) (−5.25) EFR 0.53 1.15 −0.62 0.08 0.72 −0.64 (1.60) (4.34) (−1.44) (7.86) (4.80) (−4.24) dSMt−4,t/At−4 CMA 0.16 1.33 −1.16 0.03 0.57 −0.54 (fromCRSP) (3.38) (2.81) (−2.75) (2.62) (1.74) (−1.67) EFR 0.002 0.83 −0.83 0.004 0.95 −0.95 (6.52) (4.03) (−4.02) (9.86) (1.89) (−1.89) dSMt−4,t/At−4 CMA 0.06 0.39 −0.33 0.01 0.23 −0.22 (fromCompustat) (5.35) (4.43) (−4.38) (4.85) (2.80) (−2.62) EFR 0.05 0.51 −0.46 0.01 0.52 −0.51 (6.49) (7.26) (−6.63) (5.57) (2.53) (−2.52) dQA t−4,t /At−4 CMA −0.03 0.58 −0.60 −0.01 0.16 −0.17 (−6.34) (3.80) (−4.04) (−4.25) (3.42) (−3.78) EFR 0.00 0.54 −0.53 0.02 0.32 −0.29 (0.51) (4.07) (−4.13) (4.28) (4.46) (−4.03) dPIt−4,t/At−4 CMA 0.23 0.40 -0.17 0.28 0.33 -0.05 (20.99) (12.78) (-5.69) (10.51) (20.84) (-3.14) EFR 0.03 0.17 -0.14 0.04 0.14 -0.10 (4.16) (7.91) (-8.05) (4.93) (10.25) (-7.43) B/M CMA 0.79 0.51 0.28 0.46 0.32 0.14 (14.07) (17.49) (8.94) (14.57) (14.70) (7.09) EFR 0.74 0.42 0.32 0.34 0.29 0.05 (17.12) (14.61) (11.78) (20.03) (13.00) (2.54) 32

LSZ from 3 × 3 × 3 independent triple sorts on size, book-to-market equity, and the year-overyear change in the sum of gross property, plant and equipment (PPEG) and inventories (INVT) divided by one-year lagged total assets. We use the 30th and 70th percentiles for NYSE stocks as breakpoints. The resulting 27 portfolios are value-weighted and rebalanced annually in June. The LSZ factor is the equal-weighted average of the 9 low-investment portfolios minus the equalweightedaverageofthe9high-investmentportfolios. Inuntabulatedtests,wefindthatLSZyieldsa significantaverageexcessreturnof0.32%permonth(t = 3.16)overoursampleperiod. However, its time-series correlation with the EFR factor is a relatively modest 19%. As such, neither factor subsumes the other in univariate spanning tests. Finally, in contrast to the EFR factor, the LSZ factor is redundant in both the FF5+MOM and q-factor models. In short, it is unlikely that the EFRfactorisdrivenbyfirm-leveloptimalinvestmentdecisions. Overall, the cross-sectional analysis reveals that CMA, like the EFR factor, separates firms with large positive changes in liquid assets driven by equity issuances from firms that experience noequityissuancesandnochangeinliquidassets. Theformerfirms,byreducingtheirexposureto equityfinancingriskviacashsavingsoutofequityissuanceproceeds,carryalowerriskpremium. 6 Explaining significant anomalies using the EFR factor We conclude our analysis by comparing the pricing power of the EFR factor with that of the investment factors (CMA and I/A). The test assets are always zero-cost, long-short strategies that trade value-weighted portfolios from sorts based on NYSE breakpoints. We consider the equity financing risk strategy from Table 4 as well as 22 additional strategies that trade the extreme portfolios from univariate sorts. Appendix A gives the detailed strategy construction. The sample excludes financial firms and firms with negative book equity. Asset pricing tests cover January 1990toDecember2016,wherethestartdateisdeterminedbytheavailabilityoftheEFRfactor. Our pricing tests center around comparing each strategy’s abnormal return (α) relative to four different factor models: The standard FF5+MOM model that includes CMA (αFF ), the standard CMA q-factormodelthatincludesI/A(αFF),andalternativeversionsofthesemodelswiththeinvestment I/A factorsreplacedbyEFR(αFF andαq ). EFR EFR Beforegoingintodetail,weprovideagraphicalsummaryinFigure3. Itplotstheperformance of the alternative factor models against that of the standard factor models, both in terms of abnor- 33

Figure3. ComparingthepricingpoweroftheEFRfactorwiththatoftheassetgrowthfactors. Abnormal returns 1.5 1.0 0.5 0.0 0.0 0.5 1.0 1.5 | αC FF MA | | RF F E Fα | Abnormal return t-statistics 6 21 5 4 20 9 3 2315 2 1149 11 1120 22 8 16 1 1 5 6 13 7 1817 4 3 2 0 0 1 2 3 4 5 6 | t | for αC FF MA RF F E Fα rof | t | 21 20 15 12 14 10 191 19 23 16 822 6 1 5 7 13 1 3 8172 4 1.5 1.0 0.5 0.0 0.0 0.5 1.0 1.5 | αI q A | | RFE qα | 6 21 5 4 20 9 3 23 19 15 2 37 14 18 1 2 7 16 10211 212 8 1 1 5 13 6 4 0 0 1 2 3 4 5 6 | t | for αI q A RFE qα rof | t | 21 20 23 15 19 16 8 9 1112 3 7 1418 127 1 2120 5 6 13 4 ThisfigureillustratesthepricingtestsinTable12byplottingtheperformanceofthealternativefactormodelsagainstthatofthestandardfactor modelsforthe23testassets.Theleftpanelsshowtheabsoluteabnormalreturnsofthealternativefactormodels(αFF andαq )plottedagainst EFR EFR theabsoluteabnormalreturnsofthestandardfactormodels(αFF andαq )alongwitha45-degreeline.Therightpanelsshowtheabsolute CMA I/A abnormalreturnt-statisticsforthealternativemodelsplottedagainsttheabsoluteabnormalreturnt-statisticsforthestandardmodelsalongwitha 45-degreelineandanindicationof1.96onthetwoaxes(dashedlines).Ineitherpanel,apointbelowthe45-degreelinemeansthatthealternative factormodelbringsanabnormalreturnclosertozero.DataaremonthlyandcoverJanuary1990toDecember2016. mal returns (left-most panels) as well as abnormal return t-statistics (right-most panels). The two left-most panels show that, compared with the standard models, the alternative models produce abnormal returns that are closer to zero (i.e., tend to lie below the 45-degree line). For the few strategies where this is not the case, the abnormal returns are similar in terms of magnitude and significance for either set of models. The two right-most panels show that the alternative factor models are able to generate insignificant pricing errors (absolute t-statistics below 1.96) when the corresponding standard models deliver significant pricing errors (absolute t-statistics above 1.96). 34

Looking at the two right-most panels’ bottom-right quadrants, we see that this is the case for five strategies relative to the FF5+MOM model and seven strategies relative to the q-factor model. At the same time, the two right-most panels’ top-left quadrants are, in fact, empty. That is, there are no insignificant pricing errors obtained using the standard factor models that become significant whenusingthealternativefactormodels. Table 12 provides the details of the pricing tests. The first seven test assets are baseline strategies directly related to the factors. The table’s first line shows, not surprisingly, that replacing the investment factors with EFR implies that both models can price the equity financing risk strategy from Table 4. The next six lines show that employing EFR does not hurt the pricing of strategies based on market capitalization, book-to-market equity, momentum, operating profitability, return onequity,andassetgrowth. Our starting point for the remaining test assets is the list of 46 strategies in Hou, Xue, and Zhang (2018) that generate a significant average return as well as a significant q-factor abnormal return(seetheirTables8and9). Wefurtherrestrictattentionto 1) strategies that can be constructed using only the primary Compustat quarterly/annual data files and the CRSP monthly data file (i.e., we do not consider strategies that require CRSP dailydata,Compustatsegmentdata,orI/B/E/Sanalysts’forecastsdata); 2) strategies that do not require estimation of the sorting variable through time-series or crosssectionalregressions; 3) strategies that are either rebalanced monthly and have a one-month holding period or annuallyandhaveaone-yearholdingperiod;and 4) strategies that generate a statistically significant average return (|t| > 1.96) over our sample period(January1990toDecember2016). The first three restrictions are for simplicity. The fourth restriction excludes a total of seven strategies, suggesting that the significant performance of these strategies documented by Hou, Xue, and Zhang (2018) is driven by the pre-1990 period.20 These restrictions leave us with the 20The seven insignificant strategies are those based on cash-flow-to-price (0.56% per month, t = 1.81), operating cash-flow-to-price(0.53%permonth,t=1.78),inventorychanges(−0.36%permonth,t=−1.94),operatingaccruals (−0.15% per month, t = −0.76), the change in net non-cash working capital (−0.29% per month, t = −1.43), the change in net financial assets (0.31% per month, t = 1.84), and 12-month return seasonality (0.46% per month, 35

remaining 16 strategies considered in Table 12, which we group into the following categories: R&D,profitability,assetcomposition,payoutandfinancingpolicy,valuation,andseasonality. The R&D category consists of the R&D-to-market strategy with annual and monthly updating (lines8-9). Bothgenerateaveragereturns above0.90%permonthwitht-statisticsofatleast2.70. Theabnormalreturnsrelativetothetwostandardfactormodelsareaboutaslargeasthestrategies’ average returns and statistically even stronger. Replacing the investment factors with EFR implies that both alternative models fully explain the annually updated strategy. For the monthly updated strategy,theabnormalreturnrelativetothealternativeq-factormodelhasat-statisticof1.97. The first four strategies in the profitability category (lines 10-13) are related to operating profitability. All four strategies generate significant abnormal returns relative to the standard factor models. Replacing the investment factors with the EFR factor implies that the alternative q-factor modelcanpriceallfourstrategies. Thefinalstrategyintheprofitabilitycategory(line14)isbased on the change in return on equity. It is not explained by the standard Fama-French model, but is explained by the standard q-factor model. Replacing the investment factors with the EFR factor doesnotaltertheseconclusions. In the asset composition category (lines 15-16), replacing the investment factors with EFR (i) shrinks the abnormal returns of the strategy based on net operating assets to less than three standard errors from zero and (ii) completely explains the returns to the strategy based on the industry-adjustedrealestateratio. Thetwostrategiesinthepayoutandfinancingpolicycategory(lines17-18)arebothexplained bythetwostandardmodels. Thesinglestrategyinthevaluationcategory(line19)isnotexplained by the standard Fama-French model but is explained by the standard q-factor model. Replacing theinvestmentfactorswithEFRdoesnotaltertheseconclusions. The final category considers four strategies related to return seasonality (lines 20-23). Here, the standard and alternative models have the same difficulties in explaining the strategies’ returns, withtheexceptionofthestrategybasedontheaverage11-15yearreturnseasonality(line22). For this strategy, replacing the investment factors with EFR shrinks the abnormal returns from around threestandarderrorsabovezerotoinsignificance. t = 1.68). For completeness, Appendix A also gives the detailed construction of these strategies. In general, the insignificantstrategiesdonotcauseproblemsforeithersetoffactormodels(untabulated). 36

Table 12. EFR factor pricing tests. This table compares the pricing power of the EFR factor with those of the investment factors (CMA and I/A). It shows each strategy’s average excess return as well as its abnormal return (α) relative to four different factor models: the standard FF5+MOM model that includes CMA (αFF ), the standard q- CMA factor model that includes I/A (αFF), and alternative versions of these models with the investment factors replaced I/A by EFR (αFF and αq ). The test assets are zero-cost, long-short strategies that trade in value-weighted portfolios EFR EFR fromsortsbasedonNYSEbreakpoints. TheequityfinancingriskstrategyistheoneconsideredinTable4. Allother strategiesarefromunivariatedecilesorts. AppendixAgivesthedetailedstrategyconstruction. Annualstrategiesare rebalancedattheendofJune,whilemonthlystrategiesarerebalancedattheendofeachmonth. Financialfirmsand firms with negative book equity are excluded. Test statistics (in parentheses) are adjusted for heteroscedasticity and autocorrelation. DataaremonthlyandcoverJanuary1990toDecember2016, wherethestartdateisdeterminedby theavailabilityoftheEFRfactor. Abnormalreturn(α)relativetodifferentfactormodels Baselinefactors: Baselinefactors: MKT,SMB,HML, MKT,ME,andROE RMW,andMOM Strategy E[re] αFF αFF αq αq CMA EFR I/A EFR I.Baseline (1) Equityfinancingrisk 1.04 0.93 −0.37 1.08 −0.31 (2.79) (2.55) (−1.46) (2.64) (−1.18) (2) Marketequity −0.31 −0.23 −0.10 −0.33 −0.27 (annual) (−0.96) (−1.35) (−0.62) (−1.55) (−1.31) (3) Book-to-marketequity 0.16 −0.16 −0.10 −0.02 0.29 (annual) (0.60) (−1.01) (−0.61) (−0.10) (1.11) (4) Momentum 0.82 0.09 0.07 0.09 0.03 (2.06) (0.47) (0.34) (0.17) (0.07) (5) Operatingprofitability 0.29 −0.16 −0.22 −0.15 −0.17 (OPFF/B,annual) (0.90) (−0.97) (−1.29) (−0.73) (−0.78) (6) Return-on-equity 0.59 0.26 0.26 0.06 0.07 (monthly) (1.85) (1.59) (1.56) (0.37) (0.40) (7) Assetgrowth −0.47 −0.11 −0.18 −0.07 −0.31 (annual) (−2.03) (−0.70) (−1.07) (−0.45) (−1.34) II.R&D (8) R&D-to-market 0.91 0.82 0.46 0.84 0.45 (annual) (2.78) (2.97) (1.71) (2.95) (1.64) (9) R&D-to-market 0.98 1.24 0.80 1.25 0.81 (monthly) (2.70) (3.61) (2.38) (3.00) (1.97) III.Profitability (10) OperatingprofitsbeforeR&Drelative 0.87 0.63 0.48 0.58 0.33 tolaggedassets(OPBGLN/A−1,monthly) (3.06) (3.07) (2.43) (2.82) (1.50) (11) Cash-basedoperatingprofitsrelative 0.74 0.58 0.45 0.66 0.38 toassets(COP/A,annual) (2.64) (3.58) (2.46) (3.14) (1.78) (12) Cash-basedoperatingprofitsrelative 0.66 0.62 0.50 0.66 0.39 tolaggedassets(COP/A−1,annual) (2.62) (3.69) (2.68) (3.14) (1.76) (13) Cash-basedoperatingprofitsrelative 0.49 0.44 0.23 0.43 0.11 tolaggedassets(COP/A−1,monthly) (2.16) (2.14) (1.05) (2.01) (0.52) (14) ChangeinROE 0.51 0.36 0.41 0.19 0.25 (monthly) (2.88) (2.49) (2.51) (1.05) (1.39) (Continues) 37

(Continued) Abnormalreturn(α)relativetodifferentfactormodels Baselinefactors: Baselinefactors: MKT,SMB,HML, MKT,ME,andROE RMW,andMOM Strategy E[re] αFF αFF αq αq CMA EFR I/A EFR IV.Assetcomposition (15) Netoperatingassets −0.83 −0.70 −0.61 −0.72 −0.58 (annual) (−4.06) (−3.44) (−2.96) (−3.04) (−2.36) (16) Industry-adjustedreal 0.46 0.45 0.36 0.51 0.42 estateratio(annual) (2.21) (2.25) (1.69) (2.40) (1.80) V.Payoutandfinancingpolicy (17) Netpayoutyield 0.71 0.24 0.16 0.33 0.35 (annual) (3.32) (1.21) (0.72) (1.51) (1.21) (18) Netstockissuance −0.61 −0.20 −0.17 −0.27 −0.31 (annual) (−2.31) (−0.96) (−0.82) (−1.24) (−1.35) VI.Valuation (19) Enterprisemultiple −0.58 −0.39 −0.44 −0.33 −0.52 (monthly) (−2.09) (−2.08) (−2.19) (−1.16) (−1.90) VII.Seasonality (20) Average2-5year 0.79 0.77 0.85 0.81 0.90 returnseasonality (3.19) (2.84) (2.93) (2.69) (2.95) (21) Average6-10year 1.27 1.52 1.32 1.54 1.31 returnseasonality (5.44) (5.58) (5.00) (5.54) (4.90) (22) Average11-15year 0.60 0.73 0.44 0.65 0.35 returnseasonality (2.95) (3.17) (1.70) (2.81) (1.47) (23) Average16-20year 0.53 0.64 0.62 0.68 0.71 returnseasonality (1.97) (2.28) (2.05) (2.28) (2.28) 38

Table 13. Average model performance across all and non-baseline strategies. This table reports the average absolutepricingerrors(α)andaverageabsolutet-statisticsfortheabnormalreturnsinTable12calculatedusingfour differentfactormodels: ThestandardFF5+MOM modelthatincludesCMA(αFF ),thestandardq-factormodelthat CMA includes I/A (αFF), and alternative versions of these models with the investment factors replaced by EFR (αFF and I/A EFR αq ). Thetablealsoshows,foreachquantity,thedifferencebetweentheoneimpliedbythestandardfactormodels EFR and the one implied by the alternative model (∆) as well as the two-sided p-value for the null hypotheses of a zero differencebasedonanormaldistributionapproximation.DataaremonthlyandcoverJanuary1990toDecember2016, wherethestartdateisdeterminedbytheavailabilityoftheEFRfactor. Allstrategies Non-baselinestrategies (1to23) (8to23) PanelA:StandardandalternativeFF5+MOMmodels Abnormalreturns (cid:12) (cid:12) (cid:12) (cid:12)αFF (cid:12) (cid:12) 0.53 0.65 CMA (cid:12) (cid:12) (cid:12) (cid:12)αFF (cid:12) (cid:12) 0.42 0.52 EFR ∆|α| −0.11 −0.13 p-valueforH0:∆|α|=0 0.00 0.00 Abnormalreturnt-statistics |t|forαFF 2.35 2.84 CMA |t|forαFF 1.84 2.21 EFR ∆|t| −0.51 −0.63 p-valueforH0:∆|t|=0 0.00 0.00 PanelB:Standardandalternativeq-factormodels Abnormalreturns (cid:12) (cid:12) (cid:12) (cid:12) (cid:12)αq I/A (cid:12) (cid:12) (cid:12) 0.53 0.65 (cid:12) (cid:12) (cid:12)αq (cid:12) (cid:12) (cid:12) 0.42 0.51 EFR ∆|α| −0.11 −0.14 p-valueforH0:∆|α|=0 0.04 0.01 Abnormalreturnt-statistics |t|forαq 2.03 2.55 I/A |t|forαq 1.61 1.92 EFR ∆|t| −0.42 −0.63 p-valueforH0:∆|t|=0 0.00 0.00 39

We summarize the different models’ performance in Table 13. For each standard model, we reportthemeanabsolutereturnandmeanabsolutet-statisticandcomparethesequantitieswiththe onesgeneratedwiththealternativemodels. Thelatterclearlyoutperformthestandardonesbydeliveringconsistentlylowermeanabsolutereturnsandmeanabsolutet-statistics. Thesedifferences arealsostatisticallysignificant. Asanexample,acrossthe16non-baselinestrategies,thestandard q-factormodel’smeanabsolutereturnis0.65%permonthanditsmeanabsolutet-statisticis2.55. Replacing I/A with EFR implies a significant reduction in the mean absolute return of about 20% andasignificantreductioninthemeanabsolutet-statisticofabout25%. 7 Conclusion Exposuretoequityfinancingriskisanimportantdimensionofafirm’sexpectedequityreturns. Using a measure of liquid assets relative to R&D expenditures (i.e., R&D coverage ratio) and a measure of equity issuance activity, we identify firms more or less exposed to equity financing risk. We find that firms more exposed to EFR (i.e., those with low R&D coverage ratio and no equityissuance)generatesignificantlyhigheraveragereturnsthanfirmslessexposedtoEFR(i.e., firms with a high R&D coverage ratio and high equity issuance). In addition, we construct a factor that captures exposure to equity financing risk. This factor is linked to aggregate equity issuance conditions and generates large and highly significant average excess returns that cannot beexplainedbyleadingempiricalassetpricingmodels. We find that the equity financing risk factor (i) completely subsumes the asset-growth factors from both the Fama and French five-factor model and the Hou, Xue, and Zhang (2015) q-factor modeland(ii)improvesthepricingperformanceofstandardlinearfactormodelswhenitreplaces theasset-growthfactor. Theseresultssuggestthatfactorsbasedonassetgrowthconflatevariations inexpectedreturnsduetophysicalinvestments (asnotedbyLyandresetal.,2008)withvariations due to precautionary cash savings aimed at reducing the exposure to equity financing risk. Accounting for the exposure to equity financing risk thus seems to be important for the broad cross sectionofreturns,notonlythereturnsoffirmsthatareR&D-intensive. 40

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Appendix A All strategies trade in value-weighted portfolios from sorts based on NYSE breakpoints. Quarterly earnings (IBQ) are employed in the months immediately after earnings announcement dates (RDQ). Other quarterly accounting data are lagged 4 months relative to subsequent returns to ensure no look-ahead bias. Annual accounting data for a given fiscal year is employed starting at the end of June of the following calendar year. The sample excludes financial firms (SIC codes 6000-6999) and firms with negative book equity. AssetpricingtestscoverJanuary1990toDecember2016,wherethestartdateisdeterminedbythe availabilityofquarterlydataonR&DexpendituresfortheconstructionoftheEFRfactor. A.1 Baseline strategies A.1.1 Equityfinancingrisk Attheendofmonthm−1, weform9portfoliosfromindependent3×3sortsonR&Dcoverageratioand equity issuance, where the breakpoints are the 30th and 70 percentiles for NYSE stocks. Financial slack is1-quarterlaggedquickassets(ACTQ−INVTQorelseCHEQ+RECTQ)relativetoR&Dexpenditures (XRDQ) from the latest fiscal quarter ending at least 4 months ago. Equity issuance is the cumulative monthlychangeinsplit-adjustedsharesoutstanding(changeinSHROUT×CFACSHR)timesthemonthly average split-adjusted share price (average of PRC / CFACPR) for the latest 12 months (i.e., months m− 12,...,m−1)scaledbybeginning-of-periodtotalassets(4-quarterlaggedATQ).Weonlykeepfirmswith strictly positive R&D expenditures and nonnegative equity issuance. We calculate value-weighted returns for month m and rebalance the portfolios at the end of month m. The equity financing risk strategy buys the low/low corner portfolio (high exposure to equity financing risk) and short sells the high/high corner portfolio (low exposure to equity financing risk). The first sort is at the end of December 1989. See also Table4. A.1.2 Marketequity(annual) AttheendofJuneofyeart,weformportfoliosfromadecilesortonmarketequityusingNYSEbreakpoints. MarketequityissharepricetimesnumberofsharesoutstandingfromCRSP(PRC×SHROUT)attheend ofJuneofyeart. Wecalculatemonthlyvalue-weightedreturnsfromJulyofyearttoJuneofyeart+1and rebalancetheportfoliosattheendofJuneofyeart+1. ThefirstsortisattheendofJune1989. 45

A.1.3 Book-to-marketequity(annual) At the end of June of year t, we form portfolios from a decile sort on book-to-market equity, B/M, using NYSEbreakpoints. Here, Bisbookequityforthefiscalyearendingincalendaryeart−1and M ismarket equity from CRSP at the end of December of year t −1. Book is shareholder’s equity plus deferred taxes minuspreferredstock. Shareholder’sequityisSEQ.IfSEQismissing,wesubstituteitbycommonequity, CEQ,pluspreferredstock(definedbelow),orelsebytotalassetsminustotalliabilities,AT−LT.Deferred taxes is deferred taxes and investment tax credits, TXDITC, or else deferred taxes and/or investment tax credit,TXDBand/orITCB.Preferredstockisredemptionvalue,PSTKRVorelsePSTKR,orelseliquidating value,PSTKL,orelsecarryingvalue,PSTK.Wecalculatemonthlyvalue-weightedreturnsfromJulyofyear ttoJuneofyeart+1andrebalancetheportfoliosattheendofJuneofyeart+1. Thefirstsortisattheend ofJune1989. A.1.4 Momentum At the end of month m−1, we form portfolios from a decile sort on prior 11-month returns using NYSE breakpoints. Prior11-monthreturnsisthecumulativereturnfrommonthm−12tomonthm−2, skipping the return over month m−1 (at the end of which the portfolios are formed). We calculate value-weighted returns for month m and rebalance the portfolios at the end of month m. For instance, at the end of June 2016,wesortoncumulativereturnsfromJuly2015toMay2016;calculatevalue-weightedreturnsforJuly 2016,andrebalancetheportfoliosattheendofJuly2016. ThefirstsortisattheendofDecember1989. A.1.5 Operatingprofitability(OP /B,annual) FF AttheendofJuneofyeart,weformportfoliosfromadecilesortonoperatingprofitability,OP /B,using FF NYSE breakpoints. Here, OP is Fama and French’s (2015) definition of annual operating profits for the FF fiscalyearendingincalendaryeart−1and Biscontemporaneous(notlagged)bookequity(seeAppendix A.1.3). Annualoperatingprofitsistotalrevenue(REVT)minuscostofgoodssold(COGS,zeroifmissing) minusselling,general,andadministrativeexpenses(XSGA,zeroifmissing)minusinterestexpenses(XINT, zeroifmissing). Werequireatleastoneofthethreeexpenseitemstobenon-missing. Wecalculatemonthly value-weighted returns from July of year t to June of year t +1 and rebalance the portfolios at the end of Juneofyeart+1. ThefirstsortisattheendofJune1989. 46

A.1.6 Returnonequity(monthly) At the end of month m−1, we form portfolios from a decile sort on Hou, Xue, and Zhang’s (2015) return onequityusingNYSEbreakpoints. returnonequityistotalearningsfromthelatestearningsannouncement date scaled by 1-quarter lagged book equity (IBQ/B ). Quarterly book equity, B, is shareholder’s equity −1 plusdeferredtaxesminuspreferredstock. Shareholder’sequityisSEQQ.IfSEQQismissing,wesubstitute itbycommonequity,CEQQ,pluspreferredstock(definedbelow),orelsebytotalassetsminustotalliabilities, ATQ−LTQ.Deferredtaxesisdeferredtaxesandinvestmenttax credits, TXDITCQ,orelsedeferred taxes,TXDBQ.Preferredstockisredemptionvalue,PSTKRQ,orelsecarryingvalue,PSTKQ.Wecalculate value-weighted returns for month m and rebalance the portfolios at the end of month m. The first sort is at theendofDecember1989. A.1.7 Assetgrowth(annual) At the end of June of year t, we form portfolios from a decile sort on the percentage growth in total book assets (AT), over the fiscal years ending in calendar years t − 2 and t − 1, using NYSE breakpoints. We calculatemonthlyvalue-weightedreturnsfromJulyofyearttoJuneofyeart+1andrebalancetheportfolios attheendofJuneofyeart+1. ThefirstsortisattheendofJune1989. A.2 Research and developement A.2.1 R&D-to-market(annual) At the end of June of year t, we form portfolios form a decile sort on R&D-to-market using NYSE breakpoints. R&D expenditures (XRD) are for the fiscal year ending in calendar year t−1 and market equity is from CRSP at the end of December of year t−1. We only keep firms with strictly positive R&D expenditures. We calculatemonthly value-weighted returnsfrom July of yeart to Juneof yeart+1 andrebalance theportfoliosattheendofJuneofyeart+1. ThefirstsortisattheendofJune1989. A.2.2 R&D-to-market(monthly) Attheendofmonthm−1,weformportfoliosformadecilesortonR&D-to-marketusingNYSEbreakpoints. R&Dexpenditures(XRDQ)arefromthelatestfiscalquarterendingatleast4monthsagoandmarketequity isfromCRSPattheendofmonthm−1. WeonlykeepfirmswithstrictlypositiveR&Dexpenditures. We calculate monthly value-weighted returns for month m and rebalance the portfolios at the end of month m. ThefirstsortisattheendofDecember1989. 47

A.3 Profitability A.3.1 OperatingprofitsbeforeR&Drelativetolaggedassets(OP /A ,monthly) BGLN −1 At the end of month m−1, we form portfolios from a decile sort on operating profits before R&D relative to lagged assets, OP /A , using NYSE breakpoints. Here, OP is similar to Ball, Gerakos, Lin- BGLN −1 BGLN nainmaa, and Nikolaev’s (2015) definition of annual operating profits before R&D but for the latest fiscal quarterendingatleast4monthsagoandA is1-quarterlaggedtotalassets(ATQ).Operatingprofitsbefore −1 R&D expenditures is quarterly total revenue (REVTQ) minus cost of goods sold (COGSQ) minus selling, general, and administrative expenses (XSGAQ) plus R&D expenditures (XRDQ, zero if missing). We calculatemonthlyvalue-weightedreturnsformonthmandrebalancetheportfoliosattheendofmonthm. The firstsortisattheendofDecember1989. A.3.2 Cash-basedoperatingprofitsrelativetoassets(COP/A,annual) At the end of June of year t, we form portfolios from a decile sort on cash-based operating profits relative to assets, COP/A, using NYSE breakpoints. Here, COP is Ball, Gerakos, Linnainmaa, and Nikolaev’s (2016) definition of cash-based operating profits for the fiscal year ending in calendar year t −1 and A is contemporaneous(notlagged)totalassets(AT).Cash-basedoperatingprofitsisannualtotalrevenue(REVT) minuscostofgoodssold(COGS),minusselling,general,andadministrativeexpenses(XSGA),plusR&D expenditures(XRD,zeroifmissing),minusthechangeinaccountsreceivable(RECT),minusthechangein inventory(INVT),minusthechangeinprepaidexpenses(XPP),plusthechangeindeferredrevenue(DRC + DRLT), plus the change in trade accounts payable (AP), plus the change in accrued expenses (XACC). Allchangesareannualchangesandmissingchangesaresettozero. Wecalculatemonthlyvalue-weighted returnsfromJulyofyearttoJuneofyeart+1andrebalancetheportfoliosattheendofJuneofyeart+1. ThefirstsortisattheendofJune1989. A.3.3 Cash-basedoperatingprofitsrelativetolaggedassets(COP/A ,annual) −1 At the end of June of year t, we form portfolios from a decile sort on cash-based operating profits relative tolaggedassets,COP/A ,usingNYSEbreakpoints. Here,COPisBall,Gerakos,Linnainmaa,andNiko- −1 laev’s(2016)definitionofcash-basedoperatingprofitsforthefiscalyearendingincalendaryeart−1(see AppendixA.3.2)and A istotalassets(AT)forthefiscalyearendingincalendaryeart−2. Wecalculate −1 monthlyvalue-weightedreturnsfromJulyofyeart toJuneofyeart+1andrebalancetheportfoliosatthe endofJuneofyeart+1. ThefirstsortisattheendofJune1989. 48

A.3.4 Cash-basedoperatingprofitsrelativetolaggedassets(COP/A ,monthly) −1 At the end of month m−1, we form portfolios from a decile sort on cash-based operating profits relative to lagged assets,COP/A , using NYSE breakpoints. Here,COP is similar to Ball, Gerakos, Linnainmaa, −1 and Nikolaev’s (2016) definition of annual cash-based operating profits but for the fiscal quarter ending at least 4 months ago and A is 1-quarter lagged total assets (ATQ). Cash-based operating profits is quar- −1 terlytotalrevenue(REVTQ)minuscostofgoodssold(COGSQ),minusselling,general,andadministrative expenses (XSGAQ), plus R&D expenditures (XRDQ, zero if missing), minus the change in accounts receivable(RECTQ),minusthechangeininventory(INVTQ),plusthechangeindeferredrevenue(DRCQ+ DRLTQ),plusthechangeintradeaccountspayable(APQ),plusthechangeinaccruedexpenses(XACCQ). Allchangesarequarterlychangesandmissingchangesaresettozero. Wecalculatemonthlyvalue-weighted returns for month m and rebalance the portfolios at the end of month m. The first sort is at the end of December1989. A.3.5 ChangeinROE(monthly) At the end of month m−1, we form portfolios from a decile sort on the change in return on equity (ROE) usingNYSEbreakpoints. ThechangeinROEisthemostrecentROE(seeAppendixA.1.6)minusitsvalue from4quartersago. Wecalculatemonthlyvalue-weightedreturnsformonthmandrebalancetheportfolios attheendofmonthm. ThefirstsortisattheendofDecember1989. A.4 Asset composition A.4.1 Netoperatingassets(annual) AttheendofJuneofyeart,weformportfoliosfromadecilesortonnetoperatingassetsrelativetolagged assets, NOA/A , using NYSE breakpoints. Here, NOA is operating assets minus operating liabilities for −1 thefiscalyearendingincalendaryeart−1andA istotalassets(AT)forthefiscalyearendingincalendar −1 year t −2. Operating assets are total assets minus cash and marketable securities (AT − CHE). Operating liabilitiesaretotalassets(AT)minusdebtincludedincurrentliabilities(DLC,zeroifmissing),minuslongtermdebt(DLTT,zeroifmissing),minusminorityinterests(MIB,zeroifmissing),minuspreferredstocks (PSTK,zeroifmissing),minuscommonequity(CEQ).Wecalculatemonthlyvalue-weightedreturnsfrom JulyofyearttoJuneofyeart+1andrebalancetheportfoliosattheendofJuneofyeart+1. Thefirstsort isattheendofJune1989. 49

A.4.2 Industry-adjustedrealestateratio(annual) AttheendofJuneofyeart,weformportfoliosfromadecilesortonindustry-adjustedrealestateratiousing NYSE breakpoints. A firm’s real estate ratio for the fiscal year ending in calendar year t−1 is the sum of buildingsatcost(FATB)andleasesatcost(FATL)relativetogrossproperty,plant,andequipment(PPEGT). The industry-adjusted real estate ratio is a firm’s real estate ratio minus its industry average. Industries are definedbytwo-digitSICcodes. Toalleviatetheinfluenceofoutliers,wetrimfirms’realestateratiosatthe yearly 1st and 99th percentiles before computing the industry average. We exclude industries with fewer than five firms. We calculate monthly value-weighted returns from July of year t to June of year t+1 and rebalancetheportfoliosattheendofJuneofyeart+1. ThefirstsortisattheendofJune1989. A.5 Payout and financing policy A.5.1 Netpayoutyield(annual) AttheendofJuneofyeart,weformportfoliosfromadecilesortonnetpayoutyield,NPO/M,usingNYSE breakpoints. Here, NPO is net payouts for the fiscal year ending in calendar year t − 1 and M is market equityfromCRSPattheendofDecemberofyeart−1. Netpayoutsaretotalpayoutsminusequityissuances from the cash-flow statement. Total payouts are dividends on common stock (DVC) plus total expenditure on the purchase of common and preferred stocks (PRSTKC) plus any reduction (negative yearly change) in the value of the net number of preferred stocks outstanding (item PSTKRV). Equity issuances from the cash-flowstatementarethesaleofcommonandpreferredstock(SSTK)minusanyincrease(positiveyearly change) in the value of the net number of preferred stocks outstanding (PSTKRV). We exclude firms with non-positive total payouts and firms with zero net payouts. We calculate monthly value-weighted returns fromJulyofyearttoJuneofyeart+1andrebalancetheportfoliosattheendofJuneofyeart+1. Thefirst sortisattheendofJune1989. A.5.2 Netstockissuance(annual) At the end of June of year t, we form 10 portfolios on net stock issuance, NSI, using NYSE breakpoints: FirmswithnegativeNSIaresortedintotwoportfolios(1and2);firmswithzeroNSIareinasingleportfolio (3),andfirmswithpositiveNSI aresortedinto7portfolios(4to10). Here,NSI istheyearlychangeinthe (cid:16) (cid:17) log of split-adjusted shares outstanding from the annual statement, i.e., log CSHO×AJEX . We calculate CSHO−1 ×AJEX−1 monthlyvalue-weightedreturnsfromJulyofyeart toJuneofyeart+1andrebalancetheportfoliosatthe end of June of year t +1. The net stock issuance strategy buys the extreme net-issuers (portfolio 10) and 50

shortsellstheextremenet-repurchasers(portfolio1). ThefirstsortisattheendofJune1989. A.6 Valuation A.6.1 Enterprisemultiple(monthly) At the end of month m − 1, we form portfolios from a decile sort on enterprise multiple, EM, using NYSE breakpoints. Here, EM is enterprise value relative to quarterly operating income before depreciation (OIBDPQ) for the fiscal quarter ending at least 4 months ago. Enterprise value is market equity from CRSP at the end of month m−1 plus total debt (DLCQ + DLTTQ) plus the book value of preferred stock (PSTKQ) minus cash and marketable securities (CHEQ). We exclude firms with negative enterprise value or negative operating income before depreciation. We calculate monthly value-weighted returns for month mandrebalancetheportfoliosattheendofmonthm. ThefirstsortisattheendofDecember1989. A.7 Seasonality A.7.1 Average x-yyearreturnseasonality Attheendofmonthm−1,weformportfoliosfromadecilesortonaveragex-yyearreturnseasonalityusing NYSEbreakpoints. 1. Average2-5yearreturnseasonalityistheaveragereturnacrossmonthsm−24,m−36,m−48,and m−60. 2. Average6-10yearreturnseasonalityistheaveragereturnacrossmonthsm−72,m−84,m−96,m−108, andm−120. 3. Average 11-15 year return seasonality is the average return across months m − 132,m − 144,m − 156,m−168,andm−180. 4. Average 16-20 year return seasonality is the average return across months m − 192,m − 204,m − 216,m−228,andm−240. Wecalculatemonthlyvalue-weightedreturnsformonthmandrebalancetheportfoliosattheendofmonth m. Forinstance,forthe2-5yearreturnseasonalitysortattheendofJune2016,wesortonaveragereturnsfor {July2014,July2013,July2012,July2011};calculatevalue-weightedreturnsforJuly2016,andrebalance theportfoliosattheendofJuly2016. ThefirstsortisattheendofDecember1989. 51

A.8 Insignificant strategies A.8.1 Cashflow-to-price(monthly) At the end of month m−1, we form portfolios from a decile sort on quarterly cash flow-to-price, CF/M, usingNYSEbreakpoints. Here,CF isquarterlytotalcashflowsand M ismarketequityattheendofmonth m−1fromCRSP.Quarterlytotalcashflowsareincomebeforeextraordinaryitems(IBQ)plusdepreciation (DPQ), both for the latest fiscal quarter ending at least 4 months ago. We do not employ the IBQ from the latest earnings announcement date to be consistent with the 4-month lag imposed for DPQ. We calculate monthly value-weighted returns for month m and rebalance the portfolios at the end of month m. The first sortisattheendofDecember1989. A.8.2 Operatingcashflow-to-price(annual) At the end of June of year t, we form portfolios from a decile sort on annual operating cash flow-to-price, OCF/M,usingNYSEbreakpoints. Here,OCF isannualcashflowsfromoperatingactivities(OANCF)for thefiscalyearendingincalendaryeart−1and M ismarketequityfromCRSPattheendofDecemberof year t −1. We only keep firms with positive operating cash flows. We calculate monthly value-weighted returnsfromJulyofyearttoJuneofyeart+1andrebalancetheportfoliosattheendofJuneofyeart+1. ThefirstsortisattheendofJune1989. A.8.3 Inventorychange(annual) AttheendofJuneofyeart,weformportfoliosfromadecilesortoninventorychangeusingNYSEbreakpoints. Inventory change is the change in inventory (INVT) over the fiscal years ending in calendar years t−2 and t−1 relative to the average of total assets (AT) for the fiscal years ending in calendar years t−2 andt−1. Weexcludefirmsthathavezeroinventoryforbothfiscalyearsendingincalendaryearst−2and t−1. We calculate monthly value-weighted returns from July of year t to June of year t+1 and rebalance theportfoliosattheendofJuneofyeart+1. ThefirstsortisattheendofJune1989. A.8.4 Operatingaccruals(annual) At the end of June of year t, we form portfolios from a decile sort on operating accruals using NYSE breakpoints. Operating accruals are net income (NI) minus cash flows from operating activities (OANCF) for the fiscal year ending in calendar year t − 1 relative to total assets (AT) for the fiscal year ending in calendar year t−2. We calculate monthly value-weighted returns from July of year t to June of year t+1 andrebalancetheportfoliosattheendofJuneofyeart+1. ThefirstsortisattheendofJune1989. 52

A.8.5 Changeinnetnon-cashworkingcapital(annual) At the end of June of year t, we form portfolios from a decile sort on the change in net non-cash working capital relative to lagged assets, dWc/A , using NYSE breakpoints. Here, dWc is the change in current −1 operating assets minus the change in current operating liabilities over the fiscal years ending in calendar yearst−2andt−1,while A istotalassets(AT)forthefiscalyearendingincalendaryeart−1. Current −1 operatingassetsaretotalcurrentassetsminuscashandmarketablesecurities(ACT−CHE)andcurrentoperatingliabilitiesaretotalcurrentliabilitiesminusdebtincurrentliabilities(LCT−DLC).Missingchanges indebtincurrentliabilitiesaresettozero. Wecalculatemonthlyvalue-weightedreturnsfromJulyofyeart toJuneofyeart+1andrebalancetheportfoliosattheendofJuneofyeart+1. Thefirstsortisattheend ofJune1989. A.8.6 Changeinnetfinancialassets(annual) At the end of June of year t, we form portfolios from a decile sort on the change in net financial assets relative to lagged assets, dFA/A , using NYSE breakpoints. Here, dFA is the change in financial assets −1 minusthechangeinfinancialliabilitiesoverthefiscalyearsendingincalendaryearst−2andt−1,while A is total assets (AT) for the fiscal year ending in calendar year t − 1. Financial assets are short-term −1 investments plus long-term investments (IVST + IVAO) while financial liabilities are long-term debt plus debt in current liabilities plus preferred stock (DLTT + DLC + PSTK). Missing changes in debt in current liabilities,long-terminvestments,long-termdebt,short-terminvestments,andpreferredstockaresettozero, butwerequireleastonechangetobenon-missingwhenconstructingeachofthechangeinfinancialassets and the change in financial liabilities. We calculate monthly value-weighted returns from July of year t to Juneofyeart+1andrebalancetheportfoliosattheendofJuneofyeart+1. Thefirstsortisattheendof June1989. A.8.7 12monthreturnseasonality At the end of month m − 1, we form portfolios from a decile sort on the return in month m − 12 using NYSEbreakpoints. Wecalculatemonthlyvalue-weightedreturnsformonthmandrebalancetheportfolios at the end of month m. For instance, at the end of June 2016, we sort on returns for July 2015; calculate value-weighted returns for July 2016, and rebalance the portfolios at the end of July 2016. The first sort is attheendofDecember1989. 53

Appendix B B.1 Model This section presents a stylized model of a firm’s cash balances and equity returns in the presence of riskyexternalfinancing. Ourmaingoalistoillustratehowcashbalancesaffectthefractionofafirm’svalue tied to risky external financing and, consequently, equity returns. We introduce risky external financing by assuming a cost of issuing equity that is dependent on the aggregate state of the economy. To emphasize the role of precautionary savings via equity issues, we also assume that the firm cannot rely on internally generatedcashflowsorondebtfinancing. Thelattertwoassumptionsbetterdescribefirmsthatareunable tofinancetheirinvestmentactivitieswithinternallygeneratedcashflowsandhavealowabilitytosubstitute equitywithdebt. B.1 Model setup Our model setup is based on Palazzo (2012), but features stochastic external financing costs and no internallygeneratedcashflows. Weconsideranall-equityfirminathree-periodeconomywithtimeperiods indexed by t = 0,1,2. At t = 0, the firm is endowed with an initial cash balance of c . At t = 1, after 0 therealizationoftheexternalfinancingcost,thefirmhasaninvestmentopportunityconsistingofanoption to install an asset that produces a deterministic cash flow of c at t = 2. The investment bears a fixed 2 cost I, which is known at t = 0. We assume a fixed investment cost to capture the smoothness (i.e., low volatility and low cyclicality) of R&D expenditures (e.g. Brown and Petersen (2011)). To further simplify the analysis, we assume that c is a risk-less cash flow proportional to the investment cost and equal to 2 RIeµ, where µ is a positive constant and R is the gross risk-free rate. We also assume that the firm has no intermediate cash flows in periods 0 and 1. The firm can transfer cash from one period to the next at a grossaccumulationrateofR(cid:98)≥ 0,assumedtobelowerthanthegrossrisk-freeratetopreventanunbounded accumulationofcash. Equityfinancingiscostly. WefollowBeloetal.(2019)andassumethatthecostpaidtoissueanamount (cid:16) (cid:17) E t is eλtQ(E t ), where Q(E t ) = φ 1 E t + φ I 2E t 2 is the issuance cost’s quadratic component (with φ 1 and φ 2 bothpositiveconstants)andeλt isatime-varyingscalingfactor.21 Weassume eλt = eλ−1 2 σ2 x −σxεx,t, (C.1) 21For analytical convenience, we scale the quadratic component of the equity issuance cost by the investment amount. This assumption is consistent with Hennessy and Whited (2007) and allows us to generate equity returns thatareindependentoftheinvestmentscale. 54

where λ and σ are positive parameters and where ε ∼ N(0,1) for each t is an equity issuance shock. x x,t We also assume that λ cannot exceed a maximum value of λ∗ > 0, which is equivalent to assuming a t truncatednormaldistributionfortheequityissuanceshock: −σ ε < ε∗ = λ∗ −λ+ 1σ2. Inaddition, ε x x,t x 2 x x,t is correlated with an aggregate shock, ε , thus making the issuance decision risky. In the following, we z,t assume ε ∼ N(0,1) and COV(ε ,ε ) = σ ≥ 0 for each t. Note that because ε and ε have unit z,t x,t z,t x,z x,t z,t variance,σ isalsotheircorrelation,andwemustalsohaveσ ≤ 1. x,z x,z Cashflowsinperiodtarediscountedbacktot−1usingthestochasticdiscountfactor(SDF) M t = emt = e−r−1 2 σ2 z −σzεz,t, (C.2) where r and σ are positive parameters. This in particular implies that the period 0 expected value of the z period1SDFisgivenbyE [M ] = e−r = 1/R–i.e.,theinverseofthegrossrisk-freerate. 0 1 For a given E , our assumptions imply (i) a non-negative issuance cost that is bounded above; (ii) an t issuancecostdecreasingintheexternalfinancingshock;and(iii)thatafirmwithanexternalfinancingshock morecorrelatedwiththeaggregatestatehasalargerreduction(increase)inexpectedissuancecostinbooms (recessions)thanafirmwithalesscyclicalfinancingcost. B.2 The firm’s problem Given the initial cash balance, c , and the (log) external financing cost, λ , the firm decides how much 0 0 cash to save for period 1, c , so as to maximize the market value of equity. At t = 0, if the firm chooses 1 c ≤ R(cid:98)c ,itdistributesanyexcesscashasadividend. If,however,thefirmchoosesc > R(cid:98)c ,itissuesequity 1 0 1 0 tomeetitscashneeds. Thefirm’sdividendatt = 0isthus (cid:32) (cid:33) (cid:32) (cid:33) c c d = c − 1 +∆ eλ0Q c − 1 , (C.3) 0 0 0 0 R(cid:98) R(cid:98) where∆ isanindicatorfunctionthattakesthevalue1ifc > R(cid:98)c (i.e.,ifthefirmissuesequity). Notethat 0 1 0 eventhoughthefixedinvestmentcostisknownatt = 0,thefirmmayoptimallychoosec < 1becausethe 1 stochasticissuancecostimpliesthatitmaybeoptimaltosmoothissuancesacrossperiods0and1. Inwhatfollows,weassumethatthereturnoninvestmentisgreaterthanthemaximaltotalissuancecost: eµ > 1+eλ∗ (φ +φ ). Underthisassumption,thefirmalwaysinvestsatt = 1. If,att = 1,c ≥ I,thefirm 1 2 1 distributes any excess cash as a dividend, whereas if c < I, the firm issues additional equity to cover the 1 remaininginvestmentcost. Thefirm’sdividendatt = 1isthus (cid:16) (cid:17) (cid:16) (cid:17) d = c −I +∆ eλ1Q c −I , (C.4) 1 1 1 1 55

where ∆ is an indicator variable that takes the value 1 if c < I. Because the investment generates a 1 1 deterministiccash-flowofc att = 2,thecorrespondingdividendisd = c . 2 2 2 Giventheinitialcashbalance,c ,andthe(log)issuanceshock,λ ,thefirm’scum-dividendequityvalue 0 0 at t = 0 is determined by the saving policy, c , that maximizes the present discounted value of current and 1 futuredividends. Becausem andλ arenormallydistributedwithCOV(m ,λ ) = σ σ σ ≡ β,itfollows 1 1 1 1 x z xz fromthepropertiesofthetruncatedlog-normaldistribution(Lemma1inAppendixA)thatwecanwritethe firm’sproblemas (cid:16) (cid:17) v (c ,λ ) = max d +e−r(c −I+eµI)−e−r∆ Q c −I eλ+βΓ, (C.5) 0 0 0 0 1 1 1 c1 ≥0 whereΓ = Φ (cid:18) ε∗ x −σ2 x −β (cid:19) /Φ (cid:16) ε∗ x (cid:17) andwhereΦisthestandardnormalcumulativedistributionfunction. Here, σx σx thefirsttermistheperiod0dividend,thesecondtermisthepresentdiscountedvalueofthenetpayofffrom investment, and the third term is the present discounted value of the expected period 1 total issuance cost. (cid:16) (cid:17) The latter quantity has two components. The first one, Q c − I , is the deterministic quadratic part. The 1 second one, eλ+βΓ, is the expected value of the issuance cost’s scaling factor at t = 1, which depends on thecyclicalityoftheexternalfinancingshock(β). Inwhatfollows,weassumethefollowingnecessaryand sufficientconditionforeλ+βΓtobeincreasinginβ: (cid:18) (cid:19) (cid:18) (cid:19) Condition1. Φ ε∗ x −σ2 x −β > 1 ϕ ε∗ x −σ2 x −β . σx σx σx Condition 1 is satisfied for a wide range of plausible values for the model’s parameters. It ensures that theexpectedissuancecostisincreasinginβ,implyingthatriskierfirmsarelessvaluable. B.3 Optimal savings policy When studying the optimal choice of cash balances in period 1, it is important to distinguish between thefinanciallyconstrainedandthefinanciallyunconstrainedcases. Inthelattercase,cashbalancesarehigh enough to fully cover the investment cost, i.e. R(cid:98)c ≥ I, and the firm never issues equity (∆ = ∆ = 0). In 0 0 1 thiscase,itisalwaysoptimalforthefirmtosaveinternalresourcesuptoc = I anddistributeadividendat 1 t = 0equaltoc −I/R(cid:98)> 0. 0 Theinterestingcaseisthereforewhenthefirmisconstrained,i.e. whenR(cid:98)c < I. Tobetterillustratethe 0 firm’strade-off,wewritedowntheEulerequationimpliedbyEq.(C.5): (cid:16) (cid:17) 1 (cid:34) 1+∆ eλ0 (cid:32) φ +2(cid:98)φ (cid:32) c 1 −c (cid:33)(cid:33)(cid:35) ≤ 1+∆ 1 eλ+βΓ φ 1 +2(cid:98)φ 2 (I−c 1 ) , (C.6) 0 1 2 0 R(cid:98) R(cid:98) R 56

where(cid:98)φ = φ /I. The left-hand side is the present value of the marginal cost of saving an extra dollar of 2 2 cash. If the firm saves less than the available resources (c < R(cid:98)c ), then the marginal cost is constant and 1 0 equalto1/R(cid:98), otherwisethemarginalcostjumpsbyanamountequaltoeλ0φ 1 /R(cid:98)whenc 1 = R(cid:98)c 0 andthenit increaseslinearlyintheamountsaved. The right-hand side is the present value of the marginal benefit of saving an extra dollar of cash. The marginal benefit has two components. The first, 1/R, is the present value of the extra dividend distributed (cid:16) (cid:17) attime1, whichisconstant. Thesecond, ∆ 1eλ+βΓφ1 +2(cid:98)φ2(I−c1) , isthepresentvalueofthereductioninequity R issuancecost,whichislinearlydecreasingintheamountsaved. From the above analysis, it follows that the marginal cost is non–decreasing in c , while the marginal 1 benefit is strictly increasing in c . Then an optimal saving policy with strictly positive c always exists if 1 1 the marginal benefit is larger than the marginal cost when c = 0–that is, 1+eλ+βΓ(φ +2φ ) > R/R(cid:98). In 1 1 2 whatfollows,wewillalwaysassumethatastrictlypositivesavingpolicyexistsbyimposingthefollowing condition: Condition2. 1+eλ+βΓ(φ +2φ ) > R/R(cid:98). 1 2 When the solution is strictly positive, we can have different outcomes, depending on the parameters’ values. First,thefirmcansettheoptimalsavingpolicyto I. Thischoicecanhappenifthemarginalbenefit isveryhigh(e.g.,veryhighβorveryhighλ)orthemarginalcostisverylow(e.g.,verylowλ orveryhigh 0 R(cid:98)). Alternatively, thefirmcansettheoptimal policyequaltoR(cid:98)c . This choicehappenswhenthemarginal 0 benefitisabovetheflatportionofthemarginalcostwhenc ≤ R(cid:98)c butalwaysbelowtheincreasingportion 1 0 whenc > R(cid:98)c . 1 0 Outside the two corner solutions described above, the Euler equation holds with equality and we can betterappreciatetheeffectofequityfinancingriskontheoptimalcashpolicybytakingthetotaldifferential w.r.t. β. Inthiscase,theoptimalsavingpolicyisincreasinginthecyclicalityoftheexternalfinancingshock and,asaconsequence,riskierfirmssavemore.22 Thereasonbeingthathigh-βfirmshavealargerexpected issuancecost(i.e.,ahighereλ+βΓ)and,asaconsequence,alargerprecautionarysavingmotive. In Figure 4, we highlight the importance of the time 0 equity issuance cost in determining the optimal savingpolicy. Wereportthemarginalcost(solidredline)andthemarginalbenefitforalow-riskfirm(solid 22Theclosedformfortheinteriorsolutionis (cid:16) (cid:17) (cid:16) (cid:16) (cid:17)(cid:17) 1+eλ+βΓ φ 1 +2(cid:98)φ 2 I − R 1+∆ 0 eλ0 φ 1 −2(cid:98)φ 2 c 0 c∗ 1 = 2(cid:98)φ (cid:16) ∆ 0Reλ R(cid:98) 0 +eλ+βΓ (cid:17) , 2 R(cid:98)2 whichdependsonissuanceactivityattime0,∆ . Condition1guaranteesthatdc∗/dβ>0. 0 1 57

Figure4. OptimalSavingPolicy Low Average High 1.25 1.25 1.25 MB High Risk MB Low Risk MC 1.2 1.2 1.2 1.15 1.15 1.15 1.1 1.1 1.1 1.05 1.05 1.05 1 1 1 0 0.5 1 0 0.5 1 0 0.5 1 c c c 1 1 1 Thisfigurereportsthemarginalcost(solidredline)andthemarginalbenefitforalow-riskfirm(solidblackline)andahigh-riskfirm(dashedblack line)inEq.(C.6).Thethreepanelsdifferintheirvalueofλ0,namelyforthecostofissuingequityattime0.Theleftpanelhasalowvalue(-0.50), themiddlepanelanaveragevalue(0.00),andtherightpanelahighvalue(0.50).Thecorrelationparameterσxztakesvalues0.00(lowrisk)and0.9 (highrisk).Theotherparameters’valuesare:{R=1.01;R(cid:98)=1.00;φ1 =0.10;φ2 =0.04;λ=0;σx =0.45;σz =0.15;c0 =0.60;I=1}. black line) and a high-risk firm (dashed black line) implied by our model. The three panels differ for their value of λ , namely for the cost of issuing equity at time 0. The left panel has a low value, the middle 0 panel an average value, and the right panel a high value. As explained above, the marginal cost presents a discontinuityatc = R(cid:98)c ,whilethemarginalbenefitismonotonicallydecreasinginc . 1 0 1 When issuing equity at time 0 is very cheap (left panel), the marginal benefit is always larger than the marginal cost and the firm decides to issue equity and save the full investment amount, thus completely avoiding equity issuance in the next period. When issuing equity at time 0 takes an average value (middle panel), then an interior solution exists as described in Equation C.7. In this case, both firms issue equity to save in excess of R(cid:98)c ; however the riskier firm saves more, having a higher risk exposure (i.e., a higher 0 marginal benefit). To conclude, when issuing equity at time 0 is too expensive (right panel), the optimal savingpolicyisdictatedbytheamountofavailableinternalresources,andbothfirmssaveR(cid:98)c . 0 B.4 Cash balances and expected returns Wenowinvestigatethemodel’simplicationsforexpectedequityreturns. Toensurethatthefirmtransfers somecashbetweenperiods0and1,weassumethatCondition2holds. Theexpectedgrossreturnonthefirm’sequitybetweenperiods0and1,Re ,istheratiooftheexpected 0,1 58

futuredividendsatt = 0andtheex-dividendequityvalueatt = 0, E [d +E [M d ] | λ < λ∗] Re = 0 1 1 2 2 1 . (C.7) 0,1 v (c ,λ )−d 0 0 0 0 Wecanimmediatelyverifythatwhentheoptimalpolicyc∗ isequalto I,thentheexpectedreturnisjustthe 1 risk-free rate. This outcome happens when initial cash balances are large (R(cid:98)c > I) or the time 0 equity 0 issuance cost is low. Otherwise, it follows by the properties of the truncated log-normal distribution (Eq. (D.2)inAppendixA)thattheexpectedreturnisgivenby c∗ −I+Ieµ−eλΓ∗Q(I−c∗) −E∗+eµ−eλΓ∗Q(E∗) Re = er 1 1 = er 1 1 , (C.8) 0,1 c∗ −I+Ieµ−eλ+βΓQ(I−c∗) −E∗+1eµ−eλ+βΓQ(E∗) 1 1 1 1 whereΓ∗ = Φ (cid:16) ε∗ x −σ2 x (cid:17) /Φ (cid:16) ε∗ x (cid:17) and E∗ = 1−c∗/I isthefractionoftime1investmentthatisequityfinanced. σx σx 1 1 The quantity eλΓ∗ can be interpreted as the expected scaling factor when β = 0–that is, for a firm with an issuancecostthatisuncorrelatedwiththeSDF.Giventheassumption(cid:98)φ = φ /I,expectedequityreturnsare 2 2 scale-independent. What drives the firm-level exposure to systematic risk is the fraction of cash relative to theinvestmentexpenditure. Inwhatfollowsweshowthatthelargerthefractionofthetime1investmentthat isequityfinanced,thelargertheexposuretoequityfinancingrisk(i.e.,thelargerexpectedequityreturns). WecanimmediatelyshowthatRe dependsnegativelyontheinitialcashbalancec ifeβΓ > Γ∗,namely 0,1 0 if the expected value of the scaling factor is higher for a firm with a risky issuance cost (β > 0) compared with a firm with an issuance cost that is uncorrelated with the aggregate economy (β = 0). Condition 1, which guarantees optimal cash balances will be declining in β, implies eβΓ > Γ∗, and hence it is also sufficienttoguaranteethatfirmswithhighercashbalancesrelativetotheirinvestmentcostcommandlower expectedreturns. Our stylized model introduces heterogeneity in risk driven by heterogeneity in the amount of internal resources relative to the investment expenditures. Figure 5 provides an illustration. We report the optimal savingpolicyc∗ (leftpanel)andexpectedequityreturns(rightpanel)asafunctionofcashbalancesattime 1 0 (c ) for two firms that are identical except for their cost of external financing at time 0. The right panel 0 shows how firms with larger c deliver a lower expected return, every thing else being equal. The reason 0 being that the higher c , the higher the amount that can be saved, the lower the firm’s value tied to costly 0 equityissuance,andthelowerthecovarianceofthefirm’sequityvaluewiththeaggregateshock. Atthesametime, Figure5makesclearthatthetime0equityissuancecostplaysakeyroleinshaping differences in equity returns. If two firms are identical except for their value of λ , then they can deliver 0 different expected returns. A firm with a low cost of issuing equity (solid black line) can raise equity and savecash,thusloweringtheexposuretotheequityissuanceshock. Afirmwithahighcostofissuingequity 59

Figure5. CashandReturns Optimal Saving Policy Expected Return (%) 1 1.8 Low λ High λ 0 0 0.9 1.7 0.8 1.6 0.7 1.5 0.6 1.4 0.5 1.3 0.4 1.2 0.3 0.2 1.1 0.1 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 c c 0 0 Thisfigurereportstheoptimalsavingpolicyc∗ 1 (leftpanel)andexpectedequityreturns(rightpanel)asafunctioncashbalancesattime0(c0).The solidblacklinereferstoafirmwithlowtime0issuancecost(λ0 =−0.25),whilethesolidredlinereferstoafirmwithhightime0issuancecost (λ0 = 0.25). Thedashedredlineintheleftpanelisthe45-degreeline. Theotherparameter’svaluesare: {R=1.01;R(cid:98)=1.00;φ1 =0.10;φ2 =0.04; λ=0;σx =0.45;σz =0.15;σxz =0.90;I=1}. (solidredline)saveslessandcarriesmorerisk,hencedeliveringahigherexpectedreturn. Notsurprisingly, thedifferentialinreturnsbetweenthetwofirmsshrinksastheamountofinitialresourcesbecomesbigger. B.5 Empirical predictions Our stylized model provides a number of novel predictions that link a firm’s financial policy to its expectedequityreturns. Prediction 1. A firm with high cash balances relative to its investment expenditures (i.e., a firm with a large investment coverage ratio) has a lower expected return than an otherwise identical firm with lower cashbalances. Prediction2. Equityissuancelowersafirm’sexpectedreturnbyreducingtheexposuretoequityfinancingriskviaanincreaseinthecoverageratio. Prediction 3. The above predictions crucially depend on firms being financially fragile (e.g., low cash balances, low profitability, high equity issuance cost). If this is not the case, then there is low exposure to equityfinancingriskand,consequently,weakereffectsofthecoverageratioandequityissuanceactivityon equityreturns. 60

Appendix D D.1 Properties of the truncated log-normal distribution Lemma1. Suppose X ∼ N(µ ,σ2)andY ∼ N(µ ,σ2)withCOV(X,Y) = σ . Then x x y y xy (cid:18) (cid:19) Φ y−µy −σ2 y −σxy E (cid:104) eX+Y (cid:12) (cid:12) (cid:12)Y < y (cid:105) = eµx +µy + 2 1(σ2 x +σ2 y +2σxy) (cid:18) σy (cid:19) Φ y−µy σy foranyy ∈ R,whereΦisthestandardnormalcumulativedistributionfunction. ProofofLemma1. Westartwiththreeauxiliaryresults. Inthefollowing,letZ andZ beindependent 1 2 N(0,1)-distributedrandomvariables,andleta,b,c,z ∈ Rberealconstants. First,afundamentalpropertyofthelog-normaldistributionisthat (cid:104) (cid:105) E ea+bZ1 = ea+1 2 b2 . (D.1) Second,directcomputationgivesthat (cid:104) (cid:105) E (cid:104) ecZ2 (cid:12) (cid:12) (cid:12)Z 2 < z (cid:105) = E P e ( c Z Z21 < (Z2 z < ) z) 2 1 (cid:90) z 1 Φ(z−c) = ecz(cid:48) √ e−1 2 (z(cid:48))2 dz(cid:48) = e 1 2 c2 . (D.2) Φ(z) −∞ 2π Φ(z) Third,usingtheindependenceofZ andZ andapplyingEqs.(D.1)and(D.2),itfollowsthat 1 2 (cid:104) (cid:12) (cid:105) Φ(z−c) E ea+bZ1 +cZ2 (cid:12) (cid:12)Z 2 < z = ea+ 2 1b2+1 2 c2 Φ(z) . (D.3) Toprovethelemma,notethatwecanwriteX andY intermsoftheindependentZ andZ as 1 2 (cid:113) X = µ +σ 1−ρ2 Z +σ ρ Z and Y = µ +σ Z P-almostsurely, x x xy 1 x xy 2 y y 2 whereρ = σxy isthecorrelationbetween X andY. ThelemmathenfollowsfromEq.(D.3)with xy σxσy (cid:113) a = µ +µ , b = σ 1−ρ2 , c = σ ρ +σ , and z = y−µy. x y x xy x xy y σy (cid:3) 61