The Rodney L. White Center for Financial Research. The Book-to-Price Effect in Stock Returns: Accounting for Leverage

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1 The Rodney L. Whie Cener for Financial Research The Book-o-rice Effec in Sock Reurns: Accouning for Leverage Sephen H. enman Sco A. Richardson Irem Tuna 05-05

2 The Book-o-rice Effec in Sock Reurns: Accouning for Leverage * Sephen H. enman George O. May rofessor of Accouning Columbia Universiy - Deparmen of Accouning 3022 Broadway New York, NY h: shp38@columbia.edu Sco A. Richardson Assisan rofessor of Accouning 1314 Seinberg Hall Dierich Hall Wharon School Universiy of ennsylvania, A, h: scoric@wharon.upenn.edu İrem Tuna Assisan rofessor of Accouning 1312 Seinberg Hall Dierich Hall Wharon School Universiy of ennsylvania, A, h: unaai@wharon.upenn.edu Augus 2005 *We appreciae commens received a seminars a The Universiy of ennsylvania, Columbia Universiy, SUNY Buffalo, Nore Dame Universiy, Barclays Global Invesors, Universiy of New Souh Wales, he 2005 EFMA annual meeing, and hose offered by Andrew Ang, eer Eason, Nicholas Gonedes, Rober Holhausen, Charles Lee, Oliver Li, Tjomme Rusicus, Cahy Schrand, Tom Sober, and Moo Yogo.

3 The Book-o-rice Effec in Sock Reurns: Accouning for Leverage Absrac: This paper lays ou a decomposiion of book-o-price (B/) ha ariculaes precisely how B/ absorbs leverage. The B/ raio can be decomposed ino an enerprise book-o-price (ha perains o operaions and poenially reflecs operaing risk) and a leverage componen (ha reflecs financing risk). The empirical analysis shows ha he enerprise book-o-price raio is posiively relaed o subsequen sock reurns bu, condiional upon he enerprise book-oprice, he leverage componen of B/ is negaively associaed wih fuure sock reurns. Furher, boh enerprise book-o-price and leverage explain reurns over hose associaed wih Fama and French nominaed facors including he book-o-price facor albei negaively so for leverage. The seemingly perverse finding wih respec o he leverage componen of B/ survives under conrols for size, esimaed bea, reurn volailiy, momenum, and defaul risk.

4 The Book-o-rice Effec in Sock Reurns: Accouning for Leverage Fama and French (1992) observe ha book-o-price raios (B/) are posiively correlaed wih subsequen sock reurns, a relaion ha has come o be known as he book-o-price effec. In response o his empirical regulariy, hey specify an asse pricing model, in Fama and French (1993, 1996), ha includes risk facors idenified wih B/, CAM bea, and he marke value of equiy (size). The nominaion of B/ as a feaure ha loads on a risk facor is enaive, no only because i is based on empirical analysis raher han heory, bu also because he empirical observaion can be aribued o marke mispricing raher han he pricing of risk; as Fama (1970 and 1998) explains, he inerpreaion of he B/ effec as raional pricing of risk (marke efficiency) or abnormal reurns o mispricing (marke inefficiency) canno be resolved wihou he specificaion of a model of expeced reurns. 1 Researchers have no ye agreed upon such a model. However, one aspec of asse pricing is agreed upon. An elemenary noion in finance views equiy risk (and expeced reurns o equiy) as deermined by operaing risk arising from firms business operaions (oherwise called firm risk, enerprise risk, business risk, or asse risk) and financing risk arising from borrowing ha leverages equiy invesmen in business operaions. While research has no ye idenified credible measures of operaing risk ha are consisen wih heory and robusly suppored by he daa, here is lile disagreemen abou he appropriae measure of leverage and he reurns associaed wih i. Given operaing risk, average reurns are increasing in leverage, wih leverage measured as he marke value of deb o he marke value of equiy (so-called marke leverage). The relaionship, founded on no-arbirage assumpions, is formalized in Modigliani and Miller 1 A number of papers have challenged he Fama and French inerpreaion of book-o-price as a risk characerisic. See, for example, Lakonishok, Shleifer and Vishny (1994), Daniel and Timan (1997). 1

5 (1958), bu he noion ha borrowing adds risk and expeced reurn is such a common sense one ha any observaion o he conrary would be deemed o be anomalous. In his paper we separae he leverage componen of he B/ raio peraining o financing risk from he componen ha perains o operaions and poenially o operaing risk and indeed observe an anomalous finding wih respec o he leverage componen. The difference beween he price and book value of equiy, B, is no affeced by leverage if deb is measured a marke value on he balance shee (which in mos cases is a reasonable approximaion); he difference beween price and book value is due raher o he pricing of business operaions, and hus any risk indicaed by he difference is due o operaing risk. However, he raio, B/, is affeced by boh operaing and financing aciviies (we show), and invesing in socks on he basis of heir B/ raios involves buying boh operaing and financing risk if indeed risk is he explanaion for he B/ effec. The paper presens an expression ha decomposes he B/ raio ino operaing and financing componens. The firs he book value of ne operaing asses divided by heir marke value serves as a proxy for operaing risk under he risk explanaion of he B/ effec. The second ne deb divided by he marke value of equiy is he generally acceped measure of leverage if deb on he balance shee is measured a marke value and marke prices are efficien. We find ha he operaing componen is posiively relaed o subsequen sock reurns, consisen wih boh risk and abnormal reurn explanaions. However, given he operaing componen, he leverage componen does no add o average reurns. Indeed, leverage is negaively associaed wih reurns, a resul ha is eviden for boh high and low B/ raios. The negaive correlaion survives wih conrols for conjecured operaing risk proxies wih which leverage may be negaively correlaed. The finding violaes a basic undersanding of how leverage should be 2

6 priced and poins eiher o an incomplee represenaion in common asse pricing models or o a mispricing of leverage (and, by implicaion, a mispricing of firms operaions). The negaive correlaion beween leverage and reurns survives wih conrols for facor reurns in popular pricing models, including hose for he book-o-price facor which Fama and French mainain absorbs leverage. Indeed, he enerprise book-o-price componen of B/, as well as he leverage componen, also explains reurns incremenal o facor reurns. The resuls hus indicae ha he book-o-price effec obscures a more complicaed relaionship beween reurns and he componens of B/. The paper is moivaed by he observaion ha, given marke efficiency, he B/ raio is inrinsically an accouning phenomenon; ha is, on firs order, B/ is deermined by how accounans measure book value raher han risk. If all asses and liabiliies were accouned for using unbiased mark-o-marke or fair value accouning, B/ raios would be equal o uniy for all levels of risk, (and he B/ raio could no indicae risk). A pure invesmen fund where ne asse value ypically equals marke value is a case in poin, for accounans apply mark-omarke accouning o hese funds. Boh a risky hedge fund and a money marke fund have he same B/, irrespecive of heir risk. For mos oher firms, accounans do no mark he ne asses involved wih operaions o marke. The applicaion of hisorical cos accouning, exacerbaed by he applicaion of conservaive accouning, inroduces a difference beween price and book value. 2 Be ha as i may, i mus be ha, if he B/ affec is due o risk, ha risk is capured by he applicaion of he accouning. Accordingly, accouning explanaions mus be brough o he 2 Typically hisorical cos accouning resuls in price being greaer han book value, wih more conservaive accouning yielding lower B/ raios. However, in cases where accounans fail, as required under GAA, o impair (wrie-off) asses whose value has declined below heir carrying values, he accouning can produce higher B/ raios. 3

7 examinaion of he B/ effec. This paper brings he accouning for financing aciviies -- where carrying values approximae marke value -- o he invesigaion of he B/ effec. 1. B/ Raios and Leverage Balance shees repor asses and liabiliies employed in operaions and asses and liabiliies involved in financing aciviies. The B/ raio applies a valuaion muliple o he balance shee and hus o boh he operaing and financing componens on he balance shee. However, he muliple differs for he wo ypes of aciviies. The following resaes he balance shee o disinguish operaing and financing asses and liabiliies: Balance Shee Operaions OA OL Financing FL FA ND B ND + B The book value of operaions is ne operaing asses (), he difference beween asses involved in operaions (OA) and liabiliies involved in operaions (OL). Operaing liabiliies (such as accouns payable, deferred revenues, pension liabiliies, and accrued expense liabiliies) arise from rading wih cusomers and suppliers in he course of operaions raher han borrowing in he capial marke o raise cash for operaions. The number is someimes referred o as he book value of he firm or enerprise book value. The book value of ne deb (ND) is he difference beween financing liabiliies arising from borrowing, (FL) and financial asses (FA) ha sore excess cash in ineres bearing deposis and securiies ( cash ). The balance shee 4

8 accouning equaion equaes he book value of equiy (B) o he difference beween ne operaing asses and ne deb: B = ND. Ne deb can be negaive if deb owned is greaer han deb owed; ha is, he firm is a ne credior raher han a ne debor. Indeed ne operaing asses can be negaive (hough rarely) if operaing liabiliies are in excess of operaing asses. Corresponding o he balance shee equaion, he equiy price () is equal o he difference beween he price of he operaions (enerprise value) and he price of he ne deb: = ND (This of course recognizes ha he marke value of he firm is equal o he marke value of he equiy plus he marke value of he ne deb.) Accordingly, he difference beween equiy price and book value is: ND ( ) ( ND) B =. If ne deb is carried on he balance shee a marke value, hen he difference beween he price of equiy and book value of equiy is due solely o he difference beween he price of he operaions and he book value of he operaions which accounans ypically measure ne asses a amorized hisorical cos raher han heir marke value: B = The book value of ne deb ypically approximaes is marke value. Under FASB Saemen No.115, many deb asses are required o be marked o marke (hough only in he las en years). Deb liabiliies are ypically close o marke value; supplemenal disclosures of he marke value of deb, required in he foonoes under FASB Saemen No.107, are indeed usually close o carrying values. The approximaion is assumed in he applicaion of discouned cash flow mehods of valuaion, where i is convenional o ake he book value of deb as is marke value (and subrac ha book value from he discouned cash-flow valuaion for he firm in calculaing equiy value). For fixed-rae deb, he approximaion is suspec if ineres raes or 5

9 credi qualiy have changed significanly. Our empirical analysis may be affeced, so in Secion 4 we address his issue. 3 While he difference beween price and book value may no be affeced by leverage, he raio of book value o price, B/ is. As B = ND, hen B = ND ND =. If ND is measured a marke value such ha = ND ND and = 1, hen ND = 1+ and B Rearranging, ND ND = 1 +. B ND = + 1 (1) Tha is, he B/ raio is a weighed average of he enerprise book-o-price raio, and he book-o-price raio for financing aciviies (which is uniy), and his weighed average can be expressed in he form of a leveraging equaion (1). In buying B/, one is buying he unlevered, enerprise B/, (ha is due o price being differen from book value) along wih some leverage (ha does no affec he difference beween price and book). Effecively one is buying 3 The formulaion implicily assumes ha operaing and financing aciviies are separable (hey do no generae value joinly), as is sandard. Coningen (off-balance) liabiliies ypically have zero value assigned on he balance shee, bu hese usually concern operaions. The deb of financial firms (ha add value on he spread beween borrowing and lending raes) may no be a marke value, bu our analysis excludes hese firms. 6

10 an enerprise B/ and levering he posiion. So, if expeced sock reurns associaed wih he B/ effec are rewards for risk, hose rewards are associaed wih operaing risk as measured by, he firs componen of (1), and/or addiional financial risk deermined by marke leverage, ND in he second componen of (1). Equaion (1) insrucs ha leverage inroduces a non-linear relaionship beween he (levered) B/ and he enerprise book-o-price. If he enerprise book-o-price raio is greaer han 1.0, he B/ raio increases in leverage, and he B/ raio is higher han he enerprise book-oprice if leverage is posiive (ND > 0), bu lower if leverage is negaive (ND < 0). If he enerprise book-o-price raio is less han 1.0, he B/ raio decreases in leverage, and he B/ raio is lower han he enerprise book-o-price raio if leverage is posiive, bu higher if leverage is negaive. Accordingly, if one buys a share wih B/ > 1.0, one migh be buying a share wih a relaively high enerprise book-o-price and posiive leverage, or one wih a relaive low enerprise booko-price and negaive leverage. Correspondingly, if one buys a share wih B/ < 1.0, one migh be buying a share wih a relaively high enerprise book-o-price and negaive leverage or a relaively low enerprise book-o-price wih posiive leverage. Indeed, in buying a share wih B/ > 1.0 (ha Fama and French 1992 repor ypically yields a higher reurn in he daa), one migh be buying a share where enerprise book value is acually less han enerprise price, bu leverage is negaive. In buying a share wih relaively low B/ < 1.0 (ha ypically yields a lower reurn in he daa), one migh be buying a share where enerprise book value is acually greaer han enerprise price, bu leverage is negaive. In shor, he analysis begs he quesion as o he exen o which he B/ effec is a leverage effec or an effec associaed wih he difference beween price and book value due o he accouning for operaions. 7

11 The formulaion ariculaes he conjecure in Fama and French (1992) ha B/ absorbs leverage. In a sense, his is so, bu he subleies of he relaionship beween B/ and leverage are brough o he fore. Mos imporanly, he analysis sresses ha differences beween price and book value do no arise from leverage, and in aribuing expeced sock reurns o book-o-price, one mus disinguish he leverage effec in he B/ raio from ha aribuable o he measuremen of ne asses used in operaions. Clearly, he size of he enerprise B/ raio and he amoun of leverage purchased wih high or low B/ raios depends on he correlaions beween he wo in he cross secion. We documen hese correlaions in Secion 2. If sock reurns are explained by a difference beween price and book, hey should be explained by he enerprise book-o-price, ha is, he B/ raio sripped of he leverage componen (ha does no involve a difference beween price and book value). If he enerprise book-o-price raio measures operaing risk, is relaionship wih subsequen reurns should be posiive. Furher, if for a given level of enerprise book-o-price, he invesor adds he leverage componen of B/, he leverage should add o he expeced reurn if he marke is pricing operaing risk and financing risk appropriaely. We es hese predicions in Secion Relaionships Beween Levered and Unlevered B/ Raios, Marke Leverage and Sock Reurns 2.1 Daa and Calculaion of Variables We obained our daa from wo sources. Our financial saemen daa is from COMUSTAT and sock reurns are from CRS. Our sample includes all firm-year observaions, excluding he financial services indusry (in SIC codes ), wih available daa from

12 We require he following daa iems o be available for a firm-year o be included in our analysis: oal asses (Compusa daa iem #6), income before exraordinary iems (Compusa iem #18), common shares ousanding (Compusa iem #25), book value of common equiy (Compusa iem #60), and sock price a he end of he fiscal year (Compusa iem #199). Oher variables are se equal o zero if hey are missing, bu our resuls are no sensiive o his reamen. 4 Our variable calculaions follow Nissim and enman (2001). B/ is calculaed as he raio of book value of common equiy (B) o he marke value of common equiy (). B is Compusa s common equiy (Compusa iem #60) plus any preferred reasury sock (Compusa iem #227) less any preferred dividends in arrears (Compusa iem #242,), and is measured a he end of he fiscal year. is he number of common shares ousanding (Compusa iem #25) muliplied by he sock price a he end of he fiscal period (Compusa iem #199). The adjusmen for preferred reasury sock and preferred dividends in arrears is necessary o ensure a clean disincion beween common equiy (o which he price, applies) and all oher financing, bu excluding his adjusmen does no affec our resuls. For he measure of financial leverage, ND, ND is he difference beween financial liabiliies (FL) and financial asses (FA). FL is he sum of long erm deb (Compusa iem #9), deb in curren liabiliies (Compusa iem #34), carrying value of preferred sock (Compusa iem #130), preferred dividends in arrears (Compusa iem #242), less preferred reasury sock (Compusa iem #227). FA is cash and shor-erm invesmens (Compusa iem #1). 5 4 In paricular, resuls were similar when 0.4% of he sample was removed because long-erm deb (Compusa iem # 9) was no available. 5 Even hough some ineres-bearing securiies (ha migh be considered as excess cash ) are included in Compusa Iem #32, Invesmen and Advances-Oher, we canno include hese in FA due o daa limiaions. This COMUSTAT daa iem also includes equiy securiies ha are usually par of operaions, along wih various oher 9

13 The enerprise book-o-price raio,, is measured as he raio of he book value of ne operaing asses () o he marke value of ne operaing asses ( ). is he sum of book value of common equiy and ne deb (ND), boh as defined above, by he balance shee ideniy. Similarly,, he marke value of ne operaing asses, is he sum of ND and as defined above. 6 Firms wih negaive values for and are included in our porfolio level analyses bu are excluded from our regression analyses. To minimize he influence of ouliers, we also delee he exreme perceniles of he following variables in he regression analysis: B/, ND/, /, B/ - /. This yields 132,678 firm-year observaions for he porfolio analysis and 120,753 firm-year observaions for he regression analysis. 2.2 Basic Correlaions anel A of Table 1 repors buy-and-hold reurns for 13 porfolios formed by ranking firms each year by heir (levered) B/ raios. 7 Reurns are size-adjused o absrac from he so-called size effec, and include delising reurns. Resuls using marke-adjused reurns are similar. The op (unnumbered) porfolio conains firms wih negaive book values. orfolios 1 10 are decile groups for firms wih posiive book values, wih he exreme deciles spli ino wo o idenify he op and boom 5 percen, in porfolios 1a and 10b. Reurns cover he 12-monh period beginning iems such as long-erm receivables. Many (available-for-sale) equiy securiies are marked o marke so, in unrepored analyses, we have also measured FA including Compusa Iem #32. The resuls are similar. Some par of cash should be idenified as operaing cash, bu he allocaion o operaing cash is problemaic, varies over indusries (and is presumably quie small). 6 Sricly, = B + ND + minoriy ineres and = + ND + value of minoriy ineres. The book value of minoriy ineres ypically is no carried a marke value, so our calculaions of and include minoriy ineres. This is appropriae if minoriy ineres is no carried a marke value for we wish ND o conain iems whose carrying values are a marke value. 7 The cu-offs for deermining porfolios were he deciles from he ranking in he previous year (o avoid any lookahead bias). 10

14 four monhs afer fiscal-year end when accouning daa for mos firms have been published. 8 The reurn numbers in he able are means for each year in he sample period. The difference in reurns over porfolios in anel A confirms he B/ effec. The panel also shows ha (levered) B/ is highly correlaed wih unlevered, enerprise book-o-price, ; a ranking of B/ is indeed a ranking on he difference beween price and book value ha perains o he operaing aciviies. The spread on he enerprise book-o-price is however, smaller han ha for B/; for all porfolios excep 10a, mean is closer o uniy han he corresponding B/. Leverage is he explanaion, by consrucion in leveraging equaion (1), for i is clear ha high B/ have considerably higher leverage, ND, han low B/. In buying a high B/, one is ypically buying a high bu one is also buying leverage risk. Indeed, he means of B/ - in he las column in anel A, explained by he las erm in (1), explicily make he poin. anel B of Table 1 documens mean reurns associaed wih differen levels of enerprise book-o-price. The firs hree groups conain firms wih negaive ne operaing asses, negaive enerprise prices, or boh. These firms ypically have low B/ (and low leverage) bu yield relaively high reurns, inconsisen wih he general enor of he B/ effec. (The high reurns 9 For firms ha are delised during our fuure reurn window, we calculae he remaining reurn by firs applying CRS s delising reurn and hen reinvesing any remaining proceeds in he size mached porfolio (where size is measured as marke capializaion a he sar of he reurn cumulaion period). This miigaes concerns wih poenial survivorship biases. Firms ha are delised for poor performance (delising codes 500 and ) frequenly have missing delising reurns (see Shumway 1997). We conrol for his poenial bias by applying delising reurns of 100% in such cases. Our resuls are qualiaively similar if we make no such adjusmen. We have replicaed our analyses using welve-monh buy-hold reurns ha sar six monhs afer he end of he year (i.e. for a December year end firm, our reurn inerval would sar on July 1 of he following year). This caers o cases where annual financial repors were no published wihin four monhs. Our resuls are virually idenical wih his more conservaive reurn window. 11

15 associaed wih negaive enerprise prices are consisen wih he common wisdom among fundamenal invesors ha a firm wih a sock price less han is ne cash is a good buy.) For firms wih posiive enerprise prices and book values, i is clear ha ranks reurns in he direcion consisen wih a book-o-price effec. However, wih he excepion of exremely high in porfolio 10b where leverage is somewha lower, he reurns are also idenified wih leverage, for leverage is posiively correlaed wih. anel C of Table 1 repors reurns o leverage, ND. Srikingly, here is no a srong associaion beween leverage and average reurns, conravening he noion ha financing risk should be rewarded wih higher reurn. High leverage porfolios (8-10b) have higher reurns han porfolios wih low bu posiive leverage (4-6), alhough he differences are no sriking, bu firms wih negaive leverage in porfolios 1 and 2 (holding considerable cash) have higher reurns han highly levered firms. Mean (size-adjused) reurns for porfolios 8 10b are negaive, even hough hese porfolios exhibi high leverage and high enerprise book-o price, boh purporedly risk facors ha should be rewarded wih higher reurn. Finally, anel D of Table 1 repors mean reurns associaed wih he difference beween he levered and enerprise book-o-price raios, B/ -, ha is, he amoun by which B/ differs from because of leverage, given by he las erm in he equaion (1). This leverage componen of B/ ranks B/ and also ranks reurns. However, he difference is no srongly correlaed wih (also eviden in anel B), a correlaion ha one would expec if he 12

16 differences in porfolio reurns here are explained by differences beween price and book value raher han leverage. is higher for porfolios 10a and 10b, bu so is leverage. We esimae he incremenal reurns associaed wih each componen of he leveraging equaion (1) in he nex secion. Correlaions beween he componens of course come ino play. Some of hose correlaions are eviden in Table 1. As a prelude o he nex secion, Table 2 provides a complee se of Spearman and earson correlaion coefficiens beween B/,, ND, and he leverage componen of he B/ raio, B/ -. Esimaed bea, size [measured as ln(marke value of equiy)], and boh raw and size-adjused reurns are also included. The correlaions are repored for greaer han or equal o one (anel A) and less han one (anel B), as dicaed by he equaion (1). For Spearman correlaions we use he full sample of raw daa (i.e., no reamen for ouliers) consising of 132,678 firm-year observaions. For earson correlaions we use he reduced sample of 122,371 firm-year observaions afer runcaing ouliers (as described in secion 2.1). The repored correlaions are means of annual correlaion coefficiens wih -saisics based on he ime series variaion of hese annual esimaes. While he leveraging equaion deerminisically gives he relaionship beween B/ and leverage, ND for a given firm, he relaionship beween he wo in he cross secion depends on he correlaion beween and leverage. For 1 he correlaion beween B/ and leverage posiive Spearman correlaion and for he earson -- as equaion (1) 13

17 suggess, bu he negaive correlaion beween and leverage means ha leverage effec is smaller he higher is. Accordingly he correlaion beween B/ and B/ - is high while ha beween and B/ - is low. While equaion (1) indicaes ha leverage reduces he B/ raio relaive o he enerprise book-o-price raio if he enerprise raio is less han one, he rank correlaion beween B/ and leverage for < 1 is posiive (0.127 Spearman and earson). This is explained by he posiive correlaion beween and leverage. Overall in Table 2, he correlaions beween B/ and B/ - indicae ha, because of he ineracion beween ND and in he leveraging equaion (1), he more exreme he B/, high or low, he more he B/ is explained by leverage Decomposing Book-o-price and Leverage Effecs in Sock Reurns The noion ha sock reurns reward operaing and financing risk can be formalized in a way ha incorporaes he leverage measure, ND. By he cash conservaion equaion, d = FCF F in every period, where d is ne dividends o shareholders, FCF is free cash flow from operaions and F is (ne) cash paid o ne debholders. Accordingly, if ne deb is measured a marke value such ha = - ND, he expeced sock reurn for period +1is E [ d ] = E[ + FCF ) ( ND + F ND )] ( Fama and French (1992) and Rajan and Zingales (1995) repor posiive correlaions beween B/ and leverage (variously measured), bu wihou condiioning on he enerprise book-o-price raio. 14

18 Tha is, he expeced reurn o equiy is equal o he expeced reurn for operaions (he enerprise reurn) minus he expeced reurn o he ne deb holders. The expeced equiy rae of reurn is hus given by E d FCF + 1 ND ND+ 1 + F + = E E ND 1 ND Tha is, as ND = 1, he expeced equiy reurn is a weighed average of he expeced reurn o operaions and he expeced reurn o ne deb. 10 Denoing raes of reurn for equiy, he enerprise, and deb as R, R equiy reurns, as follows:, and ND R, respecively, i follows ha leverage adds o expeced ND ND [ R ] E[ R ] + E[ R R ] E = (2) This formulaion is, of course, he sandard WACC formula, bu he derivaion is replicaed here o show ha his weighed average can be expressed as a leveraging equaion (2) similar in form o (1) (which is a saemen ha B/ is a weighed average of he enerprise book-o-price raio and he book-o-price raio of uniy for ne deb). airing he equiy reurn in equaion (2) wih he B/ leveraging equaion (1), i is clear ha, if B/ is a risk measure ha indicaes expeced equiy reurns, i imbeds operaing risk, indicaed by, ha perains o [ ] E R 1 ND +, and a leverage componen, 1 ND ND ha perains o he reurn premium for financing risk, E[ R R ]. Sock raes of Noe ha, given he effecive ineres accouning mehod for ne deb, cash flows o deb holders, F, reduce he book value of ne deb dollar for dollar; hus E[ND +1 + F +1 ] and he expeced reurn o deb is no affeced by cash flows o deb holders. Accouning mainains his condiion wih he effecive ineres mehod. 15

19 reurn and B/ raios are denominaed in he same beginning-of-period price. We examine how book values, decomposed ino operaing and financing componens (and denominaed in he same price), explain forward sock reurns (denominaed in he same price). No only does equaion (2) say ha leverage adds o expeced reurns bu also, for a given leverage, he financing reurn premium is increasing in expeced reurns from operaions (provided hese are greaer han he expeced reurn o deb). Accordingly, he ineracion beween ND and -- ha levers boh he B/ raio and reurns -- is of ineres. We firs examine how he operaing and financing componens of B/ explain differences in reurns by regressing forward reurns on he componens in cross-secion. We hen repor he resuls of facor regressions where porfolio reurns represening payoffs o he B/ componens are adjused for heir sensiiviy o reurns associaed wih facors nominaed in exan asse pricing models as rewarding (operaing and financing) risk o invesing in equiies. 3.1 Characerisic Regressions Wih he preense ha enerprise book-o-price is a risk characerisic, we specify a regression equaion: R ND + 1 = α + λ1 + λ L ε where he ellipsis indicaes omied, unidenified firm characerisics oher han ha perain o operaing risk. In absence of a credible asse pricing model, inclusion of such characerisics wih perhaps he excepion of bea is arbirary. Indeed, he inclusion of is speculaion. In conras, inclusion of leverage is jusified by leveraging equaion (2). 16

20 Given he risk explanaion for he B/ effec, λ 1 and λ 2 are prediced o be posiive. Table 3 repors resuls from esimaing annual cross-secional raw-reurn regression equaions ha include ND,, and he difference beween B/ and /, along wih oher measures ha appear in popular empirical pricing models. Regressions exclude firms wih negaive ne operaing asses and negaive enerprise prices (for which mean reurns are repored in Table 1). 11 Independen variables are runcaed a he 1s and 99 h percenile, bu resuls are no paricularly sensiive o his cuoff. Esimaes are made for each year in he sample period wih means over years repored in he able, along wih -saisics (in parenheses) esimaed from he ime-series of coefficiens. Resuls are repored for he full sample in anel A and for greaer han or equal o one and less han one in anels B and C. The B/ effec is confirmed by regression I. When is alone in regression II, i yields a posiive mean esimaed coefficien, consisen wih a risk explanaion bu also consisen wih marke mispricing. When leverage, ND is alone in regression III, he mean esimaed coefficien is no significanly differen from zero in all hree panels and negaive in anels B and C. This is surprising, given leverage adds o expeced reurns, bu could be explained by a negaive correlaion beween leverage and operaing risk. Indeed, for > 1, leverage and are negaively correlaed in Table 2. However, for < 1, he wo are posiively correlaed, ye leverage does no explain cross-secional differences in reurns. 11 Resuls in Table 3 are similar for size-adjused reurns. 17

21 This resul is sriking. Furher, wih boh ND and in regression V (and hence a conrol for supposed operaing risk), he coefficien on he leverage variable is negaive in all hree panels and significanly less han zero in anel A and also in anel C covering he 74.4% of observaions in he sample ha have less han uniy. 12 Regression VII splis ne deb ino financial liabiliies (FL) and financial asses (FA) and repors ha, again conrary o expecaion, he coefficien of financial liabiliies (deb) is negaive, while ha on financial asses is posiive (in all hree panels); FA FL, raher han, is rewarded wih a reurn premium. 13 Resuls afer including he difference beween he levered B/ and he enerprise book-oprice in regression VI add o he mysery. For all firms pooled in anel A, his leverage componen of B/ is posiively correlaed wih reurns, boh before and afer conrolling for in regressions IV and VI. This has he appearance of a reward o leverage. However, for > 1, he difference beween B/ and is increasing in leverage, by equaion (1), bu he coefficien on he difference is no significanly differen from zero. As he difference is deermined by a muliplicaive ineracion beween ND and, one would expec a posiive reurn associaion if his ineracion were beween operaing and financing risk facors, as leveraging equaion (2) suggess. For < 1, he difference is decreasing in leverage bu he coefficien is posiive. 12 Resuls are similar wih he naural logarihm of he wo variables in he regression. 13 The separaion of financial asses from financial liabiliies deals wih he objecion ha financial asses ( cash ) are no negaive deb, bu raher insrumens for hedging cash flows from operaions. See Acharya, Almeida and Campello (2004). 18

22 These resuls indicae ha he leverage porion of he B/ raio is no priced according o sandard preceps, conradicing a basic ene in finance, expressed in leveraging equaion (2): given operaing risk, leverage adds o expeced reurns. The resuls could be due o leverage being negaively correlaed wih unidenified characerisics ha load on (unidenified) risk facors. Indeed, leverage may be endogenous, wih firms choosing lower financial leverage when heir operaing risk is higher. The resuls for regression VIII in Table 3, wih he sandard risk characerisics, bea and ln(size), in he regression, do no suppor his: The coefficien on leverage is sill negaive. 14 Reurn volailiy may indicae higher risk and a choice, consequenly, o carry lower leverage, so in furher analysis we added he sandard deviaion of he (unlevered) enerprise rae of reurn, esimaed over he 252 rading days prior o he reurn period, o regression VIII. As in Ang, Hodrick, Xing, and Zhang (2004), he esimaed coefficien on he volailiy measure was negaive (hough no significan); he coefficien on leverage remained negaive (and significan). Our analysis has spli liabiliies ino operaing (OL) and financing (FL) and i could be ha firms subsiue operaing liabiliies for financing liabiliies such ha low financing leverage is associaed wih high operaing liabiliies (and hus higher operaing risk). The spearman correlaion beween ND OL and a measure of ha risk, is 0.247, indicaing ha his is no an issue, and adding OL o regression in Table 3 had lile effec on he resuls. Of course, we may no have 14 Bhandari (1988) repors a posiive relaionship beween reurn and deb-o-equiy price in cross-secional regressions ha include bea and size, esimaed from However, he posiive associaion is largely observed in years prior o 1966, no in he years ha also cover our sample period. This calls ino quesion wheher our resuls (or his) are period specific. Ang and Chen (2004) find ha he B/ effec is no eviden prior o 1960, bu bea does explain reurns. The resul is inconsisen wih he observaions is Ferguson and Shockley (2003) ha bea, measured here wih respec o an equiy marke porfolio, omis covariance wih deb asses. They show ha marke leverage correcs for he mismeasuremen of bea, bu in a direcion opposie o ha documened here. 19

23 idenified all operaing risk facors. 15 However, we repeaed he regression analysis in Table 3 wihin indusries, using he Fama and French (1997) indusry classificaion scheme. Averaging coefficiens across he 1,068 indusry-year groupings, we found very similar resuls. To he exen ha operaing risk is he same wihin indusries, hese resuls canno be aribued o leverage indicaing differences in operaing risk. 3.2 Facor Regressions As a prelude o he facor regressions, and o idenify any nonlineariies and ineracion effecs, anel A of Table 4 repors mean reurns for porfolios formed on join realizaions of and ND. The reurns here are size-adjused, o subrac any size effecs. Wihin each of he en porfolios formed in anel B of Table 1, socks are assigned each year o five porfolios ND from a ranking on. The enerprise book-o-price effec is eviden wihin each leverage quinile, bu i is he reurns over he leverage quiniles ha we are mos ineresed in. For all ND porfolios, he quinile numbers rank reurns inversely and almos always monoonically. Mean differences beween reurns for he highes and lowes leverage quinile porfolios are negaive, wih -saisics less han 2.00, excep for porfolio 10 wih he highes enerprise book-o-price raios. Even adjusing for muliple comparisons in inerpreing he - saisics in he able, i appears ha he inverse leverage effec in reurns is eviden over almos he full range of enerprise book-o-price raios. 15 The resul could also be due o a long run of negaive oucomes for highly levered firms during he sample period, such as lower inflaion han anicipaed (ha resuls in unanicipaed losses for ne debors). Bu see Secion

24 Leveraging equaion (2) saes ha expeced reurns are no only increasing in leverage bu, for a given leverage, in expeced reurns o operaions. Thus, if enerprise book-o-price is a measure of operaing risk, one would expec paricularly high reurns o be associaed wih high ND and high. This is no he case in panel A of Table 4. The mean difference beween he reurn for he highes ND quinile porfolio wihin he highes porfolio (4.0%) and ha for he lowes ND quinile porfolio (1.7%) wihin he lowes porfolio is only 2.3%, wih a -saisic of 0.45 (unabulaed). This conrass wih he mean reurn of 23.2% from invesing long in he lowes leverage quinile wihin he highes porfolio and shoring he highes leverage quinile wihin he lowes porfolio. This 23.3% is also considerably greaer han he mean 12.7% reurn from invesing long and shor in he highes and lowes porfolios (porfolios 10 and 1 in anel B of Table 1), as a -saisic of 3.95 (unabulaed) on he comparison of he wo reurns indicaes. anel B of Table 4 repeas he porfolio formaion procedure, bu now wih socks grouped, wihin each porfolio, ino five porfolios based on (levered) B/ raher han leverage. By leveraging equaion (1), leverage yields a higher B/ for a given > 1 (porfolios 9 10), and hus one expecs a higher reurn, he higher he B/, as a reward o leverage. Correspondingly, for < 1 (porfolios 1 7), leverage yields a lower B/ for a given ; hus one expecs a higher reurn, he lower he B/. However, he mean (size- 21

25 adjused) reurn differences beween he high and low B/ porfolios are no significanly differen from zero for porfolios 9 10 in anel B and posiive for porfolios 1 7. The B/ effec in sock reurns indeed includes a leverage effec, bu in a seemingly perverse way. Leveraging equaion (1) suggess ha, if he reurns reflec reward o operaing and financing risk, a relaively high reurn should be associaed wih he porfolio conaining he highes and he highes B/ (where he leverage is highes), and a relaively low reurn wih he porfolio conaining he lowes and highes B/ (where leverage is lowes). However, he difference beween reurns for high and low porfolios wihin he high B/ porfolio is only 3.6% (wih a -saisic of 0.74) while he corresponding reurn wihin he low B/ porfolio is 21.4% (wih a -saisic of 5.70). Indeed, he differences in reurns beween high and low porfolios are decreasing over B/ groups raher han increasing. The observaions modify he Fama and French view ha B/ effec subsumes leverage effecs and shows ha, o he exen ha is he case, he form is differen from wha one usually has in mind. anel C of Table 4 shows ha, by firs ranking on (levered) B/ and hen (wihin B/ porfolios) on leverage, reurns o invesing on he basis of B/ improve by idenifying he leverage componen of B/. However, one earns a discoun for leverage, no a premium: The higher he amoun of leverage purchased wihin each B/ porfolio, he lower he reurn In each panel of Table 4, he ranking in he second sage (o form he five quiniles) will involve a soring on he firs-sage ranking variable if he wo ranking variables are correlaed wihin porfolios. Accordingly, reurns over he five quiniles could, in par, reflec reurns o he firs ranking variable. For < 1 (porfolios 1-7), his is and ND no an issue for he inferences from anel A because he rank correlaion beween (in Table 2) is posiive. The Table 3 resuls also do no sugges his is a serious problem, as here we conrol for hese correlaions 22

26 anel D of Table 4 invesigaes wheher hese differences in porfolio reurns are explained by facor reurns nominaed in previous research o reward risk. Monhly excess reurns (over he risk-free rae) for each of he 50 porfolios in anel A of Table 4 were regressed, over he 480 monhs in he sample period, on mimicking reurns for he hree Fama and French (1993) facors he marke facor (MKT), size (SMB) and book-o-marke (HML) plus he reurn o he momenum facor (UMD) aribued o Jegadeesh and Timan (1993). The alpha inerceps from hese regressions are given in anel D, along wih differences beween he alpha reurns for he exreme porfolios in each column and row and -saisics on hose differences. I is clear ha differences in reurns for leverage porfolios wihin each porfolio are no explained enirely by heir sensiiviy o facor reurns, and he alpha reurns are negaively relaed o he level of leverage. In essence, we have idenified an addiional facor associaed wih leverage bu one on which leverage loads in a seemingly perverse way. As he book-o-price facor is included in hese regressions, he resuls also show ha book-o-price facor reurns do no absorb leverage effecs. Furher, he reurns on porfolios in he columns, and he associaed -saisics, indicae ha he book-o-price facor does no absorb he reurn o enerprise book-o-price -- which is he meric idenified wih he difference beween price and book value -- hough he inercep differences are associaed primarily wih he highes in a muliple regression framework. To check, however, we repeaed he analysis by subracing, from each sock s size-adjused reurn, he mean size-adjused reurn on a porfolio of which he sock was a member, formed from he firs ranking variable divided ino 50 equal-sized porfolios. Resuls were similar. 23

27 porfolio. The decomposiion of he B/ raio ino operaing and financing componens has provided an explanaion of reurns ha he aggregae book-o-price obscures. 17 In sum (o his poin), while anel C of Table 1 indicaes ha marke leverage has low correlaion wih sock reurns in he cross secion (uncondiionally), here is significan correlaion condiional upon and orhogonal o he enerprise book-o-price raio. Furher, he reurns o leverage are in excess of hose associaed wih marke, size, book-o-marke and momenum facors on which leverage could load. However, he condiional correlaion is negaive and he magniude of he excess reurns are negaively relaed o leverage. The explanaion ha he leverage loads on an addiional, unidenified operaing risk facor mus be enerained, as mus he conjecure ha leverage correcs for measuremen error in he enerprise book-o-price as a proxy for firm s exposure o common reurns. Our exploraion of possible operaional explanaions in Table 3 was unsuccessful in idenifying an omied variable. Such an explanaion requires leverage o load inversely on an unidenified facor, orhogonal o, he marke reurn, size and momenum, such ha, when he facor loading is low, leverage is high and vice versa. If, following Meron (1973), ha facor is relaed o fuure invesmen opporuniies, i would have o be ha high leverage firms can exploi hose opporuniies when hey arise. The alernaive aribuion is o marke inefficiency. Indeed, if one views he four-facor model employed in anel D of Table 4 as a saisfacory asse pricing model, he alphas repored here are abnormal reurns. Marke price, in he denominaor of also denominaes he 17 Facor regressions including only he marke facor produced similar resuls, as did regressions including he marke facor, size and momenum (bu excluding book-o-price) and regressions wih he marke facor, size and book-o-price. 24

28 ND marke leverage measure,. If he marke misprices enerprise book values, i also renders a measure of marke leverage such ha high (low) leverage oversaes (undersaes) acual leverage, causing high (low) marke leverage o be associaed wih lower (higher) sock reurns han one would expec given inrinsic financing risk. 18 Of course, if size, book-o-price, or momenum effecs are abnormal reurns raher han reurns o risk bearing, he reurns o enerprise book-o-price and leverage are incremenal o hese effecs. In paricular, low marke leverage due o a high price in he denominaor can no be aribued o momenum overpricing. Broadly, he resuls are consisen wih evidence ha almos any accouning number denominaed in price earnings, EBIT, sales, book value, enerprise ne asses predics sock reurns. We reurn o he issue in Secion A arallel Invesigaion Separaing Ne Deb from rice In response o he conjecure ha he leverage resul may be due o he denominaion in inefficien prices, Table 5 invesigaes ne deb wih a conrol for price. To do his, he able decomposes size ino an enerprise price componen and a ne deb componen. The price of equiy -- commonly referred o as size -- is a variable, beside B/, ha robusly predics sock reurns. Regression I in Table 5 shows ha he size effec is (weakly) suppored in our daa. Like B/, size can be broken down ino an unlevered componen and a leverage componen: = ND (if ne deb is carried a marke value). Accordingly, regression II in Table 5 includes enerprise price, ln( ) and ln(nd). This separaes ne deb from price, bu also seems o us o be a more naural way o specify size and o evaluae he size effec: Size is deermined by he business enerprise and neing in deb ha (in heory) is 18 In an invesigaion of reurns around changes in leverage ha resul from exchanges of deb and equiy, Koreweg (2004) infers ha he reward o leverage in he marke is oo low and documens a profiable rading sraegy involving firms wih exreme leverage. 25

29 associaed wih higher expeced reurns confounds he size effec (ha bears a negaive relaionship wih reurns). Wih he unlevering of size, he size effec is clearly sill eviden in he resuls for regression II, indeed emphaically. The mean coefficien on ne deb wihou he deflaion by price is now posiive, indicaing a premium for financing risk: Firm size peraining o operaions -- yields a reurn premium (inversely), bu levering firm value wih deb adds an addiional premium o he equiy reurn, consisen wih leveraging equaion (2). In unabulaed analysis, he finding does no change when esimaed bea is added o he regression (and he mean coefficien on bea is no significanly differen from zero). The reurn o size, of course, could be a reward o risk bu could also due o inefficien prices. Nowihsanding, delinking ne deb from (possibly inefficien) prices yields a resul consisen wih heory. However, inroducing ln() and in regressions III and IV in Table 5 flips he sign of he ne deb coefficien: Given enerprise price, adding enerprise book value furher predics reurns and resuls in a negaive condiional correlaion beween leverage and reurns, as ND in Tables 3 and 4. So i is apparen ha he negaive coefficiens on in Table 3 are eviden afer condiioning on he book value of operaions relaive o price. In sum, equiy price is he difference beween he price of operaions and he price of ne deb. Ne deb, as measured, is posiively correlaed wih reurns afer conrolling for he price of operaions, as heory suggess. However, holding consan ne operaing asses relaive o he price of operaions, sock reurns are decreasing in leverage. This seemingly odd finding requires explanaion, and we explore hose explanaions furher in Secion 4. However, we firs invesigae wheher he posiive relaionship beween leverage and reurns, prediced by heory, is eviden in he fundamenals. 26

30 3.4 A arallel Invesigaion wih Fundamenal Raes of Reurn This secion shows ha book rae of reurn is increasing in leverage, boh in heory and he daa. The one-year-ahead book rae of reurn on equiy, he accouning equivalen o he sock rae of reurn, is ROCE + 1 Earn + 1 =, ha is earnings (o common) relaive o he book value of B equiy. Earnings is income from operaions (enerprise income) less ne ineres (ineres expense minus ineres income) on ne deb: Earn = OI i. As B = ND, i follows ha, E Earn+ 1 OI + 1 i+ 1 [ ROCE ] = E = E + 1 B ND = OI + 1 ND i+ E E 1 B B ND ND E (3) = [ R ] E[ R NBC ] B This leveraging equaion is of he same form as leveraging equaion (2) and indeed (1). 19 The expeced book rae of reurn is equal o he expeced enerprise reurn, R +1 = OI +1 / plus a premium for leverage given by he amoun of book leverage, ND B and he expeced spread beween R +1 and he ne borrowing cos, NBC +1 = i +1 /ND. Unlike sock raes of reurn, pas book raes of reurn forecas fuure book raes of reurn (see Freeman, Ohlson and enman 1982 and Fama and French 2000): R forecass one-yearahead R +1. Given his forecas, equaion (3) says ha leverage should addiionally forecas 19 The equaion requires a sligh modificaion where here is a minoriy ineres, bu he adjusmen is ypically small. See enman (2004, p. 359). 27

31 one-year-ahead ROCE +1. We esimaed he following cross-secional regression separaely for firms wih R NBC and firms wih R < NBC. 20 ND ROCE + 1 = a + b1 R + b2 + B e When ROCE +1 is regressed on book leverage, ND B alone, wih all firms pooled, he mean coefficien on leverage is negaive ( wih a -saisic of -4.64) 21. However, jus as and ND are negaively correlaed in he cross secion for 1, so are R and ND. B Conrolling for R in he regression, he mean coefficien on ND is reliably posiive for B firms wih R NBC (0.023 wih a -saisic of 8.64), in conras o he coefficien on ND wih he conrol for in sock reurn regression III in Table 3. Furher, he mean 20 ROCE is before exraordinary and special iems, ne of preferred dividends. R and NBC are calculaed wih an allocaion of axes beween operaing income and ne ineres. Ne ineres in he NBC calculaion is ineres expense minus ineres income on financial asses, muliplied by (1 ax rae), plus preferred dividends. Ineres income on financial asses (no readily idenifiable on Compusa) was calculaed by applying he -bill rae o he average cash and cash equivalens (Compusa #1) for he relevan year. The ax rae was se as he Federal rae for he year plus a sae ax rae of 2%. 21 -saisics in his secion are calculaed as he mean of he esimaed coefficiens relaive o heir esimaed sandard errors. To adjus for auocorrelaion in he regression coefficiens (which is likely wih accouning measures), esimaed sandard errors are muliplied by k = n 1+ φ 2φ (1 φ ) 2 1 φ n(1 φ) where φ is he esimaed firs order auocorrelaion coefficien and n equals he number of annual regressions (see Abarbanell and Bernard 2000). 28