Industry Profitability Dispersion and Market-to-book Ratio

Transcription

1 Indusry Profiabiliy Dispersion and Marke-o-book Raio Jia Chen *, Kewei Hou, and René M. Sulz 30 January 2014 Absrac Firms in indusries ha have high indusry-level dispersion of profiabiliy have on average higher marke-o-book raios han firms in low dispersion indusries. This posiive relaion beween firms' marke-o-book raios and indusry profiabiliy dispersion is economically large and saisically significan and is robus o conrolling for variables used o explain firm-level valuaion raios in he previous lieraure. We disinguish beween four possible explanaions of his posiive relaion: (1) invesors pay more aenion o firms in indusries wih high profiabiliy dispersion; (2) firms in high dispersion indusries are overvalued; (3) he uncerainy abou average profiabiliy are higher for firms in high dispersion indusries; (4) firms in high dispersion indusries are less risky. Our resuls show ha he mispricing explanaion bes explains his posiive relaion. Furhermore, we find ha indusry profiabiliy dispersion is negaively relaed o an ex-ane measure of discoun raes. * Guanghua School of Managemen, Peking Universiy. chen.1002@gmail.com. Fisher College of Business, Ohio Sae Universiy. hou.28@osu.edu. Fisher College of Business, Ohio Sae Universiy. sulz_1@fisher.osu.edu. 1

2 1 Inroducion A cenral quesion in finance is wha explains equiy valuaion? This quesion is criically imporan for boh academic research and business pracices. Alhough researchers have boh empirically and heoreically examined he cross secion of equiy valuaion (e.g., Fama and French (1998) and Pásor and Veronesi (2003)), we do no undersand i well (Cochrane (2011)). Towards a beer undersanding of equiy valuaion, an emerging lieraure sudies he relaion beween indusry characerisics and asse prices (e.g., Hou and Robinson (2006)) and shows ha he indusry environmen ha firms are in may affec firms' operaion and equiy valuaion. In his paper, we explore he relaion beween a sandard measure of equiy valuaion, marke-o-book raio, and wihin-indusry dispersion of firm-level profiabiliy measured by he wihin-indusry sandard deviaion of reurn on equiy. We find a posiive relaion beween hese wo variables: firms in indusries ha have higher profiabiliy dispersion have on average higher marke-o-book raios. This posiive relaion is economically large. A one sandard deviaion increase in indusry profiabiliy dispersion is associaed wih an increase of in marke-obook raio, represening a 19.3% increase compared o he cross-secional mean of marke-obook raio. This posiive relaion is robus o conrolling for variables ha Fama and French (1998) and Pásor and Veronesi (2003) use o explain he cross secion of firm valuaion. We idenify four possible explanaions of his posiive relaion. Firs, invesors' limied aenion can lead o a posiive relaion beween indusry profiabiliy dispersion and marke-obook raio. If invesors pay more aenion o high dispersion indusries and relaively inadequae aenion o low dispersion indusries, hey could assign higher valuaion o firms in indusries wih high profiabiliy dispersion han firms in indusries wih low profiabiliy dispersion. Second, indusry profiabiliy dispersion can be associaed wih mis-pricing in he cross 2

3 secion of firm valuaion. Firms in indusries wih high profiabiliy dispersion can be overpriced relaive o firms in indusries wih low profiabiliy dispersion. Hence, he marke-o-book raios of firms in indusries wih high profiabiliy dispersion are higher han hose in indusries wih low profiabiliy dispersion. Third, Pásor and Veronesi (2003) argue ha he marke-o-book raio of a firm increases wih uncerainy abou average profiabiliy of he firm. If firms wih higher indusry profiabiliy dispersion have higher uncerainy abou fuure profiabiliy, hen hose firms can have higher marke-o-book raios. Fourh, if firms in indusries wih high profiabiliy dispersion are less risky and have lower risk-adjused discoun raes, all else being equal, firms in hose indusries will have higher marke-o-book raios. We consider four groups of variables proxying for hese four explanaions. Firs, we use hree variables o capure invesors' aenion: he number of analyss following a sock, he share of insiuional ownership of a sock, and a sock's rading volume or urnover. Second, we use hree variables o measure he exen o which a sock is mis-priced: he raio of fundamenal value o price of Frankel and Lee (1998), he composie equiy issuance measure of Daniel and Timan (2006), and a modified version of he indusry-wide pricing deviaion of Rhodes-Kropf, Robinson, and Viswanahan (2005). Third, Pásor and Veronesi (2003) argue ha uncerainy abou mean profiabiliy declines over ime due o learning and his effec is sronger for dividend non-payers. Hence, we use firm age and a dividend non-payer dummy as well as heir ineracion o proxy for uncerainy abou average profiabiliy. Fourh, we measure he risks of a firm using he facor loadings on he Fama-French hree facors plus a momenum facor and he volailiy of raw monhly sock reurns. 3

4 Examining he relaions beween indusry profiabiliy dispersion and he four groups of explanaory variables shows ha firms in indusries wih high profiabiliy dispersion are on average overvalued and ha hese firms end o be younger and are less likely o pay dividends. The relaions beween indusry profiabiliy dispersion and variables proxy for invesor aenion and facor risk loadings are mixed. We hen include hese explanaory variables in he regressions of marke-o-book raio on indusry profiabiliy dispersion and find ha he mispricing proxies reduce he effec of indusry profiabiliy dispersion on marke-o-book raio more han he oher groups of explanaory variables do. To furher disinguish beween hese four explanaions, we esimae indusry-level regressions of indusry profiabiliy dispersion on he indusry averages of he four groups of explanaory variables and hen use hese regressions o decompose indusry profiabiliy dispersion ino componens relaed o he four explanaions. When we use hese componens of indusry profiabiliy dispersion o explain marke-o-book raio, we find ha only he componen relaed o mispricing has he righ sign and significan explanaory power, while he componens relaed o invesor aenion, uncerainy abou mean profiabiliy, and risk do no. These resuls sugges mispricing as he main driver of he posiive relaion beween indusry profiabiliy dispersion and firm valuaion. We also sudy he relaion beween a measure of ex-ane discoun raes and indusry profiabiliy dispersion since irraionally low discoun raes can poenially be responsible for he mispricing associaed wih indusry profiabiliy dispersion. The resuls show ha here is a srong negaive relaion beween indusry profiabiliy dispersion and ex-ane discoun raes, which is consisen wih he noion ha firms in indusries wih high profiabiliy dispersion are overvalued because hey have low marke-imposed discoun raes. 4

5 We organize he res of his paper as follows. Secion 2 inroduces he daa. Secion 3 sudies he differences in profiabiliy dispersion across indusries. Secion 4 documens he posiive relaion beween indusry profiabiliy dispersion and firm valuaion. Secion 5 disinguishes beween he four possible explanaions of he posiive relaion. Secion 6 sudies he relaion beween indusry profiabiliy dispersion and he implied cos of capial. Secion 7 concludes. 2 Daa The daa sample of his paper covers all lised securiies from NYSE, Amex, and Nasdaq ha have sharecodes 10 or 11 and are a he inersecion of CRSP monhly reurn files from July 1963 o June 2010 and he Compusa fundamenals annual file from 1963 o Earnings is income before exraordinary iems from Compusa, and book equiy is common equiy from Compusa. We also obain oal asses and dividends from Compusa. We measure profiabiliy using reurn on equiy ( ROE ), which is earnings in year divided by book equiy from year -1. For each indusry, indusry profiabiliy dispersion is he cross-firm sandard deviaion of reurn on equiy, which we denoe. We also consruc an alernaive measure of indusry profiabiliy dispersion,, which is he cross-firm 80 h percenile minus he 20 h percenile of reurn on equiy. See Table 10 in he appendix for he deailed descripions of variables. 3 The Differences in Profiabiliy Dispersion across Indusries In his secion, we examine differences in profiabiliy dispersion across indusries by soring he Fama-French 49 indusries according o he ime-series average of indusry profiabiliy dispersion measured by. Table 1 shows ha here is large variaion in profiabiliy 5

6 dispersion across indusries. The average profiabiliy dispersion for Compuer Sofware is 0.258, which is he highes among all 49 indusries. Uiliies has he lowes value of average profiabiliy dispersion, which is The difference beween hese wo indusries is The average profiabiliy dispersion for Prining and Publishing is 0.152, which is a he median of all indusries. The difference beween Compuer Sofware and Uiliies is hus 122% of his median value of profiabiliy dispersion. In order o undersand wha disribuional feaures of profiabiliy cause his wide variaion in profiabiliy dispersion across indusries, we hen sudy he difference in he disribuion of profiabiliy beween high dispersion indusries and low dispersion indusries. To do ha, we use indusry profiabiliy dispersion o rank he Fama-French 49 indusries every year ino 3 groups: op five indusries, boom five indusries, and oher indusries. In he same year, we also rank individual firms ino deciles based on heir firm-specific profiabiliy. For each indusry group (high dispersion, low dispersion, and ohers) each year, we hen coun he numbers of firms falling in each profiabiliy decile rank and normalize hese numbers so ha hey add up o one for each indusry group. Finally, we average he normalized numbers across differen years, resuling in hree separae hisograms in Figure 1 for he hree groups of indusries. Profiabiliy disribuion is very differen beween he op five and boom five indusries ranked by profiabiliy dispersion. The op five indusries have more firms in he low and high profiabiliy deciles han in he middle deciles, while he boom five indusries have more firms in he middle deciles han in he exreme deciles. In oher words, indusries wih high profiabiliy dispersion have more firms performing eiher very well or very poorly relaive o he average firm. Indusries wih low profiabiliy dispersion, on he oher hand, have more firms having he average profiabiliy performance han firms performing eiher very well or very 6

7 poorly. In unrepored ess, we also sudy he differences in profiabiliy persisence beween high dispersion and low dispersion indusries. When we regress firm-level profiabiliy on lagged profiabiliy, indusry profiabiliy dispersion, and he ineracion beween lagged profiabiliy and indusry profiabiliy dispersion, he coefficien on lagged profiabiliy is significanly posiive while he coefficien on he ineracion erm is significanly negaive, suggesing ha high dispersion indusries are associaed wih lower levels of profiabiliy persisence. Therefore, firms in indusries wih high profiabiliy dispersion are no only more likely o have exreme (very good or very bad) profiabiliy performance, his exreme performance is also more ransiory han ha of exreme performers in indusries wih low profiabiliy dispersion. In Table 2, we repor he summary saisics of he primary variables used in he paper. Because he wo measures of indusry profiabiliy dispersion, and, are measured a he indusry level, he saisics for hese wo variables in Table 2 are he ime-series averages of indusry-level saisics. The saisics for oher variables in his able are ime-series averages of firm-level saisics. The sandard deviaion of, 0.066, is abou half of he mean of his variable, which is consisen wih he large variaion of in Table 1. The sandard deviaions of and M are also large relaive o heir means. 4 The Relaion beween Indusry Profiabiliy Dispersion and Firm Valuaion In Table 3, we use regression analysis o sudy wheher a firm's marke-o-book raio is relaed o he profiabiliy dispersion of he indusry ha he firm is in. We assign indusry profiabiliy dispersion o he firm in he corresponding indusry-year and esimae firm-level panel regressions of marke-o-book raio on indusry profiabiliy dispersion and oher conrol variables. Because we are ineresed in he cross-secional relaion, we use year fixed effecs in 7

8 hese panel regressions. The sandard errors are wo-way clusered by firm and year according o Peersen (2008). In Model 1, we use only as he explanaory variable. The coefficien on is posiive and saisically highly significan, indicaing a posiive relaion beween indusry profiabiliy dispersion and marke-o-book raio. The coefficien is also economically large. A one sandard deviaion increase in indusry profiabiliy dispersion is associaed wih an increase of in he marke-o-book raio 1, represening a 19.3% increase compared o he mean of marke-o-book raio in Table 2 (2.384). In Model 2, we use he alernaive measure of indusry profiabiliy dispersion,, as he only explanaory variable. The posiive coefficien on shows ha he posiive relaion beween indusry profiabiliy dispersion and marke-o-book raio is robus o using his alernaive measure. To accoun for he possibiliy ha he posiive relaion beween indusry profiabiliy dispersion and marke-o-book raio is driven by known valuaion deerminans, we conrol for variables ha have been shown by he previous lieraure o be relaed o firm valuaion. Specifically, Fama and French (1998) develop valuaion regressions ha perform well in a baery of ess. This model is in urn used by Pinkowiz, Sulz, and Williamson (2006) for firms around he world. Furhermore, Pásor and Veronesi (2003) develop a model ha explains he cross secion of marke-o-book raio. We use he variables from hese papers as conrols which include curren and fuure (nex wo years ) earnings, book asses, R&D expendiure, ineres expenses, and dividends all scaled by curren book equiy, log oal asses, firm-level volailiy of profiabiliy esimaed using he daa from he previous five years (hree years minimum), and curren and nex wo years sock reurns. 2 1 We obain his number by muliplying he coefficien on from Model 1, 6.970, by he ime-series average of cross-indusry sandard deviaion of, 0.066, from Table 2. 2 We leave ou he wo primary variables ha Pásor and Veronesi (2003) use o proxy for uncerainy abou 8

9 Model 3 includes only he conrol variables as explanaory variables, and he resuls are similar o hose in Fama and French (1998) and Pásor and Veronesi (2003), which suggess ha he conrol variables are relaed o firm valuaion in he same way in our sample as in heirs. Specifically, marke-o-book raio is on average higher for firms ha have higher fuure profiabiliy, lower fuure sock reurn, lower leverage raios, higher R&D expendiure, higher dividends, smaller asse size, and higher volailiy of pas profiabiliy. In Models 4 and 5, we regress he marke-o-book raio on measures of indusry profiabiliy dispersion and conrol variables. We call hese regressions he baseline regressions. We use in Model 4 and in Model 5, respecively. The coefficiens on he indusry profiabiliy dispersion measures remain posiive and are significan boh economically and saisically. Specifically, Model 4 shows ha a one sandard deviaion increase in is associaed wih an increase of in he marke-o-book raio, which is 17.6% of he crosssecional mean of marke-o-book raio in Table 2. Similarly, Model 5 shows ha a one sandard deviaion increase in is associaed wih an increase of in he marke-o-book raio, which is 18.1% of he cross-secional mean marke-o-book raio. These resuls sugges ha he variables ha he previous lieraure uses o explain marke-o-book raio does no subsume he posiive relaion beween indusry profiabiliy dispersion and marke-o-book raio. 5 Disinguishing beween Four Possible Explanaions 5.1 Four Possible Explanaions We indenify four possible explanaions of he posiive relaion beween indusry profiabiliy mean profiabiliy ( ln( Age ) and he non-dividend payer dummy) from he lis of conrol variables because we wan o laer explore hese variables as poenial drivers of he posiive relaion beween indusry profiabiliy dispersion and marke-o-book raio. 9

10 dispersion and firm valuaion. Firs, invesors' limied aenion can lead o his posiive relaion. If invesors' aenion o low profiabiliy dispersion indusries is inadequae, hey may be pessimisic abou firms' fuure performance in hose indusries and consequenly will assign a low valuaion o hose firms. On he oher hand, if invesors pay more aenion o high dispersion indusries, hey may be opimisic abou he firms' prospec in hese indusries. As a resul, firms in high dispersion indusries can have higher marke-o-book raios han firms in low dispersion indusries. Second, indusry profiabiliy dispersion can be associaed wih mispricing a he indusry level. If firms in indusries wih high profiabiliy dispersion are overvalued relaive o he firms in indusries wih low profiabiliy dispersion, hen he marke-o-book values of firms in high dispersion indusries should be higher han hose in low dispersion indusries. Third, Pasor and Veronesi (2003) argue ha he marke-o-book raio of a firm increases wih uncerainy abou average profiabiliy of he firm, and he resoluion of his uncerainy over ime is associaed wih a decline in he marke-o-book raio. The inuiion is simple. High uncerainy abou average profiabiliy increases he probabiliy ha he firm will have a persisenly high profiabiliy or persisenly low profiabiliy in he fuure. Because of he convexiy of compounding, a persisenly high profiabiliy has a bigger impac on he marke-obook raio han persisenly low profiabiliy. As a resul, higher uncerainy abou mean profiabiliy leads o higher marke-o-book raios. If firms in indusries ha have higher profiabiliy dispersion have higher uncerainy abou fuure profiabiliy, hen hese firms will have higher marke-o-book raios according o Pasor and Veronesi (2003). Fourh, firms ha are less risky have lower risk-adjused discoun raes, which can lead o higher valuaion according o sandard valuaion heories. If firms in indusries wih high 10

11 profiabiliy dispersion are less risky and hus have lower discoun raes, all else being equal, hese firms should have higher marke-o-book raios. 5.2 Variables Proxying for he Four Explanaions To empirically disinguish beween hese four explanaions, we consider four groups of variables, each associaed wih one of he four explanaions. The firs group of variables includes hree proxies of invesors' aenion o a sock: he number of analyss following a sock ( N _ ANLST ), he share of insiuional ownership of a sock ( INST _ OWN ), and a sock's rading volume or urnover ( TURNOVER ). N _ ANLST is he average number of analyss providing FY1 forecas in he IBES summary file in year. INST _ OWN is he average quarerly 13F repored fracion of shares held by insiuions in year. TURNOVER is he average of daily share urnover in year. When calculaing TURNOVER, we adjus for he insiuional feaures of he way ha Nasdaq and NYSE-Amex volume are compued by following Gao and Rier (2010). The second group of variables measure he exen o which a sock is mispriced. We use hree variables for his purpose: he raio of fundamenal value o price of Frankel and Lee (1998), he composie equiy issuance measure of Daniel and Timan (2006), and a modified version of he indusry-wide pricing deviaion of Rhodes-Kropf, Robinson, and Viswanahan (2005). To consruc he raio of fundamenal value o price, V / P, for a firm in a given year, we calculae he fundamenal value, V, using Equaion 3.3 in Frankel and Lee (1998), FROE r FROE r FROE r V = B + B + B + B e + 1 e + 2 e re ( 1+ re) ( 1+ re) re (1) where FROE, 1 FROE +, and FROE + 2 are forecass of reurn on equiy for year, +1, and +2, 11

12 respecively. These profiabiliy forecass are based on Hou, van Dijk, and Zhang (2012). B is book equiy. To esimae he discoun rae, r e, we esimae he Fama-French hree-facor model for each of he Fama-French 49 indusries using value-weighed indusry reurns and all available ime-series observaions and hen use he fied values of he model as he discoun raes for all firms in ha indusry. The V / P measure is he fundamenal value divided by he marke value of equiy. According o Frankel and Lee (1998), when V / P of a firm is low, he firm is overvalued relaive o oher firms. Second, we consider he composie issuance variable of Daniel and Timan (2006) as anoher measure of mispricing. Exising evidence suggess ha new issue and repurchase aciviies are indicaive of managers exploiing mispricing of heir firm s sock, i.e. firms end o issue shares when heir socks are overvalued and repurchase when heir socks are undervalued. To capure his possibiliy, we consruc he composie issuance measure by following Daniel and Timan (2006). For a firm in a given monh q, we calculae he share issuance measure as ME q NIq = ln r ( q 1, q), ME q 1 (2) where ME and q q 1 ME are he marke values of equiy of he firm for monh q and q-1, and ( 1, q) r q is he log sock reurn from he end of monh q-1 o he end of monh q. I can be inerpreed as he par of a firm s growh in marke value ha is no accouned for by he sock reurn. Issuance aciviies, including acual equiy issuance, employee sock opion plans, or any oher acions ha rade ownership for cash or services, increase he composie issuance measure, while reiring aciviies, including repurchases and dividends, reduce he measure. Splis and sock dividends do no affec he measure. To be consisen wih oher annual daa in our analysis, we consruc he annual composie issuance measure NI by summing he monhly issuance 12

13 measures wihin each year. Third, we consruc an indusry-wide pricing deviaions measure using an approach similar o Rhodes-Kropf, Robinson, and Viswanahan (2005). Specifically, we firs express he fundamenal value as a linear funcion of firm-specific accouning informaion. To do ha, we esimae a cross-secional regression of log marke value on log book value for each Fama- French 12 indusry 3 every year as follows, m =α +α b +ε (3) i 0 j 1 j i i, where m i and b i are log marke value of equiy and log book value of equiy, respecively. We esimae he regression for each indusry-year separaely o accoun for he possibiliy ha he growh raes and discoun raes vary over ime and across indusries. The fied value of he regression above is ˆ j ( ˆˆˆˆ ) v b ; α, α =α +α b, (4) i 0 j 1j 0 j 1j i where α ˆ 0 j and α 1 are he esimaed coefficiens. This fied value is a measure of he fundamenal value of he firm condiional on ime and indusry j, which capures he crosssecional variaion in firm value ha is indusry specific, while he residual value of he regression capures he firm-specific variaion. We also compue a measure of he fundamenal value ha is indusry neural: ( ) vb; α, α =α +α b, (5) i i 1 1 where α ˆ 0 = α and 0 j α ˆ 1 = α1 J J j are he averages of he esimaed coefficiens across indusries a ime. The difference beween he indusry-specific valuaion and he marke-level 3 We choose Fama-French 12 indusries raher han finer indusry classificaions because he classificaion of Fama-French 12 indusries allows for more firms in each indusry-year. 13

14 valuaion, vb ( ;, ) vb ( ;, ) α α α α, hus capures he exen o which firm i in indusry j i ˆˆ0 j 1j i 0 1 is overvalued relaive o firms in oher indusries in a given year. A high value of he difference suggess ha he firm is overvalued relaive o firms in oher indusries. We denoe his indusrywide pricing deviaion measure PD _ IND. The hird group of variables are relaed o he explanaion based on uncerainy abou average profiabiliy proposed by Pásor and Veronesi (2003). According o heir model, uncerainy abou mean profiabiliy declines over ime due o learning. All else being equal, a young firm should have a higher uncerainy abou profiabiliy han an old firm. Therefore, we include firm age in our analysis o capure uncerainy abou profiabiliy. In our empirical analysis, we measure firm age as he log of one plus he curren year minus he firs year ha a valid PERMCO appears on CRSP. We choose o use logarihm because he model of Pásor and Veronesi (2003) implies ha one addiional year of age should maer more for a young firm han for an old firm. 4 We denoe his variable ln( Age ). Pásor and Veronesi (2003) also poin ou ha wheher a firm pays dividends or no can inerac wih firm age o affec firm valuaion. To accoun for he impac of dividend, we consruc a dividend non-payer dummy, which equals one if he firm does no pay dividends in he curren year and zero oherwise. We denoe his variable ND. The fourh group of variables proxy for he explanaion ha firms in high dispersion indusries are less risky and have lower risk-adjused discoun raes, which can lead o higher marke-o-book raios. This group includes five variables. The firs four are he facor loadings on he Fama-French hree facors plus a momenum facor esimaed using monhly daa over he 4 While Pásor and Veronesi (2003) sricly follow heir model o use negaive of he reciprocal of firm age raher han log of age in heir primary analysis, hey show ha log of age generaes similar resuls. 14

15 pas five years (24 monhs minimum). b, s, h, and w are he loadings on he marke, SMB, HML, and WML facors, respecively. The fifh variable, SD _ RET, is he oal volailiy of raw monhly sock reurns over he pas five years (24 monhs minimum). 5.3 The Relaion beween Indusry Profiabiliy Dispersion and he Four Groups of Explanaory Variables In his subsecion, we examine he relaion beween indusry profiabiliy dispersion and he indusry averages of he four groups of explanaory variables. Table 4 repors he correlaions beween hem. Firs, among he variables proxying for invesor aenion, INST _ OWN and TURNOVER have posiive correlaions wih indusry profiabiliy dispersion. These correlaions are consisen wih he view ha higher indusry profiabiliy dispersion is associaed wih more invesor aenion. The number of analyss covering a firm, N _ ANLST, on he oher hand is negaively correlaed wih indusry profiabiliy dispersion, which is inconsisen wih he resuls based on insiuional ownership and urnover. Second, among he variables proxying for mispricing, V / P is negaively correlaed wih indusry profiabiliy dispersion, and boh NI and PD _ IND are posiively correlaed wih indusry profiabiliy dispersion. Thus, higher indusry profiabiliy dispersion is associaed wih lower fundamenal value o price raios, higher composie share issuance, and higher indusrylevel pricing deviaions. These resuls sugges ha firms in high dispersion indusries end o be overvalued. Third, he correlaions beween he variables proxying for uncerainy abou mean profiabiliy, ln( Age ) and ND, and indusry profiabiliy dispersion show ha firms in high 15

16 dispersion indusries end o be younger and are more likely o be dividend non-payers han firms in low dispersion indusries. These resuls sugges ha uncerainy abou mean profiabiliy can also poenially explain he posiive relaion beween indusry profiabiliy dispersion and firm valuaion. Fourh, among he risk loadings, h and w are negaively correlaed wih indusry profiabiliy dispersion, suggesing ha firms in high dispersion indusries have lower exposures o he value and momenum facors. This is consisen wih he view ha higher profiabiliy dispersion is associaed wih lower risk-adjused discoun raes. On he oher hand, boh b and s are posiively correlaed wih indusry profiabiliy dispersion, which suggess ha firms in high dispersion indusries have higher exposures o he marke and size facors. In addiion, oal volailiy, SD _ RET, is also posiively correlaed wih indusry profiabiliy dispersion. These resuls are inconsisen wih he negaive associaion beween indusry profiabiliy dispersion and risk-adjused discoun raes. Therefore, similar o he aenion-based variables, he correlaions show ha he evidence on he relaion beween risk proxies and indusry profiabiliy dispersion is also mixed. To help gauge he magniude of he correlaions in Table 4, Table 5 repors he average values of he four groups of explanaory variables for indusries wih differen levels of profiabiliy dispersion. Every year, we sor he Fama-French 49 indusries ino hree groups based on heir profiabiliy dispersion. The low and high dispersion groups have 16 indusries each and he middle dispersion group has 17 indusries. We hen calculae he equal-weighed and value-weighed averages of he explanaory variables for each indusry group as well as he differences beween he low and high dispersion groups and hen average hem over ime. Panels A and B of Table 5 show he resuls based on and Panels C and D show he resuls 16

17 based on. Table 5 Panel A shows ha firms in high dispersion indusries have on average slighly higher insiuional ownership (38.9% vs. 33.8%) and share urnover (0.4% vs. 0.2%), bu slighly lower analys coverage (7.53 vs. 7.77) han firms in low dispersion indusries, hus providing inconclusive evidence o he explanaion based on invesor aenion. Turning o mispricing proxies, firms in high dispersion indusries have on average lower fundamenal value o price raios (0.727 vs ), higher composie share issuance (0.006 vs ), and higher indusry-wide pricing deviaions (0.191 vs ) han firms in low dispersion indusries, and all he differences are highly significan. These resuls are consisen wih firms in high dispersion indusries being overvalued relaive o firms in low dispersion indusries. Firms in high dispersion indusries are also 2.48 years younger on average and are 30% more likely no o pay dividends han firms in low dispersion indusries, consisen wih he explanaion based on uncerainy abou mean profiabiliy. Finally, in erms of risk proxies, firms in high dispersion indusries have lower HML beas ( vs ) and WML beas ( vs ) bu higher marke beas (1.082 vs ) and SMB beas (0.905 vs ) as well as higher oal volailiy (0.139 vs ) han firms in low dispersion indusries. The resuls for he las hree risk measures do no suppor he explanaion ha firms in high dispersion indusries have high valuaion because of low risk-adjused discoun raes. The value-weighed resuls from Panel B of Table 5 are largely consisen wih he equalweighed resuls in Panel A wih hree noable differences. High dispersion indusries are now associaed wih higher levels of analys coverage and almos idenical composie share issuance and firm age as low dispersion indusries, which suggess ha larger firms in high dispersion indusries are older, have disproporionaely larger numbers of analyss following hem, and are 17

18 less likely o issue equiy han smaller firms. The resuls from Panels C and D based on are similar o hose in Panels A and B based on. Overall, he resuls in Table 5 indicae ha high indusry profiabiliy dispersion is associaed wih overvaluaion and high uncerainy abou mean profiabiliy, while he relaion beween profiabiliy dispersion and invesor aenion and firm risks is more mixed. 5.4 Do he Explanaory Variables Reduce he Effec of Indusry Profiabiliy Dispersion on Firm Valuaion? In Table 6, we add he four groups of explanaory variables o he baseline regressions of markeo-book on indusry profiabiliy dispersion and conrol variables. By sudying he coefficiens on indusry profiabiliy dispersion in hese regressions, we can learn wheher and how hese explanaory variables can reduce he effec of indusry profiabiliy on firm valuaion. Panel A presens he resuls based on and Panel B presens he resuls on. In Panel A, Model 1 regresses M,, on and he sandard conrol variables. i i This is essenially he same regression as Model 4 in Table 3, bu he daa sample is differen because we require he availabiliy of he addiional explanaory variables. To save space, we do no repor he coefficiens on he conrol variables. In his model, he coefficien on is posiive and saisically highly significan, which is consisen wih he resul from Table 3. In Models 2-5, we add he four groups of explanaory variables one group a a ime o Model 1. The coefficiens on in all four models are smaller han ha in Model 1 bu remain significanly posiive, suggesing ha none of he four groups of explanaory variables can compleely drive ou he posiive relaion beween indusry profiabiliy dispersion and marke-o-book raio. We see he bigges drop in coefficien in Model 3 afer conrolling for he 18

19 mispricing proxies (from in Model 1 o 3.848, a 36% drop), compared wih 17% (aenion proxies), 8% (proxies for uncerainy abou mean profiabiliy), and 14% (risk proxies) drops in Models 2, 4, and 5 respecively. These resuls sugges ha he hree mispricing proxies ( V / P, NI and PD _ IND ) have he larges effec on he posiive relaion beween indusry profiabiliy dispersion and marke-o-book raio. Finally, in Model 6, when we add all four groups of explanaory variables o Model 1, he coefficien on decreases from in Model 1 o (a 53% drop) bu remains significan. In Panel B of Table 6, we use o measure indusry profiabiliy dispersion and obain similar resuls o hose in Panel A. Specifically, he coefficien on remains posiive and significan afer conrolling for he four groups of explanaory variables. Furhermore, including he mispricing proxies in he regression resuls in he bigges reducion in he coefficien on (from in Model 1 o in Model 3), compared wih aenion proxies (2.930 in Model 2), proxies for uncerainy abou mean profiabiliy (3.231 in Model 4), and risk proxies (2.967 in Model 5), which confirms ha mispricing has a bigges conribuion o he posiive relaion beween indusry profiabiliy dispersion and firm valuaion. 5.5 Decomposing he Relaion beween Indusry Profiabiliy Dispersion and Firm Valuaion An alernaive way of examining how well he four groups of explanaory variables explain he relaion beween indusry profiabiliy dispersion and firm valuaion is o decompose indusry profiabiliy dispersion ino componens using he explanaory variables and hen sudy he effecs of hese componens on marke-o-book raio. The abiliy of hese componens o explain marke-o-book raio can help us undersand he relaive conribuions of he four explanaions o 19

20 he posiive relaion beween indusry profiabiliy dispersion and firm valuaion. We conduc his analysis in wo seps. Firs, we esimae indusry-level regressions of profiabiliy dispersion on indusry averages of proxy variables for he four explanaions and use he regression coefficiens o decompose indusry profiabiliy dispersion ino four componens, each relaed o an explanaion, and a residual componen. The resuls of hese indusry-level regressions are repored in Table 7. In he second sep, we replace indusry profiabiliy dispersion wih is componens in he firm-level valuaion regressions. Those resuls are repored in Table 8. In Table 7, he firs four models of Panel A show ha when is regressed on he explanaory variables one group a a ime, i is posiively and significanly relaed o urnover, composie share issuance, indusry-wide price deviaion, dividend non-payer dummy, and oal reurn volailiy, negaively and significanly relaed o insiuional ownership, and insignificanly relaed o analys coverage, fundamenal value o price raio, age, he ineracion erm beween age and dividend dummy, and beas on he marke, size, value, and momenum facors. When all four groups of explanaory variables are included ogeher in Model 5, urnover, indusry-wide price deviaion, and oal volailiy reain heir signs and significance whereas he res of he explanaory variables are insignifican. Togeher, hese explanaory variables capure 46% of he variaion of. In Panel B, we regress on he explanaory variables, and he resuls are similar o hose in Panel A. We use Model 5 in boh panels o decompose he wo indusry profiabiliy dispersion measures ino four componens each relaed o an explanaion by muliplying he coefficiens in Model 5 wih indusry average values of he corresponding proxies, as well as a residual componen. The various componens of are denoed (Aenion), 20

21 (Mispricing), (Uncerainy), (Risk), and (Residual). The componens of are named similarly. Panel A of Table 8 regresses firm-level marke-o-book raio on he differen componens of and he sandard conrol variables o invesigae he relaive imporance of differen explanaions in driving he posiive relaion beween indusry profiabiliy dispersion and firm valuaion. Models 1-5 show ha when he differen componens of are included individually in he regressions, every componen excep (Uncerainy) is posiively and significanly relaed o marke-o-book raio jus like. (Uncerainy), on he oher hand, is negaively and significanly relaed o marke-o-book raio, which is in he opposie direcion of he original resul. In Model 6 when we include all five componens of in he same regression, (Mispricing), (Uncerainy), and (Residual) reain heir signs and significance while he oher wo componens, (Aenion) and (Risk), become insignifican. We obain similar resuls in Panel B of Table 8 when we sudy he differen componens of. Overall, he resuls in Table 8 show ha he mispricing componen of indusry profiabiliy dispersion can beer explain is posiive relaion wih marke-o-book raio han he componens relaed o invesor aenion, uncerainy abou average profiabiliy, and risk. This is consisen wih he resul in Table 6 where we see he bigges reducion in he effec of indusry profiabiliy dispersion on marke-o-book raio afer conrolling for he mispricing proxies. These resuls sugges ha mispricing is he main channel hrough which indusry profiabiliy dispersion affecs firm valuaion. 21

22 6 Indusry Profiabiliy Dispersion and Implied Cos of Capial In his secion, we seek furher suppor of he mispricing explanaion by examining he relaion beween indusry profiabiliy dispersion and ex-ane discoun raes required by invesors. If he overvaluaion of firms in high dispersion indusries is caused by invesors assigning irraionally low discoun raes, we should see a negaive relaion beween indusry profiabiliy dispersion and ex ane discoun rae proxies. We measure ex-ane discoun raes using he implied cos of capial (ICC) esimaes of Hou, van Dijk, and Zhang (2012). They use earnings forecass from a cross-secional model o proxy for cash flow expecaions and esimae he implied cos of capial for a large sample of firms. They show ha he earnings forecass generaed by he cross-secional model are superior o analyss forecass in erms of coverage, forecas bias, and earnings response coefficien. More imporanly, hey show ha he model-based ICC is a more reliable proxy for expeced reurns han he ICC based on analyss forecass. 5 In Table 9 we regress he composie ICC measure of Hou, van Dijk, and Zhang (2012), ICC, on indusry profiabiliy dispersion and a number of conrol variables ha Hou, van Dijk, and Zhang (2012) use o explain ICC. Models 1 and 2 show ha when used alone, boh and are negaively and significanly relaed o ICC. Models 3-9 show ha ICC is negaively and significanly relaed o marke bea, size, idiosyncraic volailiy, asse growh, and analys coverage, and posiively and significanly relaed o book-o-marke raio and leverage. Finally, Models show ha afer conrolling for he ICC predicors in Models 3-9, boh and reain heir sign and explanaory power. These resuls show ha high indusry profiabiliy dispersion is associaed wih low implied cos of capial, which is consisen 5 See Hou, van Dijk, and Zhang (2012) for deails on heir ICC esimaes. 22

23 wih invesors assigning irraionally low discoun raes o firms in high dispersion indusries hus causing hose firms o be overpriced. 7 Conclusion We find ha firms in indusries ha have higher profiabiliy dispersion have on average higher marke-o-book raios han firms in low dispersion indusries. This posiive relaion is robus o conrolling for variables ha he previous lieraure uses o explain firm valuaion. We idenify four possible explanaions of his posiive relaion ha are based on invesor aenion, mispricing, uncerainy abou mean profiabiliy, and risk. Our analysis shows ha mispricing can beer explain he posiive relaion han he oher explanaions. Firms in high dispersion indusries have higher marke-o-book raios because hese firms are overvalued relaive o firms in low dispersion indusries. 23

24 References Cochrane, J. H. (2011). "Presidenial Address: Discoun Raes." Journal of Finance 66(4): Daniel, K. and S. Timan (2006). "Marke Reacions o Tangible and Inangible Informaion." Journal of Finance 61(4): Fama, E. F. and K. R. French (1998). "Taxes, Financing Decisions, and Firm Value." Journal of Finance 53(3): Frankel, R. and C. M. C. Lee (1998). "Accouning Valuaion, Marke Expecaion, and Crosssecional Sock Reurns." Journal of Accouning and Economics 25(3): Gao, X. and J. R. Rier (2010). "The Markeing of Seasoned Equiy Offerings." Journal of Financial Economics 97(1): Hou, K. and D. T. Robinson (2006). "Indusry Concenraion and Average Sock Reurns." Journal of Finance 61(4): Hou, K., M. A. van Dijk and Y. Zhang (2012). "The Implied Cos of Capial: A New Approach." Journal of Accouning and Economics. Pásor, L. and P. Veronesi (2003). "Sock Valuaion and Learning abou Profiabiliy." Journal of Finance 58(5): Peersen, M. A. (2008). "Esimaing Sandard Errors in Finance Panel Daa Ses: Comparing Approaches." Review of Financial Sudies 22(1): Pinkowiz, L., R. M. Sulz and R. Williamson (2006). "Does he Conribuion of Corporae Cash Holdings and Dividends o Firm Value Depend on Governance? A Cross-counry Analysis." Journal of Finance 61(6): Rhodes-Kropf, M., D. T. Robinson and S. Viswanahan (2005). "Valuaion Waves and Merge Aciviy: The Empirical Evidence." Journal of Financial Economics 77(3):

25 Figure 1 Normalized Number of Firms for Three Groups of Indusries Sored by Profiabiliy Dispersion Each year, he Fama-French 49 indusries are ranked ino hree groups (op five indusries, boom five indusries, and oher indusries) based on heir indusry profiabiliy dispersion,. In he same year, individual firms are also ranked ino deciles based on heir firmspecific profiabiliy. For each group of indusries in each year, we hen coun he numbers of firms falling in each profiabiliy decile rank and normalize hese numbers so ha hey add up o one for each indusry group. Finally, we average he normalized numbers across differen years, resuling in hree separae hisograms of normalized numbers of firms for he hree groups of indusries. Profiabiliy is measured by reurn on equiy, which is earnings divided by lagged book equiy. is he sandard deviaion of firm-level reurn on equiy for each indusry. 25

26 Tab le 1 Fama-French 49 Indusries Sored by Average Indusry Profiabiliy Dispersion Indusry Name Dispersion Number of Firms Compuer Sofware Pharmaceuical Producs Precious Meals Tobacco Producs Communicaion Coal Compuers Business Services Enerainmen Personal Services Healhcare Non-Meallic and Indusrial Meal Mining Peroleum and Naural Gas Elecronic Equipmen Agriculure Recreaion Transporaion Elecrical Equipmen Medical Equipmen Consrucion Consumer Goods Apparel Real Esae Resaurans, Hoels, Moels Prining and Publishing Rubber and Plasic Producs Seel Works Ec Measuring and Conrol Equipmen Wholesale Shipbuilding, Railroad Equipmen Food Producs Beer & Liquor Machinery Reail Auomobiles and Trucks Defense Chemicals Fabricaed Producs Insurance Consrucion Maerials Trading Texiles

27 Indusry Name Dispersion Number of Firms Candy & Soda Almos Nohing Shipping Conainers Aircraf Business Supplies Banking Uiliies The Fama-French 49 indusries are ranked by ime-series average of indusry profiabiliy dispersion measured by. For each indusry and each year in our sample, we calculae he dispersion of profiabiliy as he cross-firm sandard deviaion of reurn on equiy, and hen calculae he ime-series average of profiabiliy dispersion across all years. Also repored is he average number of firms for each indusry. 27

28 Tab le 2 Summary Saisics Mean Sd. Dev. Min. 20% Median 80% Max M ROE RET BOOK ASSET AGE VOLP V / P NI PD _ IND N _ ANLST INST _ OWN TURNOVER ND b s h w SD _ RET This able repors he ime-series averages of cross-secional saisics of he primary variables used in he paper. We use wo measures of indusry profiabiliy dispersion, and. For each year and each one of he Fama-French 49 indusries, is he 28

29 sandard deviaion of firm-level reurn on equiy, and is he 80h percenile minus he 20h percenile of reurn on equiy. The numbers for and in his able are ime-series averages of indusry-level saisics. For oher variables, he able repors he ime-series averages of firm-level saisics. See Table 10 in he appendix for deailed variable definiions. 29

30 Tab le 3 The Relaion beween Indusry Profiabiliy Dispersion and Firm Valuaion Dependen Variable: M M M M M (1) (2) (3) (4) (5) (12.15) (14.50) (10.52) (9.23) E (-0.08) (-0.07) (-0.03) E / + 1 B (10.48) (10.61) (11.10) E / + 2 B (4.79) (5.26) (5.06) A (-3.12) (-2.82) (-2.84) A / + 1 B (1.82) (1.91) (1.86) A / + 2 B (1.22) (1.53) (1.39) RD (1.65) (0.97) (0.94) RD / + 1 B (2.66) (2.61) (2.59) RD / + 2 B (6.25) (6.24) (6.16) I (-1.37) (-1.44) (-1.30) I / + 1 B (2.55) (2.51) (2.53) I / + 2 B (0.40) (-0.02) (0.08) D (2.68) (2.67) (2.68) D / + 1 B (5.11) (8.17) (7.80) D / + 2 B (7.82) (9.29) (9.00) ln( A ) (-1.74) (-1.40) (-1.23) VOLP (2.45) (2.34) (2.34) RET 1, (4.38) (4.53) (4.37) 30

31 RET, (-3.54) (-3.79) (-3.80) RET + 1, (-3.03) (-3.84) (-3.47) Inercep (72.11) (54.49) (10.55) (5.13) (4.93) 2 Adj. R No. of Obs This able esimaes firm-level panel regressions of marke-o-book raio on indusry profiabiliy dispersion and oher conrol variables. is he sandard deviaion of firm-level reurn on equiy for each of Fama-French 49 indusries, and is he 80h percenile minus he 20h percenile of reurn on equiy for each indusry. The conrol variables are seleced based on Fama and French (1998), Pásor and Veronesi (2003), and Pinkowiz, Sulz, and Williamson (2006). They include curren and fuure (nex wo years ) earnings, book asses, R&D expendiure, ineres expenses, and dividends each scaled by curren book equiy, log oal asses, firm-level volailiy of profiabiliy over he previous five years, and curren and nex wo years sock reurns. See Table 10in he appendix for deailed variable definiions. The panel regressions are esimaed wih year fixed effecs and sandard errors clusered by firm and year. Repored are he coefficiens and -saisics in parenheses. 31

32 (1) (2) Tab le 4 Indusry-level Pooled Correlaion Coefficiens (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) Indusry N _ ANLST (3) Indusry INST _ OWN (4) Indusry TURNOVER (5) Indusry V / P (6) Indusry NI (7) Indusry PD _ IND (8) Indusry ln( AGE ) (9) Indusry ND (10) Indusry Indusry Indusry Indusry b (11) s (12) h (13) w (14) Indusry SD _ RET (15) This able repors he pooled correlaion coefficiens of indusry-level variables, including,, and variables proxying for he four explanaions of he posiive relaion beween profiabiliy dispersion and marke-o-book raio. is he sandard deviaion of firm-level reurn on equiy for each of Fama-French 49 indusries, and is he 80h percenile minus he 20h percenile of reurn on equiy for each indusry. The variables proxying for he invesor aenion explanaion are number of analyss, N _ ANLST, insiuional ownership, INST _ OWN, and share urnover, TURNOVER. The variables proxying for he mispricing explanaion are fundamenal value o price raio, V / P, ne share issuance, NI, and indusry-level pricing deviaion, PD _ IND. The variables proxying for he uncerainy abou mean profiabiliy explanaion proposed by Pásor and Veronesi (2003) are ln( AGE ) and ND. The variables proxying for he risk explanaion are b, s, h, w, and SD _ RET. The firs four variables are he loadings on he Fama-French hree facors plus he momenum facor esimaed over he pas five years, and SD _ RET is he sandard deviaion of monhly reurns over he pas five years. 32