The Influence of Productivity on Asset Pricing

Transcription

1 December 16, 2008 The Influence of Produciviy on Asse Pricing Laurence Booh, Bin Chang, Walid Hejazi, and Pauline Shum* Absrac Ceeris Paribus, highly producive indusries should ranslae ino high economic growh and high expeced reurns. To es his, we creae a produciviy facor using 4-digi indusry-level oal facor produciviy esimaes. This facor capures he difference in sock reurns beween high and low produciviy indusries. Beween 1963 and 2002, he produciviy premium conribues on average 0.75 o 2.41 percen per annum for he range of produciviy facors we consruc. Our resuls show ha i) in accordance wih our hypohesis, produciviy has a robus, posiive impac on reurns, and his impac is bigger on smaller, growh firms, and ii) produciviy helps price asses even when size, book-o-marke, and momenum are aken ino accoun. Finally, since 1990, firms in more compeiive indusries are more likely o show higher produciviy and gain from i. JEL classificaion: G12 Keywords: Produciviy, asse pricing, Fama and French facors * Bin Chang is from he Faculy of Business & IT a he Universiy of Onario Insiue of Technology, Laurence Booh and Walid Hejazi are from he Roman School of Managemen a he Universiy of Torono. Pauline Shum is from he Schulich School of Business a York Universiy. We hank Wayne Gray and Debarshi Nandy for providing he produciviy daa, Raymond Kan, Dan Trefler, and paricipans a he 2008 Norhern Finance Associaion Conference, he Roman Docoral Suden Finance Seminar, and he Schulich Finance Brown-Bag seminar for valuable commens.

2 I. Inroducion In his paper, we examine he link beween produciviy and he cross-secion of sock reurns. Produciviy plays an imporan role in modern heories of economic growh, daing back o classic works by Ramsey (1928) and Schumpeer (1934). Ceeris Paribus, highly producive economies ranslae o high economic growh and high expeced raes of reurn. Alhough he early models did no deal wih uncerainy, he inuiion would hen follow ha uncerainy surrounding he rae of produciviy and economic growh should be a primary facor in pricing risky asses. Our focus on he producion side of he economy is in par moivaed by he poor empirical performance of he consumpion-based CAPM (CCAPM), which, while inuiively appealing, has ye o receive convincing empirical validaion. On he oher hand, he empirical weakness of he original CAPM of Sharpe (1964) and Linner (1965) has given rise o he Fama-French (1992, 1993) hree-facor model. Alhough facors such as size and book-o-marke help explain a significan par of he cross-secional variaion in sock reurns, i is sill no clear wheher hese firm characerisics reflec risk differences or marke imperfecions. Our hypohesis is ha produciviy is relaed o boh size and book-o-marke, hereby providing some economic inuiion for hese wo celebraed facors. As a robusness check, we also consider he impac of momenum as an addiional facor, alhough he link beween momenum risk and produciviy is no obvious (in fac, he correlaion beween he wo is ). Firs, wih respec o size, Schumpeer recognized he creaive desrucive forces of capialism generaed by produciviy and/or echnological change. These forces primarily affec young firms as new indusries are creaed and old ones die. Chamberlin 2

3 e al. (2002) look a how produciviy changes affec he sock marke during he Inerne Bubble, which was largely driven by young sar-ups. RBC Financial Group also noes in a research repor 1 ha, (in) 56 percen of indusries, micro employers had faser produciviy gains han he indusry average. This suggess ha more ofen han no, relaively small firms have led bigger firms in produciviy growh. Hence, produciviy should be negaively relaed o size. Second, wih respec o book-o-marke, i is in he naure of sar-ups ha book equiy has no been buil up hrough reained earnings and a consisen hisory of profiabiliy. In addiion, highly producive firms will experience high growh. Boh observaions ranslae o a lower book-o-marke raio. Our line of research follows recen effors o include addiional sae variables in he asse pricing model. 2 The idea ha asse prices may be relaed o produciviy has recenly been examined by Balvers and Huang (2007). They show ha in a compeiive complee marke economy, he marginal rae of subsiuion in consumpion of he represenaive agen is he same as he marginal rae of ineremporal ransformaion. The laer is he rae of reurn on invesmen, as in he early cerainy model of Hirshleifer (1958). Balvers and Huang implemen his idea hrough he sensiiviy of a securiy o a single aggregae produciviy shock. While he resuls from heir heoreical model are inuiively aracive, he empirical suppor is mixed. In his paper, we conribue o he empirical evidence from a differen perspecive. We make use of disaggregae (four-digi SICs) produciviy daa for he manufacuring 1 Curren Analysis, RBC Financial Group, Ocober 2006, available a: hp:// rbc.com/economics. 2 A parial lis includes uninsured idiosyncraic risk examined by Consaninides and Duffie (1996), housing by Piazzesi e al. (2003), producion by Cochrane (1991), and lagged consumpion by Campbell and Cochrane (1999). 3

4 secor, provided by he Naional Bureau of Economic Research (NBER) and he U.S. Census Bureau's Cenre for Economic Sudies (CES). We follow he facor-mimicking porfolio echnology inroduced by Fama and French (1993), which has revoluionized he empirical asse pricing lieraure, and has largely displaced he direc use of economic variables as in Chen, Roll, and Ross (1986) and facor analysis iself as in Lehmann and Modes (1988). By creaing facor mimicking porfolios wih respec o produciviy, we capure he inuiion ha i is he sock marke reacion o produciviy changes, in creaing uncerain capial gains and losses ha causes risk, raher han he produciviy changes hemselves ha influence reurns. This is imporan since i is difficul o capure uncerain capial gains and losses in a represenaive agen economy 3, as in he case of Balvers and Huang. In examining he impac of produciviy differences across indusries, we aemp o address hree main research quesions. Firs, do sock reurns reflec produciviy, a fundamenal deerminan of growh? Second, is produciviy priced in he sock marke? And hird, are he well-known facors, namely, size and book-o-marke relaed o produciviy, hereby providing hem wih an economic inerpreaion as well as insigh ino why hese firm characerisics may reflec risk facors? To preview our resuls, we find ha for he range of produciviy facors we consruced, hey conribue 0.75 o 2.41 percen annually. This is a similar order of magniude o he Fama-French size premium, bu less han he value premium. More 3 Capial gains and losses are no included in he GNP accouns since in aggregae he economy, like he represenaive agen canno consume capial gains and losses. 4

5 imporanly, produciviy has a posiive impac on reurns as we hypohesized, and i is shown o be a significan facor in pricing asses, even afer we conrol for size, book-omarke, and momenum. We also find ha he impac of produciviy on firms is no universal. Insead, i has a higher impac on small and growh firms. Furher, we show ha book-o-marke does explain priced informaion ha is unrelaed o produciviy, and i is exremely robus. Since our es asses are porfolios of manufacuring firms, our resuls also have implicaions for fund managers. Manufacuring, afer all, accouns for more han 50 percen of he S&P500 companies in We find ha size and momenum are no imporan facors for pricing asses in his secor. The remainder of he paper is organized as follows. Secion II discusses our model, daa and summary saisics. Secion III describes our asse pricing ess and resuls. Secion IV exends he analysis o examine he impac of indusry concenraion on produciviy and asse reurns. Secion V provides conclusions. II. The Model, Daa, and Summary Saisics Theoreical asse pricing models are ypically based on he firs-order condiion for a represenaive agen maximizing a von-neumann Morgensern expeced uiliy funcion. Tha is, for any securiy j, E( γ (1 R )) = 1 (1) + j 5

6 where R j is he reurn on he jh risky asse, and γ is he marginal rae of subsiuion beween ime periods 0 and 1. 4 Expanding he expecaion and assuming approximae normaliy, Rubinsein (1976) showed ha (1) can be reformulaed as an asse pricing model, E R ) = r + acov( z, R ) (2) ( j f j where he risk free rae, should one exis, is defined by he inverse of he expeced marginal uiliy in ime period 1, and a is a measure of he invesor s Pra-Arrow absolue risk aversion. Equaion (2) can be simplified in many ways. If he argumen of he invesor s uiliy funcion, z, is consumpion, hen he marginal rae of subsiuion is deermined based on consumpion, as in he CCAPM. If, in conras, he argumen in he uiliy funcion is uncerain wealh, hen he marginal rae of subsiuion is deermined by he marke porfolio, as in he CAPM. If we define z as a linear funcion of various risks in he economy, we ge a linear pricing model. For hree facors, F 1, F 2, and F 3, we have, E R ) = r + a Cov( F, R ) + a Cov( F, R ) + a Cov( F, R ( j f 1 1 j 2 2 j 3 3 j ) This specificaion resuls in a sandard muli-facor model where he expeced reurn on he j h securiy is equal o he risk free rae plus a series of risk premia deermined by he covariance of he securiy s reurn wih ha on each risk facor. From he facor analysis of Lehmann and Modes, we would expec here o be a mos hree or four facors. The reurn on he marke porfolio would be one facor, where following Cochrane (1991) and in he spiri of Hirshleifer and Ramsey, he marke reurn in a complee marke is equal o 4 The firs-order condiion is increasingly referred o as he pricing kernel and γ he sochasic discoun facor. 6

7 he reurn on invesmen. The wo or hree addiional risk facors can hen be viewed as hedging porfolios in he spiri of Meron (1973), Sapleon and Subrahmanyam (1978), and Breeden (1979). One such hedging porfolio would be he reurn on a produciviy facor which shifs he aggregae producion funcion, and hus he reurn on invesmen. In his paper, we will consider he following empirical specificaions. Firs, we examine he empirical relevance of produciviy and is impac on he overall sock marke. Second, we consider he produciviy facor wihin he conex of he Fama- French hree-facor model o see wheher size and book-o-marke proxy for he more primal produciviy facor. Finally, we exend he empirical model o include he welldocumened momenum facor. Our produciviy daa come from he NBER-CES Manufacuring Secor Daabase. This daabase conains annual indusry-level daa on oupu, employmen, payroll and oher inpu coss, invesmen, capial socks, oal facor produciviy (TFP), and various indusry-specific price indexes. We use he five-facor produciviy esimae as our measure of produciviy, where he five facors are: Capial, producion worker, nonproducion workers, energy, and non-energy maerial. TFP reflecs oupu per uni of a se of combined inpus. A change in TFP reflecs he change in oupu ha canno be accouned for by he change in ha se of combined inpus. Consequenly, TFP represens he join effecs of many forces, such as research and developmen, echnological breakhrough, economies of scale, managerial skill, and changes in he organizaion of producion. Barlesman and Gray (1996) describe he NBER produciviy daabase where five-facor TFP is measured as follows: 7

8 TFP = Q =1 α X 5 i i i where Q is real oupu, i is he share of facor i in erms of revenues, and X i is he oupu of facor i, expressed in erms of log firs differences. TFP growh is hen esimaed as he growh rae in real oupu minus he average growh rae from he five inpus, where he shares come from he Annual Survey of Manufacurers, wih he capial share being he residual so he shares sum o one. In all cases he growh raes are expressed in real erms, so he produciviy growh variable is an esimae of real produciviy growh. There is an acive research agenda as o he correc deflaor o calculae he real growh raes. 5 However, his does no seem o be significan for he resuling TFP measure. For example, he Bureau of Labour Saisics (BLS) provides muli-facor produciviy esimaes for 3-digi SIC indusries from 1987 o We aggregae capial-weighed TFP for he whole manufacuring secor and for he correlaion beween he NBER-CES measure and he BLS measure is Since he NBER-CES measure provides finer daa a he 4-digi SIC indusry level and covers a much longer ime period, we use his esimae in our ess. The produciviy daase covers digi SIC manufacuring indusries from 1958 o Our sock marke daa are from CRSP. Alhough he produciviy daa sar in 1958, merging he wo daases leaves only one indusry in he manufacuring secor for he firs four years (1958 o 1962). Hence, our empirical analysis begins in 5 See Young (1995) 6 Firm-level produciviy daa are no publicly available. Noe ha our focus on he manufacuring secor is similar o many empirical sudies in corporae finance, such as hose relaed o financing decisions. In addiion, measuring produciviy in he service indusry is challenging, due o he difficuly in measuring oupus and labour inpus (see Mark (1982)). 8

9 1963, which is also he firs year of he Fama-French facors. All produciviy series are normalized o one in Following Fama and French, he produciviy mimicking porfolio is consruced from July 1 in year o June 30 in year +1, and mached o produciviy in year -1. This is o allow a recogniion lag, so ha produciviy changes can be absorbed by he marke in he same way as for he Fama-French facors. We use monhly reurns in all of our analyses. Panel A of Table 1 repors he number of indusries wihin he manufacuring secor per year and he number of firms per indusry per year. [Table 1] To provide an overview of he imporance of produciviy, we firs consruc a capial sock-weighed produciviy growh index for he manufacuring secor as a whole. Figure 1 shows he annual sock marke reurn and he produciviy growh for he manufacuring secor from 1963 o The casual empiricism of Figure 1 suggess ha sock reurns vary posiively wih produciviy growh. This relaionship seems paricularly srong in he pos-1982 period, when he real effecs of produciviy changes are no swamped by high inflaion raes during he wo oil crises. 7 [Figure 1] Panel B of Table 1 shows he imporance of he manufacuring secor. We include hree snapsho years: 1963, he sar of he sample, 1983 as he middle, and 2002 as he end of he period. The CRSP porfolio includes socks from NYSE, AMEX, and NASDAQ. The rend in CRSP is he exac opposie of he rend in he S&P500: Manufacuring s relaive significance declined in he overall U.S. marke, bu increased 7 The correlaion beween hese wo series is 0.24 for he whole sample period, bu 0.54 afer

10 wihin blue chip socks. This difference is no doub aribued o he rapid growh of he NASDAQ marke in he 80 s and he 90 s. In 1963, 50 percen of he firms in CRSP were manufacuring firms and hey represened 56 percen of he marke capializaion. By 2002, hese proporions have decreased dramaically o 16 percen of he firms, wih 34 percen of he marke capializaion. The larger capializaion, as compared o simple firm weighs, indicaes ha he size of he firms in he manufacuring secor is larger han ha in he oher secors. Wihin he S&P500, however, manufacuring grew o represen more han half of he index in boh firm coun and marke capializaion. Table 2 repors he average annual produciviy level, he sock price index, firm size, book-o-marke raio, as well as he correlaion among hese variables. The oal sample includes 10,741 4-digi SIC indusry-year observaions. The sock price index is normalized o one in 1963, as is he produciviy level. The sock price index in a given year is one plus he cumulaive reurn since One hypohesis is ha higher profis due o increased produciviy are compeed away in more compeiive indusries, hereby reducing any impac on sock marke reurns. We use he Herfindahl index o measure he degree of compeiion, where he index is calculaed as he sum of squared shares of each firm wihin an indusry, measured using marke capializaion. Hou and Robinson (2006) and Massa, Rehman, and Vermaelen (2007) measure indusry concenraion using he Herfindahl index. 8 The inuiion is ha he higher he Herfindahl index, he more concenraed he indusry is. 8 The Herfindahl index is superior o he concenraion raio because concenraion raios ignore he number of firms wihin he indusry. Imagine wo indusries wih he same four-firm concenraion raios, bu one wih only 10 firms and he oher wih 1,000 firms. The Herfindahl index akes his difference ino accoun, whereas he concenraion raio does no. 10

11 Hence, here is an increased likelihood of reduced compeiion, as he sock marke capializaion is divided among fewer firms. Panel A in Table 2 shows ha over his long period, here has been persisen growh in produciviy, sock marke value, and firm size. Ineresingly, he correlaion beween he average produciviy level and he Herfindahl index has no been consisenly posiive or negaive. Before he 1990s, he correlaion was generally posiive indicaing ha here was greaer produciviy growh in less compeiive indusries dominaed by large firms, bu since hen he correlaion has urned negaive. Even hough he relaionship is a bes weak (only he correlaion coefficiens from 1996 o 1998 are saisically significan), his paern is suggesive of he emergence of new indusries in he 1990s during he echnology boom. Prior o ha, he echnological advance was pioneered by mosly esablished firms wih significan marke power and high Herfindahl index values. [Table 2] Panel B of Table 2 repors he average correlaion amongs he variables in Panel A. The produciviy level is highly posiively correlaed o he sock price index (0.831) and firm size (0.96), bu negaively correlaed o book-o-marke (-0.409). Nex, we creae a facor mimicking porfolio in he syle of Fama-French o capure he produciviy premium. To do his, we firs calculae he monhly equallyweighed reurn for each 4-digi SIC indusry. We use equally-weighed reurns because our hypohesis is ha produciviy is driven predominanly by smaller firms. We hen calculae he difference beween he mean indusry reurn in he op produciviy quinile and ha in he boom quinile for each monh from July in year o June of year +1. We 11

12 name his facor PFSIC4Q, ha is, he produciviy facor formed on SIC 4-digi produciviy quiniles (op quinile minus boom quinile equally-weighed porfolios). We use PFSIC4Q as he reurn on he facor mimicking porfolio hroughou his paper. As a robusness check, we also consruc alernaive facors. For example, we repea he above procedures for 3-digi SIC indusries, we use deciles insead of quiniles, and value-weighed average reurns in addiion o equally-weighed reurns. For comparison, we also calculae he indusry SMB and HML for he manufacuring secor using he Fama-French mehodology. Table 3 repors he summary saisics for PFSIC4Q and several alernaive specificaions. The average excess reurn ranges from 0.75 o 2.41 percen per year, close in magniude o he SMB for manufacuring firm, SMB M. The laer generaes 1.94 percen annually in average excess reurns, while HML M generaes 4.22 percen. Alhough he SMB and he HML for manufacuring firms have smaller excess reurns compared o hose from he full CRSP sample, hey are sill highly correlaed: he correlaion beween SMB for manufacuring and SMB for he whole CRSP daa base is 0.94, while for HML i is I is worh highlighing ha we are dealing wih an unbalanced panel, wih firms enering and exiing he sample over ime. We do no believe ha his has a significan impac on our resuls. Firs, we only consider he average reurns in he op and boom quiniles. The enrance and exi of firms in he middle quiniles do no maer. Second, even for he op and boom quiniles, we only use he difference in average reurns, no firm-specific informaion. In fac, ignoring he comings and goings of firms may acually underesimae he produciviy premium: Highly produciviy indusries arac newcomers which may have less produciviy han he curren firms and drag down he reurn in he nex year. Also, when he leas producive firms exi low-produciviy indusries, he saying firms on average have higher produciviy and higher expeced reurn han he exised firms in he same indusry 12

13 Consisen wih our argumen, mos of he produciviy facors are posiively correlaed wih SMB, and all of hem are negaively correlaed wih HML. Hence, in general erms, we can say ha produciviy does affec reurns in he capial marke and ha as hypohesized, i is closely relaed o he Fama-French size and book-o-marke facors. [Table 3] III. Can Produciviy Help Explain Sock Reurns? III.A Facor Loading on Produciviy Porfolios To see wheher produciviy helps explain sock reurns, we employ he following four facor ime-series model: R = α + β e_ R + β PF m PFSIC4Q m + ε + β SMB e_ SMB + β HML e_ HML (3) where R is he monhly excess reurn on he es porfolio, R m is he monhly CRSP value-weighed excess reurn, PFSIC4Q is he monhly produciviy facor, and e _ R m, SMB e _, and e _ HML are he monhly residuals from he following regressions: R = α + β PFSIC4Q + e m PF SMB = α + β PFSIC4Q + e PF HML = α + β PFSIC4Q + e PF 13

14 where, and and are i.i.d. error erms. The s capure he variaions in marke excess reurn, SMB, and HML ha are unrelaed o he variaions in produciviy. The above specificaion is designed, firs of all, o es he hypohesis ha produciviy affecs sock reurns as Figure 1 suggess. In paricular, we expec he produciviy facor o have a bigger impac on small firms and on growh (i.e., low booko-marke, or B/M) firms. Second, i is designed o examine wheher marke excess reurn, SMB, and HML sill have an impac on sock reurns afer conrolling for produciviy. The dependen variable, R, is he reurn on hree differen es porfolio groups. The firs group consiss of 10 equally-weighed porfolios sored by size; he second consiss of 10 equally-weighed porfolios sored by B/M; and finally, he hird consiss of 25 equally-weighed porfolios sored by boh size and B/M. These hree porfolio groups are idenical o hose used by Fama and French (1993). Panel A of Table 4 shows he resuls for he firs se of porfolios sored by size. The produciviy bea, β PF, is highly significan, and is magniude decreases monoonically wih size. Hence, in accordance wih our hypohesis, produciviy has a bigger impac on smaller firms han on larger ones. The residual impac of he marke excess reurn, as measured by β m, is also highly significan, bu i is fairly uniform across differen size porfolios. The residual impac of SMB and HML is mosly significan as well, excep for wo larger cap porfolios. Noe ha he sign of he e _ SMB bea acually urns negaive in he 9 h and 10 h decile porfolios. Overall, he posiive impac of produciviy on small firms is srong: The correlaion beween he average excess reurn on each size porfolio and is corresponding produciviy bea is high a In 14

15 addiion, he produciviy beas are larger in magniude han he beas of e _ SMB and e _ HML. [Table 4] Panel B of Table 4 shows he resuls for es porfolios formed on B/M deciles. Again, he produciviy bea, β PF, is posiive. However, he relaionship beween B/M and β PF is non-linear and U-shaped: Boh high and low B/M porfolios have larger produciviy beas. One would expec low B/M, ha is, high growh socks o be correlaed wih high produciviy, bu he relaionship for high B/M firms is a surprise. One explanaion is he indirec relaionship hrough size, ha is, B/M may be correlaed wih size. In order o disenangle he effecs of produciviy on B/M and size, Panel C of Table 4 shows he resuls for he 25 porfolios formed on boh size and B/M quiniles. Again, β PF decreases wih size. However, more imporanly, we are able o isolae he impac of produciviy on B/M porfolios by examining he bea paern wihin each size quinile. For each size porfolio, B/M has in general, a negaive relaionship wih he produciviy bea. Tha is, growh firms have a higher produciviy bea, as we hypohesized. These resuls are consisen wih Schumpeer s argumen ha produciviy changes generae new indusries (capured here by small, growh firms), and he desrucive forces of capialism make hem risky. Noe ha he residual of HML isn able o explain high growh firms (firs quinile by B/M wihin each size quinile); i eiher has he wrong sign, or is saisically insignifican. Also, he residual of SMB has he wrong sign for high value firms (fifh quinile by size). However, overall, one canno dismiss he observaion ha he residuals 15

16 of SMB and HML have imporan explanaory power in he res of he regressions, suggesing ha in addiion o proxying for produciviy, size and B/M are robus risk facors in heir own righ. III.B Asse Pricing Tess The resuls in he previous secion provided informal evidence ha produciviy helps explain he cross-secion of sock reurns. We now urn o wo formal asse pricing ess: he classic wo-pass Cross-Secional Regression (CSR) model 10 and he Sochasic Discoun Facor (SDF) model. III.B.1 Two-pass CSR approach In he wo-pass CSR model, we firs run a ime-series regression for each es porfolio. Using he esimaed porfolio beas, we hen run a cross-secional regression, and esimae he risk premium for each facor. This procedure is summarized as follows. R i = α + β ' f + ε (4) i i i = 1, 2,... T for each es porfolio i; and Ri = ˆ β ' λ + ε i i (5) i = 1... n. 10 This approach is he mos widely used asse pricing es. See for example, Fama and French (1992), Harvey and Siddique (2000), Leau and Luvdigson (2001), and Li, Vassalou, and Xing (2004), among ohers. For a discussion of his approach, see Chen, Roll, and Ross (1986), Shanken (1992), Jagannahan and Wang (1997), Ferson and Harvey (1993), and Kan and Zhang (1999). 16

17 where Ri is he excess reurn on porfolio i in monh, Ri is he average monhly excess reurn on porfolio i, f is a vecor of risk facors, β i is a vecor of facor loadings, λ is a vecor of risk premiums, n is he number of es porfolios, and T is he number of monhly observaions in he sample. 11 We esimae (5) using Generalized Leas Squares (GLS), o accoun for he fac ha he residuals may be correlaed wih each oher. To assess wheher he linear specificaion is correc, we repor Shanken (1985) s Cross-Secional Regression Tes (CSRT) saisic. This saisic measures he aggregae expeced reurn errors; is finie sample disribuion under he null hypohesis is provided by Shanken. III.B.2. Sochasic Discoun Facor Approach The oher asse pricing es we perform follows he Sochasic Discoun Facor (SDF) approach. I can be implemened using he Generalized Mehod of Momens (GMM) pioneered by Hansen (1982). The GMM mehod is widely used in asse pricing ess, including Jagannahan and Wang (1996, 2002, and 2007), Jagannahan, Kuboa, and Takehara (1998), Campbell and Cochrane (2000), Leau and Ludvigson (2001), Hodrick and Zhang (2001), Farnsworh, Ferson, Jackson, and Todd (2002), Dimar (2002), among ohers. As discussed in Cochrane (2001), here is no consensus on wheher he wo-pass CSR regression approach ouperforms he SDF approach or vice versa. Hence, we perform boh ess. The SDF approach direcly ess (1), which in excess reurn forma is: 11 This mehod is equivalen o Fama and MacBeh (1973) if he errors are uncorrelaed over ime, which may no be an unreasonable assumpion if reurns are fairly independen. 17

18 E( γ ) = 0 R i where γ is he SDF, and R i is he excess reurn on porfolio i. The radiion is o specify he SDF as a linear funcion of a series of facors, i.e., γ = a + b f, where f is a vecor of facors, a is a consan, and b is a vecor of parameers. Kan and Roboi (2008) poin ou ha his specificaion is problemaic for he following wo reasons. Firs, he specificaion es saisic is no invarian o an affine ransformaion of he facors. Second, he SDFs of compeing models can have very differen means, hus complicaing he ask of model comparison. Kan and Roboi recommend an alernaive specificaion ha defines he SDF as a linear funcion of he de-meaned facors: γ = 1- (f - e[f])'b. Wih de-meaned facors, he vecor of risk premiums is equal o: λ = var(f)b As Cochrane (2001) explains, when facors are correlaed, we should es H 0 : b j =0, o see wheher or no o include facor j in an asse pricing model, raher han es H 0 : λ =0. This is because j λ j capures wheher facor f j is priced, whereas b j capures wheher facor f j is marginally useful in pricing asses, given he oher facors. If we rejec H 0 : b j =0, hen we should include facor f j when we price asses. The lieraure compares he performance of compeing asse pricing models using he Hansen and Jagannahan (1997) disance (he HJ disance). There are wo nice inerpreaions of he HJ-disance. The firs is ha he HJ disance measures he minimum disance beween he proposed SDF and he se of correc SDFs. The second is ha i 18

19 represens he maximum pricing error of a porfolio of excess reurns ha has a uni second momen. The smaller is he HJ disance, he smaller is he pricing error. Kan and Roboi (2008) sugges ha a modificaion of he HJ disance is needed when de-meaned facors are employed. Their modified HJ disance uses he inverse of he covariance marix (insead of he second momen marix) of excess reurns as he weighing marix o aggregae pricing errors. We apply he modified HJ disance o compare model performance in his paper. We also employ Shanken (1992) s correcion o he sandard errors of λ, o accoun for he fac ha he beas esimaed in he firs sep are used as regressors in he second sep, hus creaing an errors-in-variables problem. 12 III.B.3 The Empirical Models Our goal is o address he following wo quesions in he asse pricing ess: i) does produciviy help price asses in he presence of oher facors? And ii) do he popular facors, SMB, HML, and momenum, proxy o varying degrees for produciviy? To do his, we esimae four differen models and compare heir resuls: Model 1 (CAPM): R = α + β R + ε m m Model 2 (Fama and French): R = α + β R + β SMB + β HML + ε m m SMB HML Model 3 (Fama and French wih PFSIC4Q): R = α + β PFSIC 4 Q + β R + β SMB + β HML + ε PF m m SMB HML 12 Shanken shows ha alhough he beas are esimaed wih errors, he errors end o zero as T goes o infiniy, and he esimae of λ is T-consisen when his correcion is made. 19

20 Model 4 (Fama and French wih PFSIC4Q and momenum facor, UMD): R + β = α + β PFSIC 4Q + β R UMD PF UMD + ε m m + β SMB SMB + β HML HML We use he CAPM (Model 1) and he Fama and French model (Model 2) as benchmarks. Model 3 is he Fama and French model augmened by he produciviy facor. Model 4 is furher augmened by he Fama and French version of he momenum facor, UMD. The dependen variable, R, is he excess reurn on he es porfolio. To generae dispersion across he facors, we perform a hree-way independen sor. All equiies in our manufacuring sample are sored ino hree porfolios according o produciviy, size, and B/M. Hence, we have 27 equally-weighed porfolios formed from he inersecion of he hree independen sors. Each porfolio has 474 monhly observaions. Table 5 displays he formaion and he mean excess reurn of each porfolio. [Table 5] III.B.4. Empirical Resuls Consider firs he resuls from he wo-pass CSR model. The firs sep of he model involves 27 ime-series regressions, i.e., one for each of he es porfolio. Figure 2 summarizes he esimaed beas of (or loadings on) he produciviy facor, PFSIC4Q, for he four facor model wih orhoganalized residuals in Table 4. The porfolios are ordered according o Table 5. The produciviy beas are posiive and significan for all of he es porfolios. Furher, hey monoonically decrease wih size, in he same way as for he model in Table 4, bu he relaionship wih B/M is no as clear. However, wihin each of he size-b/m porfolio, he bea is he highes in he highes produciviy porfolio. 20

21 [Figure 2] Panels A and B of Table 6 shows he resuls from he SDF approach, wih Panel A for he vecor of pricing coefficiens, b, and Panel B for he vecor of risk premiums, λ. Firs, he pricing coefficiens of PFSIC4Q facor are posiive and significan a five percen in Models 3 and 4. This resul suggess ha PFSIC4Q helps price asses, even in he presence of SMB, HML, and UMD. Second, Panel A shows ha HML is highly significan in all four models, while SMB is never significan, and neiher is UMD. Hence, our resuls sugges ha size and momenum are no useful in pricing asses in he manufacuring secor. Finally, he probabiliy value of he modified HJ disance is close o zero, hus rejecing he hypohesis ha he aggregae pricing error is zero a one percen. So i appears ha here are oher facors ha may be imporan in explaining he cross-secional variaions in sock reurns ha are no considered here. Across he four models, he modified HJ disance in Model 4 is he smalles. This means ha any misspecificaion presen in Model 4 ranslaes ino a smaller pricing error han in he oher hree models. [Table 6] Panels C of Table 6 shows he risk premium esimaes from he wo-pass CSR model. Rounded off o four digis, he esimaed λ. s are he same as hose from he SDF model in Panel B. This confirms Cochrane (2001) and Jagannahan and Wang (2002) ha he apparenly new SDF approach is almos idenical o he radiional CSR mehod. The risk premium resuls in Panels B and C can be summarized as follows. Firs, he produciviy risk premium is posiive, alhough i is only significan a 10 percen in Models 3 and 4, as is he case for he marke risk premium, M. (Noe ha he esimaed 21

22 marke risk premium is quie reasonable: In Model 4, i is 0.50 percen per monh, which ranslaes o abou six percen per annum.) Second, HML is a robus risk facor ha is priced across all four models. However, he size (SMB) and momenum (UMD) premiums are no priced. Finally, Shanken (1995) s CSRT saisics are significanly differen from zero a one percen for all four models, again suggesing model misspecificaion. 13 One migh be roubled by he drop in saisical significance in he risk premium esimaion. Ang, Liu, and Schwarz (2008) sugges ha he issue may lie in he use of porfolios - as opposed o individual socks - in asse pricing ess. They show ha while porfolios improve he esimaion of beas, hey lead o higher asympoic sandard errors in he risk premium esimaes. The poor performance of he momenum facor for manufacuring socks conrass wih he resuls from exising sudies ha use he whole CRSP daabase. To invesigae, we consruc a momenum facor using socks from he manufacuring secor only. Following Fama and French, we build six value-weighed porfolios based on size and reurns in (-12, -2) monhs o creae he manufacuring UMD. The laer has a mean of 0.5 percen per monh, in conras o a mean of 0.9 percen for he full CRSP sample. Hence, he momenum premium in he manufacuring secor is considerably lower, and he difference is no due o size, as he way UMD is consruced, i has already neuralized he size effec. In order o explore he impac of pas reurns only, we follow Jegadeesh and Timan (1993) and creae an alernaive momenum facor based solely on 13 We also esed he four models on 25 equally-weighed size/bm porfolios for he whole NYSE/AMEX/NASDAQ daabase obained from Ken French s websie. The es resuls are similar o hose in Table 6. 22

23 pas reurns. We firs sor socks ino deciles based on reurns in (-12, -2) monhs, and consruc a porfolio ha longs socks in he highes reurn decile and shors socks in he lowes reurn decile, wih a one-monh holding period. We find ha his momenum facor has a mean of -0.4 percen. We conclude ha momenum in manufacuring is much weaker han ha in he full CRSP sample. We have shown ha produciviy is a saisically significan risk facor. An imporan quesion o ask is wheher i is economically significan. Consider he impac of ignoring produciviy on reurns. As shown in Model 4, Panel C of Table 6, he produciviy premium is per monh. If we muliply i by one cross-secional sandard deviaion (i.e., he sandard deviaion of he produciviy bea esimaes in he firs sep of he wo-pass CSR approach), i ranslaes ino an excess reurn of 0.91 percen on an annual basis. This is economically significan because he Fama-French facors and momenum are already conrolled for. IV. Produciviy and Marke Srucure Nex, we examine he impac of marke srucure on he relaionship beween produciviy and sock reurns. The Herfindahl Index measures he degree of concenraion in each indusry. I is consruced as he sum of squared marke shares across all firms in he indusry. Generally speaking, he larger he Herfindahl index, he less compeiive he indusry is, and vice versa. There are wo opposie argumens abou he relaionship beween he Herfindahl index and he cross-secion of sock reurns. The firs is ha in a more compeiive indusry, firms use more advanced echnologies o improve produciviy as a maer of survival. As a resul, he produc of he Herfindahl 23

24 index and produciviy should have a negaive relaionship o sock reurns. The alernaive argumen is ha in a concenraed indusry (ie a high Herfindahl index), larger firms have he capabiliy, in erms of capial, o use he laes echnology o increase produciviy. We es he impac of he produc of he Herfindahl index and produciviy on he cross secion of indusry reurns. The manufacuring secor includes exacly 20 2-digi SIC indusries each year; we calculae he equally weighed monhly reurns for each 2- digi SIC indusries. Since Table 2 reveals ha he correlaion beween produciviy and he Herfindahl index changes sign around 1990, we divide he sample ino wo subperiods, and run a pooled OLS regression on he panel daa. Table 7 shows he es resuls. The loading on he produciviy facor iself is always posiive and significan in he wo sub-samples. However, he sign of he coefficien esimae of he ineracion erm for produciviy and he Herfindahl index changes from insignificanly posiive o significanly negaive in he second sub-period. In an unrepored es, we do he same es using 4-digi SIC indusry porfolios and find he produciviy coefficien changes from insignificanly negaive o significanly negaive. I seems ha since 1990, firms in more compeiive indusries are more likely o show higher produciviy and gain from i. We acknowledge ha in such a imes-series cross-secional seing we need o be cauious abou he OLS -saisics, since hey are usually over-saed. However, we believe ha he resuls sill provide insigh as o he impac of indusry compeiion and produciviy on equiy reurns. [Table 7] 24

25 V. Conclusion In his paper, we examine he effec ha produciviy may have on sock reurns. We creae a produciviy facor using indusry oal facor produciviy esimaes from he NBER-CES daabase. This facor capures he difference in reurns beween indusries wih high produciviy and indusries wih low produciviy. On average, he produciviy premium conribues 0.75 o 2.41 percen per annum for he range of produciviy facors we consruc, from July 1963 o December Consisen wih our hypohesis, produciviy has a robus, posiive impac on sock reurns. We also expec produciviy o come from small, growh firms. Indeed, we find ha he produciviy facor is posiively correlaed wih he Fama and French size premium, SMB, and negaively correlaed wih heir value premium, HML. In boh a CAPM and a Fama and French framework augmened by he produciviy facor, we find ha for he 10 size porfolios, he produciviy bea decreases monoonically wih size. In oher words, produciviy has a bigger impac on smaller firms han on larger ones. We also find ha wihin each size porfolio, he produciviy bea is higher in lower book-omarke porfolios. Tha is, growh firms have a higher produciviy bea. We hen examine hrough asse pricing ess wheher produciviy is priced, and we find ha i is indeed, even afer conrolling for SMB, HML, and he momenum facor, UMD. Our resuls show ha, alhough SMB and HML conain some produciviyrelaed informaion, his is no he reason ha he Fama French model is able o explain he cross-secion of sock reurns. SMB and HML appear o conain oher significan price informaion, unrelaed o produciviy. Our resuls show ha produciviy is a variable worh considering in asse pricing ess, above and beyond size and book-o- 25

26 marke. Finally, using he Herfindahl index, we find ha since 1990, firms in more compeiive indusries are more likely o show higher produciviy and gain from i. 26

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32 Figure 1 Annual Sock Reurns and Produciviy Growh in he Manufacuring Secor This figure represens he value-weighed annual sock reurns in he manufacuring secor and he capial sock-weighed produciviy growh. The sample period is from July 1963 o December Value-weighed reurns are consruced from July 1 in year o June 30 in year +1. Produciviy growh is he rae of change in he 5-facor produciviy level in he calendar year -1 for 4-digi SIC indusries Sock Reurn Produciviy Growh 0 yearjune VW Sock Reurn Prod. Growh

33 Figure 2 Loadings on he Produciviy Facor, PFSIC4Q 27 Size-B/M-Produciviy Sored Porfolios This figure plos he loadings or he coefficien esimaes of he produciviy facor. The four-facor orhogonal OLS regression model is: R = α + β * e _ HML + β * PFSIC4Q + e M * e _ Rm + βe _ SMB * e _ SMB + βe _ HML PF where R is he equally-weighed monhly excess reurn of he es porfolio, R m is he monhly marke excess reurn, PFSIC4Q is he monhly produciviy facor, e _ R, e _ SMB and e _ HML are he residuals from regressing R m, SMB, and HML on PFSIC4Q, respecively. The es porfolios are 27 size/book-o-marke/produciviy sored manufacuring porfolios. m Loadings Porfolio 33

34 Table 1 Summary Saisics on he Manufacuring Secor, This able repors he summary saisics for he manufacuring secor from July 1963 o December Panel A repors he number of indusries per year and he average number of firms per indusry per year. Panel B repors he weigh of he manufacuring secor in he CRSP marke porfolio. The CRSP marke porfolio includes socks from he NYSE, AMEX, and NASDAQ. Panel A: Indusry Classificaions Number of Indusries Indusry Classificaion Min Q1 Median Q3 Max 3-digi digi Average number of firms per indusry 3-digi digi Panel B: Relaive Imporance of he Manufacuring Secor: Snapshos Manufacuring as a Percenage of: Number of Firms Marke Capializaion Year CRSP S&P500 CRSP S&P

35 Table 2 Produciviy, Sock Price, Size, B/M, and he Herfindahl Index Manufacuring Secor, Panel A presens he summary saisics for he capial-weighed average produciviy, value-weighed sock price index, size, and B/M for each year. Panel B presens he correlaion beween each pair of variables. The produciviy level is he annual 5-facor oal produciviy esimae from he NBER-CES Manufacuring Indusry daabase. Boh he produciviy and he sock price level are normalized o one in Firm size is he marke capializaion. The book-o-marke raio is book equiy divided by marke equiy. The Herfindahl index is he sum of squared shares of each firm. The share of each firm is he marke capializaion of he firm divided by he oal capializaion of he indusry. The higher he Herfindahl index, he less compeiion here is. Three aserisks (***) indicae saisical significance a 1 percen, wo (**) indicae significance a 5 percen, and one (*) indicaes significance a 10 percen. Panel A: Annual Series Average Across All Manufacuring Indusries Sock Correlaion beween Produciviy Level Year Produciviy Level Price Index Firm Size Firm B/M and he Herfindahl index , , , , , , , , , , , , , , , , , , * , , ,016, , ,117, ,659,

36 ,114, ,969, ,153, ,715, ,006, ,303, ,537, * ,512, ,484, ,418, ** ,345, ** ,703, * ,721, ,276, * ,982, ,419, ** Panel B: Correlaion Marix Produciviy Level Sock Price Index Firm B/M Firm Size Produciviy Level Sock Price Index Firm B/M Firm Size 1 36