Research Paper 347 March Capturing the Impact of Latent Industry-Wide Shocks with Dynamic Panel Model

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1 QUANTITATIVE FINANCE RESEARCH CENTRE QUANTITATIVE F INANCE RESEARCH CENTRE QUANTITATIVE FINANCE RESEARCH CENTRE Research Paper 347 March 204 Capturng the Impact of Latent Industry-Wde Shocks wth Dynamc Panel Model KHoon Jmmy Hong, Bn Peng and Xaohu Zhang ISSN

2 Capturng the Impact of Latent Industry-Wde Shocks wth Dynamc Panel Model * KHoon Jmmy Hong a, Bn Peng b and Xaohu Zhang c, a Fnance Dscplne Group, Unversty of Technology, Sydney, Australa b Economcs Dscplne Group, Unversty of Technology, Sydney, Australa c School of Management and Governance, Murdoch Unversty, Perth, Australa Abstract Expandng the panel model of Pesaran (2006) and Ba (2009), we propose a dynamc panel specfcaton wth Bayesan approach to capture the mpact of unobservable ndustry-wde shocks to stock prce movements. We employ fundamental accountng nformaton to control company specfc shocks and equty market ndex to capture market wde common shocks. Our model s desgned to resolve the potental multcollnearty problem that s known to exst when the ndustry factors are consdered by extractng the ndustry-wde shocks usng Bayesan method. JEL classfcaton: C, C3, G2 Keywords: Common Factor Structural Error; Common Shocks; Stock Prce Movements; Accountng Fundamentals; Bayesan Gbbs Sampler * We would lke to thank Steve Satchell, YongWoong Lee and semnar partcpants at Unversty of Technology, Sydney for useful comments and dscussons. We gratefully acknowledge fnancal support from Unversty of Technology, Sydney, Busness School. All errors reman our own. Correspondng author. Tel: Emal: Xaohu.Zhang@morduch.edu.au 0

3 . Introducton Ths paper proposes a dynamc panel model wth Bayesan approach to capture the mpact of ndustry-wde shocks n explanng stock prce movements (SPM). Company specfc shocks are captured by an equty valuaton model that takes advantage of fnancal statement nformaton, whle market wde common shocks are captured by equty market ndex. The major contrbutons of ths paper are n two aspects. The techncal contrbuton of our paper s that we propose Bayesan estmaton technque to evaluate the unobservable common shocks and add more explanatory power to the tradtonal panel data set-up. The emprcal contrbuton s that we present a model to control the company specfc accountng nformaton and the market wde shocks to nvestgate ndustry-wde shocks, whch good proxes are often unavalable. Ths paper has two motvatons. Frs motvaton s the needs to pay more attenton to role of ndustry-wde shocks n explanng SPM. Fundamental analysts prmarly nvestgate the fnancal statements of a company and ts compettors so that they can estmate the future development of the value of the company. The advantage of fundamental analyss s that t has an ntutve explanatory lnk to SPM. It ought to, at least n theory, characterze the longterm, fundamental value of a stock. If the nformaton on fnancal statements accurately reveals the fundamental value of a company, then the accountng nformaton for a company, should explan a sgnfcant proporton of SPM. However, results from prevous studes show that the capablty of these accountng varables n explanng the SPM s lmted. Chen and Zhang (2007) show that, at ndvdual stock level R 2 of the lnear regressons of stock returns on accountng varables wth dfferent model specfcatons, are all less than Bettmanet et al. (2009) and Hong and Wu (204) present portfolo level evdence that the explanatory power of Ordnary Least Square (OLS) models usng accountng varables to explan portfolo returns are much lower than when

4 other momentum varables are ncluded. These results ndcate that a model explanng SPM, wth fundamental varables only s lkely to suffer from omtted varable bas. In order to overcome the potental omtted varable bas, an obvous soluton s to nclude market ndex return as an explanatory varable. The Captal Asset Prcng Model (CAPM) states that the market excess return captures the systematc exposure of ndvdual stock s excess return. Therefore, market ndex return s lkely to have statstcal sgnfcance n explanng the SPM (see Lessard, 974). If market-wde common shocks exst, the same could happen wthn an ndustry. Hao et al. (20) use an extended Cournot and Bertrand completon model to demonstrate the senstvty of SPM to ndustry-level news. They theoretcally and emprcally found that SPM are senstve to ndustry-level news, and that the returns of less proftable companes n an ndustry are more senstve to ndustry-level news than those of the more proftable companes. Harford (2005) also fnd the relevance of ndustry-specfc economc shocks to SPM. However, t argues that the proxy varables for ndustry-specfc economc shocks are hghly correlated wthn an ndustry, whch may cause multcollnearty f smultaneously ncluded n a regresson model. To address ths, Harford (2005) extract the frst prncpal component from seven observable economc shock varables. However, Harford (2005) also notes the dsadvantage as common shock varables are unobservable or have no reasonable proxy varables. Furthermore, the mpacts of these common shocks on stock returns are dfferent across dfferent companes. In such cases, the proxy varables, or prncpal component analyss, may not be effectve. Such modellng dffculty may explan why there s lmted attenton to the role of ndustry-wde shocks n explanng SPM. In order to fll ths gap, we propose a new method of aggregatng the unobserved ndustry-wde factors and treat t as a latent factor to overcome such ssues. Ths s our frst objectve / contrbuton. 2

5 Our second motvaton s to take advantage of Bayesan model. Instead of employng the conventonal estmaton methods proposed by Pesaran (2006) or Ba (2009), we adopt the Bayesan estmaton method n ths paper. Common shocks, whch exst n many ndustres and socal actvtes, could be a sgnfcant feature of both cross-sectonal and panel data sets (Andrew, 2005; Ba, 2009). The last decade has seen consderable research (see Pesaran, 2006; Ba, 2009; Moscone and Tosett, 2009) nto the effects of common shocks on paneldata model estmaton. Multfactor error structure has been ntroduced to conventonal paneldata regresson models to deal wth the mpacts of the unobservable common shocks. To estmate the models, some try to flter out the effects of the common factor (Pesaran, 2006), or put restrctons on them (Ba, 2009), so that the coeffcents of the observed varables can be estmated consstently. Algebracally the same as an exact factor structure, Ahn et al. (200, 203) consder panel data models wth tme-varyng ndvdual effects usng Generalzed Method of Moments (GMM) technque. Meanwhle, many other parametrc or nonparametrc models have recently been provded to take nto account the cross-sectonal dependence (for example Sarafds and Robertson (2009) and Chen et al. (202)). However, these models focus on estmatng the coeffcents of the regressors and avod evaluatng the effects of the common shocks. In ths paper, we examne the heterogeneous mpacts of both observed factors (accountng fundamentals and market-wde common shocks) and unobservable ndustry-wde shocks, by estmatng a panel data model wth both ndvdual-varyng slope coeffcents and ndvdual-varyng tme effects, captured by a common factor error structure. The prors are chosen to reflect the belefs of people on ths partcular model of nvestgatng ndustry-wde shocks. We address three reasons why Bayesan approach s more approprate n extractng ndustry-wde shocks under ths paper s framework. Frst, ndustry-wde shocks are shared by all companes n the same ndustry. The number of companes typcally runs from fve to 3

6 ffteen for S&P00 and t would be much larger n S&P500. The current model has 7 explanatory varables for each company, 5 fundamental varables, two varables representng ndustry-wde and market-wde shocks. Ths leaves us wth 05 parameters to estmate usng monthly observatons. Conventonal maxmum lkelhood based methods cannot handle ths therefore we use Bayesan method. Second, Gbbs samplng, wth data augmentaton, makes estmaton of the common shocks at each tme perod and the reactons of the ndvdual company to the latent shocks computatonally much smpler compare to the conventonal methods. The proposed method allows us to avod the neffcent two-stage estmaton suggested by Pesaran (2006). It also allows us to overcome the assumptons on factor structures ntroduced by Ba (2009). Thrd, unlke maxmum lkelhood method, Bayesan estmaton avods evaluatng the frst and second dervates of the lkelhood functon when calculatng the confdence nterval. In Bayesan framework, the coeffcents of determnaton can also be estmated convenently after model estmaton, whch s rarely avalable n the lterature because of the unavalablty of estmaton for factors and factor loadngs. However, n emprcal analyss, t s a valuable measurement for predcton accuracy and explanaton power of model specfcaton. Therefore, the second objectve / contrbuton of our paper s to propose an enhanced econometrc technque n capturng ndustry-wde shocks n explanng the SPM. The proposed method of nvestgatng ndustry-wde unobservable varable has two advantages. Frst, t overcomes the potental model msspecfcaton, such as omtted varable bas. Second, t allows us to nvestgate the senstvty of the stock returns to commonly shared unobservable shocks, whch has sgnfcant mplcatons for the proper valuaton of companes from the same ndustry. The senstvty of a stock return to the unobserved common shocks could ndcate how prone the company stock s to ndustry-wde trend or cyclcalty. As companes n the same ndustry are often drect compettors, nvestgatng the 4

7 senstvty of the ndustry would enhance our ablty to understand the ndustry-wde compettve relatonshp. The rest of the paper s organzed as follows. Secton 2 explans the econometrc model and the specfcatons of the emprcal model of explanng SPM, Secton 3 descrbes the data and run some prelmnary test, Secton 4 provdes the emprcal fndngs and Secton 5 concludes the paper. 2. The Models 2. Econometrc Model: Model Specfcaton The tradtonal panel data model can be wrtten as y = z θ + e, () t t t where =,..., N ndcates ndvduals; t =,..., T ndcates tme perods; y t represents the value of the dependent varable for ndvdual at tme perod t ; z t s a s vector ncludng all the explanatory exogenous varables; θ refers to the correspondng vector of coeffcents; and e t represents for the error term. As noted above, we generalze the model n () from two aspects. Frst, to allow for heterogenety, θ dffers across. Second, a factor structural error term s ntroduced to allow for cross-secton dependence. The generalzed model can be wrtten as y = z θ + e, where e = γ f + e. (2) t t t t t t s m Here θ 's refer to the ndvdual specfc coeffcents of varables z t. The varable f t 's represent the unobservable common factors at tme t. The varable γ 's represent the ndvdual specfc mpact of such common factors on the dependent varable. For dentfcaton, t s requred that m ( N ) 2 (Geweke and Zhou, 996). 5

8 Specfcally, n the applcaton of ths paper, y t represents the stock return of company at tme t ; z t ncludes all the accountng varables and the market ndex return; f t represents the ndustry-wde shocks at tme t ; the common shocks. γ measures how each company reacts to For smplcty, we wrte the above model n matrx form as follows. Y = Z θ +Λ f + ε, (3) t t t t N N Ns Ns N m m N where Y t z t y t s θ γ εt, Z = t =, θ =, Λ= a nd εt =. y Nt z Nt θ N γ N ε Nt s Then the followng condtons are standard and necessary for the Bayesan analyss (Geweke and Zhou, 996; Chan et al., 203). Assumpton : The error terms and factors are ndependent and dentcally dstrbuted across t. Specfcally, f 0 t I ~ N 0,, 0 and Σ = ε Σε t N N m ( Σ) Σ= ε dag ( σ, σ2,, σn ). Moreover, f t and ε t are not correlated wth Z t. 2.2 Econometrc Model: Bayesan Estmaton Based on the model above, we present a Gbbs sampler that generalzes the algorthm of Geweke and Zhou (996) for an m-factor model wth large T and small N to accommodate a panel data regresson model wth ndvdual-varyng slope coeffcents and factor structural error term. Both γ 's and f 's are treated as unknown parameters wth values beng drawn t from ther condtonal posteror denstes. Then, condtonal on 6 γ 's and f 's, the model of t

9 (3) reduces to the standard lnear regresson model, facltatng draws from the condtonal posteror denstes for the parameters. For pror denstes of ndvdual-varyng slope coeffcents and varances of random error terms, we consder a standard dffuse pror, that θ and s h h, where h = > 0. For pror denstes of unobservable factor loadngs, we follow Geweke and Zhou σ 2 (996) to have γ for the case wth large T and small N. Under these pror dstrbutons m and model specfcatons, the jont posteror densty for all unknown parameters (such that θ, h, γ and f t ) can be wrtten as N T h p( Θ Y,Z ) = 2 h exp y z f 2 2 ( p ) ( θ γ ) : T : T t t t = t= 2 T m/2 N ( 2p ) exp f t ft, = h t= 2 2 (4) where Θ represents for all unknown parameters. From the jont posteror densty (4) we can derve the full condtonal posteror denstes that can be used for Gbbs samplng. Partcularly, we assume that all the rank condtons needed below are satsfed. The condtonal posteror denstes of the parameter θ 's for =,, N are normal dstrbutons, gven by ˆ θ Y: T, Z : T, Θ θ ~ N, ( ) θ ZZ, (5) h where z y γ f ˆ θ = ( ZZ ) ( ZY ), Z = and Y =. T s T z T yt γ f T 7

10 The condtonal posteror denstes of h 's for =,, N are gamma dstrbutons as follows. : T : T h ( s ) h Y,Z, Θ ~ G s,, (6) h c where the shape and scale parameters are respectvely. Specfcally, f ~ (, ) z G s s, then h c h T 2 s = and s 2/ ( y z θ γ f ) 2 c T = t= t t t sh sh sc z pz ( sh, sc) = exp( z/ sc). Γ( s ) h The condtonal posteror denstes of f t 's and γ 's are drawn n the same way as Geweke and Zhou (996). Rather than estmatons for factors and factor loadngs, we are more nterested n evaluatng proportons of varaton n dependent varable y t that can be attrbuted to both observed varables and unobserved common factors. Based on draws from condtonal posteror dstrbutons, t s straghtforward to evaluate the coeffcent of determnaton, 2 R, of the model (3) takng nto account for not only observable varables of Z t 's but unobservable factors of f t 's. Specfcally, for the overall model, R N T N T 2 2 ( yˆ ) ˆ t y ε t 2 = t= = t= = = N T N T 2 2 ( y y) ( y y) t = t= = t= t, (7) where N T yt NT = t = y = such that the average stock return over all companes and all tme perods. We can also evaluate 2 R of model (3) for a partcular ndvdual/company as R T T 2 2 ( yˆ ) ˆ t y ε t 2 t= t= = = T T 2 2 ( y y ) ( y y ) t t t= t=, (8) 8

11 where y T = y such that the average stock return of the th company over all tme T t = t perods. Though the estmatons for common factors and factor loadngs are not nvarant n terms of the orderng of ndvduals, accordng to Chan et al. (203), the estmatons for 2 R are nvarant. Therefore, the applcaton results dscussed n ths paper are not nfluenced by changng the order of companes. 2.3 Fundamental Equty Valuaton Model usng Accountng Informaton In order to capture the company-specfc factors that nfluence stock returns, we employ the equty valuaton model of Zhang (2000). Ths model s also expanded n Chen and Zhang (2007) and Hong and Wu n establshng the theoretcal relatonshp between stock returns and accountng fundamentals. The model measures the characterstcs of underlyng operatons of a company usng the lnks between the future cash flows and the observed accountng data n valung equty. Equty value s a functon of two basc operatonal attrbutes: scale and proftablty. Let V t be the value of an all equty-fnance company at date t. B t s the correspondng book value of equty. X t s the earnngs generated n perod t, and g t s the company s growth opportuntes as perceved at t. g t s defned as the percentage by whch the scale of operatons (captal nvested) may grow. Let q t X t / B t- as proftablty at tme t. Let E t (X t+ ) be the expected next-perod earnngs, k s the earnngs captalzaton factor, and P(q t ) and C(q t ) are the put opton to abandon operatons and the call opton to expand operatons, respectvely. P(q t ) and C(q t ) are normalzed by the scale of operatons, B t. To smplfy the analyss, assumes that proftablty follows a random walk, q t+ = qt + e t+. Chen and Zhang (2007) derved the valuaton functon of equty as [ ] V = B q / r + P( q ) + gc( q ) Bυ( q, g, r), (9) t t t t t t t t t t t 9

12 where υ( q, g, r) q / r + P( q ) + gc( q ). Now consder ΔV t+, the change n equty value t t t t t t t t from date t to date t+. Defne υ dυ/dq t and υ 3 dυ/dr t. dυ/dg t s E(q t ) and need not to be defned agan. Let D t be the dvdends pad n perod t+. Chen and Zhang (2007) derved the perod t+ stock return, denoted R t+ as X t B t B + t B t B t B + t Rt+ = + υ qt+ + + Cq ( t) gt+ + υ rt+. (0) Vt Vt Vt Bt Vt Vt Based on (0), Chen and Zhang (2007) run the followng approxmated regresson. R = α + bx + g qˆ + δ bˆ + ω gˆ + φ rˆ + e, () t t t t t t t where R t s the annual stock return; x t = X t / V t- s the earnngs yeld, dvded by the begnnng-of-perod market value of equty; qˆ = ( q q ) B / V s the change n t t t t t proftablty, adjusted by the begnnng-of-perod rato of the book value of equty to the market value of equty, wth proftablty defed as the return on equty; bˆ = [( B B ) / B ]( B / V ) s captal nvestment, adjusted by one mnus the t t t t t t begnnng-of-perod book-to-market rato; gˆ t = ( gt gt ) Bt / Vt s the change n growth opportuntes, adjusted by the begnnng-of-perod book-to-market rato; t t t t t rˆ = ( r r ) B / V s the change n the dscount rate, adjusted by company s begnnngof-perod book-to-market rato; and et ' s are random error terms. The growth opportuntes, g, are often captured usng long-term analysts forecasts. The avalablty of these forecasts for an ndvdual company s severely lmted. The most popular alternatve s to use ndustry-wde long-term growth forecasts nstead of forecasts for ndvdual companes. However, under the current model, ths approach wll ntroduce an dentfcaton problem as g s shared by all the companes that are n the same ndustry. Therefore, the logcal soluton s to drop g and let t be absorbed n the factor structure from the model, and take the four accountng varables as our fundamental varables. 0

13 We generalze model () to take account of ndvdual-varyng mpacts of observed factors (accountng fundamentals and market-wde common shocks), and ndvdual-varyng mpacts of the unobservable ndustry-wde shocks on stock returns, as follows: R = b x + γ qˆ + δ bˆ + f rˆ + α SP500 + e t t t t e t t t = γ f t + e t (2) From here on, we refer to ths model as Model CF. In ths paper, we follow Geweke and Zhou (996), Ahn et al. (200) and Ba (2009) to assume the number of unobservable common factors s known. In partcular, we are nterested n consstently measurng the mpact of observable factors on stock prces, and estmatng the varaton n stock returns that can be explaned by both observable and unobservable factors. 3. Data and Prelmnary Tests 3. Data Descrpton and Data Issues We base our analyses on the monthly returns of the 56 stocks across sx ndustres n the S&P00 ndex between January 2003 and December 202: from the IT ndustry, 3 from the ndustral ndustry, 8 from the energy ndustry, 0 from the fnance ndustry, from the health care ndustry and three from the utltes ndustry. In order to capture mpact of ndustry-wde factors on stock returns, we conduct the analyss for each ndustry separately. We use analyst long-term forecasts from the Insttutonal Broker Estmate System (IBES) n ths paper. We follow the approach of Hong and Wu (204) n our sample constructon except that we do not adopt portfolos for our analyses. Ths gves rse to a prmary sample extendng from 2003 to 202, wth 6552 (such that N = 56 and T = 7 ) monthly company-level observatons. The company-level accountng data s avalable from the Compustat North Amerca database and Thomson Reuters Worldscope database. Stock prces

14 are sourced from Bloomberg and earnngs forecasts data are extracted from the Insttutonal Broker Estmate System (IBES). Many exstng studes of usng accountng nformaton to explan stock returns become event studes as they collect stock returns on or around the earnngs announcement date (see Chen and Zhang, 2007; Clement et al., 20). Whle such practce has a clear beneft of solatng the mpact of accountng nformaton on stock returns (and hence shows hgher statstcal sgnfcances of the estmated coeffcents), t refnes the scope of regresson analyss and does not allow the ncorporaton of other varables that may affect stock returns. As our man nterest s n the ndustry-wde factors, we use monthly stock return data based on calendar dates. Although ths expects to yeld much lower statstcal sgnfcance for the estmated coeffcents of the accountng varables, such structure allows us to overcome the restrctons of the event study framework. Mxed-frequency problem s another ssue n our dataset, snce accountng data are produced quarterly, whle stock prce data are produced monthly. In order to overcome ths, we follow the method of Hong and Wu (204). There are two dfferent types of data n our sample: stock and flow. Stock data are snapshots of the measured varable at a gven pont n tme, whereas flow data represent an accumulaton over a gven perod. Stock return, proftablty, growth opportunty and dscount rate are stock varables, but earnngs, yeld and captal nvestments are flow varables. By accumulatng monthly observatons of flow varables over a quarter, they could then become the end of the quarter observaton. Ths means the end of quarter observaton for flow varables could be, at least n theory, reverse engneered and decomposed nto monthly observatons. However, ths does not apply to stock varables. Snce all our quarterly observed varables are flow varables, weghted average s used under ths assumpton. 2

15 3.2 Cross-Sectonal Dependence Test and Number of Common Factors Before we apply Model CF to the above stock return data, we conduct formal cross-secton dependence (CD) tests to check our data set. For each ndustry, our panel data set has small N and relatvely large T, therefore we adopt the CD test proposed by Breusch and Pagan (980). Ths test s based on the followng Lagrange multpler (LM) statstc N N CD = T ˆ ρ, (3) LM = j= + 2 j where ˆj ρ s the sample estmated par-wde correlaton of the resduals. Specfcally, ee ˆˆ = ˆ ρ ˆ j = ρ j = T t jt t T 2 T eˆ ˆ t ejt t= t=, (4) where e ˆt s the estmate of e t by runnng OLS regresson for each ndvdual. Breusch and Pagan (980) show that under the null hypothess of cross-sectonal ndependence, CD LM s asymptotcally a ch-squared dstrbuton wth N( N ) 2 degrees of freedom. (Insert Table here) We conduct the CD test for each of the sx ndustres, wth Table presentng the degrees of freedom and LM statstc, CD LM, for each ndustry. The test results ndcate that crosssectonal dependence exsts for all ndustres, justfyng the applcaton of Model CF to our stock return data. (Insert Table 2 here) As prevously stated, the number of common shocks, m, that can be dentfed s less than or equal to ( N ) 2. Snce there are only three companes from the utltes ndustry, we could only dentfy one common factor for ths ndustry. For the sake of comparson, we frst set the number of ndustry-wde shocks as one for all ndustres. Due to the smlarty across 3

16 estmatons for dfferent ndustres, we focus on the stocks from the IT ndustry. Table 2 lsts the companes n the sample. Despte the dfference n the sample perod nvestgated, the descrptve statstcs of our sample data s comparable to those of Chen and Zhang (2007). We also estmate models wth two or three ndustry-wde shocks for all ndustres but the utltes ndustry, and we present and dscuss the results n Secton Emprcal Results 4. Impact of Observable Factors on Stock Returns We estmate Model CF separately for all sx ndustres. When estmatng each model, we generate 5,000 draws but dscard the frst 5,000 as a burn-n. (Insert Table 3 here) Table 3 presents the posteror statstcs, ncludng posteror mean, standard devaton and 95 per cent credble nterval (CI) for coeffcents of observable accountng varables and marketwde common shocks (the S&P500 ndex), for each company from the IT ndustry. Although, due to space lmtatons, we wll present the estmated coeffcents of the IT ndustry only, ths does not alter the fndngs of ths paper, as results from all the ndustres have consstent mplcatons (estmated results of other ndustres are avalable from the authors upon request). In order to assess the Gbbs sampler s performance, we present the sampled paths and autocorrelaton functons (ACFs) of these sample paths for all estmated coeffcents of Apple Inc. n Fgure. These plots show that the sample paths are mxed well. The sampled paths and ther ACFs of estmated coeffcents for the other companes are very smlar, and are not ncluded here. (Insert Fgure here) In general, we fnd that the market-wde common shocks, represented by the S&P500 ndex, have statstcally sgnfcant and larger mpacts on stock returns compared to the mpacts of 4

17 the ndvdual company s accountng fundamentals. S&P500 has a postve mpact on stock returns for all the IT ndustry companes, wth none of the 95 per cent CIs contanng zero, suggestng sgnfcant postve mpacts. On the other hand, most CIs of estmated coeffcents for accountng fundamentals nclude zero, ndcatng no sgnfcant mpacts from accountng fundamentals on stock returns. In addton, we fnd that the mpacts of observed accountng fundamentals on stock returns vary across companes. For example, b, the adjusted captal nvestment, only has sgnfcantly postve mpact on stock returns for three companes: Apple Inc., Intel Corporaton and Qualcomm Inc., but has no sgnfcant mpact for the other eght IT companes. Furthermore, the magntudes of such sgnfcant mpacts are dfferent, rangng from.5060 to The mpacts of market-wde common shocks, ndcated by S&P500 ndex, also vary across companes from to.363, although these mpacts are sgnfcantly postve for all companes. Therefore, the model specfcaton of ndvdualvaryng coeffcents of observable accountng fundamentals and market-wde common factors can be justfed. For model comparson, we progressvely ncrease the set of ndependent varables to explan stock returns. In partcular, we estmate another two models for all ndustres. The frst model s R = b x + γ qˆ + δ bˆ + φ rˆ + e. (5) t t t t t t Ths model s a conventonal equty valuaton model wth ndvdual-varyng coeffcents and random error term followng normal dstrbutons. In ths model, only accountng fundamentals are ncluded as explanatory varables for stock returns. We refer to ths model (5) as Model C n the followng dscusson. The second comparson model s R = b x + γ qˆ + δ bˆ + φ rˆ + α SP500 + e, (6) t t t t t t.e. n the conventonal equty valuaton model besdes accountng fundamentals, marketwde common shocks, ndcated by S&P500, s ncluded n as well. We refer to the above 5

18 model (6) as Model C2. (Insert Table 4 here) (Insert Table 5 here) Tables 4 and 5 present the estmated coeffcents for all companes from the IT ndustry by Model C and C2, respectvely. (Model C and C2 are estmated by ordnary least square method rather than Bayesan MCMC method. Results for other ndustres are avalable upon request) From these tables we can see that the ndex return has statstcally sgnfcant explanatory power n explanng the ndvdual stock returns, and we may ncur omtted varable bas by excludng the ndex return from the model. We observe three major fndngs by comparng the estmated results of the three models, CF, C and C2. Frst, Model C and C2 also show consderable varatons n estmated coeffcents across companes, whch demonstrates that there exsts strong ndvdual heterogenety wthn the IT ndustry. Second, n terms of the estmated mpacts of accountng fundamentals on stock returns, the results from Model C and Model C2 are consstent. In general, f a fundamental varable has sgnfcant mpact n Model C, t s lkely to have a sgnfcant mpact n Model C2, whch ncludes S&P500 ndex return as an explanatory varable. However, when the unobserved ndustry-wde factor s taken nto account, as n Model CF, such sgnfcant mpacts almost dsappear. Ths s mportant as t could be consdered a sgn of omtted varable bas. The accountng fundamentals could seem to capture some of the shocks from the unobserved ndustry-wde factors, when the factors are gnored. The results, wthout such factors as an explanatory varable, would be naccurate because the major drver behnd the stock prce movement s unobserved ndustry-wde factors rather than accountng fundamentals. These emprcal results mply that the seemngly statstcal sgnfcance of the company specfc accountng varables may be msleadng. Thrd, estmated mpacts from S&P500 ndex on stock returns by Model C2 and Model 6

19 CF are almost dentcal. Therefore, the explanng power of S&P500 ndex to stock prce movement s robust, and an IT company s reacton to unobserved ndustry-wde shocks seems to be uncorrelated to ts reacton to the S&P500 ndex an ndcator for market-wde common shocks. 4.2 Impact of Unobservable Common Shocks on Stock Returns (Insert Table 6 here) In ths secton, we examne the mpact of unobservable ndustry-wde shocks. We do ths by comparng the coeffcent of determnaton, R 2, of varous econometrc models estmated by Eq. (8). Results are presented n Table 6. We fnd that Model C has the lowest R 2 measures among the three model specfcatons. In Model C, Accenture has the lowest R 2 and Qualcomm has the hghest R 2. Such low level of R 2 measures ndcates that the accountng fundamentals have very lmted explanatory power on explanng SPM. It should also be noted that such low explanatory power s partally due to dfferent return computng methodology. As prevously dscussed, many exstng studes that use accountng nformaton to explan stock returns become event studes as they collect stock returns on or around the earnngs announcement date. We use monthly stock return data based on calendar dates. Although t s expected that ths wll yeld much lower statstcal sgnfcance for the estmated coeffcents of the accountng varables, such structure allowed us to overcome the restrctons of the event study framework. S&P500 ndex return, whch s desgned to capture the market-wde systematc shocks to the ndvdual stock returns, s taken nto account n Model C2. The R 2 measures sgnfcantly ncrease n Model C2 compared to those n Model C. R 2 ranges from for Apple Inc. to for Csco System. Takng Csco System as an example, 2 R of Model C s whle that of Model C2 s The result ndcates that the market- 7

20 wde systematc common shock has strong and statstcally sgnfcant explanatory power on SPM. The explanatory power of our C2 models (measured by R 2 ) s comparable to those of Bettman et al. (2009) and Hong and Wu (204), where SPM are explaned by accountng varables and market-wde common shocks. Bettman et al. (2009) report a R 2 of (Table 4 of Bettman et al., 2009) whle Hong and Wu (204) report a R 2 of 0.42 (Table 2 of Hong and Wu, 204). Ths naturally leads us to suspect an omtted varable bas that we may need to consder for not only market-wde common shocks, but also ndustry-wde shocks. When unobservable ndustry-wde shocks are taken nto account n Model CF, we gan sgnfcantly ncreased R 2 for all companes. For example, EMC Corporaton has R 2 of whle the R 2 of the same company n Model C2 s only It can been seen that the accountng fundamentals and S&P500 ndex explans per cent of the varaton n the stock prces of EMC Corporaton, and ncludng unobservable ndustry-wde shocks can explan another per cent of the varaton n ts stock prces. Smlar mprovements are seen n all the other S&P00 IT companes. However, the stock prce of EMC Corporaton s more senstve to the IT ndustry-wde shocks than other IT companes. These emprcal results demonstrate the strength of Model CF n explanng SPM. The unobserved ndustry-wde factors have statstcally sgnfcant explanatory power for SPM and, therefore, Model CF s more properly specfed compared to the other two models. From ths, we can conclude that the major drvers behnd stock prces of IT companes are observed market-wde common shocks and unobserved ndustry-wde shocks, rather than the accountng fundamentals of an ndvdual company. The results show that reactons to ndustry-wde shocks are vares for dfferent companes. Some companes are more senstve to ndustry-wde shocks, such as EMC Corporaton. Some companes are not senstve to ndustry-wde shocks, such as Mcrosoft. 8

21 4.3 Comparson across Varous Industres (Insert Table 7 here) Havng establshed the superorty of Model CF over the conventonal Model C and Model C2 n explanng SPM for the IT ndustry, t would be meanngful to examne the robustness of Model CF s performance by nvestgatng the R 2 of other ndustres. Table 7 presents the R 2 of Model CF and Model C2 for fve other ndustres n S&P00 (estmated by Eq. (7)). For all ndustres, Model CF has hgher R 2 than Model C2. Ths ndcates that the fndngs n secton 5.2 are robust. In partcular, R 2 of Model C2 for the energy ndustry s 0.28, whle that of Model CF s 0.59 more than double of the former. For the utltes ndustry, R 2 of Model CF s more than trple of that of Model C2. For the fnance and health care ndustres, Model CF can explan, approxmately, an addtonal 20 per cent of varaton n stock prces compared to Model C2. For the IT and ndustral ndustres, more than 0 per cent addtonal varaton n stock prces can be captured by Model CF. It s shown that stock prces of companes from the energy, health care and utltes ndustres are more senstve to ndustry-wde shocks. To a lesser extent, such common shocks also have an mpact on stock prces of the IT, ndustral and fnance ndustres. 4.4 Robustness Test: Number of Common Factors (Insert Table 8 here) As we dscussed n Secton 4.2, snce there are only three companes from the utltes ndustry n ths study, we can only dentfy one common factor for ths ndustry. For the sake of comparson we set a number of common shocks n Model CF as one for all ndustres and wanted to nvestgate the mpact of such specfcatons on model performance n terms of fttng our stock return data. Table 8 reports R 2 's of Model CF wth one, two and three common shocks for all ndustres except for the utltes ndustry, whch can only 9

22 accommodate models wth one common factor. The results show that ncreasng the number of common shocks cannot make Model CF ft the data sgnfcantly better. In partcular, for the IT ndustry, an ncrease n the number of common shocks has almost no mpact on 2 R of the model. For the other four ndustres (ndustral, energy, fnance and health care), there s a mnor mprovement n R 2 's when ncreasng the number of common shocks from one to two, such as an ncrease n 2 R from 0.52 to 0.59 for the ndustral ndustry. Increasng the number of common factors from two to three has almost no mpact, except the health care ndustry, and n some ndustres, such as energy and fnance, R 2 's are even reduced. These results demonstrate that our specfcaton of one common shock s reasonable, and that ncreasng the number of shocks does not dramatcally mprove the model s performance. 5. Concluson Ths paper proposes a dynamc panel model wth Bayesan approach to nvestgate the mpact ndustry level shocks n equty markets. Company specfc shocks are captured by an equty valuaton model that takes advantage of fnancal statement nformaton, whle market wde common shocks are captured by equty market ndex. The model assesses unobserved ndustry level equty market shocks usng a dynamc panel model wth Bayesan approach. There are four major fndngs from the emprcal results of ths study. ) the mpacts of observed accountng fundamentals and market-wde common shocks are heterogeneous across companes comng from the same ndustry. 2) Market-wde common shocks show more sgnfcant explanatory compare to accountng fundamentals. 3) Unobservable ndustrywde shocks explan a consderable part of SPM. 4) The extents of reactons to unobservable ndustry-wde shocks are dfferent across companes. Reactons to unobservable ndustrywde shocks are also dfferent across ndustres, wth some ndustres, such as energy, health care and utltes, beng more senstve than the IT, ndustral and fnance ndustres. 20

23 Tables and Fgures Table Breusch and Pagan s Test of Cross-Secton Dependence Ths table reports the cross-sectonal dependence tests for sx ndustres over perod IT Industral Energy Fnance Health Care Utltes Degree freedom CD LM Table 2 Sample Companes from the IT Industry Ths table reports the sample companes n the IT Industry. Apple Inc. Dell Internatonal Busness Machnes Oracle Corporaton Accenture Plc. EMC Corporaton Intel Corporaton Qualcomm Inc. Csco System Hewlett Packard Mcrosoft Table 3 Estmated Coeffcents of Observed Factors for the IT Industry from Model CF Ths table reports the estmaton results of (5) for all sample companes n the IT sector. Column Estmate reports the estmated coeffcents, Std reports the standard error of the estmated coeffcents, CI reports the 95% confdence nterval. Varable x s earnngs dvded by the begnnng-of-perod market value of equty; varable Δq s proftablty change; captal nvestment, varable Δb, s the change n the book value of equty relatve to the pror month; varable Δr s the dscount rate (0-year US Treasury bond yeld) change over the return perod; varable SP500 s the S&P500 ndex return. The sample conssts of frm-year observatons over the perod Apple Inc Accenture plc Estmate Std 95% CI Estmate Std 95% CI x (-5.657,.7444) x ( ,.33) Δq (-7.579, ) Δq (-7.344, 5.785) Δb (.2574, ) Δb ( , 0.577) Δr ( , ) Δr ( , ) SP (0.7758,.6576) SP (0.700,.5) Csco System Dell Estmate Std 95% CI Estmate Std 95% CI x (-.2696, ) x (-2.300, ) Δq (-2.856, ) Δq ( , 6.903) Δb ( , 0.259) Δb ( , 0.398) Δr ( , ) Δr ( , 0.586) SP (.0779,.6098) SP (.0379,.680) EMC Corporaton Hewlett Packard Estmate Std 95% CI Estmate Std 95% CI x (-.7994, 2.426) x ( , 0.800) Δq (-4.793, ) Δq (-0.338,.342) Δb ( , ) Δb (-0.887, 0.792) Δr ( , 0.228) Δr (-0.972, 0.396) SP (.008,.6270) SP (0.9072,.4375) Internatonal Busness Machnes Intel Corporaton Estmate Std 95% CI Estmate Std 95% CI x (-0.42,.042) x (-.3925, ) Δq ( , 0.549) Δq (-.0709, 0.44) Δb (-0.885, 0.986) Δb (0.0288, 2.984) Δr ( , 0.645) Δr ( , 0.07) SP (0.567, ) SP (0.906,.4339) Mcrosoft Oracle Corporaton Estmate Std 95% CI Estmate Std 95% CI x ( , 0.450) x (-0.57,.2434) Δq ( , ) Δq ( , 6.677) Δb ( , 0.894) Δb (-0.468, ) Δr (-0.252, 0.522) Δr ( , ) SP (0.6889,.447) SP (0.952,.4385) Qualcomm Inc Estmate Std 95% CI x (-4.8, ) Δq (-2.703, 2.32) Δb (0.8054, ) Δr ( , ) 2

24 SP (0.6695,.3405) 22

25 Table 4 Estmated Coeffcents of Observed Factors for the IT Industry from Model C Ths table reports the estmaton results of (8) for all sample companes n the IT sector. Column Estmate reports the estmated coeffcents, Std reports the standard error of the estmated coeffcents. Varable x s earnngs dvded by the begnnng-of-perod market value of equty; varable Δq s proftablty change; captal nvestment, varable Δb, s the change n the book value of equty relatve to the pror month; varable Δr s the dscount rate (0-year US Treasury bond yeld) change over the return perod; varable SP500 s the S&P500 ndex return. The sample conssts of frm-year observatons over the perod Apple Inc Accenture plc Csco System Estmate Std t-stat Estmate Std t-stat Estmate Std t-stat x Δq Δb Δr Dell EMC corporaton Hewlett Packard Estmate Std t-stat Estmate Std t-stat Estmate Std t-stat x Δq Δb Δr Internatonal Busness Machnes Intel Corporaton Mcrosoft Estmate Std t-stat Estmate Std t-stat Estmate Std t-stat x Δq Δb Δr Oracle Corporaton Qualcomm Inc Estmate Std t-stat Estmate Std t-stat x Δq Δb Δr

26 Table 5 Estmated Coeffcents of Observed Factors for the IT Industry from Model C2 Ths table reports the estmaton results of (9) for all sample companes n the IT sector. Column Estmate reports the estmated coeffcents, Std reports the standard error of the estmated coeffcents. Varable x s earnngs dvded by the begnnng-of-perod market value of equty; varable Δq s proftablty change; captal nvestment, varable Δb, s the change n the book value of equty relatve to the pror month; varable Δr s the dscount rate (0-year US Treasury bond yeld) change over the return perod; varable SP500 s the S&P500 ndex return. The sample conssts of frm-year observatons over the perod Apple Inc Accenture plc Csco System Estmate Std t-stat Estmate Std t-stat Estmate Std t-stat x Δq Δb Δr SP Dell EMC corporaton Hewlett Packard Estmate Std t-stat Estmate Std t-stat Estmate Std t-stat x Δq Δb Δr SP Internatonal Busness Machnes Intel Corporaton Mcrosoft Estmate Std t-stat Estmate Std t-stat Estmate Std t-stat x Δq Δb Δr SP Oracle Corporaton Qualcomm Inc Estmate Std t-stat Estmate Std t-stat x Δq Δb Δr SP Table 6 R 2 of Model CF, Model C and Model C2 for Companes from the IT Industry Ths table reports the estmaton of R 2 for all sample companes n the IT sector for Model C and C2, ndcated n equaton (8) and (9), respectvely. The sample conssts of frm-year observatons over the perod Company Model CF Model C Model C2 Apple Inc Accenture Plc Csco System Dell EMC Corporaton Hewlett Packard Internatonal Busness Machnes Intel Corporaton Mcrosoft Oracle Corporaton Qualcomm Inc

27 Table 7 R 2 of Model CF and Model C2 for All Industres Ths table reports the estmaton of R 2 for sx ndustres over the perod IT Industral Energy Fnance Health Care Utltes Model C Model CF Table 8 R 2 of Model CF wth Dfferent Specfcaton on Number of Common Shocks Ths table reports the estmaton of R 2 for sx ndustres wth dfferent number of factors over the perod IT Industral Energy Fnance Health Care Model CF (one factor) Model CF (two factors) Model CF (three factors) Fgure MCMC Sample Paths and ACFs of Coeffcents Estmated from Model CF for Apple Inc. Ths fgure reports the sample paths and ACFs of coeffcents estmated from model CF for Apple company. Varable x s earnngs dvded by the begnnng-of-perod market value of equty; varable Δq s proftablty change; captal nvestment, varable Δb, s the change n the book value of equty relatve to the pror month; varable Δr s the dscount rate (0-year US Treasury bond yeld) change over the return perod; varable SP500 s the S&P500 ndex return. 25

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