Can Technical Analysis be used to Enhance Accounting Information based Fundamental Analysis in Explaining Expected Stock Price Movements?

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1 Can Technical Analysis be used o Enhance Accouning Informaion based Fundamenal Analysis in Explaining Expeced Sock Price Movemens? 1 KiHoon Jimmy Hong a, and Eliza Wu a Curren Version: January, 014 a Universiy of Technology, Sydney, PO Box 13, Broadway, NSW 007, Ausralia Absrac This paper provides new empirical evidence ha price-based echnical indicaor variables can enhance he abiliy of accouning variables in explaining cross-secional sock reurns. We apply boh OLS and sae-space modelling o a sample of firms included in he Russell 3000 index over he period from o compare he roles of he wo main ypes of informaion ypically used by sock invesors. Empirical resuls reveal he imporance of accouning variables over longer erm horizons for paricularly, small-cap socks. Technical variables are shown o be imporan in he shorer erm horizons. This resul remains robus o alernaive mehodologies used. JEL classificaion: G1; G14 Keywords: Sock Reurn, Fundamenal Analysis, Technical Analysis, Momenum, Sae Space Model 1 We would like o hank YongWoong Lee for useful discussions. We graefully acknowledge financial suppor from he Accouning & Finance Associaion of Ausralia and New Zealand (AFAANZ). All errors remain our own. Corresponding auhor. Tel: address: [email protected] 1

2 Can Technical Analysis be used o Enhance Accouning Informaion based Fundamenal Analysis in Explaining Expeced Sock Price Movemens? Curren Version: January, 014 Absrac This paper provides new empirical evidence ha price-based echnical indicaor variables can enhance he abiliy of accouning variables in explaining cross-secional sock reurns. We apply boh OLS and sae-space modelling o a sample of firms included in he Russell 3000 index over he period from o compare he roles of he wo main ypes of informaion ypically used by sock invesors. Empirical resuls reveal he imporance of accouning variables over longer erm horizons for paricularly, small-cap socks. Technical variables are shown o be imporan in he shorer erm horizons. This resul remains robus o alernaive mehodologies used. JEL classificaion: G1; G14 Keywords: Sock Reurn, Fundamenal Analysis, Technical Analysis, Momenum, Sae Space Model

3 1. Inroducion In his paper, we invesigae wheher sock price based echnical analysis can enhance he effeciveness of fundamenal analysis in explaining sock price movemens (SPM hereafer). We conribue new evidence o he ongoing debae on wheher price-based or fundamenbased equiy valuaion is more useful for equiy analyss by using a sae space modelling approach o avoid poenial omied variable bias which has long plagued he comparaive analysis of hese wo alernaive approaches o equiy valuaion. Our model includes a sae variable, which represens an unobservable marke wide common facor. We also invesigae a firm size effec on he relaive imporance of accouning informaion on SPM by dividing our sample ino wo porfolios based on he marke capializaion of he sample firms. We have hree major empirical findings. Firs, we show ha combining boh echnical and fundamenal analysis can beer explain sock price movemens, compared o he cases where echnical or fundamenal analysis is employed independenly. This resul has imporan implicaions o boh academics and praciioners. Second, we uncover ha he unobserved common facor provides saisically significan explanaory power for SPM. This suppors he resuls of Duffie e al. (009) in equiy markes. Third, we find ha here exiss a significan size effec in he relaive imporance of he echnical and fundamenal variables. Explaining and predicing SPM has for a long ime araced boh academics and praciioners. There are wo long-sanding approaches o valuing socks, fundamenal and echnical analysis. Fundamenal analyss primarily use accouning informaion o sudy a company s underlying indicaors of profi such as earnings, dividends, new producs and R&D. On he oher hand, echnical analyss focus mainly on sock s own hisorical prices and reurns. I is commonly acceped ha echnical analysis performs beer in he shor erm 3

4 while fundamenal analysis is ofen believed o provide beer esimaes on long erm inrinsic values (see for example, Taylor and Allen, 199, Lui and Mole, 1998 and Amini e al., 013). Mos of he exising lieraure has focused on one or he oher aspec of SPM bu no boh. This may be he fundamenal reason why cross-secional sock reurns canno be saisfacorily explained. Fundamenal and echnical analysis or he inrinsic value and marke value of a sock price should ideally be considered ogeher in explaining SPM bu surprisingly, here has been lile aenion placed on undersanding heir complemenary roles. For example, a key assumpion of he implied cos of capial approach (ICC) of Chen, Da and Zhao (013) is ha analys earnings forecass are imely reflecions of he marginal invesors belief regarding fuure cash flows. This assumpion could be me if and only if invesors consisenly updae all available informaion in he marke, including all pas prices, demand and supply condiions as well as financial saemens. Therefore in his paper, we consider fundamenal and echnical analysis joinly o comprehensively invesigae he effec of boh aspecs on SPM. Our work is close o ha of Taylor and Allen (199), Bonllinger (005) and Beman e al. (009). However, we differeniae our sudy from earlier aemps by considering a richer se of echnical indicaors capuring price-based informaion over differen ime horizons alongside accouning variables. Imporanly, we conribue a more accurae comparison of he explanaory power provided by accouning informaion-based and price-based echnical indicaors for sock price variaions by accouning for common unobservable facors ha may also influence sock prices. For large companies ha have many equiy analyss following heir sock, mos of he fundamenal facors should be incorporaed ino pas sock prices. For small companies ha do no have many analyss following he company, here exiss greaer informaion asymmery wih respec o he company s news. If i is good news ha would push he sock price up, he execuives of he company would acively spread he informaion while if i is 4

5 bad news, he speed of informaion diffusion would be much slower. I is well documened ha he degree of informaion diffusion is much faser for larger companies. (See Chae, 005) Therefore, we expec ha he explanaory power of fundamenal facors on small-cap SPM would be more significan han ha on large-cap socks. Hence in his paper, we address 3 main research quesions. Are fundamenal and echnical analyses complemenary raher han compeiive in erms of heir informaiveness for SPM? Does fundamenal analysis have more explanaory power for he movemens in small cap sock prices han in large cap sock prices? And wha is he relaive imporance of fundamenal and echnical variables in predicing fuure SPM over differen invesmen horizons? Alhough mos acive porfolio managers claim ha hey are ineresed in invesing for he long erm, sock price momenum coninues o be one of he mos frequenly employed variables for rading sraegies. In pracice, momenum is fundamenal o many acive porfolio managers while he imporance of accouning informaion is ofen negleced because is shor erm predicive abiliy for SPM is less accurae. Therefore, by showing ha he use of accouning informaion as par of a fundamenal approach o equiy analysis can add value o sandalone echnical analysis, he empirical findings of his paper are useful for long-erm invesors and porfolio managers who are concerned wih emporary deviaions of sock prices from inrinsic values which can ofen arise. Our findings also have policy implicaions for regulaors who are ineresed in he behavioral aspecs of echnical raders ha can a imes, move asse prices excessively wihin a shor ime. This paper, in essence, decomposes he movemens in sock prices ino wo broad ypes of facors, facors driven by accouning informaion and by echnical analysis for a sample of large cap and small cap socks lised on one of he world s larges exchanges, he New York Sock Exchange (NYSE). The conribuion of his paper is as follows. The paper provides 5

6 addiional evidence ha accouning variables are useful in explaining sock price movemens over longer-erm invesmen horizons. The paper decomposes SPM ino facors ha are driven by invesors employing eiher echnical or fundamenal analyses. This allows us o invesigae under wha circumsances SPM may be srongly influenced by shor-erm invesors who end o use echnical analysis based on daily share price flucuaions or longerm invesors who end o use fundamenal analysis based on lower frequency accouning informaion. And he paper unambiguously shows ha he greaer informaion asymmery regarding small-cap socks influences he predicive power of accouning informaion over and above echnical analysis, paricularly over longer invesmen horizons. The res of he paper is organized as follows. Secion provides an overview of he relevan lieraure. Secion 3 describes he daa and approach used in our analyses whils Secion 4 discusses he empirical resuls. Finally, conclusions are provided in Secion 5.. Fundamenal Analysis vs. Technical Analysis.1. Fundamenal Analysis Fundamenal analyss use accouning informaion o sudy a company s underlying indicaors. They invesigae financial saemens of he firm and is compeiors in esimaing he fuure evoluion of he value of he company hence, is sock price movemens. One of he major purposes of accouning pracice is o help readers of financial saemens forecas a company s fuure cash flows (FASB, 1978). If he informaion on financial saemens reflecs he fundamenal values, hen he accouning informaion for a firm should explain a significan proporion of SPM. However, he lieraure so far yields mixed resuls in finding a link beween sock performance and accouning measures. 6

7 Alhough a significan proporion of sock price movemen occurs because invesors revise heir expecaions of fuure cash flows, neiher expeced cash flows nor discoun raes are observable and he radiional approach is o predic hem and calculae cash flow news and discoun rae news as funcions of he predicive variables. As Chen, Da and Zhao (013) noe, here is a growing lieraure ha shows, wih differen sample periods or cash flow measures, cash flow news can be more imporan han wha has radiionally been shown (Ang and Bekaer 007; Larrain and Yogo 008; Chen 009, Binsbergen and Koijen 010; Chen, Da, and Priesley 01). They use he prevailing marke (consensus) earnings forecass (from IBES) o back ou he firm-specific implied cos of equiy capial (ICC). Boh Ng, Solnik, Wu and Zhang (013) and Chen, Da and Zhao (013) show ha accouning measures like revisions in analyss consensus earnings forecass can explain a large proporion of SPM over longer invesmen horizons compared o shorer horizons. This is consisen wih Chen and Zhang (007), who provide heory and evidence showing how accouning variables explain cross-secional sock reurns. Based on Zhang s (000) framework used for linking equiy value o accouning measures of underlying operaions, hey derive SPM as a funcion of earnings yield, equiy capial invesmen, and changes in profiabiliy, growh opporuniies, and discoun raes. Empirical resuls of heir paper show ha he accouning variables explain abou 0% of he cross-secional price variaion. The upside of fundamenal analysis is ha i has an inuiive link o SPM. I should, a leas in heory, represen he long erm, inrinsic value of a sock. However, he downside is ha fundamenal analysis is no capable of reflecing he shor erm movemens in sock prices. There could be many reasons for his: quarerly reporing of financial repors or delays in operaional processes o reflec new marke condiions ino earning s figures and so on. The mos criical weakness of he fundamenal analysis is ha i does no accuraely predic SPM, in general in he shor erm. 7

8 .. Technical Analysis Technical analyss focus mainly on fuure sock prices given pas paerns in sock price movemens bu hey also ake ino accoun psychological aspecs in he demand for a company s sock. Sock prices flucuae remendously from day o day. Technical analyss ypically believe ha pas sock prices are good indicaors of fuure SPM. Technical analyss form heir expecaion of fuure SPM based on he pas price informaion or momenum facors. They employ many echniques, including he use of chars. Using chars, echnical analyss seek o idenify price paerns and marke rends in financial markes and aemp o exploi hese paerns. Traders and porfolio managers coninue o use echnical analysis o formulae buy and sell decisions. There is much academic ineres in he effecs of momenum on asse prices and recen sudies include Grinbla and Moskowiz (003), Choria and Shivakumar (006), Sadka (006), Zhu and Zhou (009), Marx (01), Fama and French (01), Moskowiz, Ooi and Pederson (01), Bajgrowicz and Sxaille (01) and Menkhoff e al. (01). Some earlier sudies sugges ha echnical analysis beas he marke in risk neural erms, hence is populariy. One of he simples and mos widely used rading sraegies based on echnical analysis is he Moving Average (MA) rule. I is an objecive rule-based rading sraegy in which buy and sell signals are deermined by he relaive magniudes of shor and long erm MAs. Exan sudies based on MA rules include Acar and Sachell (1997), Chiarella, He and Hommes (006) and Menkhoff (010). The MA rule ofen leads invesors o inves wih or agains he rend (ie., momenum) since i assumes ha prices rend direcionally. I akes advanage of price rends, capured as he gap beween wo MAs compued over differen horizons. The upside of echnical analysis is ha here is much evidence indicaing ha i can 8

9 accuraely predic shor erm movemens in sock prices and he rade can be profiable (see Jegadeesh and Timan, 1993, 001). This is because here is auocorrelaion in sock price processes. (see Hong and Sachell, 013) Moreover, i reflecs he behavioral aspecs of SPM. This may be anoher reason why echnical analysis performs beer han fundamenal analysis in he shor erm. However he downside is ha i has no heoreical basis and merely explains he sylized facs in he marke and invesors behavior. In paricular, i is grealy influenced by herding behavior and he crowds do no necessarily predic SPM correcly. Anoher downside is ha i only uses hisorical informaion and has no forward-looking aspec. This ypically works agains echnical analysis when here are significan regime changes in he marke condiions or in he macroeconomic rends. Technical variables, consruced based on he hisorical informaion, would no be able o foresee he movemens ha significanly deviae from he hisorical paerns..3. Blending he Two In shor, fundamenal analyss seek o deermine he inrinsic value of he company while echnical analyss end o rade based on marke forces such as he supply and demand of he sock concerned. We have seen ha boh approaches have heir own advanages and limiaions. Therefore i would be naural o assume ha boh fundamenal and echnical facors affec sock price movemens. Exising sudies ha fail o draw a srong complemenary relaionship for boh ses of deerminans end o focus only on he accouning side of he sory. However, sock price momenum could be very noisy. Hence, omiing momenum relaed variables may obscure he more sable, long erm relaionship beween SPM and accouning informaion. As such, his paper invesigaes wheher and o 9

10 wha exen accouning and echnical analyses could be complemenary o each oher for explaining SPM. Alhough no applied o he equiy marke, one of he earlies works, reporing he complemenary naure of echnical and fundamenal analyses is Taylor and Allen (199). They argue ha abou 90% of foreign exchange marke dealers rely on boh echnical and fundamenal analyses. The four facor model of Cahar (1997) is also a good example of he complemenary naure of echnical and fundamenal analyses. In ha well acceped asse pricing model, Cahar (1997) shows momenum is significan in explaining muual fund performance alongside Fama and French s (1993) hree facor model, which depends on accouning informaion (marke capializaion and he book-o-marke raio) and he marke risk premium. Beman, Saul and Schulz (009) noe ha models simulaneously incorporaing boh fundamenal and echnical explanaory variables for equiy prices are rarely used. They provide preliminary evidence o suppor ha fundamenal and echnical variables could be complemenary in explaining SPM, using US daa from 1983 o 00. However, hey only include he 5 day lagged price, book value of he firm s equiy, dilued earnings per share and consensus forecas earnings per share o explain SPM. And he analysis relies on simple OLS. This paper exends and improves upon he exan lieraure by providing a more horough and complee invesigaion wih more appropriae and robus economeric echniques. 3. Daa and Mehodology 3.1. Daa and Porfolio Consrucion We base our analyses on all socks in he Russell 3000 index ha have monhly and quarerly 10

11 daa available in CRSP beween January 1999 and December 01. Since one of he main objecives of his paper is o separaely invesigae he explanaory power condiional on firm size, he sample coverage in he Russell 3000 index is more appropriae han oher frequenly used US equiy indices such as he S&P500. As we use analyss long erm earnings forecas from he Insiuional Broker Esimae Sysem (IBES) in his paper, his resrics he firm coverage in our sample. Our sample consiss of all Russell 3000 index companies for which long erm analys earnings forecass could be obained from IBES. The sample we sudy comprise of firms wih membership in he Russell 3000 index wih daa available from boh CRSP and IBES daabases. This leaves a oal of 774 firms in he sample. We follow Chen and Zhang (007) and ake he firs consensus earnings forecas available for a given monh o ensure ha he growh opporuniy measure impounds he curren monh s earnings informaion. This ensures ha he forecas obained for monh covers he long erm forecas from monh. Chen and Zhang (007) rim 0.5% of he exreme observaions a he op and boom ends of he disribuion for each of he following variables. This pracice sysemaically eliminaes ouliers in he sample period. Our daa ypically covers 144 ime periods as we have 1 monh lag variables. Hence he larges and he smalles 0.7 observaions are subjec o rimming. Hence he 0.5% rimming crieria is no appropriae wih our curren sample. Moreover, our sample period covers he Global Financial Crisis. During financially disressed periods, he sock price co-movemens increase due o he propagaion of disress, which is ypically associaed wih greaer declines in marke values (Berger and Pukhuanhong, 01). More specifically, i is associaed wih he balance shee conracion of individual firms. Such balance shee conracion affecs he accouning variables we employ in his paper and hence his is already effecively accouned for in he model. For hese reasons, we use he enire sample wihou rimming any observaions. 11

12 Table 1 shows he descripive saisics of he sample daa. The descripive saisics of our sample daa is comparable wih hose of Chen and Zhang (007). Despie he difference in he sample period invesigaed, our summary saisics indicae ha he aggregae porfolio level daa ha we examine is comparable o he firm level daa used in Chen and Zhang (007). We include Table 1 panel A and C of Chen and Zhang (007) in Appendix 1, o faciliae his comparison. (Inser Table 1 here) The Russell 3000 index represens abou 98% of all US equiies by marke value. Because of is broad diversificaion and large number of consiuens, his index ofen makes for a popular alernaive o a represenaive oal marke index such as he Wilshire The Wilshire 5000 index, which is considered o be he benchmark for U.S. oal marke reurns, includes some socks ha are almos impossible o rade. The more sringen requiremens for inclusion ino he Russell 3000 index presens a beer represenaion of he universe of acively raded socks when compared o he Wilshire 5000 (See Russell Invesmens, 013). We follow he approach of Chen and Zhang (007) in our sample consrucion bu we differeniae our work wih he use of sock porfolio-level analyses. Chen and Zhang use a pooled sample bu his is no appropriae for our sudy as we also esimae a sae space model. Hence, insead we consruc sock porfolios based on firm size. To do his, all per share measures are muliplied by he number of shares ousanding (from IBES) o obain he aggregaed values a he individual firm level. This gives rise o a primary sample exending from 1999 o 01 wih 1,853,14 firm-monh observaions. We hen consruc wo size porfolios based on he marke capializaion of our sample firms around he median value wih each comprising 387 firms. The firs porfolio represens large cap socks and he second 1

13 porfolio represens small cap socks. We refer o he large-size porfolio as porfolio 1 and he small-size one as porfolio. The firm-level accouning daa is available from he Compusa Norh America daabase and Thomson Reuers Worldscope daabase. Sock prices are sourced from Bloomberg and earnings forecass daa are exraced from he Insiuional Broker Esimae Sysem (IBES). All accouning daa are observed quarerly while sock prices are observed monhly. As he accouning daa is available a he quarerly frequency while sock price daa is commonly sudied a he monhly frequency, his creaes a mixed-frequency problem. In order o overcome his, we need a precise undersanding of he evoluion of our quarerly daa over unobserved periods. There are wo differen ypes of daa in our sample, socks and flows. Sock daa are snapshos of he measured variable a a given poin in ime, whereas flow daa represen an accumulaion over a given period. Sock reurns, profiabiliy, growh opporuniies and discoun raes are sock variables bu earnings yield and capial invesmens are flow variables. Monhly observaions of flow variables could be cumulaed over a quarer and become he end of he quarer observaion. In reverse, his means ha he end-of-quarer observaions for flow variables can be decomposed ino daily observaions. However his does no apply o sock variables. Since all our quarerly observed variables are flow variables, weighed average is used under his assumpion. 3.. A Model of Equiy Value and Sock Reurns: Fundamenal Analysis This paper akes he equiy valuaion model of Zhang (000) and follows Chen and Zhang (007) in esablishing he heoreical relaionship beween sock reurns and accouning fundamenals. This secion briefly inroduces he equiy valuaion model ha is deailed in 13

14 Chen and Zhang (007). The model measures he characerisics of underlying operaions of a company using he links beween he fuure cash flows and he observed accouning daa in valuing equiy. Equiy value is a funcion of wo basic operaional aribues: scale and profiabiliy, hence he value of a company amouns o forecasing he relaive scale and profiabiliy of fuure operaions wih respec o hose on curren operaions. As expeced, profiabiliy (ROE) is a key measure in his model and i measures a firm s abiliy o generae value from he invesed capial and indicaes how he firm is likely o adjus is operaions going forward. The advanage of his model is ha i embeds he firm s value-creaing capial invesmen decisions wihin he se of available opporuniies as characerized by opions o grow and o downsize or abandon. (See Berger e al., 1996 and Berk e al., 1999 for he links beween real opions and firm valuaion.) Le V be he value of an all equiy-finance firm a dae. B is he corresponding book value of equiy. X is he earnings generaed in period, and g is he firm s growh opporuniies as perceived a. g is defined as he percenage by which he scale of operaions (capial invesed) may grow. Le q X / B -1 as profiabiliy (ROE) a ime. Le E (X +1 ) be he expeced nex-period earnings, k is he earnings capializaion facor, and P(q ) and C(q ) are he pu opion o abandon operaions and he call opion o expand operaions, respecively. P(q ) and C(q ) are normalized by he scale of operaions, B. To simplify he analysis, assumes ha profiabiliy follows a random walk, q ~ ~ + 1 = q + e + 1. Chen and Zhang (007) derives he valuaion funcion of equiy as [ q r + P( q ) + g C( q )] Bυ( q, g, r ) / V = B (1) 14

15 where υ q, g, r ) q / r + P( q ) + g C( q ). This implies ha he equiy value can be ( decomposed ino he amoun of equiy capial invesed, B, and he value per uni of capial, υ, which is a funcion of profiabiliy (q ), growh opporuniies (g ), and he discoun rae (r ). Zhang (000) shows ha υ is an increasing and convex funcion of q. Now consider ΔV +1, he change in equiy value from dae o dae +1. Define υ 1 dυ/dq and υ 3 dυ/dr. dυ/dg is E(q ) and need no o be defined again. Le D be he dividends paid in period +1. Chen and Zhang (007) derive he period +1 sock reurn, denoed R +1 as R X V B B + B + 1 B B + υ 1 q C( q g+ 1 + υ1 r () V V B V V = ) + 1 Eq. () shows ha he sock reurn is a funcion of he earnings yield, he change in profiabiliy, he change in equiy capial, he change in growh opporuniies, and he change in he discoun rae. Based on he relaionship represened in Eq. (), Chen and Zhang (007) run he following approximaed regression. R = α + bx + g qˆ + δ bˆ + ω gˆ + ϕ rˆ + e (3) i i i i i i i where R i is he annual sock reurn; x i = X i / V i-1 is he earnings yield divided by he beginning-of-period marke value of equiy; q ˆ = ( q q 1 ) B 1 / V 1 is he change in profiabiliy, adjused by he beginning-of-period raio of he book value of equiy o he marke value of equiy, wih profiabiliy defined as he reurn on equiy (ROE); b ˆ = [( B B ) / B ](1 B / V ) is capial invesmen, adjused by one minus he i i i 1 i 1 i 1 i 1 i i i i i 15

16 beginning-of-period book-o-marke raio; g ˆ = ( g g 1 ) B 1 / V 1 is he change in growh opporuniies, adjused by he beginning-of-period book-o-marke raio; i 1 ) Bi 1 / i 1 i i i i i r ˆ = ( r r V is he change in he discoun rae, adjused by firm s beginning-ofperiod book-o-marke raio. We ake he five accouning variables in Eq. (3) as our fundamenal variables for explaining sock price movemens The Model: Enhancing wih Technical Analysis We define he sock price movemens as price changes relaive o iniial price (wihou dividends) following he definiion of Chen, Da and Zhao (013). This is equivalen o capial gain reurns. Therefore, for porfolio i, he one-period sock price movemen from ime -1 o ime could be denoed as p i, = p i, + h i, (4) p p i, where i = (1, ). Δp i, is he one period sock reurn. We classify wo groups of variables: fundamenal (i.e. accouning-based) variables and momenum (ie. price based) variables. Fundamenal variables are hose used in Chen and Zhang s (007) valuaion model and include earnings yield (x), equiy capial invesmen (Δb), changes in profiabiliy (Δq), growh opporuniies (Δg), and discoun raes (Δr). Technical variables include various reurn moving averages (MAs) over differen measuremen horizons. We include five lagged reurns, lagged by 1, 3, 6, 9 and 1 monhs, and name hem T 1M,i,, T 3M,i,, T 6M,i,, T 9M,i, and T 1M,i,, respecively. The five lagged reurns are seleced o capure he shor erm, medium erm and long 16

17 erm influence of echnical variables. We firs examine he impac of having boh fundamenal and echnical variables under he radiional OLS framework. Hence we run (5) p i, = α + βifi, + γ iti + ε i, where β = ( β β β β β ), γ = ( γ γ γ γ γ ) i i, 1 i, i,3 i,4 i,5 i, 1 i, i,3 i,4 i,5, = ( x q b g r ), ( T T T T T ) F i, i, i, i, i, i, T i, = 1M, i, 3M, i, 6M, i, 9M, i, 1M, i, We firs provide a direcly comparable resul o he exising lieraure explaining crosssecional reurns using our size porfolios by esimaing Eq. (5) using OLS. Our preliminary check on he daa reveals ha he sample suffers from heeroskedasiciy. This is resolved by using he Newey-Wes mehod of muliplying he inverse of he residual covariance marix. This is equivalen o using he generalized leas square (GLS) mehod. While i is expeced ha he fundamenal and echnical variables will joinly explain a large proporion of SPM, here remains he possibiliy of omied variable bias in Eq. (5). I is highly likely ha here exiss oher facors causing sock prices o change and hese facors are sochasic in naure. Hence, we aggregae hese facors ino one variable and esimae i using a Kalman filering echnique and name i Z. Having a condiioning variable, Z, in he regression has wo advanages: (i) i ensures ha our residual erm is i.i.d. by reducing poenial mulicollineariy and omied variable bias and (ii) i allows us o precisely quanify he level of incremenal conribuion o he predicive power of he model, which will be invesigaed in he nex secion. This will be furher discussed in deail in Secion 3.5. Therefore we have 17

18 (6) p i, = α + βifi, + γ iti + λz + ε i, where all parameers and variables are as previously defined. Running Eq. (6) yields he relaionship beween variaions in sock prices and he fundamenal and echnical variables Esimaion Mehod: Sae Space Model Noe ha he variable Z does no have subscrip i as Z will be esimaed from boh size porfolios simulaneously. Hence all porfolios share he same Z. This is equivalen o fraily in saisics (see Duffiee e al., 009). As previously saed, a condiioning variable, Z, represens he marke wide common sochasic facors ha cause sock prices o change. Alhough used under a compleely differen framework, Goh e al. (01) noes he imporance of his ype of variable and uses an equivalen approach and also refer o i as variable Z. In explaining bond risk premia using echnical variables, Goh e al. (01) includes an economic variable, Z, which includes macroeconomics facors from Ludvigson and Ng (009). Insead, we apply a sandard Kalman filering echnique o exrac he same informaion from he marke daa. Using a sae space model ensures ha we suffer less from omied variable bias since i is no possible o include all variables ha poenially affec sock price movemens. Adoping a filering approach in he esimaion of a sae space model also allows us o be less prone o an over-fiing problem. In implemening he sae space model, we follow Hamilon (1994) closely. In his secion, however, we describe and jusify he srucure of he sae equaion. Filering also has major advanages over principal componen analysis (PCA). Firs, filering 18

19 yields a more parsimonious regression model whils allowing us o include more informaion. We mus decide he number of componens o include in a PCA and he crierion for his becomes ambiguous when he explanaory power of he firs componen is no sufficienly large. Many choose he number of PCs ha can explain more han an arbirary level of all movemens in he underlying variables of ineres (e.g. 90%) bu his may require muliple PCs o be included in subsequen regression analyses. 3 Second, filering allows us o projec he common variable, Z, by giving i a srucure. When using PCA, we canno forecas he value of principal componens. Therefore filering is more appropriae for explaining fuure sock reurns. Under he assumpion of lineariy and mulivariae Gaussian error erms, parameers of sae equaions esimaed using Kalman filer are opimal. Eq. (7) is he observaion equaion, where we inend o esimae Z wih he sae equaion. The sae equaion is modelled wih an AR(1) process. Z = ρz ρ ω (7) where -1 < ρ < 1. Z is a facor ha includes commonaliies of he sample porfolios. Therefore Z represens macroeconomic and financial marke condiions ha commonly affec he US equiy marke. This saemen is almos rue because our sample, Russell 3000 socks, represens approximaely 98% of he invesable equiies in US sock markes. By including Z, we are conrolling for unobserved macroeconomic, marke wide variabiliy ha is known o exis. I is well known ha macroeconomic facors are cyclical, herefore, Z is modelled by 3 For example, Pukhuanhong and Roll (009) use he firs 10 principal componens from a PCA o explain counry-level sock index reurns a he daily frequency. 19

20 AR(1) process, where 1 period is one quarer, consisen wih he daa inerval of he fundamenal variables. The parameer ρ would represen he cyclicaliy of he variable Z. If we employ a simple AR(1) process of Z = ρz -1 + ω, he sae equaion will inroduce an idenificaion problem. Parameers, β, γ, λ and ρ, are esimaed by ieraively maximizing he likelihood funcion where he sae variable Z is unobserved. The same values of he likelihood funcion could be obained wih various combinaions of he λ and Z, as long as he muliples of he wo are he same. Conrolling for he condiional variance of Z can correc his idenificaion problem. Therefore we impose a consrain ha he condiional variance of Z is equal o 1. This is equivalen o performing a GLS esimaion of he sae equaion. The proof is in Appendix. Once we filer he sae variable Z and forecas one period ahead for Z using he sae equaion. If Z properly represens he marke wide common shock, our ex-ane expecaion of λ is posiive and significanly differen from zero. ρ is expeced o ake a posiive value while is saisical significance canno be prediced. Cyclicaliy in marke wide shocks could be absorbed in he echnical variables. For convenience, we will refer o hese models as follow, hereafer. OLSF Model: Δp i, = α + β i F i, + ε i, (8) OLST Model: Δp i, = α + γ i T i, + ε i, (9) OLSTF Model: Δp i, = α + β i F i, + γ i T i, + ε i, (10) Sae Space Model: Δp i, = α + β i F i, + γ i T i, + λz + ε i, (11) 4. Empirical Resuls 4.1. Fundamenal Analysis wih Technical Analysis under OLS Specificaion 0

21 The exan lieraure invesigaing he impac of accouning informaion and/or echnical variables ypically use OLS (See iner alia, Chen and Zhang, 007, Beman, Saul and Schulz 009, Binsbergen and Koijen, R. 010, Bajgrowicz and Sxaille, 01). In his secion, we combine he fundamenal variables suggesed by Chen and Zhang (007) and various echnical indicaors following he radiional OLS approach and compare he resuls o he cases when separae regressions are employed, i.e we are comparing he resul of OLSF in Eq. (8) ( p i, = α + βifi, + ε ) and OLST in Eq. (9) ( i, p i, = α + γ iti + ε ) o OLSFT in Eq. i, (10) ( p i, = α + βifi, + γ iti + ε ).Table repors he resuls of OLSF and OLST and Table 3 i, repors he resuls of OLSFT. (Inser Table here) (Inser Table 3 here) In comparing OLS resuls presened in Tables and 3 we noe several sriking resuls. When echnical indicaors are used in sandalone regressions in Table, hey are much less effecive han when hey are used alongside accouning informaion in Table 3. For insance, for large cap socks in Panel A, he longer erm echnical variables, T 6M and T 1M are only mildly significan a he 10% level whils for small cap socks in Panel B, T 3M is he only saisically significan echnical variable. This suggess ha here is limied power in using echnical analysis alone and ha i is beneficial o use a combinaion of fundamenal and echnical variables when explaining sock price movemens. The R of he small cap porfolio is larger han ha of he large cap porfolio. This is consisenly shown in all of laer empirical models where we include boh he fundamenal 1

22 and echnical variables under OLS and sae space model. This is consisen wih our ex-ane expecaion ha I can be seen in Table 3 ha when fundamenal and echnical variables are used joinly o explain sock reurn variaions, he adjused R significanly increases indicaing ha echnical variables do provide subsanial incremenal informaion for explaining SPM over fundamenal variables. This evidence suggess ha here is a complemenary role for he wo ypes of securiy analyses. When hey are used joinly in an OLS esimaion, he saisical significance of some of he coefficiens improve from when hey are esimaed separaely. For insance, he esimaes for he echnical indicaors T 1M, T 3M, T 6M, T 9M and T 1M all improve for he large-cap porfolio whils he esimaes for boh fundamenal and echnical variables, b, g, T 1M, T 6M, T 9M and T 1M improve for he small-cap porfolio. Our OLS resuls affirm he exan lieraure. The explanaory power of he our OLS models (measured by R and he adjused R values) are comparable o hose of Beman e al. (009). They repor R of 0.49 when only accouning fundamenals are regressed (Table 4 of Beman e al, 009) and adjused R of when fundamenal and echnical variables are combined (Table 5 of Beman e al, 009). All variables are significan in he expeced direcion. While our resuls are fairly consisen wih he exan lieraure, we show wih he use of echnical variables represening informaion over differen ime horizons ha he coefficien of he one monh lagged reurn, T 1M, is posiive for boh size porfolios when only echnical variables are used o explain SPM. However, hey become negaive and also saisically significan when he model is augmened wih fundamenal variables. This suggess ha some of he shor erm momenum could be capured by accouning informaion and he wo ypes of variables have some overlap in heir informaiveness.

23 Taken ogeher, he evidence suggess ha he wo ses of variables are complemenary in naure raher han subsiues for one anoher. However, i should be noed ha whils he OLS resuls do no suffer from serial correlaion or heeroskedasiciy as hey are conrolled wih he Newey-Wes mehod, he residuals from Eq. (10) do rejec he Ramsey Regression Equaion Specificaion Error Tes (RESET). This suggess ha he sandard OLS model may be suffering from omied variable bias Sae Space Modelling To overcome omied variable bias, we nex use a sae space model specified by Eqns. (6)- (7). The resuls are provided in Table 4. (Inser Table 4 here) In Table 4, we observe ha he coefficien of he laen variable is saisically significan and posiive in explaining he reurns of boh size porfolios. Furhermore, he laen variable provides incremenal explanaory power for variaions in monhly SPM as he adjused R is higher when i is included alongside he fundamenal and echnical variables. Take ogeher his evidence indicaes ha he laen variable is indeed imporan for picking up hose unobservable common facors ha influence SPM and ha he OLS models ha have been used in he exan lieraure suffer from omied variable bias. Hence, prior sudies have no provided an accurae picure of he relaive imporance of fundamenal and echnical analyses for securiy pricing. 4 The Ramsey RESET provides a general specificaion es on he linear regression model for wheher nonlinear combinaions of he fied values help o explain he response variable. The es is one of he mos popular proxy ess for he omied variable bias. 3

24 The sae space model is well specified and more appropriae for modelling sock price movemens as i yields non-serially correlaed homoscedasic residuals wih he laen variable Z, designed o absolve mos of non-i.i.d. aspecs of sock reurns. Noneheless, he sae space model does no aler he signs of he esimaed coefficiens ha are saisically significan in he combined OLSFT model. Duffie e al. (009) also finds saisically significan unobserved marke wide facor in suggesing a more realisic model of he risk of large defaul losses. Our finding may be considered is equivalen in equiy marke reurn Firm Size Analysis The unobserved common facor has a significan and posiive impac on he reurns of boh he large-cap and he small-cap companies bu has a noably larger impac on he sock reurns of he laer. This indicaes ha small cap socks are more prone o marke wide shocks. In general, we find ha larger firms end o be more sensiive o accouning-based informaion. Firs, he performance of large-cap socks is more dependen on earnings. Earnings exers a greaer economic impac on he sock reurns of large firms relaive o smaller firms as one sandard deviaion increase in earnings yield (x) would increase larger firms monhly sock reurns by 1.176% bu only by 0.345% for smaller firms. Second, changes in invesmen ( b) have significan effecs on large cap firms sock performance bu no on he small cap firms. One sandard deviaion increase in invesmen made can increase monhly sock reurns by 0.69% in large firms bu only 0.14% in small firms. This corroboraes wih evidence ha he more significan invesmens made by largecap companies ends o have greaer impac on heir performance. 4

25 Third, revisions in analys s long erm earnings forecass ( g) have much higher impac on large cap sock reurns as one sandard deviaion increase in he long erm growh forecass can increase sock reurns by 0.713% and 0.187% for large and small firms, respecively. This is because analyss end o make much more accurae forecass on he fuure performance of he large cap companies as informaion is more readily available o analyss. Also, rading of large cap socks ends o be driven more by sock analyss recommendaions so i is expeced ha analys earnings forecass would provide more explanaory power for sock performance. In conras, changes in monhly profiabiliy ( q) are no significanly relaed o large cap sock performance bu are imporan for explaining small cap sock reurns. This is consisen wih he noion ha he sock reurns of larger companies are less sensiive o he shor erm swings in company profis. We noe ha larger firms are also more sensiive o echnical variables as all momenum variables are significan for he large cap socks, while he six monh lag reurn (T 6M ) is no significan for explaining variaions in small cap sock reurns. This suggess ha in he medium erm, price-based informaion is no so imporance for smaller socks relaive o fundamenal informaion. Fourh, changes in he discoun rae ( r) have saisically significan negaive influence on boh porfolios reurns. I has much higher impac on small cap sock reurns as one sandard deviaion increase in he discoun rae change can decrease sock reurns by 1.039% and 1.658% for large and small firms, respecively. The negaive relaionship mees he common expecaion and is consisen wih Chen and Zhang (007). The larger impac on small firms is also inuiive as smaller companies are more prone o changes in discoun raes. For example, small companies more likely o experience liquidiy squeeze when he discoun rae increases. 5

26 The inercep capures he mean reurn on a given sock porfolio. We noe ha he inercep is negaive and significanly differen from zero for large cap socks while i is no saisically significan for he small cap socks. This resul is consisen wih Fama and French (1993) where hey find ha small cap and value porfolios have higher expeced reurns and arguably higher expeced risk han hose of large cap and growh porfolios, all oher hings being held equal Robusness Checks OLSFT model is a benchmark model ha we use o assess he new evidence ha can be gleaned from an alernaive sae space modelling approach. We find ha he signs and he saisical significance of he esimaed parameers are consisen wih he OLSFT model. Compared wih he benchmark model, he sae space model offers higher explanaory power. Furhermore, he residual of he sae space model is less likely o suffer from he omied variable bias problem. Nex, we es he sae space model over various subsample periods. The resuls for his subsecion are no abulaed for breviy bu are available upon reques. The adjused R of he model remains seady as subsample period changes, ranging from 0.797, in , o 0.886, in Finally, we follow Chen and Zhang (007) in verifying he robusness of he resuls obained from he sae space model and analyze various pariions of he sample. We pariion he sample companies ino quariles based upon marke capializaion. We run separae regressions for he four size porfolios. The resuls show ha for all size quariles, he regression coefficiens have he same signs as prediced by he heoreical model, 6

27 suggesing ha he qualiaive resuls presened are robus across differen groupings for firm size. (Inser Table 5 here) 5. Concluding Remarks In his paper we revisi he relaive imporance of fundamenal and echnical analyses for socks. We sudy a sample of he consiuens of he Russell 3000 index from he US over he period from Using a porfolio level analysis, we consider he differences in he explanaory power of he wo main ypes of predicors for monhly sock price movemen. In order o avoid poenial omied variable bias and o improve he explanaory power of our empirical model, we employ a sae space model. Our model includes a sae variable, which represens an unobservable marke wide common facor. We find ha combining fundamenal analysis wih echnical analysis can subsanially enhance he explanaion of sock price movemens, compared o he cases where echnical or fundamenal analysis is employed independenly. The adjused R significanly increases when he boh variables are included in he esimaion model. We also find ha he unobserved common facor has saisically significan explanaory power for SPM. Lasly, we find ha here exiss a significan size effec in he impacs of he echnical and fundamenal variables. Also we find ha he adjused R increases when he common facor is aken ino accoun indicaing improved explanaory power for SPM. 7

28 Large cap sock reurns are more sensiive o earnings, change in he invesmens and change in he long erm growh expecaions han small socks reurns. Reurns of small cap socks are more sensiive o change in profiabiliy and change in discoun rae. Boh large cap and small cap sock reurns are significanly explained by heir own pas values. The inercep, which capures he mean reurn on a given sock porfolio, is negaive and significanly differen from zero for large cap socks while i is no saisically significan for he small cap socks. This may indicae ha ha small cap and value porfolios have higher expeced reurns and arguably higher expeced risk han hose of large cap and growh porfolios and is consisen wih Fama and French (1993). The conribuion of our paper o he exan lieraure can be summarized as follows. We empirically find ha blending echnical and fundamenal analysis is beneficial in explaining sock price movemens. However here exiss a sysemaic porion in residual sock price movemens ha canno be explained by he wo and his facor mus be exraced and segregaed in order o have a beer specified model. Once all hese are aken ino accoun, we find ha here is a significan size effec. The fundamenal variables, echnical variables and unobserved common facor all have differen impacs on sock price movemens depending on he size of he companies. 8

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32 Tables and Figures. Table 1. Descripive saisics of he sample This able repors he descripive saisics of he following variables. The porfolio reurn (R ) is he monhly reurn of boh porfolio; earnings yield (x ) is earnings (X ) divided by he beginning-of-period marke value of equiy (V -1 ); profiabiliy change (dq i ) is monh profiabiliy q minus monh -1 profiabiliy q -1, where q = X /B -1 muliplied by B i-1 /V i-1 ; capial invesmen (ΔB i /B i-1 ) is he change in he book value of equiy relaive o he prior monh scaled by beginning-of-period book value muliplied by B i-1 /V i-1 ; growh opporuniy change (dg i ) is he change in he median analys forecas of he long-erm growh rae following he curren year earnings announcemen relaive o ha of he prior year; he adjused growh opporuniy change is growh opporuniy change muliplied by B i-1 /V i-1 ; discoun rae change (dr i ) is he change of he 10-year US Treasury bond yield over he reurn period muliplied by B i-1 /V i-1. The sample consiss of 774 firm-year observaions over he period Panel A1: Monhly descripive saisics of he oal sample Toal Sample Mean Median Sd dev Min 1s quarile 3rd quarile Max Porfolio Reurn 0.36% 0.8% 4.59% % -1.98% 3.0% 10.3% Earnings yield (x) Profiabiliy change (dq) (%) 0.00% 0.0%.7% -13.1% -0.66% 0.66% 10.76% Capial invesmn (db) (%) 0.51% 0.5% 0.60% -.18% 0.5% 0.85% 1.80% Growh opporuniy change (dg) (%) 0.3% 0.3% 0.6% -.5% -0.04% 0.51%.13% Discoun rae change (dr) (%) 0.11% 0.00% 1.33% -8.67% -0.3% 0.48% 6.06% B/M raio Panel A: Correlaion marix of he oal sample Correlaion Marix R x dq db dg Earnings yield (x) 0.8 Profiabiliy change (dq) (%) Capial invesmn (db) (%) Growh opporuniy change (dg) (%) Discoun rae change (dr) (%)

33 Table. Esimaed resuls of Δp i, = α + β i F i, + ε i, and Δp i, = α + γ i T i, + ε i,. This able repors he esimaion resuls for Eq.s (8) and (9) in explaining monhly sock price movemens of all sample socks in he Russell 3000 index. Panel A shows he resuls for he large-size porfolio, porfolio 1, whils Panel B repors resuls for he small-size porfolio, porfolio. OLS Fundamenals repors OLSF model in Eq.s (8) and OLS Technicals repors OLST model in Eq.s (9). R and Adj R rows repor he R and he adjused R of he regression models. Variable x is earnings divided by he beginning-of-period marke value of equiy; variable Δq is profiabiliy change; capial invesmen, variable Δb, is he change in he book value of equiy relaive o he prior monh; growh opporuniy change, variable Δg, is he change in he median analys forecas of he long-erm growh rae; variable Δd is he discoun rae (10-year US Treasury bond yield) change over he reurn period. T 1M,i,, T 3M,i,, T 6M,i,, T 9M,i, and T 1M,i, are he lagged reurns of he porfolio i, lagged by 1, 3, 6, 9 and 1 monhs, respecively. The sample consiss of 774 firm-year observaions over he period *, **, *** denoe significance a he 10, 5 and 1% level of significance, respecively. Panel A OLS Fundamenals OLS Technicals Variable Esimaed Coeff -sa p-value Variable Esimaed Coeff -sa p-value x 0.63*** T 1M 0.346*** q T 3M b 0.760*** T 6M * g 1.710*** T 9M r -0.85*** T 1M * consan *** consan R 0.40 R 0.1 Adj R 0.40 Adj R Panel B OLS Fundamenals OLS Technicals Variable Esimaed Coeff -sa p-value Variable Esimaed Coeff -sa p-value x 0.093*** T 1M q 0.14** T 3M 0.18* b T 6M g 0.304* T 9M r -1.44*** T 1M consan consan R R Adj R Adj R

34 Table 3. Esimaed resuls of Δp i, = α + β i F i, + γ i T i, + ε i,. This able repors he esimaion resuls for Eq. (10) Panel A shows he resuls for he large-size porfolio, porfolio 1, whils Panel B repors resuls for he small-size porfolio, porfolio. OLS Fundamenal & Technical indicaes OLSFT model in Eq.s (10). R and Adj R rows repor he R and he adjused R of he regression models. Variable x is earnings divided by he beginning-of-period marke value of equiy; variable Δq is profiabiliy change; capial invesmen, variable Δb, is he change in he book value of equiy relaive o he prior monh; growh opporuniy change, variable Δg, is he change in he median analys forecas of he longerm growh rae; variable Δd is he discoun rae (10-year US Treasury bond yield) change over he reurn period. T 1M,i,, T 3M,i,, T 6M,i,, T 9M,i, and T 1M,i, are he lagged reurns of he porfolio i, lagged by 1, 3, 6, 9 and 1 monhs, respecively. The sample consiss of 774 firm-year observaions over he period *, **, *** denoe significance a he 10, 5 and 1% level of significance, respecively. Panel A Panel B OLS Fundamenal & Technical OLS Fundamenal & Technical Variable Esimaed Coeff -sa p-value Variable Esimaed Coeff -sa p-value x 0.393*** X 0.106*** q q 0.05*** b 0.544*** b 0.313* g 1.571*** g 0.48*** r *** r -1.04*** T 1M *** T 1M *** T 3M 0.110*** T 3M 0.073** T 6M *** T 6M T 9M *** T 9M ** T 1M ** T 1M -0.06** consan -0.06*** consan R 0.78 R Adj R Adj R

35 Table 4. Esimaed resuls of he sae space model. This able repors he esimaion resuls from he sae space model (represened in Eqs (6)-(7)) for explaining monhly sock price movemens of all sample socks in he Russell 3000 index. The sample period used is from January 1999 o December 01. Panel A shows he resuls for he large-size porfolio whils Panel B repors resuls for he small-size porfolio. Panel C shows he resuls for he model specificaion wih only he inclusion of he laen facor, Z. Panel A and B include he esimaed resuls of Eq.s (6) and Panel C includes he esimae resul of Eq.s (7). OLS Fundamenal & Technical indicaes OLSFT model in Eq.s (10). Adj R rows repors he adjused R equivalen for he OLSFT model. Variable Z is he unobserved facor ha is shared by he boh porfolios, exraced from he sae space model; variable x is earnings divided by he beginning-of-period marke value of equiy; variable Δq is profiabiliy change; capial invesmen, variable Δb, is he change in he book value of equiy relaive o he prior monh; growh opporuniy change, variable Δg, is he change in he median analys forecas of he long-erm growh rae; variable Δd is he discoun rae (10-year US Treasury bond yield) change over he reurn period. T 1M,i,, T 3M,i,, T 6M,i,, T 9M,i, and T 1M,i, are he lagged reurns of he porfolio i, lagged by 1, 3, 6, 9 and 1 monhs, respecively. The sample consiss of 774 firm-year observaions over he period *, **, *** denoe significance a he 10, 5 and 1% level of significance, respecively. Panel A Panel B Variable Esimaed Coeff z-sa p-value Variable Esimaed Coeff z-sa p-value Z 0.006*** Z 0.009*** x 0.39*** x 0.115*** q q 0.4*** b 0.449*** b 0.33* g 1.151*** g 0.30*** r *** r -1.57*** T 1M ** T 1M *** T 3M 0.108*** T 3M 0.068** T 6M *** T 6M T 9M ** T 9M ** T 1M ** T 1M ** consan -0.05*** consan Adj R Adj R Panel C Z

36 Table 5. Robusness check wih quarile porfolios. This able repors he esimaion resuls from he OLS model for quarile porfolios for explaining monhly sock price movemens of all sample socks in he Russell 3000 index. The sample period used is from January 1999 o December 01. Panel A shows he resuls for he firs quarile porfolio, Panel B repors resuls for he second quarile porfolio, Panel C repors resuls for he hird quarile porfolio and Panel D repors resuls for he las quarile porfolio. Variable x is earnings divided by he beginning-of-period marke value of equiy; variable Δq is profiabiliy change; capial invesmen, variable Δb, is he change in he book value of equiy relaive o he prior monh; growh opporuniy change, variable Δg, is he change in he median analys forecas of he long-erm growh rae; variable Δd is he discoun rae (10-year US Treasury bond yield) change over he reurn period. T 1M,i,, T 3M,i,, T 6M,i,, T 9M,i, and T 1M,i, are he lagged reurns of he porfolio i, lagged by 1, 3, 6, 9 and 1 monhs, respecively. The sample consiss of 774 firm-year observaions over he period *, **, *** denoe significance a he 10, 5 and 1% level of significance, respecively. Panel 1 Porfolio 1 Panel Porfolio Variable Esimae Coeff -sa p-value Variable Esimae Coeff -sa p-value x *** x *** dq ** dq db 0.590*** db *** dg dg *** dr dr *** T 1M T 1M T 3M T 3M *** T 6M *** T 6M T 9M * T 9M T 1M T 1M cosan *** cosan R R Adj R Adj R Panel 3 Porfolio 3 Panel 4 Porfolio 4 Variable Esimae Coeff -sa p-value Variable Esimae Coeff -sa p-value x *** x *** dq dq 0.38*** db db dg dg *** dr dr T 1M T 1M T 3M T 3M T 6M T 6M -0.13*** T 9M T 9M T 1M T 1M cosan ** cosan 0.015*** R R Adj R Adj R

37 Appendix. Appendix 1. Descripive Saisics of he daa in Chen and Zhang (007) Panel A1: Descripive saisics of he pooled sample Porfolio Toal Mean Median Sd dev Min 1s quarile 3rd quarile Max Porfolio Reurn Earnings yield (x) Profiabiliy change (dq) (%) Capial invesmn (db) (%) Growh opporuniy change (dg) (%) Discoun rae change (dr) (%) B/M raio Panel A: Correlaion marix of he oal sample Correlaion Marix R x dq db dg Earnings yield (x) 0.9 Profiabiliy change (dq) (%) Capial invesmn (db) (%) Growh opporuniy change (dg) (%) Discoun rae change (dr) (%) Noe ha Chen and Zhang (007) use annual daa while we use monhly daa. Also hey collec he annual sock reurn from days afer he year -1 earnings announcemen o one day afer he year earnings announcemen. Appendix. Condiional Variance of Equaion (7) Z = ρz ρ ω Z Z ρ ( ρ + 1 ρ ω 1) + 1 ρ = Z ρ ( ρ( ρ ρ ω ) + 1 ρ ω 1) + 1 ρ = Z ω ω Z = ρ Z0 + 1 ρ ω + ρ 1 ρ ω 1 + ρ 1 ρ ω + + ρ 1 ρ ω0 37

38 38 Therefore, we have, = + = i i i Z Z ω ρ ρ ρ Since ω ~ i.i.d. (0,1), ( ) ( ) ( ) [ ] ( ) ( )( ) ω ρ ω ρ ω ρ ω ρ ω ρ ρ ω ρ ρ i i i i i E Z E Z E Z Vaρ = = = = = = ( ) ( ) lim = = ρ ρ Z Vaρ