Implied Cost of Capital Based Investment Strategies

Transcription

1 Implied Cos of Capial Based Invesmen Sraegies Florian Eserer Swisscano David Schröder CREST * and BGSE ** This version: Absrac In he recen lieraure on esimaing expeced sock reurns, one of he mos ineresing approaches is he concep of he so-called implied cos of capial. Calculaed as he inernal rae of reurn ha equaes sock price wih discouned fuure cash-flows, his mehod has been applied o esimaing he marke risk premium as well as forecasing individual sock reurns. In his paper we invesigae several implied cos of capial approaches in heir inrinsic abiliy o predic sock reurns. Using cross-secional regression analysis and panel esimaion, we confirm is hypohesised relaion o sock reurns, bu deec qualiaive differences among sandard models employed. JEL Classificaion: G11 Keywords: Implied cos of capial, implied reurn, porfolio managemen, expeced sock reurns, panel regressions, analyss forecass We are graeful o seminar paricipans a CREST and BGSE for helpful commens and suggesions. Moreover, we would like o hank Swisscano for enabling us o use he daa. Any remaining errors are ours. Swisscano Asse Managemen AG Waisenhaussrasse 2, 8023 Zürich, Swizerland florian.eserer@swisscano.ch * Cenre de Recherche en Économie e Saisique 15, Bd Gabriel Péri Malakoff, France ** Bonn Graduae School of Economics Adenauerallee Bonn, Germany david.schroeder@uni-bonn.de

2 1 1. Inroducion Predicing he sock marke or he reurns of individual socks has been an on-going effor in academia and he money managemen indusry. Many differen sock selecion crieria and firm characerisics ha migh be useful for sock reurn predicion have been examined and analyzed horoughly. Among he mos prominen examples are pas price and earnings momenum (Chan e al., 1996), firm size (Fama and French, 1992), valuaion muliples such as he B/M raio and he D/P raio (Fama and French, 1988, 1992), and more fundamenally, he marke bea of he CAPM. However, many of hese characerisics are of an ad-hoc naure, and no derived by fundamenal valuaion analysis. In his sudy we examine he capabiliy of richer valuaion models o predic cross-secional reurns. More precisely, we analyze he abiliy of he so-called implied cos of capial o accuraely forecas sock reurns. Calculaed as he inernal rae of reurn 1 ha equaes sock price wih discouned expeced cash-flows obained from equiy analyss, his raher new concep of esimaing sock reurns has been applied o deermining he marke risk premium as well as forecasing individual sock reurns. The underlying assumpion of his mehodology, he equalizaion of marke price and fundamenal firm value, can be jusified when one is o accep marke efficiency and negligible arbirage coss. Bu even if we allow ha price is only a noisy, coinegraed proxy for inrinsic firm value, he implied cos of capial should have some explanaory power o explain sock reurns. In a firs sep, we invesigae he profiabiliy of invesmen sraegies based on various implied cos of capial (ICOC) esimaes, such as he dividend discoun model (DDM) or he residual income model (RIM), for a broad daa sample of U.K. firms from 1995 o We find ha ICOC-based invesmen sraegies are profiable and provide significanly posiive reurns when derived from hree-sage DDM and RIM approaches. However, he longer he invesmen horizon, he beer he DDMs perform compared o he RIM, whose profiabiliy deerioraes for 1 In his sudy, he erms implied cos of capial (ICOC), implied reurn, and inernal rae of reurn refer o he same concep and are used inerchangeably.

3 2 ime horizons longer han 6 monhs. Over 24 monhs, he porfolio wih he highes implied cos of capial esimaes based on he wo-sage DDM following Damodaran (1999) performed on average abou hree imes beer han he one wih he lowes expeced reurns. When examining he characerisics of he consruced porfolios, we find ha all ICOC conceps are relaed o he Fama-French risk facors B/M-raio and firm size. However, his srong relaion migh sugges ha he implied cos of capial does no predic fuure reurns iself, bu only via is relaion o hese well-known risk facors. To analyze wheher he ICOC has indeed an addiional explanaory power for sock reurns we run cross-secional regressions as well as panel regressions of sock reurns on firm characerisics and he implied cos of capial. The resuls confirm he hypohesis ha he ICOC can conain some addiional informaion for predicing sock reurns. Especially RIM based ICOC esimaes are always highly significan afer conrolling for marke bea, B/M raio and firm size. Our sudy is relaed o several sreams of lieraure. On he one hand, i akes up he pioneering works by Cornell (1999), and Claus and Thomas (2001) who applied he ICOC approach successfully o esimae an implied equiy risk premium by aggregaing firm esimaes over enire markes. Among ohers, Gebhard e al. (2001), Lee e al. (2003), and Eason e al. (2002) invesigaed implied reurns for individual firms and is relaion o firm characerisics. On he oher hand, his paper refers o he earlier aemps o explain sock reurns by Price-Value raios. Lee a al. (1999) show ha his inverse valuaion muliple where he inrinsic value is esimae wih he help of comparable presen value formulas is relaed o Dow Jones sock reurns. Alhough heir approach is raher similar o he implied cos of capial, we oped in his sudy for he laer 2. Finally, by mimicking invesmen porfolios using he ICOC as sock selecion variable, his sudy uses echniques presened by he works on momenum sraegies (Chan e al., 1996; Jegadeesh and Timan, 2001), or on conrarian invesmen (Lakonishok e al., 1994). Despie is widespread use in boh heory and pracice, here are very lile economeric foundaions of he implied cos of capial mehodology a he level of individual firms. As such, his work exens prior sudies on he invesigaion of he implied cos of equiy capial, such as 2 We have several reasons for favoring he implied reurn concep. Firs, he implied reurn is essenially an implied discoun facor which has a more inuiive inerpreaion as proxy for he shareholder s rae of expeced reurn. As such, i is more easily compared o oher common mehods o esimae he firm s cos of capial. Second, he P/V approach requires in addiion o he ICOC an esimae or assumpion of he discoun facor, which inroduces anoher possible source of errors. Third, he ICOC is more prevalen in he lieraure, allowing beer comparison o exising sudies.

4 3 by Lee e al. (2003), who analysed he deerminans of he ICOC a he firm level. A firs paper ha examines he ICOC s applicaion o acive porfolio managemen has been composed by Soz (2005), alhough resriced o he raher small DJ Soxx 50 daa se. By using various economeric approaches o explain sock reurns, his paper also conribues o he growing lieraure ha invesigaes and compares he pracical implemenaion of alernaive esimaion mehods for individual sock reurns. In fac, his sudy is one of he very few papers ha carries ou panel esimaion mehods on sock reurns for a broad daa se, comparable o Pandey (2001), or Subrahmanyam (2004). In conras o hese sudies, we perform long-horizon regressions using overlapping sock reurns, similar o Bauer e al. (2004). Moreover, his paper provides a deails comparison of ICOC approaches commonly used, he residual income models and dividend discoun models. In addiion o exising models, we presen a modified version of he RIM as proposed by Gebhard e al. (2001) ha is more coheren in he long run han exising RIM formulas. This paper proceeds as follows. In he nex secion, we describe he mehodology of he implied cos of capial in more deail and presen he various esimaion approaches employed in his sudy, he dividend discoun model and he residual income model. Secion 3 conains a brief descripion of our U.K. daa sample. Then we presen he resuls of buy-and-hold sraegies, i.e. he reurns of porfolio invesmens when we use he implied cos of capial esimae as sock selecion variable, and analyze he characerisics of hese porfolios. Finally, in secion 5, we carry ou cross-secional and panel regression ess o show ha even afer conrolling for common risk facors, he ICOC has some explanaory power o predic individual sock reurns. Secion 6 offers some concluding remarks. 2. Models for he Implied Cos of Capial In his sudy, he cos of capial of individual firms is calculaed using he mehodology of he socalled implied cos of capial. The basic idea of his concep is o esimae he fuure cos of capial wih he help of presen value models. More precisely, he cos of equiy is compued as he inernal rae of reurn ha equaes discouned payoffs per share o curren price, where

5 4 expeced cash flows are aken from equiy analyss. In he lieraure, many differen versions of he presen value model are employed o calculae he implied cos of capial. In his work, we resor o he models of mos prominen sudies on he implied cos of capial. On he one hand, we use he dividend discoun model (DDM) in he versions of Cornell (1999) and Damodaran (1999). On he oher hand, we rely on he residual income model (RIM) following he approaches of Claus and Thomas (2001) and Gebhard e al. (2001). Moreover, we also presen a new and slighly differen implemenaion of he RIM and compare i o he exising models. In he following secion, we describe he models and heir implemenaion in more deail The Dividend Discoun Model The general DDM saes ha he price of a share should equal he discouned value of fuure dividend paymens, and can be wrien as follows: E[ D ] ( 1 k) = P 0 (1) = 1 + where P 0 = curren share price, a he end of year 0, E[D] = expeced dividends per share a he end of year, k = cos of capial or, equivalenly, shareholders expeced rae of reurn. Since exac predicions of fuure dividends canno be made o infiniy, one has o make assumpions abou expeced cash-flows when implemening he DDM in pracice. The DDM following Cornell (1999) assumes an iniial 5-year phase of high dividend growh, which is followed by a ransiion phase in which he growh raes decline linearly o a lower, sable growh g l, which is hen mainained ad infinium. Thus, his model combines he plausible conjecure of a srong growh in he firs years wih realisic growh raes in he long run.

6 P 0 5 E[ D ] = 1 ( + k) 20 = 6 E[ D ] ( 1+ k) E[ D20 ]( 1+ gl ) ( k g )( 1+ ) 20 = k l (2) 5 Growh Period Transiion Period Sable Growh In he iniial phase, he dividend growh is assumed o equal he long-erm consensus earnings growh rae, obained from equiy analyss 3. In he sable phase following year 20, he dividend growh rae equals he esimaed long-erm GDP growh of he economy (Cornell, 1999). In his sudy, we assume adapive expecaions and calculae he expeced GPD growh rae as he geomeric nominal GDP growh rae over he pas 5 years. Due o is hree-sage srucure, we refer o his model as DDM3 hereafer. I is well known ha due o conflics of ineres, equiy analyss end o oversae long-erm growh projecions (see e.g. Chan e al. (2003)), which hence biases he ICOC esimaes upwards. Since his sudy focuses on he analysis of implied coss of capial of individual firms, his bias would only cause problems if here were be some sysemaic relaion beween he degree of biases and some firm characerisic. We are no aware of any sudy documening such a relaion. Damodaran (1999) proposes anoher, much simpler DDM, involving only wo phases, an iniial high dividend growh phase and a sable growh phase: P 0 5 = 1 E[ D ] ( + k) E[ D5 ]( 1+ gl ) ( k g )( 1+ ) 5 = + 1 k l (3) Growh Period Sable Growh 3 The findings of Elon e al. (1981) sugges ha analyss forecass are a good surrogae for invesor expecaions. The consensus growh rae is provided by IBES and is calculaed as he median of he expeced earnings growh raes of he conribuing sell-side equiy analyss. Noe ha esimaing such earnings growh raes has a long radiion in he U.S., bu no in European counries, where analyss have rarely published such forecass unil he las years bu have concenraed on explici earnings forecass for he nex years insead. Hence, he implemenaion of he Cornell (1999) approach for European markes leads o a considerable decrease in he available daa se. Moreover, his growh rae is usually if available he median of very few analyss only.

7 6 Similar o he hree-sage DDM, we use he consensus growh rae as provided by IBES as growh rae in he firs phase and he expeced long-erm GDP growh rae of he economy afer year 5. In he following, we refer o his model as DDM2. Noe ha all presened DDM require he annual dividend D 0 which jus has been paid ou o he shareholders. Based on D 0 i is hen possible o calculae he series of fuure dividend paymens, beginning wih D 1. In his sudy, we use he sum of all dividend paymens over he las 12 monhs, also known as 12-monhs railing dividends, as D 0. 4 We exclude all observaions from he sample, where he 12-monhs railing dividend equals The Residual Income Model Anoher popular valuaion formula is he RIM, saing ha he value of he company equals he invesed capial, plus he expeced residual income from is fuure aciviies 5 : E[ R ] ( 1 k) + P 0 = B0 (4) = 1 + wih [ R ] = E[ E ] k( B 1 ) = ( roe k) B 1 E (5) B = B 1 ( p ) E[ E ] 1 + (6) where B = book value of equiy per share a he end of year (B0 being he curren book value), E[R ] = expeced residual income per share in year, E[E ] = expeced earnings per share in year, 4 There is some conroversy in he lieraure abou how o consruc he righ D 0 or D 1, see for example Harris and Marson (1992). 5 When combined wih he so-called clean surplus relaion, he DDM can be ransformed ino he RIM (Felham and Ohlson, 1995). This relaion requires ha all gains and losses affecing book value are also included in earnings. This condiion is no always me, of course. Sock opions and capial increases, e.g. can affec he book value of equiy while leaving earnings unchanged. Sill, he relaion is approximaely fulfilled in mos cases.

8 roe = (expeced) reurn on equiy in year, p = payou raio in year. 7 Similar o he DDM, assumpions abou he fuure growh in residual incomes or earnings have o be made when implemening he model in pracice. One raher simple approach is proposed by Claus and Thomas (2001), who consider a wo-sage RIM (abbreviaed wih RIM2 in he following), assuming an iniial phase of high earnings growh raes, followed by a sable growh of residual incomes afer year five: = 1 [ E ] k( B 1 ) ( 1+ k) E[ R5 ]( 1+ gl ) ( k g )( 1+ k) 5 E P = B + + (7) 0 0 l 5 Growh Period Sable Growh Expeced earnings for he firs hree years are aken from analyss forecass, also provided by IBES. Earnings afer year 3 are esimaed by applying he IBES consensus earnings growh rae o he expeced earnings of year 3. 6 The long-erm growh rae in he second phase is presumed o equal he expeced inflaion rae calculaed as he prevailing ineres rae on 10-year reasury bonds less hree percen, he assumed real-rae (Claus and Thomas, 2001, p. 1640). Fuure expeced book values of equiy are calculaed using equaion (6). To ha end, we have o make assumpions regarding fuure payou raios. In a sligh variaion o he mehodology of Claus and Thomas (2001), we converge he curren payou raio geomerically owards 50% insead of using his raio from he firs prospecive year on o projec fuure book values. This approach seemed more realisic o us. Curren payou raions are calculaed by dividing he 12-monhs railing dividends by he 12-monhs railing earnings per share. This mehod ensures ha he paymens refer o he same ime period as he earnings. Payou raios above 1 are se o 1 in he firs year, negaive payou raios are se o 0. If he payou raio was missing due o missing dividend paymens over he las 12 monhs, we equally se he payou raio of year =1 o 0. 6 In he case where he expeced earnings esimae of year 3 was missing, we also generaed earnings in year 3 by applying he long-erm consensus growh rae o expeced earnings of year 2. If he projeced earnings in year hree were negaive, we dropped he observaion from he sample.

9 8 Gebhard e al. (2001) rely also on he RIM o calculae he implied cos of capial. However, in conras o Claus and Thomas (2001), hey focus heir assumpions no on fuure residual incomes, bu more direcly on he fuure reurn on equiy (roe - see equaion (5)), which hey assume o converge o he indusry median. More formally: [ roe ] ( 1+ k) [ roe ] ( 1+ k) [ T ] ( 1+ k) 3 T E k E k E iroe k P 0 = B0 + B 1 + B 1 + B T 1 T 1 (8) = 1 = 4 k Explici Forecass Transiion Period Terminal Value where T = is he forecas horizon of he ransiion period iroe T = expeced indusry reurn on equiy from period T onwards. Similar o Gebhard e al. (2001) we use explici forecass o calculae he expeced reurn on equiy for he nex hree years. Then we fade he roe o over T 3 years o he indusry average. The indusry average is calculaed as he average roe over he pas 60 monhs in he indusry secor he company belongs o, using he indusry secor codes of he GICS classificaion 7. The calculaion of fuure book values of equiy and assumpions regarding fuure payou raios are idenical o hose used in he RIM2 Claus and Thomas (2001) approach. Since he model by Gebhard e al. (2001) is basically a hree-sage RIM, we denoe i by he abbreviaion RIM3. While he use of indusry averages for he long-erm reurn on equiy has some appeal due o he findings of empirical analysis (Soliman 2004, Nissim and Penman 2001), he assumpions on fuure payou raios in he lieraure as well as our implemenaion seem somewha arbirary o us. Tha is why we consider here anoher version of he RIM (denoed RIM3 ) ha avoids relying on assumpions for fuure payou raios. Following he lieraure of susainable growh raes in he long run, we use he following ideniy beween payou raio p, reurn on equiy roe and he growh rae of he company g l : 7 In our sandard implemenaion we fix T=9. Insead of using he GICS classificaion, Gebhard e al. (2001) rely on he 48 Fama and French (1997) indusry classificaions. We also esed oher, more precise classificaions such as he GICS Indusry Group segmenaion, or he Indusry segmenaion, bu he resuls were much he same.

10 g roe = 1 p l gl p = 1 roe (9) 9 In order o esimae fuure developmen of a company, one has o make o assumpions for wo ou of he hree parameers. Insead of assuming he long-run payou raio p, we op o fix he long-erm growh rae of he company g l. By seing g l equal o he expeced GDP growh rae of he economy, we ensure ha no company will persisenly grow faser han he whole economy and evenually surpass i. Hence, we calculae he RIM following Gebhard e al. (2001) as presened in equaion (8), bu using differen projeced payou raios. For each company, we calculae he long-erm indusry payou raio using he relaion (9), given he expeced GDP growh of he economy and he indusry roe T. In he ransiion period, we hen fade boh payou raio and reurn on equiy owards heir long-erm levels Empirical Implemenaion To calculae he implied cos of capial for he firms using he equaions above, we employ he las available informaion as required by he formulas a he end of each calendar monh. Firms wih an incomplee daa se, i.e. one or more missing inpu variables where we could no resor o approximaions as explained above, have been ignored 8. The soluion of he equaions is sraighforward, since i is monoone in k, and can be solved ieraively. 3. Daa In our analysis, we focus on companies in he Unied Kingdom. We cover he MSCI universe from January 1990 o June The monhly daa for prices, oal reurn, book value per share, dividends per share, marke capialisaion, and reurn on equiy are aken from MSCI. All marke 8 Noe ha we do no carry ou any ime adjusmen procedures similar o oher sudies on he implied cos of capial. Since we use a monhly daa se, such adjusmens would require he exac dividend payou daes and book value adjusmens for all companies since Such daa is no easy o ge hold of nor i is reliable.

11 10 capialisaion daa are free floa adjused. The earnings esimaes as well as he long-erm growh rae are aken from IBES median esimaes. The daa se conains 423 companies and over monhly observaions. We use he firs five years o calculae he indusry roe and can calculae he firs expeced reurns saring January 1995, leaving us wih 10 years of daa. Since he number of companies included in he sudy changes over ime, we have an unbalanced panel daa se. As shown in Table 1, he indusry group wih he larges represenaion is Indusrial Goods wih 10-15% of he companies followed by Uiliies, Maerials, Reailing, and Household Producs. The average company has a marke cap 16.98bn and a book yield of The number of observaions for he DDM2, DDM3 and RIM2 is consrained by he availabiliy of he IBES long-erm growh rae and he payou raio. For he following analyses, we will use only he overlapping daa se of 12,831 observaions. However, using he more complee daa se would resul in he same resuls in mos cases. As Table 2 shows, he average expeced reurn is fairly well clusered beween 8.8% and 10.2% wih he RIM3 having he lowes average expeced reurn a 8.88% and he DDM3 having he highes a 10.17%. However, he sandard deviaion is fairly low for he DDM2 model wih only 2.54%. The sandard deviaion is somewha higher for he DDM3 and RIM3 models wih he RIM3 having he highes sandard deviaion a 4.03%. As was o be expeced, he correlaions beween he srucurally similar models DDM2 DDM3 and RIM3 RIM3 are above 90%, rendering hem o be essenially he same models as can be seen in Table 3. On he oher hand, he correlaions beween he DDM and he RIM3 models are very low and generally are below 30%. The RIM2 models has similar correlaions of around 40-50% wih eiher group, being more correlaed o he oher RIM models using Pearson correlaions, bu being more correlaed o he DDM models using Spearman Rank correlaions. 4. Invesmen Sraegies In his secion we explore wheher i is possible o generae abnormal higher-han-average reurns based on he invesmen sraegies using he ICOC as sock selecion variable. Firs, we illusrae

12 11 our porfolio formaion mehodology. Then we compare he profiabiliy of invesmen sraegies based on he various ICOC approaches as presened in he previous secion over differen ime horizons. Nex we have a closer look a he relaion beween he ICOC and common risk facors, such as firm size, book-o-marke raio, and marke bea as well as oher firm characerisics. Finally, we examine wheher he presened invesmen approach would also be profiable in pracice by presening a feasible rading sraegy including ransacion coss Porfolio Formaion Our analysis of he profiabiliy of invesmen sraegies using he ICOC as sock selecion crieria follows in principle oher well-known sudies on invesmen sraegies such as he work on price momenum sraegies by Chan e al. (1996). A he end of each monh, we rank all socks in our sample based on he implied cos of capial esimaes as described in he previous secion. Then we group hem ino 8 equally weighed porfolios based on hese rankings. Finally, we examine subsequen oal reurns, i.e. capial gains and dividend paymens, over periods from 1 o 24 monhs. To increase he power of he analysis, we use if no saed oherwise overlapping holding periods. When we consider for insance a six monhs holding period, we use all possible porfolios ha could be used such as hose from January o July, from February o Augus, and so on Evaluaion of Invesmen Sraegies In Table 4 we presen he average buy-and-hold reurns for all differen implied cos of capial conceps over a subsequen holing period of 6 (overlapping) monhs. Porfolio 1 compromises he socks wih he lowes implied cos of capial esimae, and porfolio 8 consiss of he high ICOC socks. The line below indicaes he average difference beween he wo exreme porfolios (P8- P1), i.e. he average reurn ha could have been generaed by an invesmen sraegy consising in a shor posiion of he low-icoc porfolio P1 and a long posiion in he high-icoc porfolio P8. The -saisic of his difference is given below, calculaed by regressing he monhly overlapping differences (P8-P1) on a consan using Newey-Wes HAC sandard errors wih a lag lengh ha equals he holding periods. In order o allow for a comparison of he models, we include only he

13 12 observaions where we have ICOC esimaes for all seleced approaches, reducing he sample size o observaions 9. Whereas all ICOC approaches exhibi a posiive relaion beween cos of capial and subsequen sock reurns, and hereby confirming he hypohesis of he ICOC s abiliy o predic sock reurns, he able reveals large qualiaive differences beween he employed models. The difference beween he wo exreme porfolios, as shown in he line below he porfolio reurns varies quie significanly beween he models. Whereas he reurns of he wo exreme ICOC porfolios based on RIM3 and RIM3 do diverge up o 6.4% over six monhs on average, he RIM2 approach yields only a difference of 3.5%. In erms of saisical significance of his spread, he invesmen sraegies using dividend discoun models appear o be mos reliable. No surprisingly, he small spread of he RIM2 is saisically no significan. In addiion, whereas mos models exhibi in general monoonically increasing reurns along wih increasing implied reurns, he RIM2 exhibis a large disconinuiy in he wo porfolios wih he lowes expeced reurns (P1, P2). Given he evidence for he posiive relaion beween ICOC esimaes and subsequen sock reurns over a 6 monh holding period, we nex invesigae he profiabiliy of he invesmen sraegies over differen buy-and-hold periods. In order o compare he reurns over ime and o deec differences in he ime srucure beween he ICOC models, we hence repea he previous analysis for differen invesmen horizons. Table 5 shows he average reurns of he high (P8) and low (P1) ICOC porfolios, ogeher wih heir average difference (P8-P1) and he -sa hereof wih holding periods of 1, 3, 6, 12, 18, and 24 monhs. The las wo lines give he number of observaions (decreasing wih growing invesmen horizon) and he equally weighed reurn of he whole sample. Table 5 indicaes ha all ICOC approaches yield a posiive reurn, i.e. he difference beween he high ICOC porfolio and he low ICOC porfolio is always posiive, regardless of he buy-andhold period of he porfolios. Over a holding period up o 6 monhs, he RIM3 models perform bes, aaining a difference beween he exreme porfolios up o 6.4% over 6 monhs. However, using longer rebalancing inervals, boh DDMs show a beer performance. Indeed, he saisical 9 The in he subsequen porfolio analysis as well as he regression analysis in secion 5, he sample size depends in addiion of he number of holding periods and he availabiliy of firm characerisics.

14 13 difference of a P8-P1 (DDM) invesmen sraegy does no decrease over ime, remaining significan a he 5% level. This compares o he RIM, where he reurn of an invesmen in a P8- P1 porfolio is no saisically differen from zero if he rebalancing inerval exceeds 6 monhs. In fac, afer one year, he reurn spread beween P8 and P1 does no grow anymore, suggesing ha he RIM is indeed more of a shor-erm reurn indicaor. Again, he RIM2 approach yields he wors, bu sill posiive reurns. The beer performance of he DDMs in predicing sock reurns over long horizons migh be explained by is informaional advanage. Dividend policy seems o be a signalling process conveying informaion abou fuure profis (e.g. Nissim and Ziv (2001)) ha appears o increase he accuracy of ICOC esimaes. Very clearly, RIM based approaches canno capure his addiional informaion included in dividend paymens Firm Characerisics From he preceding analysis, we found some evidence ha ICOC esimaes are relaed o subsequen sock reurns, and can hus conclude ha ICOC based invesmen sraegies are profiable. Now we go furher ino he maer and invesigae he characerisics of our invesmen porfolios. Along wih he mean ICOC esimaes and porfolio reurns, we presen in able 6 he mean B/M raio, he median firm size (divided by he level of he sock marke index), average marke bea, and average price momenum of he 8 porfolios for some seleced ICOC approaches. Price momenum is calculaed as change in share prices over he pas six monhs. The las row shows he overall averages (or means, respecively) over he whole sample size 10. All firm characerisics are measured as of he porfolios formaion dae. We refrain from presening he porfolio characerisics of he DDM2 and RIM3 models, since here are very similar o hose of he DDM3 and RIM3 approach, respecively The average marke bea lies wih below he heoreical value of 1. This can be parly explained by he fac ha due o missing long-erm growh raes, our sample conains on average more large companies han he overall marke, which usually end o have lower bea values. From a pracical perspecive, i is no he average firm bea ha is imporan, bu he marke bea of each porfolio, since individual correlaions wih he marke migh cancel ou when pooling hem ino porfolios. However, esimaes for porfolio beas did no differ significanly from he average firm bea of each porfolio. 11 This can also be seen from he raher high correlaions beween he models as presened in Table 3.

15 14 Panel A of Table 6 displays he average characerisics of he porfolios when sored according o he DDM3 esimaes. There is a fairly close inverse relaion beween he ICOC and boh pas price momenum and firm size. Large firms, as well as firms ha have seen a good share price performance over he las six monhs have on average smaller ICOC esimaes. The negaive relaion of implied reurns and firm size is in line wih he findings of Fama and French (1992, 1993) ha have deeced size as priced risk variable. However, he wo oher firm characerisics ha are usually known as risk facors, B/M raio and marke bea, are raher unrelaed o he implied reurn esimaes (wih he excepion of he B/M raio for he porfolio wih he highes ICOC which seems o conain raher cheap companies). The associaion wih pas price momenum can parly be explained by he naure of he presen value formula: since curren share price eners he equaion, companies ha have experienced a rise in share prices, have ceeris paribus a lower inernal rae of reurn. The ICOC obained from he RIM2 exhibis similar relaions o firm characerisics, as shown in Table 6, Panel B. However, firm size is now even sronger relaed o he ICOC esimaes, and bea seems o have a slighly posiive associaion o firm risk. Finally, he hird panel (C) conains he characerisics of he RIM3 porfolios. The relaionship beween ICOC and firm characerisics is raher similar o hose of he DDM3 and he RIM2, bu he effecs are more pronounced. Boh B/M raio and firm size are very srongly relaed o he ICOC esimae, marke bea is no. The close associaion of he implied reurn obained from he RIM3 o he Fama-French risk facors and price momenum is sriking, bu in line wih he findings of Lee e al. (2003), conducing regression ess of he deerminans of he ICOC obained from he RIM3 approach. Given ha boh B/M raio and firm size are known o be priced risk facors, hese resuls however quesion he validiy of he ICOC as a separaely priced facor. I could be ha he ICOC is only a mere ransformaion of B/M raio and firm size, and hence one would yield even beer reurn predicions by direcly using hose well-known firm risk characerisics as sock selecion principle. We will analyse his issue in he nex secion on regression analysis.

16 A Pracical Example The previous analysis makes a case for invesing according o he ICOC sock selecion principle. However, all presened resuls are based on wo assumpions ha are opposed o acual invesmen sraegies. Firs, he saisically significan difference beween he wo exreme porfolios is calculaed on he basis of overlapping holding periods. While he implemenaion of such a sraegy is of course nor per se impossible, usually invesmen funds o inves mos of heir funds a once which makes he generaion of such an overlapping invesmen sraegy generally no feasible. Second, and more imporan, he regular porfolio adjusmens do no come for free, bu give rise o ransacion coss. Hence, in Table 7 we presen he reurn on non-overlapping invesmen sraegies wih a holding period of 6 monhs, including ransacion coss of 2% for each porfolio reshuffling 12. The average reurn over he ime period from January 1995 o June 2005 depends hen of course on he saring monh, ranging from January 1995 o June 1995 (a he beginning of July 1995, we reshuffle he January porfolio for he firs ime). We presen wo alernaive invesmen sraegies. One approach displays he previously cied long-shor invesmen (P8-P1), he oher one consiss jus in holding a long posiion in he high ICOC porfolio (P8). As a benchmark, he line below gives he equally weighed reurn of a porfolio of all shares in he sample. Since his is a passive invesmen sraegy wihou rebalancing, is reurn is given ne of ransacion coss. All reurns in he able are calculaed as arihmeic averages over he 20 periods. Invesing in he P8 porfolio (also called long-only) and reshuffling afer every six monhs yields for almos any saring monh and any ICOC model higher reurns han a passively managed buyand-hold invesmen in he whole sock marke. Hence, even when including ransacion cos, long-only implied cos of capial sraegies ouperform he marke. On he oher hand, however, invesing in a long-shor porfolio (P8-P1) does no prove o be a profiable invesmen compared o he benchmark, wih is average reurn being below he passive buy-and-hold sraegy. We can conclude ha whereas he high ICOC companies do indeed ouperform he marke significanly, he low ICOC companies do no under perform he marke sysemaically. 12 1% for selling he porfolio and 1% for buying he new one. We absrac here form he possibiliy ha some socks may be kep in he porfolio a he rebalancing dae. Hence, he presened reurns indicae a lower bound for a possible acual range of reurns.

17 16 5. Regression ess The previous porfolio analysis indicaes ha he ICOC approach is useful o predic sock reurns. However, in many cases, he characerisics of he porfolios formed according o he implied reurn conceps exhibi a srong relaion o well-known risk facors such as B/M raio or firm size. This observaion cass doubs over he ICOC s inrinsic abiliy o predic sock reurns, since is relaion o subsequen reurns migh have is origin only in he ICOC s fairly close relaion o underlying risk facors. We use regression analysis o disenangle he predicive power of ICOC esimaes and risk facors o explain sock reurns. In he lieraure, here are wo common economeric approaches o carry ou such ess: on he one hand, many asse pricing sudies rely on he Fama-MacBeh (1973) cross-secional regressions o analyse deerminans of sock reurns (e.g. Fama and French, 1992; Chan e al., 1996). Given he naure of our daa se, we also perform panel regressions, in line wih he more recen works on deerminans of sock reurns such as Pandey (2001) and Subrahmanyam (2005). Since he panel analysis makes use of he whole daa se more efficienly, i usually provides more significan coefficien esimaes (Balagi, 2005) Cross-secional Regressions Mehodology For each monh of our daa se from January 1995 o Augus 2005, we firs esimae crosssecional regressions of acual sock reurn on he ICOC esimae, risk-facors, and oher firm characerisics: r = α + δk + γ ' X + u (10) i i i i where r i is he subsequen oal sock reurn measured over differen periods up o 24 monhs afer having observed he risk-facors and firm characerisics. The ICOC esimae is denoed by k i. X i 13 For a deailed comparison of he Fama-MacBeh (1973) and panel regression mehods, see Peersen (2004).

18 17 is a vecor of risk-facors, including marke bea and firm characerisics, and u i is he error erm. In he nex sep, we hen es wheher he average coefficien esimaes δ and γ are significanly differen from zero. The -saisics are calculaed by regressing he ime series of he coefficien esimaes on a consan. Since we use overlapping daa, he -saisic is calculaed on he basis of heeroskedasiciy- and auocorrelaion-consisen (HAC) sandard errors (Newey-Wes, 1987) wih a lag-lengh corresponding o he number of monhs over which we measure he sock reurns. Noe ha we refrain from soring he companies ino porfolio before carrying ou he Fama- MacBeh (1973) regressions. Insead we use individual firm daa for our regressions, similar o he works of e.g. Brennman (1998), or Subrahmanyam (2005). This has several reasons: On he one hand, we wan o include many differen firm characerisics in our regression analysis. As Bauer e al. (2004) poin ou, he number of porfolios needed increases exponenially wih he number of firm characerisics examined. Wih 5 groups for 5 differen characerisics e.g., we would need 5 5 porfolios. Given our daa, many of hem would conain none ore few socks. If we oped insead for choosing one or wo characerisics as soring variable only, we face he quesion which ones o selec. Brennan e al. (1998) argue ha selecing some ou of many possible explanaory variables creaes a daa-snooping bias ha is inheren in all porfolio based approaches, since he selecion of he soring variable as well he soring order can influence he resuls drasically. Especially he common pracice o consruc porfolios according o B/M-raio and size is likely o overesimae he regression resuls (Lewellen e al., 2005). Finally, he use of few porfolios, i.e. employing only one or wo soring variables, reduces he sample size significanly, resuling in esimaes wih very low power Regression Resuls Table 8 repors he ime-series averages of he slope coefficiens, along wih heir -saisics. We again invesigaed he ICOC esimaes obained from he DDM3, RIM2, and RIM3. The dependen variable, he sock reurn r i, is measured over 6 monhs afer having observed he firm characerisics X i. 14 This poin has been pu forward by Lee a al. (2003). They ry o overcome his problem by forming counryindusry porfolios o esimae a counry-indusry bea, hereby hoping o increase he accuracy of he bea esimae. Then hey run, similar o us, individual firm regressions bu include he indusry bea as a proxy for he company bea as explaining variable. Fama and French (1992) rely on his procedure as well.

19 18 Regardless of he ICOC mehod employed, he average slope coefficiens are raher small compared o heir sandard errors. Accordingly, he esimaes are saisically no significanly differen from zero. Sill, compared o bea and oher firm characerisics, he ICOC esimaes are in many cases he mos imporan explaining variable, wih he RIM3 ICOC close o being significan when used as he only regressor. In all regressions, marke bea and more ineresingly, firm size, is no relaed o sock reurns, which is agains he evidence in he previous secion and he findings of Fama and French (1992). The (weak) posiive relaion o price momenum is in line wih Chan e al. (1996). If one keeps in mind he common upward bias of coefficien esimaes of porfolio regressions in many empirical sudies (Lewellen e al., 2005), hese raher poor resuls do no appear oo disappoining, bu mus be pu ino perspecive Panel Regressions In line wih more recen sudies in he empirical finance lieraure we now refer o panel regressions o deec he predicive power of ICOC esimaes on sock reurn afer having conrolled for common risk facors of he Fama-French model. Since he panel esimaion procedure uses he whole informaion conveyed in he daa in one regression sep, we hope o increase he power of he esimaes Mehodology The basic regression equaion for sock reurns and is explaining variables in a panel daa se (pooled ime-series cross-secion) is given as follows: r i, = + δki, + γ ' X i, + ui, α (11) where he subscrip i denoes he company (cross-secion dimension) and denoes he ime period of he observaion (ime-series dimension). This general specificaion is known as pooled daa se. In many cases however, he underlying assumpion (when esimaing he pooled daa se by sandard OLS) ha he observaion of a company a ime is independen an observaion of

20 19 he same company a a differen poin in ime s is no me. Hence, he regression equaion is modified for allowing for individual effecs for each company. This individual effec can accoun for form characerisics ha are no included in he regression equaions such as he indusry secor, or unobservable facors. This model is known as he one-way individual effecs model: r i, = i + δki, + γ ' X i, + ui, α (12) One of he mos common approaches o esimae such an individual effecs model is o assume ha he individual effec α i of each firm is consan over ime. Relying on such a one-way fixed effec (FE) model hence implies ha he reurns of some companies are on average higher han he reurn of he marke, whereas some oher companies under perform he marke on average. Anoher varian of he one-way individual effecs model is he random-effecs (RE) model, ha assumes ha he individual effec α i is no consan, bu flucuaes randomly over ime wih a zero mean. To deec which model is appropriae for ou daa se, we carry ou he several common saisical ess. Firs we rely on an F-es o see wheher he esimaed fixed effecs are joinly significanly differen from zero. If he H 0 of no significance of he individual fixed effecs is rejeced, we can conclude ha a fixed-effec model is preferred o he simple pooled OLS esimaion. Second, we perform a Breusch-Pagan es on he random effecs model, o see wheher he random effecs are significanly differen from zero. If he H 0 of no significance is rejeced, we can conclude ha a random-effec model is preferred o he simple pooled OLS esimaion. Third, we conduc a Hausmann specificaion es, o see wheher he coefficiens of he FE and RE esimaion differ significanly from each oher. If he H 0 of no significan difference beween he esimaed coefficiens is rejeced, we can conclude ha a fixed-effec model is preferred o he random effecs esimaion 15. Noe ha we carry ou hese specificaion ess on non-overlapping daa ses since he sandard ess implemened by saisical packages do no correc for auocorrelaion 16. The es resuls of all samples showed ha he fixed effecs model is he preferred approach o esimae he panel regressions. We hence presen only he resuls of he FE-panel regressions. 15 Fixed-effecs esimaes are always consisen, bu random-effecs esimaes migh be more efficien. 16 We conduc hese ess for all possible non-overlapping panel daa ses. In mos cases however, he resuls do no differ across he differen non-overlapping panels and lead o he same conclusion of employing a one-way fixed effecs model.

21 20 In addiion o he one-way individual effecs model, we also could imagine a wo-way individual effecs model ha allows no only for firm-specific effecs, bu includes a ime-specific effec as well: r i, = i + λ + δki, + γ ' X i, + ui, α (13) where λ is a ime specific effec for each. By adding a fixed ime effec for each period, we reflec he fac ha during he ime period from 1995 o 2005, he capial markes in he U.K. have seen exreme movemens, such as he record highs in 2000 and he subsequen marke downurn up o The underlying deerminans of sock reurns migh have changed over his period, e.g. due o changes in he expeced equiy risk premium ha affecs all socks in he same way. The inclusion of a fixed ime effec also helps o conrol for changes in sock reurns ha sem from he calendar ime only. We implemen his ime effec by adding -1 monhly regression dummies in he one-way FE regression model. Similar o he simple fixed effecs model, we es he significance of he ime effecs by a join F-es on all ime dummies λ. Since he H 0 of no significance of all ime dummies was rejeced, we also adop he wo-way fixed effecs model Resuls of he One-way Fixed Effecs Model Table 9 presens he regression esimaes and -saisics of he one-way fixed firm effecs model of equaion (12) for he same hree ICOC esimaes as in he Fama-MacBeh regression analysis. In addiion o regression es on 6-monh sock reurns presened in panel A of he able, we also repor regressions of 12-monh reurns (panel B). The regressions are carried ou over whole overlapping panel daa se. The -saisics below he esimaes are consequenly calculaed using he FE, heeroskedasiciy robus and auocorrelaed-adjused sandard errors following Rogers (1993). The explained variance of each he model is given in he las line. As suggesed earlier, he panel approach increases he power of he esimaes decisively compared o he Fama-MacBeh procedure. In he 6-monhs reurn regressions displayed in panel

22 21 A, he ICOC coefficiens (δ) are now highly significan, regardless of he mehod chosen o calculae hem, even when including oher risk variables and firm characerisics in o he regression equaion. Similar o he Fama-MacBeh esimaions, size is negaively relaed o sock reurns, and marke bea is again only weakly relaed o sock reurns. However, using panel esimaion, he coefficiens of pas price momenum are now negaive. This compares o he posiive coefficiens of he previous Fama-MacBeh regressions and common sudies on momenum sraegies (Chan e al., 1996). This discrepancy beween he panel and Fama- MacBeh esimaion is due o varying sample sizes across he daase. Since he sample compromises more socks during periods when he marke declines, he panel esimaion pus relaively more weigh on falling socks. High marke volailiy ogeher wih many IPOs and delisings during he sample period migh explain he difference o exising sudies. Ineresingly, he hree differen ICOC models yield raher similar resuls. When using he ICOC as he only explaining variable, he RIM3 performs bes, as can be seen easily from he R 2 value. When conrolling for firm characerisics, he RIM2 yields he highes and mos significan coefficien esimaes 17. Wha happens if we increase he forecasing horizon? The regression resuls of 12-monhs sock reurns in panel B show some differences, noably for he RIM3 ICOC, which is no longer significanly relaed o sock reurns afer conrolling for risk-facors and price momenum. This essenially confirms our claim in he porfolio analysis, ha he RIM3 loses is predicive power over longer ime periods. The saisical significance of price momenum also decreases over a longer forecasing horizon. To conclude, he ICOC is no only a mere ransformaion or expression of he wo risk-facors B/M-raio and firm size (as hypohesised in he previous secion), bu adds significanly addiional power in explaining sock reurns. The RIM3 model however seems o loose some of is explanaory power over longer ime horizons, presumably since i canno make use of he informaion included in dividend paymens. 17 We have o add, however, ha he raher good resuls obained from he RIM3 are no robus o changes in he sample size. When using he whole daa se available for RIM3 regressions (14151 observaions insead of 10812), he RIM3 ICOC is no longer significan in explaining sock reurns afer conrolling for he Fama-French facors. As menioned earlier, he addiional 3339 observaions conain smaller companies (on average half he size) for which he RIM3 ICOC does no seem o be a good explanaory variable for sock reurns. In fac, in panel regression ess of his sub-sample, he ICOC coefficien is negaive and significanly differen from zero.

23 Resuls of he Two-way Fixed Effecs Model 22 Table 10 conains finally he regression resuls and -saisics of he wo-way fixed effecs model as saed in equaion (13). Again, we run he regressions on 6-monhs sock reurns, using he whole overlapping panel daa se. The -saisics are calculaed using heeroskedasiciy robus and auocorrelaed-adjused sandard errors following Rogers (1993). The las o lines conain he R 2 of each specificaion and he F-saisic of a join significance es on all ime dummies. The esimaes of Table 10 confirm he resuls of he previous one-way fixed effecs model. The inclusion of a fixed ime effec does noe reduce he significance of all ICOC esimaes as explanaory variables for sock reurns. Similarly, he wo Fama-French facors remain highly significan. On he oher hand, he ime dummies which prove o be very relevan as he F- saisic indicaes, cause price momenum and marke bea o ge insignifican. In general, he fixed ime effecs increase he R-squared of he models up o 34%. Oherwise, he conclusion remains similar. When conrolling for firm characerisics, he RIM2 yields he mos significan coefficien esimaes aken alone, he RIM3 performs bes Conclusion The recenly developed concep of he implied cos of capial has become popular ool for esimaing expeced sock reurns boh in heory and pracice. By aggregaing individual sock reurns over he enire marke, his approach is used horoughly in research o derive a forwardlooking equiy risk premium esimae. Fund managers ry o exploi he so-obained expeced reurns o creae invesmen porfolios ha yield abnormal sock reurns. Surprisingly, a sound economeric foundaion of his mehodology a he level of individual firm daa is sill missing. In his paper, we employ porfolio analysis and regression es o answer he quesion wheher he use of he implied cos of capial as proxy for expeced sock reurns can be subsaniaed by economeric evidence. 18 We also conduced 2-way FE regressions on 12-monh sock reurns. The resuls were similar o he 1-way FE esimaion: he coefficien of he ICOC from he RIM3 ges insignifican when conrolling for firm risk.

24 23 In principle, our analysis confirm he implied cos of capial s hypohesised posiive relaion o sock reurns, bu deecs large qualiaive differences among several common models examined. We find ha invesmen sraegies based on he ICOC are profiable and provide significanly posiive reurns when derived from hree-sage DDM and RIM approaches. However, he longer he invesmen horizon, he beer he DDMs perform compared o he RIM, whose profiabiliy deerioraes for ime horizons longer han 6 monhs. When examining he characerisics of he consruced porfolios, we find ha all ICOC conceps are relaed o he Fama-French risk facors B/M-raio and firm size. On average, ICOC esimaes of he DDM are less relaed o hose risk facors. In he subsequen regression analysis, panel esimaions - and o a weaker exen Fama- MacBeh regressions show ha he implied cos of capial helps o explain variaions in sock reurns even afer conrolling for oher firm risk facors. However, is inrinsic explanaory power is raher small. Our resuls have imporan pracical implicaions for managers. On he one hand his sudy shows ha he implied cos of capial offers indeed a powerful ool o esimae he firm s cos of equiy, a leas if aken joinly wih oher common risk facors. For porfolio mangers, on he oher hand, his paper pus forward empirical evidence for he profiabiliy of ICOC-based invesmen sraegies. Sill, large discrepancies beween he models underpin he imporance o carefully selec he righ approach.