An empirical application of the clean-surplus valuation model: The case of the London Stock Exchange

Transcription

1 An empirical applicaion of he clean-surplus valuaion model: The case of he London Sock Exchange S. N. Spilioi Ahens Universiy of Economics and Business, Deparmen of Business Adminisraion, Paission 76, 10434, Ahens, Greece G. A. Karahanassis Ahens Universiy of Economics and Business, Deparmen of Business Adminisraion, Paission 76, 10434, Ahens, Greece Absrac Recen sudies on equiy valuaion sugges ha securiy prices should be deermined by book value and discouned fuure abnormal earnings [Ohlson (1995), Felham and Ohlosn (1995)]. This paper examines he empirical validiy of hese heoreical models for he English equiy marke. More specifically, i uses a panel daa mehodology o sudy equiy prices for imporan secors of he economy. To anicipae he resuls, hese models appear o be reliable price valuaion models, for English equiies. Keywords: Equiy valuaion, book value, abnormal earnings, panel daa. JEL Classificaion: G1. 1

2 1. Inroducion Tradiional equiy valuaion models discoun expeced fuure dividends in order o arrive a a heoreically correc inrinsic value, which will be hen compared o he curren marke price. However, in heir recen sudies Ohlson (1995) and Felham and Ohlson (1995) sugges ha securiy prices should be deermined by book value and discouned fuure abnormal earnings. The advanages of his specificaion are ha special emphasis is given o (a) book value, hus avoiding any economic hypoheses abou fuure cash flows, and (b) he reamen of invesmens. Previous empirical sudies find ha book value and discouned fuure abnormal earnings have an imporan role o play in he deerminaion of equiy prices (see for example, Bernard (1995), Penman and Sougiannis (1998), Lee and Swaminahan (1998)). Mos of he previous sudies, however, documen hese relaionships for major developed and/or large capializaion American markes specially for he period before 1998; here is, however, lile research regarding European marke equiy prices specially for he las seven years ha several crises have aken place. In his paper, we aemp o fill his gap and examine he behavior of Ohlson s heoreical model wih equiy prices from he London Sock Exchange for he period Repeaed ess wih daa from various counries are essenial o deermining he applicabiliy of a model o acual daa. Thus, i would be paricularly imporan o examine he degree o which changes in book value and abnormal earnings explain changes in equiy prices, in a developed European marke. In addiion, he panel daa models employed in he paper overcome common mehodological problems (such as 2

3 auocorrelaion, mulicolineariy, heeroscadsiciy) and allow he esimaion of unbiased and efficien esimaors. To anicipae he resuls, he model performs very well for wo sample secors of he English economy. These resuls, in conjucion wih he heoreical meris and advanages of he model, make Olhson s approach a reliable price valuaion model, for Briish equiies. The res of his paper is organized as follows. Secion 2 discusses he relevan lieraure, secion 3 presens he daa and mehodology, and secion 4 presens he resuls. Secion 5 concludes he paper. 2. The valuaion model Fundamenal analyss, in heir aemp o idenify under-priced securiies, have employed differen approaches. Tradiional models of securiy valuaion ypically discoun fuure dividends in order o esimae he heoreical or inrinsic value of a securiy (see for example Williams (1938), Gordon (1959)). According o his view he inrinsic value of a securiy is equal o he presen value of dividends expeced from he share. Modigliani and Miller (1961), assuming perfec capial markes, raional behavior, and perfec cerainy, argued for he Invesmen Opporuniies Approach, according o which he facors ha affec he securiy price are he expeced dividends, he growh rae in expeced dividends, and facors ha proxy for he risk of he securiy. Alernaively, one could use expeced earnings and expeced growh rae in earnings insead of dividends. The resuls of empirical sudies (see for example, Friend and Pucke (1964), Gordon (1959), Fisher (1961), Durand (1955), Bower and Bower (1969)) Karahanassis and Tzoannos (1977), Karahanassis and 3

4 Philippas (1988) indicae ha he main explanaory variables of equiy prices are dividends, earnings, reained earnings, size, variabiliy in earnings, and deb o equiy raio. However, in heir recen sudies Ohlson (1990, 1991, 1995) and Felham and Ohlson (1995) sugges ha securiy prices should be deermined by book value and discouned fuure abnormal earnings. Ohlosn made hree assumpions while developing he model. Firsly, he price of a securiy is equal o: τ = 1 P = R [ d ] (1) τ f + τ where, P is he price of he securiy a ime, d is he dividend a ime, R f is 1 plus he risk free. Secondly, he change in book value beween wo periods is equal o he difference beween earnings and dividends (The Clean-Surplus Relaion). Tha is, if x is he earnings beween period -1 and, and y is he book value a ime, hen: y = y 1 + x d (2) If abnormal earnings are defined as: x (3) a = x ( R f 1) y 1 Equaion (1) hen becomes: τ = 1 P = y + R E [ x ] (4) τ f a τ + 4

5 Thirdly, Ohlson assumes linear informaion dynamics, ha is, abnormal earnings can be esimaed wih linear regression analysis. Then, he abnormal earnings for period +1 are defined as: x a a + 1 = x + v + ε1 + 1 ω (5) where he non-accouning informaion for period +1 is defined as: v + 1 = v + ε 2+ 1 γ (6) If hese assumpions hold he price of a securiy is defined as: a P y + a1 x + a2 = v (7) where a = [ ω /( R ω)] 0, and a = [ R /( R ω)( R γ )] 0 1 f 2 f f f > This specificaion has wo advanages. Firsly, special emphasis is given o book value, hus avoiding any economic hypoheses abou fuure cash flows. Secondly, he reamen of invesmens is such ha invesmens are a balance shee facor and no a facor ha reduces cash flows (for a deailed discussion see Penman and Sougiannis (1998)). Previous empirical sudies find ha book value and discouned fuure abnormal earnings have an imporan role o play in he deerminaion of equiy prices. For example, Bernard (1995) uses regression analysis o evaluae how well forecased dividends and forecased abnormal earnings explain he variaion in securiy prices, and finds ha dividends explain 29% of variaion in equiy reurns vs. 68% for he combinaion of book value and abnormal earnings. Penman and Sougiannis (1998) examine valuaion mehods based on dividend, cash flow, and abnormal earnings 5

6 esimaes, for US equiies. They find ha abnormal earnings esimaes have he smalles predicion errors han he oher variables. The larges predicion errors are observed for he free cash flow variable. Lee and Swaminahan (1998) examined wheher radiional indices (based on dividends, book o marke, earnings) and an index based on Ohlson s model can predic US equiy reurns. They find ha alhough he radiional indices have low reurn predicabiliy, he index based on Ohlson s model is more successful. Francis, Ohlson, Oswald (2000) compare he reliabiliy of value esimaes from he dividend, earnings, and abnormal earnings models for he US equiy marke. They find ha he abnormal earnings esimaes are more accurae and explain more of he variabiliy in equiy prices ha he oher variables. Karahanassis and Spilioi (2003) find ha he performance of he Ohlson model is quie similar o ha of he radiional valuaion models for he emerging Ahens Sock Exchange. To summarize, empirical resuls suppor he heoreical equiy valuaion model suggesed by Ohlson. However, hese sudies examined he validiy of he model for he developed and well-organized capial marke of he USA. Thus, i will be very ineresing o see wheher he resuls will hold for a developed European equiy marke such as he London Sock Exchange specially in his problemaic ime period. 3. Daa and Mehodology The aim of he paper is o evaluae wheher changes in book values and abnormal earnings explain changes in securiy prices, for he English equiy marke. The daa used in he sudy are obained from he London Sock Exchange S.A. and cover he 6

7 period beween More specifically, as a sample we use wo very imporan secors of he English economy, ha is, he food secor and he pharmaceuicals secor (see Appendix for more deails). Previous research has ypically used eiher ime-series or cross-secion mehods for he empirical esimaions. However, boh mehodologies have a number of drawbacks. For example, ime-series analysis is subjec o auocorrelaion and mulicolineariy problems, while cross-secion mehods are subjec o heeroscedasiciy problems and ofen fail o deec he dynamic facors ha may affec he dependen variable. This paper uses a combinaion of ime-series and cross-secion daa (panel daa analysis), a procedure ha avoids he mehodological problems of he previous mehodologies and in addiion has a number of advanages. For example, i no only provides efficien and unbiased esimaors, bu also provides a larger number of degrees of freedom available for he esimaion. This allows he researcher o overcome he resricive assumpions of he linear regression model (for a more deailed discussion see Balagi and Raj (1992) and Maddala (1987), among ohers). More specifically, he algebraic model can be represened as follows: i = 1,..., N = 1,..., T K Y i = α + µ + λ + β X + ε (8) i K = 1 K Ki i 7

8 where Y i is he value of he dependen variable for he cross secion i a ime, X Ki is he value of he K h explanaory variable for he cross secion i a ime, µ i is an unobserved cross-secion effec, λ i is an unobserved ime effec and ε i is he unobserved overall remainder. Equaion (8) can be esimaed eiher under he assumpion ha µ i and λ i are fixed so ha µ i = 0 and λ = 0, or under he assumpion ha µ i and λ i are random variables. The firs case is he well known Dummy Variable Model or he Covariance Model, while he second case is he Error Componens Model (see among ohers Kmena (1971), Griffihs e al. (1993), Hsiao (1986)). N i= 1 T i= 1 The empirical researcher is ofen faced wih he problem of choosing among he wo approaches, because i canno be known beforehand wheher he µ i and λ i are random or fixed. The Error Componens Model will lead o unbiased, consisen, and asympoically efficien esimaors only if he orhogonaliy assumpion holds (i.e. ha he explanaory variables are uncorrelaed wih he cross-secion and ime-series effecs). If ha is no rue, he Error Componens Model esimaors will be biased and inconsisen, while he Covariance Model esimaors will sill be consisen, since hey are no affeced by he orhogonaliy condiion (see for deails Madalla (1971) and Mundlack (1978)). In order o examine wheher he explanaory variables are uncorrelaed wih he crosssecion and ime-series effecs one can apply he saisical crierion developed by Hausman (1978). The null hypohesis is ha he Error Componens Model is correcly 8

9 specified, i.e. ha µ i and λ i are uncorrelaed wih he explanaory variables, X Ki. The es saisic, m, defined as m = ( ˆ β FE ˆ β GLS )( Mˆ Mˆ ) ( ˆ β ˆ β FE GLS ) (9) 2 This saisic has an asympoic χ k disribuion. Noe ha β GLS is he generalized-leas square Error Componen Model esimaor, β FE is he ordinary leas square Dummy Variable Model esimaor, M 1 is he covariance marix of β FE, and M 0 is he covariance marix of β GLS. Acceping he null hypohesis, H 0, will sugges he use of he generalized leas square esimaor. Rejecing he null hypohesis indicaes ha we should accep he alernaive, H 1, i.e. ha we should employ he Covariance Model approach. The approach employed in his sudy (as will be demonsraed in he nex secion) is he Error Componens Model. In his case, equaion (8) can be wrien as follows: K Y i = α + β X + ε (10) K = 1 i = 1,..., N = 1,..., T where i i K i Ki i ε = µ + λ + w (11) The las equaion indicaes ha he oal random effec basically consiss of hree random effecs (for deails see Wallace and Hussein (1969)). 9

10 The explanaory variables employed in he sudy are he variables suggesed by Ohlson (1995) and discussed in secion 2. More specifically, we used wo explanaory variables: book values (BV) and abnormal earnings (AE). BV is he owners equiy over he number of socks in circulaion, and AE is he difference beween curren earnings and he opporuniy cos of capial. The opporuniy cos is defined as he previous period s BV imes he cos of capial (ha is, he risk-free rae). Ohlson suggess ha for he model o be correcly specified we should expec a posiive relaionship beween AE and prices. We should also, heoreically, expec a posiive relaionship beween BV and prices. Noe ha equiy prices are calculaed as he arihmeic average of monhly average closing prices. 4. Presenaion and Inerpreaion of Resuls As a firs sage in he analysis we examine which approach o use in he esimaion of equaion (8). To his end we apply he Hausman (1978) crierion discussed above. The resuls are presened in Table 1, and seem o sugges ha (for wo indusries) he cross-secion and ime-series effecs can be considered as random variables. In oher words, µ i and λ i are uncorrelaed wih he explanaory variables, X Ki, or he Error Componen Model is correcly specified. For example, as can be seen from Table 1, he M-saisic is lower han he criical value for wo indusries. Thus, we proceed wih he esimaion using he Error Componens Model (equaion 10). [INSERT TABLE 1 HERE] According o he heoreical relaionships prediced by he Ohlson valuaion model we should expec boh book value and abnormal earnings o be posiively relaed wih 10

11 share prices. Our empirical findings are in accordance wih he heoreical predicions. Thus, our ex-ane relaionships are empirically validaed since boh variables expeced a posiive and significan influence on share prices. The resuls of esimaing equaion (10) wih he variables discussed in he previous secion are presened in Table 2. We can see ha he explanaory power of he model for he food secor is good enough ( R 2 = ). The explanaory power of he model is also very high for he pharmaceuicals secor ( R 2 = ). For wo secors he explanaory variables are highly singifican a he 5% level. Furhermore, for wo secors boh he BV and AE coefficiens have he expeced posiive sign. [INSERT TABLE 2 HERE] 5. Conclusion and Implicaion for furher Research This paper examines wheher changes in securiy prices are explained by book value and discouned fuure abnormal earnings, as suggesed by Ohlson (1995) and Felham and Ohlosn (1995). Previous sudies documen hese relaionships for major developed and/or large capializaion specially American markes. Here, we examine he behavior of equiy prices in he London Sock Exchange for he problemaic period ha several crises have ake place. The resuls indicae ha he model has high explanaory power for he food as well as he pharmaceuical secor. Also, all he coefficiens are highly singifican for wo secors. 11

12 Overall, he empirical resuls sugges ha he model performs very well for wo sample secors of he English economy. These resuls, in conjucion wih he heoreical meris and advanages of he model, make Olhson s approach an ineresing price valuaion model, for English equiies. Our resuls should be reaed wih cauion. We should recall ha in he pas many researchers using he dividend valuaion model repored equally good resuls (Karahanassis (1981), Keenan (1980)). Specifically, virually all researchers repored good resuls for he coefficien of deerminaion and he sign of he regression coefficiens. I should be sressed, hough ha he values of he coefficiens did no remain consan over ime. This is a very serious disadvanage for he purpose of using hese models for making financial decisions. Sabiliy and precision of economic funcions are also required in order o draw meaningful conclussions of he reliabiliy of an economic relaionship and of is relaive superioriy over oher alernaive relaionships. 12

13 References Balagi, B. H., and Raj, B. (1992) A survey of recen heoreical developmens in he economerics of panel daa, Empirical Economics, 17, Bower D. H. and Bower R. S. (1969), Risk and he Valuaion of Common Sock, Journal of Poliical Economy, Vol. 77, Durand D. (1955), Bank Sock Prices and he Analysis of Covariance, Economerica, Vol.23, Fisher G.R. (1961), Some Facors Influencing Share Prices, Economic Journal, Vol. LXXI, Francis J. Olsson P. and Oswald D.(2000), Comparing he Accuracy and Explainabiliy of Dividend, Free Cash Flow, and Abnormal Earnings Equiy Value Esimaes, Journal of Accouning Research, Vol. 38, Friend I. and Pucke M. (1964), Dividends and Sock Prices, American Economic Review, Vol. LIV, Gordon M. J. (1959), Dividends, Earnings and Sock Prices, Review of Economics and Saisics, Vol. XLI, Griffihs, W.E., Hill, C., and Judge, G.G. (1993) Learning and Pracicing Economerics, John Willey and Sons, INC. Hausman, J. A. (1978) Specificaion ess in economerics, Economerica, 46, Hsiao, C. (1986) Analysis of Panel Daa, Economerics Sociey Monographs, No. 11. Karahanassis G. and Tzoannos J. (1977) The Demand for Money by Business Firms: A Temporal and Cross-Secional Analysis, Applied Economics, Vol. 9, Karahanassis G. (1981) Empirical Valuaion Models: How Useful Have They Been?, Accouning and Business Research Karahanassis, G., and Philippas, N. (1988) Esimaion of bank sock price parameers and he variance componens model, Applied Economics, 20, Karahanassis, G., and Spilioi, S (2003) En Empirical Invesigaion of he Tradiional and he Clean Surplus Valuaion Model, Managerial Finance, Keenan M. (1970) Models of Equiy Valuaion: The Grea Germ Bubble, Journal of Finance, Vol. XXV, Kmena, J. (1971) Elemens of Economerics, Macmillan, New York. 13

14 Maddala, G.S. (1987) Recen developmens in he economerics of panel daa analysis, Transporaion Research, 21, Maddala, G.S. (1971) The use of variance componens models in pooling crosssecion and ime-series daa, Economerica, 39, Miller M. and Modilgianni F. (1961), Dividend Policy, Growh and he Valuaion of Shares, The Journal of Business Vol. XXXIV, Mundlak, Y. (1978) On he pooling of ime-series and cross-secion daa, Economerica, 46, Ohlson J. (1990), A Synhesis of Securiy Valuaion Theory and he Role of Dividends, Cash Flows, and Earnings, Conemporary Accouning Research Vol. 6, Ohlson J. (1991), The Theory of Value and Earnings and an Inroducion o he Ball-Brown Analysis, Conemporary Accouning Research, Vol. 7, 1-19 Ohlson J. (1995), Earnings Book Values and Dividends in Securiy Valuaion, Conemporary Accouning Research, Vol. 11, Wallace, T. and Hussain, A. (1969) The use of Error Componens Model in combining cross-secion wih ime-series daa, Economerica, 37, Williams J. B. (1938), The Theory of Invesmen Values, Harvard Universiy Press 14

15 Table 1 Are µ i and λ i uncorrelaed wih he explanaory variables? m = ( ˆ β FE ˆ β GLS )( Mˆ Mˆ ) ( ˆ β ˆ β FE GLS ) m-saisic P-Value DF Pharmaceuicals Food Noes o Table 1: Null hypohesis: he Error Componens Model is correcly specified m-saisic: Hausman s (1978) es saisic DF: degrees of freedom P-Value a 95% confidence level 15

16 Table 2 Do changes in BV and abnormal earnings explain he changes in securiy prices? K Y i = α + β X K = 1 K Ki + ε i Food Consan 1.09 (1.49) Pharmaceuicals 2.59 (3.64)* BV 0.01 (1.91)* 0.02 (8.30)* AE 0.08 (3.07)* 0.04 (3.99)* 2 R Noes o Table 2: BV: Book Value AE: Abnormal Earnings -saisics appear in parenheses * denoes significance a he 5% 16