THE SUPPLY OF STOCK MARKET RETURNS. Roger G. Ibbotson Yale University. Peng Chen Ibbotson Associates, Inc.

Transcription

1 THE SUPPLY OF STOCK MARKET RETURNS Roger G. Ibboson Yale Universiy Peng Chen Ibboson Associaes, Inc. June 2001

2 The Supply of Sock Marke Reurns Roger G. Ibboson, Ph.D. Professor in he Pracice of Finance Yale School of Managemen Chairman Ibboson Associaes, Inc. 225 N. Michigan Ave. Suie 700 Chicago, IL Phone: (312) Fax: (312) Peng Chen, Ph.D., CFA. Vice Presiden, Research Ibboson Associaes, Inc. 225 N. Michigan Ave. Suie 700 Chicago, IL Phone: (312) Fax: (312) June 2001 Commens Welcome. Ibboson & Chen The Supply of Sock Marke Reurns

3 ABSTRACT We esimae he forward-looking long-erm equiy risk premium using a combinaion of he hisorical and he supply side approaches. We decompose he hisorical equiy reurns ino supply facors including inflaion, earnings, dividends, price o earnings raio, dividend payou raio, book value, reurn on equiy, and GDP per capia. We examine each of he facors and heir relaionship wih he long-erm supply side framework. There are several key findings: Firs, he growh in corporae produciviy as measured by earnings is in line wih he growh of overall economic produciviy. Second, P/E increases accoun for only a small porion of he oal reurn of equiy (1.25% of he oal 10.70%). The bulk of he reurn is aribuable o dividend paymens and nominal earnings growh (including inflaion and real earnings growh). Third, he increase in facor share of equiy relaive o he overall economy can be fully aribued o he increase in he P/E raio. Fourh, despie he record earning growh, he dividend yield and payou raio declined sharply in he 1990s, which renders dividend growh alone a poor measure of corporae profiabiliy and fuure growh. We hen forecas he equiy risk premium hrough supply side models using his hisorical informaion. Conrary o several recen sudies ha declare he forward looking equiy risk premium o be close o zero or negaive, we find he long-erm supply of equiy risk premium is only slighly lower han he pure hisorical reurn esimae. The longerm equiy risk premium is esimaed o be abou 6% arihmeically, and 4% geomerically. Our esimae is in line wih boh he hisorical supply measures of he public corporaions (i.e., earnings) and he overall economic produciviy (GDP per capia). Ibboson & Chen 1 The Supply of Sock Marke Reurns

4 I. INTRODUCTION Numerous auhors are direcing heir effors oward differen approaches o esimaing expeced reurns on socks over bonds. These sudies can be caegorized ino four groups based on he approaches hey have aken. The firs group of sudies ry o derive he equiy risk premiums from hisorical reurns beween socks and bonds (Ibboson and Sinquefield (1976a,b)). The second group adops supply side models. The supply side models use fundamenal informaion such as earnings, dividends, or overall economic produciviy o measure he expeced equiy risk premium (e.g., Diermeier, Ibboson, and Siegel (1984), Shiller (2000), Fama and French (2000), and Arno and Ryan (2001)). The hird group adops demand side models ha derive equiy s expeced reurns hrough he payoff demanded by invesors for bearing he risk of equiy invesmens. This group includes he Capial Asse Pricing Model (Sharpe(1964) and Linner (1965)), he Arbirage Pricing Theory (Ross (1976)), and he Ibboson, Siegel, and Diermeier (1984) demand framework. The fourh group relies on opinions of financial professionals hrough broad surveys (e.g., Welch (2000)). In his paper, we adop a combinaion of he firs and second approaches. We link hisorical equiy reurns wih facors commonly used o describe he aggregae equiy marke and overall economic produciviy. These facors include inflaion, earnings, dividends, price o earnings raio, dividend payou raio, book value, reurn on equiy, and GDP per capia. We firs decompose he hisorical equiy reurns ino differen ses of componens based on six differen mehods. Then, we examine each of he componens wihin he six mehods. Finally, we forecas he equiy risk premium hrough supply side models using hisorical daa. Our long-erm forecass are consisen wih he hisorical supply of U.S. capial marke earning and GDP per capia growh over he period In an imporan disincion from he forecass of many ohers, our forecass assume marke efficiency and a consan equiy risk premium. Thus he curren high P/E raio represens he marke s forecas of higher earnings growh raes. Furhermore, our forecass are consisen wih Miller and Modigliani (1961) heory so ha dividend payou raios do no affec P/E raios and high earning reenion raes (usually associaed wih low yields) imply higher per share fuure growh. To he exen ha corporae cash is no used for reinvesmen, i is assumed o be used o repurchase a company s own shares or perhaps Ibboson & Chen 2 The Supply of Sock Marke Reurns

5 more frequenly o purchase oher companies shares. Finally, our forecass rea inflaion as a pass-hru, so ha he enire analysis can be done in real erms. Ibboson & Chen 3 The Supply of Sock Marke Reurns

6 II. THE SIX METHODS FOR DECOMPOSING HISTORICAL EQUITY RETURNS We presen six differen mehods of decomposing hisorical equiy reurns. The firs wo mehods (especially mehod 1) are models based enirely on hisorical reurns. The oher four mehods are models of he supply side. We evaluaed each mehod and is componens by applying hisorical daa from 1926 o The hisorical equiy reurn and earning daa used in his sudy are obained from Wilson and Jones (2001). 1 The average compounded annual reurn for sock marke over he period is 10.70%. The arihmeic annual average reurn is 12.56% and he sandard deviaion is 19.67%. In as much as our mehods use geomeric averages, we focus on componens of he geomeric reurn (10.70%). Laer in he paper when we do our forecass, we conver geomeric average reurns o arihmeic average reurns. Mehod 1 Building Blocks Mehod Ibboson and Sinquefield (1976a,b) develop a building blocks mehod o explain equiy reurns. The hree building blocks are inflaion, real risk-free rae, and equiy risk premium. Inflaion is represened by he changes in he Consumer Price Index (). Equiy risk premium and real riskfree rae for year, ERP and RRf, is given by ERP 1+ R = 1+ Rf 1 = R Rf 1+ Rf (1) RRf 1+ Rf = 1+ 1 = Rf 1+ (2) R = ( 1+ ) (1 + RRf ) (1 + ERP ) 1 (3) R is he reurn of U.S. sock marke represened by he S&P 500 index. is he reurn of riskfree asses represened by he income reurn of long-erm U.S. governmen bonds. 2 The Ibboson & Chen 4 The Supply of Sock Marke Reurns Rf compounded averages for equiy reurn is 10.70% from For he equiy risk premium, we can inerpre ha invesors were compensaed 5.24% per year for invesing in common socks raher han long-erm risk-free asses like he long-erm US governmen bonds. 3 This also shows ha roughly half of he oal hisorical equiy reurn has come from he equiy risk premium, and

7 he oher half is from inflaion and long-erm real risk-free rae. The average U.S. equiy reurns from 1926 and 2000 can be reconsruced as follows: R = (1 + ) (1 + RRf ) (1 + ERP) % = ( %) ( %) ( %) 1 (4) Mehod 2 Capial Gain and Income Mehod The equiy reurn can be broken ino capial gain ( cg ) and income reurn ( Inc ) based on he form in which he reurn is disribued. Income reurn of common sock is disribued o invesors hrough dividends, while capial gain is disribued hrough price appreciaion. Real capial gain ( Rcg ) can be compued by subracing inflaion from capial gain. The equiy reurn in period can hen be decomposed as follows: [(1 + ) (1 + Rcg ) ] + Inc Rinv R = 1 + (5) The average income reurn is calculaed o be 4.28%, he average capial gain is 6.19%, and he average real capial gain is 3.02%. Rinv, he re-invesmen reurn, averages 0.20% from 1926 o The average U.S. equiy reurn from 1926 and 2000 can be compued according o R 10.70% = [(1 + ) (1 + Rcg) 1] = + Inc + Rinv [( %) ( %) 1] % % (6) Figure 1 shows he decomposiion of he building blocks mehod and he capial gain and income mehod from 1926 o Mehod 3 Earnings Model The real capial gain porion of he reurn in he capial gain and income mehod can be broken ino growh in real earnings per share ( g REPS ) and growh in he price o earnings raio ( g P / E ), Rcg = P P 1 P / E E 1 = 1 = (1 + g P / E, ) (1 + g REPS, ) 1 P / E E (7) Ibboson & Chen 5 The Supply of Sock Marke Reurns

8 Therefore, he equiy s oal reurn can be broken ino four componens: inflaion; he growh in real earnings per share; he growh in he price o earnings raio; and income reurn. [( 1+ ) (1 + g REPS ) (1 + g P / E, ) ] + Inc Rinv R =, 1 + (8) The real earnings of US equiy increased 1.75% annually from The P/E raio was a he beginning of I grew o a he end of The highes P/E (136.50) was recorded in 1932, while he lowes (7.26) was recorded in The average year-end P/E raio is Figure 2 shows he price o earnings raio from 1926 o The U.S. equiy reurns from 1926 and 2000 can be compued according o R 10.70% = [ 1+ ) (1 + g ) (1 + g ) 1] = + Inc + Rinv ( REPS P / E [( %) ( %) ( %) 1] % % (9) Mehod 4 Dividends Model Dividend ( Div ) equals he earnings imes he dividend payou raio ( PO ); herefore, he growh rae of earnings can be calculaed by he difference beween he growh rae of dividend and he growh rae of he payou raio. EPS = Div PO (10) (1 + g REPS, (1 + g ) = (1 + g RDiv, PO, ) ) (11) We subsiue dividend growh and payou raio growh for he earning growh in equaion 8. The equiy s oal reurn in period can be broken ino five componens: 1) inflaion; 2) he growh rae of he price earning raio; 3) he growh rae of he dollar amoun of dividend afer inflaion; 4) he growh rae of he payou raio; and 5) he dividend yield. (1 + g ) R = (1 + ) (1 + g 1 + RDiv, P / E, ) + Inc Rinv (12) (1 + g PO, ) Figure 3 shows he annual income reurn (dividend yield) of U.S. equiy from 1926 o The dividend yield dropped from 5.15% a he beginning of 1926 o only 1.10% a he end of Ibboson & Chen 6 The Supply of Sock Marke Reurns

9 Figure 4 shows he year-end dividend payou raio from 1926 o On average, he dollar amoun of dividends grew 1.23% afer inflaion per year, while he dividend payou raio decreased 0.51% per year. The dividend payou raio was 46.68% a he beginning of I decreases o 31.78% a he end of The highes dividend payou raio (929.12%) was recorded in 1932, while he lowes was recorded in The U.S. equiy reurns from 1926 and 2000 can be compued according o (1 + g ) RDiv R = ( 1+ ) (1 + g P / E ) 1 + Inc + Rinv (1 + g PO ) % 10.70% = ( %) ( %) % % % (13) Mehod 5 Reurn on Book Equiy Model We can also break he earnings ino book value of equiy (BV) and reurn on equiy (ROE). EPS = BV ROE The growh rae of earnings can be calculaed by he combined growh rae of BV and ROE. ( 1+ g REPS, ) = (1 + g RBV, )(1 + g ROE, ) (15) We subsiue BV growh and ROE growh for he earnings growh in he equiy reurn decomposiion. The equiy s oal reurn in period can be compued by, (14) [( 1+ ) (1 + g P E, ) (1 + g RBV, ) (1 + g ROE, ) ] + Inc Rinv R = / 1 + (16) We esimae ha he average growh rae of he book value afer inflaion is 1.46% from 1926 o The average ROE growh per year is calculaed o be 0.31% during he same ime period. R 10.70% = [ 1+ ) (1 + g ) (1 + g ) (1 + g ) 1] = + Inc + Rinv ( P / E BV ROE [( %) ( %) ( %) ( %) 1] % % (17) Mehod 6 - GDP Per Capia Model Diermeier, Ibboson, and Siegel (1984) proposed a framework o analyze he aggregae supply of financial asse reurns. Since we are only ineresed in he supply model of he equiy reurns in his Ibboson & Chen 7 The Supply of Sock Marke Reurns

10 sudy, we developed a slighly differen supply mehod based on he growh of he economic produciviy. This mehod can be expressed by he following equaion: [( 1+ ) (1 + RgGDP POP, ) (1 + g FS, ) ] + Inc Rinv R = / 1 + (18) The reurn of he equiy marke over he long run can be decomposed ino four componens: 1) inflaion; 2) real growh rae of he overall economic produciviy (he GDP per capia ( g GDP / POP )); 3) he increase of he equiy marke relaive o he overall economic produciviy (increase in he facor share of equiies in he overall economy ( g FS )); and 4) dividend yields. Insead of assuming a consan facor share, we examine he hisorical growh rae of facor share relaive o he overall growh of he economy. Figure 5 shows he growh of GDP per capia, earnings, and dividends iniialized o uniy a he end of In he early 1930s, earnings, dividends, and GDP per capia level dropped significanly. Overall, GDP per capia slighly ougrew earnings and dividends, bu all grew a approximaely he same rae. In oher words, overall economic produciviy increased slighly faser han corporae earnings and dividends hrough he pas 75 years. Alhough GDP per capia ougrew earnings and dividends, he overall sock marke price grew faser han GDP per capia. This is primarily because he P/E raio increased 2.54 imes during he same ime period. We calculae ha he average annual increase in he facor share of he equiy marke relaive o he overall economy o be 0.96%. The facor share increase is less han he annual increase of P/E raio (1.25%) over he same ime period. This suggess ha he increase in he equiy marke share relaive o he overall economy can be fully aribued o he increase in he P/E raio. [ 1+ ) (1 + Rg ) (1 + g ) 1] R = + Inc + Rinv ( GDP / POP 10.70% = FS [( %) ( %) ( %) 1] % % (19) Summary of Hisorical Equiy Reurns and is Componens Figure 6 shows he decomposiion of models wo hrough six ino heir componens. The differences across he five models are he differen componens ha represen he capial gain porion of he equiy reurns. There are several imporan findings. Firs, as shown in Figure 5, he growh in corporae earnings is in line wih he growh of he overall economic produciviy. Second, P/E increases accoun for Ibboson & Chen 8 The Supply of Sock Marke Reurns

11 only 1.25% of he 10.70% oal equiy reurns. Mos of reurns are aribuable o dividend paymens and nominal earning growh (including inflaion and real earning growh). Third, he increase in relaive facor share of he equiy can be fully aribued o he increase in he P/E raio. Overall economic produciviy ougrew boh corporae earnings and dividends from 1926 hrough Fourh, despie he record earning growh in he 1990s, he dividend yield and he payou raio declined sharply, which renders dividends alone a poor measure for corporae profiabiliy and fuure earnings growh. Ibboson & Chen 9 The Supply of Sock Marke Reurns

12 III. THE LONG -TERM FORECAST OF THE SUPPLY OF EQUITY RETURNS Supply side models can be used o forecas he long-erm expeced equiy reurn. The supply of sock marke reurns is generaed by he produciviy of he corporaions in he real economy. Over he long run, he equiy reurn should be close o he long run supply esimae. In oher words, invesors should no expec a much higher or a much lower reurn han ha produced by he companies in he real economy. We believe he invesors expecaions on he long-erm equiy performance should be based on he supply of equiy reurns. The supply of equiy reurns consiss of wo main componens: curren reurns in he form of dividends and long-erm produciviy growh in he form of capial gains. We focus on hree supply side models: he earnings model, he dividends model, and he GDP per capia model (Mehod 3, Mehod 4, and Mehod 6 in secion II). We sudy he componens of he hree mehods. Specifically, we idenify which componens are ied o he supply of equiy reurns, and which componens are no. Then, we esimae he long-erm susainable reurn based on hisorical informaion on hese supply componens. Mehod 3F Forward-Looking Earnings Model According o he earnings model (equaion 8), he hisorical equiy reurn can be broken ino four componens: he income reurn; inflaion; he growh in real earnings per share; and he growh in he P/E raio. Only he firs hree of hese componens are hisorically supplied by companies. The growh in P/E raio reflecs invesors changing predicion of fuure earnings growh. Alhough we forecas ha he pas supply of corporae growh will coninue, we do no forecas any change in invesors predicions. Thus, he supply of he equiy reurn ( SR ) only includes inflaion, he growh in real earnings per share, and income reurn. [ 1+ ) (1 + g REPS ) ] + Inc Rinv SR = (, 1 + (20) The long-erm supply of U.S. equiy reurns based on he earnings mehod is 9.37%. This model uses he hisorical income reurn as an inpu for reasons ha are discussed in he laer secion Differences Beween he Earnings Model (3F) and he Dividends Model (4F). Ibboson & Chen 10 The Supply of Sock Marke Reurns

13 SR 9.37% = [(1 + ) (1 + g ) 1] = + Inc + Rinv REPS [( %) ( %) 1] % % (21) The equiy risk premium ( SERP ) based on he supply side earnings model is calculaed o be 3.97%. This is shown in Figure 7. SERP (1 + SR) % = 1 = = 3.97% (1 + ) (1 + RRf ) ( %) ( %) (22) Mehod 4F Forward-Looking Dividends Mehod The forward-looking dividend model is also referred o as he consan dividend growh model (or he Gordon model), where he expeced equiy reurn equals he dividend yield plus he expeced dividend growh rae. The supply of he equiy reurn in he Gordon model includes inflaion, he growh in real dividend, and dividend yield. As is commonly done wih he consan dividend growh model, we have used he curren dividend yield of 1.10%, insead of he hisorical dividend yield of 4.28%. This reduces he esimae of he supply of equiy reurns o 5.44%. The equiy risk premium is esimaed o be 0.24%. Figure 8 show he equiy risk premium esimae based on he earnings model and he dividends model. In he nex secion, we show why we disagree wih he dividends model and prefer o use he earnings model o esimae he supply side equiy risk premium. SR 5.54% = [(1 + ) (1 + g ) 1] = + Inc + Rinv RDiv [( %) ( %) 1] % % (23) SERP (1 + SR) % = 1 = = 0.24% (1 + ) (1 + RRf ) ( %) ( %) (24) Differences Beween he Earnings Model (3F) and he Dividends Model (4F) There are essenially hree differences beween he earnings model (3F) and he dividends model (4F). All of hese differences are reconciled in he righ bar (4F ) in Figure 8. These differences relae o he decrease in he hisorical payou raios, he low curren payou raio, and he high curren P/E raio. Ibboson & Chen 11 The Supply of Sock Marke Reurns

14 Firs, he earnings model uses he hisorical earning growh o reflec he growh in produciviy, while he dividends model uses hisorical dividend growh. Hisorical dividend growh underesimaes hisorical earning growh because of he decrease in he payou raio. Overall, he dividend growh underesimaed he increase in earnings produciviy by 0.51% per year from 1926 o The second difference is also due o he lowered payou raio as refleced in oday s curren yield. This payou raio is a a hisoric low of 31.8%, compared o he hisorical average payou of 59.2%. Applying such a low rae forward would mean ha even more earnings would be reained in he fuure han in he hisorical period. Had more earnings been reained, he hisoric earnings growh would have been 0.95% per year higher. Thus, i is necessary o adjus he 1.10% curren yield upward by 0.95% o give he 2.05% shown in he figure. Using he curren dividend payou raio in he dividend model, 4F, creaes wo errors, boh of which violae Miller and Modigliani (1961) heory. The firms dividend payou raio only affecs he form in which shareholders receive heir reurns, (i.e. dividends or capial gains), bu no heir oal reurn. Using he low curren dividend payou raio should no affec our forecas, hus he dividend model has o be upwardly adjused by boh 0.51% and 0.95%, so as no o violae M&M Theory. Firms oday likely have such low payou raios in order o reduce he ax burden of heir invesors. Insead of paying dividends, many companies reinves earnings, buy back shares or use heir cash o purchase oher companies. 6 The hird difference beween models 3F and 4F is relaed o he curren P/E raio (25.96) being much higher han he hisorical average (13.76). The curren yield (1.10%) is a a hisoric low boh because of he previously menioned low payou raio and because of he high P/E raio. Even assuming he hisorical average payou raio, he curren dividend yield would be much lower han is hisorical average (2.05% vs. 4.28%) This difference is geomerically esimaed o be 2.28% per year. The high P/E raio can be caused by 1) mis-pricing; 2) low required rae of reurn; and/or 3) high expeced fuure earnings growh rae. Mis-pricing is eliminaed by our assumpion of marke efficiency. A low required rae of reurn is eliminaed since we assume a consan equiy risk premium hrough he pas and fuure periods ha we are rying o esimae. Thus, we inerpre he high P/E raio as he marke expecaion of higher earning growh. Ibboson & Chen 12 The Supply of Sock Marke Reurns

15 To summarize, here are hree differences beween he earnings model and he dividends model. The firs wo differences relae o he dividend payou raio and are direc violaions of he Miller & Modigliani (1961) heorem. We inerpre ha he hird difference is due o he expecaion of higher han average earnings growh, prediced by he high curren P/E raio. These differences reconcile he earnings and dividend models. Mehod 6F Forward-Looking GDP Per Capia Model The idea behind he forward-looking GDP per capia model is ha equiy reurns are relaed o overall economic produciviy. This model esimaes he sock marke reurn expecaion jusified by he macroeconomic performance. Specifically, we use he growh of GDP per capia as he measure of susainable growh of he sock marke. The supply side GDP per capia model is defined here. [( 1+ ) (1 + RgGDP POP, ) ] + Inc Rinv SR = / 1 + (25) This model implies he long run supply of sock reurns should be in line wih he produciviy of he overall economy. And he long-erm growh rae of he sock marke should be in line wih he growh of he overall economical produciviy. In oher words, he growh of he equiy marke canno persisenly under- or ou-perform he overall economy. A similar approach can be found in Diermeier, Ibboson, and Siegel (1984), which proposed using he growh rae of he overall economic as a proxy for he growh rae in aggregae wealh in he long run. In his sudy, we use he GDP per capia growh rae as a proxy for he supply growh of he socks. The long-erm supply esimae of sock reurn can be calculaed from 9.66% = [ 1+ ) (1 + Rg ) 1] SR = + Inc + Rinv ( GDP / POP [( %) ( %) 1] % % (26) The equiy risk premium based on he GDP per capia model is calculaed o be 4.25%. SERP (1 + SR) % = 1 = 1 = 4.25% (1 + ) (1 + RRf ) ( %) ( %) (27) Ibboson & Chen 13 The Supply of Sock Marke Reurns

16 The equiy risk premium from he GDP per capia model is slighly higher han he esimaes from he earnings model. Figure 9 shows esimaes of he supply of equiy reurns from he wo supply side models ha we recommend. The differences among he wo equiy reurn (and he equiy risk premium) esimaes are due o he measures used o proxy he growh of he corporaions produciviy, specifically, he earnings growh and GDP per capia growh. We believe ha earnings growh and GDP per capia growh are more reliable han dividend growh, since hey are no affeced by he changes in dividend payou decisions. We find ha dividend growh does no accuraely reflec he growh of companies produciviy (measured by earnings), especially during he pas decade. Overall, he dividend growh underesimaed he increase in earnings by 0.51% per year from 1926 o This is refleced in he difference of he esimaed supply side reurns beween he earnings model and he dividends model. The earnings model and he GDP per capia model are preferred o he dividends model in esimaing he supply of reurns. To summarize, he long-erm supply of equiy reurn is esimaed o be around 9.37% and 9.66% (6.09% and 6.38% afer inflaion, respecively). The compound supply side equiy risk premium is esimaed o be around 3.97% and 4.25%. Geomeric vs. Arihmeic The esimaed equiy reurns (9.37% and 9.66%) and equiy risk premiums (3.97% and 4.25%) are geomeric averages. The arihmeic average is ofen used in porfolio opimizaion. There are several ways o conver he geomeric average ino an arihmeic average. One mehod is o assume he reurns are independenly log-normally disribued over ime. Then he arihmeic and geomeric roughly follows he following relaionship: 2 σ R A = R G +, (28) 2 where R A is he arihmeic average, RG is he geomeric average, and 2 σ is he variance. The sandard deviaion of reurns from Table 1 is 19.67%. Since almos all he variaion in equiy reurns is from he equiy risk premium (raher han he risk free rae), we need o add 1.93% o he geomeric equiy risk premium esimae o conver ino arihmeic. R R +1.93%. Adding A = G he 1.93 percen o he geomeric esimae, he arihmeic average equiy risk premium is esimaed o be around 6% (5.90% for he earning model and 6.18% for he GDP per capia model). Ibboson & Chen 14 The Supply of Sock Marke Reurns

17 IV. CONCLUSIONS We adop a combinaion of hisorical and supply side approaches o esimae he forward looking long-erm susainable equiy reurns and equiy risk premium. We analyze hisorical equiy reurns by decomposing reurns ino facors commonly used o describe he aggregae equiy marke and overall economic produciviy. These facors include inflaion, earnings, dividends, price-oearnings raio, dividend-payou raio, book value, reurn on equiy, and GDP per capia. We examine each facor and is relaionship wih he long-erm supply side framework. We forecas he equiy risk premium hrough supply side models using hisorical informaion. A complee abulaion of all he numbers from all models is presened in Table 2. Conrary o several recen sudies on equiy risk premium ha declare he forward looking equiy risk premium o be close o zero or negaive, we find he long-erm supply of equiy risk premium is only slighly lower han he sraigh hisorical esimae. The equiy risk premium is esimaed o be abou 4% in geomeric erms and 6% on an arihmeic basis. This esimae is abou 1.25% lower han he sraigh hisorical esimae. The differences beween our esimaes and he ones provided by several oher recen sudies are principally due o he inappropriae assumpions used, which violae he Miller and Modigliani Theorem. Our esimae is in line wih boh he hisorical supply measures of he public corporaions (i.e., earnings) and he overall economic produciviy (GDP per capia). Ibboson & Chen 15 The Supply of Sock Marke Reurns

18 Figure 1: Decomposiion of Hisorical Equiy Reurns Geomeric Mean = 10.70% 11% 10% 9% 8% 7% ERP 5.24% INC INC 4.28% 4.28% 6% 5% 4% RRF 2.05% RCG 3.02% g(p/e) 1.25% g(eps) 1.75% 3% 2% 1% 3.08% 3.08% 3.08% 0% 1-Building Blocks 2- Income and Capial Gain 3- Earnings ERP is equiy risk premium, RRF is he real risk free rae, is he Consumer Price Index (inflaion), INC is dividend income, RCG is real capial gain, g(p/e) is growh rae of P/E raio, and g(eps) is growh rae of earnings per share. The block on he op is he re-invesmen reurn plus he geomeric ineracions among he componens. Ibboson & Chen 16 The Supply of Sock Marke Reurns

19 Figure 2: P/E Raio For Dec / Ibboson & Chen 17 The Supply of Sock Marke Reurns

20 Figure 3: Income Reurn (Dividend Yield) % Dividend Yield (%) Ibboson & Chen 18 The Supply of Sock Marke Reurns

21 Figure 4: Dividend Payou Raio % % for Dec % for Dec Dividend Payou Raio (%) Ibboson & Chen 19 The Supply of Sock Marke Reurns

22 Figure 5: Growh of $1 a he beginning of GDP/POP Earning Dividend Ibboson & Chen 20 The Supply of Sock Marke Reurns

23 Figure 6: Decomposiion of Hisorical Equiy Reurns % 10% 9% 8% INC INC INC INC INC 4.28% 4.28% 4.28% 4.28% 4.28% 7% 6% 5% 4% 3% RCG 3.02% g(p/e) g(p/e) g(p/e) 1.25% 1.25% 1.25% 0.51% -g(po) g(eps) g(bv) g(div) 1.75% 1.46% 1.23% 0.31% g(fs) 0.96% g(gdp/pop) 2.04% g(roe) 2% 1% 3.08% 3.08% 3.08% 3.08% 3.08% 0% 2- Income and Capial Gain 3- Earnings 4- Dividends 5- Book Value 6- GDP/POP g(po) is growh rae of dividend payou raio, g(div) is growh rae of dividend, g(bv) is he growh rae of book value, g(roe) is he growh rae of reurn on book equiy, g(fs) is he growh rae of equiy facor share, and g(gdp/pop) is he growh rae of GDP per capia. Ibboson & Chen 21 The Supply of Sock Marke Reurns

24 11% Figure 7: Hisorical Earnings and Forecased Equiy Reurns Based on Earnings Models: Model 3, 3F, & 3F(ERP) 10% 9% 8% 7% INC 4.28% INC 4.28% ERP 3.97% 6% 5% 4% g(p/e) 1.25% g(eps) g(e) 1.75% 1.75% RRF 2.05% 3% 2% 1% 3.08% 3.08% 3.08% 0% 3- Hisorical 3F-Earnings Forecas 3F(ERP)-Forecas ERP Ibboson & Chen 22 The Supply of Sock Marke Reurns

25 11% Figure 8: Hisorical vs. Curren Dividend Yield Forecass Based on Earnings and Dividend Models: Model 3, 3F(ERP), 4F, 4F(ERP), and 4F' 10% 9% 8% 7% INC 4.28% ERP 3.97% AG 2.28% 6% 5% 4% g(eps) 1.75% INC (00) 2.05% INC(00) ERP 0.24% RRF 1.10% RRF 0.51% 2.05% g(div) 2.05% g(div) 1.23% 1.23% -g(po) 3% 2% 1% 3.08% 3.08% 3.08% 3.08% 3.08% 0% 3F- Hisorical Earnings Forecas 3F(ERP)-Hisorical Earnings Forecas 4F- Curren Dividend Forecas * 4F(ERP)-Curren Dividend Forecas * 4F'- Curren Dividend Forecas wih Addiional Growh ** INC(00) is he dividend yield in he year INC (00) is he dividend yield in he year 2000 assuming he dividend payou raio equal he hisorical average of 59.20%. I is calculaed o be 2.05%. AG is he addiional growh. *Violaes Miller & Modigliani (1961), since low curren dividend yields are mached wih hisorical earnings growh when dividend yields were high. ** Model 4F aemps o correcs he error in model 4F: a) use growh rae of earnings insead of growh rae of dividends; b) adjus he dividend yield o 2.05% assuming he hisorical average dividend payou raio; and c) add he addiional growh implied by he high marke P/E raio. Ibboson & Chen 23 The Supply of Sock Marke Reurns

26 Figure 9: Forecased Equiy Reurns Recommended: Model 3F & 6F 11% 10% 9% 8% 7% INC 4.28% ERP 3.97% INC 4.28% ERP 4.26% 6% 5% 4% g(eps) 1.75% RRF g(gdp/pop) RRF 2.05% 2.04% 2.05% 3% 2% 1% 3.08% 3.08% 3.08% 3.08% 0% 3F-Hisorical Earnings Forecas 3F(ERP)-Hisorical Earnings Forecas 6F-Hisorical GDP/POP Forecas 6F (ERP) - Hisorical GDP/POP Forecas Ibboson & Chen 24 The Supply of Sock Marke Reurns

27 Table 2 Hisorical and Forecased Equiy Reurns All Models (Percen). Sum (%) Inflaio n=3.08 % Real Risk- Free Rae=2. 05% Equiy Risk Premiu m=5.24 % Real Capial Gain=3.02% g(real EPS)=1.75% g(real Div)=1. 23% - g(div Payou Raio)= 0.51% g(p/e)= 1.25% g(real GDP/P OP)=2. 04% g(fs- GDP/P OP)=1. 96% Income Reurn =4.28 % Hisorical Mehod Mehod Mehod Mehod Mehod Mehod Forecas wih Hisorical Dividend Yield Mehod 3F Reinves Addiio men + nal Ineraci Growh on =2.28 % Mehod 3F (ERP) Mehod 6F Mehod 6F (ERP) Forecas wih Curren Dividend Yield Mehod 4F Mehod 4F (ERP) Mehod 4F Ibboson Associaes 25 The Supply of Sock Marke Reurns

28 REFERENCES Arno, Rober and Ryan, Ronald (2001) The Deah of he Risk Premium: Consequences of he 1990 s, Journal of Porfolio Managemen, Spring Diermeier, Jeffrey J., Ibboson, Roger G., and Siegel, Laurance B. (1984) The Supply for Capial Marke Reurns, Financial Analys Journal, March/April, Fama, Eugene F. and French, Kenneh R. (2000) The Equiy Risk Premium, Working Paper, June Fisher, Lawrence and Lorie, James H. (1968) Rae of Reurn on Invesmens in Common Sock: The Year-by-Year Record, , Journal of Business 37, No. 1 (July 1968), Green, Richard C. and Hollifield, Buron (2001) The Personal-Tax Advanages of Equiy, Carnegie Mellon Universiy Working Paper, January Gordon, Myron, 1962, The Invesmen Financing and Valuaion of he Corporaion, Irwin: Homewood, Illinois. Ibboson Associaes (2001) Socks, Bonds, Bills, and Inflaion 2001 Yearbook, Ibboson Associaes, Ibboson, Roger G., Diermeier, Jeffrey J., and Siegel, Laurance B. (1984) The Demand for Capial Marke Reurns: A New Equilibrium Theory, Financial Analys Journal, January/February, 1984, Ibboson, Roger G., and Sinquefield, Rex A. (1976) Socks, Bonds, Bills, and Inflaion: Year-By Year Hisorical Reurns ( ), The Journal of Business 49, No. 1 (January 1976), Ibboson, Roger G., and Sinquefield, Rex A. (1976) Socks, Bonds, Bills, and Inflaion: Simulaions of Fuure ( ), The Journal of Business 49, No. 3 (July 1976), Linner, John (1965) The Valuaion of Risk Asses and he Selecion of Risky Invesmens in Sock Porfolios and Capial Budges, Review of Economics and Saisics, February Miller, Meron, and Modigliani, Franco (1961) Dividend policy, Growh and he Valuaion of Shares, Journal of Business, Ocober Ross, Sephen A., (1976) Risk, Reurn and Arbirage, in I. Friend and J. Bicksler, eds., Risk and Reurn in Finance, Ballinger, Cambridge MA. Sharpe, William (1964) Capial Asse Prices: A Theory of Marke Equilibrium, Journal of Finance, Sepember Shiller, Rober J. (2000) Irraional Exuberance, Princeon Universiy Press, Princeon, NJ. Vuoleneenaho, Tuomo (2000) Undersanding he Aggregae Book-o-Marke Raio and Is Implicaions o Curren Equiy-Premium Expecaions. Harvard Universiy Working Paper. Ibboson Associaes 26 The Supply of Sock Marke Reurns

29 Welch, Ivo. "Views of Financial Economiss on he Equiy Premium and Oher Issues." The Journal of Business 73-4, Ocober 2000, Wilson, Jack W. and Jones, Charles P. (2001) An Analysis of he S&P 500 Index and Cowles Exensions: Price Indexes and Sock Reurns, , Journal of Business (Forh-Coming). Ibboson Associaes 27 The Supply of Sock Marke Reurns

30 1 We updaed he series wih daa from Sandard & Poors o include he year Some oher sudies, including Ibboson & Sinquefield (1976a,b), used U.S. Treasury Bills as he risk free rae. We chose he income reurn of U.S. long-erm governmen bonds as he long-erm risk-free rae in his sudy. 3 The 5.24% is he compounded average of he hisorical equiy risk premium. The arihmeic average is 7.02%. Unless specified, we use geomeric averages in he calculaions for he enire sudy. 4 The average P/E raio is calculaed by reversing he average E/P raio from 1926 o Book Values are calculaed based on he Book-o-Marke raios repored in Vuoleneenaho (2000). The aggregae book-o-marke raio is 2.0 in 1928 and 4.1 in We use he book value growh rae calculaed during 1928 o 1999 as he proxy for he growh rae during 1926 o The average ROE growh rae is calculaed from he derived book value and he earnings daa. 6 The curren ax codes provide incenives for firms o disribue cash hrough share repurchases raher han hrough dividends. Green and Hollifield (2001) find ha he ax savings hrough repurchases are on he order of 40-50% of he axes paid ha of disribuing dividends. Ibboson Associaes 28 The Supply of Sock Marke Reurns