Yale ICF Working Paper No March 2002

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1 Yale ICF Working Paper No March 2002 STOCK MARKET RETURNS IN THE LONG RUN: PARTICIPATING IN THE REAL ECONOMY Roger G. Ibboson Yale School of Managemen Peng Chen Ibboson Associaes, Inc. This paper can be downloaded wihou charge from he Social Science Research Nework Elecronic Paper Collecion: hp://papers.ssrn.com/absrac=274150

2 Sock Marke Reurns in he Long Run: Paricipaing in he Real Economy Roger G. Ibboson, Ph.D. Professor in he Pracice of Finance Yale School of Managemen 135 Prospec Sree New Haven, CT Phone: (203) Fax: (203) Chairman Ibboson Associaes, Inc. 225 N. Michigan Ave. Suie 700 Chicago, IL Phone: (312) Fax: (312) Peng Chen, Ph.D., CFA Vice Presiden, Direcor of Research Ibboson Associaes, Inc. 225 N. Michigan Ave. Suie 700 Chicago, IL Phone: (312) Fax: (312) March 2002 Sock Marke Reurns in he Long Run

3 ABSTRACT We esimae he forward-looking long-erm equiy risk by exrapolaing he way i paricipaed in he real economy. 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. There are several key findings: Firs, he growh in corporae produciviy 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 more han fully aribued o he increase in he P/E raio. Fourh, here is a secular decline in he dividend yield and payou raio, rendering dividend growh alone a poor measure of corporae profiabiliy and fuure growh. Conrary o several recen sudies, our supply side model forecas of he equiy risk premium is only slighly lower han he pure hisorical reurn esimae. The long-erm equiy risk premium (relaive o he long-erm governmen bond yield) 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). 1 Sock Marke Reurns in he Long Run

4 I. INTRODUCTION Numerous auhors are direcing heir effors oward esimaing expeced reurns on socks incremenal o bonds. 1 These equiy risk premium 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 as was done in Ibboson and Sinquefield (1976a,b). The second group, which includes our curren paper, uses fundamenal informaion such as earnings, dividends, or overall economic produciviy o measure he expeced equiy risk premium. The hird group adops demand side models ha derive expeced equiy reurns hrough he payoff demanded by invesors for bearing he risk of equiy invesmens, as in he Ibboson, Siegel, and Diermeier (1984) demand framework, and especially in he large body of lieraure following he seminal work of Mehra and Presco (1985). The fourh group relies on opinions of invesors and financial professionals hrough broad surveys. Our paper uses supply side models. We firs used his ype of model in Diermeier, Ibboson, and Siegel (1984). There have been numerous oher auhors who have also used supply side models, usually focusing on he Gordon (1962) consan dividend growh model. For example, Siegel (1999) predics ha he equiy risk premium will shrink in he fuure due o low curren dividend yields and high equiy valuaions. Fama and French (2002) use a longer ime period (1872 o 1999) o ge geomeric equiy risk premiums of 2.55% using dividend growh raes, and 4.32% using earnings growh raes. 2 Campbell and Shiller (2001) argue for low reurns, because hey believe he curren marke is overvalued. Arno and Ryan (2001) argue ha he forward-looking equiy risk premium is acually negaive. This sems from using he low curren dividend yield plus heir very low forecas dividend growh. We laer argue ha mixing he curren low dividend yields and payou raios wih hisorical dividend yield growh violaes Miller and Modigliani (1961) dividend heory. The survey resuls generally suppor somewha higher equiy risk premiums. For example, Welch (2000) conduced a survey among 226 academic financial economics on equiy risk premium expecaions. The 2 Sock Marke Reurns in he Long Run

5 survey shows ha he geomeric long horizon equiy risk premium forecas is almos 4%. 3 Graham and Harvey (2001) conduced a muli-year survey of CFOs of U.S. corporaions, hey find ha he expeced 10-year geomeric average equiy risk premium ranges from 3.9% o 4.7%. In his paper, we link hisorical equiy reurns wih facors commonly used o describe he aggregae equiy marke and overall economic produciviy. Unlike some sudies, our resuls are porrayed on a per share basis (per capia in he case of GDP). The facors include inflaion, earnings per share, dividends per share, price o earnings raio, dividend payou raio, book value per share, reurn on equiy, and GDP per capia. 4 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 earnings 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. 5 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 earnings 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 more frequenly o purchase oher companies shares. Finally, our forecass rea inflaion as a pass-hrough, so ha he enire analysis can be done in real erms. 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 3 Sock Marke Reurns in he Long Run

6 of he supply side. We evaluaed each mehod and is componens by applying hisorical daa from 1926 o The hisorical equiy reurn and earnings daa used in his sudy are obained from Wilson and Jones (2002). 6 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 (). The equiy risk premium and he real risk-free rae for year, ERP and RRf, are 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. Rf is he reurn of risk-free asses represened by he income reurn of long-erm U.S. governmen bonds. The compounded average for equiy reurn is 10.70% from For he equiy risk premium, we can inerpre ha invesors 4 Sock Marke Reurns in he Long Run

7 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. 7 This also shows ha roughly half of he oal hisorical equiy reurn has come from he equiy risk premium, and he oher half is from inflaion and long-erm real riskfree 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 o 2000 can be compued according o R 10.70% = [(1 + ) (1 + Rcg) 1] = + Inc + Rinv [( %) ( %) 1] % % (6) 5 Sock Marke Reurns in he Long Run

8 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 ) and growh in he price o earnings raio ( ), REPS g P / E P P / E E Rcg = 1 = 1 = (1 + g P / E, ) (1 + g REPS, ) 1 (7) P P / E E 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 during he depression in 1932 when earnings were near zero, 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. 6 Sock Marke Reurns in he Long Run

9 Div EPS = (10) PO (1 + g RDiv, ) (1 + g REPS, ) = (11) (1 + g ) PO, We subsiue dividend growh and payou raio growh for he earnings 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 earnings 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 ) = (1 + ) (1 + / ) 1 Rinv (12) RDiv, R g P E, + Inc + (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 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 7 Sock Marke Reurns in he Long Run

10 We can also break he earnings ino book value of equiy (BV) and reurn on equiy (ROE). EPS = BV ROE (14) The growh rae of earnings can be calculaed by he combined growh rae of BV and ROE. ( REPS, RBV, ROE, 1+ g ) = (1 + g )(1 + g ) (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, [( 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 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; g GDP / POP 2) real growh rae of he overall economic produciviy (he GDP per capia ( )); 3) he increase 8 Sock Marke Reurns in he Long Run

11 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 he socks marke, GDP per capia, earnings, and dividends iniialized o uniy a he end of In he early 1930s, he sock marke, earnings, dividends, and GDP per capia level dropped significanly. Overall, GDP per capia slighly ougrew earnings and dividends, bu hey 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. [ ] R = ( 1+ ) (1 + Rg GDP / POP ) (1 + g FS ) 1 + Inc + Rinv 10.70% = [( %) ( %) ( %) 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. 9 Sock Marke Reurns in he Long Run

12 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 only 1.25% of he 10.70% oal equiy reurns. Mos of reurns are aribuable o dividend paymens and nominal earnings growh (including inflaion and real earnings 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 earnings 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. 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 produced by corporaions. 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 dividend model, and he GDP per capia model (Mehod 3, Mehod 4, and Mehod 6 in secion III). 10 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 10 Sock Marke Reurns in he Long Run

13 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). SR 9.37% = [(1 + ) (1 + g ) 1] = + Inc + Rinv REPS [( %) ( %) 1] % % (21) The supply side equiy risk premium ( SERP ) based on he earnings model is calculaed o be 3.97%. This is shown in Figure 7. (1 + SR) % SERP = 1 = = 3.97% (22) (1 + ) (1 + RRf ) ( %) ( %) Mehod 4F Forward-Looking Dividends Mehod 11 Sock Marke Reurns in he Long Run

14 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 shows 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(00) + Rinv RDiv [( %) ( %) 1] % % (23) (1 + SR) % SERP = 1 = = 0.24% (24) (1 + ) (1 + RRf ) ( %) ( %) 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 wo righ bars (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. Firs, he earnings model uses he hisorical earnings growh o reflec he growh in produciviy, while he dividend model uses hisorical dividend growh. Hisorical dividend growh underesimaes hisorical earnings 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 Sock Marke Reurns in he Long Run

15 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. 11 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 earnings growh Sock Marke Reurns in he Long Run

16 SR 9.67% = [(1 + ) (1 + g ) (1 g ) 1] = + Inc(00) + AY + AG + Rinv RDiv PO [( %) ( %) ( %) 1] % % % % (25) 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. Equaion 25 presened model 4F, which reconciles he difference beween he earnings model and he dividends model. Geomeric vs. Arihmeic The esimaed equiy reurns (9.37%) and equiy risk premiums (3.97%) 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 +, (26) 2 2 where R is he arihmeic average, R is he geomeric average, and σ is he variance. The sandard A deviaion of equiy reurns 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 A G = RG +1.93%. Adding he 1.93 percen o he geomeric esimae, he arihmeic average equiy risk premium is esimaed o be 5.90% for he earnings model. 14 Sock Marke Reurns in he Long Run

17 To summarize, he long-erm supply of equiy reurn is esimaed o be 9.37% (6.09% afer inflaion) condiional on he hisorical average risk free rae. The supply side equiy risk premium is esimaed o be 3.97% geomerically and 5.90% arihmeically. 13 IV. CONCLUSIONS We adop a supply side approach 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-o-earnings 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 Appendix. 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 3.97% in geomeric erms and 5.90% 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. Also our models inerpre he curren high P/E raios as he marke forecasing high fuure growh, raher han a low discoun rae or an overvaluaion. 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). Our esimae of he equiy risk premium is far closer o he hisorical premium han being zero or negaive. This implies ha socks are expeced o ouperform bonds over he long run. For long-erm invesors, such as pension funds or individuals saving for reiremen, socks should coninue o one of he favored asse classes in heir diversified porfolios. Due o our lowered equiy risk premium esimae 15 Sock Marke Reurns in he Long Run

18 (compared o hisorical performance), some invesors should lower heir equiy allocaions and/or increase heir savings rae o mee fuure liabiliies. 16 Sock Marke Reurns in he Long Run

19 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. Including he geomeric ineracions ensures he componens sums up o 10.70% in his and subsequen figures. Table 1 in he appendix gives he deailed informaion on he reinvesmen and geomeric ineracion for all he mehods. 17 Sock Marke Reurns in he Long Run

20 Figure 2: P/E Raio For Dec / Sock Marke Reurns in he Long Run

21 Figure 3: Income Reurn (Dividend Yield) % Dividend Yield (%) Sock Marke Reurns in he Long Run

22 Figure 4: Dividend Payou Raio % % for Dec % for Dec Dividend Payou Raio (%) Sock Marke Reurns in he Long Run

23 Capial Gain GDP/POP Earnings Dividends Figure 5: Growh of $1 a he beginning of Sock Marke Reurns in he Long Run

24 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(roe) g(fs) 0.96% g(gdp/pop) 2.04% 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. 22 Sock Marke Reurns in he Long Run

25 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 23 Sock Marke Reurns in he Long Run

26 11% Figure 8: Hisorical vs. Curren Dividend Yield Forecass Based on Earnings and Dividend Models: Model 3, 3F(ERP), 4F, 4F', and 4F'(FG) 10% 9% 8% 7% 6% 5% 4% INC 4.28% g(eps) 1.75% ERP 3.97% RRF 2.05% AG 2.28% 0.95% 0.51% INC(00) INC(00) 1.10% 1.10% g(div) g(div) 1.23% 1.23% ADY -g(po) FG 4.98% INC(00) 1.10% 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'- Curren Dividend Forecas wih Addiional Growh ** 4F'- Curren Dividend wih Forecased Earning Growh *** INC(00) is he dividend yield in he year ADY is he addiional dividend yield in he year 2000 assuming he dividend payou raio equal he hisorical average of 59.20%. ADY is calculaed o be 0.95%. 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 up 0.95% assuming he hisorical average dividend payou raio; and c) add he addiional growh implied by he high marke P/E raio. *** Based on Model 4F, we forecas he real earnings growh rae will be 4.96%. 24 Sock Marke Reurns in he Long Run

27 Appendix Table 1 Hisorical and Forecased Equiy Reurns All Models (Percen). Sum (%) Inflaion =3.08% Real Risk- Free Rae=2.0 5% Equiy Risk Premium =5.24% Real Capial Gain=3.0 2% g(real EPS)=1.7 5% g(real Div)=1.2 3% - g(div Payou Raio)=0. 51% g(bv)= 1.25% g(roe)= 0.31% g(p/e)=1.25% g(real GDP/PO P)=2.04 % g(fs- GDP/PO P)=1.96 % Income Reurn=4.28% Reinves men + Ineracio n Addiion al Growh =2.28% Forecase d Earnings Growh= 4.98% Hisorical Mehod 1 Mehod 2 Mehod 3 Mehod 4 Mehod 5 Mehod % 0.31% Forecas wih Hisorical Dividend Yield Mehod 3F Mehod 3F (ERP) Mehod 6F Mehod 6F (ERP) Forecas wih Curren Dividend Yield Mehod 4F * 0.03 Mehod 4F (ERP) Mehod 4F ** 0.21 Mehod 4F * 0.21 (FG) *2000 dividend yield ** Adjus he 2000 dividend yield up 0.95% assuming he hisorical average dividend payou raio Sock Marke Reurns in he Long Run

28 REFERENCES Ang, Andrew and Geer Bekaer Sock Reurn Predicabiliy: Is I There? Columbia Universiy and NBER Working Paper. Arno, Rober and Ronald Ryan The Deah of he Risk Premium: Consequences of he 1990 s, Journal of Porfolio Managemen, Spring Campbell, John Y. and Rober J. Shiller Valuaion Raios and he Long Run Sock Marke Oulook: An Updae, NBER Working Paper, No Diermeier, Jeffrey J., Roger G. Ibboson, and Laurance B. Siegel The Supply for Capial Marke Reurns, Financial Analys Journal, March/April, Fama, Eugene F., and Kenneh R. French Disappearing dividends: Changing firm characerisics or lower propensiy o pay, Journal of Financial Economics 60, Fama, Eugene F. and Kenneh R. French The Equiy Risk Premium, Journal of Finance, April Graham, John R. and Campbell R. Harvey Expecaions of Equiy Risk Premia, Volailiy and Asymmery from a Corporae Finance Perspecive, Working Paper, Fuqua School of Business, Duke Universiy, Augus 3, Green, Richard C. and Buron Hollifield The Personal-Tax Advanages of Equiy, Carnegie Mellon Universiy Working Paper, January Gordon, Myron The Invesmen Financing and Valuaion of he Corporaion, Irwin: Homewood, Illinois. Goyal, Ami and Ivo Welch Predicing he Equiy Premium wih Dividend Raios Yale School of Managemen and UCLA Working Paper. Ibboson Associaes Socks, Bonds, Bills, and Inflaion 2001 Yearbook, Ibboson Associaes, Ibboson, Roger G., Jeffrey J. Diermeier, and Laurance B. Siegel The Demand for Capial Marke Reurns: A New Equilibrium Theory, Financial Analys Journal, January/February, 1984, Ibboson, Roger G., and Rex A. Sinquefield. 1976a. Socks, Bonds, Bills, and Inflaion: Year-By Year Hisorical Reurns ( ), The Journal of Business 49, No. 1 (January 1976), Ibboson, Roger G., and Rex A. Sinquefield. 1976b. Socks, Bonds, Bills, and Inflaion: Simulaions of Fuure ( ), The Journal of Business 49, No. 3 (July 1976), Mehra, Rajnish, and Edward Presco The Equiy Premium: A Puzzle, Journal of Moneary Economics, No. 2, Miller, Meron, and Franco Modigliani Dividend policy, Growh and he Valuaion of Shares, Journal of Business, Ocober Shiller, Rober J Irraional Exuberance, Princeon Universiy Press, Princeon, NJ. Sock Marke Reurns in he Long Run

29 Siegel, Jeremy J The Shrinking Equiy Risk Premium, Journal of Porfolio Managemen, Fall Vuoleneenaho, Tuomo Undersanding he Aggregae Book-o-Marke Raio and Is Implicaions o Curren Equiy-Premium Expecaions. Harvard Universiy Working Paper. 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 Charles P. Jones An Analysis of he S&P 500 Index and Cowles Exensions: Price Indexes and Sock Reurns, , Journal of Business 75-3,July Sock Marke Reurns in he Long-run

30 1 In our sudy, we define he equiy risk premium as he difference beween he long-run expeced reurn on socks and he long-erm risk free (U.S. Treasury) yield. We do all of our analysis in geomeric form, hen conver a he end so he esimae is expressed in boh arihmeic form and geomeric form. Some oher sudies, including Ibboson & Sinquefield (1976a,b), used he shor-erm U.S. Treasury Bills as he risk free rae. 2 I is someimes difficul o compare esimaes from one sudy wih anoher, due o changing poins of reference. The equiy risk premium esimae can be significanly differen simply due o he use of arihmeic vs. geomeric, or longerm risk free rae vs. shor-erm risk free rae (Treasury Bills), or he bond s income reurn (yield) vs. he bond s oal reurn, or long-erm sraegic forecas vs. shor-erm marke iming esimae. A more deailed discussion on arihmeic vs. geomeric can be found in secion III. 3 Welch s (2000) survey repored a 7% equiy risk premium measured as he arihmeic difference beween equiy and U.S. Treasury bill reurns. To make an apple o apple comparison, we convered he 7% number ino a geomeric equiy risk premium relaive o he long erm U.S. Governmen bond income reurn, which gives an esimae of almos 4%. 4 Each per share quaniy is per share of he S&P 500 porfolio. Hereafer, we will merely refer o each facor wihou always menioning per share, for example, earnings insead of earnings per share. 5 There are many heoreical models ha sugges ha he equiy risk premium is dynamic over ime. However, recen empirical sudies (e.g. Goyal & Welch (2001)) and Ang & Bekaer (2001)) show here is no evidence of long-horizon reurn predicabiliy by eiher earnings or dividend yields. Therefore, insead of rying o build a model for a dynamic equiy risk premium, we assume ha he long-erm equiy risk premium is consan. This provides a benchmark for analysis and discussion. 6 We updaed he series wih daa from Sandard & Poor s o include he year 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. 8 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 booko-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. 10 We decided no o use model 1, 2, and 5 in forecasing, because he forecas of model 1 & 2 would be idenical o he hisorical esimae repored in secion II. The forecas of model 5 would require more complee book value and ROE daa han we currenly have available. 11 The curren ax code provides 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 ha would have been paid by disribuing dividends. 12 Conrary o he efficien marke models, Shiller (2000) and Campbell and Shiller (2001) argue ha he price o earnings raio appears o forecas he fuure sock price change. 13 We could use he GDP Per Capia model o esimae he long-erm equiy risk premium as well. The GDP Per Capia model implies he long run sock reurns should be in line wih he produciviy of he overall economy. The equiy risk premium esimaed using he GDP Per Capia model would be slighly higher han he ERP esimae from he earnings model. This is because he GDP Per Capia grew slighly faser han corporae earnings. A similar approach can be found in Diermeier, Ibboson, and Siegel (1984), which proposed using he growh rae of he overall economy as a proxy for he growh rae in aggregae wealh in he long run. Sock Marke Reurns in he Long-run

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