Long-Run Sock Reurns: Paricipaing in he Real Economy Roger G. Ibboson and Peng Chen In he sudy repored here, we esimaed he forward-looking long-erm equiy risk premium by exrapolaing he way i has paricipaed in he real economy. We decomposed he 1926 2 hisorical equiy reurns ino supply facors inflaion, earnings, dividends, he P/E, he dividendpayou raio, book value, reurn on equiy, and GDP per capia. Key findings are he following. 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. The bulk of he reurn is aribuable o dividend paymens and nominal earnings growh (including inflaion and real earnings growh). Third, he increase in he equiy marke relaive o economic produciviy can be more han fully aribued o he increase in he P/E. Fourh, a secular decline has occurred in he dividend yield and payou raio, rendering dividend growh alone a poor measure of corporae profiabiliy and fuure growh. Our forecas of he equiy risk premium is only slighly lower han he pure hisorical reurn esimae. We esimae he expeced long-erm equiy risk premium (relaive o he long-erm governmen bond yield) o be abou 6 percenage poins arihmeically and 4 percenage poins geomerically. N umerous 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 he auhors ook. The firs group of sudies has aemped o derive he equiy risk premium from he hisorical reurns of socks and bonds; an example is Ibboson and Sinquefield (1976a, 1976b). The second group, which includes our curren work, has used fundamenal informaion such as earnings, dividends, or overall economic produciviy o measure he expeced equiy risk premium. The hird group has adoped 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, Diermeier, and Siegel (1984) demand framework and, especially, in he large body of Roger G. Ibboson is professor of finance a Yale School of Managemen, New Haven, Connecicu. Peng Chen, CFA, is vice presiden and direcor of research a Ibboson Associaes, Chicago. lieraure following he seminal work of Mehra and Presco (1985). 2 The fourh group has relied on opinions of invesors and financial professionals garnered from broad surveys. In he work repored here, we used supplyside models. We firs used his ype of model in Diermeier, Ibboson, and Siegel (1984). Numerous oher auhors have used supply-side models, usually wih a focus on he Gordon (1962) consandividend-growh model. For example, Siegel (1999) prediced ha he equiy risk premium will shrink in he fuure because of low curren dividend yields and high equiy valuaions. Fama and French (22), sudying a longer ime period (1872 1999), esimaed a hisorical expeced geomeric equiy risk premium of 2.55 percenage poins when hey used dividend growh raes and a premium of 4.32 percenage poins when hey used earnings growh raes. 3 They argued ha he increase in he P/E has resuled in a realized equiy risk premium ha is higher han he ex ane (expeced) premium. Campbell and Shiller (21) forecased low reurns because hey believe he curren marke is overvalued. Arno and Ryan (21) argued ha he forward-looking equiy risk premium is acually negaive. This conclusion was based on he low 88 23, AIMR
Long-Run Sock Reurns curren dividend yield plus heir forecas for very low dividend growh. Arno and Bernsein (22) argued similarly ha he forward-looking equiy risk premium is near zero or negaive (see also Arno and Asness 23). The survey resuls generally suppor somewha higher equiy risk premiums. For example, Welch (2) conduced a survey of 226 academic financial economiss abou heir expecaions for he equiy risk premium. The survey showed ha hey forecased a geomeric long-horizon equiy risk premium of almos 4 pps. 4 Graham and Harvey (21) conduced a muliyear survey of chief financial officers of U.S. corporaions and found heir expeced 1-year geomeric average equiy risk premium o range from 3.9 pps o 4.7 pps. 5 In his sudy, we linked hisorical equiy reurns wih facors commonly used o describe he aggregae equiy marke and overall economic produciviy. Unlike some sudies, ours porrays resuls on a per share basis (per capia in he case of GDP). The facors include inflaion, EPS, dividends per share, P/E, he dividend-payou raio, book value per share, reurn on equiy, and GDP per capia. 6 We firs decomposed hisorical equiy reurns ino various ses of componens based on six mehods. Then, we used each mehod o examine each of he componens. Finally, we forecased 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 1926 2 period. In an imporan disincion from he forecass of many ohers, our forecass assume marke efficiency and a consan equiy risk premium. 7 Thus, he curren high P/E represens he marke s forecas of higher earnings growh raes. Furhermore, our forecass are consisen wih Miller and Modigliani (1961) heory, in ha dividend-payou raios do no affec P/Es 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, we assumed i 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 he enire analysis can be done in real erms. Six Mehods for Decomposing Reurns We presen six differen mehods for decomposing hisorical equiy reurns. The firs wo mehods (especially Mehod 1) are based enirely on hisorical reurns. The oher four mehods are mehods of he supply side. We evaluaed each mehod and is componens by applying hisorical daa for 1926 2. The hisorical equiy reurn and EPS daa used in his sudy were obained from Wilson and Jones (22). 8 The average compound annual reurn for he sock marke over he 1926 2 period was 1.7 percen. The arihmeic annual average reurn was 12.56 percen, and he sandard deviaion was 19.67 percen. Because our mehods used geomeric averages, we focus on he componens of he 1.7 percen geomeric reurn. When we presen our forecass, we conver he geomeric average reurns o arihmeic average reurns. Mehod 1. Building Blocks. Ibboson and Sinquefield developed a building blocks model o explain equiy reurns. The hree building blocks are inflaion, he real risk-free rae, and he equiy risk premium. Inflaion is represened by changes in he U.S. Consumer Price Index (). The equiy risk premium for year, ERP, and he real risk-free rae for year, RRf, are given by, respecively, and ERP = 1 + R ---------------- 1 1 + Rf = R Rf ------------------ 1 + Rf RRf = 1 + Rf -------------------- 1 1 + = Rf -------------------------, 1 + where R, he reurn of he U.S. sock marke, represened by he S&P 5 Index, is R = (1 + )(1 + RRf )(1 + ERP ) 1 (3) and Rf is he reurn of risk-free asses, represened by he income reurn of long-erm U.S. governmen bonds. The compound average for equiy reurn was 1.7 percen for 1926 2. For he equiy risk premium, we can inerpre ha invesors were compensaed 5.24 pps a year for invesing in common socks raher han long-erm risk-free asses (such as long-erm U.S. governmen bonds). This calculaion also shows ha roughly half of he oal hisorical equiy reurn has come from he equiy risk premium; he oher half is from inflaion and he long-erm real risk-free rae. Average U.S. equiy reurns from 1926 hrough 2 can be reconsruced as follows: 9 (1) (2) January/February 23 89
Financial Analyss Journal R = ( 1 + )( 1 + RRf )( 1 + ERP) 1 1.7% = ( 1 + % ) ( 1 + 2.5% ) ( 1+ 5.24% ) 1. The firs column in Figure 1 shows he decomposiion of hisorical equiy reurns for 1926 2 according o he building blocks mehod. Mehod 2. Capial Gain and Income. The equiy reurn, based on he form in which he reurn is disribued, can be broken ino capial gain, cg, and income reurn, Inc. Income reurn of common sock is disribued o invesors hrough dividends, whereas 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: R = [(1 + )(1 + Rcg ) 1] + Inc + Rinv, (4) where Rinv is reinvesmen reurn. The average income reurn was calculaed o be percen in he sudy period, he average capial gain was 6.19 percen, and he average real capial gain was 3.2 percen. The reinvesmen reurn averaged.2 percen from 1926 hrough 2. For Mehod 2, he average U.S. equiy reurn for 1926 2 can hus be compued according o R = [( 1 + )( 1 + Rcg ) 1] + Inc + Rinv 1.7% = [( 1 + % ) ( 1 + 3.2% ) 1] + % +.2%. The second column in Figure 1 shows he decomposiion of hisorical equiy reurns for 1926 2 according o he capial gain and income mehod. Mehod 3. Earnings. The real-capial-gain porion of he reurn in he capial gain and income mehod can be broken ino growh in real EPS, g REPS, and growh in P/E, g P/E : Rcg = P ---------- 1 P 1 = P E ------------------------- E ----------- 1 P 1 E 1 E 1 = ( 1 + g P E, ( + REPS, ) 1. Therefore, equiy s oal reurn can be broken ino four componens inflaion, growh in real EPS, growh in P/E, and income reurn: R = [( 1 + ) 1 + g REPS, ( + P E, ) 1] + Inc + Rinv. The real earnings of U.S. equiy increased 1.75 percen annually beween 1926 and 2. The P/E, as Figure 2 illusraes, was 1.22 a he beginning of 1926 and 25.96 a he end of 2. The highes P/E (136.5 and off he char in Figure 2) was recorded during he Grea Depression, in December 1932, when earnings were near zero, and he lowes in he period (7.7) was recorded in 1948. The average year-end P/E was 13.76. 1 (5) (6) Figure 1. Decomposiion of Hisorical Equiy Reurns by Six Mehods, 1926 2 Percen 11 1 9 8 7 ERP 5.24 6 5 4 3 2 1 RRF 2.5 RCG 3.2 g(p/e) 1.25 g(reps) 1.75 g(p/e) 1.25.51 g(rdiv) 1.23 g(po) g(p/e) 1.25 g(rbv) 1.46.31 g(roe) g(fs).96 g(gdp/pop) 2.4 1. Building Blocks 2. Capial Gain and Income 3. Earnings 4. Dividends 5. Book on Equiy 6. GDP per Capia Noes: The block on he op of each column is he reinvesmen reurn plus he geomeric ineracions among he componens. Including he geomeric ineracions ensured ha he componens summed o 1.7 percen in his and subsequen figures. The able ha consiues Appendix A gives deailed informaion on he reinvesmen and geomeric ineracion for all he mehods. 9 23, AIMR
Long-Run Sock Reurns Figure 2. P/E, 1926 2 P/E 4 35 3 25 2 15 1 5 25 3 35 4 45 5 55 6 65 7 75 8 85 9 95 The U.S. equiy reurns from 1926 and 2 can be compued according o he earnings mehod as follows: R = [( 1 + )( 1 + g REPS )( 1 + g P E ) 1] + Inc + Rinv 1.7% = [( 1 + % ) ( 1 + 1.75% ) ( 1 + 1.25% ) 1] + % +.2%. The hird column in Figure 1 shows he decomposiion of hisorical equiy reurns for 1926 2 according o he earnings mehod. Mehod 4. Dividends. In his mehod, real dividends, RDiv, equal he real earnings imes he dividend-payou raio, PO, or REPS RDiv = --------------- ; (7) PO herefore, he growh rae of earnings can be calculaed by he difference beween he growh rae of real dividends, g RDiv, and he growh rae of he payou raio, g PO : ( 1 + g REPS, ) = ( ------------------------------- 1 + g RDiv, ) ( 1 + g PO, ). If dividend growh and payou-raio growh are subsiued for he earnings growh in Equaion 6, equiy oal reurn in period can be broken ino (1) inflaion, (2) he growh rae of P/E, (3) he growh rae of he dollar amoun of dividends afer inflaion, (4) he growh rae of he payou raio, and (5) he dividend yield: R = ( 1 + ( + P E, ) 1 + g RDiv, --------------------------- 1 1 + g PO, + Inc + Rinv. (8) (9) Figure 3 shows he annual income reurn (dividend yield) of U.S. equiy for 1926 2. The dividend yield dropped from 5.15 percen a he beginning of 1926 o only 1.1 percen a he end of 2. Figure 4 shows he year-end dividend-payou raio for 1926 2. On average, he dollar amoun of dividends afer inflaion grew 1.23 percen a year, while he dividend-payou raio decreased.51 percen a year. The dividend-payou raio was 46.68 percen a he beginning of 1926. I had decreased o 31.78 percen a he end of 2. The highes dividend-payou raio was recorded in 1932, and he lowes was he 31.78 percen recorded in 2. The U.S. equiy reurns from 1926 hrough 2 can be compued in he dividends mehod according o R = ( 1 + ) ( 1 + g P E ) 1 + g RDiv ---------------------- 1 1 + g PO + Inc + Rinv 1.7% = 1 + 1.23% ( 1 + % ) ( 1 + 1.25% ) ------------------------ 1 1.51% + % +.2%. The decomposiion of equiy reurn according o he dividends mehod is given in he fourh column of Figure 1. Mehod 5. Reurn on Book Equiy. Earnings can be broken ino he book value of equiy, BV, and reurn on he book value of equiy, ROE: EPS = BV (ROE ). (1) The growh rae of earnings can be calculaed from he combined growh raes of real book value, g RBV, and of ROE: 1 + g REPS, = (1 + g RBV, )(1 + g ROE, ). (11) January/February 23 91
Financial Analyss Journal Figure 3. Income Reurn (Dividend Yield), 1926 2 Dividend Yield (%) 9 8 7 6 5 4 3 2 1 25 3 35 4 45 5 55 6 65 7 75 8 85 9 95 Figure 4. Dividend-Payou Raio, Year-End 1926 2 Dividend Payou Raio (%) 14 12 1 8 6 4 2 25 3 35 4 45 5 55 6 65 7 75 8 85 9 95 Noe: The dividend-payou raio was 19.52 percen in December 1931 and 929.12 percen in December 1932. In his mehod, BV growh and ROE growh are subsiued for earnings growh in he equiy reurn decomposiion, as shown in he fifh column of Figure 1. Then, equiy s oal reurn in period can be compued by R = [ ( 1 + )( 1 g + )( 1 g P E, + ) 1 g RBV, ( + ROE, ) 1] + Inc + Rinv. (12) We esimaed ha he average growh rae of he book value afer inflaion was 1.46 percen for 1926 2. 11 The average ROE growh a year during he same ime period was calculaed o be.31 percen: R = [( 1 + ) ( 1 + g ) 1 g P E ( + )( 1 + g BV ROE ) 1] + Inc + Rinv 1.7% = [( 1 + % )( 1+ 1.25% )( 1+ 1.46% )( 1+.31% ) 1] + % +.2%. Mehod 6. GDP per Capia. Diermeier e al. proposed a framework o analyze he aggregae supply of financial asse reurns. Because we were ineresed only in he supply model of he equiy reurns in his sudy, we developed a slighly differen supply model based on he growh of economic produciviy. In his mehod, he marke reurn over he long run is decomposed ino (1) 92 23, AIMR
Long-Run Sock Reurns inflaion, (2) he real growh rae of overall economic produciviy (GDP per capia, g GDP/ POP), (3) he increase in he equiy marke relaive o overall economic produciviy (he increase in he facor share of equiies in he overall economy, g FS ), and (4) dividend yields. 12 This model is expressed by he following equaion: R = [ ( 1 + )( 1 g + ) 1 g GPD POP, ( + FS, ) 1] + Inc + Rinv. (13) Figure 5 shows he growh of he U.S. sock marke, GDP per capia, earnings, and dividends iniialized o uniy ($1.) a he end of 1925. The level of all four facors dropped significanly in he early 193s. For he whole period, GDP per capia slighly ougrew earnings and dividends, bu all four facors grew a approximaely he same rae. In oher words, overall economic produciviy increased slighly faser han corporae earnings or dividends over he pas 75 years. Alhough GDP per capia ougrew earnings and dividends, he overall sock marke price grew faser han GDP per capia. The primary reason is ha he marke P/E increased 2.54 imes during he same ime period. Average equiy marke reurn can be calculaed according o his model as follows: R = [( 1 + ) ( 1 + g ) 1 g GDP POP ( + ) 1] FS + Inc + Rinv 1.7% = [( 1 + % )( 1 + 2.4% )( 1+.96% ) 1] + % +.2%. We calculaed he average annual increase in he facor share of he equiy marke relaive o he overall economy o be.96 percen. The increase in his facor share is less han he annual increase of he P/E (1.25 percen) over he same ime period. This finding suggess ha he increase in he equiy marke share relaive o he overall economy can be fully aribued o he increase in is P/E. The decomposiion of hisorical equiy reurns by he GDP per capia model is given in he las column of Figure 1. Summary of Equiy Reurns and Componens. The decomposiion of he six models ino heir componens can be compared by looking a Figure 1. The differences among he five models arise from he differen componens ha represen he capial gain porion of he equiy reurns. This analysis produced several imporan findings. Firs, as Figure 5 shows, he growh in corporae earnings has been in line wih he growh of overall economic produciviy. Second, P/E increases accouned for only 1.25 pps of he 1.7 percen oal equiy reurn. Mos of he reurn has been aribuable o dividend paymens and nominal earnings growh (including inflaion and real earnings growh). Third, he increase in he relaive facor share of equiy can be fully aribued o he increase in P/E. Overall, economic produciviy ougrew boh corporae earnings and dividends from 1926 hrough 2. Fourh, despie he record earnings growh in he 199s, he dividend yield and he payou raio declined sharply, which renders dividends alone a poor measure for corporae profiabiliy and fuure earnings growh. Figure 5. Growh of $1 from he Beginning of 1926 hrough 2 1925 = $1. 1,. 1. 1. $91 $44 $36 $24 1..1 25 3 35 4 45 5 55 6 65 7 75 8 85 9 95 Capial Gain GDP/POP Earnings Dividends January/February 23 93
Financial Analyss Journal Long-Term Forecas of Equiy Reurns 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. Therefore, we believe invesors expecaions for 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. In his secion, we focus on wo of he supply-side models he earnings model and he dividends model (Mehods 3 and 4). 13 We sudied he componens of hese wo models by idenifying which componens are ied o he supply of equiy reurns and which componens are no. Then, we esimaed he long-erm, susainable reurn based on hisorical informaion abou hese supply componens. Model 3F. Forward-Looking Earnings. According o he earnings model (Equaion 6), he hisorical equiy reurn can be broken ino four componens he income reurn, inflaion, he growh in real EPS, and he growh in P/E. Only he firs hree of hese componens are hisorically supplied by companies. The growh in P/E reflecs invesors changing predicions of fuure earnings growh. Alhough we forecased ha he pas supply of corporae growh will coninue, we did no forecas any change in invesor predicions. Thus, he supply side of equiy reurn, SR, includes only inflaion, he growh in real EPS, and income reurn: 14 SR = [( 1 + )( 1 + g REPS, ) 1] + Inc + Rinv. (14) The long-erm supply of U.S. equiy reurns based on he earnings model is 9.37 percen, calculaed as follows: SR = [( 1 + ) ( 1 + g REPS ) 1] + Inc + Rinv 9.37% = [( 1 + % )( 1 + 1.75% ) 1] + % +.2%. The decomposiion according o Model 3F is compared wih ha of Mehod 3 (based on hisorical daa plus he esimaed equiy risk premium) in he firs wo columns of Figure 6. Figure 6. Hisorical vs. Curren Dividend-Yield Forecass Based on Earnings and Dividends Models Percen 11 1 9 8 7 6 5 4 3 g(p/e) 1.25 g(reps) 1.75 g(reps) 1.75 ERP 3.97 RRF 2.5 () 1.1 g(rdiv) 1.23 AG 2.28 M&M 1.46 () 1.1 g(rdiv) 1.23 FG 4.98 () 1.1 2 1 Model 3. Hisorical Equiy Reurns Model 3F. Using Hisorical Earnings Model 4F. Equiy wih Risk Premium (hisorical earnings) Model 4F. Using Curren Dividends Model 4F 2. Using Curren Dividends wih Addiional Growh Model 4F 2. Using Curren Dividends wih Forecased Earnings Growh Noes: Inc() is he dividend yield in year 2. FG is he real earnings growh rae, forecased o be 4.98 percen. Model 4F 2 correcs Model 4F as follows: add 1.46 pps for M&M consisency and add 2.24 pps for he addiional growh, AG, implied by he high curren marke P/E. 94 23, AIMR
Long-Run Sock Reurns The supply-side equiy risk premium, ERP, based on he earnings model is calculaed o be 3.97 pps: ERP ( 1 + SR) = ------------------------------------------------- 1 ( 1 + ) ( 1 + RRf ) 1 + 9.37% = ( ----------------------------------------------------------- 1 + % )( 1 + 2.5% ) 1 = 3.97%. The ERP is aken ino accoun in he hird column of Figure 6. Model 4F. Forward-Looking Dividends. The forward-looking dividends model is also referred o as he consan-dividend-growh model (or he Gordon model). In i, 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 dividends, and dividend yield. As is commonly done wih he consandividend-growh model, we used he curren dividend yield of 1.1 percen insead of he hisorical dividend yield of percen. This decision reduced he esimae of he supply of equiy reurns o 5.44 percen: SR = [( 1 + ) ( 1 + g RDiv ) 1] + Inc( ) + Rinv 5.54% = [( 1 + % )( 1+ 1.23% ) 1] + 1.1% +.2%, where Inc() is he dividend yield in year 2. The equiy risk premium was esimaed o be.24 pps: ( 1 + SR) ERP = ------------------------------------------------- 1 ( 1 + ) ( 1 + RRf ) = 1 + 5.54% ( ----------------------------------------------------------------- 1 + % ) + ( 1 + 2.5% ) 1 =.24%. Figure 6 allows a comparison of forecased equiy reurns including he equiy risk premium esimaes 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 supplyside equiy risk premium. Differences beween he Earnings Model and he Dividends Model. The earnings model (3F) and he dividends model (4F) differ in essenially wo ways. The differences relae o he low curren payou raio and he high curren P/E. These wo differences are reconciled in wha we will call Model 4F 2 shown in he wo righ-hand columns of Figure 6. Firs, o reflec growh in produciviy, he earnings model uses hisorical earnings growh whereas he dividend model uses hisorical dividend growh. Hisorical dividend growh underesimaes hisorical earnings growh, however, because of he decrease in he payou raio. Overall, he dividend growh underesimaed he increase in earnings produciviy by.51 pps a year for 1926 2. Today s low dividend yield also reflecs he curren payou raio, which is a a hisorical low of 31.8 percen (compared wih he hisorical average of 59.2 percen). Applying such a low rae o he fuure would mean ha even more earnings would be reained in he fuure han in he hisorical period sudied. Bu had more earnings been reained, he hisorical earnings growh would have been.95 pps a year higher, so (assuming he hisorical average dividend-payou raio) he curren yield of 1.1 percen would need o be adjused upward by.95 pps. By using he curren dividend-payou raio in he dividend model, Model 4F creaes wo errors, boh of which violae Miller and Modigliani heory. A company s dividend-payou raio affecs only he form in which shareholders receive heir reurns (i.e., dividends versus capial gains), no heir oal reurns. The curren low dividendpayou raio should no affec our forecas. Companies oday probably have such low payou raios o reduce he ax burden on heir invesors. Insead of paying dividends, many companies reinves earnings, buy back shares, or use he cash o purchase oher companies. 15 Therefore, he dividend growh model has o be upwardly adjused by 1.46 pps (.51 pp plus.95 pp) so as no o violae M&M heory. The second difference beween Model 3F and Model 4F is relaed o he fac ha he curren P/E (25.96) is much higher han he hisorical average (13.76). The curren yield (1.1 percen) is a a hisoric low because of he previously menioned low payou raio and because of he high P/E. Even assuming he hisorical average payou raio, he curren dividend yield would be much lower han is hisorical average (2.5 percen versus percen). This difference is geomerically esimaed o be 2.28 pps a year. In Figure 6, he addiional growh, AG, accouns for 2.28 pps of he reurn; in he las column, he forecased real earnings growh rae, FG, accouns for 4.98 pps. The high P/E could be caused by (1) mispricing, (2) a low required rae of reurn, and/or (3) a high expeced fuure earnings growh rae. Mispricing as a cause is eliminaed by our assumpion of marke efficiency, and a low required rae of reurn is eliminaed by our assumpion of a consan equiy risk premium hrough he pas and fuure periods ha we are rying o esimae. Thus, we inerpre he high P/E as he marke expecaion of higher earnings growh and he following equaion is he model for January/February 23 95
Financial Analyss Journal Model 4F 2, which reconciles he differences beween he earnings model and he dividends model: 16 SR = [( 1 + ) ( 1 + g RDiv )( 1 g PO ) 1] + Inc( ) + AY + AG + Rinv 9.67% = [( 1 + % )( 1 + 1.23% )( 1 +.51% ) 1] + 1.1% +.95% + 2.28% +.2%. To summarize, he earnings model and he dividends model have hree differences. The firs wo differences relae o he dividend-payou raio and are direc violaions of M&M. The hird difference resuls from he expecaion of higher-hanaverage earnings growh, which is prediced by he high curren P/E. Reconciling hese differences reconciles he earnings and dividends models. Geomeric vs. Arihmeic. The esimaed equiy reurn (9.37 percen) and equiy risk premium (3.97 pps) are geomeric averages. The arihmeic average, however, is ofen used in porfolio opimizaion. One way o conver he geomeric average ino an arihmeic average is o assume he reurns are independenly lognormally disribued over ime. Then, he arihmeic average, R A, and geomeric average, R G, have roughly he following relaionship: σ 2 R A = R G + -----, 2 (15) where σ 2 is he variance. The sandard deviaion of equiy reurns is 19.67 percen. Because 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 pps o he geomeric esimae of he equiy risk premium o conver he reurns ino arihmeic form, so R A = R G + 1.93 pps. The arihmeic average equiy risk premium hen becomes 5.9 pps for he earnings model. To summarize, he long-erm supply of equiy reurn is esimaed o be 9.37 percen (6.9 percen afer inflaion), condiional on he hisorical average risk-free rae. The supply-side equiy risk premium is esimaed o be 3.97 pps geomerically and 5.9 pps arihmeically. 17 Conclusions We adoped a supply-side approach o esimae he forward-looking, long-erm, susainable equiy reurn and equiy risk premium. We analyzed hisorical equiy reurns by decomposing reurns ino facors commonly used o describe he aggregae equiy marke and overall economic produciviy inflaion, earnings, dividends, P/E, he dividendpayou raio, BV, ROE, and GDP per capia. We examined each facor and is relaionship o he long-erm supply-side framework. We used hisorical informaion in our supply-side models o forecas he equiy risk premium. A complee abulaion of all he numbers from all models and mehods is presened in Appendix A. Conrary o several recen sudies on he equiy risk premium declaring he forward-looking premium o be close o zero or negaive, we found Appendix A. Summary Tabulaions for Forecased Equiy Reurn Mehod/Model Sum Inflaion Real Risk-Free Rae Equiy Risk Premium Real Capial Gain g(real EPS) g(real Div) g(payou Raio) A. Hisorical Mehod 1 1.7 2.5 5.24 Mehod 2 1.7 3.2 Mehod 3 1.7 1.75 Mehod 4 1.7 1.23.51 Mehod 5 1.7 Mehod 6 1.7 B. Forecas wih hisorical dividend yield Model 3F 9.37 1.75 Model 3F (ERP) 9.37 2.5 3.97 C. Forecas wih curren dividend yield Model 4F 5.44 1.23 Model 4F (ERP) 5.44 2.5.24 Model 4F 2 9.37 1.23.51 Model 4F 2 (FG) 9.37 a 2 dividend yield. b Assuming he hisorical average dividend-payou raio, he 2 dividend yield is adjused up.95 pps. 96 23, AIMR
Long-Run Sock Reurns he long-erm supply of he equiy risk premium o be only slighly lower han he sraigh hisorical esimae. We esimaed he equiy risk premium o be 3.97 pps in geomeric erms and 5.9 pps on an arihmeic basis. These esimaes are abou 1.25 pps lower han he hisorical esimaes. The differences beween our esimaes and he ones provided by several oher recen sudies resul principally from he inappropriae assumpions hose auhors used, which violae he M&M heorem. Also, our models inerpre he curren high P/E 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 public corporaions (i.e., earnings) and overall economic produciviy (GDP per capia). The implicaion of an esimaed equiy risk premium being far closer o he hisorical premium han zero or negaive is ha socks are expeced o ouperform bonds over he long run. For long-erm invesors, such as pension funds and individuals saving for reiremen, socks should coninue o be a favored asse class in a diversified porfolio. Because our esimae of he equiy risk premium is lower han hisorical performance, however, some invesors should lower heir equiy allocaions and/or increase heir savings rae o mee fuure liabiliies. Noes 1. In our sudy, we defined 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. [Some oher sudies, including Ibboson and Sinquefield (1976a, 1976b) used shor-erm U.S. T-bills as he risk-free rae.] We did all of our analysis in geomeric form, hen convered o arihmeic daa a he end, so he esimae is expressed in boh arihmeic and geomeric forms. 2. See also Mehra (23). 3. Comparing esimaes from one sudy wih anoher is someimes difficul because of changing poins of reference. The equiy risk premium esimae can be significanly differen simply because he auhors used arihmeic versus geomeric reurns, a long-erm risk-free rae versus a shor-erm risk-free rae, bond income reurn (yield) versus bond oal reurn, or long-erm sraegic forecasing versus shor-erm marke-iming esimaes. We provide a deailed discussion of arihmeic versus geomeric reurns in he secion The Long-Term Forecas. 4. Welch s survey repored a 7 pp equiy risk premium measured as he arihmeic difference beween equiy and T-bill reurns. To make an apples-o-apples comparison, we convered he 7 pp number ino a geomeric equiy risk premium relaive o he long-erm U.S. governmen bond income reurn, which produced an esimae of almos 4 pps. 5. For furher discussion of approaches o esimaing he equiy risk premium, see he presenaions and discussions a www.aimrpubs.org/ap/home.hml from AIMR s Equiy Risk Premium Forum. 6. Each per share quaniy is per share of he S&P 5 porfolio. Hereafer, we will merely refer o each facor wihou always menioning per share for example, dividends insead of dividends per share. 7. Many heoreical models sugges ha he equiy risk premium is dynamic over ime. Recen empirical sudies (e.g., Goyal and Welch 21; Ang and Bekaer 21) found no evidence, however, of long-horizon reurn predicabiliy by using eiher earnings or dividend yields. Therefore, insead g(bv) g(roe) g(p/e) g(real GDP/ POP) g(fs-gdp/pop) Income Reurn Reinvesmen + Ineracion Addiional Growh Forecased Earnings Growh.33.32 1.25.34 1.25.35 1.25.31 1.25.31 2.4.96.32.26.27 1.1 a.3.7 2.5 b.21 2.28 1.1 a.21 4.98 January/February 23 97
Financial Analyss Journal of rying o build a model for a dynamic equiy risk premium, we assumed ha he long-erm equiy risk premium is consan. This assumpion provided a benchmark for analysis and discussion. 8. We updaed he series wih daa from Sandard and Poor s o include he year 2. 9. Appendix A summarizes all he abulaions we discuss. 1. The average P/E was calculaed by reversing he average earnings-o-price raio for 1926 2. 11. Book values were calculaed from he book-o-marke raios repored in Vuoleneenaho (2). The aggregae book-omarke raio was 2. in 1928 and 4.1 in 1999. We used he growh rae in book value calculaed for 1928 1999 as he proxy for he growh rae for 1926 2. The average ROE growh rae was calculaed from he derived book value and he earnings daa. 12. Insead of assuming a consan equiy facor share, we examined he hisorical growh rae of he equiy facor share relaive o he overall growh of he economy. 13. We did no use Mehods 1, 2, and 5 in forecasing because he forecass of Mehods 1 and 2 would be idenical o he hisorical esimae repored in he previous secion and because he forecas of Mehod 5 would require more complee BV and ROE daa han we currenly have available. We did use Mehod 6 o forecas fuure sock reurns bu found he resuls o be very similar o hose for he earnings model; herefore, we do no repor he resuls here. 14. This model uses hisorical income reurn as an inpu for reasons ha are discussed in he secion Differences beween he Earnings Model and he Dividends Model. 15. The curren ax code provides incenives for companies o disribue cash hrough share repurchases raher han hrough dividends. Green and Hollifield (21) found ha he ax savings hrough repurchases are on he order of 4 5 percen of he axes ha invesors would have paid if dividends were disribued. 16. Conrary o efficien marke models, Shiller (2) and Campbell and Shiller argued ha he P/E appears o forecas fuure sock price change. 17. We could also use he GDP per capia model o esimae he long-erm equiy risk premium. This model implies longrun sock reurns should be in line wih he produciviy of he overall economy. The equiy risk premium esimaed by using he GDP per capia model would be slighly higher han he ERP esimae from he earnings model because GDP per capia grew slighly faser han corporae earnings in he sudy period. A similar approach can be found in Diermeier e al., who proposed using he growh rae of he overall economy as a proxy for he growh rae in aggregae wealh in he long run. References Ang, Andrew, and Geer Bekaer. 21. Sock Reurn Predicabiliy: Is I There? Naional Bureau of Economic Research (NBER) Working Paper 827 (April). Arno, Rober D., and Clifford S. Asness. 23. Surprise! Higher Dividends = Higher Earnings Growh. 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Homewood, IL: Irwin. Goyal, Ami, and Ivo Welch. 21. Predicing he Equiy Premium wih Dividend Raios. Working paper. Yale School of Managemen and UCLA. Graham, John R., and Campbell R. Harvey. 21. Expecaions of Equiy Risk Premia, Volailiy and Asymmery from a Corporae Finance Perspecive. Working paper, Fuqua School of Business, Duke Universiy (Augus). Green, Richard C., and Buron Hollifield. 21. The Personal- Tax Advanages of Equiy. Working paper, Carnegie Mellon Universiy (January). Ibboson Associaes. 21. Socks, Bonds, Bills, and Inflaion: 21 Yearbook. Chicago, IL: Ibboson Associaes. Ibboson, Roger G., and Rex A. Sinquefield. 1976a. Socks, Bonds, Bills, and Inflaion: Year-by-Year Hisorical Reurns (1926 1974). Journal of Business, vol. 49, no. 1 (January):11 47.. 1976b. Socks, Bonds, Bills, and Inflaion: Simulaions of he Fuure (1976 2). Journal of Business, vol. 49, no. 3 (July):313 338. Ibboson, Roger G., Jeffrey J. Diermeier, and Laurance B. Siegel. 1984. The Demand for Capial Marke Reurns: A New Equilibrium Theory. Financial Analyss Journal, vol. 4, no. 1 (January/February):22 33. Mehra, Rajnish. 23. The Equiy Premium: Why Is I a Puzzle? Financial Analyss Journal, vol. 59, no. 1 (January/ February):54 69. Mehra, Rajnish, and Edward Presco. 1985. The Equiy Premium: A Puzzle. Journal of Moneary Economics, vol. 15, no. 2 (March):145 161. Miller, Meron, and Franco Modigliani. 1961. Dividend Policy, Growh and he Valuaion of Shares. Journal of Business, vol. 34, no. 4 (Ocober):411 433. Shiller, Rober J. 2. Irraional Exuberance. Princeon, NJ: Princeon Universiy Press. Siegel, Jeremy J. 1999. The Shrinking Equiy Risk Premium. Journal of Porfolio Managemen, vol. 26, no. 1 (Fall):1 17. Vuoleneenaho, Tuomo. 2. Undersanding he Aggregae Book-o-Marke Raio and Is Implicaions o Curren Equiy- Premium Expecaions. Working paper, Harvard Universiy. Welch, Ivo. 2. Views of Financial Economiss on he Equiy Premium and Oher Issues. 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