A Review of the Methodology of Forecasting Long-term Equity Returns

A Review of he Mehodology of Forecasing Long-erm Equiy Reurns Richard Fizherber Presened o he Insiue of Acuaries of Ausralia Biennial Convenion 23-26 Sepember 2007 Absrac There are wo main approaches o forecasing he long-erm reurn from equiies as an asse class. The firs is o assume a premium over ineres raes or bond reurns, jusified by he risk-averse behaviour of porfolio invesors. The second approach is o projec dividend income assuming a link wih inflaion and/or pariy wih gross domesic profi. Excep for GDP pariy, hese mehods are all suppored, superficially, by hisorical daa. However he causal jusificaions for eiher he risk premium or he inflaion link are dubious - which reduces he saus of hese assumpions from laws of naure o hisorical regulariies upon whose fuure we can only speculae. In a business environmen in which hisorical cos accouning prevails, reurn-on-shareholders' equiy is he key variable which deermines he underlying long-erm reurn from equiy porfolio invesmen which is moneary and no real in naure. Adjusmens are required when hisorical cos accouning is no sricly applied. Key words: Equiy premium, reurn on shareholders' equiy, inflaion, long-erm equiy reurn forecasing

Execuive Summary 1 Inroducion The inroducion idenifies he main mehods used for projecing long-erm equiy reurns and summarises heir main underlying assumpions. 2 Crieria deermining model validiy Here we discuss crieria ha have been suggesed for validaing hese ypes of models. This secion briefly reviews he philosophical debae abou regulariies versus laws of naure and he crucial role played by causaliy. In predicing he fuure, causal laws offer a much more reliable basis han hisorical regulariies. 3 The equiy premium - law or regulariy? The causal link beween risk-averse invesor behaviour and he hisorical equiy premium has no been esablished, leaving he equiy premium as a regulariy. Neverheless i is ofen simply assumed ha an equiy premium exiss as a law of naure. 4 Dividend growh raes. Very long-erm "buy-and-hold" reurns can be esimaed from he curren dividend yield and an esimaed dividend growh rae. There are wo main mehods of esimaing fuure dividend growh: inflaion and GDP pariy. These mehods ake no accoun of he effec, if any, of reained profis. In his respec, he saisical evidence is ambiguous. 5 The naure of company profis: real income or moneary income? The naure (ie real or moneary) of company profis depends on he prevailing accouning sysem. When hisorical cos accouning is applied, company earnings and dividends are moneary and no real in naure. Consequenly he long-erm growh of earnings and dividends is caused by reained profis. Adjusmens are required when hisorical cos accouning is no sricly applied. Wih his excepion, any hisorical link beween earnings and/or dividends wih inflaion is a regulariy, no a law of naure. 6 The shareholders' equiy framework. Saring wih he "accouning equaion" we develop he equaions required for esimaing long-erm equiy asse class reurns when hisorical cos accouning prevails. The key variables are reurn on shareholders' equiy and overall price/book raios. Price/book raios give he same answers as he more normal price/earnings raios under he shareholders' equiy esimaion framework. 2

7 Illusraive calculaions This secion illusraes he use of he shareholders' equiy framework by esimaing 10 and 20 year raes of reurn for Ausralian equiies under wo scenarios - a coninuaion of curren reurn on shareholders' equiy and a reversion o hisorical norms. 8 The relaive meris of price/book and price/earnings raios There is a link beween price/book raios, price/earnings raios and reurn on shareholders' equiy. If we know any wo of hese variables, he hird is also known. 9 Discussion Iniial condiions, he uni of measuremen used in company accouning and fuure reurn on shareholders' equiy largely deermine he naure (ie real or moneary) and size of long-erm equiy asse class reurns. Because successive changes in marke index levels are no independen, here are serious problems applying a mean-variance framework o long-erm reurns. The "risk" averse behaviour of porfolio invesors, inflaion and real economic growh generally have lile or no direc influence on long-erm equiy reurns. 3

1 Inroducion. This paper reviews he mehodology of esimaing long-erm equiy reurns and he soundness of commonly used underlying assumpions. When mahemaical models are used, we are concerned wih boh he form of he model as well as he numerical values of key parameers. For a mehodology o be reliable, he underlying assumpions need o be appropriae before we can selec numerical values for key variables. We herefore begin by idenifying he main assumpions on which mehods of projecing long-erm equiy reurns are based and he crieria ha should be used o discriminae beween reliable and unreliable mehodology. As far as reliabiliy is concerned causaion is crucial. We hen consider he main mehods of projecing equiy reurns in he ligh of his more general discussion of how o discriminae beween compeing mehods. Here we assess he causal impac of volailiy, inflaion, economic pariy and inernal corporae reurns on longerm equiy porfolio reurns. Making reliable ex-ane esimaes of long-erm reurns from equiies as an asse class has long been an issue of ineres o he acuarial profession. One of he earlies Ausralian papers was Owen (1962). Based on an examinaion of he hisorical record over he period 1882-1960 and he assumpion ha he fuure would be like he pas Owen esimaed he fuure long-erm reurn for Ausralian equiies would lie beween 9.5 and 13.5% per annum. "There is lile evidence ha he yield paern exhibied over he las 80 years will no coninue and i seems appropriae o assume ha for he long-erm invesor he expeced fuure yield [ie geomeric mean oal reurn per annum] from ordinary shares will be 11.5% ± 2%." Based on pre-1980 figures calculaed by he ASX Saisician (1996), he ASX Accumulaion index has risen from 165.9 o 39,070 over he 46.5 years since he end dae of Owen's calculaions, or 12.5% per annum. Wih he benefi of hindsigh, i is remarkable how accurae Owen's forecas proved o be in he half-cenury since given he poor qualiy, by oday's sandards, of he daa a his disposal. Graham (1973) used reurn on shareholders' equiy o esimae fuure dividend income and capial growh from US index porfolios in a way ha was closely relaed o he framework oulined by Hemsed (1962). Under his approach dividends grow a a rae deermined by reurn on shareholders' equiy and he proporion of profis no disribued in dividends. Reurn on shareholders' equiy is rarely menioned in discussions of prospecive long-erm equiy reurns. Perhaps he approach never became popular because i reas company profis as moneary income and ignores inflaion and real economic growh. Wilkie (1986) proposed a comprehensive sochasic invesmen model involving bonds and cash as well as equiies. The module dealing wih equiies was based on a dividend sream ha mached price inflaion, subjec o lags and random flucuaions. This was combined wih a model of dividend yields which flucuaed in a saionary manner. Sripped of is sochasic feaures, he equiy module of his model herefore assumed a dividend sream which grew wih inflaion in he long-erm. Wilkie argued a he ime (p343): "I is clear ha dividends, which are measured in money erms, ough, oher hings being equal, o be relaed o he general level of money prices elsewhere in he economy. Boh are measured by he same numeraire of curren pounds. I is, herefore, appropriae o relae company dividends direcly in some way o he index 4

being used as a measure of general prices, which for my purposes is he Reail Prices Index, or is predecessors." Wih a saionary dividend yield, i follows ha he long-erm reurn from a porfolio conforming o he Wilkie model will be approximaely equal o he iniial dividend yield plus he fuure average rae of inflaion. (I is possible o disable he inflaion maching feaure of he sandard Wilkie model, bu his would eliminae one of is key feaures.) In he broader financial communiy, i has become common o esimae "expeced" oal reurn as he sum of a fixed ineres reurn and an equiy "risk" premium. In he sandard finance ex by Brealey and Myers (2003), we read (in he conex of calculaing he cos of capial on page 157): Remember ha [he currenly expeced rae of reurn on he marke porfolio] is he sum of he risk-free rae.. and a premium for risk. Anoher popular approach ouside he acuarial profession is o assume ha dividends grow wih Gross Domesic Produc based on general economic reasoning wihou making any assumpions abou fuure marke prices. For example, Rier (2002, p163) argues ha: "For predicing fuure dividend growh raes, all one has o do is o assume an economywide growh rae and assume ha he raio of labor income o capial income is consan." If we assume ha dividends grow indefiniely wih GDP and/or inflaion, hen we can find he rae of reurn ha equaes he presen value of fuure dividends wih curren marke prices. Thus we see wo main approaches o forecasing he long-erm reurn from equiies as an asse class: (a) (b) he firs approach is o use differen versions of a oal reurn model, ofen based on hisorical sock price and dividend daa. Such models can eiher relae direcly o oal reurn (ie income and capial appreciaion), hisorical values of a premium over bond reurns or hisorical values of a "real" reurn (ie oal reurn adjused o exclude inflaion). he second approach is o projec dividend income assuming growh from inflaion, pariy wih Gross Domesic Profi or growh from reained profis. Where oal reurn is esimaed from an assumed dividend growh rae and he curren dividend yield, his is someimes described as a dividend discoun model or a dividend growh model. Dividend growh models are normally deerminisic in naure, alhough he shares module of he Wilkie model could be regarded as a sochasic dividend growh model. The acuarial profession's own early educaional maerial endorses boh he equiy premium approach and he idea ha a dividend sream should grow by more han he rae of price inflaion, represening real growh in companies' profis alhough his source of growh is no specified. For example in he Faculy and Insiue of Acuaries (2006, Uni 10 page 4) we read: "The iniial running [dividend] yield on ordinary shares is low bu dividends should increase wih inflaion and real growh in a company's earnings. 5

The expeced overall fuure reurn on ordinary shares ough o be higher han for mos oher classes of securiy o compensae for he greaer risk of defaul and for he variabiliy of reurns." From his illusraive (bu by no means exhausive) descripion of examples of forecasing, or modelling, equiy reurns we can classify hese approaches according o heir underlying assumpions and mehods of implemenaion as shown in Table 1. However, we need o recognise some variaions on hese four basic mehods. For example, he earnings growh model described by Yakoubov e al (1999) could be regarded as a sochasic dividend growh model because here is an underlying reliance on he argumen ha earnings (and consequenly dividends) move wih inflaion even hough i recognises significan variaions in payou raios. Table 1 Mehods of esimaing fuure long-erm equiy reurns Approach Underlying assumpion Mehod of implemenaion Hisorical Consan real dividend sream GDP pariy Reurn on shareholders' equiy Equiy premium, rae of reurn, or real rae of reurn are independen random variables wih consan mean and variance. Company earnings and dividends are real income and should move broadly in line wih a general price index. Company earnings and dividends are a roughly consan proporion of GDP and should grow wih boh inflaion and real economic growh. Company profis are paid in dividends or reained as he source of corporae growh. Inflaion and real economic growh are no relevan. Esimae parameers from hisorical daa and hen assume hey will apply in fuure adding in an assumed risk free reurn or rae of inflaion as required Prospecive reurn is equal o he curren dividend yield plus he fuure rae of inflaion Prospecive reurn is equal o he curren dividend yield plus he rae of growh of nominal GDP Prospecive reurn is equal o he curren dividend yield plus he reained proporion of fuure reurn on shareholders' equiy A few years' ago, Barker (2003) addressed he quesion of forecasing he long-erm reurn ha invesors could expec from Ausralian equiies. Using mos of hese mehods, he esimaed a very long-erm "underlying rae" of 9% per annum and a somewha lower 10 year reurn from invesmens made a he ASX All Ordinaries index level of 3300 poins in March 2002. A he ime, Barker was able o reconcile he conflicing answers arising from differen approaches. Bu, wha do we do when differen mehods produce wildly differen answers? Forward esimaion of he equiy premium, a problem ofen relaed o forecasing equiy reurns, has recenly hrown up a wide divergence of opinion in he USA wih large discrepancies emerging from differen mehodology. In an exensive review of research lieraure on he equiy premium, Derrig and Orr (2004) noe ex-ane esimaes which "vary widely from abou [minus] 1% o abou 9% [per annum],... ". 6

These differences can someimes be aribued o differen values for key variables such as assumed raes of fuure inflaion or ineres raes. Such differences of opinion on fuure parameer values are commonplace. However we are firs concerned wih fundamenal differences in mehodology from which large divergences in opinion can emerge. For example, in regard o he problem of forward esimaion of he equiy premium, Rier (2002) provides an example of he exen o which divergen opinion can arise from differen mehods: "Many exbooks encourage sudens o use he hisorical arihmeic average equiy risk premium of 9% [per annum] for compuing he cos of equiy capial.... The numbers I am abou o compue using forward looking esimaes sugges ha 1% is a more defensible number." Such discrepancies lead naurally o challenging quesions. Does i remain valid o apply he hisorical approach using he equiy premium if he resuling numbers do no make sense when compared wih a dividend discoun model? Or is here somehing seriously flawed wih he mehodology of using hisorically based esimaes a any ime? Was Owen (1962) jus lucky, or was here some hidden and valid assumpion ha made his esimae reliable? Is i valid o use he hisorical average risk premium as an esimae of he fuure risk premium or should we use a dividend discoun model o esimae oal reurn and deduc inflaion and/or bond raes o esimae he fuure equiy risk premium? If we are ineresed in oal reurn, why use a dividend discoun model o esimae oal reurn, deduc a riskless rae of reurn o esimae he equiy premium and hen add back a riskless rae of reurn o esimae oal reurn? I is relaively simple o creae a sochasic model using eiher yearly reurns or he annual equiy premium as a series of independen random variables. Including sochasic feaures in dividend projecion models is more complicaed. A he very leas such models require a sochasic model of he dividend yield as well as any random feaures ha may be buil ino he basic dividend projecion. Also, an argumen can be advanced for using earnings raher han dividends in such models as suggesed by Yakoubov e al (1999): ".. [P/E] raios are widely acceped as a beer indicaor of equiy valuaion han dividend yields. Earnings growh as a ime series is easier o model han dividend growh, as earnings growh is more reacive o changes in he economy whils dividend growh is smoohed by company direcors." The mehods summarised in Table 1 have quie differen underlying assumpions. Consequenly, if one mehod is universally valid, hen presumably oher mehods are no. Alernaively one se of assumpions may be more suiable for shor-erm problems and a differen se of assumpions for longer-erm quesions. For example a random walk model may be suiable for shor-erm modelling of share reurns, bu for evaluaing adequae reserves for long-erm guaranees, he random walk may be quie unsuiable. (See, for example, Mauriy Guaranees Working Pary, 1980.) How do we decide which models are valid o use in a paricular siuaion, given a se of models wih compleely differen, and poenially incompaible, underlying assumpions? The relaive meris of sochasic and deerminisic models are discussed by Whielock-Jones (2003). I is naurally difficul o compare models of hese wo differen ypes and here 7

seems o be a naural endency o assume ha sochasic models provide more informaion han deerminisic ones. "Sochasic models are quie differen from deerminisic models and can provide much more useful informaion... There are many quesions ha can be asked wih a sochasic model bu no wih a deerminisic model." However, he same assumpions ofen underlie boh deerminisic and sochasic models, emerging as fixed parameers in deerminisic models and mean parameers of key random variables in sochasic models. If any of he implici assumpions are invalid, a sochasic model will no necessarily be any beer han a deerminisic one and vice-versa. For example, he use of hisorical equiy reurn daa as a basis for a simple mean-variance model for equiy reurns will generally rely on he saed, bu someimes implici, assumpion ha raes of reurn are independen and idenically disribued (IID) random variables wih consan mean and variance. If eiher he independence or consan mean assumpions are invalid, he sochasic model is clearly invalid. However a deerminisic model which uses an esimae of expeced fuure raes of reurn based on he hisorical arihmeic average rae of reurn will no be valid eiher. When we are dealing wih fuure long-erm reurns he invalidiy of hese assumpions canno be dismissed lighly because he effec is likely o be cumulaive. In some cases, here may be some feaure of a sochasic model which makes i inferior o, say, a long-erm deerminisic approach. Suppose annual raes of reurn depend on some oher facor - such as book-marke raios. Raes of reurn in successive years are hen neiher independen nor idenically disribued. When book-marke raios are unusually high or low a he sar dae, a model which ignores his facor will produce unreliable resuls. In such circumsances, a mean-variance sochasic model relying on he IID assumpion could be less valid han a simple deerminisic model which allows for mean reversion in book-marke raios. 8

2 Crieria deermining model validiy Alhough here is a vas lieraure in he hisory and philosophy of science dealing wih he validiy of scienific heories, here has no been much aenion o he idenificaion of crieria for disinguishing beween valid and invalid mehods of modelling invesmen reurns wihin he acuarial profession. In one of he few papers ha ouch his subjec, Huber and Verrall (1999) argue he need for an underlying heory in "acuarial economic models" as disinc from "purely daa-based mehods of developing economic models". In a sandard acuarial ex, Whielock-Jones (2003, p155) discusses he acuarial modelling process and emphasises he imporance of ongoing comparison of oupu and model forecass: "The feedback componen of he modelling process is crucial. We mus subjec all our models o regular and horough evaluaion by comparing model oupu wih realworld experience." A similar commen was made by Hardy (1996, p963) in her wrien conribuion o he discussion of a paper ha was criical of financial economics: "[The auhor] misundersands he modelling process. He is criical of models where he assumpions used o derive resuls do no, in fac, hold; bu his is exacly how much modelling is conduced; we make simplifying assumpions o consruc a model; we ge resuls; we es he resuls agains he real world o assess wheher he underlying simplificaion has invalidaed he resuls. We ry o develop beer models which do no require he srong assumpions which we sared wih." Wih invesmen reurns, paricularly equiies, large variaions would make i exremely difficul, if no impossible, o discover ha a model was invalid wihou many years of daa. Consequenly, while his feedback approach may be adequae for models of (say) he incidence of moor vehicle damage, he feedback monioring process is unlikely o be adequae for models of invesmen reurns because he answers will become known oo lae. A second objecion is ha he "feedback" mechanism adaps models o regulariies, i is no normally concerned wih esablishing laws of naure by independen analysis of causaion. As we shall see, he quesion of causaion and he disincion beween regulariies and laws of naure is a key deerminan of validiy wih models ha ry o predic fuure long-erm equiy reurns. The mehods of esimaing fuure reurns from equiies described in Table 1 involve some sor of economeric model alhough he "accouning equaion" is iniially more imporan in he case of he reurn on shareholders' equiy approach. Huber (1997, p186) suggesed ha: "The main crieria by which economeric models should be evaluaed include wheher he model is consisen wih prior economic heory, saisfies various goodness-of-fi ess, is parsimonious and has consan parameers hisorically." Huber laer acknowledged ha consisency wih prior economic heory was "no decisive". However, consisency wih heory and saisfying goodness-of-fi ess are no necessarily valid crieria anyway for wo reasons. Firs, as a sandard ex such as Chalmers (1999) poins ou, how we inerpre daa is heavily influenced by wha we already accep. The second issue, paricularly relevan wih saisical ess, is ha mehods of measuremen ofen involve underlying assumpions which are crucial. Failure o pass a saisical es could be due o he inappropriaeness of assumpions underlying he es as much as feaures of he daa. For example, many ess of sock-marke heories such as he inverse relaionship beween price/earnings raios and subsequen relaive 9

sock reurns (he "low p/e effec") involve saisical ess which implicily assume, as a null hypohesis, ha we are dealing a sequence of IID random variables and, in his case, ha here is no relaionship beween price/earnings raios and raes of reurn. Failure of he null hypohesis could be due o failure of he IID assumpion raher han he presence of a low p/e effec. Worse sill, we may accep he null hypohesis because a low p/e effec and non-iid reurns creae compensaing errors in our es. Even when saisical ess indicae he exisence, or absence, of paricular feaures in hisorical daa, he job is only parly done. Wih acuarial models, such as hose used o esimae invesmen reurns, he real issue is no wheher a model fis he pas, bu wheher i will fi he fuure as well. For example, hisorical daa demonsraes boh an equiy premium and long-erm reurns ha exceed inflaion. Is i valid o assume ha fuure long-erm equiy reurns will exceed bond reurns and inflaion? Graham (1973) was possibly ahead of his ime when he argued ha i was no appropriae o assume a link beween inflaion and fuure sock reurns unless i was possible o esablish a direc link (which could now be inerpreed as causaliy) beween inflaion and earnings (and in consequence share prices): "The reader will objec ha in he end our calculaions make no allowance for an increase in common-sock earnings and values from our projeced 3% annual inflaion. Our jusificaion is he absence of any sign ha he inflaion of he pas has had any direc effec on per-share earnings." This specific quesion of a link beween inflaion and equiy reurns is discussed in more deail in secion 5. In a way, we are ineresed in heories esed agains he hisorical record as he basis for forecasing he fuure. In science here is a similar problem of esablishing, hrough experimen and observaion, wha will happen in ou-of-sample periods. Some philosophers of science (see, for example Chalmers, 1999) argue ha idenifying causaion is a necessary condiion for esablishing a sound scienific heory. Hisorical daa can ofen be used o sugges scienific hypoheses o explain phenomena such as he equiy premium; bu unil a saisfacory explanaion for is cause has been esablished, he phenomenon remains a regulariy raher han a law of naure. A phenomenon ha is a law of naure is a naural oucome of, in his case, he financial sysem. Consequenly a law of naure idenifies a endency which will remain presen in he fuure. A regulariy is a phenomenon ha we have observed, perhaps on numerous occasions, where here is nohing bu hisorical correlaion o jusify ha i will coninue. Chalmers argues (pp291-220) ha causes and laws are inimaely linked and i is laws (and no regulariies) ha can be relied upon o apply in ou-of-sample periods: "Once he assumpion is made ha eniies in he world are wha hey are by virue of he powers and capaciies hey possess, and I claim ha ha assumpion is implici in scienific pracice as well as everyday life, hen he laws describing hose powers and capaciies, idenified in experimenal siuaions, can be presumed o apply ouside of hose siuaions oo." Therefore, if we are o adop a mehod of forecasing which assumes a link beween equiy reurns and inflaion, we firs need o esablish a causal link. Unforunaely, conducing experimens o esablish laws of naure is no possible in capial markes in he same way ha experimenaion can be conduced in (say) physics. In capial markes we do no have he luxury of holding all bu one variable consan while we examine he effec of changing he one variable in which we ineresed, nor do we have he faciliy o repea hisory wih (say) a 10

differen level of inflaion. The bes we can hope for is hisorical daa where one poenial causal facor (eg inflaion) is absen or abnormally high and oher causal facors (eg invesor behaviour, real GDP growh) are sable. Even hen, we are limied o confirmaion of a regulariy, no a cause. Observing ha sock reurns have exceeded inflaion in he pas, even if he saisical evidence passes he mos exhausive goodness-of-fi ess, only esablishes a link beween inflaion and sock prices as a regulariy - no a law of naure. The argumen ha company earnings and dividends are real raher han moneary in naure, if i is rue, idenifies he cause necessary o link long-erm sock reurns and inflaion as a law of naure. We herefore need o carefully clarify he real or moneary naure of company profis. Such an analysis needs o be independen of hisorical ime-series daa because sandard analysis of such daa usually makes assumpions (eg saisical independence) ha may be relevan o he way he daa is inerpreed. Similarly hisorical sudies sugges an equiy premium as a saisical regulariy. If we can esablish ha he equiy premium is caused by "risk-averse" behaviour of invesors, hen he equiy premium becomes a law of naure. There is a grea deal a sake in he "equiy premium puzzle" posed by Mehra and Presco (1985), because i challenges he causal naure of he equiy premium and he onological quesion as o wheher he equiy premium really exiss (ie as a law of naure) is far from resolved. This is discussed in more deail in secion 3. I is no possible, here, o adequaely cover he general philosophical argumen abou causalism and he reader is referred o Chalmers (1999) as a saring poin. A more subsanial discussion appears in "Causaion and laws of naure" edied by Sankey (1999). A a meeing of he UK Insiue o debae he role of financial economics in acuarial invesmen work 15 years ago, Pemberon (1993, p408) said: "A new orhodoxy wihin scienific mehodology is causalism, which rejecs Humean aemps o reduce causes o regulariies, and insis [sic] ha causes be aken seriously. We need causes and no jus correlaions. This debae is no well known amongs acuaries - many of he ideas seem arcane o members of our profession " The discussion which follows relies on he proposiion ha a model used o generae a reliable esimae of long-erm fuure raes of reurn from equiies mus esablish he cause(s) of any of is essenial feaures. While hisorical daa can be used o sugges suiable models, backesing hisorical daa wihou independenly esablishing causaion is inadequae. (Perhaps we should no profess o be able o "make financial sense of he fuure" unil he causes of relevan hisorical phenomena are idenified.) We may, for example, noice ha hisorical long-erm raes of inflaion, increases in dividends and capial appreciaion in sock prices have all averaged 4-6% per annum. Such an observaion naurally suggess a possible link beween dividend growh and inflaion bu his evidence is only circumsanial. If dividends have hisorically grown a 4-6% per annum for oher reasons, hey may coninue o do so, irrespecive of wha happens o inflaion in fuure. If, however, we can esablish a causal link beween inflaion and dividend growh, hen we have every reason o believe ha 10% annual inflaion will be accompanied by a similar growh in dividends and we can confidenly build such an assumpion ino a forecasing model or invesmen policy. Similarly, if risk averse behaviour causes equiies o be priced a levels which ensure a premium over bond reurns, hen we have every reason o believe ha such a premium will coninue unless here is a change in invesor behaviour. However, if he hisorical equiy 11

premium is due o oher facors, hen hese facors - and no invesor behaviour - will deermine he fuure performance of equiies relaive o cash and/or bonds. Wheher he equiy premium is due o risk-aversion and/or wheher here is a direc link beween inflaion and sock reurns are herefore quesions of he umos imporance when i comes o producing reliable long-erm forecass of fuure equiy reurns. The quesion of he inflaion link becomes even more imporan where equiies are held as inflaion maching asses in defined benefi pension funds. If here is a causal link hen errors in forecasing fuure inflaion on one side of he balance shee will be compensaed by a corresponding error on he oher side. If here is no causal link hen i is quie speculaive o inves in equiies as a long-erm hedge agains inflaion because his sraegy relies on hisorical regulariies. 12

3 The equiy premium: law or regulariy? The equiy risk premium (broadly speaking, he exen o which socks ouperform bonds) has araced a considerable amoun of research ineres since he appearance of he well-known paper by Mehra and Presco (1985) eniled The equiy premium: a puzzle. This paper challenged he generally acceped jusificaion for he exisence of he equiy premium ha i was caused by risk averse invesor behaviour - on he grounds ha he hisorical level of he equiy premium was oo large o be explained by risk aversion. In a rerospecive review of research published since heir 1985 paper, Mehra and Presco (2003, p911) refleced on heir formulaion of wha has become known as he equiy premium puzzle: "... sandard heory is consisen wih our noion of risk ha, on average, socks should earn more han bonds. The puzzle arises from he fac ha he quaniaive predicions of he heory are an order of magniude differen from wha has been hisorically documened. There have been wo relaively recen reviews of he subsequen research ino his puzzle Mehra and Presco (2003) and Derrig and Orr (2004). These reviews were wrien for slighly differen audiences - respecively academic financial economiss and pracicing acuaries - bu hey essenially agreed on wo crucial observaions: (a) (b) he equiy premium puzzle has no been solved 20 years afer is formulaion, and widely diverging esimaes of he prospecive (or ex ane) equiy premium are being published in respeced journals. Boh of hese poins are imporan maers if we are making esimaes of oal reurn ha involve he equiy premium as a building block. The imporance of failing o idenify causaion was no los on Mehra and Presco (2003) in heir rerospecive review of academic research. They conceded (p911) ha failure o esablish a causal link beween invesor behaviour and he equiy premium would render invalid some of he cenral paradigms of financial economics: The [equiy premium] puzzle canno be dismissed lighly because much of our economic inuiion is based on he very class of models ha fall shor so dramaically when compared o financial daa. I underscores he failure of paradigms cenral o financial and economic modeling o capure he characerisic ha appears o make socks comparaively so risky. Hence he viabiliy of using his class of models for any assessmen... is hrown open o quesion." Mehra and Presco (p921) hen seemed ready o concede ha he causal relaionship, which has been aken as self-eviden for so long, may no exis: "The difficuly ha, collecively, several model classes have had in explaining he equiy premium as a compensaion for bearing risk leads us o conclude ha perhaps i is no a 'risk premium' bu raher due o oher facors." Anoher review of he equiy premium research ha adops a slighly differen perspecive was wrien for he acuarial profession by Derrig and Orr (2004). They observe (p47) ha research ino he cause and/or size of he equiy premium seems o have been proceeding on wo frons. Firs, here is an aemp o explain he size of he hisorical premium in erms of new models and differen assumpions abou invesors. This research is essenially looking 13

for a causal explanaion based on facors such as borrowing consrains, axes and liquidiy preference as well as risk-aversion. On he second research fron, here is a concered effor o obain esimaes of he [equiy risk premium] ha are derived from hisorical daa and/or sandard economic models. This research is concerned wih fuure levels (or ex-ane esimaes) of he equiy premium. Auhors of exs and academic papers advocae and/or explore a variey of mehods. Some esimaes are simply adjused values based on he hisorical record which, more or less, reain he concep of he equiy premium as a law of naure. For example, Brealey and Myers (2003 pp157-160) suggesed esimaes based on he hisorical record wih some adjusmens o allow for idenified changes in circumsances. They concluded we believe ha a range of 6 o 8.5% is reasonable for he Unied Saes. The approaches in he lieraure surveyed by Derrig and Orr seem consisen wih he conclusions of Mehra and Presco (2003) who, having acknowledged ha he equiy premium may no be a risk premium hen argue ha a span of 100 years is a long series when i comes o economic daa over he long-erm he equiy premium is likely o be similar o wha i has been in he pas. In erms of any debae over wheher he equiy premium is a law of naure or a regulariy, Mehra and Presco sugges, in effec, ha in he absence of a plausible explanaion as o why he fuure is likely o be any differen from he pas, we have sufficien supporing daa o assume ha he equiy premium will coninue as a reliable regulariy, even if i is no a law of naure. If philosophers of science such as Chalmers are correc in suggesing ha regulariies canno be assumed o repea hemselves in ou-of-sample periods i is quie significan ha some people are beginning o sugges ha he equiy premium is no a law of naure. For example, Derrig and Orr acknowledge: No simple model of he [equiy risk premium] has been universally acceped. If he premium is a law of naure hen he hisorical record is a valid mehod of esimaing fuure values wih or wihou minor adjusmen. On he oher hand, esimaes close o Rier s defensible number of 1% per annum ofen use mehodology ha is independen of he hisorical record hereby abandoning any preence ha he equiy premium is a law of naure. A he very leas, some of hese approaches o esimaing he ex-ane equiy risk premium demonsrae a lack of faih in basing fuure esimaes on he assumpion ha riskaverse invesor behaviour will coninue and ha his behaviour causes he equiy premium. The mere publicaion and debae over such ex-ane esimaes demonsraes widespread accepance of Mehra and Presco's conclusion ha he equiy premium may no be a risk premium afer all. A second aspec of his debae is eviden in he mehodology used o derive some of he forward looking esimaes of he fuure equiy premium. The jusificaion ha is ofen given for ex-ane esimaes differing significanly from he hisorical record has a significan bearing on marke efficiency in boh weak and semi-srong forms. Implicily or explicily, some of hese jusificaions accep he idea ha hindsigh is no longer required o assess markes as high or low. This judgemen can be based on fundamenals or some sor of mean reversion following eiher a subsanial rise or fall in he sock marke. Consider, for example, his argumen from Mehra and Presco (2003, p927): ".. when sock valuaions are high relaive o fundamenals, he ex-ane equiy premium is likely o be low. However, i is precisely in hese imes, when he marke has risen sharply, ha he ex-pos or he realised premium is likely o be high. Conversely, afer a major correcion, he ex-ane (expeced) premium is likely o be high while he realised premium will be low. This should no come as a surprise since reurns o sock have been documened o be mean-revering." 14

To reain he concep of he equiy premium, are financial economiss prepared o concede he ruh of phenomena ha are inconsisen wih marke efficiency as well as a fuure "risk" premium ha no longer has anyhing o do wih risk? The argumen ha low markes are associaed wih high equiy premiums and vice-versa illusraes ye anoher feaure of regulariies, as disinc from laws of naure. Wih saisical regulariies, we do no know he direcion of he causaion. Has he equiy premium fallen because markes have risen or have markes risen because he equiy premium has fallen? If, however, we are dealing wih a causal relaionship, changes in oucomes naurally follow from changes in he causal variable, bu no he oher way around. To use he example cied by Chalmers (p215): [if smoking causes lung cancer] we can hope o decrease he occurrence of lung cancer by eliminaing smoking bu canno hope o comba smoking by finding a cure for cancer. Nowihsanding he debae abou he cause of he equiy premium and, perhaps wihou noicing ha many ex-ane esimaes have desered he equiy premium as a law of naure, i sill seems common pracice o simply assume ha he equiy premium exiss as some sor of marke price of risk even if ex-ane esimaion is exremely difficul. For example, Derrig and Orr (2004, p45) observe: he equiy risk premium (ERP) is an essenial building block of he marke value of risk.... Risky discoun raes, asse allocaion models and projec coss of capial are common acuarial uses of ERP as a benchmark rae". Similarly Brealey and Myers (2003, p157) imply ha he fuure value of he equiy premium, while difficul o esimae, remains a law of naure because i will sill be deermined by he reward for bearing risk required by porfolio invesors. As a law of naure, caused by risk aversion, i is difficul o make ex-ane esimaes because we do no know if he fuure riskaverse behaviour of invesors will be differen from wha has been observed in he pas: Even wih 75 years of daa we can esimae he risk premium exacly, nor can we be sure ha invesors are demanding he same reward for risk as hey were 60 or 70 years ago. The implici assumpion ha he equiy premium exiss, and is widespread adopion in a variey of siuaions, seems o ignore he fac ha he crucial onological quesion - does he equiy risk premium exis as a reward for risk? - is far from resolved. Two recen surveys of published academic and praciioner research by Mehra and Presco (2003) and Derrig and Orr (2004) demonsrae very deep and fundamenal disagreemen abou boh he causes and level of he equiy premium. 15

4 Dividend growh raes. If we solve a mahemaical equaion linking he curren price of a sock or index level o he discouned presen value of all fuure dividends we obain an esimae of he very long-erm reurn achieved by a buy-and-hold invesor. As a rough rule of humb, he oal reurn is equal o he curren dividend yield plus an assumed dividend growh rae. This formula may need sligh adjusmens for he iming of dividend paymens, wheher he dividend yield is hisorical, curren or prospecive, ec. The main difficuly in applying his formula lies in obaining a reliable forecas of fuure long-erm dividend growh. There have been four basic approaches o his problem and he debae beween regulariy and causaliy lurks below he surface. There are significan differences of opinion as o he causes of growh in company earnings and dividends. One approach o esimaing fuure dividend growh is o assume ha dividends will grow in pariy wih nominal GDP. A second approach is o assume ha earnings and dividends are more or less consan in real erms and simply grow wih inflaion. These wo approaches seem o be he mos common. However, Graham (1973) argued ha he reenion of earnings, and no inflaion, was he underlying driver of growh in earnings (and presumably herefore dividends) in he consiuens of he Dow Jones index. Excluding is sochasic feaures, he UK Mauriy Guaranees Working Pary (1980) model assumed a consan rae of growh wih his parameer based on he hisorical record. If dividends remain a roughly consan proporion of GDP, hen hey grow wih boh inflaion and real growh in GDP. From he perspecive of he economis rying o forecas ax revenues, he "GDP pariy" assumpion may be quie sound. However, he perspecive of he porfolio invesor is quie differen. Even if dividends do mainain approximae pariy wih GDP a a naional economic level, assuming porfolio invesors enjoy he same rae of growh in dividend income ignores he fac ha invesors in socks have o pay cash for any new shares creaed and an adjusmen is required. If invesors do no ake up a pro-raa enilemen of all new shares as hey become available, hen heir share of underlying profis and dividend income will decline relaive o GDP. To quoe Bernsein and Arno (2003, p48) The problem wih his assumpion [ha sock prices grow wih GDP] is ha per share earnings and dividends keep up wih GDP only if no new shares are creaed. (Wheher discussing individual companies or indices, earnings and dividends adjused for he issue of new shares are generally described as per-share earnings and dividends.) Bernsein and Arno compare earnings growh wih GDP growh in a number of counries over he 20h cenury based on he daa appearing in Dimson e al (2002). They repored ha here had been an average diluion, compared o GDP, of 2.3% per annum in non-war-orn counries and 4.1% in war-orn counries. Bernsein and Arno also noe ha his diluion of 2.3% per annum corresponds wih he ne new share issuance in he US over he period 1926-2001 which hey esimae by comparing growh in marke capialisaion wih changes in sock price indices. Bernsein and Arno conclude ha: In sable naions, a roughly 2 percen ne annual creaion of new shares he Two Percen Diluion leads o a separaion beween long-erm economic growh and long erm-growh in dividends per share, earnings per share, and share price. So, any esimae of long-erm fuure sock reurns ha assumes dividends, earnings and sock prices will mainain pariy wih GDP mus allow for he diluion effec of ne share issuance 16

which, according o he hisorical record, has been approximaely 2% per annum in counries no seriously affeced by war. Why hen has his diluion averaged 2% per annum? One possibiliy is ha GDP grows in real erms whereas i is ofen claimed, a leas implicily, ha we should expec companies o simply susain heir earnings (and dividends) in real erms. This was he assumpion behind Wilkie's model and also he model of Yakoubov e al. However, his view is no confined o he acuarial profession. For example, he argumen ha companies should be expeced o susain heir earnings in real erms is implici in he remarks of Rier (2002, p165): "Adjused for business cycle effecs, he earnings yield on socks is an esimae of he real reurn on socks. The earnings yield is no an esimae of he expeced nominal reurn on socks." In his calculaion of price/adjused 10-year earnings raios in Irraional Exuberance, Shiller (2000, p7), used "he en-year average of real earnings for he denominaor, along he lines proposed by Benjamin Graham and David Dodd in 1934." Thus, Shiller's calculaions conained an adjusmen for inflaion only, no GDP pariy. Alhough no discussed, his mehod of calculaion herefore involved he implici assumpion ha susainable earnings per share (ie adjused for he ne issue of new shares) could be esimaed from a 10-year average of earnings per share adjused for inflaion only wihou allowing for any exra growh. The reason behind he common asserion ha company earnings, dividends and share prices should grow wih inflaion in he long-erm is no always clear. However, here appears o be a "common sense" view ha company earnings and dividends are real in naure, in much he same way ha operaing coss such as wages and raw maerials are also real. Consider, for example, he following recollecion of Marshall (2004) in The Acuary: "The leer from [a previous corresponden] presens a challenge o hose of us who argued nearly 40 years ago ha he naural home for pension fund asses was in equiies. in my case, his was based on he sound acuarial basis of maching in he belief, suppored by common sense and hisory, ha incomes and dividends would be correlaed as closely as is as likely beween a monoonic and a cyclical series." Benjamin Graham, however, (1973, p21) had very differen ideas abou he cause of growh of per-share earnings (and herefore also dividends and sock prices in he long-erm). He wen o some lengh o poin ou ha he growh in per-share earnings of he consiuens of Dow Jones Indusrial Averages over he period 1950-1970 were due o reained profis increasing shareholders' equiy and ha inflaion was no a facor: all he large gain in he earnings of he DJIA uni in he pas 20 years was due o a proporionaely large growh of invesed capial coming from re-invesed profis. The only way ha inflaion can add o common sock values is by raising he rae of earnings on capial invesmen. On he basis of he pas record his has no been he case. A he discussion of he Wilkie model, Plymen (1986, pp390-391) echoed one of Graham's commens when he said: ".. Surely he whole poin of he concep of he equiy mehod of financing is ha dividends are disribued much below he earnings, every year here is a cerain amoun of plough-back which surely earns a reasonable rae of reurn and builds up he underlying srengh of he business and makes for higher dividends in fuure." 17

Nowihsanding he inclusion of basic accouning in he acuarial educaion sysem, he reenion of profis is no ofen recognised as relevan o he growh of earnings, dividends and, in he long-erm, sock prices. In his respec he repor of he UK Mauriy Guaranees Working Pary (1980, p143) is very ineresing: "I is clear ha dividends and company earnings, on which hey depend, are expressed in money erms and, oher hings being equal, should rise pari passu wih oher prices. Experience however has no borne his ou. There is some correlaion he combinaion of irregular inflaion and an irregular influence of inflaion on dividends leads o he same sochasic model for dividends as we have chosen." We noe he preconceived belief ha dividends and earnings are real in naure, acknowledgemen ha his is no suppored by "experience", no menion of reained profis and no causal explanaion for he dividend growh componen of he Mauriy Guaranees Working Pary model oher han a very indirec link wih inflaion. We can discard he GDP pariy approach for projecing dividend income on he ground ha i does no allow for new share issues (ne of buy-backs) and ha he "wo per-cen diluion" suggesed by Bernsein and Arno is a regulariy. This shorcoming was eviden in all counries wih esablished sock markes in he 20h cenury. This leaves us wih wo poenial causal facors for long-erm dividend growh - inflaion and reained profis. The available hisorical daa is no much help in clarifying his maer. In Ausralia, here are serious doubs abou he accuracy of dividend daa available before 1980. (I is now believed ha frequenly cied hisorical sudies in Ausralia have oversaed oal reurn and he equiy premium by approximaely 2% per annum. See Fizherber, 2006 and Brailsford e al, 2007.) Neverheless wih a long enough ime frame we can use hisorical price index daa o esimae hisorical dividend growh because, over a very long period, growh in dividends, earnings and sock prices should be roughly he same. Over 100 years a change in dividend yields by a facor of 1.5 would lead o a difference of 0.4% beween dividend growh and capial appreciaion. (If he dividend yield underlying a marke index increases from 4% o 6% over 100 years he rae of capial appreciaion would be 0.4% per annum less han would have been he case if he dividend yield had been he same a he beginning and end of he period under review. If he dividend yield falls from 4% o 2.67%, he rae of capial appreciaion would be 0.4% per annum more.) In Ausralia a leas, hisorical sock price index daa exending back 100 years seems more reliable han earnings or dividend daa over his period. We herefore ake sock price growh as a rough indicaor of dividend growh and compare his wih inflaion over he 20h cenury as shown in Table 2 for he US, he UK and Ausralia. These figures were calculaed from daa given in Dimson e al (2002). Table 2 Share Price index growh 1900-2000 (logarihmic) Ausralia (% pa) UK (% pa) USA (%pa) Capial growh 5.8 5.0 5.3 Inflaion 4.0 4.0 3.1 In hese hree counries, we see ha capial growh, and herefore dividend growh over his 100 year period, has a leas mached inflaion, suggesing ha here may be some addiional 18

benefi from reained profis or real economic growh. This presens us wih one possible explanaion for long-erm dividend growh - inflaion plus some benefi from reained profis and/or real economic growh. An alernaive explanaion is ha long-erm growh in earnings and dividends (and herefore share prices) is driven by reained company earnings of 4-6% per annum of shareholders' equiy, possibly wih some addiional benefi from inflaion or real economic growh. (The available daa on reained earnings over his exended hisorical period is very limied, excep for some US daa.) Insofar as deciding wheher long-erm growh in share prices (and herefore dividends and earnings) is driven by inflaion, economic growh or reained profis, he available hisorical daa is herefore capable of a muliude of plausible inerpreaions. Perhaps, however, we should noe ha he effecs of reained profis of 4-6% per annum of shareholders' equiy and inflaion canno be addiive o heir full exen. If hey were, hen he long-erm rae of growh of earnings (and in consequence dividends and sock prices) over he 20h cenury in hese hree counries would have been approximaely 8-10% per annum raher han 5-6% per annum. However, even if he hisorical evidence were less ambiguous any relaionship remains a regulariy raher han a law of naure. To devise a valid model of he fuure, we sill need o esablish causaion. Having done so, i will be eviden ha reained profis is he only direc cause of long-erm growh in he underlying per-share earnings of a marke index porfolio when hisorical cos accouning prevails. Inflaion is only a facor o he exen ha i possibly leads o a higher reurn on shareholders' equiy (hereby also increasing reained earnings as a percenage of shareholders' equiy) or ha hisorical cos accouning is no sricly followed. 19

5 The naure of company profis: real income or moneary income? Sock indices such as he ASX All Ordinaries are carefully adjused o eliminae he effec of ne share issues. A similar adjusmen needs o be made when dividends or earnings are modelled as par of a process for deriving long-erm sock reurns. The argumen ha pershare earnings (ie company profis afer adjusmen for he issue of new shares) can only grow in he long-erm from reained profis direcly conradics he widely-held view ha company capial is predominanly held in real asses and, in consequence, company profis can also grow wih inflaion wihou any addiional equiy capial. If, on he oher hand some profis are reained and company capial is held in real asses, hen company profis should grow in he long-erm wih boh inflaion and reained profis. In Ausralia, he UK and he US, he available daa suggess he rae of long-erm growh is considerably less han he combined poenial impac of boh inflaion and parial profi reenion. A possible answer o his riddle lies in he almos universal adopion of he hisorical cos accouning convenion. This convenion ensures ha he money value (and no he real value) of shareholders' equiy is mainained before couning he surplus as profi. In oher words, companies may inves in real asses bu, as a general rule, heir financial saemens rea real asses as moneary ones. (There have been some excepions in Ausralia and he UK, noably some permanen fixed asses such as rademarks, land and inangibles ha are bona-fide real asses bu no depreciable plan and equipmen.) Here is a simplified example: a small consuling firm issues $100,000 in shares o is direcors o fi ou a small office; he direcors pay all of he profis o hemselves and hey depreciae he cos of he fi-ou over he erms of he lease and do no buy any more asses. Their iniial balance shee would hen be: Balance shee a commencemen of lease Liabiliies Asses Shareholders' equiy $100,000 Fixed asses $100,000 As hey depreciae heir fi-ou over he erm of he lease, heir fixed asses a he end of he lease will be zero, bu heir equiy will sill be $100,000 and his will now be in cash. So he firm's balance shee a he end of he lease will be: Balance shee a conclusion of lease Liabiliies Asses Shareholders' equiy $100,000 Fixed asses Nil Cash $100,000 If, say, his fi-ou had a erminal value greaer han zero and he asses were sold, his would give rise o a profi which would appear in he profi and loss accoun, no he balance shee. Consequenly any benefi from inflaion in relaion o depreciable fixed asses will appear in repored earnings where i will be refleced in he repored reurn on shareholders equiy. While his illusraion relaes o jus one simplified example, company accouns show he combinaion of a number of individual asses for which he same argumen applies. Consequenly he argumen ha hisorical cos accouning preserves he moneary value (and no he real value) of depreciable plan in company balance shees applies quie generally. 20

A second class of real asses reaed as moneary ones under hisorical cos accouning is invenories of finished and parly finished goods. To illusrae his argumen we rever again o a simplified example. Suppose a company manufacures widges and does no reain any profis. I sars he year wih $100 in shareholders equiy which has been spen buying raw maerials. The compleed goods are sold a $120. In relaion o his line of business, is opening balance shee will show $100 of invenory and $100 of shareholders equiy. Is profi will be $20 which is paid in axes and dividends. Once he goods are sold and profis are disribued $100 in equiy will remain irrespecive of he rae of inflaion. If he cos of raw maerials has risen, he company will need o borrow or raise addiional equiy for he nex cycle. However, he abiliy of companies o increase deb is consrained by gearing raios and, sooner or laer, addiional equiy will be required. If we now consider he company s balance shee a wo imes - a he sar of he manufacuring cycle and afer he goods are sold and profis are disribued, hen we see (as wih depreciable plan) ha i is only he money value of shareholders equiy ha is mainained. Balance shee a commencemen of widge cycle Liabiliies Asses Shareholders' equiy $100 Invenories $100 Balance shee a conclusion of cycle Liabiliies Asses Shareholders' equiy $100 Invenories Nil Cash $100 These wo examples can be criicised as oversimplificaions ha ignore deb finance. As far as oversimplificaion is concerned company operaions are he combinaion of very large numbers of such simple ransacions, which can be added ogeher and he oversimplificaion does no invalidae he argumen ha can be made from such micro-ransacions. The addiional complicaion of deb, or cash balances, merely adds fixed moneary asses o one or boh sides of a balance shee and does no aler he proposiion ha shareholders' equiy is accouned for in money erms. When hisorical cos accouning applies o all company asses and liabiliies, inflaion is no a facor and i is fairly sraighforward o show ha given a consan reurn on shareholders equiy and a consan proporion of profis paid in dividends, hen per share earnings, dividends and shareholders equiy should all increase a he same rae calculaed from he reained proporion of reurn on shareholders equiy. A demonsraion of his growh rae formula appears in Hemsed (1962). Where hisorical cos accouning is sricly applied, his growh rae should apply, irrespecive of he rae of inflaion. In boh Ausralia and he UK in much of he 20 h cenury, he applicaion of he hisorical cos accouning convenion was modified in relaion o permanen fixed asses such as land and buildings. These asses were periodically wrien-up in company balance shees and he consequen changes in asse values were reaed as an abnormal or exraordinary iem and excluded from he normal profi calculaion. This has been less prevalen in he USA where he hisorical cos convenion has been more rigidly applied. Anoher issue wih boh Ausralia and he UK is he limied availabiliy of reurn on shareholders equiy daa. 21

In more recen imes, hisorical financial daa has become more complicaed by he disribuion of profis in share buy-backs in lieu of dividends, he elecom-media-echnology bubble and he hisorically high levels of reurn on shareholders equiy. I is difficul o place a precise dae on hese developmens, bu resricing he period o 1920-1989 should avoid hese issues in US daa. The daa shown in Table 3 has been copied and calculaed from daa ha appeared in Value- Line (1990) relaing o he Dow Jones Indusrial Average over he period 1920-1989. Reurn on book value (as shareholders equiy is ofen called by US securiy analyss) and payou raios boh flucuae from year o year. Wha we require is an esimae of he reained profis as a percenage of shareholders equiy for which here is no perfec mehod of calculaion. Given he wide variaion in pay-ou raios, he produc of ( 1 minus average payou-raio ) and average reurn-on-book-value seems prone o error. From he average earnings and dividend yields of 7.8% and 4.7% respecively we can indirecly esimae an average payou raio of 4.7 7.8 or 60%, so ha roughly 40% of earnings were reained over his period. The average "reurn on book value" was 11.6%, so he average value of reained earnings as a percenage of shareholders' equiy was 11.6% 40% or 4.6% per annum. If earnings growh in he long-erm is driven by reained profis, hen he long-erm rae of growh of earnings over he period 1920-1989 should herefore have been approximaely 4.6% per annum. As can be seen from Table 3, his is more or less wha happened. Table 3 Growh in per share values of Dow Jones Indusrial Averages Earnings, Book value and Dividends 1920-1989 DJIA 1920 1989 Compound Growh rae (% pa) Book value 48.2 1206 4.8 Earnings 9.1 224 4.8 Dividends 5.8 103 4.3 DJIA average 90 2510 4.9 When considering sock price reurns over any period, he quesion of changes in he marke valuaion of earnings needs o be considered. However, he price/earnings raio a he beginning and end of his period were roughly he same. As already noed, his observaion also applies o reurn on book-value. Consequenly he average compound rae of growh of per-share earnings, book value (ie shareholders' equiy) and he index were all roughly he same and wha we would expec from growh was driven by he reenion of earnings. I could, of course, be argued ha he dividend growh rae of 4.3% per annum is also consisen wih GDP pariy or inflaion assuming no added benefi from reained profis. This argumen is conradiced by Hemsed's elemenary demonsraion of wha happens under hisorical cos accouning. I is impossible for company profis no o grow in he long-run from he parial ploughback of profis unless reurn-on-shareholders'-equiy ends o zero. Also, here is a sunning couner-example o his criicism in he hisory of Berkshire Hahaway Inc over he period 1964-2005. Wih minor excepions, Berkshire Hahaway has no issued nor repurchased any of is sock, nor has i paid dividends. This simplifies our calculaions because all of is reurn on shareholders' equiy has been reinvesed and we do no need o worry abou he difference beween per-share daa and unadjused daa. I also follows ha he average rae of growh of book-value should be approximaely he same as average reurn on book-value. 22

If long-erm growh in earnings is due o inflaion, hen we would expec earnings growh o be around 4% per annum. However, if growh is due reained profis hen he hisorical growh in earnings and he company's sock price (assuming roughly comparable price/earnings raios as he beginning and end of he sudy period) should be commensurae wih he average reurn on is shareholders' equiy, which can be esimaed from he average increase in per-share book value of 21.5% per annum. (Berkshire Hahaway, 2006 p2.) Afer allowing for he effec of a modes re-raing of he company over 41 years (as shown in an improvemen in he company's price/book raio), he oal reurn, as a sock invesmen, has been 23% per annum. This rae of capial appreciaion makes some sense in relaion o he likely level of reurn on shareholders' equiy achieved by his company, bu i is no in he same ball-park as he rae of inflaion. These case sudies, he Dow-Jones consiuens over he period 1920-1989 and Berkshire Hahaway over he period 1964-2005 relae o siuaions where he hisorical cos convenion is applied. The daa is consisen wih he argumen which follows direcly from hisorical cos accouning and flucuaing reurn-on-shareholders'-equiy ha long-erm growh in pershare earnings is caused by he reenion of profis. The daa is inconsisen wih he idea ha inflaion is an addiional or subsiue causal facor. The reason ha inflaion is no direcly relevan is he widespread adopion of he hisorical cos accouning convenion. We now consider he opposie case where here is negligible reenion of profis, shareholders' equiy is predominanly invesed in income producing real propery and hisorical cos accouning has been modified o he exen hese real asses are reaed as real iems in balance shees. Subjec o cyclical flucuaions and he deerioraion of buildings wih age (and he renals hey can command), we should herefore expec he underlying per-share disribuable income of he ASX Lised Propery Trus index porfolio o move wih inflaion. As a general rule, his is real income because he changing values of he underlying asses have, in he pas, been wrien up in balance shees as exraordinary iems and no disribued as profi. This is beginning o change as hese rus unis become "sapled" o managemen companies or developmen arms and ax rules make i beneficial o disribue realised capial gains; bu for mos of he period since incepion of he ASX indices in 1979, he hisorical cos accouning convenion has been modified o preserve he underlying naure of heir propery asses in he accouning reamen of uniholders' equiy. If a building were revalued upwards by (say) $10 million, his bypassed he income saemen and uniholders' equiy increased by he same amoun. (I is only fairly recenly ha realised capial gains have been disribued o uniholders.) From hese accouning consideraions we would herefore expec o see growh in income and capial values from inflaion alone, provided he underlying capial values were refleced in uni prices and he underlying renals mainained some pariy wih inflaion. As he daa shown in Table 4 demonsraes, his is more or less wha has happened. (Alhough he 26 year growh raes are calculaed correc o one basis poin, he closeness of he resuls is probably accidenal and we should no read oo much ino his close correspondence beyond suppor for he general argumen ha inflaion is he main cause of long-erm growh in income and he wo growh raes should be roughly he same.) 23

Table 4 ASX Lised Propery Truss 1980-2006 (S&P 200 since 2002) Dae 31/12/79 31/12/80 31/12/05 31/12/06 Price index 500 491.7 1931.9 2431.0 Accumulaion index 1000 1064.2 31876.8 42725.7 26 year growh rae CPI (June quarer) 47.0 154.3 4.68% pa Index porfolio income disribuions 41.6 137.8 4.71% pa (To calculae he income derived in 1980 from an invesmen of 500 on 31/12/1979 we use he accumulaion indices o calculae ha he index porfolio, wih income reinvesed, would have grown o 500 1064.2 1000 = 532.1 compared o 491.7 wihou income reinvesed giving an income of 40.4. This calculaion assumes all income accrues on he las day of he year which can be inaccurae when here have been significan changes in levels, as in 2006. The resuls shown in Table 4 are derived by he same mehod using monh-end indices for greaer accuracy.) Based on he naure of accouning, we argue ha he naure of business income, wheher real, moneary or a mixure of real and moneary, depends on he prevailing accouning convenions and he proporion of a balance shee held in permanen real asses. Hisorical cos accouning, when sricly applied, measures money income no real income. If here are reained profis, long-erm per-share profis and dividends will rise as an ineviable consequence of such profi reenion. Wheher here is any addiional benefi from inflaion depends on he proporion of he balance shee invesed in real asses and he way accouning convenions are applied. 24

6 The shareholders' equiy framework. We now consider, in more deail, he shareholders' equiy framework for esimaing long-erm equiy reurns. An early formulaion was published by Hemsed (1962) who showed ha wih a consan reurn on shareholders' equiy and a consan payou raio, he very long-erm buyand-hold reurn achieved by an invesor was equal o he dividend yield a he ime of purchase plus he rae of growh of dividends. This growh rae was deermined by reained profis in relaion o shareholders' funds. Hemsed was ineresed in individual companies, whereas we are concerned here wih an asse class or marke index porfolio. Reurn on shareholders' equiy, as repored by lised companies, is normally defined as he ne profi afer ax divided by average shareholders' equiy. Hemsed, on he oher hand, simplified his algebra by defining a variable he called PR as ne profi divided by shareholders' equiy a he beginning of he year. Also, if we are o develop a more sophisicaed model, we need values for he key variables ha can change from year o year. Mos dividend discoun models, of which Hemsed's algebra is an example, assume indefinie reenion of a porfolio. If we wish o calculae an n- period reurn, we also need a mehod of calculaing marke values from projeced values of dividends, earnings or shareholders' equiy. (By n-period reurn, we mean he inernal rae of reurn assuming disposal a ime n including dividend income.) The shareholders' equiy framework, exended o provide esimaes of n- period reurns, requires four basic ideas, equaions or procedures: (i) We begin wih he so-called accouning equaion which says ha shareholders' equiy a he end of a year is equal o shareholders' equiy a he beginning of he year plus profis earned during he year less dividends paid (or provided for) ou of hese profis: ShEq = ShEq + NPAT D 1 where ShEq is he oal shareholders' equiy of he consiuens of he marke porfolio a ime, NPAT is he oal afer ax profis of all companies in he porfolio in he ime inerval ( - 1, ) and D is he oal dividends paid or provided for from hese profis. This equaion assumes, for he ime being, ha here are no capial ransacions or balance shee adjusmens ha do no pass hrough profi and loss accouns. Wih half-yearly company reporing, as is normal in Ausralia, roughly equal halfyearly dividends end o be paid approximaely hree monhs afer he end of each sixmonhly financial reporing period. I follows ha approximaely 05. D will be paid a - 0.25 and + 0.25. Consequenly i is reasonably accurae o assume ha all of he dividends due in respec of profis earned in a financial year are paid a he end of he year, ie ha D will be paid a ime. (A slighly differen assumpion may be required where dividends are no normally paid half-yearly - for example in he USA where dividends are normally paid quarerly.) (ii) We recognise reurn on shareholders' equiy as an imporan causal variable: As noed, companies normally calculae heir reurn on shareholders equiy by dividing heir ne profi by heir average shareholders equiy. However, under he 25

shareholders equiy framework, reurn on shareholders equiy is a key causal variable, consequenly, he oal ne profi afer ax (NPAT ) of all companies in he marke index porfolio is he produc of he reurn on shareholders' equiy of he "marke" porfolio (RoSe) and he average shareholders equiy: ( ) NPAT = RoSe 05. ShEq + ShEq 1 where he subscriped vales for NPAT and RoSe relae o heir values over he ime inerval beween - 1 and. (iii) We need an algorihm for deermining dividends: When companies repor heir profis hey normally also declare heir dividends. The percenage of profi disribued in dividends is usually called he pay-ou raio. Tradiionally, payou-raios have been around 60%; however companies ofen mainain dividends when hey have incurred losses and do no necessarily increase heir dividends when he have jus "had a very good year". Consequenly, if earnings flucuae (as hey should in a sochasic model), here is a need for an algorihm for projecing dividends raher han he applicaion of a fixed payou raio of (say) 60%. (I is for his reason ha Yakoubov el al preferred o base heir sochasic model on a projecion of earnings raher han dividends o avoid wha hey described as "smoohing by company managemen".) If he payou raio is assumed o be consan over ime a PoR hen i can be shown ha: ShEq = ShEq 1 { 1+ 05. RoSe ( 1 PoR) } 1 05. RoSe ( 1 PoR) { } ( ) NPAT = RoSe 05. ShEq + ShEq, and 1 D = PoR NPAT (iv) For finie n-period ime-frames, we also need a mehod for esimaing marke value a ime n. The shareholders' equiy framework provides a mehod for projecing earnings, dividends and shareholders' equiy for he marke index porfolio. Any of hese hree variables can be used o generae a marke value and he values of his pricing mechanism can be a sochasic process. For example, he UK Mauriy Guaranees Working Pary (1980) projeced dividends as a sochasic model and generaed marke prices using a dividend yield. The logarihm of he dividend yield was modelled using a firs order auoregressive process. If we decide o use a price/book raio for he purpose of generaing marke values, hen we now define an aggregae price/book raio as PB = MV ShEq where MV is he oal capializaion of all companies in he marke index porfolio a and ShEq is he oal shareholders equiy of he same companies. To complee he esimaion of an n-period asse class reurn under he shareholders equiy framework we need he iniial price/book raio PB 0 and algorihms or sochasic models for projecing he following iems: 26

(a) he reurn on shareholders equiy for he period ( - 1, ), RoSe for values of = 1, 2 n : (b) he price/book raio a ime n, PB n, and (c) he oal dividends paid in respec of he period ( - 1, ), D (assumed payable a ime ) for values of = 1, 2 n. (In an Ausralian conex where half-yearly dividends are sandard pracice, we can improve our calculaions slighly by assuming ha 05. D 0 is paid jus afer ime 0 and 05. Dn is paid jus before ime n.) While we need a saring value for oal shareholders equiy a ime 0, ShEq 0, we are ineresed in raes of reurn raher han he dollar value of aggregae profis ec, so he resuls of our calculaions do no depend on his number, which can be se o some convenien figure such as 1 or 100. The basic accouning equaion assumes ha none of he consiuen companies of he index porfolio issue or buy back any shares during his period. There is no compleely saisfacory way of dealing wih new issues or buybacks. This is a complex issue. If, as is usually he case, he price of new shares or buybacks is close o he marke price hen he value of such enilemens may be sufficienly small o ignore when modelling a marke porfolio. As a firs sep in correcing his error he issue and repurchase of shares has herefore been ignored. This is no o deny ha such ransacions ake place bu, as a firs sep, he mos suiable accouning framework adjusmen is o ignore issues and buybacks on he grounds ha his corresponds, reasonable closely, wih he way sock marke index porfolios are adjused. The accepabiliy of he basic accouning equaion does no depend on companies no issuing or repurchasing shares, bu he way he marke index porfolio is adjused o allow for hese ransacions. (Wha is wrong, implici in he GDP pariy argumen, is o accep undilued earnings figures and ignore he cos of new equiy issues.) The mehodology described above projecs accouning variables on he assumpion ha he hisorical cos accouning convenion is sricly applied excep for inflaion induced revaluaions of permanen fixed asses which, unil recenly, used o bypass he profi and loss accoun as abnormal or exraordinary iems. When he resuling rae of reurn is calculaed is unis are hose of he accouning sysem, which may be parly real. So, if he consiuens of he marke index porfolio hold (say) 10% of heir saed shareholders equiy in genuinely real asses ha are reaed as real asses we need o recognise he resuling rae of reurn as 10% real and allow for 10% of he projeced rae of inflaion o obain a final resul. The quesion of profis bypassing profi and loss accouns is a complex issue. Apar from he subleies of he definiions, he rules deermining he classificaion of profis have been inconsisen over ime. Concepually, we can rewrie he accouning equaion: ShEq = ShEq + NPAT + XPAT D 1 where NPAT denoes aggregae profis appearing in companies' profi and loss accouns and XPAT represens afer ax profis and oher adjusmens o asse values ha are no included in NPAT. When he ASX indices commenced (in 1979), such adjusmens o permanen asse values (boh realised and unrealised) were ofen excluded from NPAT, bu 27

his is no longer normally he case. In projecing he ASX All ordinaries index porfolio forward, herefore, his adjusmen has no been aken ino accoun, however care would be required in some specialised secors. 28

7 Illusraive calculaions. A simple scenario approach is now used o produce illusraive 10 and 20 year oal reurn esimaes for he ASX All Ordinaries Index porfolio. The raw daa is aken from he informaion provided by AspecHunley which is readily accessible o regisered cusomers of a leas one online broker. These figures are used for illusraive purposes. While hey are believed o be reliable, AspecHunley (2004) emphasise ha anyone ".. acing on such informaion do[es] so enirely a heir own risk". We esablish iniial values for reurn on shareholders' equiy by dividing he marke aggregae price/book raio by he marke aggregae price/earnings raio. We also esimae he laes payou raio as he produc of he dividend yield and he price/earnings raio. The raw daa and he implied reurn on shareholders' equiy and payou-raios are shown in Table 5. Table 5 Esimaion of "iniial condiions" As a 30/6/2007 ASX All Ordinaries Price/earnings raio 18.01 Price/Book raio 2.68 Dividend yield 3.4% Iniial RoSe 14.9% Pay-ou raio 61% Using hese iniial values and he equaions shown in secion 6, we now projec shareholders' equiy, dividends and erminal marke values over 10 and 20 years under wo differen scenarios and hen calculae he inernal rae of reurn achieved by an invesor buying a marke levels ruling on 30 June 2007 and holding he index porfolio. In Scenario A i is assumed ha curren levels of reurn on shareholders' equiy coninue and price/book raios are he same in 10 or 20 years ime as hey are oday. This scenario also implicily assumes ha he price/earnings raios are he same in 10 or 20 years' ime as hey are oday. Flucuaions in price/book or price/earnings raios in he inervening period over he nex 10 years or beween 10 and 20 years do no affec hese calculaions. In scenario B, we assume ha reurn on shareholders' equiy revers o a more radiional level of 9% per annum for he ASX All Ordinaries Index porfolio over he nex 5 years and ha he price/book raio revers o 1.5. (This implicily assumes a erminal price/earnings raio of 16.7.) In boh scenarios, inflaion is assumed a 3% per annum and he "real" conen of he index porfolio is aken as 10%. Of less imporance, hese calculaions assume a consan payou raio hroughou as calculaed in Table 5. The resuling esimaes of raes of reurn for 10 and 20 year holding periods are shown in Table 6. 29

Table 6 Esimaed 10 and 20 year annualised raes of reurn As a 30/6/2007 ASX All Ordinaries Scenario A 10 or 20 years 9.6% Scenario B 10 years 20 years 1.6% 4.1% 30

8 The relaive meris of price/book and price/earnings raios. The use of price/book raios in modelling usually aracs criicism on he grounds ha he book value of shareholders' equiy is jus an accouning number relaing o he hisorical cos of balance shee iems and is irrelevan. Also, a more widely acceped valuaion yardsick is he price/earnings raio. However, under he shareholders' equiy framework models based on price/book and price/earnings raios produce almos he same answer because he price/book raio is equal o he price/earnings raio muliplied by reurn on shareholders' equiy and he raio of average o year end shareholders' equiy: ( ) MV MV NPAT 05. ShEq + ShEq PB = = = PE RoSe 1 ShEq NPAT ShEq ShEq where PE is he price/earnings raio a ime. The final erm in his formula will be close o one for an index porfolio, so ha: PB PE RoSe There are wo furher reasons for using price/book raher han price/earnings raios in longerm equiy reurn modelling, one pracical, one heoreical. The pracical reason involves calculaing marke prices when companies are making losses. This is rare in he case of index porfolios, bu i has happened. In hese circumsances price/earnings raios based on negaive earnings make no sense. However, i does make sense o say ha when reurn-onshareholders equiy is zero, he marke aggregae price/book raio migh be one. The heoreical reason revolves around he prospec ha, in more normal imes, price/earnings raios are likely o be posiively correlaed wih reurn-on-shareholders' equiy. If companies are "doing well", his seems likely o affecs confidence and be refleced in marke valuaions of earnings (ie price/earnings raios). The use of price/book raios (in conjuncion wih reurn-on-shareholders' equiy) is an imporan improvemen because i allows for boh facors in esimaing marke values. For example, in he calculaions for scenario B i has been implicily assumed ha if reurn-onshareholders'-equiy falls, hen he price/earnings raio will fall also. If here is a endency for reurn-on-shareholders' equiy o mean-rever, hen raional informed invesors should apply lower price/earnings raios when reurn-on-shareholders'-equiy is high and vice-versa. However, here is some evidence ha insead of anicipaing mean-reversion in reurn-onshareholders'- equiy, invesors expec he opposie as Graham (1973, p320) noed many years ago: If, as many ess show, he earnings muliplier ends o increase wih profiabiliy i.e., as he rae of reurn on book value increases, hen he arihmeical consequence of his feaure is ha [marke] value ends o increase direcly as he square of he earnings.. Models based on price/earnings raios (or dividend yields) herefore need o ake reurn-onshareholders'-equiy (and consequenly price/book raios) ino accoun. Consequenly, when used in conjuncion wih reurn-on-shareholders'-equiy, valuaions based on price/book raios indirecly incorporae he more normal yardsick of price/earnings raios ino he calculaion. There will be many insances where he use of price/book raios makes no sense in relaion o individual companies, paricularly hose who can reasonably expec o susain a high level of 31

reurn on shareholders' equiy. However, we are concerned here wih modelling he index porfolio, no individual companies or indusries. Wihin he shareholders equiy framework, he mos imporan variable in very long-erm modelling is reurn-on-shareholders -equiy and, if using a sochasic model, he mos imporan parameer is he mean average value for his variable. This is because RoSe deermines he rae of growh of shareholders' equiy as well as he level of earnings and dividends. When esimaing reurns over finie periods of (say) 10-20 years, reurn on shareholders' equiy is also imporan because i seems likely o influence he way such earnings are priced by he marke. Anoher dimension of his quesion is ha he book value of shareholders' equiy ignores individual companies' "brand value" - he value of heir businesses on an ongoing concern ha is no refleced in heir accouns. We could perhaps define he "rade value" of a company a ime as he sum of he book value of is shareholders' equiy plus is "brand value": TrV = BrV + ShEq Having done so, however, how do we adjus our calculaions of growh raes, and how do we calculae brand value for an index porfolio objecively? If reurn-on-shareholders' equiy is based on companies' rade values, raher han he book value of shareholders' equiy, i would undersae he per-share corporae growh unless i included he growh in brand value over ime. Alernaively, we could argue ha, adjused for new share issues, shareholders' equiy and brand value will end o grow in parallel and ha he correc way o allow for he rae of per-share growh in brand value as well as book-value is reained profis in relaion o bookvalue. In any even, "srong brands" help companies (and oher organisaions) sell heir goods and services profiably and are herefore refleced in reurn on shareholders' equiy. 32

9 Discussion The shareholders' equiy framework. As can be seen from he above formulaion, here are four key unresolved issues wih he shareholders' equiy framework: (a) (b) (c) (d) wha are he forces ha deermine reurn on shareholders' equiy for he marke index porfolio? Is RoSe a saionary process over ime? Wha is is long-erm mean, if i exiss? how do marke index valuaions reac o changes in reurn on shareholders' equiy? Are reurn on shareholders' equiy, price/earnings raios and (in consequence) price/book raios reacing in similar ways o he same economic and financial forces? how should he "accouning equaion" be adjused o allow for new shares and buybacks? how should we deal wih changes in accouning rules, boh in he fuure and when inerpreing hisorical daa? As an illusraion, he calculaions in secion 7 provide esimaes of 10 and 20-year reurns on wo ses of assumpions: (i) ha curren levels of reurn on shareholders' equiy and price/book raios coninue and (ii) ha reurn on shareholders' equiy and price/book raios rever o hisorical norms over five years. I has been assumed ha he adjusmen o he accouning equaion ha corresponds wih index consrucion is o ignore new issues and buybacks. While we are hampered by he lack of qualiy hisorical daa relaing o reurn-onshareholders' equiy and corresponding marke aggregae price/earnings or price/book raios, here has also been lile research ino he forces ha drive reurn-on-shareholders'-equiy. Is i reasonable o assume ha i will flucuae abou (say) 9% in a saionary manner? Wha is he long-erm mean of he process? Or has here been some fundamenal change in he economic and financial environmen ha has led o recen levels ha are appreciably higher? Perhaps, more aenion would be given o hese issues if here were more recogniion of he imporance of reurn-on-shareholders'- equiy. I could be argued ha hese problems are avoided by using an hisorical approach based on raes of reurn calculaed from sock marke daa, an esimae of he hisorical equiy premium or a dividend growh model based on GDP pariy or company profis being real income. Approaches based on hisorical index daa Provided here is no change in he mean level of reurn-on-shareholders'-equiy hen an hisorical approach based on raes of reurn will produce generally he same esimaed longerm rae of compound reurn as he shareholders' equiy framework. This is subjec o he proviso ha here is no large change in reurn-on-shareholders'-equiy and marke values in relaion o book/value and/or price/earnings raios over he period of he hisorical sudy. Alernaively, he hisorical period can be long enough for he effec of changes in marke valuaions o be small. The implici assumpions underlying he long-erm esimae of Owen (1962) were herefore ha fuure reurn-on-shareholders'-equiy in he fuure would be he same as ha underlying 33

his observaion period and ha marke levels in relaion o earnings would no change markedly from hose ruling a he dae of his sudy. Alhough we know ha reurn-onshareholders' equiy flucuaed around 9% per annum in he period 1957-1980 and has subsequenly move higher, we will probably never know wha i was beween 1875 and 1957 - which is 95% of he period of his sudy. I follows from his observaion ha, sooner or laer, he analysis of hisorical daa needs o be reconciled wih corporae financial saemens if we are ineresed in reliable long-erm rae of reurn esimaes. A relaed aspec of he use of hisorical daa is he common assumpion of saisical independence of successive raes of reurn. I is usually argued ha, while his may only be approximaely correc, i is sufficienly correc for mos pracical purposes. We can relae marke levels o shareholders' equiy as follows: MV MV ShEq + 1 ShEq = = NPAT NPAT 2 MV NPAT RoSe So he price of he index porfolio is equal o he produc of is price/earnings raio, is reurn on shareholders' equiy and average shareholders' equiy - i is herefore he produc of wo erms which are likely o be mean revering and a hird erm which is non-saionary, bu which changes slowly over ime wih only a fracion of he variabiliy of he firs wo erms. From his simple argumen we can draw wo imporan conclusions: (a) (b) successive changes in index levels are no independen, even hough hey may give ha impression in he shor-erm, and shor-erm volailiy will grossly overesimae volailiy in long-erm raes of reurn because he wo facors giving rise o shor-erm volailiy are probably meanrevering saionary processes. These observaions sugges serious problems in applying a mean-variance framework o longerm reurn modelling. In his respec Bernsein (1997) made he following commens relaing o 200 years of US financial hisory: "A srange and unexpeced conclusion emerges. Socks are fundamenally less risky han bonds, no only because heir reurns have been consisenly higher han hose of bonds over he long run, bu also because less uncerainy surrounds he long-erm reurns ha invesors can expec on he basis of pas hisory." Dividend growh models Dividend growh models, when based on company profis or dividends being real in naure are ignoring he effec of he parial ploughback of profis. Over ime periods wih inflaion of he order of 5% per annum, he denial of ploughback and accepance of profis as income ha is real in naure are herefore compensaing errors. As he case of Berkshire Hahaway shows, a model based on dividends growing wih inflaion will no work when he effec of ploughback is no he same as he rae of inflaion. I migh be argued ha a dividend growh model based on growh arising mainly from reained profis would be reliable, however such a model ignores he possibiliy ha he iniial dividend level is, for some reason, unusual. If reurn-on-shareholders'-equiy is unusually high by hisorical sandards (as is currenly he case) hen such a model will no allow for he risk of dividends being reduced if corporae reurn on equiy were o rever o hisorical levels. I is possible ha curren levels of corporae profiabiliy will be susained, bu his 34

implici assumpion would be hidden in such a dividend growh model a he presen ime. The shareholders' equiy framework makes such an implici assumpion obvious as well as providing a mechanism for considering he alernaive scenario ha reurn-on-shareholders'- equiy will rever o some lower figure over ime. While we may accep he argumen ha dividends should mainain broad pariy wih GDP, his assumes here is no cos in aking up a pro-raa share of any new shares ha are issued by all consiuens of he marke index porfolio. To mainain a dividend sream ha mainains pariy wih GDP, shareholders' equiy mus also mainain a similar pariy and he amoun of addiional funds required will herefore be equal o he difference beween hose required o finance nominal growh of GDP and hose reained hrough plowback of reained profis. According o he shareholders' equiy framework, his is he cause of he wo-percen diluion observed by Arno and Bernsein (2002). However o adop a model which assumes ha he fuure diluion will also be 2% per annum, wihou idenifying wha caused he hisorical diluion o have been 2% per annum, is o accep a regulariy as a law of naure. The choice beween mean-variance models, dividend growh models and he shareholders' equiy framework As he early educaional "CT1 Core Reading" from he Faculy and Insiue of Acuaries (2006) demonsraes, he facors officially regarded by he acuarial profession as relevan o he long-erm reurn from ordinary shares are dividend yields, inflaion, real growh and "risk". These are he only facors menioned. As he shareholders' equiy framework demonsraes, he only one of hese four facors of any grea direc relevance is he dividend yield. Inflaion has a small influence bu his has been confused wih he effec of ploughback and, in consequence, has been exaggeraed. The models suggesed by he Mauriy Guaranees Working Pary (1980), Wilkie (1986) and Yakoubov e al (1999) all allow for changes in marke prices relaive o dividends or earnings. However reurn-on-shareholders' equiy and he role of reained profis in financing per-share growh are barely menioned. Of comparable imporance, i seems o be more or less assumed ha earnings and/or dividends will rise wih inflaion. Have we in he profession ignored, for oo long, he imporance of reurn on shareholders' funds and he implicaions of hisorical cos accouning? A imes of high inflaion, hese accouning problems are discussed - see Parker and Gibbs (1974) - only o be forgoen when inflaion subsides. Parker and Gibbs made his observaion a he ime in relaion o previous bous of inflaion, and, in his respec, hisory has repeaed iself. However when inflaion is 3% per annum, here is sill a considerable long-erm difference beween 10% reurn on shareholders' equiy being a real reurn and a moneary one. Those who ake a differen view and believe ha company profis and dividends are real income o invesors need o be righ. If hey are wrong, he widespread presumpion of a link beween inflaion and long-erm equiy reurns eliminaes any pressure for he accouning reforms necessary o make company profis and dividends real in naure. These wo issues, he way long-erm equiy reurns are driven by reurn on shareholders' equiy and he fac ha his is (wih some excepions) a moneary reurn under hisorical cos accouning, are all bu ignored by mean-variance and dividend growh models. I migh be possible o modify mean-variance and dividend growh models o ake hese maers ino accoun - bu would i no be more sraighforward o sar wih he shareholders' equiy framework? Wih his approach, he implied level of corporae profiabiliy (or reurn on shareholders' equiy) and he way i is assumed markes will be priced relaive o "fundamenals" is ransparen. 35

In relaion o he ASX All Ordinaries Index a he curren ime (June 2007), a mean-variance approach migh sugges an "expeced" long-erm rae of reurn equal o he long-erm bond rae approximaely (6%) plus a risk premium of 3%, while a dividend growh model migh sugges a similar oal reurn equal o he curren dividend yield (3.4%) plus a dividend growh rae of approximaely 6% per annum. Assuming he daa presened in able 5 is correc, hese esimaes (wheher based on he exisence of a risk premium or sandard assumpions abou dividend growh) conain a hidden assumpion ha curren levels of reurn on shareholders' equiy will persis indefiniely. This assumpion is no hidden wih a model based on he shareholders' equiy framework and, as illusraed in Table 6, he answers can someimes be very differen if we allow for mean-reversion in reurn-on-shareholders' equiy and he mean-reversion price/book raios ha is likely o follow. I migh be argued ha unil we undersand he economic forces driving reurn on shareholders equiy long-erm forecass of equiy asse class reurns based on hisorical values of reurn on shareholders' equiy are, like he equiy premium approach, also based on a regulariy. However, unlike he "risk" premium, recognising he imporance of reurn-onshareholders'-equiy and is moneary naure reurn-on-shareholders' equiy is he firs sep in esablishing a chain of causaion. In all he debae abou sock marke levels and oher quesions ha depend on long-erm equiy reurns (including esimaes of he fuure equiy premium and he adequacy of he 9% compulsory superannuaion guaranee), here has been lile discussion of he susainabiliy of curren levels of reurn on shareholders' equiy, ye his is one crucial variable on which answers o hese quesions depend. The shareholders' equiy long-erm modelling framework makes his abundanly clear. Acknowledgemen Two drafs of his paper were carefully read by a peer reviewer who wishes o remain anonymous. This review led o a number of improvemens and he reviewer's commens are graefully acknowledged. 36

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Appendix Deails of calculaions shown in Table 6. As a ASX All Ords 30/06/2007 P/E 18.01 PB(0) 2.68 D/P 0.034 RoSe(0) 0.1488 Div/Book 0.0911 PoR 0.6123 PPN real 0.1 Inflaion 0.03 Scenario AASX All Ords IRR 0.095 0.095 Incl infla 0.098 0.098 RoSe() ShEq()NPAT() D() PB() CF10() CF20() 0 0.1488 100.00 14.88 4.56 2.68-263.44-263.44 1 0.1488 105.94 15.32 9.38 9.38 9.38 2 0.1488 112.23 16.23 9.94 9.94 9.94 3 0.1488 118.90 17.20 10.53 10.53 10.53 4 0.1488 125.96 18.22 11.16 11.16 11.16 5 0.1488 133.44 19.30 11.82 11.82 11.82 6 0.1488 141.37 20.45 12.52 12.52 12.52 7 0.1488 149.77 21.66 13.26 13.26 13.26 8 0.1488 158.66 22.95 14.05 14.05 14.05 9 0.1488 168.09 24.31 14.89 14.89 14.89 10 0.1488 178.07 25.76 15.77 2.68 485.12 15.77 11 0.1488 188.65 27.29 16.71 16.71 12 0.1488 199.86 28.91 17.70 17.70 13 0.1488 211.73 30.62 18.75 18.75 14 0.1488 224.30 32.44 19.87 19.87 15 0.1488 237.63 34.37 21.05 21.05 16 0.1488 251.74 36.41 22.30 22.30 17 0.1488 266.70 38.57 23.62 23.62 18 0.1488 282.54 40.86 25.02 25.02 19 0.1488 299.32 43.29 26.51 26.51 20 0.1488 317.10 45.86 28.08 2.68 863.87 39

As a ASX All Ords 30/06/2007 Addiional Scenario B assumpions (reversion in RoSe and Price/book afer m years. m 5 Rose(m) 0.09 P/B(m) 1.5 Scenario B ASX All Ords IRR 0.013 0.038 Incl infla 0.016 0.041 RoSe() ShEq() NPAT() D() PB() CF10() CF20() 0 0.1488 100.00 14.88 4.56 2.68-263.44-263.44 1 0.1370 105.46 14.08 8.62 8.62 8.62 2 0.1253 110.71 13.54 8.29 8.29 8.29 3 0.1135 115.69 12.85 7.87 7.87 7.87 4 0.1018 120.34 12.01 7.35 7.35 7.35 5 0.0900 124.62 11.02 6.75 6.75 6.75 6 0.0900 129.04 11.41 6.99 6.99 6.99 7 0.0900 133.62 11.82 7.24 7.24 7.24 8 0.0900 138.37 12.24 7.49 7.49 7.49 9 0.0900 143.28 12.67 7.76 7.76 7.76 10 0.0900 148.37 13.12 8.04 1.50 226.57 8.04 11 0.0900 153.64 13.59 8.32 8.32 12 0.0900 159.09 14.07 8.62 8.62 13 0.0900 164.74 14.57 8.92 8.92 14 0.0900 170.59 15.09 9.24 9.24 15 0.0900 176.65 15.63 9.57 9.57 16 0.0900 182.92 16.18 9.91 9.91 17 0.0900 189.42 16.76 10.26 10.26 18 0.0900 196.15 17.35 10.62 10.62 19 0.0900 203.11 17.97 11.00 11.00 20 0.0900 210.32 18.60 11.39 1.50 321.18 40