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

Transcription

1 A Review of he Mehodology of Forecasing Long-erm Equiy Reurns Richard Fizherber Presened o he Insiue of Acuaries of Ausralia Biennial Convenion 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

2 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

3 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

4 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 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 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

5 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

6 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 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

7 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

8 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

9 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

10 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 (pp ) 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

11 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

12 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

13 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

14 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 pp ) 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

15 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

16 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 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

17 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 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, pp ) 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

18 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 (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 (logarihmic) Ausralia (% pa) UK (% pa) USA (%pa) Capial growh Inflaion 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

19 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

20 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