Predicting the equity premium with dividend ratios:Reconciling
the evidence
Neil M.Kellard a,⁎,John C.Nankervis a ,Fotios I.Papadimitriou b
a
写信的格式怎么写Esx Business School and Esx Finance Centre,University of Esx,United Kingdom b School of Management,University of Southampton,United Kingdom
a r t i c l e i n f o a
b s t r a
c t
Article history:Received 26April 2009Received in revid form 19March 2010Accepted 6April 2010Available online 11April 2010This paper evaluates the ability of dividend ratios to predict the equity premium.We conduct an in
and out-of-sample comparative study and apply the Goyal and Welch (2003)graphical method to
equity premia derived from the UK FTSE All-Share and the S&P 500indices.Preliminary in-sample
univariate regressions reveal that in both markets the equity premium contains an element of
predictability.However,the considered out-of-sample models outperform the historical moving
average only in the UK context.This is con firmed by the graphical diagnostic which further
indicates that dividend ratios are uful predictors of UK excess returns.Our paper provides a
possible explanation of why dividend ratios might be more informative in the UK market by
linking the findings to the disappearing dividend phenomenon.Finally,Campbell and Shiller
(1988)identities are employed to account for the time-varying properties of the dividend ratio
and dividend growth process.It is shown that by instrumenting the models with the identities,
forecasting ability can be further improved.全国高考人数
©2010Elvier B.V.All rights rerved.JEL classi fication:C22C32C53Keywords:Equity premium
Stock return predictability
Dividend ratios
Out-of-sample prediction
1.Introduction
The predictability of stock market returns is one of the most controversial and intenly debated issues in empirical finance.A voluminous literature around the issue has evolved during the last two decades,primarily asssing US market data and rendering an overall asssment extremely dif ficult.The dividend –price ratio and the dividend yield rank amongst the most popular candidates ud to predict stock market returns (Lewellen,2004;Hodrick,1992;Fama and French,1988;Campbell and Shiller,1988;Rozeff,1984).1However,finding in-sample statistical signi ficance is not conclusive evidence that variables have out-of-sample power or that predictability is economically signi ficant.Ang and Bekaert (2007),Goyal and Welch (2003)and Bossaerts and Hillion (1999)all cast doubt on the evidence documented by early authors,reporting negative results when out-of-sample tests 2are employed.
This paper provides a comparative study,evaluating the in and out-of-sample performance of dividend ratios when ud to predict the equity premium across the US and UK stock markets.Recent studies (e McMillan,2003;Pesaran and Timmermann,Journal of Empirical Finance 17(2010)539–551
⁎Corresponding author.Esx Business School,Esx Finance Centre,University of Esx,Wivenhoe Park,Colchester,CO43SQ,United Kingdom.Tel.:+441206874153;fax:+441206873429.
E-mail address:nkellard@esx.ac.uk (N.M.Kellard).
1Other financial and macroeconomic predictive variables include the earnings-to-price ratio (Lamont,1998),the book-to-market ratio (Pontiff and Schall,1998),the short-term interest rate (Ang and Bekaert,2007),the yield spread (Fama and French,1989),and the consumption –wealth ratio (Lettau and Ludvigson,2001).
2It is typically believed that out-of-sample tests provide a measure against data mining.Nevertheless,Rapach and Wohar (2006)and Inoue and Killian (2004)both show that,if appropriate tests are employed,in-sample and out-of-sample tests are equally reliable.Rapach and Wohar (2006)argue the ca for a predictable component in stock returns is strengthened by this
result.
0927-5398/$–e front matter ©2010Elvier B.V.All rights rerved.
doi:10.1016/j.jemp fi
n.2010.04.002
Contents lists available at ScienceDirect
Journal of Empirical Finance
j o ur n a l h o m e p a g e :ww w.e l s ev i e r.c o m /l o c a t e /j e m pf i n
2000)suggest that dividend yields may prent out-of-sample predictive power in the UK context.We examine formally whether systematic differences exist in the predictive ability of UK and US dividend ratios and offer an explanation of the contradictory findings between the two markets.
Turning to our methodological approach,a battery of in and out-of-sample tests are adopted;including the Goyal and Welch (henceforth GW,2003)recursive residuals (out-of-sample)graphical technique,allowing us to dynamically obrve when predictability occurred in the two markets.The initial data t analyd contains monthly obrvations covering the period from 1975to 2009for the FTSE All-Share index 3and the S&P 500index.
Strikingly,strong support for the predictability of the UK equity premium is uncovered,using both the graphical diagnostic and conventional in-sample and out-of-sample tests.In particular,the graphical diagnostic highlights the period from the late 1990s onwards as highly predictable.On the other hand,there is much less evidence in favour of predictability for the S&P 500data.The results appear to con firm the emerging conclusion from the extant literature that UK dividend ratios poss
s more predictive ability than their US counterparts.Indeed,it is shown that by instrumenting the models with Campbell and Shiller (1988)identities,forecasting ability can be yet further improved within the UK context.
Of cour,the question remains of why the FTSE All-Share dividend ratios show more predictive ability than the S&P 500?A line of enquiry is to investigate the relative fraction of firms offering dividends over the sample period.If the fraction of offering firms is higher in one market,it would be expected ceteris paribus ,for that market to prent more predictability if such predictability exists.
Fama and French (2001)stress the phenomenon of the ‘disappearing dividend ’in the US,documenting the tendency of publicly traded non-financial,non-utility firms to pay less dividends since 1978.Explanations include the changing characteristics of the typical firm,in particular due to the new listings of low pro fit/high growth opportunity firms that are conquently less likely to post a dividend.Other rationale includes the large increa in US firms repurchasing their own shares (e Skinner,2008;Grullon and Michaely,2004).Finally,Amihud and Li (2006)propo an explanation for the US ‘disappearing dividend ’phenomenon,which they argue is partly due to a decline in the information content of dividend announcements.
作业的拼音
To our knowledge,there is less work on the fraction of UK firms offering dividends.Both von Eije and Megginson (2008)and Benito and Young (2003)uncover an increasing proportion of UK quoted companies omitting cash dividends.To examine the issue further,we obtained annual dividends data for the FTSE All-Share and S&P 500indices,providing evidence on the proportion of companies that actually issue dividends for the period 1975–2009.Although in both markets there is a tendency of firms to pay less dividends,it is shown that the phenomenon is not so pronounced for the FTSE All-Share.We therefore argue that dividends have been relatively more important in the FTSE All-Share over the sample period,conveying more information and prenting more predictive ability.
As a final robustness check,we examined the predictability of dividend ratios for the Dow Jones Industrial Average index.The Dow Jones is comprid of 30large companies which we show have a greater propensity to post dividends than S&P 500firms.In line with our proposition,dividend ratios from the Dow Jones clearly outperform,in a predictive n,ratios from the S&P 500!
The paper is organized as follows.Section 2discuss the data,describing the main variables and the transformations employed in the later empirical analysis.Section 3prents the methodology,whilst Section 4offers the results and discuss the empirical findings.A final ction concludes the study.
2.Data
The FTSE All-Share is the most comprehensive UK stock market index.In our study,monthly data is employed,covering the period from 1975:04to 2009:11.The corresponding data for the US market were derived from the S&P 500composite index.All data were obtained from DataStream,the starting date reprenting the extent of UK data availability from that databank .The u of a monthly frequency is particularly advantageous,allowing the examination of intra-annual predictability.
A number of variables are relevant to the study.Firstly,and as is common in the literature,log returns on the index are ud:
艾薇儿身高r m ;t =log R m ;t h i =log P t +D t ðÞ=P t −1½ ð1Þ
where P is the stock index level and D the paid dividends.Next,the log returns on the three-month risk-free Treasury bill (called R f ,t )are calculated:
r f ;t =log 1+R f ;t
h i ð2ÞThe dividend –price ratio DP t is the log of the aggregate dividends D t divided by the aggregate stock market value P t :
DP t =log D t =P t ½
ð3Þwhilst the dividend yield ratio DY t is de fined:
DY t =log D t =P t −1½ ð4Þ3The FTSE All-Share is the most commonly employed index in UK stock return predictability studies.
540N.M.Kellard et al./Journal of Empirical Finance 17(2010)539–551
Finally,the equity premium is denoted by EQP t and is the return on the stock market (r m ,t )minus the return on a short-term risk-free Treasury bill (r f ,t ):
EQP t =r m ;t −r f ;t ð5ÞFor completeness,Fig.1plots the time ries of the equity premium and the dividend ratios.4Interestingly,the figure shows the tendency for all dividend ratios to decline until 2001and then resume an upward trend thereafter.In a proportionate n,this suggests that dividends have become relatively more important over the last ten years.We shall return to this later.
3.Methodology
3.1.In-sample predictability
To evaluate in-sample predictive ability,we estimate the following regression model:
静悄悄类似词语EQP t =α+βx t −1+εt ð6Þwhere the predictive variable x t −1can be either the lagged dividend –price ratio (DP t −1)or the lagged dividend yield (DY t −1).The predictive ability of x t −1is assd by examining the t -statistic corresponding to β,the OLS estimate of βin Eq.(6),as well as the goodness of fit measure,R 2.The null hypothesis tested is that of no β=0against the alternative that there is β≠0.
3.2.Out-of-sample predictability
A market timing investor would be interested in knowing if s/he could take advantage of the dividend ratios in order to predict the equity premium.Thus,the question is how the “conditional dividend ratio models ”would perform when compared to the “unconditional historical equity premium model ”(the prevailing simple moving average).As in GW,forecasting regressions are estimated only with then-available data.Both the conditional models and our naive benchmark model are estimated as recursive forecasts to predict one-month-ahead equity premia.
Our next goal is to compare the out-of-sample forecasts from the dividend model predictive regressions against the historical mean.If the conditional dividend ratio model outperforms the prevailing moving average,then this implies that the dividend ratios add uful information and impro
ve predictive ability.First we report the statistics on the out-of-sample prediction errors obtained in different sample periods.In particular,we document the mean,standard deviation,root mean square error (RMSE)and mean absolute error (MAE)of equity premium prediction errors.Finally,we compute the Diebold and Mariano (1995)test statistic for equal predictive accuracy.
3.3.A graphical evaluation method for the out-of-sample performance
Following GW,we employ a graphical method as a complementary diagnostic for equity premium and stock return prediction.The procedure consists of plotting the cumulative sum –squared error from the unconditional model minus the cumulative sum –squared error from the dividend ratio model (denoted by Net −SSE T for a sample size of T obrvations).Expresd algebraically:
Net −SSE T =∑T t SE Prevailing Mean t −SE Dividend Model t h i ð7Þ
where SE t is the squared out-of-sample prediction error in obrvation t .The unconditional SE is obtained when the prevailing up-to-date equity premium average is ud to forecast the following month's equity premium.The conditional prediction errors of the dividend models are obtained from recursive regressions with either DP t −1or DY t −1as the sole predictor of the following month's equity premium.Clearly,a positive value indicates that the dividend ratio model has outperformed the
unconditional model so far.In addition,a positive slope indicates that the dividend model had lower forecasting error in a given month (i.e.superior performance).
Although graphing recursive residuals is relatively simple,GW stress its neglect by the literature implies some possible insights regarding predictability have typically been overlooked.In particular,the methodology allows for a dynamic identi fication of predictability.Time periods where dividend ratios succeed (or fail)in predicting the equity premium relative to the prevailing mean can be clearly obrved.As a conquence,the graphical procedure can be ud to enhance information derived from more conventional summary measures.GW claim that the graphical diagnostic reveals any predictability shown by US summary measures is caud primarily by outliers.On the other hand,it is possible that when the summary measures indicate no predictability,the graphical procedure may reveal pockets of forecastability which are hidden when an averaging procedure is employed.
4A table of descriptive statistics is available on request.
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基坑工程
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542N.M.Kellard et al./Journal of Empirical Finance17(2010)539–551
Fig.1.Time ries graphs.i)The UK equity premium,ii)the UK log dividend–price ratio,iii)the UK log dividend yield,iv)the US equity premium,v)the US log dividend–price ratio,vi)the US log dividend yield.Explanation:the above graphs plot the time ries of the log equity premium,the log dividend–price ratio and the log dividend yield respectively.All variables are described in Section2.
3.4.Instrumenting the changing dividend ratio process
GW argue that changes in dividend ratio autocorrelation and in the ability to predict changes in dividend growth could themlves imply changes in the dividend ratio's ability to predict the equity premium.The process changes can be ud to enhance the dividend ratio forecasting coef ficients for the equity premium.To explain this in more detail,consider the Campbell and Shiller (1988)approximate prent value relation with time-varying expected returns.Assuming that dividends and returns follow log-linear process,the approximation begins with the following identity:
1≡1+R m ;t
+1 −11+R m ;t +1 ⇒1≡1+R m ;t +1 −11+P t +1+D t +1−P t t ≡1+R m ;t +1 −1P t +1+D t
+1t ð8Þ
After some algebra,we find that the log dividend –price ratio can be approximated by the following relationship 5:
d t −p t ≈r m ;t +1−Δd t +1−k +ρd t +1−p t +1ÀÁð9Þor if w
e isolate returns on the left-hand side:
r m ;t +1≈d t −p t ðÞ−ρd t +1−p t +1ÀÁ+Δd t +1+k ð10ÞNow taking covariances with DP t and dividing by the variance of DP t we have:
Cov r m ;t +1;DP t
Var DP t ≈1−ρCov DP t +1;DP t ÀÁVar DP t +Cov Δd t +1;DP t ÀÁVar DP t ⇒βr m ;t +1;DP t ≈1−ρβDP t +1;DP t +βΔd t +1;DP t ð11Þ
where βY ,X denotes the coef ficient of X in a regression of Y on X and a constant.
The new model employs Eq.(11).6To estimate Eq.(11)we initially carry out recursive estimations of the following regressions of the dividend –price ratio and the dividend growth on the lagged dividend –price ratio:
厨房用具大全清单
DP t
+1=α0s +α1s DP t +u 1t +1;t =1;…;p +s −1;s =1;…;T −p ð12ÞΔd t +1=γ0s +γ1s DP t +u 2t +1;
t =1;…;p +s −1;s =1;…;T −p ð13Þwhere T denotes the sample size,p denotes the in-sample size and s is the number of out-of-sample obrvations.Once we have obtained the estimated recursive coef ficients α1s and γ̂1s from the above regressions,we can u Eq.(11)to calculate the instrumented betas β1s as follows:
β˜1s =1−ρα1s +γ1s ;s =1;…;T −p ð14ÞAccordingly,using the above instrumented betas,the indirect Campbell and Shiller forecasts are constructed as follows:
r ˆm ;t +1=βˆ0s +β˜1s DP t ;s =1;…;T −p ð15ÞOn the other hand,direct forecasts (the straight dividend model)are constructed simply by using the equation:
r m ;t +1=β0s +β1s DP t +u t +1;t =1;…;p +s −1;s =1;…;T −p ð16Þand estimating recursively using OLS.
康定4.Results
4.1.In-sample fit
Table 1tabulates the results of the univariate regressions that associate the log equity premium with the lagged dividend –price ratio (DP t −1)and the lagged dividend yield (DY t –1).In order to give a more complete view of the in-sample performance of the dividend ratios,we also report results for two other periods which include obrvations either up to 1995or to 2000.
5
Lower ca letters denote logs while k and ρare parameters of linearization.6Note that the approximations work only for returns and not for equity premia and also for dividend –price ratios but not for dividend yields.543
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