1959_Gordon Dividends, Earnings, and Stock Prices.pdf

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Dividends, Earnings, and Stock PricesAuthor(s): M. J. GordonSource: The Review of Economics and Statistics, Vol. 41, No. 2, Part 1 (May, 1959), pp. 99-105Published by: The MIT PressStable URL: http://www.jstor.org/stable/1927792

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DIVIDENDS, EARNINGS, AND STOCK PRICES

M. J. Gordon*

T HE threepossiblehypotheseswithrespectto what an investor pays for when he ac-

quires a share of common stock are that he is

buying (i) both the dividendsand the earnings,

(2) the dividends,and (3) the earnings. It may

be arguedthat most commonlyhe is buying the

priceat some future date, but if the futureprice

will be relatedto the expecteddividendsand/or

earnings on that date, we need not go beyond

the three hypotheses stated. This paper will

critically evaluate the hypotheses by derivingthe relation among the variables that followsfrom each hypothesis and then testing the the-

ories with cross-section sample data. That is,price, dividend, and earningsdata for a sampleof corporationsas of a point in timewill be used

to test the relation amongthe variables predict-ed by each hypothesis.

The variation in price amongcommonstocksis of considerableinterest for the discovery of

profitable nvestmentopportunities, orthe guid-

ance of corporate financial policy, and for the

understandingof the psychology of investment

behavior.' Althoughone would expect that this

interest would find expression in cross-section

statistical studies, a search of the literature isunrewarding.

Cross-sectionstudies of a sort are used ex-

tensively by security analysts to arrive at buy

and sell recommendations.The values of certain

attributes such as the dividendyield, growth in

sales, and managementability are obtainedand

compared or twoor morestocks. Then, by some

weightingprocess, a conclusionis reachedfrom

this information that a stock is or is not an

attractive buy at its currentprice.2 GrahamandDodd go so far as to state that stock prices

should bear a specified relation to earnings anddividends, but they neither present nor cite datato support the generalization.3 The distin-guished theoretical book on investment valueby J. B. Williams contains several chaptersde-voted to the application of the theory, but hisempiricalwork is in the tradition of the invest-ment analyst's approach.4 The only study alongthe lines suggested here that is known to thewriter is a recent one on bank stocks by DavidDurand.5

In contrast with the dearth of published stud-ies the writer has encountered a number ofunpublished cross-section regressions of stockprices on dividends, earnings, and sometimesother variables. In these the correlations werehigh, but the values of the regressioncoefficientsand their variation among samples (differentindustries or different years) made the eco-nomic significanceof the results so questionablethat the investigators were persuadedto aban-don their studies. There is reason to believethat the unsatisfactory nature of the findings is

due in large measure to the inadequacy of thetheory employed in interpretingthe model, andit is hoped that this paper will contribute to amore effective use of cross-section stock pricestudies by presentingwhat might be called the

elementary theory of the variation in stockprices with dividends and earnings.

Before proceeding, t may be noted that therehave been some time series studies of the varia-tion in stock prices with dividends and othervariables. The focus of these studies has been

the relation between the stock market and thebusiness cycle6 and the discovery of profitable

* The researchor this paperwas supportedby the Sloan

ResearchFund of the Schoolof IndustrialManagementat

MassachusettsInstitute of Technology. The author hasbenefitedfrom the advice of ProfessorsEdwin Kuh, EliShapiro,and GregoryChow. The computationswere donein part at the M.I.T. ComputationCenter.

'Assumethat the hypothesis tock price,P f (xi, X2,...),

is stated so that it can be tested, and it is found to do agood job of explaining he variation n price amongstocks.The model and its coefficients herebyshed light on whatinvestorsconsiderand the weight they give these variablesin buying commonstocks. This information s valuabletocorporationsnsofar as the pricesof their stocks influencetheirfinancialplans. It is also true that a stock sellingat aprice above or below that predictedby the model deservesspecialconsideration y investors.

2Illustrationsof this method of analysismay be foundin texts on investmentanalysissuch as: Grahamand Dodd,SecurityAnalysis, 3rd ed. (New York, i95i); and Dowrieand Fuller, nvestments New York, I94I).

' GrahamandDodd,op. cit., 454 ff.'The Theory of Investment Value (Cambridge, 938).

5Bank StockPricesand the Bank CapitalProblem,Occa-sional Paper 54, National Bureau of Economic Research(New York, I957).

'J. Tinbergen, "The Dynamics of Share-PriceForma-tion," this REVIEW,XXi (November I939), 153-60; andPaul G. Darling,"A SurrogativeMeasureof BusinessCon-

[99]



Ioo THE REVIEW OF ECONOMICS AND STATISTICS

investment opportunities.7They have not been

concernedwith explainingthe variationin priceamong stocks, and it is questionable whether

such data can be effectively used for this pur-pose. Auto-correlation n the time series would

impair the significanceof the regressioncoeffi-cients for many of the variables. Possibly evenmore important,the use of time series assumesthat the coefficientof a variableis constantover

time but different among stocks. The exact op-

posite is assumed in any attempt to explainpreferenceamong investmentopportunities.

The Sample

To test each of the theories, price, dividend,

and earnings data were obtained for four in-

dustries and two years, so that there are eight

samplesin all. The years chosenwere I95I andI954, and the industries and number of cor-

porations for each industry are Chemicals,32;

Foods, 52; Steel, 34; and MachineTools, 46.

Including only those corporationswhich con-

formed to a narrowdefinitionof the industriesmentioneddid not provide samples of adequatesize. Therefore, certain fringe classifications

were included in each category. For instance,Chemicals includes pharmaceutical manufac-

turers,and Steel includesforgingmanufacturers

and certain other fabricatorsof steel as well asthe basic steel producers. In general, while the

corporations included in each sample can be

consideredto comeunderthe label, there is con-

siderable variation among them in such attri-

butes as size, profitability,structureof the mar-

kets in which they buy and sell, and investor

status.8

The use of eight samples rather than one

providesa morerigoroustest of the hypotheses.The industryand year selection of the data has

the further advantage of allowing the use of

a priori economic knowledge in evaluating theregression statistics. For instance, if the divi-

dend coefficient s consideredan estimate of therate of profit, we want to know whether theestimate is reasonableon groundsbroader thanstatistical significance. Good preferred stockssold in these years at dividendyields of four to

five per cent, and companiesacquiredin merg-ers were purchased for about five times theirearnings before income taxes. Therefore, wewould expect the rate of profit on commonstocks to fall between four and ten per cent andthe coefficient in question to fall between tenand twenty-five. Further, we would expect aparticularrankin the coefficients. Corporationsin the chemical industry are consideredto havethe advantages of, size, growth, and stability;foods represent an industry that is consideredstable; steels representan industry with largecorporationswhich are consideredvulnerabletocyclical fluctuations; and machine tools repre-sent an industry of comparatively small cor-porationswhich are also vulnerableto the busi-ness cycle. Accordingly, one might expect therate of profit to vary among the industries inthe order just given. Further, I95I was a yearof war profits with the outlook for the futuresomewhat uncertain. By contrast, while therewas some talk of recession in I954, there waslittle evidence that the high level of income ex-

tending back a number of years would fallsharply in the near future. Accordingly, onemight expect that the coefficients would differin a predictablemanner between the two years.

DividendsandEarnings

Given the task of explainingthe variation in

price among common stocks, the investigatormay observe that stockholdersare interested in

both dividendand incomeper share and derive

immediately from this observation the model:

P = ao + a,D + a2Y (I)

where P = the year-end price, D = the year's

dividend, and Y = the year's income. Theequation may be considered of interest solelyfor the multiple correlationbetween the actualand predictedprice, in which case no meaningcan be given to the regressioncoefficients. Al-

ternatively, the equation may be read to meanthat the coefficientsa, anda2represent he valuethe market places on dividends and earningsrespectively, a possible objective being the

fidence and Its Relation to Stock Prices," Journal of Finance,

x (December I955), 442-58.

'The outstanding example of this is The Value Line In-

vestment Survey. In addition, numerous articles in the

Analysts Journal and the Journal of Finance analyze the

change over time of price with other variables. A paper of

some interest is D. Harkavy, "The Relation Between Re-

tained Earnings and Common Stock Prices for Large, Listed

Corporations," Journal of Finance, viii (September I953),

I83-97.

'A list of the corporations and a description of how they

were selected may be obtained from the writer on request.



DIVIDENDS, EARNINGS, AND STOCK PRICES

measurementof the relative importanceof thetwo variables. However, a share of stock likeany other asset is purchased for the expectedfuture income it provides. This incomemay bethe dividend or it may be the earningspershare,

but it cannot be both. The model is thereforeconceptually weak.

The unfortunate consequence of this prag-matic approachto the measurementof the vari-ation in stock prices with dividend and earningsis illustrated by the data of Table i. The divi-dend coefficientfor chemicals in I95I is nega-tive and machine tools has the highest coeffi-cient. Between I95I and I954 the chemicalscoefficientchanges from approximatelyzero to25. Many of the dividend coefficientsare ma-

terially below ten, and inI954

the highest co-efficient is five times the lowest. The income

coefficients,with the exception of chemicals in

I95I, are extraordinarily low as measures of

the price the market is willing to pay for earn-

ings.

Machine tools in I95I and chemicals in I954

have income coefficientsthat are not significant-

ly different from zero, and three of the other

coefficients are materially below five. Armed

only with the theory just stated, it would be

most difficult to infer from the data the exist-

ence of a logical structure in the pricing of

commonstocks.

The DividendHypothesis

The hypothesis that the investor buys thedividend when he aquiresa shareof stock seemsintuitively plausible because the dividend isliterally the payment stream that he expects to

receive. In implementing he hypothesis it mustbe recognized that the stockholder is interestedin the entire sequence of dividend paymentsthat he may expect and not merely the currentvalue. For the purpose of arrivingat an opera-tional model we may represent this infinite se-quence by two quantities, one the current divi-dend and the other a measure of the expectedgrowth in the dividend.

Among the events which will lead to an in-crease in a corporation'sdividend are: success-

ful tradingon its equity, an increasein its returnon investment, and selling additional commonstock when the rate of profitthe corporationcanearn is above the rate at which its stock is sell-ing. However, there is no doubt that the mostimportantand predictablecause of growth in acorporation'sdividend is retainedearnings. Forthose interested in a more rigorousargument ithas been shownthat if a corporation s expectedto earn a return r on investment and retain afraction b of its income, the corporation'sdivi-dend can be expectedto growat the rate br.9 If

the investmentor book value per share of com-mon stock is B, then

br Y-D y Y-D(2)

Y B B(2

Investors are interested in growth and not rateof growth, since a high rate of growth startingwith a low initial value will pay off in the heavi-ly discounted distant future, and it will not beas attractive as a lower rate of growth startingfrom a higher initial value. Therefore, in a

model where price and dividend are absolutequantities, it is likely that retained earningsper share without deflation by book value is a

bettermeasureof growththanthe rateof growth.The previous discussion has provided the

economic rationalefor using the equation

P = ao + a, D + a2 (Y-D) (3)

TABLE I.- MODEL I, REGRESSION OF PRICE ON

DIVIDEND AND INCOME

Constant Coefficientand MultipleSample term standarderrorof correlation

D Y

I95I-Chemicals -7.0 -.8 I6.7 .93

(5.2) (3.I)

Foods .J 7.0 5.5 .90

(I-5) (.9)

Steels 5.5 6.6 2.0 .86

(i.8) (.6)

Machine ools 2.4 I2.0 .8 .90

(I.2) (.5)

I954- Chemicals -3.0 25.7 .3 .92

(5.2) (3.3)Food -4 I0.4 5.6 .9I

(2.2) (I.0)

Steels 8.7 8.4 2.0 *94

(I -7) (.8)

Machine tools 6.3 5.5 4.I .89

(I-4) (.6)

'The argument is developed more fully in M. J. Gordon

and Eli Shapiro, "Capital Equipment Analysis: The Re-

quired Rate of Profit," Management Science, DiI (October

I956), I02-IO.



I02 THE REVIEW OF ECONOMICS AND STATISTICS

to represent the hypothesis that the investorbuys the dividend when he acquires a share ofstock. The reciprocalof the dividend coefficientmay be looked on as an estimate of the rate ofprofit the market requires on common stocks

without growth, and the retained earnings co-efficient is the estimate of what the market iswilling to pay for growth.

Table 2 presents the eight sample estimatesof the model's coefficients. The I95i dividendcoefficients are considerably superior to thoseof Model I under the criteria stated earlier fortheir absolute and relative values. Only themachinetools coefficientappears comparativelyhigh. The I954 coefficients vary among the in-dustries as expected and they fall within the

expected range. The spread in the coefficientsis only one-half the range of those in Model I,but it still seems quite large. In particularonemight wonder at the high chemicals-I954 co-efficient,the low steels-i95I and machinetools-I954 values, and the strong inverse correlationbetween the coefficientsand the constant terms.

Turning now to the retained earnings coeffi-cients, what would we expect of them? Sincethey representthe price the market is willing topay for growth in the dividend, with retainedearnings servingas an index of growth,the only

statement with respect to their values that fol-lows from the theory is that they should bepositive. It may be thought nonetheless thattheir values seem low, and the absence of sta-tistical significanceat the five per cent level fortwo coefficients,machine tools-I95I and chem-

icals-Ig954,s particularlydisturbing. The reallysurprising result is the negative chemicals co-efficients for I954. On the other hand there issome a priori credibilityin the findings. Growthis most uncertainand it becomes quantitativelyimportant by comparisonwith the current divi-

dend in the distant future. Also, apart from theI954 chemicals there is a rough correspondencebetween the rank of the coefficientsand notionsas to the comparative stability of earningsamongthe industries.

The readermay have noted (i) the multiplecorrelationcoefficients n Tables i and 2 are thesame for each industry year, (2) the earningsand retainedearnings coefficients,a2and a2 arethe same, and (3) the dividend coefficienta, = a,+ a2. On the firstpoint, in both equations price

is a linearfunction of the samevariables,so thatthey both yield the samecorrelationcoefficients.The earnings and retained earnings coefficientsare the same, since the change in earnings is thesame as the change in retained earnings when

the dividend is held constant. The difference nthe dividend coefficients is due to the fact thatin equation (i) the increasein dividendinvolvesa correspondingreductionin retainedearnings,whereas in equation (3) retained earnings isheld constant.

The dividend hypothesis provides a morereasonable interpretation of equation (i) thanthe interpretationgiven in the previous section.If growth is valued highly, an increase in thedividend with a correspondingreduction in re-tained earnings will not increase the value of ashare as much as when a low value is placed ongrowth. There is some tendency for the a, co-efficientsto vary among industries accordingly.Another point to be noted is that the standard

errorof a, is below that for a,. This combinedwith the higher values of the formercoefficientsmeans that the change in price with the divi-dend can be predicted with much greater accu-racy when retained earnings are held constantthan when the increase comes out of retainedearnings.

The EarningsHypothesis

The thirdhypothesis is that the investor buysthe income per share when he acquires a share

TABLE 2. - MODEL II, REGRESSION OF PRICE ON

DIVIDEND AND RETAINED EARNINGS

Constant Coefficientand MultipleSample term standarderrorof correlation

D Y-D

I 95 I-Chemicals -7.0 I5.9 I6.7 .93(2.7) (3 .)

Foods .1 I 2.5 5-5 .90

(I.I) (.9)

Steels 5.5 8.6 2.0 .86

(I.5) (.6)Machine tools 2.4 I2.8 .8 .90

(I.0) (.5)

I954- Chemicals -3.0 30.0 .3 .92

(2.6) (3-3)

Foods -.4 I5.9 5.6 .9I

(I.5) (I.0)Steels 8.7 I0.4 2.0 .94

(I -4) (.8)Machine tools 6.3 9.6 4.I .89

(I.2) (.6)



I04 THE REVIEW OF ECONOMICS AND STATISTICS

crease, other things being the same, with the

maturityof the bond.

Refinementsn theModel

Equation(3) is an extremelysimpleandcrude

expression of the dividend hypothesis, and in-sofar as the valuesof the coefficientsaresuspect,

it may be due to limitations of the model. In

this section we shall discuss the more important

limitations,suggesthow they may be dealt with,

and then present data for a modelthat attempts

to overcomesomeof these limitations.i. Correlation between the variables and

variation in the coefficientsamong industries is

due in part to the scale factor. The problemmay be stated as follows. Assume a sample of

n corporationsfor all of which the dividend isthe same, the price differs among the shares,

and the average of the prices is higher than the

dividend. There is no correlationbetweendivi-dend and price. However, if n numbers are

selected at randomand the price and dividendof each share is multipliedby one of these num-

bers, correlationbetween the variables will be

created. Further, if each of the n randomnum-

bers is first multiplied by a constant greaterthan one, the correlationand the regressionco-

efficient will be larger the larger the value of

this constant. The presence of so-called high-pricedandlow-pricedstocks in a samplereflects

in somepart this scale factor. It is possible that

by deflatingthe data, say by book value,and/or

usinglogs we will moderatethe influenceof scale

on the coefficients.2. The independentvariablesin equation(3)

are the current values of dividendsand retained

earnings. These quantitiesare of interest, how-

ever, only because they represent the latest

available information for the prediction of fu-

ture dividends. Insofar as these currentvaluesdepartfromaveragesover somepriorperiodfor

extraordinary easons, nvestmentanalystsmain-

tain that the changes should be discounted to

arrive at what might be considered normal

values. This suggests that some combinationof

currentvalues and averagesover a priorperiodfor dividendsand retained earningswould pro-

vide a superiorexplanation of the variation in

price amongshares.3. The value the marketplaceson a dividend

expectation derived from past dividends and

retainedearningsmaybe expectedtovary among

corporationswith the confidence n the dividend

stream. This would suggest that the price of a

share varies with other variables such as the

size of the corporation,the relation of debt to

equity, and the stability of its earning record.Insofar as the values of these variables vary

amongindustries, failure to include them intro-

duces variation and error in the dividend andretainedearningscoefficients.

4. In the present model the variationin price

with growth in the dividend is estimated by

using an index of growth, retained earnings,as

the independentvariable. A model in whichit is

possible to use the rate of growth itself might

yield better results. More important,the defini-

tion of the rate of growthhas considerablethe-oretical merit to date nothing superior has

been proposed but there are empiricalprob-

lems involved in using it. Variationin account-

ing practice amongfirmsmakes the use of book

value as a measure of return on investment

questionable. Also, the instability of corporate

retained earnings and the possibility that they

vary over time differentlyamongindustriesmay

makethe use of past values to predictthe future

an heroic assumption. This is particularlytrue

if investors give considerableweight, rationally

or otherwise, to other variables in predictingfuture earnings.

Table 3 presents the regressionstatistics for

the followingmodel

P=po+/ d+ 32 (d-d)

+/33g+34 (g-g). (7)

In this equation:

P = year-end ricedividedby bookvalue,

d = averagedividend or the priorfive yearsdividedby bookvalue,

d=

currentyear'sdividenddividedby book

value,g = average etained arningsortheprior ive

yearsdividedby bookvalue,g = current ear'sretained arnings ividedby

bookvalue.

The deflationby book value was undertaken

to eliminate the scale effect discussedprevious-ly.'2 The objective was only partially accom-

plished, since correlation exists between the

'The use of deflatedvariables n regression nalysis s adebatablequestion. See David Durand, op. cit., 56; and



DIVIDENDS, EARNINGS, AND STOCK PRICES I05

TABLE 3. REGRESSION OF PRICE ON DIVIDEND, RETAINED EARNINGS, CHANGE IN DIVIDEND,

CHANGE IN RETAINED EARNINGS, ALL DEFLATED BY BOOK VALUE

Coefficientand standarderrorof

Constant _ _ - MultipleSample term d d-d g g-g correlation

I95I - Chemicals -.23 I2.42 9.79 I8.74 I4.36 .8o

(2.63) (5.98) (5.96) (5.6o)

Foods .04 I4.04 8.o6 3.I6 4.57 .90

(I .04) (2.49) (I.3 9) (I .58)

Steels .I5 9.88 6.38 I.45 .4I .88

(I.05) (I.87) (I.09) (i.o6)

Machine tools .I2 I2.62 5.93 .I2 I.II .9I

(I.I7) (2.75) (.99) (.80)

I954-Chemicals .54 I7.38 I2.7I .I2 3.44 .79

(2.92) (8.93) (6.39) (4.78)

Foods -.03 I5.5I 8.74 5.15 5.96 .92

(I.04) (2.82) (I.66) (I.67)

Steels .I8 9.69 3.85 2.02 2.85 *9I

(.99) (I.I3) (.68) (.67)

Machine tools .05 II.65 6.o6 3.70 I.92 .87

(I.I6) (I.74) (I.I2) (I.04)

deflated and undeflatedvariables. For instance,correlationbetweenP andp forthe eightsamplesranged from zero to .65 and was more than .4for six of the samples.

The use of d and (d- d) assumes that theinvestor values a stock on the basis of the aver-age dividendduringthe priorfive years and the

amountby which the currentvalue differsfrom

this average. The same reasoning applies to g

and (g- g), which by the way should be inter-preted as deflated retained earningsand not as

growth rates in the context of this model. The

coefficients ,8 may be interpreted as follows:

1/3= /2 (or /3 = 4) implies that the investorsignore the average dividend for the prior five

years and consider only the current dividend;

2 = o implies that the current dividend is ig-nored; ,81> A32 mplies hat investorsadjusttoa change in the dividend with a lag,'3 i.e., the

elasticity of expectations is less than one. The

oppositeis true if 83, /32.Turning to the data of Table 3 we see that

five of the eight multiplecorrelationcoefficientsare lower than in Table 2, and for some the

differenceis large. This is due to the deflation

by book value. For dividends,deflationand/or

the use of both the average value and the de-parture from average appears to have donesome good. The range of the dividend coeffi-cient has been reduced by comparison withTable 2, and the change in dividend coefficientis interesting. All but the chemicals coefficientsare significant at the five per cent level, and

they all are less than the d coefficients. There-fore, as expected, a rise in the dividend is dis-

counted until the average has risen to the newlevel.

The growth coefficients,however, are disap-pointing. First, the values for g are if anythingpoorer than the values for Y- D in Table 2.

Second, three of the eight coefficientsare notstatistically significantat the five per cent level.Third, for some of the samples 34 3, whichmeans that investors are either indifferent topast performance or prefer a share for whichretainedearningshas increasedto one forwhich

it has fallen.The performanceof the model just discussedin explainingthe variationin priceamong stocksis far superiorto the simple empiricalapproachpresented earlier. However, considerableroom

for improvement remains. The lines alongwhich it will be realized appear to be a more

effective representationof growth and the rec-ognitionof variableswhich influencethe valua-tion of a dividend expectation. Solution of thescale problemthrougha different structuralre-

lation amongthe variablesmay also be of value.

Edwin Kuh and John R. Meyer, "Correlation and Regres-

sion Estimates when the Data are Ratios," Econometrica,

xxin (October 955), 400-i6.

'We are talking about an unexpected change in the

dividend, since d is the percentage that the dividend bears

to book value. A rise in the dividend proportional to the

rise in book value counts as no change in the dividend.

1959_Gordon Dividends, Earnings, and Stock Prices.pdf

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