Journal of Accounting Research Vol, 29 No, 1 Spring 1991

Printedin U.S.A.

Earnings as an Explanatory Variable for Returns
PETER D. EASTON* AND TREVOR S. HARRISf

1. Introduction
In this paper we investigate whether the level of earnings divided by price at the beginning of the stock return period is relevant for evaluating earnings/returns associations.^ The primary model motivating this research relies on the idea that book value (owners' equity) and market value are both "stock" variables indicating the wealth of the firm's equity holders. The related "flow" variables (after adjusting for dividends) are, respectively, earnings divided by price at the beginning of the return period {A/P~i) and market returns. It then follows that earnings divided by beginning of period price should be associated with stock returns. Although models based on a relation between market value and book value are used occasionally in the accounting research literature (see, for example, Landsman [1986], Harris and Ohlson [1987], and Barth
* Macquarie University and University of Chicago; tColumbia University. The paper is a revised version of working papers entitled "An Empirical Evaluation of Accounting Income Numbers: Further Evidence" and "Evidence of Accounting Earnings as an Index of Change in Value." The authors would like to acknowledge comments from workshop participants at the following universities; Arizona, Auckland, California at Berkeley, California at Los Angeles, Columbia, CUNY-Baruch College, Harvard, Macquarie, Michigan, New South Wales (AGSM), and Southern California. Special thanks are due to Vic Bernard, Jim Haggard, Robert Lipe, Jim Ohlson, Eric Noreen, Stephen Penman, Ram Ramakrishnan^ Jake Thomas, and anonymous referees. The study was partly funded by the Faculty Research Fund, Columbia Business School, Columbia University and by the Institute of Professional Accounting, Graduate School of Business, University of Chicago. ^ The variable of interest is not the standard earnings-to-price ratio which is based on contemporaneous, or past, earnings divided by contemporaneous, or past, price (A_i/P_,). 19 Copyright ©, Institute of Professional Accounting 1991

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JOURNAL OF ACCOUNTING RESEARCH, SPRING 1991

[1989]), another frequently used model expresses price as a multiple of earnings. This latter model is generally used to motivate empirical studies of the relation between security returns and change in earnings or between abnormal returns and unexpected earnings (see, for example. Beaver, Lambert, and Morse [1980] (henceforth BLM) and Collins and Kothari [1989] (henceforth CK)). However, we show that the assumption that price is a multiple of earnings also implies that the earnings level variable iA/P-i) is a relevant explanatory variable for returns. Although all the valuation models discussed in this paper indicate the potential relevance of the level of current earnings divided by beginningof-period price, they do not exclude the relevance of change in earnings divided by beginning-of-period price (AA/P_i). For example, differences between the book value and stock price could be a function of earnings. Thus, while the primary motivation of the empirical analysis is to evaluate the relevance of the earnings level variable (A/P-i), the analysis also considers and tests the relevance of the change in earnings variable (AA/P_i) for explaining stock returns. The results provide evidence that current earnings divided by beginning-of-period price iA/P-i) is associated with stock returns. Univariate regressions show that A/P-^ and AA/P.i are each associated with returns. In multiple cross-sectional regressions of annual returns on both the levels iA/P-i) and the changes (AA/P-i) variables, the coefficient on earnings levels is statistically significant (at 1% or better) in all years, while the coefficient on earnings changes is significant (at this level) in less than half the years. Additional analysis suggests that the relevance of the earnings level variable iA/P-i) for assessing the association between returns and earnings does not derive merely from a correlation between the two earnings variables. The primary empirical analyses focus on raw returns as the dependent variable because it is the return measure defined in the valuation models which we invoke. However, much of the empirical literature evaluating the association between earnings and security prices considers the relation between unexpected (abnormal) returns and unexpected earnings. A measure of unexpected earnings frequently used in association studies involving annual return windows is change in earnings, sometimes deflated by the beginning-of-period price. Given the measurement error inherent in any unexpected earnings measure and the relevance of the earnings levels variable (A/P_i) in the return association tests, it is pertinent to consider whether earnings levels are useful when considering the unexpected return/unexpected earnings relation. In multiple regressions of annual cumulative abnormal returns—based on a (monthly) market model—on both A/P_j and AA/P_,, the earnings levels variable has statistically significant explanatory power over the earnings change variable, and vice versa. Given that both earnings variables measure unexpected earnings with error, we suggest, in the spirit of Brown et al.

EARNINGS AS AN EXPLANATORY VARIABLE

21

[1987], that studies which use the residual from a regression of annual abnormal returns on unexpected earnings might mitigate the effect of measurement error by including both earnings level and earnings change variables as measures of unexpected earnings. The relevance of the earnings levels variable suggests new opportunities in our search for a better understanding of the associations between accounting earnings and returns. For example. Lev [1989], who expresses concern about the pervasiveness of low R^ statistics in returns/earnings association studies, cites the focus on earnings levels as a potential direction for improvement. The models relating earnings variables and security returns are presented in section 2. After describing the data and sample selection procedure in section 3, empirical analyses of the relation between the earnings variables and security returns are documented in section 4. Section 4 also addresses the issue of whether earnings levels and earnings changes capture the same or different information. The use of earnings divided by beginning-of-period price as an instrument for unexpected earnings is addressed in section 5. Section 6 contains a summary of the results and some conclusions.

2. The Relation Between Earnings and Returns
2.1 RETURNS AND EARNINGS ASSOCIATIONS BASED ON A BOOK VALUE VALUATION MODEL

The idea that price and book value are both measures of the "stock" value of the shareholders' equity may be expressed more formally as:
P,, = BVj, + uj, (1)

where Pjt is the price per share of firm j at time t, BVj, is the book value per share of firm j at time t, and u,, is the difference between Pjt and The difference between market and book values (uj,) can result from many factors including the choice of conservative accounting practices and other information incorporated in price but not yet reflected in accounting values. The relation between the "flow" variables—accounting earnings and security returns^may be obtained by taking first differences of the variables in equation (1). This yields: + u;,. But, in general:
ABVj, = Aj, ~ dj, (3)

(2)

where Aj, is accounting earnings per share of firm j over the time period

22

P, D. EASTON AND T. S. HARRIS

£ — 1 to t, and dj, is dividends paid per share of firm ; over time period t - 1 to t,^' Substituting (3) into (2), rearranging, and dividing by Pj^-i yields: + d,,)/P,,^, = AjJPj,-, -h u;. (4)

Tbat is, if stock price and book value are related, as we might expect, then earnings divided by beginning-of-period price should be an appropriate variable for explaining returns.'
2.2 RETURNS AND EARNINGS ASSOCIATIONS BASED ON AN EARNINGS VALUATION MODEL

Because some of the empirical literature focuses on an earnings-based valuation model, we consider an alternative model wbicb expresses price as a multiple of earnings. That is:
Pj, = f>Ajt + Vj^. (5)

Oblson [1989a] demonstrates tbat the Miller and Modigliani [1961] dividend irrelevance proposition requires tbat if a dividend is paid on security 7 at time t, then equation (5) must be written as:^
Pj, -h djt = pAj, + Vj,. (6)

It follows that:'^
Pj,^,] + vj,. (7)

That is, there is a linear relation between change in earnings divided by beginning-of-period price and security returns over that period.''
^ In the empirical analysis all data are adjusted to reflect the implicit assumption that prices, dividends, and accounting variables are calculated based on the shareholding at a particular point in time. Further, in principle, dj, reflects net withdrawals by the firm's owners. •' The factors included in Uj, and uJ, are not germane to this paper. The variable u", is relevant for the empirical analysis and is considered in section 4. ^ The coefficient p is frequently assumed to be constant across firms and time periods (see, for example, BLM in an empirical analysis and Ohlson [1989a] in a theoretical framework). ^ Changes in earnings have been used in a way similar to equation (7) in BLM which uses equation (5) to test the following form of the earnings/return relation:

While CK examine change in earnings via the relation:

in a reverse regression framework. ^ Implicit in equation (7) is the assumption that a dividend is paid at time t but there is no dividend paid at time t - 1. If a dividend is paid at t - 1, equation (7) becomes:
PJ.-,] - dj,-JP,,-, + vj,. {la)

EARNINGS AS AN EXPLANATORY VARIABLE

23

Of particular relevance to this study is the fact that dividing equation (6) by beginning-of-period price yields: (P,, + d,,)/P,,-, = p[A^,/P,,-,l + vj,. (8) This equation suggests that from an earnings valuation perspective, earnings levels (divided by beginning-of-period price) will be associated with returns. The return variable (AP,, + dj,)/Pj,-i can be obtained from (8) by subtracting one from each side of the equation and then expanding the left-hand side.'
2.3 COMBINING BOTH VALUATION PERSPECTIVES

As a practical matter, for most companies the stock price is likely to be a function of both book value and earnings. For example, Ohlson [1989a] presents a model that suggests that the variable u^, in equation (1) is partly a function of earnings. By combining a "book value only" model (similar, in principle, to equation (4)) and an "earnings only" model (summarized, in principle, by equation (7)) he proposes a valuation relation in which price is a weighted function of book value and earnings." In a similar manner, equations (4) and (7) may be combined to give: (AP,, + dj,)/P,,-, = kp[XAjP,,.,] + (1 - k)[AjJP,,.,] + w,, (9) where /? is a factor for weighting the contribution of change in earnings versus earnings levels in the explanation of stock returns. In the empirical analyses, we examine the relations between earnings and returns implied by (0 equations (4) or (8) for earnings levels, ((() equation (7) for earnings changes, and (iii) equation (9) for both earnings measures together,^
2.4 POTENTIAL CONFOUNDING EFFECTS

Prior empirical research has also examined the relation between earnings/price ratios and returns. Basu [1977], for example, finds a positive
For practical pur]joses, both d^,-i/P;,-i and, in particular, the cross-sectional variation in this variable are sufficiently small so as to have no effect in the empirical analyses which include an intercept term. ' Equations (4) and (8) both express returns as a function of earnings levels divided by beginning-of-period price. Reconciliation of these equations requires:

This is a familiar definition of earnings under certainty with p equal to the reciprocal of the required rate of return plus one (Ohlson [1989bl). "Ohlson's [1989a] model provides a role for earnings and hook value in a dynamic uncertainty environment that relies on the simple "clean-surplus" relation (that is, ABV,, = Aj, - dj,) and the Miller and Modigliani [1961] propositions. While we provide a more heuristic analysis, it should be noted that relations (4), (7), and (9) are consistent with the Ohlson model in which earnings and book value are defined as "primitive" and fundamental economic variables. ^ The variables u",, vj,, and iVj, are important in this paper only as they affect the empirical analyses. Thus, we leave discussion of these terms to section 4.

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P. D. EASTON AND T. S. HARRIS

association between returns and historical earnings/price ratios. This result potentially affects the interpretation of the empirical results. Since: A,/P;,-! = ^AjJPj,^, + A,,_i/P,,_, (10) it is not possible to distinguish between (i) the combined explanatory power (for returns) of change in earnings divided by beginning-period price and prior-period earnings (i.e., for period t - 2 to ( - 1) divided by the price at the beginning of the return period (Aj,-i/-Pjf-i), and {ii) the explanatory power of current earnings (i.e., for period t - 1 to £) divided by beginning-of-period price. Inclusion of any two of the variables in equation (10) as explanatory variables in a regression model precludes inclusion of the third. Therefore, we consider the explanatory power of each of the three earnings variables represented in equation (10) and then compare these to the explanatory power of the empirical counterpart of equation (9). It has also been shown that returns vary with firm size (Banz [1981] and Reinganum [1981]); size is just one proxy for variables which may explain security returns but are omitted from equation (9). For example, size could proxy for a variable which causes Uj, (in equation (1)) to differ from zero. Given past empirical accounting research and the question being addressed in this paper, we choose not to pursue a search for potential additional explanatory variables.

-3. Data and Sample Selection
The sample is selected from the period 1969-86 using the criteria: (/) annual earnings per share and the factor to adjust for stock splits and stock dividends are available on the 1987 Compustat Primary, Secondary, Tertiary and Full Coverage Annual Industrial File; (ii) security price and the factor to adjust for stock splits and stock dividends are available on the Center for Security Prices {CRSP) Daily Returns File for the first trading day of the ninth month prior to the fiscal year-end; and {iii) monthly security return data are available on the CRSP Monthly Returns File for 69 months prior to and 3 months after the fiscal yearend. This selection procedure results in a sample of 20,188 firm-year observations. An additional 192 firm-year observations are deleted because either Ajt/Pjt-], ^jt/Pjt-i, or Ajt-i/Pjt-i is not between +1.5 and —1.5.'"

Earnings and price variables are adjusted for stock splits and stock dividends."
'" This truncation rule was imposed to ensure that the results were not unduly affected by a few outlying (unusual) observations. However, truncation did not change the substance of the results. " All analyses are based on a return period extending from 9 months prior to 3 months after tbe fiscal year-end, corresponding roughly with the period between earnings announcements. The analyses were repeated for the subsample of 2,947 firms with no change in fiscal year-end and the date of announcement of fourth-quarter earnings available on the

EARNINGS AS AN EXPLANATORY VARIABLE

25

4. Empirical Analyses
To better understand the empirical validity of the models described in section 2, and the role of the current level of earnings, we consider first the correlations between stock returns and each of the earnings variables. The correlations are described via univariate regressions to facilitate a comparison with the multivariate regression which empirically estimates the relation expressed in equation (9). The analyses facilitate consideration of the incremental explanatory power of the levels and changes variables and the extent to which overall explanatory power is improved by the incorporation of the levels variable (Lev [1989]).
4.1 UNIVARIATE ANALYSES

re We begin with univariate regressions of returns and the earnings levels and changes variables. The re regression models are:
+ an[Ajt/Pjt~i] + ^ (11)

and: Rj, = 0« + 0n[AAy,/Pj,-,] + 4 ^ where: R (P + Although the presence of an intercept is not implied by the theoretical relations that underpin these regressions (equations (4) and (7)), the omitted variables that may explain security returns (incorporated in u"t or vjt) may have, on average, a nonzero effect implying nonzero intercept t e r m s (cttQ a n d t/ito).

(12)

These and all other regression models are estimated for the pooled cross-section and time-series sample as well as for each year it) of available data. The results from regressions of the models in (11) and (12) are reported in table 1. In the regression using the pooled sample of all 19,996 firm-year observations as well as in the annual cross-sectional regressions, the coefficients an and .^n are significantly different from zero at the 0.01 level. The R-^ from the pooled regression based on the levels model in equation (11) is 7.5% compared to the i?^ of 4% from the equivalent regression for the changes model in equation (12). For the year-by-year regressions, the R'^ from the levels model is higher tban thefi^from the changes model in 14 of the 19 years and is at least twice as high in 7 of these years. While the R'^ from the changes model (12) is higher than the R'^ from the levels model (11) in 5 of the years,
Compustat Quarterly Industrial File. Returns (and abnormal returns) were calculated for the 12 months up to and including the earnings announcement month. Since the results for the analyses of this subsample are qualitatively similar to those of the larger sample, only the results based on the larger sample are reported.

TABLE 1 Simple RegressiorLS of Annual Security Returns on Deflated Earnings Leuels and Earnings Changes Levels Model:^ Rj, = am + anAjtlPjt-\ + i]t Changes Model: flj, = 4,,o + (pnAAjt/Pji^^ + i%

Year ALL 1986 1985 1984 1983 1982 1981 1980 1979 1978 1977 1976 1975 1974 1973 1972 1971 1970 1969 1968 Mean^

A,JT> 0.11 (30.8)** 0,19 (20.5)** 0.23 (21.3)** 0.03 (3.5)** 0.27 (14.7)** 0.40 (24.2)** -0.08 (-6.6)** 0.32 (18,1)** 0.02 (1,0) 0.18 (9.9)** 0,04 (3.2)** 0.05 (4.3)** 0.33 (19.7)** -0.20 (-20.6)** -0,23 (-14.7)** -0,05 (-3.7)** 0.08 (4.9)** 0,01 (0.4) -0,20 (-12.2)** 0.12 (4.3)** 0.82 (40.3)** 0,72 (13.1)** 1.08 (17,8)** 0.98 (18.2)** 0.81 (7,7)** 0.55 (6.8)** 0.86 (13.0)** 0.91 (10.8)** 0.73 (8.4)** 0.73 (7.9)** 0,69 (11.0)** 1.05 (15.6)** O.QQ (12.3)** 0.78 (16.6)** 1,21 (9.6)** 0.70 (5.3)** 1.29 (8,9)** 1.39 (8.6)** 1.46 2,52 (7.3)** 1.02 (10.0)** 0.075 0.104 0.182 0.195 0.042 0.034 0,117 0.084 0.055 0.050 0.098 0.189 0.133 0.230 0.099 0.033 0.094 0.098 0.072 0.090 0« 0,18 (57,0)** 0.21 (22.2)** 0,29 (26.2)** 0.09 (10.9)** 0.31 (18.2)** 0.46 (29.6)** 0.00 (0.4) 0.45 (33.2)** O.U (9.3)** 0.26 (20.2)** 0.10 (11.0)** 0.16 (15.5)** 0.45 (31.0)** -0.12 (-13.8)** -0.14 (-12,4)** -0.02 (-1,4) 0.13 (9.5)** 0.09 (8.0)** -0.12 (-10.2)** 0.27 (16,4)**

Pji-i

0.55 (29.0)** 0.39 (7.6)** 0.61 (10.7)** 0.41 (7.2)** 0,73 (7.8)** 0.62 (8.0)'"' 0.50 (7.8)** 0,71 (9.7)** 0.67 (9.1)** 0.72 (9,8)** 0.80 (13.3)** 0.63 (11.1)** 0.53 (8.4)** 0.65 (13,1)** 0.70 (7.1)** 0.30 (2.7)** 0.88 (6.0)** 1.12 (6,2)** 1.33 (6.1)** 1.66 (5.2)** 0.74 (9.7)**

0.040 0.037 0.074 0,036 0.043 0,046 0.044 0.070 0.063 0,075 0.137 0.105

19,996 1,459 1,414 1,368 1,333 1,288 1,279 1,249 1,212 1,162 1,105 1,039 977

0.157 0.057 0.008 0.045 0.054 0.055 0,049

917 833 788 750 678 612 533

((-Rlatisiics are provided in parentheses.! * Significant at 0,01 £ d < O.O.^i. ** Significant at iv ^ 0.01. ' Description of regression variahles: Rj, ia the return on a share of firm j over the 12 months extending from 9 months prior to the iiscal year-end to 3 months after the fiscal year-end, Aj, is accounting earnings per share of firm j for period t, and P,,_, is the price per share of firm j at time ( - 1. ^ JV is the number of observations in ihe regression. •'This is the mean ol the yearly coefficients, estimated to test for the effect of cross-sectional correlations in the error terms.

EARNINGS AS AN EXPLANATORY VARIABLE

27

there are no years in which it is twice as high,^^ These results indicate that, as the models described in section 2 suggest, the current earnings level variable, AjJPjt-i, is correlated with stock returns, Tbese univariate results suggest also that we can expect both levels and changes variables to be associated with returns,^^ Given the equality expressed in equation (10), we also consider the association between Ajt-i/Pjt-i and returns by estimating the following regression model: Rjt - e«) + Bn[A,-i/Pj,^,] + e% (13) The results from the regressions based on model (13) are reported in table 2. The coefficients from the pooled regression are statistically significant at the 0.01 level. However, the R^ is 0.003 as compared to R'^ of 0.075 and 0.040 from the pooled regressions of equations (11) and (12), respectively. The results from the annual cross-sectional regressions indicate statistically significant On coefficients (at the 0.01 level) in 7 of the 19 years. In all years the R^ from regressions of equation (13) are lower than the R'^ from regressions of the levels model (11) by several multiples. While this is generally also true of comparisons between the i?^ from regressions of the models in equations (13) and (12), in one year (1984) the regression based on Ajt-i/Pjt-i has an R^ of 0,059 while the regression based on AAjt/Pjt-i has an R^ of 0.036. As a result of the equality expressed in equation (10) it is necessary to interpret the univariate regressions with caution. But, it is useful to note that there are years (for example, 1973 and 1976) in which the R"^ from regressions on Ajt-i/Pjt-i are zero while the Rh from the regression based on Ajt/Pjt-i are at least 80% higher than the Rh from the equivalent regressions based on AAjt/Pji-i. Thus, overall, these results suggest that the difference in associations between security returns and the earnings levels [Ajc/Pjt-x) and earnings changes {AAjt/Pjt-i) variables reflects more than the earnings/price effect documented by, for example, Basu [1977]. Another reason to interpret the results with caution is the potential bias in the coefficients due to cross-sectional correlation in the error terms of the regressions. Bernard [1987] suggests that for regressions based on annual returns, if it is assumed that each annual regression is independent, then the mean and standard error of the coefficients obtained from the annual regressions may be used to test whether this mean is statistically different from zero. If it is, then the bias from any cross-sectional correlation will not be sufficient to negate the statistical
^ There is no statistical reason to use the comparison of R^ being twice as high. We use ^ this simply to provide a sense of the order of magnitude of the difference. Our focus on ft^ stems from the emphasis on this statistic in recent review papers by Bernard [1989] and Lev [1989] who note that this statistic has been consistently low in earnings/returns association studies. '^ We also calculated the Spearman correlations between stock returns and each of the earnings variables (not reported). The results were qualitatively the same as the correlations which can be imputed from the K^s reported in table 1.

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P. D. EASTON AND T, S. HARRIS TABLE 2
Regressions of Annual Security Returns and Prior-Period Earnings Divided by Beginning-of-Period Price Prior Earnings Model:' Rj, = 0to + 6nAjt-i/Pjt-i + t% Year ALL 1986 198S 1984 1983 1982 1981 1980 1979 1978 1977 1976 1975 1974 1973 1972 1971 1970 1969 1968 0.17 (45.9)** 0.21 (20.7)** 0,26 (21.7)** 0.07 (8,2)** 0.33 (18.4)** 0.45 (24,3)** -0.03 (-2.1)** 0.46 (22.4)** 0.16 0.3)** 0.32 (19,9)** 0.13 (11.2)** 0,18 (14.8)** 0,19 (8.4)** 0.25 (4,2)** 0,35 (4.9)** 0,55 (9,3)** -0.10 (-1.0) -0,14 (-1.5) 0.37 (4.7)** -0.09 (-0.9) -0.26 (-2.5)* -0.34 (-3,7)** -0.14 (-2,2)* 0.06 (0,9) 0,16 (2.0)* 0.34 (4.2)** 0.01 (0.1) 0.21 (1.8) 0,38 (2.5)* 0,66 (3,2)** 0.60 (1,7) 0.45 (1.3) 0.18 (2,5)*

R'
0,003 0,011 0,016 0,059 0.000 0,002 0.016 0.000 0.005 0.011 0.004 0.000 0,003 0.018 0.000 0.004 0.007 0.013 0.005 0.003 19,996 1,459 1,414 1,368 1,333 1,288 1,279 1,249 1,212 1,162 1,105 1,039

0.42 (22.5)**
-0.15 (-11,8)** -0.12 (-8.6)** -0,02 (-1.5) 0.12 (7,4)** 0.04 (2.1)* -0.15 (-6.6)** 0.26 (10,0)**

977 917 833 788 750 678 612 533

Mean^

(t-statistics are provided in parentheses.) " Significant st 0.02