http://jaf.sagepub.com/ & Finance Journal of Accounting, Auditing http://jaf.sagepub.com/content/6/2/233 The online version of this article can be found at: DOI: 10.1177/0148558X9100600204 1991 6: 233 Journal of Accounting, Auditing & Finance Stephen H. Penman An Evaluation of Accounting Rate-of-return Published by: http://www.sagepublications.com On behalf of: Stern School of Business Sponsored by The Vincent C. Ross Institute of Accounting Research, The Leonard N. found at: can be Journal of Accounting, Auditing & Finance Additional services and information for http://jaf.sagepub.com/cgi/alerts Email Alerts: http://jaf.sagepub.com/subscriptions Subscriptions: http://www.sagepub.com/journalsReprints.nav Reprints: http://www.sagepub.com/journalsPermissions.nav Permissions: http://jaf.sagepub.com/content/6/2/233.refs.html Citations: What is This? - Apr 1, 1991 Version of Record >> at UNIV OF COLORADO LIBRARIES on July 3, 2012 jaf.sagepub.com Downloaded from
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http://jaf.sagepub.com/& Finance
Journal of Accounting, Auditing
http://jaf.sagepub.com/content/6/2/233The online version of this article can be found at:
DOI: 10.1177/0148558X9100600204
1991 6: 233Journal of Accounting, Auditing & FinanceStephen H. Penman
An Evaluation of Accounting Rate-of-return
Published by:
http://www.sagepublications.com
On behalf of:
Stern School of BusinessSponsored by The Vincent C. Ross Institute of Accounting Research, The Leonard N.
found at: can beJournal of Accounting, Auditing & FinanceAdditional services and information for
1. Introduction What does accounting rate-of-return (ROE) mean? This ratio (net income
divided by book value of equity) is regarded as the primary summary measure in traditional ratio analysis. For example, the “Du Pont system” of financial statement analysis aggregates most of the traditional financial statement ratios to ROE in the form
ROE = net income/sales X sales/assets X assets/equity, (1)
where the first two components (profit margin and turnover ratio) are further decomposed by line-item components of the income statement and balance sheet. However, how one utilizes this ratio in a financial statement analysis that elicits investment value (price) is not understood. This paper examines what ROE means for the pricing of stocks.
Investment analysis can be characterized as discovering two types of (accounting) information which together yield the price of a stock. First, there is information that provides indications of future earnings (profitability) and, second, information that provides an indication of the rate at which those expected future earnings are discounted (that is, risk). ’ In traditional ratio analysis, ROE is nominated as a profitability measure. However, there are vague notions that it also reflects expected rate-of-return (risk) and certainly one can see from ( I ) that it is related to (book) leverage which presumably is related to risk. The paper evaluates ROE as an indicator of profitability and as an indicator of risk.
The analysis of ROE as a measure of risk is described in Section 4 of the paper and the analysis of ROE as a measure of expected profitability is described in Section 5 . Section 2 describes the data and Section 3 provides
*Walter A. Haas School of Business University of California at Berkeley An earlier version of this paper was titled “The Pricing of Earnings and Book Values and an
1. Ohlson (1990) demonstrates the equivalence of the present value of future expected dividends
Evaluation of Accounting Rate-of-Return. ”
(price) and discounted aggregated future earnings.
233
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some empirical observations that provide a basis for the interpretation of the findings reported in Sections 4 and 5 .
2. Data The analysis utilizes accounting rates-of-return for firms over the 18-
year period from 1969 to 1986. Rate-of-return is calculated as annual earn- ings (before extraordinary items) deflated by book values at the beginning of the fiscal year. For each year of the sample period, the earnings and book values were obtained for all firms on the combined 1987 Compustat annual file and research file that had data for the relevant year.* These files contain all firms carried by Compustat during the period and, according to the suppliers of the Compustat service, include all firms listed on the NYSE and AMEX during the period. Price and returns data were obtained from files supplied by the Center for Research in Security Prices at the University of Chicago. In the paper, the subscript will be used to refer to firms and the subscript to refer to points in time.
Throughout the paper earnings and ROE are defined in terms of earnings before extraordinary items and discontinued operations rather than net in- come. This ensures that the interpretations of the results are with respect to normal operating income.
3. Some Initial Observations Curiously, given its prominence in ratio analysis, there has been little
theoretical analysis of ROE. There have been some attempts, for example, in Solomon (1966), Vatter (1966), and Livingstone and Salamon (1970), to reconcile accounting return-on-assets to “internal rate-of-return” which, under certain conditions, satisfies the present value criterion for profitability analysis. The only paper that describes prices of stocks in terms of ROE in an equilibrium framework is Ohlson (1990), and it is to that paper that we will refer in the analysis. The representation of price in the Ohlson paper that is helpful here is one that reconciles book value (B,) to price (Pi,) in terms of future earnings:
2. Compustat covers 20 years of data, 1968 through 1987, for the version used. However, as beginning-of-year book values were required for each year, 1968 data could not be used. Further. the 1987 version of the file used contained data for f i rms with fiscal years up to June of that year only, so 1987 data were deleted, leaving 18 years.
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where p is (one plus) the discount rate (which can be subscripted i ) , E,[.] is expectation given information at time t, and xait + is earnings (xi, + J in excess of normal earnings in year t + 7:
(3)
Given clean surplus accounting in calculating earnings, (2) is an equivalent representation of price in terms of the present value of expected dividends. The factor, p, is the normal rate-of-return on equity investments, so (2) and (3) describe stock price as greater (less) than book value when expected future earnings are greater (less) than those implied by a normal rate-of- return applied to beginning-of-period book values. This condition is (ap- proximately) the same as expected future rates-of-return being greater (less) than normal rates-of-return.3
Financial statement analysis can thus be characterized as observing in- formation (in financial statements) that projects future accounting rates-of- return. One piece of information-the summary number of traditional ratio analysis-is the current ROE (at time t) and the question here, then, is how ROE projects into future ROE. In this perspective, ROE is a profitability measure. Another question is whether ROE relates to risk, that is, to the discount rate, p.
Not only has there been little theoretical work on ROE, but also little empirical work. Cross-sectional differences in ROE have been observed (over industries, for example) and the time-series property of mean reversion has been documented in Beaver (1970), Lookabill (1976), and Freeman, Ohlson and Penman (1972). Recently, Board and Walker (1990) have re- ported positive correlations between “unexpected” rates-of-return and “ab- normal” stock returns. This section adds some further observations that will aid in the design and interpretation of the main analysis in the paper.
The first observation is in answer to the question: To what extent does ROE capture returns on common stocks? For each of the years 1969 through 1986, the following cross-sectional regression equation was estimated from
Xf,+i = Xi,+. - (p-1) Bit+?-, .
3. This statement is an approximation because it is only true with 100% dividend payout. This is because ROE is defined here as return on beginning-of-period book values and the price-to-book com- parison is on the basis of end-of-period book values. Thus the statement is strictly true if beginning book values are the same as ending book values each period, that is, when dividends equal earnings (with clean surplus accounting).
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all firms with annual stock returns (R,,) and accounting rates-of-return (ROE,,) in the relevant year:
R,, = A , + A,ROE,, + W,, . (4) The total number of firms in the estimations was 35,978, an average of 1999 per year.' Estimates of A2 ranged from ,376 to 1.456, with a mean of .879 over the 18 years. The t-statistic on the mean (calculated from the time-series of estimated coefficients) was 10.98 when the mean was assessed against zero, and - 1.92 when assessed against unity. The mean estimate of A , was .049 with a t-statistic of .95. Values of 0 and 1 for X I and A, respectively are consistent with accounting rates-of-return and stock rates- of-return being the same, on average. Indeed, the model of Ohlson (1990) describes accounting rates-of-return as oscillating around stock rates-of- return. However, R2 values ranged from .02 to .19 with a mean of .09 so that, while over time mean returns and mean ROE are similar, ROE does not explain a large portion of the cross-sectional variation in annual stock returns: as a representation of annual returns, annual ROE is deficient.
The fact that ROE does not measure realized returns is, of course, well appreciated. However, the estimates demonstrate a positive relationship between the two (in every year). This is consistent both with ROE capturing some information about profitability that is reflected by returns and with ROE reflecting differential expected returns (risk). The purpose of this paper is to disentangle these two explanations. Further, if ROE is a profitability measure, we seek the appropriate specification that indicates how returns are related to ROE information.
Given prices are based on expected future abnormal accounting rates- of-return (as described in equation (2)) and, as our inquiry concerns ob- served, current accounting rates-of-return. The critical question is how observed ROE projects future ROE. The second empirical observation in this section addresses this issue.
Table 1 describes the behavior of ROE over time. It summarizes, for a base year 0 and subsequent years indicated, median accounting rates-of- return for 20 portfolios formed by ranking firms in each year on their ROE. Each calendar year in the period 1969 to 1985 is a base year. ROE values in the table for the base year and subsequent years are means of medians for all such years in the sample period. The year 1986 is not included as a base year because there are no subsequent years in the sample period. The final column in the table gives the number of firms in all base years. Below
4. Here. and in other parametric analyses using ROE, some firms with very large ROE were excluded, as were firms with negative book values.
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the figures for portfolio 20 (the lowest ROE portfolio), differences in values for the extreme portfolios, 1 and 20, and portfolios 2 and 19 are given. Below these, mean estimated rank correlations over years between portfolio median ROE in the base year and in the relevant subsequent year are reported.
Two observations can be made from an examination of Table I . First, firms with high (low) current ROE (in year 0) tend to have high (low) ROE in the future. Second, differences between ROE tend to decrease overtime. While firms with ROE around the median (portfolios 10 and 11) have the same ROE, on average, 12 or 15 years later, firms in extreme portfolios, with ROE quite different from the median ROE in year 0, have ROE 12 to 15 years later that are much similar to the median ROE then and to the median in year 0.’ This, of course, is the mean reversion property of ROE previously documented. These two observations together indicate that ROE is mean reverting, but not purely so. Even after 9 to 15 years, the mean estimated rank correlations between portfolio ROE in these years and those in year zero are of the order of .75 to .80. It appears that, on average, current ROE indicates future ROE.
If current ROE projects future ROE with a fixed parameter common to all firms, then, given equation ( 2 ) , financial statement analysis is complete after calculating current ROE, and ROE is truly a summary measure. Tables 2 and 3 cast considerable doubt on this notion, however. Equation (2) says that market-to-book comparisons distinguish future ROE. So, Table 2 gives the same description of ROE values as in Table 1 except that portfolios are formed on market-to-book ratios (P/B) in the base year rather than ROE. P/B ratios are observed three months after the end on the fiscal year for which earnings and year-end book values are reported. It is clear that P/B rank orders ROE in the base year, with mean estimated rank order corre- lations between portfolio ranks and ROE of .99. It is also apparent that P/B indicates persistence in ROE. The high ROE for high P/B portfolios are high in subsequent years and the low ROE for low P/B portfolios are low in subsequent years.
Table 3 is further enlightening of the ability of P/B to distinguish per- sistence in ROE. Panel A of that table reports ROE values for portfolios formed on ROE in the base year, but only for firms with P/B ratios above the median (firms in P/B portfolios 1-10 in Table 2), and panel B gives the same display for firms with P/B below the median (firms in P/B portfolios
5 . Two caveats are given with this interpretation. First, because there are fewer calendar years in the calculations for years far ahead of year 0, the values reported for these years are less precise. Second, there are no observations for subsequent years for firms that do not survive for the full period after year 0.
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11-20 in Table 2). This is the same presentation as in Table 1 but with firms partitioned at the median P/B ratio.6 The median ROE values for a given ROE portfolio are quite similar in Panels A and B in the base year, and similar to those in base year in Table 1. However, values in subsequent years differ across the two panels for a given ROE portfolio. High ROE firms with high P/B have considerably higher ROE in subsequent years than firms with high ROE and low P/B. Similarly, low ROE firms with low P/B have considerably lower ROE in subsequent years than firms with low ROE and high P/B. In short, P/B is not only positively related to ROE in the base year but also indicates the speed of reversion towards the median ROE in subsequent years.
The ability of market-to-book ratios to distinguish current and future ROE makes sense. After all, the ratio represents the pricing of book values. If the assets underlying the back values currently produce high earnings per unit of book value and are expected to do so in the future, then the measured book values will be priced by a higher multiple, and conversely so for low profitability. The point is that current ROE does not necessarily indicate the level of future ROE. Further information is necessary to distinguish per- sistent ROE from transitory ROE. ROE alone is not a satisfactory summary measure for fundamental analysis. The finanical statement analysis question is: What line items in the financial statements (which are aggregated in ROE) provide that indication of persistence. It is clear from an inspection of Tables 2 and 3 that this information will be correlated with the P/B ratio; that is, that information will explain the level and persistence of ROE and thus it will explain how book values are priced.
Tables 2 and 3 can be viewed as a validation of equation (2). Ohlson (1990) also describes market-to-book ratios in terms of current observed ROE along with other information:
where v,, is information about future profitability other than that provided by the earnings or book values that go into the ROE calculation, and
The autoregressive “persistence” parameter, w,, falls between 0 and I and descAbes the evolution of abnormal earnings X”,,, given other information:
6. The number of stocks for a given ROE portfolio in Panels A and B do not aggregate to those in Table I because stock prices were not observed for some firms for calculation of the P/B ratio.
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xP,+ 1 = ~ J P , -t vi, + E,,+ I 9 (6) where E , ~ + , has an expectation of zero. This explicitly describes P/B in terms of the projection from current ROE to future ROE (persistence of ROE)’ and provides a role for other information in assessing profitability as well. The “other information” of course can include line items other than earnings and book values.
This discussion views ROE as a profitability measure. However, Tables 2 and 3 are also instructive with respect to ROE being (positively) related to risk. Market-to-book ratios are sometimes interpreted as risk measures, with the relationship being an inverse one. The ability to earn “excess returns” from investment positions based on P/B [documented in Nicholson (1968), Rosenberg, Reid and Lanstein (1983, Ou and Penman (1987) and Fairfield and Harris (1989)] has been interpreted as a reward to risk, for example. If one accepts this, it is clear that ROE does not capture the same aspect of risk, for Table 2 indicates that ROE is positively correlated with P/B .
4. Accounting Rate-of-Return and the Evaluation of Risk Interpreting ROE as a measure of risk has an appeal: One expects high-
risk firms to yield high book rates-of-return, thus demonstrating the risk- return tradeoff. As mean stock rates-of-return are related to risk, so are book rates-of-return. Indeed, the results from estimating equation (4) are consis- tent with this interpretation.
This section examines the relationship between ROE and systematic risk, “beta.” Equation (1) contains a leverage term and systematic risk of equity is related to the leverage of the equity. (Of course, the leverage in equation (1) is book leverage, not market leverage.)
Table 4 presents the results of estimating the following cross-sectional regression equation in each of the years, 1969 through 1986:
ROEir=yo+ ytfiir;eiry (7) where filt is an estimate of systematic risk obtained by estimating the “market model” using monthly returns over a period of up to 60 months prior to the beginning of the return period in equation (7). Mean estimates of the coefficients (with t-statistics based on the mean observed coefficients) and mean R2 values over the years are given at the bottom of the table.
The estimates of the slope coefficient, yI, are negative in all years except
7. The substitution of ROE for abnormal earnings in this statement is again strictly appropriate only for 100% dividend payout. See footnote 3. Thus, in general, it is an approximation.
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two, and only in one of those years is the estimate significantly greater than zero. This observed negative relationship is associated with low R2 values. One must recognize that measurement error in estimated betas biases the result toward a finding of no association. However, these results, taken on face value, provide little support for a positive relationship between ROE and beta.8 If ROE is positively related to p, then it must be the case that the cross-sectional variability of ROE due to risk is so small relative to that induced by differential profitability that it cannot be detected, at least by these procedures .9
8. In 1978 Nils Hakansson told me that ROE was not related to beta and that this was a curiosity.
9. Note also that Lookabill (1976) shows that changes in ROE are not related to changes in estimated systematic risk.
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5. Accounting Rate-of-Return and the Evaluation of Profitability
Given the results in Table 5 , the observed positive relationship between stock rates-of-return and ROE in equation (4) is interpreted as ROE indi- cating profitability. However, it is unclear (and doubtful) that equation (4) is the appropriate specification for relating ROE to equity returns. This section investigates how ROE might be evaluated for updating value (prices). Revisions in prices reflect revisions in projections of future earnings (along with changes in value due to current earnings being generated). We ask how the expression of earnings in terms of units of book value in an ROE calculation aids in the projection from current earnings to future earnings.
There is a considerable amount of work [following papers by Kormendi and Lipe (1987) and Easton and Zmijewski (1989)l on the implications of current earnings innovations for future earnings and how this relates to returns. The central notion in this work is “earnings persistence”: The more “persistent” the earnings produced by the innovation, the higher the change in earnings will be “multiplied” in the contemporaneous price change. The metric that measures this multiplier has been dubbed the “earnings response coefficient.” Here we ask whether these multipliers are related to ROE.
Earnings persistence is indicated by an information set (other than current earnings) that predicts future earnings and thus indicates whether current earnings are indicative of those predicted future earnings. If current earnings are not so, they are relatively unimportant in valuation, and are interpreted as “transitory.” In most of the work to date, persistence has been deemed a fixed firm-specific parameter which is inferred from a very limited infor- mation set, the observed time-series of earnings. Although studies have had some success in explaining “earnings response coefficients” on the basis of these estimated parameters, the limited information set involved, along with the stationarity assumptions implicit in estimating them over lengthy time periods, suggest that these measures are less than satisfactory. (Further, in most studies, persistence parameters are estimated using ex post in- formation. )
Jennings (1988a, 1988b), Penman (1989), and Ali and Zarowin (1990) have had some success in distinguishing multipliers of annual earnings changes with accounting information that provides indications of future earnings. These studies employ many line items and ratios of line items in their persistence indicators. Here we consider only the minimalist accounting information that can be produced along with earnings, the book value of equity. By design of double entry, accounting earnings (the summary number in the income statement) cannot be produced without at least one other
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number, and that number is book value (the summary number in the balance sheet). The question is: If earnings are compared to book value in an ROE calculation, does that comparison give an indication of whether current earnings are persistent or not? As background, Tables 2 and 3 indicate that ROE is not sufficient as such an indicator.
Book values potentially provide “persistence” information, one would think, because they are measures of the value of assets from which future earnings will be generated. They complement earnings because they are stocks rather than flows. As such, they might provide indications of future earnings against which current earnings can be evaluated. This thinking is prompted by the results in Freeman, Ohlson and Penman (1972). That paper documents that one-year-ahead earnings changes are negatively correlated with ROE. If current earnings are high when compared to book values, then probably they are abnormally high and will be lower in the future. If earnings are low relative to book values, they can be assessed as being “temporarily depressed” and will probably “rebound” in the future. Thus earnings rel- ative to book value identify transitory earnings. This suggests that the mul- tiplier of earnings changes is lower for high or low ROE than for ROE around the median (a “normal” ROE), that is, the multipliers are “u-shaped” over ROE.
This reasoning presumes that book values convey information about future earnings. Consider a special case where book values are sufficient for information about future profitability. Here, price equals book value (P/B = 1). By equation (2), expected future ROES are normal (equal to p). Any deviation of current ROE from normal will indicate purely transitory earnings and so little weight would be given to earnings innovation as an indication of future earnings or price. This is the pure case of the Freeman, Ohlson and Penman reasoning. Suppose, now, that book values were rel- atively uninformative about future earnings such that market values deviate from book values (P/B f 1 by a substantial amount). This might be induced by accounting measurement methods, for example. Then, earnings might be more representative of future earnings than book values, and investors might rely on flows from assets rather than the measured stocks to make inferences about future profitability, along with other information. Thus an ROE which is different from normal, p, may indicate “poor” book values and earnings that are indicative of future earnings, that is, “persistent” earnings. In this case, non-normal ROE would be associated with higher multipliers of earnings changes, in contrast to the Freeman, Ohlson and Penman scenario.
Given that, in the cross-section, there can be “poor” book values and “good” book values, there may be no relationship between ROE and earn-
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ings change multipliers. The relationship, then, is an empirical matter. A test of such a relationship is a test of the informativeness of book values for making cross-sectional distinctions regarding earnings persistence.
These considerations are reflected in equation (5). There the deviation of price from book value (indicating the informativeness of book values) is expressed in terms of the “persistence” parameter, ol. In the pure Freeman, Ohlson and Penman case (P/B = l ) , this is zero (other information ignored). The further this is from zero (the more persistent is ROE), the greater the deviation of P/B from unity. Indeed, Table 3 described P/B as indicating the persistence of ROE. In short, P/B indicates the informativeness of book values relative to earnings and other information, and this indicates the persistence of earnings. ROE alone is ambiguous about persistence because it provides no information about the informativeness of book values. As seen from Table 3, further information about the persistence of ROE is needed to project future profitability, and that information is reflected in a market-to-book ratio.
How might these considerations be reflected in a specification using returns? Ohlson (1990) shows that an equivalent representation equations (2) and (5) is (ignoring diviends):
p,, = k,(lxll+ ( 1 - k)B,l+ a21vt1, (8)
where X,, and B,, are earnings and book values, as before,
p= P/(P - 1)
k = ( p - 1)..1,=(p- 1) [ o , / ( p - o , ) l
is an earnings multiplier, and
which falls between 0 and 1. Returns are thus represented by:”
pi1 - pi1 - 1
pit- I Rit =
where A indicates changes over the period t - 1 to t, and X, = Bi, - B, - , given clean surplus accounting. The multiplier of the earnings change, A X , is Kip which depends on wi, the persistence of ROE. To discover how these multipliers might be related to ROE, the following equation was estimated each year from firms partitioned on their observed ROE,,:
10. The equation is easily modified to include dividends in the return.
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where a + ui, captures the price revisions of other information, the mean return effects of which may be non-zero. This other information may be correlated with the included earnings variables. Tests of significant differ- ences in coefficient estimates over levels of ROE were conducted by esti- mating, for each year, the following equation:
&it X i t 4
mit 4
Ril=ao+ u p j + b,, - + b,p j -+ b,, - j = I pit-1 j = l Pit-1 Pit- I
where Dj, j = 1,2,3, or 4, takes a value of one if a firm's ROE falls in ROE portfolios 1-4, 5-8, 13-16, and 17-20 in Table 1 , respectively. Tests of differences in the earnings change multipliers over different levels of ROE involve assessments of the estimates of coefficients, bIj, j = 1,2,3,4. If book values are uninformative about earnings persistence, then b,j = 0, for all j # 0. This is stated as the null hypothesis. If book values identify transitory earnings, following the Freeman, Ohlson and Penman scenario, then bIj < 0, all j # 0, and more negative for b,, and bI4. This is stated as the alternative hypothesis.
Table 5 presents the results of estimating equation (10) for 20 ROE portfolios in each of the 18 years. These portfolios correspond roughly to those in Table 1 , as a comparison of the mean ROE indicates. I ' Results for all firms (without regard to ROE values) are given at the bottom of the table. The mean values of the estimated regression parameters are given to the right of the table, along with some test statistics. The left side of the table gives some numbers that are helpful in interpreting the results. After the mean portfolio ROE, the table gives mean values of contemporaneous de- flated earnings changes (the first explanatory variable) and one-year-ahead deflated earnings changes. The earnings changes in year t are relatively large (abstracting from sign) for extreme ROE portfolios, but reversals in the signs of these earnings changes from t to t + 1 are apparent. This dem- onstrates earnings changes that will, on average, be in the opposite direction in the immediate future, indicating transitory earnings which project lower b, values. This corresponds to the Freeman, Ohlson and Penman finding which is strongest for the extremes of ROE. The column prior to the results
1 I . However, firms in Table 1 without returns data are not included, so the numbers in each portfolio are less.
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for the estimated regression parameters gives the mean estimated betas for stocks in the ROE portfolios. These, we have seen, are not positively related to ROE in a linear fashion. The table indicates higher-than-average betas in both extremes of the ROE distribution. If capitalization rates are related to beta risk, this suggests lower values of b, (= k,k) for extreme ROE portfolios, consistent with the u-shaped prediction above (but for a different reason).
It appears from Table 5 that estimates of b, are lower for extreme, “non- normal” ROE values than for central, “normal” ROE values. The mean estimate of b,, in equation ( 1 1 ) (with t-statistic) is 1.229 (5.52) correspond- ing to central ROE values. Those for b,j, j = 1,2,3,4, are - .367 ( - 2.06), .138 (.53), - .514 ( - 2 . 5 3 , and - .804 (-4.60) , respectively. Thus sig- nificantly lower multipliers are observed for the top 20 percent of ROE values and the bottom 40 percent. The null hypothesis is rejected in favor of the alternative, with a note that the multiplier effect appears stronger for low ROE values, and is only indicated for extreme high ROE values. The findings stand with controls for beta,” so we conclude that ROE provides indications of the future profitability implied by an earnings change.
Table 5 indicates that the R2 values increase when ROE is held constant by ROE group. The mean (adjusted) RZ value for all firms pooled over ROE groups, given at the bottom of the table, is .I6 (ranging from .06 to .25 over years) while that from estimating equation ( 1 I ) with the dummy var- iables is .25 (ranging form .15 to .35). Allowing the b, coefficients to vary no doubt contributes to this. However, one can see that the estimated b2 coefficients on the earnings variable for ROE groups also increase over that for all firms pooled together, so ROE contributes in an additional way to explain return differences across firms.
The increase in the b, coefficient estimates with ROE stratification can be explained as follows. The estimate of b, for all firms pooled is .977, which is not significantly different from 1.0, as assessed by a t-test on the time series of estimated coefficients. Thus, on average over all circumstan- ces, a dollar of annual income (before extraordinary items) is valued at a dollar in the market. These earnings are additions to book values, so as book values change by additions of earnings, prices change by the same amount, on average.I3 Another way of saying this is that annual earnings (relative to beginning-of-period price) do not correlate with the contem-
12. This was assessed by estimating equation ( 1 I ) for different levels of beta 13. This applies to annual earnings (before extraordinary items). Easton, Hams and Ohlson (19%)
show that the coefficient increases for longer “windows.”
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poraneous change in unrecorded goodwill (price in excess of book values). Easton, Harris and Ohlson (1990) demonstrate that14
where Agw,, = ( P , - B,) - (Pi t - I - B , - , ) . (12)
Goodwill, of course, is price that is not yet reflected in book values, and, given equation (2), is information about expected furture earnings that has not been “realized” in current earnings and thus added to book values. The comparison of current earnings to beginning-of-period price (Xi,/Pi, - I ) is a comparison of a one-year realization of earnings relative to the expectation of long-run future earnings at the beginning of the period. The estimated b, coefficient for all firms pooled indicates that this realization does not, on average, produce revisions in expectations of future earnings that are ex- pressed in beginning-of-period price and, thus, does not explain Agw, once earnings changes are controlled for. This can be demonstrated directly by estimating each year, with all firms pooled,
The estimates of a and b, (and their t-statistics) are the same as at the bottom of Table 5, and the estimate bf2 (b2 - 1.0) is - .024 with a t-statistic of -.20. The observed mean R2 is only .04, indicating that the earnings changes explain little about the price changes due to information other than earnings.
In contrast, the average mean R2 over the 20 portfolios when equation (13) was estimated for each ROE group was .15. When equation (1 1) was estimated with Agw as the dependent variable, the mean R2 was .14. The mean estimate of the coefficient, b,, - 1 was 1.254 (t-statistic 4.88) and those for b, - 1, j = 1,2,3,4 were - .508 (-2.37), -.603 (-3.98),
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.245 (1.03), and -2.056 (-7.57). Holding ROE constant, earnings (rel- ative to beginning price) cross-sectionally distinguishes future unrealized earnings and thus explains increases of prices over increases in book value
Why is this? The technical answer, of course, is that ROE explains some of the variance in Agw and, once this variance is eliminated by holding ROE constant, the remaining variance can be explained by earnings ini- tialized by beginning price. The economic answer is given by a consideration of the nature of goodwill. By equation (2) this is the present value of future excess profits over a normal rate-of-return and, by equation ( 5 ) and the evidence in Table I , these are projected by current ROE. Substituting equa- tion ( 5 ) into the expression for Agw ( I 2), one obtains
(Agw).
where xBi, is given by (3). Thus the Agw portion of returns depends on the current abnormal earnings (relative to beginning-of-period price), its per- sistence, other information at the end of the period, and the beginning-of- period book-to-market ratio. ROE is an expression of abnormal earnings. We have seen that ROE gives some information about persistence. It also appears to be correlated with other information: The estimated intercepts in Table 5 capture the mean effect of information other than in the regressors, and ROE rank orders these. l5 These considerations point to ROE explaining Agw so that once this is controlled for, one observes the earnings variable (earnings relative to beginning price) also explaining Agw .
The influence of opening book-to-market ratio in explaining Agw can be explicitly controlled for. This standardizes for the beginning-of-period goodwill which reflects the incoming ROE and other information that proj- ects future ROE. Including it in the specification explicitly initializes firms in the cross-section for predictions (at t - 1) of future ROE, of which Xai, is a realization. Equation (11) was estimated adding B,, - JPi, - I as a regressor. Further, to capture correlation of ROE with other information, ROEi,, was added as well:I6
15. The estimates of the intercept dummies in equation ( I I ) , a,, j = I ,2,3,4 were significantly
16. The specification of intercept dummies allows for some variation in ROE. different from zero, with the exception of a,, supporting this conclusion.
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where [a] represents the right-hand-side of equation ( I 1) minus the intercept and the disturbance term. The estimates of the blj and b, coefficients were similar to before. The mean estimate of b, was .282 (with a t-statistic of 3.46) and that of b, was .084 (7.07). Controlling for opening market-to- book, ROE explains the implications of earnings for future earnings and thus the pricing of earnings in the market. Further, ROE correlates with information other than earnings that projects future earnings and which explains price changes in addition to those implied by earnings. The mean adjusted R2 observed for this regression was .27. This is a large improvement over that observed for estimating equation (10) and, indeed, over the typical R2 values observed for annual returns/earnings regressions that are cata- logued in Lev (1990). This, it should be noted, has been achieved with adding only one other accounting variable-the book value of equity-to the earnings variable typically included in these specifications.
6. Conclusions Accounting rate-of-return (ROE) is traditionally regarded as the major
summary number in financial statement analysis. This paper has evaluated the role of ROE in assessing cross-sectional differences in prices and price changes (returns). The empirical findings are as follows:
1 .
2 .
3.
4.
5 .
ROE is best interpreted as a profitability measure, not a risk measure (Table 4). Observed ROE indicates future profitability (Table 1) and thus dis- tinguishes market-to-book ratios (Table 2). ROE is not sufficient for distinguishing future profitability and thus is not a satisfactory summary measure for financial statement anal- ysis. A further research question is whether (and how) a decompo- sition of ROE might improve the assessment of future profitability. Information so discovered will correlate with market-to-book ratios which distinguish current and future profitability (Table 3). The comparison of earnings to book values in the ROE calculation provides information about how earnings project to future earnings (“persistence”): Book values are informative about the transitory nature of earnings (Table 5). ROE contributes to the explanation of the change in unrecorded goodwill (the portion of returns not explained by dollar addition of earnings to book values). First, it identifies when earnings project
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higher or lower future earnings [Table 5 and equation (1 l)]. Second, it appears to correlate with information other than earnings that pre- dict future profitability and thus explains stock returns [equation
Given earnings, the role of financial statement analysis is to explain the change in goodwill, that is, to explain changes in expected future earnings not indicated by current earnings. The paper shows that ROE (which involves one further piece of information, book values) serves to update goodwill, and the R2 values observed are impressive by traditional standards. However, as evidenced by the relationship of ROE to market-to-book ratios, it is incomplete for this task.
A number of the results here confirm predictions of the model of Ohlson (1990). Note, however, that while the model has been relied upon to develop many of the tests, there is an aspect here which is not present in that model. Ohlson’s model specifies the “persistence parameter,” oi (which we have referred to) as a constant not related to ROE. In this paper, persistence is viewed as a cross-sectional and time-varying attribute and the comparison of earnings to book values gives information on that persistence.
(1511.
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