Very preliminary. Comments welcome. Value-relevant properties of smoothed earnings. December, 2002

Transcription

1 Very preliminary. Comments welcome. Value-relevant properties of smoothed earnings December, 2002 by Jacob K. Thomas and Huai Zhang Columbia Business School, New York, NY University of Illinois at Chicago, Chicago, IL We thank K.R. Subramanyam and workshop participants at University of Southern California and the University of Utah (2 nd Annual Winter Accounting Workshop) for helpful comments and the Faculty Research Fund of Columbia Business School for financial support.

2 Value-relevant properties of smoothed earnings Abstract Both prior research and the popular financial press suggest that earnings smoothing is associated with higher valuations, per dollar of reported earnings. Apparently, smoothing causes reported earnings to be a less noisy measure of permanent earnings that can be sustained over the longterm. We extend those results to examine whether earnings smoothing is associated with higher valuations per dollar of permanent earnings, proxied by forecasted earnings, and find that earnings smoothing is associated with higher forward P/E ratios. We then investigate the extent to which this result is due to earnings smoothing being associated with higher growth and lower risk, the two effects that generate higher forward P/E ratios. Our results suggest that earnings smoothing is positively related to forecast growth and negatively related to risk, with the growth effect being more evident than the risk effect.

3 Value-relevant properties of smoothed earnings I. Introduction There is considerable anecdotal evidence provided in support of the view that managers make discretionary accounting choices to smooth reported earnings (Smith et al., 1994). One of many rationales offered for this behavior is that smoothed earnings are rewarded with higher valuations. The results in Hunt et al. (2000) suggest that smoothing reduces the noise between reported and value-relevant permanent earnings, and this reduced measurement error results in higher multiples on reported earnings. We extend that research to examine whether factors other than reduced measurement error may also be relevant. To do so, we switch the value driver from reported earnings to forecast earnings (a proxy for permanent earnings) and examine whether earnings smoothing is associated with higher valuations per dollar of permanent earnings (i.e., higher forward price-earnings ratios). Observing such a relation suggests that effects other than the measurement error explanation are also important. And to provide indirect evidence on these other effects, we examine the relation between earnings smoothing and the two factors that impact forward price-earnings (P/E) ratios: risk and forecast growth. Our objective is to add to the available evidence on value-relevant properties of smoothed earnings. While both empirical and theoretical research have explored other reasons why firms might smooth reported earnings, the valuation effects of earnings smoothing are potentially the most important. Somewhat paradoxically, these valuation effects are hard to document, primarily because earnings smoothing is not easily measured, and relatively little theory has been offered to explain why in equilibrium different firms smooth earnings to different extents. Two possible rationales suggested in the prior literature are a) firms with better prospects signal their strength by building reserves and smoothing earnings, a strategy that other firms are unable to mimic 1, and b) firms with higher growth prospects may face greater incentives to smooth earnings, to 1 General Electric and Microsoft are two firms frequently mentioned as examples of cases where substantial reserves are maintained, by understating earnings on average, to generate smoothly rising earnings streams 1

4 avoid the disproportionately large price drops in stock price that result if earnings growth is not maintained (e.g. Skinner and Sloan, 2002). We hope that the regularities documented here and in related empirical work will encourage development of theory on value-relevant earnings smoothing. As noted earlier, empirical investigations are hampered by the difficulty associated with separating reported earnings into pre-smoothed earnings and the accrual component used to smooth reported earnings. While models of nondiscretionary accruals can be used to estimate earnings before those accruals, concerns have been raised that estimates of nondiscretionary accruals are associated with considerable measurement error (e.g., Dechow et al., 1995, and Thomas and Zhang, 2000). Also, not all discretionary accruals are designed to smooth reported earnings. To the extent that the difference between estimated discretionary accruals and the smoothing component of accruals is associated with P/E ratios (via growth or risk), a spurious relation between earnings smoothing and P/E ratios will be observed. Because of these concerns, we opted for an alternative approach and use the observable volatility of forecast earnings as a proxy for the value-relevant portion of the unobservable volatility of pre-smoothed earnings. We view pre-smoothed earnings as consisting of permanent, transitory, and price-irrelevant components (see Ramakrishnan and Thomas, 1998, for examples of how accounting rules create these components). While a substantial portion of the volatility of pre-smoothed earnings is likely due to the volatility of transitory and price-irrelevant earnings components, ignoring those volatilities does not create much error because they have little impact on the stock market s perceptions of risk and growth, the two determinants of P/E ratios. In essence, even though the volatility of the permanent earnings component, measured by the volatility of forecasted earnings, represents only a fraction of the volatility of pre-smoothed earnings, we assume as a first approximation that it captures the value-relevant portion of the volatility of pre-smoothed earnings. We then measure the impact of smoothing on valuations per dollar of permanent earnings by regressing forward P/E ratios on both the volatility of reported earnings and the volatility of 2

5 permanent earnings. Since volatility in reported earnings is a combination of the volatility of presmoothed earnings and the volatility of the accrual component designed to smooth reported earnings, the coefficient on volatility of reported earnings should capture the effects of earnings smoothing. This coefficient, which measures the impact of reducing reported earnings volatility by one unit, given a fixed level of volatility of the permanent earnings component, is our primary measure of the valuation effect of earnings smoothing. The volatility of reported earnings is measured as the time-series variability of rolling four-quarter earnings per share (EPS) and our primary measure of the volatility of permanent earnings, referred to hereafter as intrinsic earnings volatility, is based on the time-series variability of two-year out forecasts of annual EPS. Our empirical investigation proceeds as follows. Since prior research has considered the link between prices and reported earnings far more often than that between prices and forecasted earnings, we investigate first the relation derived between forward P/E ratios and risk and growth (e.g., Penman, 2001). We confirm that analysts earnings growth forecasts and a variety of popular proxies for risk (along with the level of the prevailing risk-free rate) explain crosssectional variation in forward P/E ratios as predicted by that relation. The explanatory power and consistency with the predicted relation are higher in this paper, relative to that in prior research (e.g. Beaver and Morse, 1978). In addition to the improvement in fit due to the use of forward earnings rather than trailing earnings, we find that using earnings-price (E/P) ratios rather than price-earnings ratios further improves the specification. We then investigate whether earnings smoothing is associated with forward E/P ratios, by regressing forward E/P ratios on the volatility of reported earnings and intrinsic earnings volatility. Note that risk and growth are intentionally excluded from this regression. Since intrinsic earnings volatility and earnings smoothing do not appear in the relation derived for price-earnings ratios, they should play no role in a properly specified regression of E/P ratios on 3

6 risk and growth. 2 Our approach is a) to investigate if intrinsic earnings volatility and earnings smoothing are related to E/P ratios when risk and growth are omitted, and b) to determine whether any observed relation in a) can be explained by the underlying relations between those two variables (intrinsic volatility and smoothing) and the two determinants of E/P ratios (risk and growth). In essence, we first estimate regressions of E/P ratios on intrinsic and reported earnings volatility, and then estimate regressions of risk and growth on the same regressors. A summary of our findings is as follows. The regressions of E/P ratios on reported earnings volatility and intrinsic volatility indicate that firms with smoothed earnings are associated with higher P/E ratios. (Even though our regressions are based on E/P ratios, we find it more intuitive to invert those results and discuss them in terms of P/E ratios.) Similar results are observed when we control for a different measure of smoothed earnings suggested in the literature (e.g., Barth et al., 1999 and Myers and Skinner, 1999): the number of consecutive earnings increases observed in prior periods. Our results are robust to measures of smoothing derived by estimating discretionary accruals from different variants of the Jones (1991) model (results available upon request), as well as to an alternative measure of intrinsic volatility (volatility of cash flow from operations). Our regressions of growth on reported earnings volatility and intrinsic volatility suggest that firms with smoothed earnings are strongly associated with higher forecast growth. Repeating the analysis with risk measures indicates that smoothed earnings are associated with lower risk, although the strength of this relation is not as strong and varies across risk measures. Finally, even though it is not the focus of our study, we find that intrinsic earnings volatility exhibits the same valuation relation as earnings smoothing: lower intrinsic earnings volatility is associated with higher P/E ratios, and also associated with lower risk and higher growth. 2 Even though intrinsic earnings volatility and earnings smoothing might affect the stock market s perception of risk and growth, once those perceptions are included as regressors, intrinsic volatility and earnings smoothing should play no role. 4

7 The next section surveys the relevant prior literature and Section III develops our regression models. Section IV covers sample formation and variable definitions. Section V discusses the results and Section VI concludes the paper. II. Prior research on earnings smoothing Academic research has attempted to document evidence of earnings smoothing. For example, Gaver et al. (1995) find a negative association between discretionary accruals and current pre-managed earnings. Defond and Park (1997) find that managers make positive (negative) discretionary accruals when current earnings are poor (good) and future earnings are expected to be good (poor), suggesting that they borrow earnings from (save earnings for) the future when they expect their fortunes to improve (decline). There is also evidence consistent with earnings management designed to achieve smoothing-related objectives other than smoothing over time. Examples of such behavior include the avoidance of losses, earnings decreases, and negative forecast errors (e.g., Burgstahler and Dichev, 1997, DeGeorge, Patel, and Zeckhauser, 1999, Barth et al., 1999, Meyers and Skinner, 1999) and rounding up earnings toward targets perceived to be relevant to unsophisticated investors (e.g. Carslaw, 1988, Thomas, 1989, and Das and Zhang, 2002). Different theories have been proposed to explain why managers might smooth earnings. In Fudenberg and Tirole (1995), managers smooth reported earnings because of incumbency rents and information decay (i.e., more recent information is given more weight in evaluating managers). In Trueman and Titman (1988), managers smooth reported earnings to reduce the perceived volatility of economic earnings, thereby lowering various claimants (e.g., debt holders) assessment of the probability of bankruptcy and favorably affecting the terms of trade between the firm and its (non-investor) stakeholders. Ronen and Sadan (1981) and Chaney and Lewis (1995) investigate smoothing behavior as a credible signal of high quality earnings. Kirschenheiter and Melumad (2001) develop a model in which smoothing earnings is part of an equilibrium reporting strategy designed to increase the inferred precision of reported earnings. 5

8 Less attention has been paid by academic research, however, on how the stock market evaluates smoothed earnings. While the popular financial press is replete with conjectures about investors disliking earnings surprises and being willing to pay a premium for smoother earnings streams (e.g. Fox, 2002), only a handful of studies have investigated this issue. Barth et al. (1999) find that firms reporting long strings of annual earnings increases are priced at a premium, and when that string is broken the premium declines rapidly. They find that the coefficient on earnings in their valuation regression (similar in concept to the trailing P/E ratio) is higher for firms with unbroken strings of earnings increases, even after controlling for growth and risk. Hunt et al. (2000) examine the effect of smoothing due to two separate sources on the coefficient on reported earnings: a) accounting rules that effectively reduce volatility as operating cash flows are converted to income before discretionary accruals, and b) managerial efforts to smooth that income further by making discretionary accruals before disclosing reported earnings. 3 They split firms into two equal groups (above and below industry medians) for each type of smoothing, and find that both types of smoothing raise the earnings multiple. After extensive sensitivity analyses confirm the robustness of their results, Hunt et al. (2000) conclude that both types of smoothing are associated with higher valuations, because they smooth reported earnings toward the permanent earnings that the firm can sustain in the future. Since valuations reflect permanent earnings, reducing the error with which reported earnings measure permanent earnings increases the valuation multiple on reported earnings. While the evidence in Hunt et al. (2000) is consistent with this measurement error explanation for the higher valuations observed for firms with smoothed earnings, it does not exclude the possibility that there are other explanations that are also relevant. Specifically, firms might signal lower risk or higher growth prospects via greater smoothing of reported earnings. 3 See Subramanyam (1996) for evidence consistent with this view, and Sankar and Subramanyam (2001) for an economic model that supports smoothing via discretionary accruals. 6

9 To investigate this possibility, we examine whether smoothed earnings also result in higher valuations per dollar of permanent earnings. III. Price-earnings regression models Whereas intuitive links among E/P ratios, risk, and growth can be derived from the Gordon (1962) dividend growth model, more general relations have been derived based on the abnormal earnings or residual income specification. The relations derived for trailing P/E ratios (e.g., Penman, 2001) and forward P/E ratios (e.g., Claus and Thomas, 2001) are provided below in equations (1) and (2), respectively. p0 + d e 0 0 = ( 1+ k) k ae 1 + e0 1 + ae ( 1+ k) e ( 1+ k) (1) p e ae 2 ae3 = k e1 ( 1+ k ) e1( 1+ k ) where p 0 = current price, e 0 =earnings reported for current year, d 0 =dividends for current year, e 1 =earnings forecast for next year, k=cost of equity, ae t = ae t -ae t-1 is the change in expected abnormal earnings (ae), where ae t is defined as expected earnings for period t less k times the beginning book value of equity. (2) Given our primary interest in forward P/E ratios, we focus on equation (2). In effect, the P/E ratio is determined by a) the inverse of k (which is a function of the risk-free rate and risk) and b) the growth term in brackets, which represents the present value of growth in abnormal earnings, scaled by current or forward earnings. Inverting these relations, we can show that the E/P ratio should be positively related to risk and negatively related to growth. We prefer to use regressions based on E/P ratios, over those based on P/E ratios, since they are less likely to be affected by the small denominator problem (when earnings is close to zero). 4 Also, this 4 We consider only positive earnings values in our empirical analysis to avoid the discontinuities and nonlinearities caused by negative earnings. 7

10 specification allows for a simple control for prevailing levels of the risk-free rate by including it as an additional regressor. There is no role in these relations for volatility in reported earnings. Therefore, any observed relation between E/P ratios and reported earnings volatility should be indirect and due to underlying relations between the two factors that determine E/P ratios (the market s perceptions of risk and growth) and the two components of reported earnings volatility (intrinsic earnings volatility and managerial efforts to smooth earnings). It is easy to see why intrinsic earnings volatility might be positively related to E/P ratios, because of a positive relation between intrinsic volatility and risk. The relation between intrinsic volatility and growth is less obvious, however. For example, whereas mature firms with low growth prospects might exhibit low intrinsic volatility, other low-growth firms in financial distress might exhibit high intrinsic volatility. Holding aside some unexpected relation between intrinsic volatility and growth, the expected positive relation between intrinsic volatility and risk suggests that firms with low intrinsic volatility would be associated with low E/P ratios or high P/E ratios. The relation between smoothed earnings and E/P ratios is likely to be less direct than that between intrinsic volatility and E/P ratios. As mentioned in the introduction there are a number of hypothesized ways that managerial efforts to smooth intrinsic volatility affect the relations above. Firms with better prospects might build greater reserves and smooth more, causing the market to rationally reward them with lower E/P ratios, because current and near-term earnings understate long-term permanent earnings. Alternatively, firms with higher growth prospects might have incentives to maintain earnings streams that grow smoothly. While both these examples suggest a negative relation between smoothing and E/P ratios, it is possible to construct other examples where managerial efforts to smooth earnings result in higher E/P ratios. 8

11 IV. Sample Formation and Variable Definitions Our sample is drawn from the intersection of IBES and quarterly Compustat (industrial, research and full coverage files) datasets. We conduct our analysis at the quarterly level, rather than at the annual level, to increase sample size. The IBES summary file, with consensus analyst forecasts for different horizons as of the middle (the Thursday following the second Friday) of each month, is used to identify the most recent set of monthly observations available before the earnings announcement for each firm quarter. Since IBES adjusts all data for stock splits and dividends, firm-quarters that split subsequently have smaller magnitudes for actual EPS. If these firms that split more often are also valued higher, these lower levels of split-adjusted EPS will result in lower measured volatility, and create a spurious negative relation between volatility and P/E ratios. We reverse the split adjustment made by IBES, by multiplying all variables by the split adjustment factor. However, when computing time-series volatility, we ensure that the prior quarters used are on the same split-adjusted basis as the most recent quarter. When examining the time-series of reported (or actual) earnings, we generate an annualized or rolling four-quarter EPS (EPS for this quarter plus the prior 3 quarters) to remove seasonal effects. We base our measures of the time-series volatility of reported earnings on two different assumptions of how earnings evolve. First, we follow the conventional wisdom frequently mentioned in the popular financial press and assume that annualized EPS follows a trend process, with earnings reverting toward that trend. Our measure of volatility (STDERR) is the standard error of the regression of these 12 annualized EPS numbers on time. There is, however, considerable research suggesting the presence of a substantial seasonal random walk component in quarterly earnings (e.g. Watts and Leftwich, 1977). To better represent this process, our second measure of earnings volatility is the standard deviation of seasonally-differenced quarterly earnings (SDSRW), over the prior 12 quarters. We elected to measure earnings volatility using the time-series of actual EPS as reported by IBES, which removes certain onetime items from the EPS reported by the firm, since we believe that volatility induced by items that are clearly visible to the market as being transitory are less likely to be value-relevant. 9

12 Since the economic value of one share is somewhat arbitrary, given that it can be changed by stock splits, and varies across firms and over time, the volatility of EPS should properly be deflated for scale differences in per share amounts. We considered scaling EPS volatility by share price as well as the level of EPS, but discovered that such scaling created a spurious positive and negative relation, respectively, with the E/P ratio (which is the dependent variable in certain regressions). We elected instead to not scale reported volatility but to also calculate intrinsic volatility using per share amounts. This way, any differences across sample firmquarters in the magnitudes of per share amounts are controlled for by common variation in these two regressors, and are not reflected in the estimated regression coefficients on these two variables. We considered a variety of measures of intrinsic volatility, reflecting the variability of earnings before managerial efforts to smooth them. Since the level of pre-smoothed earnings is not observed, any measure based on publicly observable data is likely to be associated with error. Also, we do not attempt to capture ex ante smoothing (see Myers and Skinner, 1999), which reflects the choice of accounting methods and estimates designed to reduce the structural or expected variability of earnings, even before the earnings stream is observed. We focus only on ex post smoothing, representing managerial efforts to reduce the variability of reported earnings after observing information about this period s results. Our primary measure of intrinsic volatility (STDERRFCST) is derived from the timeseries volatility of forecasted earnings. We believe that analysts forecasts of earnings for the next full year (EPS2) reflect a measure of permanent or core earnings, and revisions in this measure are very strongly related to stock returns (e.g. Liu and Thomas, 1999). Thus, the timeseries volatility of earnings forecasts offers a simple and direct measure of the intrinsic volatility of pre-smoothed earnings. As mentioned above, we compute intrinsic volatility at the per share level, so that scale differences across per share amounts in our measures of reported and intrinsic earnings volatility are not reflected in the multiple regression coefficients on these volatility measures. 10

13 Our secondary measure of intrinsic volatility (STDCFO) is derived from the time-series volatility of operating cash flows, per share. While the volatility of operating cash flows might be viewed as a natural proxy for intrinsic volatility, it is affected by operating decisions, such as unusual inventory purchases or payments of accounts payables, that are not related to inherent volatility. To the extent that the accruals process is designed to smooth out such fluctuations by converting cash flows to earnings, cash flow volatility is a poor proxy for intrinsic volatility. Also, observed levels of operating cash flows are likely to be negatively related to observed growth, which in turn may be related to forecast growth (which is a dependent variable in some regressions and a determinant of E/P ratio, the dependent variable in other regressions). In sensitivity analyses, we include this measure of cash flow volatility as an additional regressor to check whether our primary measure of intrinsic volatility remains significant. STDERRFCST and STDCFO equal the regression standard errors from regressions of EPS2 and annualized operating cash flows, respectively, on time. As with our measure of reported earnings volatility, STDERR, we use the prior 12-quarters to estimate these regressions. For regressions involving STDCFO, the number of observations with non-missing values declines by about 40 percent because a) cash flows from operations are not reported for some industries, and b) the cash flow format was first required after To be included in the sample, firm-quarters must satisfy the following four requirements: a) price as supplied by IBES is positive; b) long-term earnings growth rate forecast is positive and less than 50%; c) the earnings-to-price ratio (measured using the ratio of Compustat quarterly earnings per share to fiscal quarter end stock price) is greater than 0 and less than 1; and d) STDERR and the two-year-out EPS forecasts are non-missing. Our sample includes 61,836 firm-quarter observations from 1988:I to 2000:IV. The number of observations in the different quarters ranges from 553 for 1988:I to 1,649 for 1999:III. The actual number of observations available varies across regressions, due to missing values for the specific variables included in each regression. 11

14 Before considering the regressions of E/P ratios, growth and risk on intrinsic volatility and earnings smoothing, we provide a description of differences across firms with different volatilities of reported earnings. We form deciles each quarter based on the two measures of reported earnings volatility (STDERR and SDSRW) and provide in Table 1 the mean values of a variety of measures that describe value-relevant properties such as risk, forecast earnings growth, and intrinsic volatility. 5 The different variables considered, along with a brief description (see the Appendix for more details), are as follows: SIZE (log of market value of equity as of the current quarter end); LTG (long-term growth rate forecast for EPS); LOGBP or log of the book-to-market ratio (book value divided by the market value at current quarter end); STDRET (standard deviation of monthly returns over the prior 48 months); BETA (computed by regressing the previous 36 monthly returns on the equally weighted market return of all firms listed on NYSE, AMEX, and NASDAQ); UPEARN (the number of consecutive positive seasonally-differenced quarterly earnings over the prior 12 quarters); STDERRFCST; and STDCFO. UPEARN, which is the measure of earnings smoothing used in prior studies, is our secondary measure of earnings smoothing, while STDERRFCST and STDCFO are our primary and secondary measures of intrinsic earnings volatility, respectively. We also report the mean values for the forward and trailing E/P ratios: EPS2P and EP. EPS2P and EP are respectively measured by the two-year ahead EPS forecast scaled by price at quarter end and the rolling 4-quarter EPS (that quarter plus the prior 3 quarters), scaled by price at quarter-end. While we believe the measures we use to proxy for risk and growth are the best available, it is particularly difficult to capture fully the cumulative effect of growth in abnormal earnings over the long-term. Our proxy. LTG, only captures growth over the near-term (over the next business cycle, which is assumed to represent the next five years), and refers to growth in EPS, not growth in abnormal earnings. 5 The patterns observed for median values are essentially similar. 12

15 Given the remarkable similarity between the results reported in Panels A and B of Table 1, for deciles of STDERR and SDSRW (the two measures of reported earnings volatility), respectively, the discussion below applies equally to both panels. The relation between earnings volatility and SIZE suggests a shallow U-shape, where firms with extreme volatility are slightly larger than firms with intermediate volatility. There is a clear negative relation between earnings volatility and LTG, suggesting that firms with smoother reported earnings are associated with higher perceived growth in EPS. To the extent the next three measures (LOGBP, STDRET, and BETA) are risk proxies, they all indicate a positive relation between earnings volatility and risk, suggesting that firms with smoother reported earnings are less risky. 6 Since reported earnings volatility reflects the combination of intrinsic volatility and earnings smoothing, we expect reported earnings volatility to be positively related to the two intrinsic volatility measures and negatively related to measures of earnings smoothing. The results reported under the columns UPEARN, STDERRFCST and STDCFO confirm that expectation. Firms with less volatile reported earnings are far more likely to have smoothed earnings (indicated by a larger value of UPEARN, or a longer unbroken string of consecutive earnings increases), and they exhibit lower intrinsic volatility (STDERRFCST and STDCFO). The relations described in the last two columns of Table 1, linking earnings volatility to forward and trailing E/P, confirm the popular wisdom that firms with less volatile reported earnings are valued more highly per dollar of earnings (have lower E/P ratios). Note, however, that this relation is not as steep for the middle deciles and is more visible for the higher and lower reported earnings volatility deciles. V. Results We continue with our descriptive results and report in Table 2 the pairwise correlations among the different variables. The Pearson correlations are reported above the main diagonal, and the Spearman (rank) correlations are reported below the main diagonal. Given the large 6 See for example, Fama and French (1992) for the motivation to consider these risk measures. 13

16 sample size, almost all the reported correlations are significant at the 1 percent level. The number of observations with data available for each variable is reported in the bottom row. Since the pooled regressions we estimate combine data from different calendar quarters with different interest rate regimes (relevant for the level of k, which in turn affects the level of E/P), we also include the level of the risk-free rate (RFRATE), represented by the yield on 10-year Treasury bonds. The Pearson and Spearman correlations between different pairs of variables are generally consistent (i.e., when significant, they are of the same sign). Two sets of exceptions noted relate to BETA and SIZE. The Pearson and Spearman correlations between BETA and LOGBP and those between BETA and STDCFO are of opposite sign. Also, consistent with the non-monotonic (U-shaped) relation between SIZE and the two reported earnings volatility measures in Table 1, the Pearson and Spearman correlations between SIZE and those two variables are inconsistent. Similar inconsistency is noted for the correlations between SIZE and the two measures of intrinsic volatility, STDERRFCST and STDCFO. The correlations between trailing E/P and the different measures of risk and growth as well as all the corresponding relations for forward E/P are consistent with the functional form represented in equations (1) and (2). E/P is positively related to the risk-free rate and to risk and negatively related to growth. As expected, we often observe large correlations within different measures for the same construct. Our next analysis examines the ability of our growth and risk measures to jointly explain cross-sectional variation in E/P ratios. By identifying the extent to which the relations predicted by equations (1) and (2) are observed in our data, this analysis allows us to identify the extent to which our measures of risk and growth are reasonable proxies for the market s perceptions of risk and growth. Since these growth and risk measures appear as dependent variables in later analyses, it is important to establish the extent to which they are incrementally related to the underlying constructs. 14

17 Table 3 contains the results of regressions of trailing and forward E/P on the risk-free rate (RFRATE) and the various growth and risk proxies described above. Even though we focus on the forward E/P regressions, we include the trailing E/P results to provide a reference point. The different regression specifications are reported in the columns numbered 1 through 3. The dependent variable examined is noted in the first row, and the number of observations for each regression and the adjusted R 2 values are reported in the next two rows. For the different regressors, we report in each cell the following three values: a) the coefficient from the pooled regression, b) the p-value associated with the two-tailed t-test on that coefficient, and c) the p- value associated with the two-tailed t-test on the mean of the distribution of coefficients obtained by estimating each regression within each fiscal quarter between 1988:I to 2000:IV. The results for regression 1, which describes cross-sectional variation in the trailing E/P ratio, suggest that the regression is reasonably well-specified. The adjusted R 2 of about 24 percent is high for pooled firm-level regressions, and all the coefficients are of the predicted sign and very significant in almost all cases. The presence of a substantial and significant intercept suggests, however, that there is room to further improve the specification. The results for regression 2, which describes cross-sectional variation in the forward E/P ratio, are similar to those noted for trailing E/P ratios. The adjusted R 2 value is even higher (about 28 percent) and, more important, all of the coefficients are very significant for both the pooled regressions and the quarter-by-quarter regressions. The results for regression 3 show that the relation between the forward E/P ratio and our proxies for risk and growth remains significant even after the trailing E/P ratio is introduced as an additional regressor. (The dramatic increase in adjusted R 2 values is to be expected given the high correlation between trailing and forward E/P ratios.) While trailing and forward E/P ratios are conceptually similar, it has been shown that forward earnings are more closely related to share prices than trailing earnings (e.g Liu, Nissim, and Thomas, 2000). The stronger relation observed for forward earnings is likely due to trailing earnings containing both permanent and transitory earnings components, whereas forward 15

18 earnings is more homogeneous and consists mostly of permanent earnings components. This analysis confirms that our measures for risk and growth represent reasonable proxies for the market s expectations of the underlying constructs. And the better fit observed in Panel B supports our use of forward earnings as a measure of permanent earnings. Table 4 contains the results of estimating our first set of regressions relating to earnings volatility. We investigate whether earnings smoothing is related to E/P ratios, when proxies for risk and growth are excluded from the regression. Recall that under our methodology the coefficient on reported earnings volatility represents the effect of earnings smoothing (when intrinsic earnings volatility is controlled for). We begin again with the trailing E/P ratio (in Panel A) to provide a reference, but our main interest is in Panels B and C, where the forward E/P ratio is examined. Panel C is similar to Panel B, except we also include the trailing E/P ratio as a control variable when explaining variation in forward E/P. Similar to the analysis in regression 3 of Table 3, we are investigating in Panel C whether intrinsic volatility and earnings smoothing explain variation in forward E/P, beyond the (substantial) amount explained by trailing E/P. In each panel of Table 4, we begin with our measure of intrinsic volatility (STDERRFCST) and then in incremental steps add the risk free rate, SIZE and STDERR to the regression. Regression 4, which considers our primary measures of intrinsic volatility and earnings smoothing, represents our main result in each panel. We then examine whether our main result is robust to the inclusion of our secondary measures of intrinsic volatility (STDCFO) and earnings smoothing (UPEARN). Note that the sample sizes for the regressions including STDCFO are considerably smaller because of the many firm-quarters with missing values for that variable. The results reported in Panel A suggest the following. First, the trailing E/P ratio is positively related to intrinsic volatility (STDERRFCST), and this relation is maintained even after including controls for the risk-free rate, and size (in regressions 2 and 3). Second, the coefficient on reported volatility (STDERR), our proxy for earnings smoothing, is also positively related to trailing E/P ratios, which suggests that earnings smoothing is related to higher trailing P/E ratios 16

19 (our main result in regression 4). The sensitivity analysis in regression 5 indicates that UPEARN, our alternative measure of earnings smoothing, is not significant. The sensitivity analysis in regression 6 indicates that STDCFO is also significantly positive, along with our primary measure of intrinsic volatility. Curiously, our primary measure of earnings smoothing (STDERR) is no longer significant in regression 6. Also, the coefficient on RFRATE, which is very significantly positive in the other regressions, is suddenly negative. While these differences in results may be caused by a different and smaller sample for regression 6, the results in Table 3 suggest a different possibility: that our regressions are not as well specified for trailing E/P ratios, relative to that for forward E/P ratios, and this leads to less reliable inferences when trailing earnings are used. The results in Panel B of Table 4 indicate similar results for forward E/P ratios: intrinsic volatility is always positively related to forward E/P and reported earnings volatility is also positively related. Unlike the trailing E/P results in Panel A, the coefficient on UPEARN is significant and negative, and the coefficient on STDERR is not affected by the introduction of STDCFO. In essence, both our primary and secondary measures for intrinsic volatility as well as the primary and secondary measures for earnings smoothing show strong and consistent relations with forward E/P: lower intrinsic volatility and more earnings smoothing are associated with higher valuations. Also, we observe a more stable pattern of coefficient values in the different rows of Panel B, relative to that observed for trailing E/P in Panel A. The results in Panel C of Table 4 confirm that the results observed for forward E/P ratios remain unchanged even after including trailing E/P ratios as an additional regressor. The coefficients on reported and intrinsic earnings volatility continue to be positive and significant, and the coefficients on UPEARN and STDCFO, in regressions 5 and 6, remain significant. Note that the coefficient on RFRATE declines substantially when the trailing E/P ratio is included as an additional regressor. In sum, smoothed earnings are associated with higher valuations per dollar of forward or permanent earnings. Apparently, smoothed earnings are associated also with higher growth and/or lower risk, the two determinants of E/P ratios. 17

20 The results reported in Table 5 provide evidence on the relation between earnings smoothing and growth/risk. We consider one measure of growth (LTG) and three measures of risk (BETA, STDRET, and LOGBP), and the corresponding results are reported in Panels A through D, respectively. Each measure of growth and risk is regressed on intrinsic and reported earnings volatility. Although SIZE has been viewed as a risk measure in the prior literature, we suspect that earning volatility and earnings smoothing may be related to SIZE for reasons other than the risk link. Therefore, we include SIZE as a control variable in all regressions, but do not study it as a dependent variable. The results in Panel A of Table 5 indicate that growth forecasts are strongly negatively related to intrinsic earnings volatility and positively related to earnings smoothing (indicated by a negative sign on reported earnings volatility). That is, lower intrinsic earnings volatility and managerial efforts to smooth earnings are both associated with higher forecast growth, which in turn explains the higher P/E ratios noted in Table 4. Incorporating SIZE in regression 2 does not alter the results observed in regression 1. The positive and significant coefficient on UPEARN in regression 3 confirms that this measure of earnings smoothing is incrementally associated with higher growth. Similarly, the negative and significant coefficient on STDCFO in regression 4 suggests that our secondary measure of intrinsic volatility is incrementally associated with higher forecast growth. The coefficient on STDERR remains negative and significant across all regressions. The results in Panel B of Table 5 indicate that lower intrinsic earnings volatility and managerial efforts to smooth earnings are both associated with lower BETA risk, which is again consistent with the higher P/E ratios noted in Table 4. This inference is based on the positive coefficients on STDERRFCST and STDERR observed in regression 1. The positive coefficient on STDERR is, however, not significant in the quarter-by-quarter test (the third value in that cell is 0.540). That result appears to be driven by correlation with SIZE, since the coefficient on STDERR becomes strongly significant when SIZE is introduced in regression 2. Turning to the incremental information content of the secondary measures of earnings smoothing and intrinsic 18

21 volatility, we find results that are partially inconsistent with the results in regression 2. First, the coefficient on UPEARN in regression 3 is significantly positive, which suggests that earnings smoothing is associated with higher risk. This result is puzzling, since the coefficient on STDERR remains significant and positive in regression 3. In regression 4, the coefficient on STDCFO is positive and significant, which is consistent with our main result that intrinsic volatility is positively related to BETA (positive coefficient on STDERRFCST). We find, however, that the coefficient on STDERR is no longer significant, indicating that the relation between earnings smoothing and BETA is not robust. The results in Panel C of Table 5 provide mixed results regarding the relation between risk, as measured by the standard deviation of returns over the prior 48 months (STDRET), and intrinsic and reported earnings volatility. Whereas the observed positive relation between intrinsic volatility (STDERRFCST) and risk is consistent with intuition and other results in this table, the observed negative relation between reported volatility and risk suggests that earnings smoothing is associated with higher perceived risk. The positive coefficient observed on UPEARN in regression 3 also suggests a positive relation between earnings smoothing and risk. Introducing STDCFO in regression 4 does not change the main findings: whereas lower intrinsic volatility is associated with lower risk, earnings smoothing appears to be associated with higher risk. The final set of results in Panel D of Table 5 relates to the relations between risk as measured by the logarithm of the book-to-price ratio (LOGBP) and intrinsic volatility and earnings smoothing. The results are strongly consistent with the view that lower intrinsic volatility and earnings smoothing are associated with lower risk. In regression 1, the coefficients on STDERR and STDERRFCST are significantly positive, and those results are maintained when SIZE is controlled for in regression 2. The results of regressions 3 and 4, which also incorporate the secondary measures of earnings smoothing and intrinsic volatility, confirm our main findings. 19

22 Overall, the relation between E/P ratios and earnings smoothing described in Table 4 is mainly due to the strong link between earnings smoothing and growth observed in Table 5. That is, firms with smoothed earnings are associated with higher growth, and therefore higher valuations. Even though one might intuitively expect strong links between earnings smoothing and perceived risk, we find that this link is not as strong as the link between earnings smoothing and growth, and depends on the risk measure examined. Turning to the relation between E/P ratios and intrinsic volatility described in Table 4, it is due to both the strong relation between intrinsic volatility and growth as well as the strong relation between intrinsic volatility and risk. Firms with lower intrinsic volatility are associated with lower risk and higher growth, which imply higher valuations. VI. Conclusion This study provides initial evidence on the valuation impact of smoothing reported earnings. Specifically, we extend the results in Hunt et al. (2000) that find an association between earnings smoothing and higher trailing P/E ratios. They conclude that the higher valuations associated with smoothed earnings are likely due to reported earnings being smoothed toward permanent earnings. We examine the relation between earnings smoothing and forward P/E ratios to investigate whether factors other than the measurement error perspective noted by Hunt et al. (2000) might also play a role. Observing higher forward P/E ratios for firms with smoothed earnings implies a higher valuation per dollar of permanent earnings, which cannot be explained by a measurement error perspective. Valuation models predict that forward E/P ratios are explained by the level of discount rates (which are determined by risk-free rates and risk) and anticipated growth. The volatility of reported earnings, which represents the joint effect of intrinsic volatility and managerial efforts to smooth that volatility, plays no direct role in these models. Earnings volatility may be related, however, to E/P ratios via links between earnings volatility and the market s perceptions of 20

23 growth and risk. Our study provides preliminary evidence on the extent to which earnings smoothing is related to risk and growth, the two factors that are directly linked to the E/P ratio. Separating reported earnings volatility into its two components is hampered by our inability to observe managerial efforts to smooth the intrinsic volatility in reported earnings. Rather than estimate discretionary accruals to separately identify earnings smoothing, we focus on estimating intrinsic volatility from the variation over time in consensus forecasts of future earnings. By focusing on variation in a measure of permanent or core earnings, we believe this variation captures well the value-relevant portion of the underlying volatility in earnings before efforts to smooth that volatility. When both intrinsic volatility and reported earnings volatility are introduced jointly as regressors, the coefficient on reported earnings volatility should capture the effect of earnings smoothing, since it represents the incremental variation in reported earnings not captured by intrinsic volatility. We find evidence of higher valuations per dollar of trailing and forward EPS for firms with lower volatility of reported earnings. After separating reported earnings volatility into its two components, we find that both lower intrinsic volatility and earnings smoothing are associated with higher price-earnings ratios. Our evidence also suggests that these relations are due to associations between these two components of reported earnings volatility and the market s expectations of growth and risk: a) firms engaging in more earnings smoothing exhibit a strong relation with higher growth and a weaker relation with lower risk, and b) firms with lower intrinsic volatility are strongly associated with higher growth and lower risk. We hope this evidence will invigorate efforts to build a better understanding of why earnings smoothing is associated with higher perceived growth and lower perceived risk. 21

24 Appendix Variable definitions dataxx refers to the corresponding data item from the quarterly Compustat file, and the IBES forecast data is taken from the summary and detailed files. When calculating STDERR, STDERRFCST, and SDSRW, the time-series is split-adjusted to ensure that all observations are on the same basis as the most recent quarter. BETA is the slope from a regression of monthly returns over the prior 36 months on the corresponding monthly returns of an equally weighted market index (NYSE, AMEX, and NASDAQ). SIZE is the natural log of market capitalization at the end of the quarter (data14 multiplied by data61). LOGBP is the natural log of the book-to-market ratio, at the end of the quarter, equal to book value (data60) divided by market value (data14 multiplied by data61). STDRET is the standard deviation of monthly returns over the prior 48 months. STDERR is the standard error of the regression of rolling 4-quarter EPS (actual EPS for that quarter plus EPS for the prior three quarters, from IBES) on time, estimated over the prior 12 quarters. UPEARN is the number of times the company reports consecutive earnings increases (positive seasonally-differenced quarterly EPS, based on actual IBES EPS) during the previous 12 quarters. STDERRFCST is the standard error of the regression of two-year-ahead EPS forecasts (from the IBES summary file) on time, estimated over the prior 12 quarters. The forecasts have been multiplied by the split adjustment factor to reverse the split adjustment done by IBES. STDCFO is the standard error of the regression of rolling 4-quarter per share cash flow from operations (data108) on time, estimated over the prior 12 quarters. The number of shares is taken from IBES summary file and adjustments are made to ensure that the number of observations is not affected by stock splits or dividends during the estimation period. SDSRW is the standard deviation of seasonally-differenced quarterly EPS (actual EPS per IBES), over the prior 12 quarters. The EPS values have been multiplied by the split adjustment factor to reverse the split adjustment done by IBES. LTG is the consensus (mean) long term growth rate forecast for EPS, from the IBES summary file. EPS2P is the forward E/P ratio, equal to the mean of the three most recent two-year out EPS forecasts (from the detailed IBES file) scaled by price reported by IBES. EP is the trailing E/P ratio, equal to the actual EPS according to IBES for that quarter and prior 3 quarters, scaled by price reported by IBES. 22