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Prices lead earnings in Brazil?

1 introduction

Stock prices follow the expectations of investors and are conditioned on the information available at any given time. It may be assumed that this relationship occurs rationally but without obeying specific rules. Each investor has his/ her own decision model that is influenced by his/her indifference to the various risk and return configurations established for the assets. Accounting earnings, meanwhile, also capture much of this information; however, they do so subject to the limitations imposed by objectivity, by conservatism and by the rules for the recognition of revenue within the accounting model itself, which render them informationally untimely.

To some extent, prices and earnings can be considered to be signs of the same state of reality, although they are not contemporaneous. This situation appears more clearly in light of market efficiency. Accounting earnings tend to have a delayed response to the relevant events considered by the market when valuing stock (Beaver, Lambert & Morse, 1980). The primary implication of this delay is that only part of the contemporaneous variation in earnings is a surprise to the market with respect to the expectations regarding future earnings (Collins, Kothari, Shanken & Sloan, 1994; Kothari & Zimmerman, 1995).

The portion of information about future earnings that is not expressed by current earnings is an important variable that is omitted in the traditional model of the return-earnings relationship contributes, alongside the competing effect of information obtained from other sources, to obtaining low and biased response coefficients for earnings and a low explanatory power for the models (1) (Kothari & Zimmerman, 1995; Kothari, 2001).

The prices lead earnings hypothesis addresses part of this problem. Under this concept, it is assumed that prices contain more information about future earnings than the series of current and past earnings, i.e., prices have informational content regarding future earnings (Beaver et al., 1980; Kothari & Zimmerman, 1995). One implication of this phenomenon is that market expectations for earnings are different from expectations based on the earnings time series. This time series is described as a random walk in much of the literature, meaning that past earnings cannot anticipate the subsequent variations (Kothari & Sloan, 1992).

Important studies have explored, directly or indirectly, or recognized the lack of informational timeliness between prices and earnings, for example, Beaver, Lambert and Morse (1980), Kothari and Sloan (1992), Kothari (1992), Collins, Kothari, Shanken and Sloan (1994), Ayers and Freeman (2000) and Truong (2012). However, despite the relevance of the topic to accounting research in the capital markets, with a few exceptions such as Galdi and Lopes (2008), Pimentel and Lima (2010), Santos and Lustosa (2010), Sales (2011) and Paulo, Sarlo Neto and Santos (2012), it has been little explored for the Brazilian stock market. This study of the temporal aspects of the return-earnings relationship therefore aims to bridge this gap in the national literature and to provide theoretical and methodological contributions to advance the understanding of this relationship on the national scene.

The study therefore aims to identify the timing of the return-earnings relationship in Brazil, which ultimately is the primary indicator of the prices lead earnings hypothesis. To that end, the following research questions will be studied:

* Is there informational timeliness between the quarterly stock returns and quarterly accounting earnings of publicly traded Brazilian firms?

* Do the quarterly stock returns of publicly traded Brazilian companies anticipate information regarding future quarterly earnings?

* What is the timing of the return-earnings relationship?

Informational timeliness is understood here to be a significant relationship between two variables, in this case accounting earnings and stock returns, when considered at the same moment in time. The timing is used to indicate the degree of the time lag between the occurrences of the variables when a significant relationship between them is verified. For example, in a contemporaneous relationship, the timing is zero; however, where there is 1 lag between the variables, the timing is -1, and so on.

In general, the results obtained showed a lack of informational timeliness between returns and earnings with a timing equal to 1, where returns anticipate earnings in the subsequent period, i.e., prices can anticipate earnings. However, the study shows that current earnings are contemporaneous when future earnings are introduced into the analyzed relationship. These findings, among others obtained in the study, offer an important contribution to the improvement of the operational and analytical models employed by Brazilian studies investigating the return-earnings relationship, given that many of them do not commonly consider or only partly consider these time lag effects when defining such models.

Furthermore, these findings provide additional support for the forecasting of future earnings for investors or investment analysts in that they indicate that the current stock return has informational content in relation to future earnings, notably for the subsequent period.

The remainder of the paper is organized as follows. Section 2 presents the empirical evidence obtained in previous studies, discusses the theoretical aspects underlying the price leads earnings hypothesis and states the research hypotheses. Section 3 addresses the methodological aspects of the study. Section 4 presents and analyzes the results obtained and Section 5 presents our final considerations.

2 DEVELOPMENT OF THE RESEARCH HYPOTHESES

2.1 Theoretical Framework.

The traditional model for the price-earnings ratio assumes the following: (i) the earnings of a period contemporaneously reflects all of the information contained in that period's return, (ii) only the information contained in earnings (expected future cash flows) affects the price of stock, (iii) earnings follow a random walk and (iv) the rate of dividend payout is 100% (Kothari, 1992).

Kothari (1992) emphasizes that the purpose of premise "iv" is to simplify the econometric analysis of the price-earnings ratio and that it does not sacrifice the economic intuition associated with a more realistic payout rate. Regarding premise "iii", despite the existence of divergences, for some time, much of the literature has been assembling a substantial body of evidence indicating that the time series of annual earnings follow a random walk or a random walk with a trend (Kothari, 2001).

Premises "i" and "ii" are unrealistic and contrary to the implications of market efficiency, an underlying hypothesis assumed in the accounting research on capital markets. In an efficient market, the stock price ([P.sub.t]) instantly reflects the expectations of its participants regarding future cash flows. In addition, earnings ([X.sub.t]), due to limitations imposed by the accounting model, especially the criteria for the recognition of revenues and expenses, tend to incorporate the information already reflected in [P.sub.t] systematically with a delay. It therefore follows that [P.sub.t] is informationally richer about future earnings than the series of current and past earnings. In other words, the market expectations and the expectations based on the time series of [X.sub.t] become different, a phenomenon (hypothesis) known as prices lead earnings (Beaver et al., 1980; Lev, 1989; Kothari, 1992, 2001).

The first study that addressed this phenomenon was that of Beaver et al. (1980). The results obtained confirmed that [P.sub.t] is informationally richer than [X.sub.t]. Other important studies were those of Kothari (1992), Kothari and Sloan (1992) and Kothari and Zimmerman (1995), who discussed and demonstrated the effects of this phenomenon on econometric models that addressed the price-earnings ratio--traditionally used up until then in the international literature--and offered alternatives to mitigate them.

This informational superiority of P t, according to Beaver et al. (1980), may occur for various reasons. For example, (i) X can be considered to be an aggregation of earnings of smaller intervals, thus P can be used to obtain information about pre-aggregated series that is lost in the temporal aggregation process, (ii) there are events that affect future earnings and that are not reflected in X and (iii) X can be represented by a process comprising more than one stochastic variable.

If [X.sub.t] follows a random walk, all information expressed in [P.sub.t] is already contained in the past series of [X.sub.t]. However, if [P.sub.t] contains information about future earnings, it must therefore have violated the random walk premise because the future variations of [X.sub.t] can be anticipated by market participants. It is for this reason that Beaver et al. (1980) assumed that [X.sub.t] is formed by a compound process as expressed in equation (1):

[X.sub.t] = [x.sub.t] + [[epsilon].sub.t] 1

where [x.sub.t] is the portion of [X.sub.t] that reflects the events that also affect [P.sub.t], called undistorted earnings; [[epsilon].sub.t] is white noise, known as distorted earnings, which represents the impact of [X.sub.t] on adjustments or events that do not affect [P.sub.t].

Kothari (1992) and Kothari and Zimmerman (1995) argue that when [P.sub.t] is informationally richer, the variation of Xf is composed of a portion ([a.sub.t,t-1], ..., [a.sub.t,t-n]) that was previously incorporated by Pt-1... Pt-n and by a random portion that represents a market surprise (st). It is with this random portion that a contemporaneous relationship could be found.

Extending this idea to the compound process shown in equation (1), it is possible to assume that

[x.sub.t] = [s.sub.t] + [N.summation over (n=1)] [[alpha].sub.t,t-n][??] 2a

[X.sub.t] = [s.sub.t] + [N.summation over (n=1)] [[alpha].sub.t,t-n] + [[epsilon].sub.t] 2b

where [a.sub.t,t-n] is the portion of [X.sub.t] (first subscript t = year to which X refers) anticipated by the market in period t-n (second subscript).

The portion [x.sub.t] is not observable, therefore, s and [N.summation over (n=1)] [[alpha].sub.t,t-n] cannot be isolated or measured. However, according to Beaver et al. (1980), [X.sub.t] offers a distorted measure of [x.sub.t] due to the existence of [[epsilon].sub.t], and therefore, [X.sub.t] measures variations of [P.sub.t] with error.

It is noteworthy, however, that apart from the effects of this distortion, the informational dynamic between [X.sub.t] and [P.sub.t] imposes problems on the contemporary relationship between these variables. As only N the portion [s.sub.t] correlates with variations in [P.sub.t], because [N.summation over (n=1)] [[alpha].sub.t,t-n] is irrelevant to the explanation of these variations, and as [P.sub.t] anticipates information that will only be expressed in future earnings ([N.summation over (n=1)] [[alpha].sub.t,t+n])--variables omitted in the traditional model and uncorrelated with [s.sub.t]--the econometric consequences noted by Beaver et al. (1980) are exacerbated. This result is demonstrated by the low explanatory power offered by the traditional model of the price-earnings ratio and the low magnitude and bias of the response coefficient of [X.sub.t] (Lev, 1989; Kothari & Zimmerman, 1995; Kothari, 2001).

Collins et al. (1994) found that the relationship between [P.sub.t] and [X.sub.t] has poor timeliness and identified that the informational untimeliness of [X.sub.t] is the main determinant of this phenomenon. The authors found that future variations of [X.sub.t] were able to explain the current variations of [P.sub.t], i.e., [P.sub.t] anticipated the portion [N.summation over (n=1)] [a.sub.t,t+n].

Basu (1997) found that [X.sub.t] is asymmetrically timely in relation to bad news signaled by negative changes in [P.sub.t], a finding that introduces additional aspects to the subject because it shows the effect of accounting conservatism on the informational portion [s.sub.t]. This fact tends to exacerbate the problems of the poor timeliness between [X.sub.t] and [P.sub.t] because it indicates that as well as being reduced, timeliness is apparently also incomplete and skewed.

Another line of research has been exploring the influence of other aspects on the prices lead earnings phenomenon, such as ownership structure, investor characteristics, analyst coverage, governance structure, level of long-term investments, goods produced and size, which have increased the understanding of the topic. In general, studies have shown that these factors affect the informational non-synchronization of [X.sub.t] and [P.sub.t] (Ayers & Freeman, 2000, 2003; Jiambalvo, Rajgopal, & Venkata chalam, 2002; Lee, 2007).

Along the same line, Ayers and Freeman (2000) studied the association between firm size and the timing of returns relative to the average variation in sectoral annual earnings and the variation in firm-specific annual earnings. A positive association was found between size and the degree of anticipation of future earnings for both analyzed variations. Moreover, the results also suggested that the stock prices of large firms anticipate information that affects the entire industry, so their returns can anticipate a portion of the small firms' returns.

Jiambalvo, Rajgopal and Venkatachalam (2002) and Ayers and Freeman (2003) found a positive association between the institutional ownership percentage in firms' ownership structures and the prices lead earnings phenomenon. For Jiambalvo, Rajgopal and Venkatachalam (2002), this association occurs because institutional investors are more sophisticated and have advantages in acquiring and processing information that are only reflected in future earnings, which would impose lower informational synchronization as these investors' ownership increases.

Ayers and Freeman (2003) also evaluated the influence of analyst coverage on the degree of anticipation of future earnings displayed in stock prices. As observed for institutional investors, the results for analyst coverage showed a positive association. In addition, Ayers and Freeman (2003) found that such factors are incremental to each other in this association and their influence on the degree of anticipation is independent of firm size.

Lee (2007), in turn, presented evidence to suggest that operational (durability of products produced) and market (product power in the market) characteristics are positively associated with the anticipated recognition of future earnings, while the level of investment in long-term assets is negatively associated with this anticipation.

Another interesting study is that of Truong (2012), which explores the relationship between options trading and the extent to which prices anticipate future earnings. Truong (2012) found that the stock prices of firms with listed options anticipate more information about future earnings. In addition, a positive relationship was identified between the options trading volume and this anticipation. Another result reported was that among firms with listed options, stock prices in the post-listing period reflected better and faster information about future earnings than those in the prelisting period.

In Brazil, the studies are still preliminary. For example, Galdi and Lopes (2008) and Pimentel and Lima (2010) obtained evidence of a long-term relationship between accounting earnings and stock prices. In addition, among the firms analyzed, they observed a greater number of occurrences where stock price anticipated information contained in the accounting earnings, at least at a timing equal to -1. According to Galdi and Lopes (2008), the latter finding is somewhat expected considering the informational untimeliness of accounting earnings.

Sales (2011) obtained results indicating that the market anticipates information contained in [X.sub.t], pricing stock during the period to which it relates and after the closure of the same. This result is consistent with the findings of Santos and Lustosa (2010). Sales (2011) also found evidence of the existence of a lead-lag type structure between the variations in [P.sub.t] and [X.sub.t], which according to the author suggested that future earnings can explain part of the variation in [P.sub.t] that is not explained by [X.sub.t]. However, notwithstanding the functional relationship employed, from a time perspective, what is observed is that [P.sub.t] may explain part of future earnings ([N.summation over (n=1)] [[alpha].sub.t,t+1]) and not the reverse.

Paulo, Sarlo Neto and Santos (2012), assuming the prices lead earnings hypothesis and the asymmetric timeliness evidenced by Basu (1997) as an underlying idea, studied within the context of the Brazilian stock market the informational content expressed by [X.sub.t] when disclosed. The results indicated that [P.sub.t] only showed abnormally significant variations in response to bad news; this result is aligned with the perception of information asymmetry for [s.sub.t].

2.2 Hypotheses.

Based on the theoretical assumptions and empirical evidence presented and discussed in the previous section, it is possible to conclude that the primary effect of the informational superiority of [P.sub.t] due to its ability to quickly incorporate the relevant events that will only be reflected in future variations of [X.sub.t], the essence of the prices lead earnings hypothesis is poor or even a lack of timeliness between these variables. Thus, finding the existence of timings above zero may confirm this hypothesis in the Brazilian market. The following research hypotheses were therefore formalized:

[H.sub.0a]: The relationship between the quarterly stock returns and the quarterly accounting earnings of publicly traded Brazilian firms is not contemporaneous.

[H.sub.0b]: The quarterly stock returns of publicly traded Brazilian firms anticipate information regarding future quarterly earnings.

[H.sub.0c]: The timing of the return-earnings relationship of publicly traded Brazilian firms is greater than or equal to 1.

3 METHODOLOGY

3.1 Data.

The empirical analysis included the quarterly data of non-financial firms listed on the Sao Paulo Stock Exchange (Bolsa de Valores de Sao Paulo--Bovespa) for the period between 03/1999 and 03/2012. Only those firms presenting financial statements for that period, for the quarters ended 03/31, 06/30, 09/30 and 12/31 and for which the stock price was available on these dates or the day immediately after were included in the study sample. The final sample consisted of 205 firms and resulted in panel data consisting of 8,440 firm-quarters. All data were obtained from the Economatica database.

The accounting variables earnings per share (EPS) and book value of equity per share (BVPS) were used, which served as a control for the effect of firm size. Both variables were deflated by the stock price at the beginning of the period (end of the previous period). The EPS growth rate, referred to here as EPSGR, was determined by the natural logarithm of the difference between the EPS in two consecutive periods [ln([EPS.sub.it]/[EPS.sub.it-1])].

The stock price return was also calculated logarithmically. The stock price was adjusted by earnings according to criteria adopted by Economatica. When possible, preferred stocks were selected because of their greater liquidity.

As detailed below, the study was conducted in two stages, with the use of four econometric models, which required the use of two sets of variables. Observations located in the first and last percentiles of each variable series were excluded to minimize the econometric effect of outliers on the model results. This process resulted in a final sample of 4,177 firm quarters for the first group of variables and 3,321 for the second.

3.2 The Model.

Basically, the three functional relationships represented below were explored:

Accounting Earnings = f (Stock Return) 3

Stock Return = f (Accounting Earnings) 4

Stock Return = f (Accounting Earnings,

Stock [Ret.sub.t+1], Stock [Ret.sub.t+2], Stock [Ret.sub.t+3]) 5

For all of these relationships, the respective econometric models were estimated using pooled regressions and panel data. To evaluate the suitability of pooled regression, the indication of a structural break in the model was considered at a significance level of at least 10% using the Chow test. Where a break exists (the alternative hypothesis of the test), the use of panel data is recommended. The choice of the appropriate modeling type for the panel, i.e., fixed effects or random effects models, was based on the Hausman test, the null hypothesis of which indicates the existence of random effect components in the estimated multivariate relationship.

The econometric models employed were based on Beaver et al. (1980)--model (6)--and Collins et al. (1994)--models (7), (8) and (9). In these studies, variations of EPS were used; therefore, the EPSGR variable was used herein. However, [EPS.sub.it]/[p.sub.it-1] was used because of its superiority in the presence of prices lead earnings, as highlighted by Kothari (1992). Furthermore, the model estimates using these two variables offer additional opportunities to evaluate the adequacy of these proxies for accounting earnings on the return-earnings (earnings-return) relationship in Brazil.

The functional relationship (3) was estimated using econometric model (6), below, which is based on Beaver et al. (1980). This model is also known as the inverted or reverse regression model, so called because it reverses the traditional relationship in which stock returns (change in price p) are a function of the variation in earnings per share ([DELTA]EPS). Two estimations were performed where the dependent variables were [EPS.sub.it]/[P.sub.it-1], and [EPSGR.sub.tt].

[X.sub.it] = [[beta].sub.0] + [4.summation over (k=0)] [[beta].sub.k+1][R.sub.it-k] + [[beta].sub.6][R.sub.it-6] + [[beta].sub.7][R.sub.it-8] + [[beta].sub.8][[BVPS.sub.it]/[P.sub.t-1]] + [[epsilon].sub.it] 6

where

[X.sub.it] = [EPS.sub.it]/[P.sub.it-1] or [EPSGR.sub.it]. [EPS.sub.it] = earnings per share of firm i in quarter t [P.sub.it-1] = stock price of firm i at the end of quarter t-1 [EPSGR.sub.it] = [EPS.sub.it] growth rate, obtained by the natural logarithm of the difference between EPSs in t and t-1 [R.sub.it] = logarithmic return of the stock of firm i in quarter t (t - 1 ... t - 8)

[BVPS.sub.it] = book value of equity per share of firm i in quarter t; used as a proxy for size for control purposes

If the variations in the stock price express information that only reflects future earnings, it is likely that past returns are linked to current accounting earnings. To evaluate this aspect, quarterly returns were used that were both contemporaneous to earnings and lagged by 1 to 4, 6 and 8 quarters, aiming to analyze the informational relationship of the immediately preceding quarter up to a two-year lag. It is assumed, therefore, that investor expectations about future earnings are evaluated in response to the new information brought by quarterly earnings and revised and incorporated into prices in the short and medium terms. If, therefore, the prices lead earnings hypothesis is true in Brazil, it may be expected that [[beta].sub.1] is not significant or else has low magnitude, depending on the representativeness of st. The relationships of the other coefficients to the lagged returns are expected to prove to be positive and significant. These results will specifically allow hypothesis [H.sub.0b] to be operationally tested and will provide input that together with the other models will allow hypothesis [H.sub.0c] to be tested.

Establishing the same reasoning above, although from the perspective of accounting earnings, it is possible to assume that current earnings respond in an untimely fashion to the current returns. Thus, assuming a traditional functional relationship between returns and earnings, adding earnings for subsequent periods would offer a better level of explanation of this relationship. Based on this notion, the functional relationship (4) was explored by means of the econometric models below:

[R.sub.it] = [[beta].sub.0] + [[beta].sub.1][X.sub.it] + [[beta].sub.2][[BVPS.sub.it]/[P.sub.it-1]] + [[epsilon].sub.it] 7

[R.sub.it] = [[beta].sub.0] + [3.summation over (k=0)][[beta].sub.k+1] + [[beta].sub.5][[BVPS.sub.it]/[P.sub.it-1]] + [[epsilon].sub.it] 8

where [X.sub.it] assumes [EPS.sub.it]/[P.sub.it-1] or [EPSGR.sub.it] in the respective estimations. Model (7) is the traditionally studied relationship (Kothari, 2001) and model (8) is based on Collins et al. (1994).

However, as the informational portions of [X.sub.t] and [X.sub.t+k] that are already anticipated by past prices [N.summation over (n=1)] [[alpha].sub.t,t-n] and [N.summation over (n=1)] [[alpha].sub.t+k,t-n], would not be correlated with [R.sub.t], there are measurement errors in the model for the coefficients of [X.sub.t] and [X.sub.t+k], the extent of which depends on the deviation of price variations associated with the expectations in t. In the specific case of [X.sub.+k], there is an additional source of error arising from the informational portion not anticipated by [R.sub.t], which will only be reflected in future returns, [N.summation over (n=1)] [[alpha].sub.t+k,t+n] (Collins et al. 1994; Kothari, 2001). To mitigate some of the effects of these measurement errors related to [X.sub.t+k], future stock returns were used ([R.sub.t+1], [R.sub.t+2] and [R.sub.t+3]), as proposed by Collins et al. (1994).

The following model was therefore used, operationalizing the functional relationship (5):

[R.sub.it] = [[beta].sub.0] + [3.summation over (k=0)] [[beta].sub.k+1][X.sub.it+K] + [3.summation over (k=1)][[beta].sub.k+4][R.sub.it+k] + [[beta].sub.8][[BVPS.sub.it]/[P.sub.it-1]] + [[epsilon].sub.it] 9

It should be stressed that the significance test of the coefficient [[beta].sub.1], especially in model (7), represents the primary operational test of hypothesis [H.sub.0a] because if [[beta].sub.1] is significantly different from zero, signs of timeliness will be obtained and therefore this hypothesis would be rejected. Furthermore, it should be noted that the results obtained with models (7), (8) and (9) will also be required for the proper evaluation of the propositions contained in hypotheses [H.sub.0b] and [H.sub.0c].

4 ANALYSIS OF RESULTS

The descriptive statistics of the group of variables used in the first step of the analysis and their correlation matrix are shown in Tables 1 and 2, respectively. After excluding the outliers that were included in the first and last percentiles of the series of each variable, with the exception of the control variable, the initial sample was reduced to 4,177 observations.

In the first subset of data, the variables representing accounting earnings have very different characteristics, which is to be expected given the means by which each variable was calculated. It can be observed that the series [EPS.sub.it]/[P.sub.it-1], despite having greater amplitude, has a lower standard deviation and a lower coefficient of variation (11.07 versus 156.83) than [EPSGR.sub.it]. That difference indicates a certain superiority for this variable because its series exhibits less variability. With regard to returns, there is an apparent similarity in the statistics for these two variables. However, it is interesting to note that there is an almost monotonic increase for all variables as their lags increase, in particular in periods t-6 and, especially, t-8. This possibly shows the influence of the returns of previous periods that were not attained by other series (t, ..., t-4).

The correlation matrix presented in Table 2 shows the existence of a similar linear behavior between accounting earnings and returns for the current and prior periods. There are few correlations observed for the variable [EPSGR.sub.it] these correlations, although significant, do not exceed 0.047. Among these correlations, there is a negative correlation with respect to [R.sub.t-6], which is intriguing given the remaining correlations observed for other periods. However, the reason for this result may be linked to the series of [R.sub.t-6], given that other negative correlations are observed for that series in relation to the returns of other periods, specifically from quarter t-3. The variable [EPS.sub.it]/[P.sub.it-1] exhibits a uniform sequence of highly significant correlations of the same sign and, although the oldest return series have slightly different descriptive characteristics, no correlation pattern was observed that revealed an important influence for the returns from much older periods. This preliminary analysis also suggests the superiority of [EPS.sub.it]/[P.sub.it-1] in the studied relationship.

The first relationship examined was that proposed by model (6), where the variable representing accounting ear nings is estimated as a function of contemporaneous and lagged stock returns. Table 3 shows the results obtained.

In both models, the results reveal a weak or nonexistent relationship between the contemporaneous returns and accounting earnings, indicating the low informational representativeness of the portion st. However, the results indicate that there is a significant level of association if the returns from previous periods are considered.

The estimation involving [EPSGR.sub.it] indicates that the returns for quarters -3 ([[beta].sub.4]), -6 ([[beta].sub.6]) and -8 ([[beta].sub.8]) exhibit a significant relationship with this variable. An apparent response pattern was not, however, observed as expected. The intermittency in the quarters and the different signs of the coefficients cannot be explained in general terms, with the exception of the hypothesis that the variable [EPSGR.sub.it] is unrepresentative of the relationship studied here. This lack of representativeness is suggested by the low or nonexistent correlation with returns (Table 2), and it contributes to the low explanatory power of the model (Adjusted [R.sup.2] equal to 0.38% (2)).

Conversely, in the estimation with the dependent variable [EPS.sub.it]/[P.sub.it-1], there is explanatory power of over 70%, and a response pattern consistent with the theory can be observed. The returns for periods -1 to -6 have positive and highly significant coefficients, the values of which show an increasing trend as the lags decrease. This result suggests that the information expressed in current accounting earnings was already being anticipated by the stock price at least six months previously, which is consistent with the prices lead earnings hypothesis. In light of the results, it can be assumed that approximately 6% of the variations in the return of period -6, for example, are related to variations in current accounting earnings and likewise for the following periods until period -1, where there would be an approximately 15% association between the variables in question. This perception is reinforced by the linear movements of returns and accounting earnings, signaled by the significant level of correlation observed (Table 2). These results, in general, are consistent with those obtained by Galdi and Lopes (2008) and Sales (2011).

In the second stage of the study, the returns contemporaneous with stock price were estimated on the basis of accounting earnings and the future returns of that price, so a new subset of variables was employed. The exclusion of outliers resulted in a total of 3,321 observations. Table 4 shows the descriptive statistics of these variables.

The series of returns comprising this second data subset show behavior similar to that shown in Table 1, i.e., the descriptive statistics increase as the lags increase. Here it can be observed, for example, that [R.sub.t+3] has a mean and a standard deviation lower than those exhibited by [R.sub.t]. This behavior is also observed for the mean values of the series of variables representing accounting earnings but is not observed for the respective standard deviations; there is a reverse trend for [EPS.sub.it+k]/[P.sub.it+1], and it is not is possible to determine a pattern for [EPSGR.sub.it+k].

As observed in Table 5, the variable [EPSGR.sub.it+k] is smaller than the variable [EPS.sub.it+k]/[P.sub.it-(1-k)] in terms of the correlation with current and future returns. Considering also the correlations listed in Table 2, it can be inferred that the linear behavior of EPSGR has little association with the behavior of past, current and future returns. In fact, it appears that [EPS.sub.it+k]/[P.sub.it-(1-k)] displays a reverse behavior. Moreover, it can be observed that the correlations between this variable and past returns appear to be higher than those for the current and future periods. For example, the correlation of earnings in t+1 with returns in t is greater than those with returns in t+1, t+2 and t+3. Likewise, this relationship occurs for the earnings in t+2 because the correlations with the returns in t and t +1 are higher than those observed for periods t+2 and t+3 and higher than earnings in t+3. This finding suggests that some of the movements for earnings have been "anticipated" by price variations at least a quarter in advance.

For model (7), satisfactory adjustments (highly significant F statistics) and acceptable explanatory power for the association studied can be observed in both estimations as shown in Table 6.

Current accounting earnings were not significant, which is consistent with the results obtained with model (6) and is thus consistent with the prices lead earnings hypothesis. Moreover, these results are consistent with Collins et al.'s (1994) findings, which were achieved using a similar model estimated based on pooled data.

The inclusion of earnings from future periods in the relationship above generated random effects in the established multivariate relationship, as verified using the Hausman test (not significant), which required the estimation of the regressions using the random effects model. This result may indicate that the fixed effects identified in model (5) were generated by the omission of these variables because these are significantly correlated with current earnings and equity, as shown in Table 5.

A premise underlying this study is that the current variations in stock price capture information that will only be reflected in future earnings, so the inclusion of these would increase the explanatory power already verified by model (7). However, as shown in Table 7, the explanatory power did not increase. Instead, the adjusted [R.sup.2] of the estimates decreased. However, it is true that the included variables correlate with those already used, which tends to reduce their effect on the explanatory power. Moreover, the difference between the techniques used to estimate the models must be considered in this comparison.

One interesting aspect is the significance of coefficient [[beta].sub.1] relative to variable [EPS.sub.it]/[P.sub.it-1]. Alone, this variable was not significant in relation to [R.sub.t]; however, the inclusion of future variations allowed for the establishment of such significance. This result suggests that variations in current earnings are only associated with variations in [R.sub.t] when combined with the variations from the following periods, i.e., when the econometric effects of these variations are eliminated from the current earnings. One possible explanation for this finding may be the linear behavior of these variables. According to Table 5, the current earnings show a correlation of 0.0303 with [R.sub.t] (significant only at 10%), while they are correlated with the earnings of the following periods (t+1, t+2 and t+3) at highly significant levels and with coefficients above 0.78. The earnings of the following periods, in turn, also have a highly significant correlation with [R.sub.t], the coefficients of which are greater than 0.08. However, it is intriguing that the earnings in t+2 and t+3 have also not been shown to be significant.

Regarding the estimation involving [EPSGR.sub.it+k], there is a lack of explanatory power, although the earnings in t+1 exhibit a significant coefficient. It is difficult to interpret these results beyond the observations made for the correlation coefficient: there is a weak correlation between the current return and the variation in earnings in t+1. This result is in keeping with the prices lead earnings notion, but does not represent robust empirical evidence.

These findings can be attributed to measurement errors for these variables. As mentioned in the previous section, these variables have informational portions that do not correlate with the current return, but do with the past returns and, in the case of future earnings, also with the contemporaneous returns (future). These errors cause biases in the estimators and affect the explanatory power of the models because these informational portions represent omitted variables. The inclusion of future returns tends to mitigate some of these problems. Model (9) contemplates that alternative.

The results suggest that the inclusion of future returns reduced some of the problems displayed by model (8). It is clear, first, that there is no longer an indication of the presence of random effects in the model. The explanatory power of the estimates was significantly improved, from 1.99% to 4.53% and from 0.01% to 3.51%. The significance of the coefficients was virtually unchanged. It is important to note that of the returns included, [R.sub.t+1] exhibited a significant coefficient in relation to [EPS.sub.it+k]/[P.sub.it-(1-k)] and [R.sub.t+2] and [R.sub.t+3] the estimation involving the variable [EPSGR.sub.t+3]. Still regarding this estimation, the variable EPSGRt+3 also began to show a significant coefficient.

These results suggest that it is not possible to rule out a contemporary relationship, but it would only be incremental relative to the earnings of future periods. In addition, future returns may enhance the explanatory power of the model, a finding in keeping with the assumptions made in this study.

To explore this last observation, model (7) was estimated using a stepwise forward analysis for future earnings in an isolated and incremental manner. In this task, only the variable [EPS.sub.it+k]/[P.sub.it-(1-k)] considered because it had shown better results in the estimates as a whole. The variable [R.sub.t+1] was included in every step, given its significance in the estimation of model (9).

The results confirm that the contemporary relationship between earnings and returns is only revealed when future earnings are considered in the estimation. The relationship was clear with the inclusion of earnings in t+1, t+2 and t+3, alone or pooled. It also appears that the explanatory power of the model increased almost monotonically with the gradual inclusion of these variables, increasing from 3.52% to 4.50%. [R.sub.t+1] proved to be significant in all estimations and played an important role because its inclusion generated fixed cross-components, thus requiring estimation by the fixed effects model. The control level of the firms' idiosyncrasy also contributed to the improvement of the explanatory power of the estimates, as was observed in simulations without this variable.

Despite the significance of current earnings observed in models (6) and (7) and in the final estimates, the dependency on earnings in the following periods apparently weakens the evidence of their timeliness with [R.sub.t]. However, it can be observed that there is an informational portion contained in current earnings that is contemporaneous to [R.sub.t] but that can only be obtained after eliminating the effects of the earnings from the following periods on this portion. This finding is consistent with Kothari (1992) and Kothari and Zimmerman (1995) because it demonstrates the [s.sub.t] portion, which represents the portion of current earnings that is a surprise to the market and therefore correlated with [R.sub.t].

It is interesting to note that in addition to the significance of the current earnings coefficient, its increase in magnitude (in absolute terms) can also be observed in all estimations, suggesting that the effects of [s.sub.t] on [R.sub.t] are representative but obscured by the omission of the [N.summation over (n=1)] [[alpha].sub.t+k,t+n] portion. The indication of a negative relationship contradicts the theory; however, it is possible that the relationship could be explained by the effects of conservatism, which impose a bias with respect to bad news about [s.sub.t]. This explanation is in keeping with the results obtained by Paulo, Sarlo Neto and Santos (2012).

Another aspect that should be considered in the present analysis is the possible effect on the return-earnings relationship of the recent adoption of international accounting standards in Brazil. The evidence gathered in this regard indicates that the associative capacity of accounting earnings should have improved (Lima, 2010 Rodrigues, 2012). However, dimensions such as informational content, conservatism, timeliness and persistence should not have been impacted by the adoption of a new set of accounting standards (Lima, 2010, Rodrigues, 2012, Santos, Lima, Freitas, & Lima, 2011).

These results suggest that the adoption of international standards has generated residual effects on the timing of the return-earnings relationship, especially in light of the findings related to timeliness and conservatism. Moreover, despite the improvement of the associative capacity of accounting earnings, the findings obtained with models (7) and (8) show that an improvement in that capacity was not sufficient to eliminate non-timeliness. However, it should be noted that the time window analyzed here considers the periods pre and post adoption of those standards, which may obscure observation of their effects.

5 FINAL CONSIDERATIONS

The present study aimed to identify the timing of the return-earnings relationship in Brazil because it was assumed that this level is an indicator of the prices lead earnings hypothesis. The study was developed using four econometric models based on the proposals of Beaver et al. (1980) and Collins et al. (1994).

The results, in general, are consistent with the theoretical assumptions explored herein because there is evidence that returns anticipate information about future earnings and that the representativeness of current earnings is residual. The findings suggest that prices have informational content regarding future earnings, thereby indicating that the prices lead earnings phenomenon occurs in Brazil.

Specifically with regard to the research hypotheses, hypothesis [H.sub.04] must be rejected because the results obtained with models (6) and (7) do not provide evidence for the contemporaneity of the return-earnings relationship, although the inclusion jointly or alone of future quarterly earnings in the estimation did reveal such timing. It is thus found that the elimination of the effects of future earnings on current earnings in measuring the association between the latter and the current returns elicited the informational representativeness of portion [s.sub.t].

The results obtained with the reverse regression, model (6), indicate that quarterly returns anticipate the information contained in future quarterly earnings, thus leading to the rejection of hypothesis [H.sub.0b]. It is worth noting that this anticipation would have occurred at least 8 quarters ago, a process that lasted until the quarter immediately preceding the current one. These results were consistent with those obtained with models (7) and (9) with respect to the associative capacity of future quarter earnings with the current return.

However, despite the empirical evidence mentioned above, it was not possible to determine the timing of the quarterly return-earnings relationship in Brazil because if on one hand, past returns are associated with current earnings, on the other, the significance of future earnings in explaining current returns depends on the arrangement of the independent variables considered in the model. The evidence of timeliness between the returns and current earnings, even if dependent on the inclusion of future earnings, does not dispel the indication of a timing equal to zero, thus leading to the rejection of hypothesis [H.sub.0c].

Furthermore, an additional finding refers to the superiority of variable [EPS.sub.it]/[P.sub.it-1] compared to [EPSGR.sub.it] in terms of its representation of accounting earnings in the relationships analyzed, which is consistent with the results presented by Kothari (1992).

The findings in this study contribute to the national literature because they provide a greater understanding of the temporal aspects of the return-earnings relationship in Brazil, which was hitherto relatively unexplored from the perspective employed here. Furthermore, the results indicate that it is possible to improve the models aimed at studying the associative capacity of current earnings using a methodological refinement, the inclusion of future earnings for at least one period, thus contributing to the advancement of research in the area. In a practical sense, the indication of the anticipative capacity of stock returns of Brazilian firms in relation to their future earnings suggests for investors, financial analysts, firms and creditors that the stock return may represent a useful informational source in their assessment of a firm's capacity to generate earnings. In addition, as the results presented here demonstrate to some extent the untimeliness of accounting earnings, they may be an indication, at least for investors, of a qualitative deficiency in accounting information. The results can also provide support for standard setters and regulators when assessing the usefulness of the financial-accounting information that is disseminated in Brazil for those users and, ultimately, of the adequacy of the accounting standards observed.

This study presents a number of methodological limitations, among them being a lack of the following: (i) a specific analysis of the properties of accounting earnings time series and their components, (ii) an effective assessment of the effects of the adoption of international standards; and (iii) a direct analysis of the influence of market factors, such as investor characteristics, the governance structure of firms, and analyst coverage, among others. However, each of these limitations, given the breadth of the empirical studies they would require and the complexity of the topic, offers interesting research avenues that should be explored to advance the understanding of the return-earnings relationship, a fundamental pillar of accounting research in capital markets.

References

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Ayers, B. C., & Freeman, R. N. (2003). Evidence that analyst following and institutional ownership accelerate the pricing of future earnings. Review of Accounting Studies, 8, 47-67.

Basu, S. (1997). The conservatism principle and the asymmetric timeliness of earnings. Journal of Accounting and Economics, 24 (1), 3-37.

Beaver, W., Lambert, R., & Morse, D. (1980). The information content of security prices. Journal of Accounting and Economics, 2 (1), 3-28.

Collins, D. W., Kothari, S. P., Shanken, J., & Sloan, R. G. (1994). Lack of timeliness and noise as explanations for the Low Contemporaneous Return-Earnings Association. Journal of Accounting and Economks, 18 (3), 289-324.

Galdi, F. G., & Lopes, A. B. (2008). Relacao de longo prazo e causalidade entre o lucro contabil e o preco das acoes: evidencias do mercado latino-americano. RevSta de Administracao da USP, 43 (2), 186-201.

Jiambalvo, J., Rajgopal, S., & Venkatachalam, M. (2002). Institutional ownership and extent to which stocks prices reflect future earnings. Contemporary Accounting Research, 19 (1), 117-145

Kothari, S. P. (1992). Price-earnings regressions in the presence of prices lead earnings: earnings level versus change specifications and alternative deflators. Journal of Accounting and Economks, 15 (2-3), 173-202.

Kothari, S. P. (2001). Capital markets research in accounting. Journal of Accounting and Economks, 31 (1-3), 105-231.

Kothari, S. P., & Sloan, R. G. (1992). Information in price about future earnings: implications for earnings response coefficients. Journal of Accounting and Economks, 15 (2-3), 143-171.

Kothari, S. P., & Zimmerman, J. L. (1995). Price and return models. Journal of Accounting and Economks, 2g (2), 155-192.

Lee, J. J. (2007, August). Cross-sectional determinants of the extent to which stock prices earnings. Workmgpaper: Hong Kong Baptist University. Recuperado em 1 fevereiro, 2013, de http://www.af.polyu. edu.hk/jcae_af/paper2008/concurrent/S.4a%20Lee.pdf.

Lev, B. (1989). On the usefulness of earnings and earning research: lessons and directions from two decades of empirical research. Journal of Accounting Research, 27, 153-192.

Lima, J. B. N. (2010). A relevanda da mformacao contabti e o processo de convergendapara as Normas IFRS no BrasU. Tese de doutorado, Programa de Pos-Graduacao em Ciencias Contabeis, Departamento de Contabilidade e Atuaria, Faculdade de Economia, Administracao e Contabilidade da Universidade de Sao Paulo, Sao Paulo, SP, Brasil.

Paulo, E., Sarlo Neto, A., & Santos, M. A. C. (2012). Reacao do preco das acoes e intempestividade informacional do lucro contabil trimestral no Brasil. Advances vn Sckntific and Apphed Accounting, 5 (1), 54-79.

Pimentel, R. C., & Lima, I. S. (2010). Time-series properties of earnings and their relationship with stock prices in Brazil. Busness and Economks Research Journal, 1 (4), 43-65.

Rodrigues, J. M. (2012). Convergenda contabu internacional?: uma analise da qualidade da informacao contabil em razao da adocao dos padroes internacionais de contabilidade editados pelo IASB. Tese de doutorado, Programa Multi-institucional e Inter-regional de PosGraduacao em Ciencias Contabeis, UnB, UFPB, UFRN, Brasil.

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Santos, L. P. G., Lima, G. A. S. F., Freitas; S. C., & Lima, I. S. (2011). Efeito da Lei 11.638/07 sobre o conservadorismo condicional das empresas listadas BM&FBOVESPA. RevSta Contabrndade e Fnancas--USP, Sao Paulo, 22 (56), 174-188.

Santos, M. A. C., & Lustosa, P. R. B. (2010). Importancia relativa do conteudo informacional do resultado contabil no mercado acionario brasileiro. AnaS do Congresso USP de Controladoria e Contabrndade, Sao Paulo, SP, Brasil, 10.

Truong, C. (2012). Options trading and the extent that stock prices lead future earnings information. Journal of Busness Fnance & Accounting, 39 (7-8), 960-996.

(1) The problems presented by the traditional model of the return-earnings relationship have been discussed in the accounting literature for many years. An example of this discussion is Lev's (1989) study.

(2) Although inappropriate, the estimation was performed using the fixed effects model, and the adjusted [R.sup.2] was found to be equal to -1.83%. This result indicates that the low explanatory power was not caused by the estimation technique used, which corroborates the finding of the low explanatory power offered by EPSGR.

Table 1

Descriptive statistics

Variable                      Mean     Median    Minimum

[EPS.sub.it]/[p.sub.it-1]    -0.0460   0.0255    -8.8334
[EPSGR.sub.it]               0.0059    0.0358    -3.2736
[BVPS.sub.it]/[p.sub.it-1]   0.4964    0.8294   -244.3480
[R.sub.t]                    0.0452    0.0356    -0.6124
[R.sub.t-1]                  0.0426    0.0333    -0.6251
[R.sub.t-2]                  0.0423    0.0319    -0.6668
[R.sub.t-3]                  0.0466    0.0383    -0.6931
[R.sub.t-4]                  0.0470    0.0382    -0.6729
[R.sub.t-6]                  0.0522    0.0414    -0.6931
[R.sub.t-8]                  0.0556    0.0458    -0.7418

Variable                     Maximum    Standard Dev.

[EPS.sub.it]/[p.sub.it-1]     0.5318       0.5092
[EPSGR.sub.it]                3.2991       0.9253
[BVPS.sub.it]/[p.sub.it-1]   107.5110      12.1136
[R.sub.t]                     0.8755       0.2104
[R.sub.t-1]                   0.8097       0.2111
[R.sub.t-2]                   0.8214       0.2141
[R.sub.t-3]                   0.8396       0.2202
[R.sub.t-4]                   0.8206       0.2217
[R.sub.t-6]                   0.8745       0.2325
[R.sub.t-8]                   0.9676       0.2407

[EPS.sub.it] is earnings per share of firm i in quarter t.

[p.sub.it-1] is the stock price of firm i at the end of
quarter t-1.

[EPSGR.sub.it] is the [EPS.sub.it] growth rate, obtained by
the natural logarithm of the difference between EPSs in t
and t - 1.

[R.sub.it] is the logarithmic return of the stock of firm
i in quarter t (t-1...t-8).

[BVPS.sub.it] is the book value of equity per share of firm
i in quarter t and is used as a proxy for size for control
purposes.

Table 2 Correlation matrix

                 [EPS.sub.it]/   [EPSGR.sub.it]   [R.sub.t]
                 [p.sub.it-1]

[EPS.sub.it]/          1           -0.0283 *      0.0640 ***
  [p.sub/it-1]
[EPSGR.sub.it]                         1           -0.0184
[R.sub.t]                                             1
[R.sub.t-1]
[R.sub.t-2]
[R.sub.t-3]
[R.sub.t-4]
[R.sub.t-6]
[R.sub.t-8]
[BVPS.sub.it]/
  [p.sub.it-1]

                 [R.sub.t-1]   [R.sub.t-2]   [R.sub.t-3]

[EPS.sub.it]/    0.0917 ***    0.0574 ***    0.0718 ***
  [p.sub/it-1]
[EPSGR.sub.it]     -0.0234       0.0159      0.0461 ***
[R.sub.t]        0.1263 ***      0.0111      -0.0349 **
[R.sub.t-1]           1        0.0937 ***     0.0300 *
[R.sub.t-2]                         1        0.1045 ***
[R.sub.t-3]                                       1
[R.sub.t-4]
[R.sub.t-6]
[R.sub.t-8]
[BVPS.sub.it]/
  [p.sub.it-1]

                 [R.sub.t-4]   [R.sub.t-6]

[EPS.sub.it]/    0.0554 ***    0.0647 ***
  [p.sub/it-1]
[EPSGR.sub.it]     0.0069      -0.0352 **
[R.sub.t]          0.0116      -0.0691 ***
[R.sub.t-1]        -0.0245     -0.0473 ***
[R.sub.t-2]       0.0265 *       -0.0011
[R.sub.t-3]      0.0998 ***    -0.0445 ***
[R.sub.t-4]           1          0.0107
[R.sub.t-6]                         1
[R.sub.t-8]
[BVPS.sub.it]/
  [p.sub.it-1]

                 [R.sub.t-8]   [BVPS.sub.it]/
                                [p.sub.it-1]

[EPS.sub.it]/     0.0327 **      0.7056 ***
  [p.sub/it-1]
[EPSGR.sub.it]    0.0352 **       -0.0029
[R.sub.t]        -0.0803 ***     0.0329 **
[R.sub.t-1]      -0.0908 ***       0.0018
[R.sub.t-2]      -0.0780 ***      -0.0049
[R.sub.t-3]      -0.0509 ***       0.0138
[R.sub.t-4]        0.0000          0.0093
[R.sub.t-6]       0.0271 *         0.0156
[R.sub.t-8]           1            0.0193
[BVPS.sub.it]/                       1
  [p.sub.it-1]

*, ** and *** represent significance at the
10%, 5% and 1% levels, respectively.

Table 3 Model (6) results

[X.sub.it] = [[beta].sub.0] + [4.summation over (k=0)]
[[beta].sub.k+1] [R.sub.it-k] + [[beta].sub.6] [R.sub.it-6] +
[[beta].sub.7] [R.sub.it-8] + [[beta].sub.8] [[BVPS.sub.it]/
[p.sup.t-1]] + [[epsilon].sub.it]

Coefficients         [EPS.sub.it]/[p.sub.it-1]      [EPSGR.sub.it]

[[beta].sub.0]        -0.0785 (-15.7777) ***       0.0006 (0.0364)
[[beta].sub.1]           0.0369 (1.7850) *        -0.0596 (-0.8658)
[[beta].sub.2]          0.1499 (7.2805) ***       -0.1003 (-1.4568)
[[beta].sub.3]          0.0614 (3.0427) ***        0.0702 (1.0391)
[[beta].sub.4]          0.0818 (4.1406) ***      0.1877 (2.8528) ***
[[beta].sub.5]          0.0651 (3.3707) ***        0.0083 (0.1281)
[[beta].sub.6]          0.0601 (3.2354) ***      -0.1441 (-2.3344) **
[[beta].sub.7]           0.0346 (1.9238) *        0.1409 (2.3483) **
[[beta].sub.8]         0.0200 (18.4664) ***       -0.0002 (-0.2039)

Panel modeling             Fixed Effects            Random Effects

Chow Test                   1S.6574 ***                2.2795 *
Hausman Test                47.4286 ***                5.27543
Breusch-Pagan Test                                   24.0171 ***
Adjusted [R.sup.2]            73.47%                    0.38%
F                          52.57603 ***                   --

Number of observations: 4,177. Outliers corresponding to the first
and last percentiles of each variable series were excluded, with
the exception of the control variable. [X.sub.it] is the dependent
variable of the model. Two estimations were performed, one in which
[X.sub.it] was assumed to be [EPS.sub.it]/[p.sub.it-1] and another
where [X.sub.it] was [EPSGR.sub.it]. The t-statistic is shown in
parentheses below the relevant coefficient.

*, ** and *** represent significance at the 10%, 5% and 1% levels,
respectively.

Table 4

Descriptive statistics

Variable                        Mean     Median    Minimum

[R.sub.t]                      0.0658    0.0568    -0.6668
[EPS.sub.it]/[p.sub.it-1]     -0.0767    0.0316   -11.4879
[EPS.sub.it-1]/[p.sub.it]     -0.0807    0.0306   -11.5601
[EPS.sub.it-2]/[p.sub.it-1]   -0.0909    0.0298   -16.7955
[EPS.sub.it-3]/[p.sub.it-2]   -0.09101   0.0285   -16.7955
[EPSGR.sub.it]                 0.0464    0.0565    -2.7939
[EPSGR.sub/t-1]                0.0360    0.0503    -2.7324
[EPSGR.sub/t-2]                0.0363    0.0537    -2.7657
[EPSGR.sub/t-3]                0.0014    0.0382    -2.9108
[R.sub.t-1]                    0.0563    0.0455    -0.6497
[R.sub.t-2]                    0.0460    0.0375    -0.6497
[R.sub.t-3]                    0.0394    0.0356    -0.6493
[BVPS.sub.it]/[p.sub.it-1]    -0.6774    0.7887   -490.6530

Variable                      Maximum   Standard
                                        Deviation

[R.sub.t]                     0.8881     0.2155
[EPS.sub.it]/[p.sub.it-1]     0.5131     0.7829
[EPS.sub.it-1]/[p.sub.it]     0.4714     0.7851
[EPS.sub.it-2]/[p.sub.it-1]   0.4116     0.8518
[EPS.sub.it-3]/[p.sub.it-2]   0.3612     0.8704
[EPSGR.sub.it]                2.9545     0.7429
[EPSGR.sub/t-1]               2.8491     0.7113
[EPSGR.sub/t-2]               2.6974     0.7007
[EPSGR.sub/t-3]               2.7131     0.7312
[R.sub.t-1]                   0.8214     0.2065
[R.sub.t-2]                   0.8097     0.2030
[R.sub.t-3]                   0.7691     0.1988
[BVPS.sub.it]/[p.sub.it-1]    92.4912    21.4974

[EPS.sub.it] is earnings per share of firm i in quarter t
(t + 1, t + 2, t + 3).

[p.sub.it-1] is the stock price of firm i at the end of
quarter t (t - 1, t + 2, t + 3).

[EPSGR.sub.it] is the [EPS.sub.it] growth rate, obtained by

the natural logarithm of the difference between EPSs in t
and t-1.

[R.sub.it] is the logarithmic return of the stock of firm i
in quarter t (t - 1 ... t - 8).

[BVPS.sub.it] is the book value of equity per share of firm i
in quarter t and is used as a proxy for size for control
purposes.

Table 5 Correlation matrix

                  [R.sub.t]   [EPS.sub.it]/   [EPS.sub.it+1]/
                              [P.sub.it-1]      [P.sub.it]

[R.sub.t]             1         0.0303 *        0.0865 ***
[EPS.sub.it]/                       1            0.859 ***
  [P.sub.it-1]
[EPS.sub.it+1]/                                      1
  [P.sub.it]
[EPS.sub.it+2]/
  [P.sub.it+1]
[EPS.sub.it+3]/
  [P.sub.it+2]
[EPSGR.sub.it]
[EPSGR.sub.t+1]
[EPSGR.sub.t+2]
[EPSGR.sub.t+3]
[R.sub.t+1]
[R.sub.t+2]
[R.sub.t+3]
[BVPS.sub.it]/
  [P.sub.it-1]

                  [EPS.sub.it+2]/   [EPS.sub.it+3]/   [EPSGR.sub.it]
                   [P.sub.it+1]      [P.sub.it+2]

[R.sub.t]           0.0803 ***        0.0887 ***          0.0221
[EPS.sub.it]/       0.8353 ***        0.7831 ***         -0.0272
  [P.sub.it-1]
[EPS.sub.it+1]/     0.8787 ***        0.8768 ***        0.009 ***
  [P.sub.it]
[EPS.sub.it+2]/          1            0.8951 ***          0.0038
  [P.sub.it+1]
[EPS.sub.it+3]/                            1              0.0109
  [P.sub.it+2]
[EPSGR.sub.it]                                              1
[EPSGR.sub.t+1]
[EPSGR.sub.t+2]
[EPSGR.sub.t+3]
[R.sub.t+1]
[R.sub.t+2]
[R.sub.t+3]
[BVPS.sub.it]/
  [P.sub.it-1]

                  [EPSGR.sub.t+1]   [EPSGR.sub.t+2]   [EPSGR.sub.t+3]

[R.sub.t]            -0.0327 *          0.0015             0.019
[EPS.sub.it]/        0.0309 *           -0.0012           0.0248
  [P.sub.it-1]
[EPS.sub.it+1]/       -0.0192           0.0196            0.0086
  [P.sub.it]
[EPS.sub.it+2]/       -0.0048           -0.027           0.0378 **
  [P.sub.it+1]
[EPS.sub.it+3]/       -0.007            -0.0001           -0.0124
  [P.sub.it+2]
[EPSGR.sub.it]      -0.3888 ***       -0.0482 ***       -0.1229 ***
[EPSGR.sub.t+1]          1            -0.3876 ***       -0.055 ***
[EPSGR.sub.t+2]                            1            -0.3694 ***
[EPSGR.sub.t+3]                                              1
[R.sub.t+1]
[R.sub.t+2]
[R.sub.t+3]
[BVPS.sub.it]/
  [P.sub.it-1]

                  [R.sub.t+1]   [R.sub.t+2]

[R.sub.t]         0.0986 ***     0.0389 **
[EPS.sub.it]/      0.0308 *       0.0171
  [P.sub.it-1]
[EPS.sub.it+1]/    0.0403 **     0.0341 **
  [P.sub.it]
[EPS.sub.it+2]/   0.0833 ***     0.0411 **
  [P.sub.it+1]
[EPS.sub.it+3]/   0.0714 ***    0.0830 ***
  [P.sub.it+2]
[EPSGR.sub.it]    0.0734 ***     0.0300 *
[EPSGR.sub.t+1]      0.004      0.0627 ***
[EPSGR.sub.t+2]    -0.0281 *      -0.0141
[EPSGR.sub.t+3]     0.0072        0.0037
[R.sub.t+1]            1        0.1000 ***
[R.sub.t+2]                          1
[R.sub.t+3]
[BVPS.sub.it]/
  [P.sub.it-1]

                  [R.sub.t+3]   [BVPS.sub.it]/
                                 [P.sub.it-1]

[R.sub.t]           -0.0127         0.0092
[EPS.sub.it]/      0.0397 **        0.7824
  [P.sub.it-1]
[EPS.sub.it+1]/     0.0247          0.7608
  [P.sub.it]
[EPS.sub.it+2]/   0.0503 ***        0.7411
  [P.sub.it+1]
[EPS.sub.it+3]/   0.0482 ***        0.7376
  [P.sub.it+2]
[EPSGR.sub.it]      -0.0123           0
[EPSGR.sub.t+1]    0.0276 *         0.0025
[EPSGR.sub.t+2]   0.0507 ***       -0.0062
[EPSGR.sub.t+3]     0.0215          0.0007
[R.sub.t+1]         0.0109          0.0081
[R.sub.t+2]       0.1075 ***        0.0087
[R.sub.t+3]            1            0.0216
[BVPS.sub.it]/                        1
  [P.sub.it-1]

*, ** and *** represent significance at the 10%, 5% and 1%
levels, respectively.

Table 6 Model (7) results

[R.sub.it] = [[beta].sub.0] + [[beta].sub.1][X.sub.it]
+ [[beta].sub.2][[BVPSi.sub.t]/[P.sub.it-1]] +
[[epsilon].sub.it]

Coefficients                  [X.sub.it]

                 [EPS.sub.it]/   [EPSGR.sub.it]
                 [P.sub.it-1]

[[beta].sub.0]      0.0640           0.0649
                 (17.0800) ***   (17.5682) ***
[[beta].sub.1]      -0.0183          0.0050
                  (-1.6860) *       (0.9860)
[[beta].sub.2]      -0.0006         -0.0010
                   (-1.2180)      (-2.3093) **

Panel modeling   Fixed Effects   Fixed Effects

Chow Test          3.0406 **       5.4102 **
Hausman Test      14.8883 ***      7.2134 ***
Adjusted             3.33%           3.27%
  [R.sup.2]
F                 1.5862 ***       1.5757 ***

Number of observations: 3,321. Outliers
corresponding to the first and last percentiles
of each variable series were excluded with the
exception of the control variable. [X.sub.it] is
one of the independent variables of the model.
Two estimations were performed, one in which
[X.sub.it] was assumed to be [EPS.sub.it]/
[P.sub.it-1] and another in which [X.sub.it] was
[EPSGR.sub.it]. The t statistic is shown in
parentheses below the relevant coefficient.

*, ** and *** represent significance at the 10%,
5% and 1% levels, respectively.

Table 7 Model (s) results

[R.sub.it] = [[beta].sub.0] + [3.summation over (k=0)]
[[beta].sub.k+1][X.sub.it+k] + [[beta].sub.5]
[[BVPS.sub.it]/[P.sub.it-1]] + [[epsilon].sub.it]

Coefficients                         [X.sub.it+k]

                     [EPS.sub.it+k]/    [EPSGR.sub.it+k]
                     [P.sub.it-(1-k)]

[[beta].sub.0]            0.0676             0.0625
                       (9.1450) ***       (8.2171) ***
[[beta].sub.1]           -0.0384             0.0033
                      (-3.5800) ***         (0.5731)
[[beta].sub.2]            0.0440            -0.0008
                       (3.5542) ***       (-1.1930) **
[[beta].sub.3]            0.0159            -0.0006
                         (1.4078)           (0.0872)
[[beta].sub.4]            0.0192             0.0050
                        (1.7903) *          (0.8595)
[[beta].sub.5]           -0.0010            -0.0002
l                     (-2.8126) ***        (-0.6780)

Panel modeling        Random Effects     Random Effects

Chow Test               2 8115 ***         4.5867 ***
Hausman Test              4.2871            7.2 763
Breusch-Pagan Test        0.0521             0.7722
Adjusted [R.sup.2]        1.99%              0.01%

Number of observations: 3,321. Outliers corresponding to
the first and last percentiles of each variable series
were excluded with the exception of the control variable.
[X.sub.it] is one of the independent variables of the model.
Two estimations were performed, one in which [X.sub.it] was
assumed to be [EPS.sub.it+k]/[P.sub.it-(1-k)] and another
in which [X.sub.it] was [EPSGR.sub.it]. The t statistic is
shown in parentheses below the relevant coefficient.

*, ** and *** represent significance at the 10%, 5% and 1%
levels, respectively.

Table 8 Model (9) results

[R.sub.it] = [[beta].sub.0] + [3.summation over (k=0)]
[[beta].sub.k+1] + [3.summation over (k=1)][[beta].sub.k+4]
+ [[beta].sub.8][[BVPS.sub.it]/[P.sub.it-1]] +
[[epsilon].sub.it]

Coefficients                         [X.sub.it+k]

                     [EPS.sub.it+k]/    [EPSGR.sub.i+k]
                     [P.sub.it-(1-k)]

[[beta].sub.0]            0.0681            0.0642
                      (16.5422) ***      (16.0316) ***
[[beta].sub.1]           -0.0379            0.0018
                       (3.2902) ***        (0.3102)
[[beta].sub.2]            0.0407            -0.0072
                       (3.1436) ***        (-1.0394)
[[beta].sub.3]            0.0132            0.0008
                         (1.1388)          (0.1134)
[[beta].sub.4]            0.0220            0.0050
                        (1.8280) *       (0.8325) ***
[[beta].sub.5]            0.0435            0.0083
                       (2.3450) **         (0.1281)
[[beta].sub.6]           -0.0070            -0.1441
                        (-0.3701)        (-2.3344) **
[[beta].sub.7]           -0.0329            0.1409
                       (-1.6989) *        (2.3483) **
[[beta].sub.8]           -0.0007            -0.0002
                         (1.3881)          (-0.2039)

Panel modeling        Fixed Effects      Fixed Effects

Chow Test               4.9077 ***        5.7257 ***
Hausman Test           47.9602 ***        55.5329 ***
Adjusted [R.sup.2]        4.53%              3.51%
F                       1.7845 ***        1.6006 ***

Number of observations: 3,321. Outliers corresponding to
the first and last percentiles of each variable series
were excluded, with the exception of the control variable.
[X.sub.it] is one of the independent variables of the
model. Two estimations were performed, one in which
[X.sub.it] was assumed to be [EPS.sub.it]/[P.sub.it-1]
and another in which [X.sub.it] was [EPSGR.sub.it]. The
t statistic is shown in parentheses below the relevant
coefficient.

*, ** and *** represent significance at the 10%, 5% and
1% levels, respectively.

Table 9 Model results (7)--Further analysis

Variables                         Estimations

                       (a)             (b)             (c)

                                  Coefficients

Constant             0.0613          0.0646          0.0642
                  (15.7900) ***   (16.4900) ***   (16.2700) ***
[EPS.sub.it]/        -0.0181         -0.0354         -0.0306
  [P.sub.it-1]     (-1.6700) *    (-3.1410) ***   (-2.7090) ***
[EPS.sub.it+1]/                      0.0595
  [P.sub.it]                      (5.2530) ***
[EPS.sub.it+2]/                                      0.0378
  [P.sub.it+1]                                    (3.8270) ***
[EPS.sub.it+3]/
  [P.sub.it+2]
[R.sub.t+1]          0.0491          0.0489          0.0423
                  (2.6520) ***    (2.6550) ***    (2.2800) ***
[BVPS.sub.it]/       -0.0005         -0.0009         -0.0005
  [P.sub.it-1]      (-1.1080)      (-1.8380) *      (-0.9982)
Hausman Test       50.6856 ***     42.8122 ***     43.0311 ***
Adjusted              3.52%           4.33%           3.93%
  [R.sup.2]
F                  1.6171 ***      1.7626 ***      1.6903 ***

Variables                         Estimations

                       (d)             (e)             (f)

                                  Coefficients

Constant             0.0653          0.0657          0.0666
                  (16.4800) ***   (16.6200) ***   (16.7300) ***
[EPS.sub.it]/        -0.0246         -0.0400         -0.0379
  [P.sub.it-1]    (-2.2610) **    (-3.4810) ***   (-3.2860) ***
[EPS.sub.it+1]/                      0.0503          0.0423
  [P.sub.it]                      (4.1440) ***    (3.2 740) ***
[EPS.sub.it+2]/                      0.0219          0.0131
  [P.sub.it+1]                     (2.0680) **      (1.1290)
[EPS.sub.it+3]/      0.0447                          0.0216
  [P.sub.it+2]     4.6380) ***                     (1.8200) *
[R.sub.t+1]          0.0440          0.0450          0.0442
                   (2.3810) **     (2.4320) **     (2.3850) **
[BVPS.sub.it]/       -0.0003         -0.0008         -0.0006
  [P.sub.it-1]      (-0.5711)      (-1.6550) *      (-1.3040)
Hausman Test       38.8427 ***     41.7925 ***     42.2857 ***
Adjusted              4.14%           4.43%           4.50%
  [R.sup.2]
F                  1.7287 ***      1.7772 ***      1.7862 ***

Number of observations: 3,321. Outliers corresponding to
the first and last percentiles of each variable series
were excluded with the exception of the control variable.
The estimations were performed using the fixed effects
model. The t statistic is shown in parentheses below the
relevant coefficient.

*, ** and *** represent significance at the 10%, 5% and
1% levels, respectively.


1 INTRODUCAO

O preco das acoes decorre das expectativas dos investidores, condicionadas ao conjunto informacional disponivel em um dado momento. Assume-se que isso ocorra de forma racional, porem sem obedecer a regras especificas. Cada investidor possui um modelo decisorio proprio, que e influenciado pela sua indiferenca as diversas configuracoes de risco e retorno estabelecidas para os ativos. O lucro contabil, por sua vez, tambem captura grande parte desse conjunto informacional, entretanto sujeito as limitacoes impostas pela objetividade, pelo conservadorismo e pelas regras para o reconhecimento das receitas, proprias do modelo contabil, que o tornam informacionalmente intempestivo.

Em certa medida, precos e lucros podem ser considerados sinais de um mesmo estado da realidade, entretanto nao contemporaneos. Situacao esta que se mostra mais evidente a luz da eficiencia de mercado. O lucro contabil tende a apresentar uma resposta atrasada aos eventos relevantes considerados pelo mercado quando da formacao do preco das acoes (Beaver, Lambert, & Morse, 1980). A primeira implicacao disso e que apenas uma parte da variacao contemporanea do lucro representa uma surpresa para o mercado, a respeito das expectativas sobre os lucros futuros (Collins, Kothari, Shanken, & Sloan, 1994; Kothari & Zimmerman, 1995).

A parcela informacional acerca dos lucros futuros nao expressa pelo lucro corrente representa uma importante variavel que e omitida no modelo tradicional da relacao preco-lucro, o que contribui, ao lado do efeito concorrente das informacoes obtidas em outras fontes, com a obtencao de baixos e enviesados coeficientes de resposta para o lucro e baixo poder explicativo dos modelos (1) (Kothari & Zimmerman, 1995; Kothari, 2001).

A hipotese prices lead earnings contempla parte dessa problematica. Sob essa ideia, assume-se que os precos contem mais informacoes sobre os lucros futuros se comparados a serie dos lucros corrente e passados, ou seja, os precos possuem conteudo informacional em relacao aos lucros futuros (Beaver et al., 1980; Kothari & Zimmerman, 1995). Uma implicacao desse fenomeno e que as expectativas do mercado acerca dos lucros sao diferentes das expectativas baseadas na serie temporal dos lucros. Como esta serie temporal, para boa parte da literatura, e descrita como um passeio aleatorio, os lucros passados nao podem prever as suas sucessivas variacoes (Kothari & Sloan, 1992).

Importantes estudos ja exploraram, direta ou indiretamente, ou reconheceram a nao contemporaneidade informacional entre precos e lucros, por exemplo, Beaver, Lambert, e Morse (1980), Kothari e Sloan (1992), Kothari (1992), Collins, Kothari, Shanken, e Sloan (1994), Ayers e Freeman (2000) e Truong (2012). Contudo, apesar da relevancia do tema para pesquisa contabil em mercado de capitais, com poucas excecoes, tais como Galdi e Lopes (2008), Pimentel e Lima (2010), Santos e Lustosa (2010), Sales (2011), e Paulo, Sarlo Neto, e Santos (2012), ele foi pouco explorado no mercado acionario brasileiro. Sendo assim, a investigacao de aspectos temporais da relacao retorno-lucro tem por motivacao preencher a lacuna existente na literatura nacional e, consequentemente, oferecer contribuicoes teoricas e metodologicas ao avanco da compreensao dessa relacao no cenario nacional.

Desse modo, o presente estudo tem por objetivo identificar o nivel temporal da relacao retorno-lucro no cenario brasileiro que, em ultima analise, e o principal indicador da hipotese prices lead earnings. Para tanto, serao investigadas as seguintes questoes de pesquisa:

* Ha contemporaneidade informacional entre o retorno trimestral das acoes e o lucro contabil trimestral das firmas brasileiras de capital aberto?

* O retorno trimestral das acoes das firmas brasileiras de capital aberto antecipa informacoes acerca dos lucros trimestrais futuros?

* Qual o nivel temporal da relacao retorno-lucro?

A contemporaneidade informacional e aqui entendida como a relacao significativa entre duas variaveis, no caso o lucro contabil e o retorno das acoes, considerando-se um mesmo momento no tempo. Ja o nivel temporal e empregado para indicar o grau de defasagem temporal entre os momentos das variaveis, quando verificada uma relacao significativa entre elas. Por exemplo, em uma relacao contemporanea, o nivel temporal sera zero, por outro lado, havendo 1 lag de defasagem entre as variaveis, o nivel temporal sera -1, e assim por diante.

De uma maneira geral, os resultados obtidos evidenciam a nao contemporaneidade informacional entre os retornos e os lucros em um nivel temporal igual a 1, onde o retorno antecipa o lucro do periodo seguinte, ou seja, os precos podem antecipar os lucros. Muito embora a investigacao tenha indicado que o lucro corrente mostra-se contemporaneo quando introduzidos os lucros futuros na relacao analisada. Essas constatacoes, dentre as demais obtidas no estudo, oferecem importantes contribuicoes ao aprimoramento dos modelos analiticos e operacionais empregados por estudos brasileiros na investigacao da relacao retornolucro, tendo em vista que boa parte deles, comumente, nao considera, ou considera parcialmente, os efeitos dessa defasagem temporal quando da definicao daqueles modelos.

Outrossim, essas constatacoes oferecem subsidios adicionais para a previsao de lucros futuros por parte de investidores ou analistas de investimento, na medida em que indicam que o retorno corrente das acoes possui conteudo informacional em relacao aos lucros futuros, notadamente, o do periodo seguinte.

O restante do artigo esta dividido da seguinte maneira: a secao 2 apresenta as evidencias empiricas obtidas em estudos anteriores, discute os aspectos teoricos subjacentes a hipotese price leads earnings e declara as hipoteses de pesquisa. Na secao 3, sao tratados os aspectos metodologicos empregados. A secao 4 apresenta e analisa os resultados obtidos e a secao 5 apresenta as consideracoes finais.

2 DESENVOLVIMENTO DAS HIPOTESES DE PESQUISA

2.1 Fundamentacao Teorica.

O modelo tradicional da relacao preco-lucro assume que: (i) o lucro de um periodo reflete contemporaneamente toda informacao refletida no retorno desse periodo; (ii) apenas a informacao contida nos lucros (fluxos de caixa futuros esperados) afeta o preco das acoes; (iii) os lucros seguem um passeio aleatorio; e (iv) a taxa de payout dos dividendos e de 100% (Kothari, 1992).

Kothari (1992) destaca que o objetivo da premissa "iv" e simplificar a analise econometrica da relacao preco-lucro, e que ela nao sacrifica a intuicao economica associada a uma taxa de payout mais realista. Ja no tocante a premissa "iii", apesar da existencia de divergencias, boa parte da literatura, ha algum tempo, tem reunido um substancial conjunto de evidencias que indicam que as series temporais dos lucros anuais seguem um passeio aleatorio ou um passeio aleatorio com tendencia (Kothari, 2001).

Contudo, as premissas "i" e "ii" sao pouco realistas e contrariam as implicacoes da eficiencia de mercado, hipotese subjacente assumida pela pesquisa contabil em mercado de capitais. Em um mercado eficiente, o preco das acoes ([P.sub.t]) reflete, instantaneamente, as expectativas dos seus participantes acerca dos fluxos de caixa futuros. Por outro lado, o lucro ([X.sub.t]), em razao das limitacoes impostas pelo modelo contabil, sobretudo os criterios de reconhecimento de receitas e despesas, tende a incorporar, sistematicamente com atraso, as informacoes ja refletidas em [P.sub.t]. Assim, temse que estes ([P.sub.t]) sao informacionalmente mais ricos acerca dos lucros futuros do que as series dos lucros correntes e passados, ou seja, as expectativas do mercado e aquelas baseadas nas series temporais de [X.sub.t] passam a ser diferentes, fenomeno (hipotese) conhecido como prices lead earnings (Beaver et al., 1980; Lev, 1989; Kothari, 1992, 2001).

O primeiro estudo que contemplou esse fenomeno foi o de Beaver et al. (1980). Os resultados por eles obtidos confirmam que [P.sub.t] e informacionalmente mais rico do que [X.sub.t]. Outros estudos importantes foram os de Kothari (1992), Kothari e Sloan (1992), e Kothari e Zimmerman (1995), que discutiram e demonstraram os efeitos desse fenomeno sobre os modelos econometricos que tratam da relacao preco-lucro, tradicionalmente utilizados, ate entao, na literatura internacional, e ofereceram alternativas para mitiga-los.

Essa superioridade informacional de [P.sub.t], de acordo com Beaver et al. (1980), pode advir de diversas razoes, por exemplo: (i) o [X.sub.t] pode ser visto como uma agregacao de lucros de intervalos menores, assim [P.sub.t] pode ser utilizado para obter informacoes sobre as series pre-agregadas, perdidas naquele processo de agregacao temporal; (ii) ha eventos que afetam os lucros futuros e que nao estao refletidos em [X.sub.t]; e (iii) [X.sub.t] pode ser representado por um processo composto por mais de uma variavel estocastica.

Se [X.sub.t] segue um passeio aleatorio, toda informacao expressa em [P.sub.t] ja estaria contida na serie passada de [X.sub.t]. Contudo, se [P.sub.t] contem informacoes sobre os lucros futuros, tem-se, portanto, violada aquela premissa de passeio aleatorio, pois as variacoes futuras de [X.sub.t] poderiam ser previstas pelos participantes do mercado. E essa e uma das razoes para Beaver et al. (1980) terem assumido que [X.sub.t] e formado por um processo composto, conforme expresso pela equacao (1):

[X.sub.t] = [x.sub.t] + [[epsilon].sub.t] [1]

em que [x.sub.t] e a parcela de [X.sub.t] que reflete os eventos que tambem afetam [P.sub.t], denominada lucro nao distorcido; e [[epsilon].sub.t] o termo white noise, chamado de lucro distorcido, que representa o impacto sobre [X.sub.t] de ajustes ou eventos que nao afetam [P.sub.t].

Kothari (1992) e Kothari e Zimmerman (1995) argumentam que, quando [P.sub.t] e informacionalmente mais rico, a variacao de [X.sub.t] e composta por uma porcao ([[alpha].sub.t,t-1], [[alpha].sub.t,t-n]) que foi previamente incorporada por [P.sub.t-1] ... [P.sub.t-n], e por uma parcela aleatoria que representa uma surpresa para o mercado ([s.sub.t]), e e com essa parcela que seria possivel verificar uma relacao contemporanea.

Estendendo essa ideia para o processo composto da equacao (1), e possivel assumir que

[x.sub.t] = [s.sub.t] + [N.summation over (n=1)] [[alpha].sub.t,t-n] [2a]

[X.sub.t] = [s.sub.t] + [N.summation over (n=1)] [[alpha].sub.t,t-n] + [[epsilon].sub.t] [2b]

em que at [[alpha].sub.t,t-n] e a parcela de [X.sub.t]--primeiro subscrito (ano a que se refere X)--antecipada pelo mercado no periodo t-n --segundo subscrito.

A parcela [x.sub.t] nao e observavel, consequentemente, [s.sub.t] e [N.summation over (n=1)] [[alpha].sub.t,t-n] nao podem ser isolados ou mensurados. Contudo, de acordo com Beaver et al. (1980), [X.sub.t] oferece uma mensuracao distorcida de [x.sub.t] em razao da existencia de [[epsilon].sub.t], tem-se, entao, que [X.sub.t] mede as variacoes de [P.sub.t] com erro.

Entretanto, vale ressaltar que, alem dos efeitos dessa distorcao, a propria dinamica informacional entre [X.sub.t] e [P.sub.t] impoe problemas a relacao contemporanea entre essas variaveis. Como somente a parcela [s.sub.t] correlaciona-se com as variacoes de [P.sub.t], uma vez que [N.summation over (n=1)] [[alpha].sub.t,t-n] e irrelevante para a explicacao destas, e [P.sub.t] antecipa informacoes que somente estarao expressas nos lucros futuros ([N.summation over (n=1)] [[alpha].sub.t,t+n]), variaveis omitidas no modelo tradicional e nao correlacionadas com [s.sub.t], tem-se agravadas as consequencias econometricas pontuadas por Beaver et al. (1980), o que se revela pelo baixo poder explicativo oferecido pelo modelo tradicional da relacao preco-lucro e pela baixa magnitude e enviesamento do coeficiente de resposta de [X.sub.t] (Lev, 1989; Kothari & Zimmerman, 1995; Kothari, 2001).

Collins et al. (1994) constataram que a relacao entre [P.sub.t] e [X.sub.t] apresenta baixa contemporaneidade e identificaram que a intempestividade informacional de [X.sub.t] e o principal determinante desse fenomeno. Eles verificaram que as variacoes futuras de [X.sub.t] foram capazes de explicar aNs variacoes correntes de [P.sub.t], ou seja, [P.sub.t] antecipou a parcela [N.summation over (n=1)] [[alpha].sub.t,t-n].

Ja Basu (1997) verificou que [X.sub.t] e assimetricamente tempestivo em relacao as mas noticias sinalizadas pelas variacoes negativas de [P.sub.t], constatacao que introduz aspectos adicionais ao tema, pois evidencia os efeitos do conservadorismo contabil sobre a parcela informacional st, o que tende a agravar ainda mais os problemas da baixa contemporaneidade entre [X.sub.t] e [P.sub.t], uma vez que indica que esta, alem de reduzida, aparentemente e incompleta e enviesada.

Uma outra linha de pesquisa vem explorando a influencia de outros aspectos, tais como composicao acionaria, caracteristicas dos investidores, cobertura dos analistas, estrutura de governanca, nivel de investimentos de longo prazo, bens produzidos, tamanho, sobre o fenomeno prices lead earnings, o que tem ampliado a compreensao do tema. De uma maneira geral, as pesquisas tem demonstrado que esses fatores afetam o nao sincronismo informacional entre [X.sub.t] e [P.sub.t] (Ayers & Freeman, 2000, 2003; Jiambalvo, Rajgopal, & Venkatachalam, 2002; Lee, 2007).

Nessa linha, Ayers e Freeman (2000) investigaram a associacao entre tamanho da firma e o nivel temporal dos retornos em relacao a variacao media do lucro anual setorial e a variacao do lucro anual especifica a firma. Foi identificada uma associacao positiva entre o tamanho e o grau de antecipacao dos lucros futuros para ambas as variacoes analisadas. Alem disso, os resultados tambem sugerem que os precos das acoes de grandes firmas antecipam informacoes que afetam todo o setor, de modo que os seus retornos podem antecipar parte dos retornos de pequenas firmas.

Ja Jiambalvo, Rajgopal, e Venkatachalam (2002) e Ayers e Freeman (2003) constataram uma associacao positiva entre percentual de participacao institucional na estrutura de propriedade das firmas e o fenomeno prices lead earnings. Para Jiambalvo, Rajgopal, e Venkatachalam (2002), isso se da em virtude de que os investidores institucionais seriam mais sofisticados e teriam vantagens em adquirir e processar informacoes somente refletidas nos lucros futuros, o que imporia um menor sincronismo informacional conforme o aumento da participacao desses investidores.

Ayers e Freeman (2003) tambem avaliaram a influencia da cobertura dos analistas sobre o grau de antecipacao dos lucros futuros apresentado pelos precos das acoes. Assim como verificados para os investidores institucionais, os resultados evidenciaram uma associacao positiva para a cobertura dos analistas. Alem disso, Ayers e Freeman (2003) verificaram que tais fatores sao incrementais entre si nessa associacao e que a influencia deles sobre aquele grau de antecipacao independe do tamanho da firma.

Lee (2007), por sua vez, apresenta evidencias que sugerem que caracteristicas operacionais (durabilidade dos produtos produzidos) e mercadologicas (poder do produto no mercado) sao positivamente associadas ao reconhecimento antecipado de lucros futuros, enquanto o nivel de investimentos em ativos de longo prazo mostra-se negativamente associado a essa antecipacao.

Um outro interessante estudo e o de Truong (2012), no qual e explorada a relacao entre a negociacao de opcoes e a extensao na qual os precos antecipam lucros futuros. Truong (2012) verificou que os precos das acoes de firmas com lista de opcoes antecipam mais informacoes sobre lucros futuros em relacao as demais, alem disso, identificou uma relacao positiva entre o volume de negociacao das opcoes e essa antecipacao. Outro resultado encontrado foi que, dentre as firmas com lista de opcoes, os precos das acoes no periodo de pos listagem refletiam melhor e mais rapido informacoes sobre os lucros futuros, se comparados com aqueles do periodo de pre listagem.

No Brasil, os estudos ainda sao preliminares. Por exemplo, Galdi e Lopes (2008) e Pimentel e Lima (2010) obtiveram evidencias da existencia de um relacionamento de longo prazo entre o lucro contabil e o preco das acoes, bem como, dentre as firmas analisadas, verificaram um maior numero de ocorrencias em que o preco das acoes teria antecipado a informacao contida no lucro contabil, pelo menos em um nivel temporal igual a -1. De acordo com Galdi e Lopes (2008), esta ultima constatacao e algo esperado tendo em vista a intempestividade informacional do lucro contabil.

Sales (2011), por sua vez, obteve resultados que indicam que o mercado antecipa a informacao contida em [X.sub.t] precificando as acoes durante o periodo a que se refere e apos o encerramento deste. O que e condizente com as constatacoes de Santos e Lustosa (2010). Sales (2011) tambem encontrou evidencias da existencia de uma estrutura do tipo lead-lag entre as variacoes em [P.sub.t] e [X.sub.t], a qual, segundo ela, sugeriria que os lucros futuros explicariam parte das variacoes em [P.sub.t] nao explicadas por [X.sub.t]. Contudo, nao obstante a relacao funcional empregada, temporalmente, o que se observa, e que [P.sub.t] pode explicar parte dos lucros futuros [N.summation over (n=1)] [[alpha].sub.t,t+1]) nao o inverso.

Ja Paulo, Sarlo Neto, e Santos (2012), assumindo como ideia subjacente a hipotese prices lead earnings e a tempestividade assimetrica evidenciada por Basu (1997), investigaram, no mercado acionario brasileiro, o conteudo informacional expresso por [X.sub.t] quando da sua divulgacao. Os resultados indicaram que [P.sub.t] so apresentou variacoes anormalmente significativas frente as mas noticias, o que se alinha a percepcao de assimetria informacional de [s.sub.t].

2.2 Hipoteses.

Com base nos pressupostos teoricos e evidencias empiricas apresentados e discutidos na secao anterior, e possivel depreender que o principal efeito da superioridade informacional de [P.sub.t], decorrente da sua capacidade de incorporar rapidamente os eventos relevantes que somente serao refletidos nas variacoes futuras de [X.sub.t], essencia da hipotese prices lead earnings, e a baixa ou, ate mesmo, nula contemporaneidade entre essas variaveis. Desse modo, a constatacao de niveis temporais superiores a zero pode indicar a confirmacao dessa hipotese no mercado brasileiro. Assim, foram formalizadas as hipoteses de pesquisa abaixo: H0a: A relacao entre o retorno trimestral das acoes e o lucro contabil trimestral das firmas brasileiras de capital aberto nao e contemporanea.

[H.sub.0a]: O retorno trimestral das acoes das firmas brasileiras de capital aberto antecipam informacoes acerca dos lucros trimestrais futuros.

[H.sub.0b]: O nivel temporal da relacao retorno-lucro das firmas brasileiras de capital aberto e maior ou igual a 1.

3 METODOLOGIA

3.1 Os Dados.

A analise empirica realizada contemplou dados trimestrais das firmas nao financeiras listadas na Bolsa de Valores de Sao Paulo (Bovespa), referentes ao periodo compreendido entre 03/1999 e 03/2012. Integraram a amostra da pesquisa apenas aquelas firmas que apresentaram as demonstracoes contabeis para esse periodo, referentes aos trimestres encerrados em 31/03, 30/06, 30/09 e 31/12, e para as quais estavam disponiveis as cotacoes das suas acoes nestas datas ou no dia imediatamente posterior. A amostra final foi composta por 205 firmas e resultou em um painel de dados formado por 8.440 firmas-trimestres. Todos os dados foram obtidos no banco de dados Economatica.

Foram utilizadas as variaveis contabeis Lucro por Acao (LPA) e Patrimonio Liquido por Acao (PLA), a qual desempenhou a funcao de controle do efeito tamanho das firmas. Ambas as variaveis foram deflacionadas pelo preco da acao do inicio do periodo (final do periodo anterior). Tambem foi utilizada a taxa de crescimento do LPA, aqui denominada VLPA, apurada pelo logaritmo natural da diferenca entre o LPA de dois periodos consecutivos [ln([LPA.sub.it]/[LPA.sub.it-1])].

O retorno do preco das acoes tambem foi apurado sob a forma logaritmica. O preco das acoes foi ajustado pelos proventos, segundo os criterios adotados pelo Economatica. Quando possivel, foram selecionadas acoes do tipo preferencial em razao da sua maior liquidez.

Conforme sera detalhado adiante, a investigacao foi realizada em 2 etapas, com o emprego de 4 modelos econometricos, o que exigiu a utilizacao de 2 conjuntos de variaveis. A fim de minimizar o efeito econometrico de valores extremos sobre os resultados dos modelos, foram excluidas as observacoes que se situavam nos primeiro e ultimo percentis da serie de cada variavel. Isso resultou uma amostra final de 4.177 firmas-trimestres para o primeiro grupo de variaveis e 3.321 para o segundo.

3.2 O Modelo.

Basicamente, foram exploradas as tres relacoes funcionais abaixo representadas:

Lucro Contabil = f (Retorno da Acao) [3]

Retorno da Acao = f (Lucro Contabil) [4]

Retorno da Acao = f (Lucro Contabil,

Ret. [Acao.sub.t+1], Ret. [Acao.sub.t+2], Ret. [Acao.sub.t+3]) [5]

Para todas essas relacoes, os respectivos modelos econometricos foram estimados com o emprego de regressoes combinadas (pooled regressions) e de dados em painel. A avaliacao quanto a adequacao da regressao combinada considerou a indicacao, a um nivel de significancia de, pelo menos, 10%, da ocorrencia de quebra estrutural do modelo, por meio do teste de Chow. Havendo quebra (hipotese alternativa do teste), e recomendavel a utilizacao do painel de dados. Ja a escolha entre a modelagem apropriada para o painel, isto e, os modelos de efeitos fixos ou efeitos aleatorios, foi baseada no teste de Hausman, cuja hipotese nula aponta para a existencia de componentes de efeitos aleatorios na relacao multivariada estimada.

Os modelos econometricos empregados sao baseados em Beaver et al. (1980)--modelo (6)--e Collins et al. (1994)--modelos (7), (8) e (9). Nesses estudos, foram utilizadas variacoes do LPA, por isso aqui o emprego da variavel VLPA. Entretanto, a decisao de tambem utilizar [LPA.sub.it]/[p.sub.it-1] deve-se ao fato da sua superioridade quando da presenca de prices- lead- earnings, conforme destaca Kothari (1992). Alem disso, as estimacoes dos modelos com a utilizacao dessas duas variaveis oferecem oportunidades adicionais a avaliacao da adequacao dessas proxies do lucro contabil na relacao retorno-lucro (lucroretorno) no cenario brasileiro.

A relacao funcional (3) foi estimada por meio do modelo econometrico (6), abaixo, que e baseado em Beaver et al. (1980), tambem conhecido como modelo invertido, ou regressao reversa, assim chamado por inverter a tradicional relacao em que o retorno das acoes (variacao no preco p) e funcao da variacao do lucro por acao (ALPA). Foram realizadas 2 estimacoes, onde as variaveis dependentes foram [LPA.sub.it]/[p.sub.it-1] e [VLPA.sub.it].

[X.sub.it] = [[beta].sub.0] + [4.summation over (k=0)] [[beta].sub.k+1][R.sub.it-k] + [[beta].sub.6][R.sub.it-6] + [[beta].sub.7][R.sub.it-8] + [[beta].sub.8] [[PLA.sub.it]/[p.sub.t-1]] + [[epsilon].sub.it] [6]

onde

[X.sub.it] = [LPA.sub.it]/[p.sub.it-1] ou [VLPA.sup.it].

[LPA.sub.it] = lucro liquido por acao da firma no trimestre t.

[p.sub.it-1] = preco da acao da firma i no termino do trimestre t-1.

[VLPA.sub.it] = taxa de crescimento do LPAit, obtida pelo logaritmo natural da diferenca entre os LPAs em t e t-1.

[R.sub.it] = retorno logaritmico da acao da firma i no trimestre t (t-1 ... t-8).

[PLA.sub.it] = patrimonio liquido por acao da firma i no trimestre t. E utilizada como proxy do tamanho para fins de controle.

Se as variacoes do preco das acoes expressam informacoes so refletidas nos lucros futuros, e provavel que retornos passados estejam associados ao lucro contabil corrente. Para avaliar esse aspecto, foram utilizados retornos trimestrais contemporaneos ao lucro, bem como defasados em 1 a 4, 6 e 8 trimestres, de modo a analisar relacao informacional do trimestre imediatamente anterior ate uma defasagem de 2 anos. Assume-se, portanto, que as revisoes das expectativas dos investidores acerca dos lucros futuros, em resposta as novas informacoes trazidas pelos lucros trimestrais, sao revisadas, e incorporadas nos precos, no curto e medio prazos. Assim, se a hipotese prices lead earnings e verdadeira no Brasil, espera-se que [[beta].sub.1] nao seja significativo ou, do contrario, apresente baixa magnitude, o que dependera da representatividade de [s.sub.t]. Ja em relacao aos demais coeficientes relacionados aos retornos defasados, espera-se que se mostrem positivos e significativos. Tais resultados permitirao, especificamente, testar operacionalmente a hipotese [H.sub.0b], bem como fornecerao subsidios que, conjuntamente com os dos demais modelos, permitirao o teste da hipotese [H.sub.0c].

Estabelecendo o mesmo raciocinio acima, entretanto, sob a otica do lucro contabil, e possivel assumir que o lucro corrente responde de maneira intempestiva ao retorno corrente, sendo assim, assumindo relacao funcional tradicional entre retorno e lucro, a adicao de lucros de periodos subsequentes ofereceria um melhor nivel de explicacao para essa relacao. Sob essa ideia, foi explorada a relacao funcional (4), por meio dos modelos econometricos abaixo:

[R.sub.it] = [[beta].sub.0] + [[beta].sub.1][X.sub.it] + [[beta].sub.2] [[PLA.sub.it]/[p.sub.it-1]] + [[epsilon].sub.it] [7]

[R.sub.it] = [[beta].sub.0] + [3.summation over (k=0)] [[beta].sub.k+1] [X.sub.it+k] + [[beta].sub.5] [[PLA.sub.it]/[p.sub.it-1]] + [[epsilon].sub.it] [8]

que [X.sub.it] assume [LPA.sub.it]/[p.sub.it-1] ou [VLPA.sub.it], nas respectivas estimacoes. O modelo (7) e a relacao tradicionalmente estudada (Kothari, 2001), ja o modelo (8) baseia-se em Collins et al. (1994).

Contudo, como as parcelas informacionais de [X.sub.t] e [X.sub.t+k] ja antecipadas pelos precos passados, [N.summation over (n=1)] [[alpha].sub.t,t-n] e [N.summation over (n=1)] [[alpha].sub.t+k,t-n], nao seriam correlacionadas com [R.sub.t], tem-se, portanto, erros de mensuracao no modelo sobre os coeficientes de [X.sub.t] e [X.sub.t+k], cuja extensao dependera dos desvios das variacoes dos precos associadas as expectativas em t. Ja no caso especifico de [X.sub.t+k], ha uma fonte adicional de erros advinda da parcela informacional nao antecipada por [R.sub.t], que somente estara refletida nos retornos futuros, [N.summation over (n=1)] [[alpha].sub.t+k,t+n] tnn (Collins et al., 1994; Kothari, 2001). Para mitigar parte dos efeitos desses erros de mensuracao relacionados a [X.sub.t]nk, foram utilizados retornos futuros das acoes ([R.sub.tn1], [R.sub.tn2] e [R.sub.tn3]), conforme proposto por Collins et al. (1994). +

Desse modo, foi utilizado o seguinte modelo, operacionalizando a relacao funcional (5):

[R.sub.it] = [[beta].sub.0] + [3.summation over (k=0)] [[beta].sub.k+1][X.sub.it+k] + [3.summation over (k=1)] [[beta].sub.k+4][R.sub.it+k] + [[beta].sub.8] [[PLA.sub.it]/[p.sub.it-1]] + [[epsilon].sub.it] (9)

Frise-se que o teste de significancia do coeficiente [[beta].sub.1], sobretudo no modelo (7), representara o principal teste operacional da hipotese [H.sub.0a], uma vez que, sendo [[beta].sub.1] estatisticamente diferente de zero, ter-se-a sinais de contemporaneidade e, portanto, essa hipotese sera rejeitada. Outrossim, vale salientar que os resultados obtidos com os modelos (7), (8) e (9) tambem serao necessarios a correta avaliacao das proposicoes contidas nas hipoteses [H.sub.0b] e [H.sub.0c].

4 ANALISE DOS RESULTADOS

As estatisticas descritivas do grupo de variaveis utilizadas na primeira etapa da analise, bem como a sua matriz de correlacao sao apresentadas nas Tabelas 1 e 2, respectivamente. Depois da exclusao dos valores extremos que figuravam nos primeiro e ultimo percentis da serie de cada variavel, com excecao da variavel de controle, a amostra inicial foi reduzida para 4.177 observacoes.

Nesse primeiro subconjunto de dados, as variaveis representativas do lucro contabil apresentam caracteristicas bastante distintas, o que e de se esperar, haja vista a forma por meio da qual cada uma delas foi calculada. Percebe-se que a serie de [LPA.sub.it]/[p.sub.it-1], apesar de apresentar maior amplitude, possui menor desvio padrao e menor coeficiente de variacao (11,07 contra 156,83) do que [VLPA.sub.it]. O que ja indica uma certa superioridade dessa variavel, pois sua serie apresenta menor variabilidade. No tocante aos retornos, observa-se uma aparente similaridade nas suas estatisticas, entretanto e interessante notar que ha um aumento quase que monotonico para todas elas a medida que se aumentam os lags, com destaque para os periodos t-6 e, sobretudo, t-8. Possivelmente, isso demonstra a influencia dos retornos de periodos anteriores nao alcancados pelas demais series (t, ..., t - 4).

A matriz de correlacao apresentada na Tabela 2 ja evidencia a existencia de um comportamento linear semelhante entre o lucro contabil e os retornos dos periodos corrente e anteriores. Ha poucas correlacoes observadas para a variavel [VLPA.sub.it], as quais, apesar de significativas, nao ultrapassam 0,047. Dentre elas, verifica-se uma correlacao negativa em relacao a [R.sub.t-6], o que, aparentemente, e intrigante, haja vista as demais correlacoes verificadas para os outros periodos. Contudo, a razao pode estar vinculada a serie de [R.sub.t-6], tendo em vista que outras correlacoes negativas sao observadas para ela, em relacao aos retornos dos demais periodos, precisamente a partir do trimestre t-3. Ja a variavel [LPA.sub.it]/[p.sub.it-1] apresenta uma sequencia uniforme de correlacoes altamente significativas e de mesmo sinal e, embora as series de retorno mais antigas apresentem caracteristicas descritivas um pouco diferentes, nao se observou nenhum padrao de correlacao que revelasse uma influencia relevante dos retornos de periodos muito antigos. Essa analise preliminar tambem sugere a superioridade de [LPA.sub.it]/[p.sub.it-1] na relacao ora estudada.

A primeira relacao analisada foi aquela proposta pelo modelo (6), em que a variavel representativa do lucro contabil e estimada em funcao dos retornos, contemporaneos e defasados, das acoes. A Tabela 3 exibe os resultados obtidos.

Em ambos os modelos, os resultados revelam a fraca, ou inexistente, relacao entre o retorno contemporaneo e o lucro contabil, indicando a baixa representatividade informacional da parcela st. Por outro lado, indicam que ha algum nivel significante de associacao, se considerados retornos de periodo anteriores.

Na estimacao envolvendo [VPLA.sub.it], tem-se a indicacao de que os retornos relativos aos trimestres -3 ([[beta].sub.4]), -6 ([[beta].sub.6]) e -8 ([[beta].sub.8]) exibem uma relacao significativa com essa variavel. Nao se observa, entretanto, um padrao aparente de resposta de acordo com o esperado. A intermitencia nos trimestres e os diferentes sinais dos coeficientes nao podem ser explicados em termos gerais, com excecao da hipotese de que a variavel [VPLA.sub.it] e pouco representativa da relacao aqui estudada, o que e sugerido pela baixa, ou inexistente, correlacao com os retornos (Tabela 2), que tambem contribui com o baixo poder explicativo do modelo ([R.sup.2] ajustado igual a 0,38% (2)).

Por outro lado, na estimacao cuja variavel dependente e [LPA.sub.it]/[p.sub.it-1], verifica-se um poder explicativo acima dos 70% e observa-se um padrao de resposta consistente com a teoria. Os retornos dos periodos -1 a -6 apresentam coeficientes positivos e altamente significativos, cujos valores demonstram uma tendencia crescente a medida que sao diminuidos os lags. Isso sugere que informacoes expressas no lucro contabil corrente ja estavam sendo antecipadas pelo preco das acoes ha, pelo menos, 6 meses, o que e condizente com a hipotese prices lead earnings. A luz dos resultados, seria possivel supor que cerca de 6% das variacoes do retorno do periodo -6, por exemplo, estariam relacionadas com variacoes do lucro contabil corrente e do mesmo modo para os periodos seguintes, ate que, no periodo -1, seriam alcancados, aproximadamente, 15% de associacao entre as variaveis em questao. Essa percepcao e reforcada pelo comportamento dos movimentos lineares dos retornos e do lucro contabil, sinalizado pelo nivel significativo de correlacao observado (Tabela 2). Esses resultados, de uma maneira geral, alinham-se com aqueles obtidos por Galdi e Lopes (2008) e Sales (2011).

Na segunda etapa da pesquisa, os retornos contemporaneos do preco das acoes foram estimados em funcao do lucro contabil e dos retornos futuros desse preco, por isso um novo subconjunto de variaveis foi empregado. A exclusao dos valores extremos das variaveis resultou em um total de 3.321 observacoes. A Tabela 4 evidencia as estatisticas descritivas dessas variaveis.

As series de retornos que integram esse segundo subconjunto de dados apresentam comportamento semelhante aquele evidenciado na Tabela 1, isto e, as estatisticas descritivas aumentam a medida que os lags tambem aumentam. Aqui, verifica-se que, por exemplo, [R.sub.t+3] possui media e desvio padrao menores do que aqueles apresentados por [R.sub.t]. Esse comportamento tambem e verificado para as medias das series das variaveis representativas do lucro contabil, o que nao e observado para os respectivos desvios padroes, uma vez que para [LPA.sub.it+k]/[p.sub.it+k] verifica-se uma tendencia inversa e para [VLPA.sub.it+k] nao e possivel precisar um padrao.

Conforme e possivel observar na Tabela 5, a variavel [VLPA.sub.it+k] mostra-se inferior a variavel [LPA.sub.it+k]/[p.sub.it(1-k)], no que compete a correlacao com os retornos correntes e futuros. Considerando tambem as correlacoes apresentadas na Tabela 2, e possivel inferir que o comportamento linear VLPA pouco se associa ao comportamento dos retornos passados, corrente e futuros. Por outro lado, verifica-se que [LPA.sub.it+k]/[p.sub.it-(1-k)] apresenta comportamento inverso. Ademais, observa-se que as correlacoes entre essa variavel e os retornos passados mostram-se superiores, se comparadas aquelas dos periodos corrente e futuros. Por exemplo, a correlacao do lucro em t + 1 com o retorno em t-e superior aquelas com os retornos em t + 1, t + 2 e t + 3, do mesmo modo verifica-se em relacao ao lucro de t + 2, pois a correlacao com o retorno em t e-t + 1 mostra-se superior aquelas observadas para os periodos t + 2 e t + 3, e em relacao ao lucro de t + 3. Essa constatacao sugere que parte dos movimentos dos lucros ja teria sido "antecipada" pelas variacoes dos precos, pelo menos, com um trimestre de antecedencia.

Para o modelo (7), observam-se, em ambas as estimacoes, ajustes satisfatorios (estatisticas F altamente significativas) e poder explicativo aceitavel para a relacao estudada, conforme evidenciado na Tabela 6.

O lucro contabil corrente nao se mostrou significativo, o que e coerente com os resultados obtidos com o modelo (6), estando, dessa forma, condizente com a hipotese prices lead earnings. Outrossim, esses resultados alinham-se as constatacoes de Collins et al. (1994), realizadas por meio de uma modelagem semelhante, estimada com base em um nivel agregado de dados (pooled).

A inclusao de lucros de periodos futuros na relacao aci ma gerou efeitos aleatorios na relacao multivariada estabelecida, conforme verificado por meio do teste de Hausman (nao significativo), o que exigiu a estimacao das regressoes por meio do modelo de efeitos aleatorios. Isso pode indicar que os efeitos fixos identificados no modelo (5) eram gerados pela omissao dessas variaveis, uma vez que sao significativamente correlacionadas com o lucro corrente e com o patrimonio liquido, conforme evidenciado na Tabela 5.

Uma premissa subjacente a este estudo e que as variacoes correntes do preco das acoes capturam informacoes que somente serao refletidas em lucros futuros, portanto a inclusao destes permitiria o aumento do poder explicativo ja verificado para o modelo (7). No entanto, conforme evidenciado na Tabela 7, isso nao ocorreu. Pelo contrario, os [R.sup.2] ajustados das estimacoes diminuiram. Entretanto, e bem verdade que as variaveis incluidas sao correlacionadas com aquelas ja utilizadas, o que tende a reduzir os seus efeitos sobre o poder explicativo. Alem disso, as diferencas entre as tecnicas empregadas para estimar os modelos devem ser consideradas nessa comparacao.

Um aspecto que chama a atencao e a significancia do coeficiente [[beta].sub.1], relativo a variavel [LPA.sub.it]/[p.sub.it-1]. Sozinha, essa variavel nao se mostrou significativa na relacao com [R.sub.t], entretanto a inclusao das variacoes futuras permitiu o estabelecimento dessa significancia. Isso sugere que as variacoes do lucro corrente somente se associam as variacoes de [R.sub.t] quando conjugadas com aquelas dos periodos seguintes, ou seja, quando eliminados os efeitos econometricos destas sobre o lucro corrente. Uma possivel explicacao para essa constatacao pode ser decorrente do comportamento linear dessas variaveis. De acordo com a Tabela 5, o lucro corrente apresenta uma correlacao de 0,0303 (significativa somente a 10%) com [R.sub.t], enquanto correlaciona-se com os lucros dos periodos seguintes (t + 1, t + 2 e t + 3) em niveis altamente significativos e com coeficientes superiores a 0,78. Estes, por sua vez, tambem apresentam correlacao altamente significativa com [R.sub.t], cujos coeficientes se mostram superiores a 0,08. Contudo, e intrigante que os lucros de t + 2 e t + 3 tambem nao tenham se mostrado significativos.

Ja em relacao a estimacao envolvendo [VLPA.sub.it+k], observase a inexistencia de poder explicativo, muito embora o lucro em t + 1 apresente um coeficiente significativo. E dificil interpretar esses resultados, alem daquilo que se observou com o coeficiente de correlacao: ha uma fraca correlacao entre o retorno corrente e a variacao do lucro em t + 1. Isso se alinha com a ideia do prices lead earnings, porem nao representa uma evidencia empirica robusta.

Essas constatacoes podem ser atribuidas aos erros de mensuracao dessas variaveis. Conforme ja mencionado na secao anterior, essas variaveis possuem parcelas informacionais que nao se correlacionam com o retorno corrente, mas sim com os retornos passados e, no caso dos lucros futuros, tambem com os retornos a eles contemporaneos (futuros). Esses erros causam vieses nos estimadores e afetam o poder explicativo dos modelos, pois essas parcelas informacionais representam variaveis omitidas. A inclusao de retornos futuros tende a mitigar parte desses problemas. O modelo (9) contemplou essa alternativa.

Os resultados sugerem que a inclusao dos retornos futuros reduziu parte dos problemas apresentados pelo modelo (8). Percebe-se, inicialmente, que nao ha mais a indicacao da presenca de efeitos aleatorios no modelo. O poder explicativo das estimacoes foi sensivelmente aprimorado, passando de 1,99% para 4,53%, e de 0,01%, para 3,51%. Ja a significancia dos coeficientes ficou, praticamente, inalterada. Importante notar que, dos retornos incluidos, [R.sub.t+1] apresentou coeficiente significativo na relacao com [LPA.sub.it+k]/[p.sub.it-(1-k)], e [R.sub.t+2] e [R.sub.t+3], na estimacao envolvendo a variavel VLPA. Ainda nesta estimacao, a variavel [VLAP.sub.t+3] tambem passou a apresentar um coeficiente significativo.

Esses resultados sugerem que nao e possivel descartar a relacao contemporanea, porem somente de forma incremental aos lucros de periodos futuros e que retornos futuros podem aprimorar o poder explicativo do modelo, constatacao que se alinha as premissas assumidas neste estudo.

A fim de explorar essa ultima constatacao, o modelo (7) foi estimado por meio de um stepwise forward para os lucros futuros, de forma isolada e incremental. Nessa tarefa, so foi considerada a variavel [LPA.sub.it-k]/[p.sub.it(1-k)], em razao de ter apresentado melhores resultados nas estimacoes como um todo. Em todos os passos, foi incluida a variavel [R.sub.t+1], dada a sua significancia na estimacao do modelo (9).

Os resultados confirmam que a relacao contemporanea entre o lucro e o retorno somente e revelada quando considerados os lucros futuros na estimacao. Isso ocorreu com a inclusao dos lucros em t + 1, t + 2 e t + 3, isolada ou conjuntamente. Verifica-se tambem que o poder explicativo do modelo aumentou quase que monotonicamente, com a inclusao gradativa dessas variaveis, indo de 3,52% a 4,50%. [R.sub.t+1] se mostrou significativo em todas as estimacoes e desempenhou um papel importante, uma vez que a sua inclusao gerou componentes fixos transversais, exigindo, assim, a estimacao por meio do modelo de efeitos fixos, cujo nivel de controle da idiossincrasia das firmas tambem contribuiu para o aprimoramento do poder explicativo das estimacoes, conforme foi possivel constatar em simulacoes realizadas sem essa variavel.

Apesar da significancia do lucro corrente observada nos modelos (6) e (7) e nas ultimas estimacoes, a dependencia dos lucros dos periodos seguintes, aparentemente, enfraquece a evidencia de sua contemporaneidade com [R.sub.t]. Entretanto, o que se observa e que existe uma parcela informacional contida no lucro corrente que e contemporanea a [R.sub.t], mas que so pode ser obtida depois de eliminados os efeitos dos lucros dos periodos seguintes sobre ela. Essa constatacao e condizente com Kothari (1992) e Kothari e Zimmerman (1995), pois evidencia a parcela [s.sub.t], que representa a porcao do lucro corrente que e surpresa para o mercado e, portanto, correlacionada com [R.sub.t].

Interessante notar que, alem da significancia do coeficiente do lucro corrente, tambem se observa, em todas as estimacoes, o aumento da sua magnitude, em termos absolutos, sugerindo assim que os efeitos de st sobre [R.sub.t] sao representativos, porem obscurecidos pela omissao da parcela [N.summation over (n=1)] [[alpha].sub.t+k,t+n]. A indicacao de uma relacao negativa contraria a teoria, no entanto e possivel que possa ser explicado pelos efeitos do conservadorismo, que impoe um vies voltado as mas noticias sobre [s.sub.t], o que se alinha aos resultados obtidos por Paulo, Sarlo Neto, e Santos (2012).

Um outro aspecto que merece ser contemplado na presente analise refere-se aos possiveis efeitos decorrentes da recente adocao das normas internacionais de contabilidade no Brasil sobre a relacao retorno-lucro. As evidencias reunidas a respeito indicam que a capacidade associativa do lucro contabil teria sido aprimorada (Lima, 2010, Rodrigues, 2012), por outro lado, dimensoes como o conteudo informacional, o conservadorismo, a tempestividade e a persistencia nao teriam sido impactadas pela adocao do novo conjunto normativo contabil (Lima, 2010, Rodrigues, 2012, Santos, Lima, Freitas, & Lima, 2011).

Esses resultados sugerem que a adocao das normas internacionais tenha gerado efeitos residuais sobre o nivel temporal da relacao retorno-lucro, sobretudo em funcao das constatacoes relacionadas a tempestividade e ao conservadorismo. Alem disso, mesmo considerando o aprimoramento da capacidade associativa do lucro contabil, verifica-se que, com base nas constatacoes obtidas com os modelos (7) e (8), a melhora nessa capacidade nao teria sido suficiente para eliminar a nao contemporaneidade. Contudo, vale salientar que a janela de tempo aqui analisada considera os periodos pre e pos adocao daquelas normas, o que pode obscurecer a constatacao dos seus efeitos.

5 CONSIDERACOES FINAIS

O presente estudo teve como objetivo identificar o nivel temporal da relacao retorno-lucro no cenario brasileiro, uma vez que foi assumido que esse nivel e um indicador da hipotese prices lead earnings. A investigacao se desenvolveu por meio de 4 modelos econometricos, baseados na proposta de Beaver et al. (1980) e Collins et al. (1994).

Os resultados obtidos, de uma maneira geral, sao coerentes com os pressupostos teoricos aqui explorados, pois ha evidencias de que os retornos antecipam informacoes acerca dos lucros futuros e de que a representatividade do lucro corrente e residual. As constatacoes sugerem que os precos possuem conteudo informacional em relacao aos lucros futuros, indicando, assim, que o fenomeno prices lead earnings ocorre no Brasil

Especificamente no que se refere as hipoteses de pesquisa, tem-se a rejeicao da hipotese [H.sub.0a], uma vez que os resultados obtidos com os modelos (6) e (7) nao evidenciaram a contemporaneidade da relacao retorno-lucro. Muito embora a inclusao, conjunta ou isolada, de lucros trimestrais futuros na estimacao tenha revelado esse nivel temporal. Verificou-se, assim, que a eliminacao dos efeitos dos lucros futuros sobre o lucro corrente na mensuracao da associacao entre este e o retorno corrente trouxe a tona a representatividade informacional da parcela [s.sub.t].

Os resultados obtidos com a regressao reversa, modelo (6), indicaram que os retornos trimestrais antecipam informacoes contidas nos lucros trimestrais futuros, levando assim a rejeicao da hipotese [H.sub.0b]. Vale registrar que essa antecipacao teria ocorrido ha, pelo menos, 8 trimestres, processo que se estendeu ate o trimestre imediatamente anterior ao corrente. Esses resultados foram condizentes com aqueles obtidos com os modelos (7) e (9), no tocante a capacidade associativa dos lucros de trimestres futuros com o retorno corrente.

No entanto, apesar das evidencias empiricas acima mencionadas, nao foi possivel precisar o nivel temporal da relacao retorno-lucro trimestral no Brasil, pois constatou-se que, se de um lado os retornos passados associam-se aos lucros correntes, de outro, a significancia dos lucros futuros na explicacao dos retornos correntes depende do arranjo de variaveis independentes consideradas no modelo. A evidencia de contemporaneidade entre o retorno e o lucro corrente, mesmo que dependente da inclusao de lucros futuros, nao permite afastar a indicacao da existencia de um nivel temporal igual a zero, rejeitando-se, assim, a hipotese [H.sub.0c].

Outrossim, uma verificacao adicional refere-se a superioridade da variavel [LPA.sub.it]/[p.sub.it-1], em relacao a [VLPA.sub.it] no tocante a sua representacao do lucro contabil nas relacoes analisadas, indo ao encontro dos resultados apresentados por Kothari (1992).

As constatacoes realizadas neste estudo contribuem com a literatura nacional na medida em que oferecem uma maior compreensao de aspectos temporais da relacao retorno-lucro no cenario brasileiro, tema pouco explorado sob a perspectiva aqui empregada, e indicam que e possivel aprimorar os modelos voltados a investigacao da capacidade associativa do lucro corrente por meio de um refinamento metodologico, com a inclusao de lucros futuros, pelo menos, relativos a um periodo, contribuindo assim com o avanco das pesquisas na area. Em um sentido pratico, a indicacao acerca da capacidade preditiva do retorno das acoes de firmas brasileiras em relacao aos seus lucros futuros sugere, para investidores, analistas financeiros, firmas e credores, que o retorno da acao pode representar uma fonte informacional util nas suas avaliacoes acerca da capacidade de geracao de lucros das firmas. Por outro lado, como os resultados aqui apresentados demonstram, em certa medida, o quao intempestivo e o lucro contabil, eles podem ser um indicativo, pelo menos para os investidores, de uma deficiencia qualitativa da informacao contabil, de modo que podem oferecer subsidios para os normatizadores e reguladores na avaliacao da utilidade da informacao contabil-financeira que e divulgada no Brasil para aqueles usuarios e, em ultima instancia, na adequacao dos padroes contabeis observados.

O presente estudo apresenta uma serie de limitacoes metodologicas, dentre elas, a ausencia de: (i) uma analise especifica acerca das propriedades das series temporais do lucro contabil e dos seus componentes; (ii) uma avaliacao efetiva dos efeitos da adocao das normas internacionais; e (iii) uma analise direta acerca da influencia de fatores de mercado, tais como caracteristicas dos investidores, estrutura de governanca das firmas, cobertura dos analistas etc. Contudo, cada uma dessas limitacoes, dada a amplitude das investigacoes empiricas a elas necessarias e a complexidade do tema, oferece interessantes avenidas de pesquisa que devem ser exploradas a fim de avancar na compreensao da relacao retorno-lucro, pilar fundamental da pesquisa contabil em mercado de capitais.

Referencias

Ayers, B. C., & Freeman, R. N. (2000). Why do large firms' price antecipate earnings earlier than small firms' price? Contemporary Accounting Research, 17(2), 191-212.

Ayers, B. C., & Freeman, R. N. (2003). Evidence that analyst following and institutional ownership accelerate the pricing of future earnings. Review of Accounting Studies, 8, 47-67.

Basu, S. (1997). The conservatism principle and the asymmetric timeliness of earnings. Journal of Accounting and Economics, 24 (1), 3-37.

Beaver, W., Lambert, R., & Morse, D. (1980). The information content of security prices. Journal of Accounting and Economics, 2 (1), 3-28.

Collins, D. W., Kothari, S. P., Shanken, J., & Sloan, R. G. (1994). Lack of timeliness and noise as explanations for the Low Contemporaneous Return-Earnings Association. Journal of Accounting and Economics, 18 (3), 289-324.

Galdi, F. G., & Lopes, A. B. (2008). Relacao de longo prazo e causalidade entre o lucro contabil e o preco das acoes: evidencias do mercado latino-americano. Revista de Administracao da USP, 43 (2), 186-201.

Jiambalvo, J., Rajgopal, S., & Venkatachalam, M. (2002). Institutional ownership and extent to which stocks prices reflect future earnings. Contemporary Accounting Research, 19 (1), 117-145

Kothari, S. P. (1992). Price-earnings regressions in the presence of prices lead earnings: earnings level versus change specifications and alternative deflators. Journal of Accounting and Economics, 15 (2-3), 173-202.

Kothari, S. P. (2001). Capital markets research in accounting. Journal of Accounting and Economics, 31 (1-3), 105-231.

Kothari, S. P., & Sloan, R. G. (1992). Information in price about future earnings: implications for earnings response coefficients. Journal of Accounting and Economics, 15 (2-3), 143-171.

Kothari, S. P., & Zimmerman, J. L. (1995). Price and return models. Journal of Accounting and Economics, 20 (2), 155-192.

Lee, J. J. (2007, August). Cross-sectional determinants of the extent to which stock prices earnings. Working paper: Hong Kong Baptist University. Recuperado em 1 fevereiro, 2013, de http://www.af.polyu. edu.hk/jcae_af/paper2008/concurrent/S.4a%20Lee.pdf.

Lev, B. (1989). On the usefulness of earnings and earning research: lessons and directions from two decades of empirical research. Journal of Accounting Research, 27, 153-192.

Lima, J. B. N. (2010). A relevancia da informacao contabil e o processo de convergencia para as Normas IFRS no Brasil. Tese de doutorado, Programa de Pos-Graduacao em Ciencias Contabeis, Departamento de Contabilidade e Atuaria, Faculdade de Economia, Administracao e Contabilidade da Universidade de Sao Paulo, Sao Paulo, SP, Brasil.

Paulo, E., Sarlo Neto, A., & Santos, M. A. C. (2012). Reacao do preco das acoes e intempestividade informacional do lucro contabil trimestral no Brasil. Advances in Scientific and Applied Accounting, 5 (1), 54-79.

Pimentel, R. C., & Lima, I. S. (2010). Time-series properties of earnings and their relationship with stock prices in Brazil. Business and Economics Research Journal, 1 (4), 43-65.

Rodrigues, J. M. (2012). Convergencia contabil internacional: uma analise da qualidade da informacao contabil em razao da adocao dos padroes internacionais de contabilidade editados pelo IASB. Tese de doutorado, Programa Multi-institucional e Inter-regional de PosGraduacao em Ciencias Contabeis, UnB, UFPB, UFRN, Brasil.

Sales, I. C. H. (2011). A dinamica da relacao entre os lucros contabeis e os retornos acionarios nas empresas brasileiras de capital aberto. Dissertacao de mestrado, Programa Multi-institucional e InterRegional de Pos-Graduacao em Ciencias Contabeis UnB, UFPB, UFRN, Universidade de Brasilia, Brasilia, DF, Brasil.

Santos, L. P. G., Lima, G. A. S. F., Freitas; S. C., & Lima, I. S. (2011). Efeito da Lei 11.638/07 sobre o conservadorismo condicional das empresas listadas BM&FBOVESPA. Revista Contabilidade e Financas--USP, Sao Paulo, 22 (56), 174-188.

Santos, M. A. C., & Lustosa, P. R. B. (2010). Importancia relativa do conteudo informacional do resultado contabil no mercado acionario brasileiro. Anais do Congresso USP de Controladoria e Contabilidade, Sao Paulo, SP, Brasil, 10.

Truong, C. (2012). Options trading and the extent that stock prices lead future earnings information. Journal of Business Finance & Accounting, 39 (7-8), 960-996.

(1) Os problemas apresentados pelo modelo tradicional da relacao retorno-lucro ha muito tempo vem sendo discutidos na literatura contabil. Exemplo disso e o estudo de Lev (1989).

(2) Apesar de inapropriada, foi realizada a estimacao por meio do modelo de efeitos fixos e verificou-se que o [R.sup.2] ajustado foi igual a -1,83%. Esse resultado indica que o baixo poder explicativo verificado nao se deve a tecnica de estimacao utilizada. Isso corrobora a constatacao do baixo poder explicativo oferecido por VLPA.

Mateus Alexandre Costa dos Santos

Master in Accounting Sciences and Doctoral candidate of the Multi-institutional and Inter-regional Graduate Program of Accounting Sciences,--Federal University of Brasilia, Federal University of Paraiba, Federal University of Rio Grande do Norte

E-mail: mateusalexandrecs@hotmail.com

Anderson Luiz Rezende Mol

Ph.D., Department of Administrative Sciences, Federal University of Rio Grande do Norte

E-mail: mol@ufrnet.br

Luiz Carlos Marques dos Anjos

Master, School of Economics, Administration and Accounting, Federal University of Alagoas

E-mail: luiz@consultorcontabil.com

Josicarla Soares Santiago

Master, Department of Applied Social Sciences, Federal University of Paraiba

Email: josicarlass@yahoo.com.br

Received on 9-29-2012--Desk acceptance on 10.3.2012--3rd version approved on 6.4.2013

Tabela 1

Estatisticas descritivas

Variavel                     Media    Mediana    Minimo

[LPA.sub.it]/[p.sub.it-1]   -0,0460   0,0255     -8,8334
[VLPA.sub.it]               0,0059    0,0358     -3,2736
[PLA.sub.it]/[p.sub.it-1]   0,4964    0,8294    -244,3480
[R.sub.t]                   0,0452    0,0356     -0,6124
[R.sub.t-1]                 0,0426    0,0333     -0,6251
[R.sub.t-2]                 0,0423    0,0319     -0,6668
[R.sub.t-3]                 0,0466    0,0383     -0,6931
[R.sub.t-4]                 0,0470    0,0382     -0,6729
[R.sub.t-6]                 0,0522    0,0414     -0,6931
[R.sub.t-8]                 0,0556    0,0458     -0,7418

Variavel                     Maximo    Desvio Padrao

[LPA.sub.it]/[p.sub.it-1]    0,5318       0,5092
[VLPA.sub.it]                3,2991       0,9253
[PLA.sub.it]/[p.sub.it-1]   107,5110      12,1136
[R.sub.t]                    0,8755       0,2104
[R.sub.t-1]                  0,8097       0,2111
[R.sub.t-2]                  0,8214       0,2141
[R.sub.t-3]                  0,8396       0,2202
[R.sub.t-4]                  0,8206       0,2217
[R.sub.t-6]                  0,8745       0,2325
[R.sub.t-8]                  0,9676       0,2407

[LPA.sub.it] e o lucro liquido por acao da firma i no
trimestre t.

[p.sub.it-1] e o preco da acao da firma i no termino do
trimestre t-1.

[VLPA.sub.it] e a taxa de crescimento do LPAi, obtida
pelo logaritmo natural da diferenca entre os LPAs em
t e t-1.

[R.sub.it] e o retorno logaritmico da acao da firma i
no trimestre t (t-1 ... t-8).

[PLA.sub.it] e o patrimonio liquido por acao da firma i
no trimestre t, e utilizada como proxy de tamanho para
fins de controle.

Tabela 2

Matriz de correlacao

                [LPA.sub.it]/   [VLPA.sub.it]   [R.sub.t]
                [p.sub.it-1]

[LPA.sub.it]/         1           -0,0283 *     0,0640 ***
[p.sub.it-1]

[VLPA.sub.it]                         1          -0,0184

[R.sub.t]                                           1

[R.sub.t-1]

[R.sub.t-2]

[R.sub.t-3]

[R.sub.t-4]

[R.sub.t-6]

[R.sub.t-8]

[PLA.sub.it]/
[p.sub.it-1]

                [R.sub.t-1]   [R.sub.t-2]   [R.sub.t-3]   [R.sub.t-4]

[LPA.sub.it]/   0,0917 ***    0,0574 ***    0,0718 ***    0,0554 ***
[p.sub.it-1]

[VLPA.sub.it]     -0,0234       0,0159      0,0461 ***      0,0069

[R.sub.t]       0,1263 ***      0,0111      -0,0349 **      0,0116

[R.sub.t-1]          1        0,0937 ***     0,0300 *       -0,0245

[R.sub.t-2]                        1        0,1045 ***     0,0265 *

[R.sub.t-3]                                      1        0,0998 ***

[R.sub.t-4]                                                    1

[R.sub.t-6]

[R.sub.t-8]

[PLA.sub.it]/
[p.sub.it-1]

                [R.sub.t-6]   [R.sub.t-8]   [PLA.sub.it]/
                                            [p.sub.it-1]

[LPA.sub.it]/   0,0647 ***     0,0327 **     0,7056 ***
[p.sub.it-1]

[VLPA.sub.it]   -0,0352 **     0,0352 **       -0,0029

[R.sub.t]       -0,0691 ***   -0,0803 ***     0,0329 **

[R.sub.t-1]     -0,0473 ***   -0,0908 ***      0,0018

[R.sub.t-2]       -0,0011     -0,0780 ***      -0,0049

[R.sub.t-3]     -0,0445 ***   -0,0509 ***      0,0138

[R.sub.t-4]       0,0107        0,0000         0,0093

[R.sub.t-6]          1         0,0271 *        0,0156

[R.sub.t-8]                        1           0,0193

[PLA.sub.it]/                                     1
[p.sub.it-1]

*, ** e ***--significante a 10%, 5% e 1%, respectivamente.

Tabela 3

Resultados Modelo (6)

[X.sub.it] = [[beta].sub.0] + [4.summation over (k=0)]
[[beta].sub.k+1][R.sub.it-k] + [[beta].sub.6][R.sub.it-6]
+ [[beta].sub.7][R.sub.it-8] + [[beta].sub.8]
[[PLA.sub.it]/[p.sub.t-1]] + [[epsilon].sub.it]

Coeficientes               [X.sub.it]

                 [LPA.sub.it]/    [VLPA..sub.it]
                  [p.sub.it-1]

[[beta].sub.0]      -0,0785           0,0006
                 (-15,7777) ***      (0,0364)

[[beta].sub.1]       0,0369          -0,0596
                   (1,7850) *       (-0,8658)

[[beta].sub.2]       0,1499          -0,1003
                  (7,2805) ***      (-1,4568)

[[beta].sub.3]       0,0614           0,0702
                  (3,0427) ***       (1,0391)

[[beta].sub.4]       0,0818           0,1877
                  (4,1406) ***     (2,8528) ***

[[beta].sub.5]       0,0651           0,0083
                  (3,3707) ***       (0,1281)

[[beta].sub.6]       0,0601          -0,1441
                  (3,2354) ***     (-2,3344) **

[[beta].sub.7]       0,0346           0,1409
                   (1,9238) *      (2,3483) **

[[beta].sub.8]       0,0200          -0,0002
                 (18,4664) ***      (-0,2039)

Modelagem do     Efeitos Fixos       Efeitos
Painel                              Aleatorios

Teste de Chow     18,6574 ***        2,2795 *

Teste de          47,4286 ***        5,27543
Hausman

Teste de                           24,0171 ***
Breusch-Pagan

[R.sup.2]            73,47%           0,38%
ajustado

F                 52,57603 ***          --

Numero de observacoes: 4.177. Foram excluidos os valores
extremos que correspondiam aos primeiro e ultimos percentis
da serie de cada variavel, com excecao da variavel de
controle. [X.sub.it] e a variavel dependente do modelo. Foram
realizadas 2 estimacoes, onde [Y.sub.it] assumiu, em cada uma
delas, [LPA.sub.it]/[p.sub.it-1] e [VLPA.sub.it]. A estatistica
t dos coeficientes e apresentada entre parenteses e abaixo de
cada um deles.

*, ** e ***--significante a 10%, 5% e 1%, respectivamente.

Tabela 4 Estatisticas descritivas

Variavel           Media     Mediana    Minimo     Maximo    Desvio
                                                             Padrao

[R.sub.t]          0,0658    0,0568     -0,6668    0,8881    0,2155
[LPA.sub.it]/     -0,0767    0,0316    -11,4879    0,5131    0,7829
  [p.sub.it-1]
[LPA.sub.it+1]/   -0,0807    0,0306    -11,5601    0,4714    0,7851
  [p.sub.it]
[LPA.sub.it+2]/   -0,0909    0,0298    -16,7955    0,4116    0,8518
  [p.sub.it+1]
[LPA.sub.it+3]/   -0,09101   0,0285    -16,7955    0,3612    0,8704
  [p.sub.it+2]
[VLPA.sub.it]      0,0464    0,0565     -2,7939    2,9545    0,7429
[VLPA.sub.t+1]     0,0360    0,0503     -2,7324    2,8491    0,7113
[VLPA.sub.t+2]     0,0363    0,0537     -2,7657    2,6974    0,7007
[VLPA.sub.t+3]     0,0014    0,0382     -2,9108    2,7131    0,7312
[R.sub.t+1]        0,0563    0,0455     -0,6497    0,8214    0,2065
[R.sub.t+2]        0,0460    0,0375     -0,6497    0,8097    0,2030
[R.sub.t+3]        0,0394    0,0356     -0,6493    0,7691    0,1988
[PLA.sub.it]/     -0,6774    0,7887    -490,6530   92,4912   21,4974
  [p.sub.it-1]

[LPA.sub.it] e o lucro liquido por acao da firma i no trimestre t
(t+1, t+2, t+3).

[p.sub.it] e o preco da acao da firma i no termino do trimestre t
(t-1, t+1, t+2).

[VLPA.sub.it]. e a taxa de crescimento do [LPA.sub.it], obtida
pelo logaritmo natural da diferenca entre os LPAs em t e t-1.

[R.sub.it] e o retorno logaritmico da acao da firma i no
trimestre t (t-8 ... t-1, ..., t+1 ... t+3).

[PLA.sub.it] e o patrimonio liquido por acao da firma i no
trimestre t, e utilizada como proxy de tamanho para fins de
controle.

Tabela 5 Matriz de correlacao

                  [R.sub.t]   [LPA.sub.it]/   [LPA.sub.it+1]/
                              [p.sub.it-1]      [p.sub.it]

[R.sub.t]             1         0,0303 *        0,0865 ***
[LPA.sub.it]/                       1            0,859 ***
  [p.sub.it-1]                                       1
[LPA.sub.it+1]/
  [p.sub.it]
[LPA.sub.it+2]/
  [p.sub.it+1]
[LPA.sub.it+3]/
  [p.sub.it+2]
[VLPA.sub.it]
[VLPA.sub.t+1]
[VLPA.sub.t+2]
[VLPA.sub.t+3]
[R.sub.t+1]
[R.sub.t+2]
[R.sub.t+3]
[PLA.sub.it]/
  [p.sub.it-1]

                  [LPA.sub.it+2]/   [LPA.sub.it+3]/   [VLPA.sub.it]
                   [p.sub.it+1]      [p.sub.it+2]

[R.sub.t]           0,0803 ***        0,0887 ***         0,0221
[LPA.sub.it]/       0,8353 ***        0,7831 ***         -0,0272
  [p.sub.it-1]      0,8787 ***        0,8768 ***        0,009 ***
[LPA.sub.it+1]/
  [p.sub.it]             1            0,8951 ***         0,0038
[LPA.sub.it+2]/
  [p.sub.it+1]                             1             0,0109
[LPA.sub.it+3]/
  [p.sub.it+2]                                              1
[VLPA.sub.it]
[VLPA.sub.t+1]
[VLPA.sub.t+2]
[VLPA.sub.t+3]
[R.sub.t+1]
[R.sub.t+2]
[R.sub.t+3]
[PLA.sub.it]/
  [p.sub.it-1]

                  [VLPA.sub.t+1]   [VLPA.sub.t+2]   [VLPA.sub.t+3]

[R.sub.t]           -0,0327 *          0,0015           0,019
[LPA.sub.it]/        0,0309 *         -0,0012           0,0248
  [p.sub.it-1]       -0,0192           0,0196           0,0086
[LPA.sub.it+1]/
  [p.sub.it]         -0,0048           -0,027         0,0378 **
[LPA.sub.it+2]/
  [p.sub.it+1]        -0,007          -0,0001          -0,0124
[LPA.sub.it+3]/
  [p.sub.it+2]     -0,3888 ***      -0,0482 ***      -0,1229 ***
[VLPA.sub.it]
[VLPA.sub.t+1]          1           -0,3876 ***       -0,055 ***
[VLPA.sub.t+2]                           1           -0,3694 ***
[VLPA.sub.t+3]                                            1
[R.sub.t+1]
[R.sub.t+2]
[R.sub.t+3]
[PLA.sub.it]/
  [p.sub.it-1]

                  [R.sub.t+1]   [R.sub.t+2]   [R.sub.t+3]

[R.sub.t]         0,0986 ***     0,0389 **      -0,0127
[LPA.sub.it]/      0,0308 *       0,0171       0,0397 **
  [p.sub.it-1]     0,0403 **     0,0341 **      0,0247
[LPA.sub.it+1]/
  [p.sub.it]      0,0833 ***     0,0411 **    0,0503 ***
[LPA.sub.it+2]/
  [p.sub.it+1]    0,0714 ***    0,0830 ***    0,0482 ***
[LPA.sub.it+3]/
  [p.sub.it+2]    0,0734 ***     0,0300 *       -0,0123
[VLPA.sub.it]
[VLPA.sub.t+1]       0,004      0,0627 ***     0,0276 *
[VLPA.sub.t+2]     -0,0281 *      -0,0141     0,0507 ***
[VLPA.sub.t+3]      0,0072        0,0037        0,0215
[R.sub.t+1]            1        0,1000 ***      0,0109
[R.sub.t+2]                          1        0,1075 ***
[R.sub.t+3]                                        1
[PLA.sub.it]/
  [p.sub.it-1]

                  [PLA.sub.it]/
                  [p.sub.it-1]

[R.sub.t]            0,0092
[LPA.sub.it]/        0,7824
  [p.sub.it-1]       0,7608
[LPA.sub.it+1]/
  [p.sub.it]         0,7411
[LPA.sub.it+2]/
  [p.sub.it+1]       0,7376
[LPA.sub.it+3]/
  [p.sub.it+2]          0
[VLPA.sub.it]
[VLPA.sub.t+1]       0,0025
[VLPA.sub.t+2]       -0,0062
[VLPA.sub.t+3]       0,0007
[R.sub.t+1]          0,0081
[R.sub.t+2]          0,0087
[R.sub.t+3]          0,0216
[PLA.sub.it]/           1
  [p.sub.it-1]

*, ** e ***--significante a 10%, 5% e 1%, respectivamente.

Tabela 6 Resultados Modelo (7)

[R.sub.it] = [[beta].sub.0] + [[beta].sub.1][X.sub.it] +
[[beta].sub.2] [[PLA.sub.it]/[p.sub.it-1]] +
[[epsilon].sub.it]

Coeficientes     [X.sub.it]

                 [LPA.sub.it]/   [VLPA.sub.it]
                 [p.sub.it-1]

[[beta].sub.0]   0,0640          0,0649
                 (17,0800) ***   (17,5682) ***
[[beta].sub.1]   -0,0183         0,0050
                 (-1,6860) *     (0,9860)
[[beta].sub.2]   -0,0006         -0,0010
                 (-1,2180)       (-2,3093) **

Modelagem        Efeitos         Efeitos
do Painel        Fixos           Fixos

Teste de Chow    3,0406 **       5,4102 **
Teste de         14,8883 ***     7,2134 ***
  Hausman
[R.sup.2]        3,33%           3,27%
  ajustado
F                1,5862 ***      1,5757 ***

Numero de observacoes: 3.321. Foram excluidos os valores extremos
que correspondiam aos primeiro e ultimos percentis da serie de
cada variavel, com excecao da variavel de controle. Xtl e uma das
variaveis independentes do modelo. Foram realizadas 2 estimacoes,
onde Xtl assumiu, em cada uma delas [LPA.sub.it]/[p.sub.it-1] e
[VLPA.sub.it]. A estatistica t dos coeficientes e apresentada
entre parenteses e abaixo de cada um deles.

*, ** e ***--significante a 10%, 5% e 1%, respectivamente.

Tabela 7 Resultados Modelo (8)

[R.sub.it] = [[beta].sub.0] + [3.summation over (k = 0)]
[[beta].sub.k+1][X.sub.it+k] + [[beta].sub.5]
[[PLA.sub.it]/[p.sub.it-1]] + [[epsilon].sub.it]

Coeficientes         [X.sub.it+k]

                     [LPA.sub.it+k]/    [VLPA.sub.it+k]
                     [p.sub.it-(1-k)]

[[beta].sub.0]            0,0676            0,0625
                       (9,1450) ***      (8,2171) ***
[[beta].sub.1]           -0,0384            0,0033
                      (-3,5800) ***        (0,5731)
[[beta].sub.2]            0,0440            -0,0008
                       (3,5542) ***      (-1,1930) **
[[beta].sub.3]            0,0159            -0,0006
                         (1,4078)          (0,0872)
[[beta].sub.4]            0,0192            0,0050
                        (1,7903) *         (0,8595)
[[beta].sub.5]           -0,0010            -0,0002
                      (-2,8126) ***        (-0,6780)

Modelagem                Efeitos            Efeitos
do Painel               Aleatorios        Aleatorios

Teste de Chow           2 8115 ***        4,5867 ***
Teste de Hausman          4,2871            7,2 763
Teste de                  0,0521            0,7722
  Breusch-Pagan
[R.sup.2] ajustado        1,99%              0,01%

Numero de observacoes: 3.321. Foram excluidos os valores extremos
que correspondiam aos primeiro e ultimos percentis da serie de
cada variavel, com excecao da variavel de controle. [X.sub.it] e
uma das variaveis independentes do modelo. Foram realizadas 2
estimacoes, onde [X.sub.it] assumiu, em cada uma delas
[LPA.sub.it+k]/[p.sub.it-(1-k)] e [VLPA.sub.it]. A estatistica t
dos coeficientes e apresentada entre parenteses e abaixo de cada
um deles.

*, ** e ***--significante a 10%, 5% e 1%, respectivamente.

Tabela 8 Resultados Modelo (9)

[R.sub.it] = [[beta].sub.0] + [3.summation over (k=0)]
[[beta].sub.k+1][X.sub.it+k] + [3.summation over (k=1)]
[[beta].sub.k+4][R.sub.it+k] + [[beta].sub.8]
[[PLA.sub.it]/[p.sub.it-1]] + [[epsilon].sub.it]

Coeficientes     [X.sub.it+k]

                 [LPA.sub.it+k]/        [VLPA.sub.it+k]
                 [p.sub.it-(1-k)]

[[beta].sub.0]   0,0681 (16,5422) ***   0,0642 (16,0316) ***
[[beta].sub.1]   -0,0379 (3,2902) ***   0,0018 (0,3102)
[[beta].sub.2]   0,0407 (3,1436) ***    -0,0072 (-1,0394)
[[beta].sub.3]   0,0132 (1,1388)        0,0008 (0,1134)
[[beta].sub.4]   0,0220 (1,8280) *      0,0050 (0,8325) ***
[[beta].sub.5]   0,0435 (2,3450) **     0,0083 (0,1281)
[[beta].sub.6]   -0,0070 (-0,3701)      -0,1441 (-2,3344) **
[[beta].sub.7]   -0,0329 (-1,6989) *    0,1409 (2,3483) **
[[beta].sub.8]   -0,0007 (1,3881)       -0,0002 (-0,2039)

Modelagem do     Efeitos Fixos          Efeitos Fixos
Painel

Teste de Chow    4,9077 ***             5,7257 ***
Teste de         47,9602 ***            55,5329 ***
  Hausman
[R.sup.2]        4,53%                  3,51%
  ajustado
F                1,7845 ***             1,6006 ***

Numero de observacoes: 3.321. Foram excluidos os valores extremos
que correspondiam aos primeiro e ultimos percentis da serie de
cada variavel, com excecao da variavel de controle. [X.sub.it] e
uma das variaveis independentes do modelo. Foram realizadas 2
estimacoes, onde [X.sub.it] assumiu, em cada uma delas,
[LPA.sub.it]/[p.sub.it-1] e [VLPA.sub.it]. A estatistica t dos
coeficientes e apresentada entre parenteses e abaixo de cada um
deles.

*, ** e ***--significante a 10%, 5% e 1%, respectivamente.

Tabela 9

Resultados Modelo (7)--Analise adicional

Variaveis          Estimacoes

                           (a)                     (b)

                   Coeficientes

Constante          0,0613 (15,7900) ***   0,0646 (16,4900) ***
[LPA.sub.it]/      -0,0181 (-1,6700) *    -0,0354 (-3,1410) ***
  [p.sub.it-1]
[LPA.sub.it-1]/                            0,0595 (5,2530) ***
  [p.sub.it]
[LPA.sub.it-2]/
  [p.sub.it+1]
[LPA.sub.it-3]/
  [p.sub.it+2]
[R.sub.t+1]        0,0491 (2,6520) ***     0,0489 (2,6550) ***
[LPA.sub.it]/       -0,0005 (-1,1080)      -0,0009 (-1,8380) *
  [p.sub.it-1]
Teste de Hausman       50,6856 ***             42,8122 ***
[R.sup.2]                 3,52%                   4,33%
  ajustado
F                       1,6171 ***             1,7626 ***

Variaveis          Estimacoes

                            (c)                    (d)

                   Coeficientes

Constante          0,0642 (16,2700) ***    0,0653 (16,4800) ***
[LPA.sub.it]/      -0,0306 (-2,7090) ***   -0,0246 (-2,2610) **
  [p.sub.it-1]
[LPA.sub.it-1]/
  [p.sub.it]
[LPA.sub.it-2]/     0,0378 (3,8270) ***
  [p.sub.it+1]
[LPA.sub.it-3]/                             0,0447 4,6380) ***
  [p.sub.it+2]
[R.sub.t+1]         0,0423 (2,2800) ***     0,0440 (2,3810) **
[LPA.sub.it]/        -0,0005 (-0,9982)      -0,0003 (-0,5711)
  [p.sub.it-1]
Teste de Hausman        43,0311 ***            38,8427 ***
[R.sup.2]                  3,93%                  4,14%
  ajustado
F                       1,6903 ***              1,7287 ***

Variaveis          Estimacoes

                            (e)                     (f)

                   Coeficientes

Constante          0,0657 (16,6200) ***    0,0666 (16,7300) ***
[LPA.sub.it]/      -0,0400 (-3,4810) ***   -0,0379 (-3,2860) ***
  [p.sub.it-1]
[LPA.sub.it-1]/     0,0503 (4,1440) ***    0,0423 (3,2 740) ***
  [p.sub.it]
[LPA.sub.it-2]/     0,0219 (2,0680) **        0,0131 (1,1290)
  [p.sub.it+1]
[LPA.sub.it-3]/                              0,0216 (1,8200) *
  [p.sub.it+2]
[R.sub.t+1]         0,0450 (2,4320) **      0,0442 (2,3850) **
[LPA.sub.it]/       -0,0008 (-1,6550) *      -0,0006 (-1,3040)
  [p.sub.it-1]
Teste de Hausman        41,7925 ***             42,2857 ***
[R.sup.2]                  4,43%                   4,50%
  ajustado
F                       1,7772 ***              1,7862 ***

Numero de observacoes: 3.321. Foram excluidos os valores extremos
que correspondiam aos primeiro e ultimos percentis da serie de
cada variavel, com excecao da variavel de controle. As estimacoes
foram realizadas por meio do modelo de efeitos fixos.
A estatistica t dos coeficientes e apresentada entre parenteses
e abaixo de cada um deles.

*, ** e ***--significante a 10%, 5% e 1%, respectivamente.
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Title Annotation:articulo en ingles
Author:dos Santos, Mateus Alexandre Costa; Mol, Anderson Luiz Rezende; dos Anjos, Luiz Carlos Marques; Sant
Publication:Revista Contabilidade & Financas
Date:Sep 1, 2013
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