Seasonal Random Walk Research Articles

Conservatism and Cross‐Sectional Variation in the Post–Earnings Announcement Drift

ABSTRACTAccounting conservatism allows me to identify a previously undocumented source of predictable cross‐sectional variation in Standardized Unexpected Earnings' autocorrelations viz. the sign of the most recent earnings realization and present evidence that the market ignores this variation (“loss effect”). It is possible to earn returns higher than from the Bernard and Thomas (1990) strategy by incorporating this feature. Additionally, the paper shows that the “loss effect” is different from the “cross quarter” effect shown by Rangan and Sloan (1998) and it is possible to combine the two effects to earn returns higher than either strategy alone. Thus, the paper corroborates the Bernard and Thomas finding that stock prices fail to reflect the extent to which quarterly earnings series differ from a seasonal random walk and extends it by showing that the market systematically underestimates time‐series properties resulting from accounting conservatism.

Predictability in Financial Analyst Forecast Errors: Learning or Irrationality?

ABSTRACTIn this paper, we propose a rational learning‐based explanation for the predictability in financial analysts' earnings forecast errors documented in prior literature. In particular, we argue that the serial correlation pattern in analysts' quarterly earnings forecast errors is consistent with an environment in which analysts face parameter uncertainty and learn rationally about the parameters over time. Using simulations and real data, we show that the predictability evidence is more consistent with rational learning than with irrationality (fixation on a seasonal random walk model or some other dogmatic belief).

Audit and Nonaudit Fees and the Market's Reaction to Earnings Announcements

Effective February 05, 2001, publicly traded companies are required to disclose audit and nonaudit fees paid to their external auditors. These fee data have been used to test whether auditor independence is impaired when the external auditor provides nonaudit services to a client, usually by examining whether certain earnings characteristics are related to nonaudit fees in ways that suggest impairment. This paper follows in that tradition by testing whether the earnings response coefficient (ERC), a proxy for earnings quality, is associated with engagement profitability. Residual fees derived from a two-stage regression model that prices audit and nonaudit services simultaneously are used to proxy for engagement profitability. If the market perceives abnormally profitable engagements as a threat to auditor independence, then we would expect the ERC to be lower for firms with positive fee residuals. The paper examines the residual fee-ERC relation for annual earnings announcements immediately before and after first-time fee disclosure. We report results for alternative measures of unexpected earnings (I/B/E/S forecast errors and deviations from a seasonal random walk), different formulations of residual fees (as a dichotomous and continuous variable) and different samples. For total fees and audit fees, there is a positive association between ERCs and the level of residual fees. For nonaudit fees, there is only one combination of unexpected earnings and residual fee formulation where we observe a significantly negative association between ERCs and residual fees. The findings for audit fees are consistent with a market that interprets abnormally high audit fees as a signal of a firm's commitment to high earnings quality. The restrictive conditions under which we find a negative association between nonaudit fees and ERCs provide limited support for the contention that perceived auditor independence is impaired by abnormally high nonaudit fees.

Predictability in Financial Analyst Forecast Errors: Learning or Irrationality?

In this paper, we propose a rational learning-based explanation for the predictability in financial analysts' earnings forecast errors documented in prior literature. In particular, we argue that the serial correlation pattern in analysts' quarterly earnings forecast errors is consistent with an environment in which analysts face parameter uncertainty and learn rationally about the parameters over time. Using simulations and real data, we show that the predictability evidence is more consistent with rational learning than with irrationality (fixation on a seasonal random walk model or some other dogmatic belief).

Differential Earnings Behavior and the Security Market Assessment of Variation in Seasonal Earnings Patterns

We provide new evidence regarding the anomalous security market behavior that pertains to the predictability of abnormal security returns at future quarterly earnings announcements (Bernard and Thomas [1990]) as well as the security market's ability to form quarterly earnings expectations that are consistent with the market factoring in the serial correlation in the seasonally differenced quarterly earnings series (Ball and Bartov [1996]; Soffer and Lys [1999]). Consistent with extant work, we find that just prior to the quarterly earnings announcement date, the security market's expectation of quarterly earnings is consistent with the market recognizing the serial correlation in seasonally differenced quarterly earnings but underestimating its magnitude. When we treat all firms as exhibiting the same quarterly earnings process, our results reinforce the findings of Soffer and Lys (1999) that security market earnings expectations at the beginning of the quarter are consistent with investors not recognizing the serial correlation in the seasonally differenced quarterly earnings series. By distinguishing between those firms whose quarterly earnings process is inconsistent with a seasonal random walk (SRW) process (i.e., “bad-fit” firms) vis-à-vis those firms whose quarterly earnings process is better described by the SRW process (i.e., “good-fit” firms), we provide additional insights on this relationship throughout the quarter leading up to the quarterly earnings announcement date. Specifically, we find that security market expectations of quarterly earnings are consistent with a market that recognizes the differential time-series properties of quarterly earnings. That is, at the beginning of the quarter, for the “bad-fit” (“good-fit”) firms, we find that the security market acts as if it is aware (unaware) of the correct sign of the serial correlation in the seasonally differenced quarterly earnings series. However, the security market still acts as if it underestimates the magnitude of the serial correlation.

Discussion—Differential Earnings Behavior and the Security Market Assessment of Variation in Seasonal Earnings Patterns

Soffer and Lys (1999) investigate the fraction of predictable positive serial autocorrelation in seasonally differenced earnings reflected in stock prices and find no appreciation of serial correlation immediately after quarterly earnings announcements. Bathke, Lorek, and Willinger (2004) reexamine this result by separating firms with earnings that appear to follow a seasonal random walk (good-fit firms) from the remainder (bad-fit firms). They find that the Soffer and Lys result of zero autocorrelation implied by stock prices represents the combination of a negative implied autocorrelation for good-fit firms and a positive implied autocorrelation for bad-fit firms. This discussion considers different interpretations of that finding.

Use of Interim Earnings Information on the Helsinki Stock Exchange

In this paper we study how the market uses the information on current and past interim earnings. Our hypothesis is that investors focus on a comparison of year-to-year changes in interim earnings. We provide further evidence on how the market acts in the face interim earnings announcements in an emerging market. The data is based on the Finnish market covering the years 1992-2002. We found, consistent with Ball and Bartov [1], evidence that investors underestimate the magnitude of the serial correlation in interim earnings. The results suggest that investors use, at least in part, a seasonal random walk model when forming earnings expectations.

Small and Large Trades Around Earnings Announcements: Does Trading Behavior Explain Post-Earnings-Announcement Drift?

This paper analyzes trade-initiation by small and large traders for one year following earnings announcements and examines the predictive ability of event-time trading for future returns. With earnings surprises based on a seasonal random walk expectations model, small traders react slightly more weakly than large traders, during the event window, to the first surprise in a series of similar surprises, but more strongly than large traders to the later surprises. With earnings surprises based on analyst forecasts, small traders react more weakly than large traders regardless of the past series. Large traders trade in the direction of the earnings surprise for one month after the earnings announcement, while small traders do not. Starting in month two this switches and small traders trade in the direction of the surprise, while large traders do not. The strength of the small trade event-time reaction is a weak positive predictor of returns in the first month after the announcement and a weak negative predictor of drift after the first month. Large trade reaction is generally a negative predictor of future drift. The collection of evidence points to both small and large trader underreaction to earnings announcements, with small trader underreaction more severe in the first month. In month one, large traders capitalize on drift, but after that small traders seem to correct and possibly overreact.

Earnings Expectations and Investor Clienteles

Prior research suggests that some investors may hold earnings expectations that are biased toward seasonal random walk (SRW) predictions. We provide direct evidence that the net buying activity of small (large) traders around earnings announcements is significantly positively associated with SRW (analyst) forecast errors. Further, after controlling for firm-specific variables, e.g., institutional holding, small-trader activity is positively associated with the importance of SRW forecast errors (relative to analyst forecast errors) in explaining stock returns around earnings announcements. Taken together these results suggest that a specific subset of investors (those implementing small trades) hold systematically biased expectations and affect stock prices.

Just-in-time inventory systems innovation and the predictability of earnings

Firms that adopt just-in-time (JIT) inventory practices do so in order to realize cost savings and improve product quality, but an unexpected benefit to such firms could be a more predictable earnings stream. We examine the relationship between implementation of just-in-time inventory practices and the predictability of future quarterly earnings for a matched-pair sample of 82 firms, half of which have publicly announced that they have adopted JIT inventory practices. We find that one- and four-step-ahead forecasts of quarterly earnings, using either a Brown–Rozeff [Journal of Accounting Research (1979) 179–189] ARIMA or a seasonal random walk expectation model, are more accurate for the firms that have adopted JIT.

Post‐Earnings Announcement Drift and the Dissemination of Predictable Information*

AbstractBuilding on the work of Bernard and Thomas 1990, we develop a model to infer the degree to which the information in an earnings announcement is incorporated into investors' expectations for the subsequent earnings announcement at any point in time between the two announcements. We are unable to reject the null hypothesis that investors' earnings expectations are based on a seasonal random walk and reflect none of the implications of the immediately prior earnings announcement up to 15 trading days after that announcement. By mid‐quarter, expectations are significantly more sophisticated than a seasonal random walk. Two trading days before the next earnings announcement, as much as one half of the information in the prior earnings announcement is reflected in earnings expectations. We also find that the dissemination of information, albeit predictable information, speeds the incorporation of prior earnings information into earnings expectations.Our results suggest that as information about future earnings that could have been discerned from the earlier announcements (because past earnings surprises predict future ones) is disseminated in a more transparent form, investors revise their earnings expectations to reflect this information. Thus, the investors' expectations appear to incorporate more and more of the serial correlation in earnings surprises as the quarter progresses, even though they do not consider per se the serial correlation in earnings surprises in forming their expectations.

Detecting Seasonal Unit Roots: an Approach Based on the Sample Autocorrelation Function

In this paper we suggest a new and consistent procedure designed to test for the presence of unit roots in quarterly time series, be they at the zero or seasonal frequencies. For each frequency the proposed statistic is based on the correlogram of a transformation (which removes unit roots that may exist at frequencies other than that of interest) of the residuals from a regression of the observed series on relevant deterministic components. Each statistic is proportional to the maximum lag length for which the residual autocorrelations at all lower lag lengths are strictly positive. Critical values for each test statistic are calculated using Monte Carlo simulation assuming a seasonal random walk data‐generation process (DGP). The robustness properties of each statistic to different integrated DGPs are examined along with their respective power characteristics. These simulations indicate that the procedure suggested in this paper provides a useful complement to the set of test statistics proposed by Hylleberg et al. (‘Seasonal integration and cointegration’, Journal of Econometrics, Vol. 44 (1990), pp. 215–238).

The Incremental Informativeness of Stock Prices for Future Accounting Earnings*

AbstractThis study extends previous research that documents a stock price reaction leading accounting earnings. The primary issue is that prior studies use a naive earnings expectation model (random walk) as the benchmark for the information content of lagged returns and do not adequately address the “incremental” information content of lagged returns. This study identifies and estimates firm‐specific models of earnings to control directly for the autocorrelation in earnings. The explanatory power of lagged prices with respect to this earnings residual is investigated using both a multiple regression model of lagged returns and a multiple time‐series vector autoregressive model.In‐sample estimation of the models provides clear evidence that stock prices impound information about future earnings incremental to the information contained in historical earnings data. Holdout period analysis of the earnings forecasts from these lagged return models finds that both models outperform the naive seasonal random walk expectation, but neither model outperforms the more sophisticated Box‐Jenkins forecasts. On an individual firm basis, earnings forecasts supplemented with the lagged return data tend to be less precise than the Box‐Jenkins forecasts, but the price‐based models demonstrate an ability to rank the earnings forecast errors from the time‐series models. The analysis helps to characterize the limitations of lagged returns as a means of predicting future earnings innovations.

Investor Sophistication and Market Earnings Expectations

This paper investigates whether sophisticated investors rely more on analyst forecasts than on time-series model forecasts in forming expected earnings. Although analyst forecasts are generally more accurate than time-series model forecasts (e.g., O'Brien [1988]), analyst forecasts are not clearly superior to time-series model forecasts as a proxy for expected earnings (e.g., Brown et al. [1987b]). Recent research has concluded that earnings expectations reflected in stock prices at least partially reflect a seasonal random walk (SRW) model (Bernard and Thomas [1990] and Abarbanell and Bernard [1992]). In particular, Ball and Bartov [1996] find that market earnings expectations incorporate the sign of the serial correlation in seasonally differenced earnings but underestimate the correlation magnitude (see also Maines and Hand [1996]). These findings suggest that at least some market participants ignore public information in forming expected earnings; I examine whether information usage is correlated with investor sophistication and/or the degree to which investors are informed.

How naive is the stock market's use of earnings information?

Rendleman, Jones, and Latané (1987) and Bernard and Thomas (1990) hypothesize and report evidence that investors use a ‘naive’ seasonal random walk model, at least in part, for quarterly earnings. We show that the market acts as if it: (1) does not use a simple seasonal random walk model; (2) does exploit serial correlation at lags 1–4 in seasonally-differenced quarterly earnings; (3) does use the correct signs in exploiting serial correlation at each lag; but (4) underestimates the magnitude of serial correlation by approximately 50% on average. We discuss the consistency of alternative hypotheses with our evidence.

Earnings forecasting research: its implications for capital markets research

Since the early 1980s, earnings forecasting research has become much more closely aligned with capital markets research. Capital markets research requires a proxy for the (unobservable) market earnings expectation and earnings forecasting research has provided such proxy measures. Questions considered in this paper include: (1) if annual earnings follow a random walk or an IMA (1,1) model, does this mean that earnings changes cannot be predicted? (2) Do stock prices act as if quarterly earnings follow a seasonal random walk with drift process? (3) Is the predictive model which is best on the forecast accuracy dimension also best on the market association dimension? (4) How do analysts formulate their earnings expectations? (5) What is the role of earnings forecasting in ‘earnings response coefficient’ and ‘post-earnings announcement drift’ studies? (6) What is the likely role of earnings forecasting research in future capital market studies?

Tests of Analysts' Overreaction/Underreaction to Earnings Information as an Explanation for Anomalous Stock Price Behavior

ABSTRACTThis study examines whether security analysts underreact or overreact to prior earnings information, and whether any such behavior could explain previously documented anomalous stock price movements. We present evidence that analysts' forecasts underreact to recent earnings. This feature of the forecasts is consistent with certain properties of the naive seasonal random walk forecast that Bernard and Thomas (1990) hypothesize underlie the well‐known anomalous post‐earnings‐announcement drift. However, the underreactions in analysts' forecasts are at most only about half as large as necessary to explain the magnitude of the drift. We also document that the “extreme” analysts' forecasts studied by DeBondt and Thaler (1990) cannot be viewed as overreactions to earnings, and are not clearly linked to the stock price overreactions discussed in DeBondt and Thaler (1985, 1987) and Chopra, Lakonishok, and Ritter (Forthcoming). We conclude that security analysts' behavior is at best only a partial explanation for stock price underreaction to earnings, and may be unrelated to stock price overreactions.

Evidence that stock prices do not fully reflect the implications of current earnings for future earnings

Evidence presented here is consistent with a failure of stock prices to reflect fully the implications of current earnings for future earnings. Specifically, the three-day price reactions to announcements of earnings for quarters t + 1 through t + 4 are predictable, based on earnings of quarter t. Even more surprisingly, the signs and magnitudes of the three-day reactions are related to the autocorrelation structure of earnings, as if stock prices fail to reflect the extent to which each firm's earnings series differs from a seasonal random walk.

Some exact results on the sample autocovariances of a seasonal ARIMA model

AbstractA seasonal random walk is an ARIMA process such that the first difference of order s (s ≥ 1) is a white noise. Given a series of observations from a particular linear transformation of a seasonal random walk, we study the autocovariances c'(k) based on uncentered data and the autocovariances c(k) based on centered data. In both cases, we provide exact, explicit formulae for the mean, variance, and covariance of the sample autocovariances. It is seen that the moments of the c(k)'s are different from those of the c'(k)'s, even asymptotically. Several analytical results presented in the paper were derived by using a symbolic manipulation program.