Stock market adjustment to earnings announcement in the presence of accounting irregularity allegations.
Following the collapse of Enron in November 2001, announcements of accounting irregularities and financial misrepresentations engulfed the financial market, causing a crisis of confidence in management, corporate governance, and financial reporting. Responses to high-profile corporate accounting scandals have included legislation such as the Sarbanes-Oxley Act of 2002 and regulatory changes regarding corporate governance. Our study systematically investigates reactions of market participants to earnings announcements by firms that allegedly were engaged in accounting irregularities. We investigate whether investors change their behavior when firms with accounting irregularity allegations announce earnings and how rapidly investors adjust to earnings announcements by such firms.
Extant research on financial statement misrepresentation has focused mostly on descriptive data about restating firms and restatement characteristics. (See, for example, Wu, 2002; Palmrose et al., 2004; and Agrawal and Chadha, 2005.) These studies document that firms who restate financial information tend to have weak oversight of management. Relative to their industry, they tend to be smaller, more highly leveraged, less profitable, less likely to have audit committees, and more likely to be involved in litigation with shareholders. Other concurrent research focuses on the relation between restatements and market returns, documenting that there is a significant negative average stock price reaction to restatement announcement. (See, for example, Dechow et al., 1996; Wu, 2002; Anderson and Yohn, 2002; and Palmrose et al., 2004.) A firm's accounting problems typically are revealed through its financial report restatement. An earnings restatement is essentially an official admission by managers of past financial misstatement. Rather than focusing on the firms that restated financial information, our paper is centered on firms with allegations of accounting irregularities that were covered by the press and other media.
Our study extends the extant research on the financial statement misrepresentation by positing two questions about the market reaction to earnings announcement in conjunction with accounting irregularity allegations. The first question we ask is whether investors, facing accounting irregularity allegations, change their behavior in the market as earnings information is released and, as a result, post-announcement abnormal returns are associated with the information content of irregularity allegations. It is well documented in the literature that stock markets do not respond to earnings announcements in a manner that fully reflects the true earnings process (Rendleman et al., 1982; Foster et al., 1984; Freeman and Tse, 1989; Bernard and Thomas, 1989 and 1990; Bartov, 1992; Ball and Bartov, 1996; Chan et al., 1996; and Bartov et al., 2000). Because earnings information released by firms that are allegedly involved in accounting irregularities may not be credible to investors, one might expect to observe unusual market reaction to earnings announcements following irregularity allegations. We address this question by examining the time-series pattern of post-event abnormal returns for firms with allegations of accounting irregularities. Specifically, we compute daily average abnormal returns from a series of out-of-sample forecasted returns and present autocorrelations for the abnormal returns, sorting our earnings announcement event sample into two groups--good news and bad news. Also, we compare the magnitude of cumulative abnormal returns before the allegations with that after the allegations to highlight the market reaction to earnings announcement following irregularity allegations.
We find that in the presence of accounting irregularity allegations, the earnings announcement of good news induces lesser market response than the announcement of bad news. It appears that good news on earnings in the presence of irregularity allegations is discounted by investors as they assess management's credibility as well as future earnings and cash flows. We find no significant post-earnings announcement drift for good news, while there is a short-term underreaction to bad news after irregularity allegations.
The second question we address is how rapidly investors adjust to earnings information for companies with accounting irregularity allegations. A large empirical literature has investigated the stock market's adjustment to earnings announcements. There is much agreement on the market reaction for individual firms that stock prices do not adjust instantaneously to information contained in earnings releases (Ball and Brown, 1968; Joy et al., 1977; Watts, 1978; Rendleman et al., 1982; Foster et al., 1984; Bernard and Thomas, 1989, 1990).  In contrast to the previous research, our study is limited to firms with accounting irregularity allegations. We investigate the possible asymmetry of the market response to good and bad news announcements by such firms, with the market taking time to impound information conveyed by earnings releases. The speed of adjustment to earnings information is measured by the error-correction-type model allowing for partial adjustment of returns to new information. In an effort to explain why investors may change their speed of adjustment to earnings information, we test whether stock volatility helps explain the speed of adjustment to earnings announcement.
We find that the market adjusts more rapidly to good news than to bad news and the asymmetric market response to earnings surprises is significantly more acute after irregularity allegations are made than before the allegations. This is due primarily to the behavior that investors, if accounting irregularity allegations have been made, delay the speed at which they adjust to bad news while quickening the speed of adjustment to good news, apparently because firms tend to conceal bad news and promote good news. We find no relation between stock volatility and the speed of adjustment to earnings announcement when the news is good. When the news is bad, however, stock volatility negatively affects the speed of adjustment, deterring investors from impounding earnings surprises into stock prices.
Data and Methodology
The sample companies are firms for which there are press releases and other media coverage reporting accounting irregularities over the period from November 1997 to December 2009. We initially identify 79 U.S. companies with allegations or news of accounting irregularities by searching various sources of news releases and reports, including Dow Jones and Lexis-Nexis. To identify companies, we searched for phrases such as accounting fraud or accounting irregularities. We added to the resulting list by searching websites such as www.weissratings.com and www.forbes.com. We identify the dates when the firms were first publicly known to have been involved in accounting irregularities.
While identifying the sample companies, some firms were excluded for the following reasons. First, we exclude any firms with stock traded on the Pink Sheets because reliable return data are not available for these stocks. We also exclude any firms that had extensive data missing. Missing data generally are attributable to extended trading suspensions, stock delistings, bankruptcies, and mergers. The resulting sample includes 56 firms.
As our objective is to investigate any changes in market reaction to earnings announcements after accounting irregularity allegations, it is necessary to determine earnings announcement dates for the period before and after accounting irregularities are known to the public. For our purposes, a good (bad) news announcement is one when actual earnings are higher (lower) than expected by the analysts. To determine the announcement date, we explore various sources of news releases including Dow Jones and Lexis-Nexis, as well as finance websites such as finance.yahoo.com. We obtain news information that could be classified as good or bad news. Announcement dates for the period prior to accounting irregularity allegations are identified for good and bad news at least six months before the month that accounting irregularities are known to the public. The corresponding dates for the period after accounting irregularity allegations are the earnings announcement dates following the first month of accounting irregularity allegations.
The sample period surrounding the earnings announcements runs for 31 business days: earnings announcement date, ten days before, and 20 days after the announcement date. In cases where there were confounding effects of other information that was released near the time of the earnings announcement, we use the next available earnings announcement date. Firms that had announcements of the following events within a 31-day window are presumed to have a confounding effect: dividend changes, stock splits, credit rating changes, lawsuits, and new debt and equity financing. The return data are from the daily CRSP files with dividend adjustments.
Table 1 provides a brief description of the accounting irregularity allegations faced by firms in our sample. As indicated in the table, all of the irregularities involve assertions of revenue or expense manipulation, and a large number of the allegations that are covered by the media are concentrated after Enron's collapse in late 2001.
Market Reaction to Earnings Announcements
Because earnings information from a company involved in accounting irregularity allegations may not be credible to investors, it is reasonable that the market may react differently to earnings announcements following irregularity allegations. In this section, we examine market reaction to earnings announcements by analyzing the pattern of post-earnings announcement abnormal returns.
Following Fama et al. (1969), abnormal returns are measured within the conventional market model for out-of-sample tests.  That is, we generate abnormal returns from a series of out-of-sample forecasted returns from rolling regressions of a stock's return on the market return, i.e.,
[AR.sub.it] = [R.sub.it] - E([R.sub.it]|[R.sub.mt]) (1)
[AR.sub.it] = The abnormal return for firm i at day t;
[Ri.sub.t] = The observed return on stock i at day t;
E(R.sub.it][R.sub.mt)] = The (out-of-sample) expected return for stock i at day t conditional on market returns; and
[R.sub.mt] = The equally-weighted S&P 500 return at day t. 
The daily average abnormal return across sample companies, [AR.sub.t], is obtained as
[AR.sub.t] = 1/N [N.summation over (i=1)][AR.sub.it] (2)
N = The total number of sample companies. 
Panel A of Table 2 reports the means for daily average abnormal returns before and after accounting irregularity allegations for days t = 0 through 20 after the earnings announcement date for sample companies. As expected, the immediate abnormal performance following earnings announcements is significantly positive (negative) for good (bad) news. The average abnormal return subsequent to the good news announcements is mostly higher than that subsequent to bad news announcements, a result consistent with the findings of Kadiyala and Rau (2004). The absolute values of abnormal returns following bad news announcements are mostly higher than those following good news, implying that post-earnings announcement drift is more evident following bad news. In the period prior to irregularity allegations, post-event abnormal returns show the same sign as the immediate performance over a three-day event window (t = +1 through +3) but are statistically insignificant, indicating that there is no pronounced short-term drift in post-event abnormal performance. Similarly, post-event abnormal returns over a 20-day event window are all insignificant in the period prior to the irregularity allegations. In the period after irregularity allegations, there is a significant amount of delayed short-term responses of stock returns to earnings announcements for bad news, whereas there is no drift for good news. It appears that after irregularity allegations are made, the market anticipates good news sufficiently with no significant market reaction following the good news while the market under-reacts to bad news.
To examine the time-series behavior of abnormal returns, Panel B of Table 2 presents autocorrelations for abnormal returns of sample companies. It shows that the autocorrelation coefficients for the first lag in the period prior to irregularity allegations are significantly positive for good news, implying the presence of speculative inefficiency, i.e., lagged abnormal returns might have contained information about future abnormal returns. The first-order autocorrelation coefficients are smaller and statistically insignificant for other cases. Because the square of the autocorrelation coefficient indicates the extent to which an abnormal return variation can be predictable, the smaller values of autocorrelation coefficients imply that abnormal return variations are difficult to predict for other cases. It follows that abnormal returns have become less predictable for both good and bad news after irregularity allegations are made. This phenomenon is salient for bad news and can be explained by a higher volatility for bad news documented later in this paper. At two or three lags, autocorrelation coefficients are all insignificant, implying no evidence of abnormal return predictability. Similar results can be found from the Ljung-Box Q-statistics for which the null hypothesis is jointly-zero autocorrelation coefficients up to the nth lag. The calculated Q-statistics for three and five lags were all insignificant (except for good news before irregularity allegations are made), indicating that time dependence of abnormal returns is trivial.
Cumulative Average Abnormal Returns (CARs)
The cumulative average abnormal return (CAR) over days (-10, 20) is measured as
[+20.summation over (t=-10)][AR.sub.t]. (3)
Figure 1 plots the CARs over days (-10, +20) around earnings announcement based on the type of news for our sample companies. Up until day -3, the CARs of good news before irregularity allegations hover around zero and then drastically rise, reaching a high of 8.9 percent on the announcement date. After the announcement date the CARs rise insignificantly until day +6 and subsequently fluctuate with some turbulence. This pattern suggests that there is no statistically significant post-earnings announcement drift for good news in the period prior to irregularity allegations, a result consistent with the findings of the recent literature on stock price reaction to news announcements (Easterwood and Nutt, 1999; Chan, 2003; and Taffler et al., 2004). A similar pattern can be observed for the period following irregularity allegations. The CARs rise insignificantly until day +3 and then fall. What distinguishes the CARs of good news for two periods of pre- and post-irregularity allegations is that the CARs of good news jump to a lesser extent on the announcement date in the period following irregularity allegations relative to the period prior to irregularity allegations. This indicates that the earnings announcement of good news induces lesser market response in the presence of irregularity allegations.
[FIGURE 1 OMITTED]
The lower panel of Figure 1 presents the market response to a bad news earnings announcement. In the period prior to irregularity allegations, the CARs for bad news fall insignificantly until day +2 after the announcement date and then trend rising with a fair amount of turbulence. After irregularity allegations are made, the corresponding CARs fall significantly until day +4 after the announcement date, indicating that there is a significant amount of short-term drift after earnings announcements. As opposed to the good news, the bad news remarkably experiences larger market responses in the presence of irregularity allegations.
Taken as a whole, while there is no significant drift after earnings announcements in the period prior to irregularity allegations, there is a significant amount of short-term post-earnings announcement drift for bad news in the period following accounting irregularity allegations. In the presence of accounting irregularity allegations, the magnitude of the market response is relatively small for good news, but relatively large for bad news. The positive earnings surprise in the presence of irregularity allegations presumably is discounted by investors as they assess management's credibility as well as future earnings and cash flows.
Firm Size and Leverage Effect on CARs
It is known that stock price reactions to an earnings announcement can be affected by the size of the firm (El-Gazzar, 1998; Palmrose et al., 2004) and the level of financial leverage (Fisher and Verrecchia, 1997; Core and Schrand, 1999; and Palmrose et al., 2004). To test for the interactive effect with the firm size and level of financial leverage, we regress the cumulative average abnormal returns (CARs) of sample companies on the average abnormal return differential between sample firms with high and low market values and the average abnormal return differential between firms with high and low debt-to-equity (D/E) ratios. To form these factors, we rank all sample firms according to their market values and D/E ratios. We place 20 sample firms with the highest market values and D/E ratios. Similarly, we place 20 firms with the lowest market values and D/E ratios. These data are collected from the 10-K or 10-Q that immediately followed the announcement month. The test results are provided in Panel C of Table 2 by good or bad news announcement type. The values of regression coefficients are small in magnitude and statistically insignificant for all cases, indicating that size and financial leverage are not significantly associated with CARs of our sample companies.
Buy and Hold Average Abnormal Returns (BHARs)
To check the robustness and sensitivity of the CAR measurement metric, we also rerun our analyses using buy-and-hold abnormal returns.  The buy-and-hold abnormal return is given by:
[BHAR.sub.in] = [n product.sub.t=1] (1 + [R.sub.it])- [n product.sub.t=1] E([R.sub.it])]. (4)
[FIGURE 2 OMITTED]
The buy-and-hold average abnormal returns (BHARs) are obtained by averaging buy-and-hold abnormal returns across sample firms. Figure 2 plots the BHARs over days (-10, +20) around earnings announcement based on the type of news. As shown in the figure, results from the BHAR methodology are essentially the same as those from the CAR measurement metric. In the period following irregularity allegations, there is a significant amount of short-term drift with bad news, while there is no significant post-earnings announcement drift for good news. The extent to which the market responds to earnings announcement is smaller for good news but larger for bad news in the period following irregularity allegations.
Speed of Adjustment to Earnings Announcements
Large empirical studies have reported evidence that the speed of adjustment to information contained in earnings releases is gradual rather than instantaneous. In this section, we investigate the speed at which markets adjust to earnings announcements in the presence of accounting irregularity allegations.
Measuring the Adjustment Speed
We consider the standard partial adjustment model for empirical analysis of adjustment speed because it can succinctly capture much of the lagged adjustment to new information. The process is specified as
[R.sub.i,t] - [R.sub.i,t-1] = (1 - [[lambda].sub.i])([R.sup.*.sub.i,t]- [R.sub.i,t-1]) + [u.sub.i,t], 0 [less than or equal to] [[lambda].sub.i] [lambda] 1 (5)
[R.sub.i,t] = The actual return on stock i at time t;
[R.sup.*.sub.i,t] = The expected rate of return on stock i at time t; and
[u.sub.i,t] = The error term.
Equation (5) represents that the change in stock return will respond partially to the difference between the expected rate of return and the past information on the return. This model is similar in spirit to that of Amihud and Mendelson (1987), Damodaran (1993), and Jones and Lipson (1999). The rate of response is determined by the magnitude of the coefficient of adjustment, [[lambda].sub.i]. As [[lambda].sub.i] approaches zero (unity), stock returns adjust very rapidly (slowly) to new information.
Let the market model characterize the rate of return expected by investors when new information arrives to the market. Assuming that investors use the market model parameters estimated from previously-released return information to form an expected rate of return, we can consider the following equation for the expected return:
[R.sup.*.sub.i,t] = [alpha].sub.i] + [[beta].sub.i][R.sub.m,t] (6)
[R.sub.m,t] = The return on market portfolio at time t;
[[alpha].sub.i] and [[beta].sub.i] = Parameter estimates obtained from regressions of [R.sub.i,t-1] on [R.sub.m,t].
Substituting equation (6) into equation (5) and rearranging gives
[R.sub.i,t] - [R.sub.i,t-1] = -(1 - [[lambda].sub.i])[[R.sub.i,t-i] - ([[alpha].sub.i] + [[beta].sub.i][[R.sub.m,t]] + [u.sub.i,t]. (7)
Adding and subtracting [[beta].sub.i][R.sub.m,t-1] inside the bracket of equation (7) and rearranging yields the following error-correction-type representation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
Equation (8) is estimated with constant term, [[delta].sub.i], as follows:
[DELTA][R.sub.i,t] = [[delta].sub.i] + [[theta].sub.i][[Phi].sub.i,t-1] + [[lambda].sub.i][DR.sub.m,t] + [u.sub.i,t], - 1 [less than or equal to] [[theta].sub.i] [less than or equal to] 0 (9)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
As specified, stock returns change in response to the previous period's deviation from market model equilibrium, the change in market returns, and the stochastic shock. The large (small) negative values of [[theta].sub.i] imply that the change in stock returns is rapidly (slowly) responsive to the previous period's deviation from market model equilibrium. The regression for equation (9) is conducted in two steps. First, time series data of [[PHI].sub.i,t-1] are obtained by residuals from regression of [R.sub.i,t-1] on [R.sub.m,t-1] for each sample firm. Then, time-series estimates of [[theta].sub.i] were estimated using the rolling regression (in the same manner as conducted in abnormal return estimation) within the maximum likelihood method with a constraint of -1 [less than or equal to] [[theta].sub.i] [less than or equal to] 0. The estimator of [[lambda].sub.i] is deduced from [[lambda].sub.i] = 1 + [[??].sub.i].
The results for cross-sectional average of [[lambda].sub.i] are presented as time-series movements in Figure 3. It appears that in the period prior to irregularity allegations, the speed of adjustment in the seven-day period following the earnings announcement is slower for bad news than for good news. This indicates that the market responds asymmetrically to good and bad news. Note that the larger the coefficient of adjustment, the slower is the market response to new information. This phenomenon is more salient in the period after irregularity allegations. For example, the estimated coefficient of adjustment at t = +5 before irregularity allegations is 0.063 for good news and 0.069 for bad news while the corresponding coefficient after irregularity allegations falls to 0.042 for good news but rises to 0.078 for bad news. This means that in the period after irregularity allegations, the market responds more rapidly to good news while it responds more slowly to bad news, thus magnifying the asymmetry of adjustment speed between good and bad news. Figure 3 further suggests that the short-term response to bad news is slower than that to good news, regardless of irregularity allegations. This finding, as opposed to classic findings, is consistent with growing body of recent research that the market takes more time to incorporate bad news than good news (Womack, 1996; Easterwood and Nutt, 1999; Hong et al., 2000; Brooks et al., 2003; Chan, 2003; and Taffler et al., 2004). 
[FIGURE 3 OMITTED]
Figure 3 also reveals that there is no noticeable change in adjustment speed following the good news announcements, whereas there is a sizable slowdown in adjustment speed for bad news, especially after irregularity allegations. This indicates that investors respond to good news with little or no change in the adjustment speed but take longer to adjust when the news is bad. As mentioned earlier, this is perhaps because firms tend to conceal bad news and promote good news.
Test of Changes in Adjustment Speed
To examine more closely possible changes in adjustment speed in the presence of irregularity allegations, we employed three statistical tests: two nonparametric tests and a parametric t-test. The first nonparametric test is the sign test used by Brown and Warner (1980) and has the following test statistic:
z = [absolute value of P - 0.5] - (0.5/n) / 0.5/[square root of n] (10)
P = The actual proportion of positive changes in adjustment coefficient; and
n = The total number of observations.
In the sign test for a given sample, the null hypothesis is that the proportion of the adjustment coefficient of bad news being greater than the adjustment coefficient of good news is equal to 50 percent. The sample pairing procedure for the sign test is as follows: the observation for t = 0 of the (cross-sectional) average adjustment coefficient following irregularity allegations is matched with that for t = 0 of the average adjustment coefficient before irregularity allegations; the observation for t = +1 of the average adjustment coefficient after irregularity allegations is matched with that for t = + 1 of the average adjustment coefficient before irregularity allegations; and so on until t = +20. This procedure provides a total of 21 daily paired-observations for comparisons of good and bad news. The second nonparametric test we use is the Wilcoxon signed rank test under which the null hypothesis is that distributions of adjustment coefficient are the same between the two types of news. We repeat the same test for comparisons of pre- and post-irregularity allegations.
The results are presented in Table 3. Panel A of Table 3 presents the results of the hypothesis that the adjustment coefficient before/after irregularity allegations are made is greater for bad news than for good news. In the period before irregularity allegations, there is little or no difference in the adjustment coefficient between the good and bad news over a 21-day period. Yet the corresponding coefficient is significantly different as we observe an 11-day period (the result is not reported here): The adjustment coefficient is greater for bad news than for good news, indicating that the market responds rapidly to good news relative to bad news in the short run.
In the period following irregularity allegations, both the t-test and nonparametric tests confirm that the market responds significantly rapidly to good news relative to bad news. For example, Panel A of Table 3 reveals that after irregularity allegations are made, the adjustment coefficient is significantly greater (by an average of 0.027) for bad news than for good news for all of the time over a 21-day window. The results indicate that the market responds asymmetrically to good and bad news.
Panel B of Table 3 presents the results of the hypothesis that the adjustment coefficient for good/bad news is greater in the period after irregularity allegations than in the period before the allegations. The results reveal that the speed at which the market responds to good news is more rapid in the period after irregularity allegations than in the period before irregularity allegations. On the other hand, investors seem to be significantly slower to react to bad news in the period after irregularity allegations than in the period before the allegations, perhaps to ascertain whether there is any new pertinent information about returns.
In sum, the statistical evidence suggests that irregularity allegations lead investors to delay the speed at which they adjust to bad news. The market response becomes significantly more rapid to good news, but slower to bad news, in the period after irregularity allegations. The asymmetric market response to earnings surprises is more acute after irregularity allegations than before the allegations.
Volatility and the Adjustment Speed
One body of recent research documents that the post-earnings announcement drift is attributable to arbitrage risk (Shleifer and Vishny, 1997; Wurgler and Zhuravskaya, 2002; and Mendenhall, 2004). As illustrated by these researchers, the major effect of arbitrage is to eliminate the drift...but arbitrage may not be fully effective in doing so when stocks are volatile. If arbitrage activity is deterred due to greater stock volatility, the market response to earnings surprise can be delayed. This suggests that stock volatility affects the speed of adjustment to new information. We thus hypothesize that the speed of adjustment to new information is negatively affected by the stock volatility faced by investors. Existing theory suggests that the size of firm and the number of investment analysts have a positive effect on the speed of adjustment (Lo and MacKinlay, 1990; Holden and Subrahmanyam, 1992; Foster and Viswanathan, 1993; and Brennan et al., 1993). Our test presents an additional important determinant that can be contained in explaining the speed of adjustment.
Measuring the Volatility
To examine the relationship between the volatility and the speed of adjustment to earnings information, we first measure the time series movement of return volatility around the earnings announcement date. Specifically, the conditional volatility of an individual sample stock is estimated from the time path of residual variance for which individual stock returns are regressed on constants within an exponential GARCH (EGARCH) framework developed by Nelson (1991).  The model has an error process that is conditionally heteroskedastic with time-varying variance given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
[[sigma].sup.2.sub.i,t] = The conditional variance of residual for return on stock i at time t;
[[pi]sub.i,t] = The standardized residual for return on stock i at time t;
[k.sub.0], [k.sub.1], [k.sub.2], [k.sub.3] = Parameters.
The results are presented in Figure 4. The upper panel of Figure 4 reveals that in the period before accounting irregularity allegations, the volatility gradually moves upward for bad news for about ten days after the earnings announcement date. It thus appears that there exists a post-earnings volatility drift for bad news while there is little or no change in the volatility for good news. In the period following irregularity allegations, the volatility of stock returns steadily increases by a phenomenal magnitude for bad news after the earnings announcement date, but there is virtually no change in the corresponding volatility for good news. This suggests that the volatility drift for bad news increases greatly after accounting irregularity allegations, while there is no noticeable change in the corresponding drift for good news.
[FIGURE 4 OMITTED]
Granger Causality Tests
In order to derive a test for the relationship between the stock return volatility and the speed of adjustment to earnings releases, we perform Granger causality regressions that allow us to determine whether the volatility affects the adjustment speed or vice versa.  We consider the following version of the Granger causality regressions:
[[lambda].sub.t] = [a.sub.0] + [J.summation over (j=1)] [b.sub.j][[sigma].sub.t-j] + [J.summation over (j=1)] [c.sub.j][[lambda].sub.t-j] + [e.sub.1,t] (12)
[[sigma].sub.t] = [a.sub.1] + [J.summation over (j=1)] [d.sub.j][[lambda].sub.t-j] + [J.summation over (j=1)] [g.sub.j][[sigma].sub.t-j] + [e.sub.2,t] (13)
[[lambda].sub.t] and [[sigma].sub.t] = The daily cross-sectional average of [[lambda].sub.i,t] and [[sigma].sub.i,t].
If the volatility does not Granger cause the speed of adjustment, bi (j = 1, 2, ..., J) should be zero in equation (12). These regressions were fitted with J = 4 as it had the smallest value of Akaike information criterion. In running the regressions, the number of data points has expanded to 101 (t = -50 to +50) for the causality test, and any confounding events also are removed for rolling regressions in the manner as described previously. To avoid a possible spurious regression, we first test whether the sequences of [[lambda].sub.t] and [[sigma].sub.t] are stationary using the augmented Dickey-Fuller test. Although the results are not reported here, we found that the null hypothesis that the sequences are non-stationary cannot be accepted at the 5 percent significance level.
The results of the Granger causality tests are provided in Table 4. The tests for causality running from volatility to adjustment speed (denoted by [[sigma].sub.i] [right arrow] [[lambda].sub.i]) suggest that there is a unidirectional Granger causality running from volatility to adjustment speed when the news is bad, whereas there is no causality when the news is good. For the right half of the table (denoted by [[lambda].sub.i] [right arrow] [[sigma].sub.i]), there is no evidence that any set of lagged values of adjustment speed Granger causes stock volatility. Finally we note that volatility predicts adjustment speed well but the reverse is not held, as measured by [R.sup.2].
In sum, the direction of causality from volatility to adjustment speed is only supported as the news is bad. For good news, there is no causality relation between stock volatility and adjustment speed.
The relationship between stock volatility and speed of adjustment to earnings surprises is tested only for bad news, as the two variables are not associated with each other for good news. As stated earlier, it is already known that the speed of adjustment to new information is positively affected by the size of the firm and the number of investment analysts. Thus, in looking for the effects of the stock volatility on the speed of adjustment, we hold these two variables constant. As shown in the previous section, the adjustment speed is significantly delayed for bad news after irregularity allegations are made. In this section, we test whether the speed of adjustment is affected by stock volatility when earnings surprises are negative. It is possible that stock price adjustments due to movements in stock volatility take time, suggesting the inclusion of lagged values of stock volatility. In general the model can be written as
[[lambda].sub.t] = [[kappa].sub.0] + [n.summation over (k=0)] [[phi].sub.k][[sigma].sub.t-k] + [[eta].sub.t] (14)
[[kappa].sub.0] and [[phi].sub.k] = Parameters to be estimated; and [[eta].sub.t] = The error term.
Equation (14) is estimated in OLS with White's (1980) heteroskedasticity-consistent covariance matrix. Significantly positive values of the coefficient [[phi].sub.k] (k = 0, 1, 2, ..., n) indicate that the speed of adjustment to earnings information is delayed due to higher volatility. Note that the greater the estimated values of [[phi].sub.k], the slower is market response to earnings surprises. The regression results for samples of bad news in the period before and after irregularity allegations are presented in Table 5.
Panel A of Table 5 reveals that in regression 1, the parameter estimate of the coefficient on the contemporaneous volatility is positive (0.481) as predicted and significantly different from zero at the 1 percent level. In regressions 2 and 3, the coefficient estimates on the lagged volatility are positive, but neither is significantly different from zero. The results suggest that in the period prior to irregularity allegations, the adjustment speed is contemporaneously affected by the stock volatility without any significant lagged effect. On the other hand, Panel B shows that the coefficient estimates for the first lag of stock volatility are all positive (0.269 for regression 2 and 0.244 for regression 3) and statistically significant, indicating that the adjustment speed after irregularity allegations is significantly delayed by contemporaneous and lagged stock volatility as well.
This paper investigates how investors behave in the market as earnings information is released by firms with accounting irregularity allegations and how quickly investors adjust to earnings announcements made by these firms. In order to offer any explanation for possible change in the speed of adjustment, we also examine whether stock volatility has any effect on the speed of adjustment. Earnings announcement can be either positive or negative surprise (good or bad news) to the market, and both surprises are examined in this paper. For our purposes, a positive (negative) surprise is one when actual earnings are higher (lower) than expected by the analysts.
We find that in the period before accounting irregularity allegations there is no evidence of post-earnings announcement drift in the market response to earnings releases, whether good or bad news. After irregularity allegations are made, the market anticipates good news sufficiently with no significant market reaction following the good news, while there is a significant amount of delayed short-term responses to bad news. That is, the earnings surprise induces greater market responses when surprises are negative than they are positive in the presence of irregularity allegations. It appears that good news on earnings in the presence of irregularity allegations is discounted by investors as they assess management's credibility as well as future earnings and cash flows.
Evidence presented in this study indicates that the market response to earnings announcement is more rapid to good news than to bad news. Investors take more time for bad news perhaps to ascertain whether there is any new pertinent information about returns. The asymmetric market response to earnings surprises is significantly more acute after irregularity allegations are made. Investors, facing accounting irregularity allegations, delay the speed at which they adjust to bad news while quickening the speed of adjustment to good news.
We find no relation between stock volatility and the speed of adjustment when the news is good. Yet when the news is bad, the stock volatility has a significantly negative contemporaneous effect on the speed of adjustment, and the effect is significantly lagged in the period following irregularity allegations. Stock volatility appears to deter investors from impounding negative earnings surprises into stock prices. As suggested by past experiences in the stock market, bad news can lead to greater market volatility unless sufficiently anticipated by investors. Empirical evidence presented in this study indicates that the greater volatility arising from bad news leads to slower market responses.
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Kyung-Chun Mun *
Truman State University
Sandra K. Fleak
Truman State University
George Emir Morgan
Virginia Polytechnic Institute & State University
* The comments of an anonymous referee have been helpful in improving this paper. Also, the authors benefited from comments of participants at the 2007 Southern Finance Conference, Charleston, South Carolina. The first two authors gratefully acknowledge financial support from the School of Business, Truman State University.
 In contrast, Kothari et al. (2006) claim that stock prices react rapidly to earnings announcements in aggregate data.
 Fama (1998) claims that the market model approach preferably can be used to measure abnormal returns in studying the reaction of stock prices to earnings announcements. It also is suggested that the market model can circumvent the bad model problem in generating expected returns (Schwert, 1983; Fama and French, 1993; and Kothari and Warner, 1997).
 Post-announcement expected returns for each company are obtained as follows: first, we initially estimate the intercept and slope coefficient from the regression of [R.sub.it] on [R.sub.mt] using the data set of 100 observations from t = -11 to t = -110. The estimates of the two parameters then will be used to obtain expected returns for the following date (t = -10). Daily expected returns are successively estimated with a 100-day moving window for each sample company over 20 days after earnings announcement (t = +20). Any confounding events (described earlier) within the 100-day window are excluded from the rolling regression by removing 25 daily observations of returns surrounding the event date (four days before the event date, the event date, and 20 days after the event date) and adding 25 new observations, thus maintaining a 100-day window.
 Loughran and Ritter (2000) claim that an equally-weighted approach is more relevant for the traditional event study analysis than is a value-weighted approach.
 It is often claimed in the literature that BHAR methodology is appropriate as it correctly measures investor experience (Barber and Lyon, 1997). The main difference between CARs and BHARs come from the compounding effect: BHARs incorporate compounding, while CARs do not.
 In contrast, researchers in the earlier literature claim that the price adjustment to bad news is more rapid than that to good news (Jones and Litzenberger, 1970; Joy et al., 1977; and Ball, 1978).
 It is widely known that negative stock returns are followed by higher volatility than positive returns of an equal sample size, the so-called asymmetric effect of stock returns (Black, 1976; Nelson, 1991). The asymmetric effect of innovation on volatility can be captured effectively by the EGARCH model.
 As a preliminary screening of the relationship between the volatility and the speed of adjustment, we employ a rank-order correlation method. The rank-order correlations between the two variables are 0.89 and 0.92 (p value = 0.02 and 0.01) for bad news and 0.08 and 0.13 (p value = 0.84 and 0.71) for good news, indicating that there is a significant association between volatility and adjustment speed when the news is bad, but that the two variables are not associated when the news is good.
Table 1--Sample Companies with Accounting Irregularity Allegations Allegations of Initial Time Accounting Company Name of Allegations Irregularities AIG February 2005 Overstated profits and understated liabilities and underwriting losses AOL Time Warner July 2002 Used questionable accounting procedures to inflate advertising fees and sales Apollo Group October 2009 Improperly recognized revenue Apple Computer June 2006 Used improper accounting related to stock options granted to Steve Jobs Applied Digital Solutions April 2002 Lacked proper accounting controls and recognized revenues before sales to customers were complete Beazer Homes USA, Inc March 2007 Used various techniques to achieve earnings targets Bristol Myers Squibb June 2002 Inflated revenues by forcing more inventory on wholesalers than would be sold Cablevision Systems June 2003 Overstated earnings by mishandling expenses and fabricating invoices Carter's Inc. October 2009 Improperly accounted for customer discounts Cendant Corporation April 1998 Increased reported profit inappropriately by reporting membership fees earlier than the associated costs were amortized CMS Energy Corp May 2002 Overstated revenues using round-trip trades, buying energy from other companies and then selling it back at the same price Computer Associates February 2002 Inflated revenue by International extending contracts in the middle of the contract term and recording the revenue with out writing down the revenue for the period overlapping with the old contract Computer Sciences Corp. May 2007 Made several significant accounting errors over multiple years Comverse Technology March 2006 Improperly accounted for stock options and expenses Cutter & Buck July 2002 Inaccurately reported sales by distribution channels Dell September 2006 Misstated prior financial reports, including issues relating to accruals, reserves, and other balance sheet items Diebold Inc. May 2006 Used bill and hold revenue recognition Dollar General April 2001 Made unspecified misstatements of income with possibly fraudulent accounting Duke Energy July 2002 Increased revenues by using round-trip energy trades El Paso Energy May 2002 Used round-trip trades to artificially increase trading volume and increase revenues Fannie Mae September 2004 Manipulated earnings by applying improper accounting methods Freddie Mac June 2003 Manipulated earnings by applying improper accounting methods General Electric Co. August 2009 Used aggressive accounting to avoid missing consensus earnings expectations Gerber Scientific April 2002 Overstated earnings by inappropriately writing down inventory or establishing reserves. Goodyear Tire & Rubber October 2003 Inaccurately reported earnings due to improper adjustment of accrual accounts Great Atlantic & Pacific May 2002 Used improper inventory Tea Co accounting and vendor allowances Halliburton May 2002 Included project cost overruns as revenue before customers agreed to pay and failed to report losses to investors by not writing off disputed bills Hanover Compressor February 2002 Inflated earnings to meet expectations of Wall Street HUB Group February 2002 Reported unspecified accounting irregularities in a subsidiary company International Rectifier March 2007 Used aggressive revenue Corporation recognition techniques Lucent Technologies Inc. November 2000 Used revenue recognition policy not generally accepted, resulting in materially overstated revenues and net income McAfee March 2002 Inflated revenue through premature recording Merck Co. Inc. June 2002 Overstated its revenues by reporting copayments made to pharmacies as revenue even though retained by the pharmacy and never paid to Merck Microsoft March 2002 Incorrectly reported unearned revenue, thus incorrectly reporting income MicroStrategy Inc. March 2000 Used improper revenue recognition for software sales and service contracts, causing overstated revenues and earnings SC Software March 2004 Manipulated revenues through stock option irregularities Northwest Pipe Co. October 2009 Overstated earnings by recognizing revenue too early Overstock.com Inc. October 2008 Used improper accounting for customer refunds and order cancellations to manipulate future earnings PNC Financial Services January 2002 Shifted bad loans and Group investment losses to off-balance-sheet special purpose entities ProQuest February 2006 Inflated earnings through material irregularities in royalty accounts Suntech Power Holdings Co. October 2009 Used aggressive revenue recognition techniques Symmetry Medical Inc. October 2007 Overstated revenue and income taxes Qualcomm February 2002 Improperly reported revenue related to equity received from startup companies in exchange for licenses Qwest Communications February 2002 Inflated revenues through capacity swaps and reported revenues from sales of equipment with resultant agreements to purchase services from the equipment buyers using the same equipment Rayovac April 2001 Created an impression of increased demand for company products by reporting revenues resulting from inducements for customers to take unneeded inventory Rite Aid October 1999 Used improper accounting practices related to some closed stores SunPower Corporation November 2009 Understated cost of goods sold to manipulate financial results to meet income projections Supervalu June 2002 Intentionally misstated inventory for at least four years, thus overstating income Trump Hotels & Casinos January 2002 Misled investors by reporting pro forma income that departed from generally accepted accounting principle Tyco December 1999 Used accounting methods that misled investors about the growth of acquired companies United Rentals January 2006 Improperly recognized revenue from transactions involving undisclosed inducements VeriFone Systems Inc. December 2007 Manipulated inventory levels to increase income Waste Management November 1997 Improperly recognized revenue and exaggerated assets values Williams Companies January 2002 Failed to disclosure contingent liabilities and the nature of assets and liabilities of an off-balance sheet Special purpose entity Xerox June 2002 Improperly recognized lease revenues, failed to write off bad debts, and improperly classified transactions Zomax March 2005 Improperly accounted for expenses and failed to reconcile certain balance sheet accounts properly Note that the initial time of irregularity allegations is expressed in month because it is difficult to obtain the first date of allegations that is uniform among data sources. Table 2--Summary Statistics of Daily Abnormal Returns after Earnings Announcements Panel A: Mean (%) Days after Earnings Announcement (t) News 0 +1 +3 Pre-AIA Good 8.614 0.662 0.245 (1.37) ** (1.27) (1.83) Bad -7.896 -1.458 -1.336 (1.65) ** (1.13) (0.98) Post-AIA Good 5.881 0.966 0.776 (1.25) ** (1.17) (1.38) Bad -17.66 -2.625 -1.771 (1.81) ** (1.06) * (0.79) * Days after Earnings Announcement (t) News +5 +10 +20 Pre-AIA Good 0.679 0.085 0.156 (2.03) (1.68) (1.45) Bad -0.669 -0.984 1.028 (1.21) (2.63) (1.87) Post-AIA Good -0.322 -0.114 0.089 (1.05) (0.66) (0.71) Bad -0.269 0.983 0.244 (1.64) (1.84) 10.621 AIA signifies accounting irregularity allegations. Numbers in parentheses are (cross-sectional) standard errors. ** (*) represents 1 percent (5 percent) significance level. Panel B: Autocorrelation AIA News [[rho].sub.1] [[rho].sub.2] [[rho].sub.3] Pre-AIA Good 0.469 * 0.232 0.179 Bad 0.256 0.144 0.205 Post-AIA Good 0.255 0.223 0.169 Bad 0.172 0.169 0.148 AIA News [Q.sub.3] [Q.sub.4] Pre-AIA Good 9.34 14.62 (0.045) * (0.027) * Bad 1.55 4.66 (0.74) (0.14) Post-AIA Good 3.68 6.78 (0.43) (0.49) Bad 2.12 5.89 (0.36) (0.18) AIA signifies accounting irregularity allegations. Numbers in parentheses are p-values. * represents 5 percent significance level. Panel C: Firm Size and Leverage Effect The firm size and financial leverage effect on cumulative average abnormal return (CAR) is tested by running the following regression equation: [CAR.sub.t] = a + [b.sub.1][DELTA][DELTA][R.sub.t] (market value) + [b.sub.1][DELTA][DELTA][R.sub.t] (D/E ratio) + [[eta].sub.t] where [DELTA][DELTA][R.sub.t] (market value) = the AR differential between sample firms with high and low market values; [DELTA][DELTA][R.sub.t] (D/E ratio) = the [DELTA]R differential between sample firms with hij4h and low D/E ratios. Pre-AIA Post-AIA Estimates Good News Bad News Good News Bad News a 0.1366 -0.0392 0.0316 -0.1367 (2.94) ** (-0.88) (1.82) (-2.14) * [b.sub.1] -0.0309 -0.0486 -0.063 -0.0338 (-0.56) (-1.06) (-0.78) (-1.04) [b.sub.2] -0.0097 -0.0248 0.0145 0.0160 (-0.04) (-0.31) (0.62) (1.59) AIA signifies accounting irregularity allegations. Numbers in parentheses are t-statistics. * represents 5 percent significance level. Table 3--Tests of Changes in Adjustment Coefficient after Earnings Announcements: Panel A: Comparison of Good and Bad News Nonparametric Test Wilcoxon n AIA % Positive Sign Test Signed Rank Test 21 Pre-AIA 66.17 11.37 1.34 21 Post-AIA 100.0 4.51 5.06 Parametric Test n AIA Mean Change (%) t-statistic 21 Pre-AIA 0.0001 0.11 21 Post-AIA 0.029 14.26 Note: The pre-(post-) AIA in the table indicates that the adjustment coefficient is greater for bad news relative to good news during the pre-(post-) irregularity allegations. For a statistical comparison of good and bad news, 21 days (0 to +20) of adjustment coefficient for good news are compared with the identical length of days (0 to +20) of adjustment coefficient for bad news in both periods. The first nonparametric test is the sign test for which z-statistics are provided. The second nonparametric test is the Wilcoxon signed rank test of no difference in distributions between good and bad news. The parametric test has the null hypothesis that the difference in mean is zero and t-statistic is provided for the significance. Panel B: Comparison of Pre-and Post-Accounting Irregularity Allegations Nonparametric Test Wilcoxon n News % Positive Sign Test Signed Rank Test 21 Good 0.00 -4.88 -5.14 21 Bad 93.17 4.64 5.03 Parametric Test n Mean Change (%) t-statistic 21 -0.021 -12.76 21 +0.008 6.21 Note: Good (bad) news in the table indicates that the adjustment coefficient of good (bad) news is greater during the post- irregularity allegations relative to the pre-irregularity allegations. Table 4-Granger Causality Tests The following Granger causality regressions are run: [[lambda].sub.i,t] = [a.sub.0] + [J.summation over (j=1)] bj [[sigma].sup.2.sub.0,t-j] + [J.summation over (j=1)] cj [[lambda].sub.1,t-j] + [e.sub.1i,t] [[sigma].sup.2.sub.i,t-j] = [a.sub.1] + [J.summation over (j=1)] dj [[lambda].sup.2.sub.i,t-j] + [J.summation over (j=1)] gj [[sigma].sup.2.sub.i,t-j] + [e.sub.2i,t] These regressions are fitted with J = 4 [[sigma].sub.1] [right arrow] [[lambda].sub.i] AIA News Adjusted [R.sup.2] F(4,88)- statistic Pre-AIA Good 0.6662 0.8129 (0.597) Bad 0.9011 2.7867 (0.036) * Post-AIA Good 0.8129 1.6825 (0.183) Bad 0.9234 8.652 (0.000) ** [[lambda].sub.1] [right arrow] [[lambda].sub.i] AIA News Adjusted [R.sup.2] F(4,88)- statistic Pre-AIA Good 0.0532 0.8166 (0.432) Bad 0.0616 0.6243 (0.567) Post-AIA Good 0.1273 1.6625 (0.197) Bad 0.0984 1.8622 (0.243) Figures in parentheses are p-values. * (**) indicates statistical significance at 5 percent (1 percent) level. Table 5--Tests for Relation between Adjustment Speed and Stock Volatility: Bad News The model is of the following format: [[lambda].sub.t] = [[kappa].sub.0] + [n.summation over (k=0)] [[phi].sub.k][[sigma].sub.t-k] + [[eta].sub.t] where [[lambda].sub.t] and [[sigma].sub.t] are the cross-sectional average of adjustment speed and stock volatility, respectively; and [[phi].sub.k] and (k = 0,1,2, = ..., n) are parameters to be estimated; and [[eta].sub.t] = the error term. Significantly positive values of the coefficient [[phi].sub.k] indicate that the speed of adjustment to earnings information is delayed due to higher volatility. Note that the greater the estimated values of [[phi].sub.k], the slower are market responses to earnings surprises. White's (1980) heteroskedasticity-consistent covariance matrix is used for the regression. Panel A: Regression Results before Accounting Irregularity Allegations Regression Number of Lags [[kappa].sub.0] [[phi].sub.0] 1 n = 0 0.057 0.481 (17.66) ** (5.45) ** 2 n = 1 0.056 0.433 (18.19) ** (5.21) ** 3 n = 2 0.057 0.427 (22.38) ** (3.69) * Regression [[phi].sub.1] [[phi].sub.2] Adjusted [R.sup.2] 1 -- -- 0.325 2 0.098 -- 0.394 (0.78) 3 0.072 0.053 0.417 (0.29) (0.16) Panel B: Regression Results after Accounting Irregularity Allegations Regression Number of Lags [[kappa].sub.0] [[phi].sub.0] 1 n-0 0.057 0.469 (25.64) ** (9.66) ** 2 n = 1 0.055 0.286 (26.21) ** (4.68) ** 3 n = 2 0.056 0.261 (27.32) ** (2.79) ** Regression [[phi].sub.1] [[phi].sub.2] Adjusted [R.sup.2] 1 -- -- 0.715 2 0.269 -- 0.739 (3.87) ** 3 0.244 0.012 0.764 (3.08) * (0.09) Figures in parentheses are t-statistics. (**) indicates statistical significance at 5 percent (1 percent) level.
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|Author:||Mun, Kyung-Chun; Fleak, Sandra K.; Morgan, George Emir|
|Publication:||Quarterly Journal of Finance and Accounting|
|Date:||Mar 22, 2010|
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