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Stock market adjustment to earnings announcement in the presence of accounting irregularity allegations.

Introduction

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). [1] 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

Data

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.

Abnormal Returns

Following Fama et al. (1969), abnormal returns are measured within the conventional market model for out-of-sample tests. [2] 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)

where:

[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. [3]

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)

where:

N = The total number of sample companies. [4]

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

[CAR.sub.-10,t] =

[+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. [5] 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)

where:

[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)

where:

[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)

where:

[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). [6]

[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)

where:

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). [7] The model has an error process that is conditionally heteroskedastic with time-varying variance given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

where:

[[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. [8] 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)

where:

[[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.

Hypothesis Tests

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)

where:

[[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.

Conclusions

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.

[1] In contrast, Kothari et al. (2006) claim that stock prices react rapidly to earnings announcements in aggregate data.

[2] 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).

[3] 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.

[4] 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.

[5] 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.

[6] 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).

[7] 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.

[8] 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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Article Details
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Author:Mun, Kyung-Chun; Fleak, Sandra K.; Morgan, George Emir
Publication:Quarterly Journal of Finance and Accounting
Geographic Code:1USA
Date:Mar 22, 2010
Words:9906
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