ࡱ> dy Rbjbj םם> 4(C&{    $ V&'4''')r),**TUVUVUVUVUVUVUZ]]PVU/),));, G,VU//''gV...O,/'/'TU.),TU..HBPD'Pys +-C@U}V0VC8].|]0PDPD]i8GB*h*J.*<0+B*B*B*VUVU.B*B*B*V),),),),]B*B*B*B*B*B*B*B*B* : Managers Incentives and Management Forecast PrecisionQiang ChengHYPERLINK "mailto:qcheng@bus.wisc.edu"qcheng@bus.wisc.eduUniversity of Wisconsin-MadisonTing LuoHYPERLINK "mailto:luot@sem.tsinghua.edu.cn"luot@sem.tsinghua.edu.cnTsinghua UniversityHeng YueHYPERLINK "mailto:yueheng@gsm.pku.edu.cn"yueheng@gsm.pku.edu.cnBeijing UniversityApril, 2010Abstract:Our study examines whether managers manage forecast precision for self-interested purposes. We find that managers are more likely to release vague guidance for more negative news when they are about to make equity financing or to sell stocks on their personal accounts We also find that managers are more likely to manage forecast precision 1) when the litigation risk is low because risk of lawsuit and reputation loss can restrain their opportunistic behavior in forecast precision; 2) when their credibility is determined by their prior forecast accuracy because managers would be reluctant to hurt their credibility by issuing biased forecasts and would be more likely to take the precision strategy.Keywords: Management Forecast; Managers Incentives; Forecast Precision(Very preliminary)Please do not quote without permissionWe thank Zhaoyang Gu, Jing Liu, James Ohlson, Jian Xue, Yue Li and conference participants at the Four-school Accounting Research Conference. We are responsible for all errors. IntroductionManagement forecasts are important channels that managers use to convey their private information to investors and guide the market expectation (Hassell and Jennings 1986). In contrast to mandatory disclosures such as annual reports, management forecasts are voluntary. Managers have large discretion on whether, how, and what to disclose in the management forecasts. Prior research finds that management forecasts convey useful information (e.g., Pownall, et al. 1993; Baginski and Hassell 1990; Coller and Yohn 1997). Motivated by the usefulness of management forecasts, prior research also examines the determinants of management forecasts (e.g., Skinner 1994, 1997; Lang and Lundholm 2000; Cheng and Lo 2006). However, despite managers great discretion on the characteristics of management forecasts (e.g., precision and horizon) and the importance of such characteristics, how managers incentives affect the characteristics of management forecasts are not well understood (Hirst et al. 2008).  In this paper, we focus on one important characteristic of management forecast, forecast precision and examine how managerial incentive affects the choice of forecast precision. Forecast precision is one important characteristic that managers can determine when making forecasts. Of the population of management forecasts compiled by Thomas Financial, more than 80% of the quantitative forecasts are in the range format (i.e., a minimum and a maximum) and there is a large variation in forecast width. In addition to its large variation, forecast precision also has a significant impact on market reaction to management forecasts. Theoretical papers, such as Kim and Verrecchia (1991) and Subramanyam (1996), argue the magnitude of markets response to a disclosure is positively related to its precision. Empirical studies, by examining stock returns and analyst revision, also report supportive evidence. However, despite its variation and impact, the determinant of management forecast precision is not well-understood. This gap in the literature is particularly puzzling given how much discretion managers have in deciding the precision of such forecasts, such as how large is the width of their forecasts. One might even argue that managers have higher discretion in deciding whether to release a vague or precise forecast than whether to provide a forecast in the first place (Hirst et al. 2008). Managers cannot always intentionally withhold information; doing so will expose them to high litigation risk and great reputation loss. In fact, it is part of managers fiduciary duty to update or correct preexisting disclosures, including information disclosed in previous earnings announcements (Skinner 1994). Because of the short-horizon of management forecasts, managers also have little discretion in issuing biased forecasts, because investors can use the subsequent audited earnings report to evaluate the forecasted numbers. Therefore, we argue that managerial incentives can lead them to choose a forecast precision in their best interest, although the precision of managers private information is an important determinant as well. However, we do want to stress that whether to provide a forecast has the first-order effect on market reaction, and choosing a desirable precision given the issuance of management forecast has the second-order effect. We rely on prior research and identify two managerial incentives: equity issuance and insider trading. Prior research indicates that managers strategically use management forecasts to affect the markets perception about a firm. For example, Lang and Lundholm (2000) find that companies increase their disclosure activities before seasoned equity offerings, consistent with managers intent to increase stock prices and offering proceeds. Managers intent to increase stock price before seasonal equity offering is also underpinning the large literature on earnings management before SEO (e.g., Teoh, Welch and Wong 1998). The second managerial incentive is based on the literature on insider trading. A long-standing notion in the literature is that managers will employ their private information to sell shares when stock price is high and buy shares when stock price is low. Built on this, Cheng and Lo (2006) predict that managers will disclose bad news before buying shares and disclose good news before selling shares. While they do not find evidence consistent with the second prediction, they find that managers are more likely to disclose bad news before insiders buy shares on their personal accounts. These studies suggest that managers disclose earnings forecasts strategically to influence market prices.If the precision of management forecasts has an impact on stock price and the above managerial incentives exist, we would expect to observe an association between forecast precision and managerial incentives. The direction of the association depends on the nature of the news and the incentives. Prior research indicates that managers prefer a higher stock price before SEO. Thus, for good news disclosed before SEO, we predict it to be of higher precision and for bad news disclosed before SEO, we predict it to be of lower precision, because prior research indicates that less precise forecasts have a smaller market impact. Since in general bad news have lower precision than good news forecasts (Skinner 1994), we test the prediction separately for good news forecasts and bad news forecasts. That is, we test whether precision increases (decreases) with the magnitude of the good (bad) news. We have the same prediction for insider sales and the opposite prediction for insider purchase because managers benefit from higher stock price for sales and from lower stock price for purchases. To test our hypotheses, we examine a sample of 7,466 management earnings forecasts issued during the 1999-2006 period. Using the negative of forecasts width to measure forecast precision, we confirm that good (bad) forecasts are more (less) precise, as documented in prior research (Choi et al. 2009). The evidence is consistent with notion that managers strategically decide forecast precision so as to increase (or decrease) markets reaction to good (or bad) news. For bad news issued before SEO, we find that managers are more likely to release vague guidance for more negative news. We do not find that the precision level is correlated with the magnitude of the news for good news forecasts issued before SEO. Similarly, we find that for bad news issued before insider sales, the precision decreases with the magnitude of the news and we do not find results for good news released before insider sales. For management forecasts disclosed before insider purchases, we find that the precision is decreasing with the magnitude of the good news and we do not find significant results for bad news forecasts.These results are consistent with our predictions. Managers issue less precise bad news before equity issuance and insider sales to reduce the blow of bad news to stock prices, and they issue less precise good news to reduce the positive impact of good news on stock price before insider purchases. We do not find results good news disclosed before equity issuance and insider sales or bad news disclosed before insider purchases. Managers opportunistic behaviors are not without any cost. They are subject to litigation risk and reputation loss once their manipulation is detected. We argue that litigation risk can moderate their opportunistic behavior in forecast precision. To test this prediction, we split the sample into low-litigation group and high-litigation group, and then replicate the analysis for each group. We find that the results documented above are largely driven by the low litigation group. We do not find consistent results for the high litigation group except that bad news disclosed before insider sales are less precise. Following similar procedures, we find that managers are more likely to manage forecast precision when their credibility is determined by their prior forecast accuracy because managers would be reluctant to hurt their credibility by issuing biased forecasts and would be more likely to take the precision strategy.Our paper contributes to the literature in several important ways. First, our paper extends the voluntary disclosure literature by providing evidence that managers strategically determine forecast precision in their earnings guidance. The theoretical model in Hughes and Pae (2004) suggest managers tendency for playing the precision game. Our study provides empirical evidence supportive for their argument.Second, we indentify managers trading incentives, either on behalf of firms or on their personal accounts, can drive them to play the precision game. Previous studies have found that managers tend to manage the markets perception by their earnings guidance. However, these studies mainly focus on whether to disclose information, or whether the disclosed information is biased. Our study proposes another strategy that managers could take in their forecast decision. By managing the precision of forecast news, managers could affect market reaction to disclosure and gain from the temporary mispricing. Hirst et al. (2008) suggests that forecast characteristics are the most controllable yet the least studied component of management forecasts and calls for future research on this direction. Previous studies primarily focus on such forecast characteristics as stand-alone vs. bundled or disaggregation vs. aggregation or others, that managers might employ to serve specific purposes. To the best of our knowledge, no previous studies have built up a link between managers incentives and forecast precision. Our paper contributes to the literature by identifying managers opportunistic behavior in forecast precision.The remainder of the paper proceeds as follows. Section 2 discusses related literatures on management forecasts and develops our hypotheses. Section 3 describes our empirical design and the results of empirical tests. Section 4 reports the analysis for market reaction and forecast precision. The final section concludes the paper.Related literature and hypotheses developmentManagers have information advantages over outside investors about firm values. Besides mandatory reporting required by the regulators, managers provide voluntary disclosure as well to reduce information asymmetry, to guide market perception, and to reduce the cost of capital. Management earnings forecast is the most common type of voluntary disclosure (Hirst et.al. 2008). The literature finds that management forecast is an informative guidance that has significant impact on the capital markets (e.g., Baginski and Hassell 1990; Matsumoto 2002; Pownall, et al. 1993; Rogers and Stocken 2005). Since management forecasts are voluntary, managers have large discretion on whether to make the disclosure, when to make the disclosure, and what are the contents and form of the disclosure. The extant literature indicates that managers would exploit their discretion on management forecasts for self-serving purposes. For example, Nagar et al. (2003) argue that equity-based compensation drives managers to issue more frequent forecasts to avoid equity mispricing that could adversely impact their wealth. Rogers and Stocken (2005) find that managers have incentives to time their bad news forecasts to take advantage of a lower purchase price. Different incentives lead to various disclosure strategies. Previous research primarily focuses on the likelihood, the frequency, and the bias of forecasts. Matsumoto (2002) find that managers use earnings guidance to guide down analysts expectation, so as to reduce the frequency of negative surprise and the associated adverse market reaction. Frankel et al. (1995) and Lang and Lundholm (2000) find that firms increase the frequency of disclosure and issue more favorable news prior to raising external capital. Cheng and Lo (2006) demonstrate that managers disclose more bad news before they buy stocks on their personal accounts. Brockman et al. (2008) find that the frequency and magnitude of bad news (good news) disclosure are higher (lower) before share repurchase, presumably to deflate stock prices so that firms can buy back shares at a lower price. The evidence overall indicates that the frequency of management forecasts is determined by managers incentives. Managers could temporarily affect the market response via their voluntary guidance and benefit from doing so. Although managers have the opportunity to exploit their discretion over earnings guidance, investors can use the subsequent audited earnings report and information from other sources to evaluate management forecast. If managers are believed to have withheld information or have issued biased forecasts, investors may sue managers and their reputation might be damaged. Therefore, managers could strategically make the disclosure less verifiable but still able to stimulate specific market response. Managing forecast precision is a feasible choice. Managers can choose their forecast precision. They can issue point estimate, range estimate, or qualitative estimates. And for range forecasts, they can choose how large the range between the minimum and maximum estimates is. The literature suggests that forecast precision affects market reaction to earnings guidance. Theoretical models by Kim and Verrecchia (1994) and Subramanyam (1996) show that information with higher precision leads to larger market reaction. Baginski et al. (1993) indicates that the degree of market response to management forecasts varies with forecast form, and point forecasts lead to greater responses relative to range forecasts. If this is the case, managers can strategically choose forecast precision so as to affect market reaction for self-interested purposes. Hughes and Pae (2004) shows that the entrepreneur discloses only high (low) precision information, for estimates above (below) the prior expectation of the asset value. That is, entrepreneurs choose high precision for good news to increase stock prices and low precision for bad news to reduce the blow to stock prices. Equity IssuanceWhen firms are about to sell stocks, they have incentive to increase stock prices because firm can receive more proceeds if stock prices are higher. Managers can affect stock prices through earnings management (Teoh, Welch and Wong 1998), as well as through voluntary disclosures. Consistent with this argument, Lang and Lundholm (2000) find that issuing companies dramatically increase their disclosure activities before seasoned equity offerings. They also find that firms which abnormally increase their disclosure activities before equity offering experience positive returns in that period, and negative returns after equity issuance. The evidence suggests managers use voluntary disclosure to inflate prices. Richardson, Teoh and Wysocki (2004) indicate that firms that are net issuer of equity are more likely guide analysts expectation downward to beatable targets. However, the literature also reports conflicting evidence. For example, Frankel, McNichols and Wilson (1995) find that management forecasts are not optimistic prior to equity issuance, probably due to the potential reputation loss. In brief, managers are documented to release biased forecasts when they are about to issue equity, but the concern of reputation loss might deter them from doing this. Hence, managers would take the strategy of managing forecast precision before raising external fund, purported to manage share prices upward while avoid the potential reputation loss. The above argument is summarized as the following hypothesis:Hypothesis 1a: The relationship between forecast precision and forecast news is stronger when firms are about to raise external fund. Insider TransactionsWhen managers trade shares on their personal accounts, they have the incentive to maximize trading profits by utilizing their information advantage. Noe (1999) finds that managers sell more shares after good news than after bad news, and buy more after bad news than after good news, suggesting managers intention to selecting the timing of their trades. Building on Noes finding, Cheng and Lo (2006) argue that managers change the frequency of voluntary disclosure before insider trading. They hypothesize that managers who plan to sell shares will disclose good news or defer bad news, and managers who plan to buy shares will disclose bad news or defer good news. However, insider trading has been under scrutiny by the regulators. Thedisclose or abstain rule requires that anyone in possession of material nonpublic information should either disclose it to the public before trading or abstain from trading. Consistent with managers incentives to affect the stock price before insider trading, Cheng and Lo (2006) find that managers are more likely to disclose bad news before buying shares, but they find that managers do not change the frequency of voluntary disclosure before insider sales, consistent with the litigation argument. However, given the disclosure of news, managers can increase trading profits by choosing forecast precision to influence market response to the disclosure. The benefit of selling shares is higher when stock price is higher; thus we expect that managers are more likely to be vague (precise) for bad (good) news when they are about to sell stocks, while they would be more likely to release vague (precise) for good (bad) news when they are about to buy stocks. The hypothesis is summarized as follows: Hypothesis 1b: The relationship between forecast precision and forecast news is stronger when managers are about to sell stocks on their personal accounts. Hypothesis 1c: The relationship between forecast precision and forecast news is weaker when managers are about to buy stocks on their personal accounts. Mitigating factorsLitigation RiskWhen making decisions on whether to manipulating forecast precision, managers have to consider their cost and benefit function. By strategically disclosing vague or precise information before equity financing and insider trading, managers can increase their trading profits by influencing market response to their desired direction. However, this strategy is not without any cost. If detected, opportunistic behaviors for self-interests are subject to litigation risk and reputation loss. The higher risk involved, the less likely managers would play precision game. We argue that risk of lawsuit can serve as a monitoring mechanism and work against managers intention to manage forecast precision in order to increase trading profits. The hypothesis is formalized as: Hypothesis 2: Managers are more likely to play precision game when they are exposed to lower litigation risk.Managers Perceived Forecast ReliabilityInvestors do not always distinguish between forecasts with various forecast precision. Prior studies report mixed results on the relation between forecast form and stock returns. For example, Baginski et al. (1993) report that the more precise the forecast, the stronger the relation between unexpected earnings and expected returns. In contrast, Pownall et al. (1993) find no effects on stock returns from forecast form. Hirst et al. (1999) proposes investors judgment as an explanation for the mixed finding. They argue that forecast precision standalone does not necessarily affect investor judgment on future earnings, rather, it matters when investors perceive the information source as reliable. Their evidence shows that stock returns varies with forecast precision more substantially when managers used to release accurate earnings guidance. Given that managers motivation in manipulating forecast precision is to increase their trading profits, they would take this strategy when their manipulation is able to produce the desired influence on stock prices. Hence, we argue that managers would be more likely to play precision game for self-interested purposes, when the market perceives their forecasts as reliable and then would determine their response through forecast precision. The hypothesis is summarized as: Hypothesis 3: Managers are more likely to play precision game when investors tend to perceive their forecasts as reliable. Data and Empirical Design3.1 Sample and dataWe obtain our sample from the intersection of the First Call Historical Database (FCHD), COMPUSTAT and the Center for Research in Security Prices (CRSP) over the 1999 to 2006 period. Management forecasts data are obtained from FCHD. We use forecasts of quarterly earnings per share (EPS). To focus on earnings forecasts rather than pre-announcements, we eliminate forecasts issued on, or after, the corresponding fiscal period-end because earnings forecasts during a quarter does not need to be furnished to SEC, but a preannouncement after the quarter ends must be. Managers issue both quantitative forecasts and qualitative forecasts. Quantitative forecasts take the form of point (a specific number) or range (a range with upper and bottom estimates) estimates of earnings. Qualitative forecasts are estimates that do not have any specific estimates of earnings. Some qualitative forecasts are open-end forecasts with only minimum or maximum estimates. Qualitative and open-end forecasts are excluded from our analysis, because we are unable to determine the magnitude of earnings news for these forecasts. We obtain 40,602 point or range estimates of current quarterly earnings issued between the previous earnings release dates and the quarter-end dates. We further remove management forecasts that are not the initial guidance released over this period, because a longer horizon lengthens the period over which a manager can benefit from playing the precision game and makes it hard for investors to verify the forecasts.We use the negative of forecast range, Width, to represent forecast precision. Width is a continuous variable and represents the difference of the high-end estimate and the low-end estimate. We multiply Width by -1 to get our measurement of Precision. We exclude 4,732 observations with insufficient data to calculate Width. We also exclude observations with insufficient data to determine forecast news and other management forecast characteristics, such as forecast error and forecast horizon.We collect financial data from Compustat, return data from CRSP, and analyst forecast data from IBES. Insider trading data are obtained from Thomson Financial and equity financing data are withdrawn from SDC. We exclude firms with insufficient data on these databases. The sample selection procedure, as summarized in Table 1, yields a final sample of 7,466 management forecasts of quarterly earnings. Table 2 describes the distribution of management forecasts. Panel A reports the change in the frequency of management forecasts. The frequency exhibits an overall increase, from 158 in 1999 to 1,574 in 2006. Consistent with the extant literature, management forecasts are distributed evenly across the four quarters, with frequencies of 1,662, 2,270, 1,469, 2,065 in the first, second, third and fourth quarters, respectively. As shown in Panel B, management forecasts in our sample has 1,165 (16%) point estimates and 6,301 (84%) range estimates. We classify a management forecast as good (bad, confirming) news if the point estimate, or the mid-point for range forecasts, is above (below, equal to) the most recent mean analyst forecast prior to the management forecast date. Panel C reports the distribution of sample across earnings news: 3,159 (42%) disclose good news, 4,201 (56%) disclose bad news and 106 (2%) are confirming forecasts. Consistent with Skinner (1994), managers are more likely to disclose bad news, presumably to avoid large price drop. Table 3, Panel A reports the descriptive statistics of main variables for the sample. Variables are defined as in Appendix A. Forecast precision (Precision) is on average -0.10. Management forecasts on average convey bad news (FN=-0.005, p-value < 0.01) and are on average optimistic (FE=0.001, p-value < 0.01). Management forecasts are issued about 86 days prior to the earnings announcement date on average. Panel B presents the relation between forecast precision and forecast news (Figure 1 graphically depicts this link). There is a pronounced positive relation in the bad-news sample, more vague forecasts in deciles with more negative news and more precise forecasts in deciles with less negative news. However, there is no sigfniciant relation between forecast precision and forecast news for the good-news sample. The contrast between the good-news sample and bad-news sample is consistent with the finding in prior research (e.g., Choi et al. 2009) that managers would try to avoid large drop in stock prices and are more likely to manage bad-news forecasts. Hence, we partition the full sample into two, good-news and bad-news, for all analyses that examine the relation between forecast precision and managers incentives. Table 4, Panel A presents the correlation coefficients among management forecast precision, management forecast news, and management forecast errors. Consistent with the precision management hypothesis, we observe a significant positive correlation between Precision and management forecast news. There is a positive link between forecast news and forecast error, consistent with more favorable (unfavorable) news being more optimistically (pessimistically) biased. Table 4, Panel B provides the correlations for the independent variables used to test our hypotheses. 3.2 Empirical DesignIn this section, we examine, first, the relation between management forecast news and forecast precision, and second, the impact of management incentives on forecast precision, and last, the mechanisms that can work on the effects of those incentives. Research Design for Hypothesis 1Managers who care about short-term stock prices would be more likely to play precision game when issuing earnings guidance. Then we identify the incentives that make managers care more about stock prices and examine their effect on the relation between forecast news and forecast precision. We estimate the following model using a cross-sectional ordinary least square (OLS) regression: EMBED Equation.3  (1)The models variables are defined and discussed below:Forecast precision (Precision): We first calculate forecast range, Width, of a management forecast. For a point forecast it is defined as 0, and for a range forecast it is the absolute value of the difference of the high-end estimate and the low-end estimate, divided by the absolute value of the sum of the high-end estimate and the low-end estimate. We multiply Width by -1, so that high precision is corresponding to a high value of Precision.Forecast news (FN): Forecast news, FN, is defined as:FN = (Management forecast Consensus analyst forecast)pre-release share priceManagement forecast of EPS is either the point estimate or the mid-point of a range estimate of the firms earnings. Management forecasts above the last consensus analyst forecasts are classified as good news, while those below the last consensus analyst forecasts are classified as bad news. We classify management forecasts equal to the last consensus analyst forecasts as confirming news. We rely on the absolute value of FN to measure forecast news and construct two news variables, FN_Pos and FN_Neg. FN_Pos is equal to the absolute value of FN when FN is positive and is set to be 0 when FN is negative . FN_Neg is equal to the absolute value of FN when FN is negative and is set to be 0 when FN is positive. Hence, large value of FN_Pos represents more positive news and large value of FN_Neg represents more negative news. These variables are zero for confirming news.Equity issuance (EquIssue): Equity issuance, EquIssue, captures a firms activity in equity issuance subsequent to managers forecasts. EquIssue equals 1 if a firm obtains external equity financing in the thirty-day window after the management forecast, and 0 otherwise. Because managers care about short term share prices if they are about to sell stocks, we expect that they have the incentive to mitigate (enhance) the negative (positive) price reaction for negative (positive) news forecasts.Insider trading (Insider): Insider trading, Insider, is measured over the thirty-day window beginning the first day of the management forecast. An insider is defined as a person who serves as the CEO, chairman of the board, vice president, or director. Inside includes all open market transactions in the firms shares or options. Since the volume of insider trading is characterized by large acquisitions or disposals, we define two indicator variables, Insider_Sell and Insider_Buy. Insider_Sell equals 1 when the net insider trading subsequent to management forecast is a net sale and 0 otherwise. Insider_Buy equals 1 when the net insider trading subsequent to management forecast is a net purchase and 0 otherwise. Control variables: In addition to forecast news, we include several control variables. First, forecast behavior is found to be associated with firm size (Baginski and Hassel 1997) and growth opportunities (Bamber and Cheon 1998). We use the natural log of a firms market capitalization of the previous quarter, denoted as Size, to proxy for firm size. A firms market value to book value of equity ratio, M/B, is used as a measure of a firms growth opportunities. M/B is calculated as the ratio of the previous quarters market capitalization divided by the previous quarters book value of equity. Second, full Disclosure (FD) regulation, enacted on October 23, 2000, prohibits the information pre-disclosure to any intermediaries like analysts and grants all investors equal access to a firms material information. Early evidence suggests that FD affects voluntary disclosure practices (Heflin et al. 2003). We expect that managers are more likely to release vague forecasts in the post-FD period than in the pre-FD period, because the regulation for voluntary disclosure has become tighter. The indicator variable, FD, equals 1 when a management forecast is issued after year 2000, and 0 otherwise. Third, managers face incentives to misrepresent their information that are not directly observable but are implicitly revealed through their forecasting behavior (Rogers and Stocken 2005). We use forecast error to control for managements implicitly revealed incentives that affect forecast form. Forecast error, FE, is calculated as subtracting actual EPS from the management forecast, divided by the pre-release share price. Fourth, it is more difficult to forecast a firms earnings when the firm is unprofitable (Rogers and Stocken 2005), the indicator Loss equals 1 when the forthcoming earnings are negative, and 0 otherwise. Fifth, if firms are followed by a larger number of analysts, managers would be monitored to maintain a reputation for credible communication (Skinner 1997, Lennox and Park 2006), hence they are more likely to release precise forecasts. However, as documented in Baginski and Hassel (1997), greater analyst following represents more information, which drives managers to produce more precise forecasts. We use the log transformation of analyst following, Analyst, to control for this effect. Sixth, we introduce forecast horizon, Horizon, because as closer to the official announcement date, managers have more private information and are able to make precise forecasts. Horizon equals the number of calendar days between the forecast release date and the earnings announcement date.Last, if firms operate in an uncertain environment, it is harder for managers to forecast firms earnings precisely. We control for operating environment using return volatility, RetVol, and research and development expenditure, R&D. RetVol is the variance in daily stock returns over the 250 trading days prior to the forecast date, and R&D is calculated as research and development cost divided by net sales. Result for Hypothesis 1 Before looking at results of our regression model, we examine the univariate relationship between forecast precision and forecast news. We first partition the sample into two groups, Good_News and Bad_News, based on the sign of forecast news. Then we form 20 deciles for each subsample according to absolute values of forecast news, which we denote as forecast surprise. Decile 1 includes firms with the lowest management forecast surprises, and group 20 includes firms with the highest forecast surprises. We then calculate the mean of forecast precision in each decile. The results are depicted in Figure 1. As we can see, average forecast precision is decreasing with FS in the Bad_News sample, which is consistent with the positive correlation reported in Table 4, while the trend is much weaker in the Good_News sample. Gu and Xue (2007) document that analyst forecast dispersion has a U-shaper relationship with earnings surprise, with greater dispersion in negative surprise. The pronounced negative relationship between forecast precision and forecast news in the Bad_News sample, exhibited in figure 1, might be one of the factors that have driven their finding. Table 5 reports the results for the regression analysis of management incentives and forecast precision. First, the coefficient on EquIssue FN_Neg is significantly negative, which indicates that, for negative news issued before equity issuance, managers are more likely to release vague forecasts when their guidance convey more negative news to avoid large price drop. The coefficient on EquIssue FN_Pos is not significant, which is consistent with that managers are more concerned on large drop in stock prices and are more likely to manage bad-news forecasts. Another reason that might contribute to this asymmetric finding across good-news forecasts and bad-news forecasts, is that the behavior of disclosing positive news before selling stocks has a high risk of litigation on its own, because in this case managers are subject to the criticism that they have managed the timing of good-news disclosure in order to make trading profits. This concern can restrain managers from further managing forecast precision at will.Second, the coefficient on InsiderSell FN_Neg is significantly negative. The negative coefficient indicates that, for negative news issued before insider sales, forecast precision decrease with the magnitude of negative news. That is, managers issue vague bad news in order to reduce the price drop before sales and reduce the trading loss. Similar to the finding in equity issuance, the coefficient on InsideSell x FN_Pos is not significant.Third, the coefficient on InsideBuy FN_Pos is negative and marginally significant (P-value=0.07). The positive coefficient suggests that, for good news issued before insider purchase, forecast precision decreases with the magnitude of positive news. That is, managers issue vague good news before insider purchase to delay positive reaction from the market and increase the trading profits. Contrary to the finding in equity financing and insider sales, we do not find significant coefficient on FN_Neg in the case of insider purchase. The contrast further corroborates our previous argument. Managers are subject to the criticism that they have managed the timing of bad-news disclosure in order to increasing purchasing profits, which restrain managers from further managing the precision of bad-news forecasts before insider purchase.Overall, we find that managers issue less precise bad news before equity issuance and insider sales to reduce the blow of bad news to stock prices, and they issue less precise good news to reduce the positive impact of good news on stock price before insider purchases. We do not find results good news disclosed before equity issuance and insider sales or bad news disclosed before insider purchasesRegarding the control variables, the associations among forecast horizon (Horizon), operating profitability (Loss), post-FD (FD), analyst following (Analyst), return volatility (RetVol), research and development cost (Rd) and forecast precision are significantly negative. And the associations between forecast error (FE), firm size (Size) and forecast precision are significantly positive. The coefficient on the market-to-book ratio (M/B) is not significant. Research Design for Hypothesis 2Hypothesis 2 predicts that litigation risk would work against managers incentive to play precision game to increase their trading profits. We use an industry dummy variable, Litig, to identify management forecasts issued by high-risk firms (Ali and Kappapur 2001, Matsumoto 2002). Litig is equal to 1 when the forecast firm is classified in one of the following high-risk industries: SIC codes 2833-2836, 3570-3577, 7370-7374, 3600-3674, and 5200-5961. Litig is set to be 0 if the forecast firm belongs to other industries. Hence, higher value of Litig represents more litigation risk. We partition the full sample into two subsamples, one with Litig equal to 1 and the other with Litig equal to 0, and then we rerun equation (2) for these two subsamples respectively. The results are presented in Table 6. The results in the full sample analysis remain unchanged in the low litigation sample, but the high litigation sample only yields one consistent coefficient on Insider_Sell FN_Neg. Overall, the evidence shows that managers in industries with low litigation risk are more likely to manage forecast precision than in industries with high litigation risk, when they are about to sell stocks on behalf of the firms or purchase stocks on their personal accounts.Research Design for Hypothesis 3Hypothesis 3 predicts that managers are more likely to play the precision game rather than issue biased forecasts when their credibility is determined by forecast accuracy. Hutton and Stocken (2009) find that the accuracy of managers prior earnings forecasts affects the credibility of their subsequent forecasts. Their evidence shows that the stock price response to management forecast news is increasing in prior forecast accuracy. We construct a variable for the effect of forecast accuracy on management credibility, AccCred, based upon their study. Specifically, we employ the following model: EMBED Equation.3 Where, Ret is the event period return measured as the cumulative daily return less the size-decile-matched CRSP index from the day of to one day after the forecast release date. FN is as previously defined. Record is defined by subtracting management forecast accuracy from analyst forecast accuracy and taking the average of the difference for all prior earnings guidance, where forecast accuracy is the absolute value of the difference between actual EPS and management forecast, divided by the pre-release share price and then multiplied with minus 1. More positive difference indicates managers are superior to analysts in forecasting future earnings. High value of Record indicates an accurate forecast record. We run equation (3) over the 5-year window before current management forecasts and separately for each 3-digit SIC industry with a minimum of 20 prior forecasts. This requirement restricts our sample from 7,446 observations to 5,990 observations. On average, the coefficient on FN x Record is positive, consistent with Hutton and Stocken (2009) that managers with a good forecast record are more credible. We also find great variance of the coefficients across industries. Hence, we define AccCred equal to 1 if  EMBED Equation.3  is positive, and 0 otherwise. High value of AccCred indicates that managers credibility is determined by their prior forecast accuracy. We partition the full sample into two, one with AccCred equal to 1 and the other with AccCred equal to 0, and then we rerun equation (2) for these two subsamples respectively. The results are presented in Table 7. The results in the full sample analysis remain unchanged in the high AccCred sample, but the low AccCred sample only yields a consistent coefficient on Inside_Sell x FN_Neg. Overall, the evidence shows that if managers credibility is determined by their forecast accuracy, they are more likely to take the precision strategy for self-interested purposes, especially when they are about to sell stocks on behalf of the firms or purchase stocks on their personal accounts.Further AnalysisAs discussed in Section 2, prior studies report mixed results on the relation between forecast form and stock returns. Given the mixed evidence, it might be worthwhile in our paper to examine the differential market impact. We construct the following model for testing: EMBED Equation.3 Where, Ret, FN_Pos, FN_Neg and Precision are as defined in the previous analyses. Control variables are firm size (Size), the market-to-book ratio (M/B), current forecast accuracy (Accuracy), analyst forecast dispersion (AnaDisp). Size, M/B and Accuracy are as previously defined, and AnaDisp is the standard deviation across individual analyst analysts released 90 days before management forecast, divided by the absolute value of forecast consensus. Precision and all control variables are taken decile ranks and scaled to the range of [0,1] and then interacted with FN_Pos and FN_Neg in equation (4). We incorporate forecast accuracy in the model to account for managers private information set and analyst forecast dispersion to control for the public information set. To mitigate the noise effects, we remove observations with multiple return data in the same event window, which reduces the sample size to 6,963.Empirical results are presented in Table 8. The coefficient on FN_Neg is negative while the interaction term of FN_Neg x Precision is significantly negative. The evidence suggests that investors decrease their response to bad news forecasts if the information is vague. The coefficient on FN_Pos is positive while the interaction term of FN_Pos x Precision is not significant, implying that forecast form does not affect investors response for good news forecast. The weaker evidence for good news disclosure is consistent with the prior findings in Section 3 that managers are more likely to play precision game for bad news forecasting. We leave it to future research to explore why the results are weak for good news. ConclusionOur study examines whether managers manage forecast precision for self-interested purposes. We find that managers are more likely to release vague guidance for more negative news when they are about to make equity financing or to sell stocks on their personal accounts, but the positive news before equity financing and insider sales does not show a pronounced pattern. We find contrary evidence for insider purchase that managers are more likely to release vague guidance for more positive news, but we do not find significant evidence for bad-news forecasts. The contrast implies the effect of potential litigation risk. Specifically, the behavior of disclosing positive news before selling stocks and disclosing negative news before purchasing stocks has a high risk of litigation on its own, because in this case managers are subject to the criticism that they have managed the timing of disclosure in order to make trading profits. This concern can restrain managers from further managing forecast precision at will. We further examine a set of mechanisms that might work on or against the relation between forecast precision and managerial incentives. We find that managers are more likely to manage forecast precision 1) when the litigation risk is low because risk of lawsuit and reputation loss can restrain their opportunistic behavior in forecast precision; 2) when their credibility is determined by their prior forecast accuracy because managers would be reluctant to hurt their credibility by issuing biased forecasts and would be more likely to take the precision strategy. Our paper makes several contributions to the literature. First, our paper extends the voluntary disclosure literature by providing evidence that managers strategically determine forecast precision in their earnings guidance. Second, we indentify trading incentives, either on behalf of firms or on their personal accounts, that can drive managers to play precision game. Our study proposes an alternate strategy other than releasing biased forecasts that managers could take in their forecast decision. To the best of our knowledge, no previous studies have built up a link between managers incentives and forecast precision. APPENDIX APrecision Management Hypotheses are tested using the following variables:AccCred=equal to 1 if the coefficient of 'FNxRecord' in the model 'Ret=FN+Record+FNxRecord' is positive, and 0 otherwise. Accuracy=equal to 1 if current forecast accuracy is greater than the sample median and 0 otherwise. Current forecast accuracy is calculated as the absolute value of the difference between actual EPS and management forecast, divided by the pre-release share price and then multiplied with minus 1.AnaDisp=standard deviation across individual analyst analysts released 90 days before management forecast, divided by the absolute value of forecast consensus.Analyst =analyst following, defined as the log transformation of the number of analysts that follow a firm.EquIssue=equity financing. 1 if a firm makes external financing by equity issuance over the thirty-day window beginning the first day of the management forecast, and 0 otherwise. FD =indicator variable of Full Disclosure Regulation (FD), equal 1 when a management forecast is issued after year 2000, and 0 otherwise.FE =forecast error, calculated as subtracting actual EPS from the management forecast, divided by the pre-release share price.FN =forecast news is calculated as (Management forecast of EPS Consensus analyst forecast of EPS)pre-release share price.FN_Pos =positive forecast news. Equal 0 when FN is negative and equal to the absolute value of FN when FN is positive.FN_Neg =negative forecast news. Equal 0 when FN is positive and equal to the absolute value of FN when FN is negative.Horizon =forecast horizon, equal the number of calendar days between the forecast release date and the earnings announcement date.Inside_Buy=insider purchase. 1 when the net insider trading subsequent to management forecast is positive and 0 otherwise.Inside_Sell=insider sales. 1 when the net insider trading subsequent to management forecast is negative and 0 otherwise.Litig =litigation risk, equal 1 if a management forecast is issued by high-risk firms: SIC codes 2833-2836, 3570-3577, 7370-7374, 3600-3674, and 5200-5961, and 0 otherwise.Loss =profitability of the forecasted earnings, equal 1 when the forthcoming earnings is negative, and 0 otherwise.M/B=growth opportunities, calculated as the ratio of the previous quarters market capitalization divided by the previous quarters book value of equity.Precision=forecast precision, defined as forecast width, Width, multiplied with minus 1.Record=average forecast accuracy of all prior earnings guidance and forecast accuracy is calculated as the absolute value of the difference between actual EPS and management forecast, divided by the pre-release share price and then multiplied with minus 1.Rd=research and development cost divided by net sales.Reliab=equal to 1 if average difference between management forecast accuracy and analyst forecast accuracy is larger than the sample median and 0 otherwise. Average difference is calculated by subtracting management forecast accuracy from analyst forecast accuracy and taken average for all prior earnings guidance. Forecast accuracy is calculated as the absolute value of the difference between actual EPS and management forecast, divided by the pre-release share price and then multiplied with minus 1.Ret=event period return measured as the cumulative daily return less the size-decile-matched CRSP index from the day of to one day after the forecast release date.RetVol=variance in daily stock returns over the 250 trading days prior to the forecast dateSize =firm size, calculated as the natural log of a firms market capitalization of the previous quarter.Width =forecast width. 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Table 1 Sample Selection and Data RequirementsPoint or range estimates of current quarterly earnings issued between the previous earnings announcement dates and before the quarter-end dates0 40,602 Less: Estimates not initially issued after the previous earnings release date9,563Estimates with insufficient data for forecast precision 4,732 Estimates with insufficient data for determining management forecast news 9,102 Estimates with insufficient data for other management forecast characteristics 5,907 Firms with insufficient data on Compustat, CRSP, IBES, Thomson Financial or SDC3,832 Sample for testing hypotheses 7,466 Table 2Descriptive Statistics of Management Earnings ForecastsPanel A: Number of management forecast quarters0Quarter0000Year1234Total%199944443535158(2%)2000437227104246(3%)2001169230160239798(11%)2002204305169246924(12%)20032333051983001,036(14%)20042933902823681,333(18%)20053074382653871,397(19%)20063694863333861,574(21%)Total1,662(22%)2,270(30%)1,469(20%)2,065(28%)7,466(100%)Panel B: Form of forecastsForm0Point1,165(16%)Range6,301(84%)Total7,466(100%)Panel C: Management Forecast Earnings NewsType of management forecast newsPer management forecastGood News3,159(42%)Bad News4,201(56%)Confirming106(2%)Total7,466(100%)Distributional properties for the sample of 7,466 point and range management earnings forecasts released in the year 1999 through 2006. Table 3Descriptive StatisticsPanel A: Descriptive Statistics of Main VariablesPercentile0Mean5%25%50%75%95%Std. Dev.Forecast Precision (Precision)-0.10**-0.33 -0.10 -0.05 -0.10 0.000.17 Management Forecast News (FN)-0.005**-0.011 -0.002 -0.003 0.001 0.009 0.006 Equity Issuance (EquIssue)0.01**0.00 0.00 0.00 0.00 0.00 0.09 Inside Trading (Inside)0.18**-1.00 0.00 0.00 1.00 1.00 0.62 Litigation (Litig)0.36**0.00 0.00 0.00 1.00 1.00 0.48 Effect of Forecast Accuracy on Credibility (AccCred)0.64**0.00 0.00 1.00 1.00 1.00 0.48 Management Forecast Accuracy (Accuracy)0.004**0.00 0.0006 0.002 0.004 0.012 0.01 Management Perceived Reliability (Reliab)-0.002**-0.016-0.005-0.00010.0010.0060.009Management Forecast Error (FE)0.001**-0.006 -0.002 0.00 0.002 0.01 0.012 Management Forecast Horizon (Horizon)85.7**34 84 91 96 112 23.84 Firm Growth (M/B)6.26**1.061.812.694.159.48226.24Firm Size (Size)7.47**5.23 6.42 7.32 8.43 10.14 1.50 Firm Profitability (Loss)0.09**0.00 0.00 0.00 0.00 1.00 0.29 Analyst Following (Analyst)1.54**0.69 1.10 1.39 1.95 2.71 0.65 Research and Development Cost (Rd)0.07**0.00 0.00 0.00 0.11 0.27 0.15 Return Volatility (RetVol)0.03**0.01 0.02 0.03 0.04 0.06 0.01  Table 3 (continued)Panel B: Forecast Precision and Forecast NewsForecast PrecisionDeciles of forecast surpriseGood_NewsBad_News1-0.047-0.0832-0.05-0.0493-0.049-0.064-0.074-0.075-0.066-0.0636-0.051-0.0747-0.066-0.088-0.085-0.0959-0.069-0.07610-0.093-0.11311-0.066-0.10712-0.074-0.12813-0.066-0.12914-0.056-0.15615-0.07-0.15916-0.055-0.19217-0.067-0.18718-0.055-0.22119-0.058-0.214200-0.064-0.204*,**significant at .05 and .01 level, respectively, using a two-tailed test based upon the Student's t test and the Wilcoxon signed ranked test for medians.Descriptive statistics for the sample of 7,466 management earnings forecasts released inthe years 1999 through 2006.Forecast surprise is defined as the absolute values of forecast news (FN). All variables are defined in Appendix A. Table 4 Correlation MatricesPanel A: Correlations between Precision, FN, and FE0PrecisionFNFEPrecision1FN0.23**1FE0.02*0.12**1Panel B: Correlations between Independent Variables Used to Test Precision Adjustment Hypothesis0EquIssueInsideLitigAccuracyReliabAccCredSizeM/BLossAnalystHorizonRdRetVolEquIssue1Inside0.011Litig-0.04**0.08**1Accuracy-0.01-0.04**0.011Reliab0.02-0.02*0.05**0.25**1AccCred0.010.06**0.14**-0.04**0.011Size-0.04**0.03**-0.05**-0.11**-0.25**-0.021M/B0.12**0.01-0.010.000.0050.010.001Loss-0.01-0.07**0.12**0.20**0.07**-0.05**-0.24**0.001Analyst-0.04**0.000.12**-0.03*-0.09**-0.03**0.37**-0.010.001Horizon0.000.10**0.09**0.05**0.020.03**-0.04**0.00-0.05**0.021Rd-0.010.04**0.37**0.04**0.10**0.05**-0.08**0.000.29**0.08**0.04**1RetVol0.00-0.020.35**0.08**0.10**-0.05**-0.36**0.000.38**-0.01-0.08**0.33**1*,**significant at .05 and .01 levels, respectively, using a two-tailed test.Correlation matrices for the sample of 7,466 management earnings forecasts released in the years 1999 through 2006.All variables are defined in Appendix A. Table 5 Results for the Precision Management HypothesisRegression results for the sample of 7,466 management forecasts released in the years 1999 through 2006. The coefficients and related t-statistics are estimated using the following model: EMBED Equation.3 Dependent Variable: Forecast Precision (Precision)VariablePredicted SignCoefficientsP-ValueFN_Pos+2.5860.001FN_Neg--5.060.001EquIssuenone0.0070.79EquIssue x FN_Pos+0.0580.991EquIssue x FN_Neg--24.4710.014Inside_Sellnone0.0310.001Inside_Sell x FN_Pos+-1.6680.162Inside_Sell x FN_Neg--12.7520.001Inside_Buynone0.0080.269InsideBuy x FN_Pos--3.2240.071InsideBuy x FN_Neg+0.2830.835FEnone0.2540.102Horizon--0.00010.069M/Bnone00.675Sizenone0.0190.001Loss--0.0160.039FD--0.0370.001Analystnone-0.0080.015Volatility--1.1320.001Rd--0.0910.001Adjusted R-Square13.86%n07,466P-Values are based on two-tailed test.All variables are defined in Appendix A.0000 Table 6Relation between Forecast Precision, Forecast News, and Management Incentives(conditional on litigation risk)Regression results for the sample of 7,466 management forecasts released in the years 1999 through 2006. The coefficients and related t-statistics are estimated using the following model: EMBED Equation.3 Dependent Variable: Forecast Precision (Precision)Low LitigHigh LitigVariablePredicted SignCoef.P-ValueCoef.P-ValueFN_Pos+2.0920.0010.313 0.881FN_Neg--5.1720.001-5.660 0.001EquIssuenone-0.0190.4120.067 0.401EquIssue x FN_Pos+0.5210.9012.243 0.942EquIssue x FN_Neg--24.5250.006-19.455 0.498Inside_Sellnone0.0250.0010.042 0.001Inside_Sell x FN_Pos+-1.8350.1030.480 0.876Inside_Sell x FN_Neg--11.7390.001-14.327 0.001Inside_Buynone0.0070.3430.003 0.879InsideBuy x FN_Pos--3.3070.050-0.103 0.985InsideBuy x FN_Neg+1.6780.242-0.896 0.738FEnone0.6660.001-0.093 0.712Horizon-00.8010.000 0.219M/Bnone00.5750.001 0.042Sizenone0.0150.0010.025 0.001Loss--0.0340.0010.005 0.744FD--0.0250.004-0.053 0.004Analystnone-0.010.0030.000 0.956Volatility--0.9710.001-0.903 0.001Rd--0.1840.001-0.057 0.004Adjusted R-Square15.16%11.64%n04,7762,690P-Values are based on two-tailed test.All variables are defined in Appendix A.0000000 Table 7Relation between Forecast Precision, Forecast News, and Management Incentives(conditional on effect of forecast accuracy on managerial credibility)Regression results for the sample of 5,990 management forecasts released in the years 1999 through 2006. The coefficients and related t-statistics are estimated using the following model:  EMBED Equation.3 Dependent Variable: Forecast Precision (Precision)Low AccCredHigh AccCredVariablePredicted SignCoef.P-ValueCoef.P-ValueFN_Pos+1.199 0.4022.696 0.016FN_Neg--3.761 0.001-6.394 0.001EquIssuenone-0.046 0.4110.041 0.318EquIssue x FN_Pos+22.430 0.362-2.792 0.829EquIssue x FN_Neg--2.545 0.873-78.670 0.001Inside_Sellnone0.037 0.0010.032 0.001Inside_Sell x FN_Pos+0.117 0.96-2.908 0.14Inside_Sell x FN_Neg--15.520 0.001-14.573 0.001Inside_Buynone0.014 0.3340.007 0.548InsideBuy x FN_Pos--0.412 0.914-5.845 0.034InsideBuy x FN_Neg+-4.443 0.1101.358 0.517FEnone0.022 0.9010.890 0.037Horizon--0.001 0.4730.000 0.052M/Bnone0.000 0.7250.000 0.759Sizenone0.019 0.0010.022 0.001Loss--0.012 0.369-0.002 0.848FD--0.051 0.076-0.043 0.023Analystnone-0.012 0.055-0.004 0.397Volatility--1.443 0.001-1.300 0.001Rd--0.006 0.802-0.112 0.001Adjusted R-Square12.41%14.93%n02,1673,823P-Values are based on two-tailed test.All variables are defined in Appendix A.0000000 Table 8Forecast Precision and Market Response to Management ForecastsRegression results for the sample of 6,963 management forecasts released in the years 1999 through 2006. 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All variables are defined in Appendix A. Figure 1:Forecast News and Forecast PrecisionFor the whole sample of 7,466 observations, we first partition the sample into two groups, Good_News and Bad_News, based on the sign of forecast news. Then we form 20 deciles for each subsample according to forecast surprises and forecast surprise is defined as the absolute values of forecast news (FN). Decile 1 includes firms with the lowest management forecast surprises, and group 20 includes firms with the highest management forecast surprises. We then calculate the mean of forecast precision in each decile. Refer to Appendix A for variable definitions. Hirst et.al. (2008) note that extant literature mainly focused on why managers choose to issue a forecast and the likely consequences of those decisions. They call for more research on managers choices on forecast characteristics.  Other characteristics include horizon, level of details, and supplemental information etc. More detailed review of management forecasts literature can be found in Cameron (1986) and Hirst, Koonce and Venkataraman (2008). Rogers and Stocken (2005) finds the credibility of management forecasts varies with their incentives and the market ability to detect misrepresentation. The extent of market response may depend on the ability that the market detects the misrepresentation. (see Rogers and Stocken 2005).  Other studies (such as Pownall et al. 1993) however find insignificant relationship between market response and forecast form.  Estimating the variable for effect of forecast accuracy on managerial credibility, AccCred, restricts the sample from 7,466 to 5,990 . Analysis for market response restricts the sample from 7,466 to 6,963, because observations with multiple stock returns on the same day can generate noise and are thus removed.PAGE PAGE 36 PAGE 31Many prior studies do similar analysis about precision after examining the frequency of MF: Baginski et al. 2004; Ajinkya et al. 2005 JAR; Amed and Dullman 2005 JAR.  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|$$Ifl8Nzf8$!"+&'R+>,2/03v48'z''&'''D'';''''l''p86<<<<_1332742981FpspsOle |CompObj }fObjInfoOlePres000!PEquation Native 5_1332742982($F`Ms`MsOle 7 (  .   2&@2 & MathTypeSymbolG aXwaw @wmf-2 Q"ey2 Qby2 "by2 by2 by2 by2 by2 by2 v!by2 v0by2 v6by2 vbySymbol[ $Xwaw @wmf-2 Q!+y2 Qv+y2 Qy2 Q+y2 )y2  +y2 s+y2 y2 +y2 H&y2 +y2 V+y2 l y2 v0+y2 v)y2 v~ +y2 v+y2 v +y2 vj=yTimes New RomanXwaw @wmf- 2 Q Variables 2 QControl 2 Q" InsideBuy 2 QJ Negt2 QFN 2 /Buyt 2 *Inside 2 O'Posi2 #FN 2 (Buyi 2 *Inside 2 Sell 2 Inside 2  Negi2 FN 2 `,Sell 2 h'Inside 2 #Posi2 f FN 2 Sell 2 Inside 2 EquIssue 2  NegI2 HFN 2 v>*EquIssue 2 v&PosI2 v<#FN 2 vEquIssue 2 v4NegI2 vFN 2 vv PosI2 v FN 2 vF PrecisionTimes New RomanXwaw @wmf-2 Q0 _N2 ._N2 ;&_N2 _N2 _N2  _N2 R+_N2 "_N2 _N2 _N2 v%_N2 v_N2 vb _N Times New RomanXwaw @wmf-2 112 h"102 h902 h802 702 u602 502 "402  302 -202 10 & "Systemmf !-C0?} Precision= 1 FN_Pos+ 2 FN_Neg+ 3 EquIssue+ 4 FN_PosEquIssue+ 5 FN_NegEquIssue+ 6 Inside_Sell+ 7 FN_PosInside_Sell+ 8 FN_NegInside_Sell+ 9 Inside_Buy+ 10 FN_PosInside_Buy+ 11 FN_NegInsideBuy+ControlVariables+ FMicrosoft Equation 3.0 DS Equation Equation.39q7 (  CompObj#&fObjInfoOlePres000%'PEquation Native 5.   2&@2 & MathTypeSymbolG aXwaw @wmf-2 Q"ey2 Qby2 "by2 by2 by2 by2 by2 by2 v!by2 v0by2 v6by2 vbySymbol[ $Xwaw @wmf-2 Q!+y2 Qv+y2 Qy2 Q+y2 )y2  +y2 s+y2 y2 +y2 H&y2 +y2 V+y2 l y2 v0+y2 v)y2 v~ +y2 v+y2 v +y2 vj=yTimes New RomanXwaw @wmf- 2 Q Variables 2 QControl 2 Q" InsideBuy 2 QJ Negt2 QFN 2 /Buyt 2 *Inside 2 O'Posi2 #FN 2 (Buyi 2 *Inside 2 Sell 2 Inside 2  Negi2 FN 2 `,Sell 2 h'Inside 2 #Posi2 f FN 2 Sell 2 Inside 2 EquIssue 2  NegI2 HFN 2 v>*EquIssue 2 v&PosI2 v<#FN 2 vEquIssue 2 v4NegI2 vFN 2 vv PosI2 v FN 2 vF PrecisionTimes New RomanXwaw @wmf-2 Q0 _N2 ._N2 ;&_N2 _N2 _N2  _N2 R+_N2 "_N2 _N2 _N2 v%_N2 v_N2 vb _N Times New RomanXwaw @wmf-2 112 h"102 h902 h802 702 u602 502 "402  302 -202 10 & "Systemmf !-C0?} Precision= 1 FN_Pos+ 2 FN_Neg+ 3 EquIssue+ 4 FN_PosEquIssue+ 5 FN_NegEquIssue+ 6 Inside_Sell+ 7 FN_PosInside_Sell+ 8 FN_NegInside_Sell+ 9 Inside_Buy+ 10 FN_PosInside_Buy+ 11 FN_NegInsideBuy+ControlVariables+ FMicrosoft Equation 3.0 DS Equation Equation.39q7 (  .   2&()44 lal$$Ifl!vh5z555555D55 ;5 5 5 5 l55p#vz#v#v#v#v#v#vD#v#v ;#v #v #v #v l#v#vp:V l886,,,5z555555D55 ;5 5 5 5 l55p9/ alkdN$$Ifl8Nzf8$!"+&'R+>,2/03v48'z''&'''D'';''''l''p86<<<<44 lal]$IfK$L$l!vh5#v:V l;6,59/ $IfK$L$l!vh5 5U5#v #vU#v:V li6,5 5U59/ ]$IfK$L$l!vh5#v:V l;6,59/ $IfK$L$l!vh55,5#v#v,#v:V l, t6,55,59/ /  / U$IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ / / / / / / / / / /  / $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/ $IfK$L$l!vh55,5 55 #v#v,#v #v#v :V l, t6,55,5 55 9/  / _$$If!vh5$D#v$D:V l8$D6,5$D9/ ad$$If!vh5<6#v<6:V l8$D6,5<69/ ad$$If!vh5#v:V l8$D6%,59/ a_$$Ifl!vh5,D#v,D:V l8:6,5:9/ al$$Ifl!vh5V/555555#vV/#v#v#v#v#v#v:V l:6,5&555559/ / / / / al$IfK$L$l!vh5p5p5858#vp#v8:V lJ t6,589/  / $IfK$L$l!vh5p5p5858#vp#v8:V l; t6,589/ $IfK$L$l!vh5p5p5858#vp#v8:V l; t6,589/ $IfK$L$l!vh5p5p5858#vp#v8:V l; t6,589/ -$$Ifl!v h555555h555 5 5 5 #v#v#v#vh#v#v#v #v #v #v :V l8:6, 555555 5 5 5 9 / alkdX$$Ifl8  l!-&*V/48;?@C,D&&&&&&&&&&&&:6000044 lalu$$Ifl!vh5@C5#v@C#v:V l8:6,5959/ al$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l; t(26,585L5H5855$5H5 5 H5 5 5 5\99/  / nkd$IfK$L$l;88 Rv!%(,/A3'8'L'H'H'8'$'H''H''''\ t(26888844 la$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,,585L5H5855$5H5 5 H5 5 5 5\99/ nkd$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8'$'H''H'''&\ t(26888844 la$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,,585L5H5855$5H5 5 H5 5 5 5\99/ nkd $IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8'$'H''H'''&\ t(26888844 la$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,,585L5H5855$5H5 5 H5 5 5 5\99/ nkd$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8'$'H''H'''&\ t(26888844 la$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,,585L5H5855$5H5 5 H5 5 5 5\99/ nkd$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8'$'H''H'''&\ t(26888844 la$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,,585L5H5855$5H5 5 H5 5 5 5\99/ nkd$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8'$'H''H'''&\ t(26888844 lay$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,585L5H5855$5H5 5 H5 5 5 5\9/ nkd$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8''$'H''H'''&\ t(26888844 lay$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,585L5H5855$5H5 5 H5 5 5 5\9/ nkdк$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8''$'H''H'''&\ t(26888844 lay$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,585L5H5855$5H5 5 H5 5 5 5\9/ nkd$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8''$'H''H'''&\ t(26888844 lay$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,585L5H5855$5H5 5 H5 5 5 5\9/ nkd$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8''$'H''H'''&\ t(26888844 lay$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,585L5H5855$5H5 5 H5 5 5 5\9/ nkd$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8''$'H''H'''&\ t(26888844 lay$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,585L5H5855$5H5 5 H5 5 5 5\9/ nkd|$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8''$'H''H'''&\ t(26888844 lay$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l, t(26,,585L5H5855$5H5 5 H5 5 5 5\9/ nkdg$IfK$L$l,88 Rv!%(,/A3'8'L'H'H'8''$'H''H'''&\ t(26888844 la$IfK$L$l!vh585L555855$55 5 5 5 5 55\#v8#vL#v#v8#v#v$#v#v #v #v #v #v 5#v\:V l; t(26,585L5H5855$5H5 5 H5 5 5 5\9/  / nkdR$IfK$L$l;88 Rv!%(,/A3'8'L'H'H'8''$'H''H''''\ t(26888844 la$$Ifl!vh5455555#v4#v#v#v#v#v:V l8:6,5*555559/ al_$$Ifl!vh5,D#v,D:V l8:6,5:9/ alj$$Ifl!vh5r #vr :V l8$6H,5r 9/ alyt~j$$Ifl!vh5r #vr :V l8$6H,5r 9/ alyt~$$Ifl!vh5 55+5555#v #v#v+#v#v#v#v:V l8$6H,5 55+55559/ alyt~Dd\R  S A@?"?2o&Ye鰩\EC\`!o&Ye鰩\EC\(2 0JNxVMlLQ>ס-Ei͌*'BJjE$7}l;XU҅ ;? J"bSH{}ͻ3,׹={n hK@eO{;RqR.,v<^HT"Fh-~F3ݝNcGK SpÞi\U (-҅,=~L7d.r# z CB?xUq ^fo7~M/i-`cKd<zς" `昔O<^V\g={׮/&TMƏ/Mt6oc2Ά|h1"R|$gb7<;KyGL0Ic2:Rȥ;w!7'8ϤYՎml~o!_/dو졼9c(Y*(%sE{QL ~݈ SԹ~QHhk5\03Bu:k;ӳVu3sf]և,FvSڦ6:6[ScW]r6=GmSmiN&C9at6,C"'6U.,"?prͶ˯U^"/V<ubA^錙)ywKyTmmX'"#O[g56Y/G 6Żd|\_-vޅ]E.Nsס-Ei͌*'BJjE$7}l;XU҅ ;? J"bSH{}ͻ3,׹={n hK@eO{;RqR.,v<^HT"Fh-~F3ݝNcGK SpÞi\U (-҅,=~L7d.r# z CB?xUq ^fo7~M/i-`cKd<zς" `昔O<^V\g={׮/&TMƏ/Mt6oc2Ά|h1"R|$gb7<;KyGL0Ic2:Rȥ;w!7'8ϤYՎml~o!_/dو졼9c(Y*(%sE{QL ~݈ SԹ~QHhk5\03Bu:k;ӳVu3sf]և,FvSڦ6:6[ScW]r6=GmSmiN&C9at6,C"'6U.,"?prͶ˯U^"/V<ubA^錙)ywKyTmmX'"#O[g56Y/G 6Żd|\_-vޅ]E.Ns?@BCDEFHIJKLMNOPQRT@2 & MathTypeSymbolG aXwaw @wmf-2 Q"ey2 Qby2 "by2 by2 by2 by2 by2 by2 v!by2 v0by2 v6by2 vbySymbol[ $Xwaw @wmf-2 Q!+y2 Qv+y2 Qy2 Q+y2 )y2  +y2 s+y2 y2 +y2 H&y2 +y2 V+y2 l y2 v0+y2 v)y2 v~ +y2 v+y2 v +y2 vj=yTimes New RomanXwaw @wmf- 2 Q Variables 2 QControl 2 Q" InsideBuy 2 QJ Negt2 QFN 2 /Buyt 2 *Inside 2 O'Posi2 #FN 2 (Buyi 2 *Inside 2 Sell 2 Inside 2  Negi2 FN 2 `,Sell 2 h'Inside 2 #Posi2 f FN 2 Sell 2 Inside 2 EquIssue 2  NegI2 HFN 2 v>*EquIssue 2 v&PosI2 v<#FN 2 vEquIssue 2 v4NegI2 vFN 2 vv PosI2 v FN 2 vF PrecisionTimes New RomanXwaw @wmf-2 Q0 _N2 ._N2 ;&_N2 _N2 _N2  _N2 R+_N2 "_N2 _N2 _N2 v%_N2 v_N2 vb _N Times New RomanXwaw @wmf-2 112 h"102 h902 h802 702 u602 502 "402  302 -202 10 & "Systemmf !-C0?} Precision= 1 FN_Pos+ 2 FN_Neg+ 3 EquIssue+ 4 FN_PosEquIssue+ 5 FN_NegEquIssue+ 6 Inside_Sell+ 7 FN_PosInside_Sell+ 8 FN_NegInside_Sell+ 9 Inside_Buy+ 10 FN_PosInside_Buy+ 11 FN_NegInsideBuy+ControlVariables+ FMicrosoft Equation 3.0 DS Equation Equation.39qVL{ v .  @@E&E & MathType`xL7;h;7y qWx1$$Ifl; G3Vy#& &&c&'&&&'&&{ t96j,,,,44 la]yt~d$$If]!v h5 55c555555 5 5 {#v #v#vc#v#v#v#v#v#v #v #v {:V l; t96j,,,, , 5 55c555555 5 5 {9 / a]yt~kdA$$Ifl; G3Vy#& &&c&'&&&'&&{ t96j,,,,44 la]yt~d$$If]!v h5 55c555555 5 5 {#v #v#vc#v#v#v#v#v#v #v #v {:V l; t96j,,,, , 5 55c555555 5 5 {9 / a]yt~kdgE$$Ifl; G3Vy#& &&c&'&&&'&&{ t96j,,,,44 la]yt~d$$If]!v h5 55c555555 5 5 {#v #v#vc#v#v#v#v#v#v #v #v {:V l; t96j,,,, , 5 55c555555 5 5 {9 / a]yt~kdH$$Ifl; G3Vy#& &&c&'&&&'&&{ t96j,,,,44 la]yt~L$$If]!v h5 55c555555 5 5 {#v #v#vc#v#v#v#v#v#v #v #v {:V l; t96j, 5 55c555555 5 5 {9 / a]yto`kd?L$$Ifl; G3Vy#& &&c&&&&&&&&{ t96j,,,,44 la]yto`L$$If]!v h5 55c555555 5 5 {#v #v#vc#v#v#v#v#v#v #v #v {:V l; t96j, 5 55c555555 5 5 {9 / a]yto`kdO$$Ifl; G3Vy#& &&c&&&&&&&&{ t96j,,,,44 la]yto`$$If]!v h5 55c555555 5 5 {#v #v#vc#v#v#v#v#v#v #v #v {:V lJ t96j, 5 55c555555 5 5 {9 / /  / / / a]yto`kdR$$IflJ G3Vy#& &&c&&&&&&&&{ t96j,,,,44 la]yto`L$$If]!v h5 55c555555 5 5 {#v #v#vc#v#v#v#v#v#v #v #v {:V l; t96j, 5 55c555555 5 5 {9 / a]yto`kdsV$$Ifl; G3Vy#& &&c&&&&&&&&{ t96j,,,,44 la]yto` $$If]!v h5V55555555 {#vV#v#v#v#v#v#v#v#v {:V l; t96j, 5V55555555 {9 / a]yto`$$If]!vh5B5555555{#vB#v#v#v#v#v#v#v{:V l; t96j,5B5555555{9/  / a]yto`Dd\R  S A@?"?2o&Ye鰩\EC\G\`!o&Ye鰩\EC\(2 0JNxVMlLQ>ס-Ei͌*'BJjE$7}l;XU҅ ;? 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