Analysts Annual Forecasts and Quarterly Earnings Releases by Stephen

Analysts’ Annual Forecasts and Quarterly Earnings Releases by Stephen J. Ciccone* Abstract ________________________________________________________________________ This study examines analysts’ annual earnings forecasts and “updated” naïve forecasts that incorporate quarterly earnings releases. The updated naïve forecasts provide a measure for direct comparison with analyst forecasts and also a control for changes in forecasting difficulty. The results show that the updated naïve forecasts are more accurate when forecasting loss firm earnings and less biased overall than the analysts. In addition, when controlling for forecasting difficulty, the trends of decreasing analyst forecast errors over the forecasting horizon and over the sample period are considerably weaker than previous studies indicated. The trend of increased analyst pessimism is unaffected, however. ________________________________________________________________________ __________________________________________ * University of New Hampshire, Whittemore School of Business and Economics, McConnell Hall, 15 College Road, Durham, NH 03824. Phone: 603.862.3343; Email: stephen.ciccone@unh.edu. I. Introduction A number of studies evaluating analyst forecast accuracy reach several near unanimous conclusions: analyst accuracy increases as the forecasting horizon shortens (e.g., Richardson, Teoh, Wyscoki, 2004), analyst accuracy has improved over time (e.g., Brown, 1997), and analyst forecasts are now pessimistically biased (e.g., Brown, 2001). While many early studies of analyst forecasts controlled for forecasting difficulty by including some type of naïve forecast, usually last year’s earnings (e.g., Elton Gruber, and Gultekin, 1984), more recent studies typically exclude this control. As a result, certain conclusions regarding forecast accuracy or optimism might be misleading. The purpose of this study is to reevaluate analysts’ annual forecast accuracy and optimism using naïve forecasts that incorporate quarterly earnings information. Four “updated” naïve forecast models are utilized. Despite being only slightly more complicated, the updated naïve forecasts are clearly superior to naïve forecasts using only last year’s earnings. The updated naïve forecasts are useful for two types of analyses. The first is a direct comparison between the analyst forecasts and the updated naïve forecasts. The second is an evaluation of analyst forecast trends, both over the forecasting horizon and over the sample period. Theil’s Inequality Coefficient, computed as the sum of the analyst forecast error variance divided by the sum of the naïve forecast variance, is particularly well suited for these purposes. Although most studies using the ratio place last year’s earnings in the denominator, the denominator can easily be adjusted to incorporate quarterly earnings releases. This updated Theil’s Inequality Coefficient provides a direct measure for comparing analyst and naïve forecasts, while including a 2 built-in control for forecasting difficulty over the forecasting horizon and over the sample period. A significant amount of the testing herein relies on this measure. Other testing procedures utilize linear regression models using forecast error as the dependent variable and logit regression models using forecast optimism as the dependent variable. In the direct comparison, the updated naïve forecasts perform admirably versus the analysts, actually outperforming the analysts when forecasting for loss firms. The updated naïve forecasts also tend to contain less bias near the end of the forecasting period. In the trend analysis, after using the updated naïve forecasts to control for forecasting difficulty, analyst forecasts do not significantly improve over the forecast horizon. This result is important because it implies that, despite the broad information set available to analysts, most of the forecast error reductions over the forecasting horizon are simply attributable to quarterly earnings releases. Furthermore, analysts’ annual forecasts do not notably improve throughout most of the time period studied. Rather, the previously observed trend of increased accuracy is associated with increased earnings smoothness and more accurate naïve forecasts. In contrast, the trend of increased forecast pessimism maintains its strength when controlling for the updated naïve forecasts, although analyst bias is a clear function of updated naïve forecast bias. This paper is organized as follows. Section II reviews relevant literature. Section III explains the data and presents preliminary statistics. discusses the main results. Section V concludes. Section IV presents and 3 II. Literature Review A. Early Studies of Analyst Performance In many early studies of analyst forecasts, the central topic was the accuracy of the analysts relative to the time series models. Some of the first studies (e.g., Cragg and Malkiel, 1968; Elton and Gruber, 1972) concluded that the analysts were less accurate. This unpleasing result was questioned by several researchers including Brown and Rozeff (1978). They argued that analysts must be more accurate than time series models because analysts are more expensive (and hence must be worth the extra compensation) and can incorporate greater amounts of information into their forecasts. Using more modern techniques than the first studies, Brown and Rozeff (1978) and others, including Fried and Givoly (1978) and Collins and Hopwood (1980), support this argument empirically. Unfortunately, although illuminating, the studies during this period all suffer from small sample sizes (typically around 50 firms), having been undertaken well prior to the easy availability of analyst forecasts covering a large, diverse set of firms. Contemporaneous studies evaluated characteristics of analyst forecasts including forecast bias, sources of forecast error, and properties of forecasts over time. For example, Elton Gruber, and Gultekin (1984) show that analyst errors steadily decrease over the twelve months prior to fiscal year end. They also show that earlier forecast errors are more related to industry misestimates and later forecast errors are more related to firm-specific misestimates. A particularly relevant study by Crichfield, Dyckman, and Lakonishok (1978) compares analyst forecasts with several simple models including a naive model, a moving average model, and three quarterly models, their “k=4” quarterly model being the same as the models used in this study. They conclude that analyst 4 forecast error decreases throughout the forecast horizon except for their k=4 quarterly model. Despite the exception, Crichfield, Dyckman, and Lakonishok (1978) conclude that analyst forecast error decreases as the forecasting horizon shortens. Like contemporary studies, their studied suffered from a small sample size, consisting of only 46 firms. Other notable studies include O’Brien (1988), who also finds analysts are superior to time series models, and Brown, Richardson, and Schwager (1987), who attempt to find the source of analysts’ information superiority versus time series models. Although few subsequent studies directly compared analyst and time series forecasts, later studies concluded that analysts do not properly incorporate time series properties of earnings, especially serial correlation, in their forecasts (e.g., Mendenhall, 1991; Abarbanell and Bernard, 1992; Ali, Klein, and Rosenfeld, 1992). In addition, later studies would uncover systematic biases in analyst forecasts as discussed in the next section. B. Studies of Bias and Error Trends Analyst forecasts were originally found to be optimistically biased (e.g., O’Brien, 1988; Debondt and Thaler, 1990). However, several recent papers have documented the emergence of a pessimistic bias. For example, Brown (2001) finds that the median forecast of an annual sample of firms changed in the 1990s from being optimistically biased to being pessimistically biased. Richardson, Teoh, and Wysocki (2004) observe a similar trend, while also evaluating optimism over the fiscal year. They show that forecasts made earlier in the fiscal period tend to be optimistic, but forecasts made later in the fiscal period tend to be pessimistic. 5 Concurrent with the increasing pessimism has been an increase in forecast accuracy, also extensively documented. Brown (1997) show decreasing forecast errors for both S&P 500 and non-S&P 500 firms. Richardson, Teoh, and Wysocki (2004) observe a downtrend in forecast errors over the forecasting horizon and over time. The downward trends in optimism and error are supported by various theories. Degeorge, Patel, and Zeckhauser (1999) argue that the pessimistic bias arises because managers strive to meet or beat analyst forecasts. They support this argument by showing that small positive surprises are considerably more prevalent than small negative surprises. Matsumoto (2002) argues that firm managers guide analysts toward pessimistic targets and then beat that target. Brown (1996, 1997) believes that analyst forecasts have improved over time. Although the studies mentioned above have firmly supported the trends of increased accuracy and pessimism, this study provides a re-examination of these trends. Reverting back to testing procedures utilizing naïve forecasts to control for forecasting difficulty, the naïve forecasts of annual earnings are improved by incorporating quarterly earnings releases, as discussed in the next section. III. Data and Preliminary Statistics A. Data The Institutional Brokers Estimate System (IBES) summary files are used to obtain the analyst annual forecast (AF) and actual earnings per share (EPS) data.1 For each firm, mean forecasts of earnings per share available in the 12 months prior to and including the fiscal year end are obtained. The first month is labeled “1,” while the fiscal Note that IBES EPS (or “Street” EPS) may be different from GAAP EPS (e.g., Bradshaw and Sloan, 2002). 1 6 year end month is labeled “12.” Thus, for a firm with a December 31 fiscal year end, the mean analyst forecast is called AF 1 in January and AF 12 in December. The last monthly mean forecast available prior to the earnings release date is also obtained (labeled as “Last”), giving each firm a maximum possible total of 13 monthly consensus forecasts. The Last forecast month is usually after the fiscal year end. All results are robust to the use of median rather than mean forecasts.2 The testing uses an optimism measure and two error measures: Theil’s Inequality Coefficient, which is discussed in the next section, and forecast error. Analyst forecast error (AFE) is computed as the absolute value of the difference between EPS and the forecast, deflated by the first available IBES price in the current fiscal year.3 Analyst forecast optimism (AFO) occurs when the mean forecast is greater than the corresponding actual earnings. Analyst forecasts are compared with four “updated” naïve forecasts (UNF). Previous year’s earnings, UNF Q0, is the usual naïve forecast measure. Three additional naïve forecasts are also evaluated. UNF Q1 is computed as four times first quarter earnings. UNF Q2 is computed as twice the sum of first and second quarter earnings. UNF Q3 is computed as four times the average of the first, second, and third quarter earnings. Although there are multiple possibilities for the updated naïve forecasts, the ones used in this study are used because their intuitiveness and simplicity. They are also similar to those of Crichfield, Dychman, and Lakonishok (1978) and Lorek (1979), the latter referring to the forecasts as “simplistic” forecasts. Formally, the updated naïve forecasts are expressed below for fiscal year t: 2 3 The correlation between the mean and median is greater than 0.99 in any of the 13 months. Some studies define forecast error as the signed error and define forecast accuracy as the (unsigned) absolute forecast error. In this study, all errors are unsigned. 7 UNF Q0t = At-1, UNF Q1t = 4 × Q1t, UNF Q2t = 2 × (Q1t + Q2t), UNF Q3t = 4 × [(Q1t + Q2t + Q3t) / 3], (1) (2) (3) (4) where At-1 is annual earnings in year t-1 and Qjt is quarterly earnings in quarter j of year t. UNF error (UNFE) is computed by deflating absolute UNF by price in the same manner as AFE. All results are robust to using actual earnings instead of price as the deflator to compute AFE and UNFE. Updated naïve forecast optimism (UNFO) occurs when the updated naïve forecast is greater than corresponding actual earnings. To be included in the sample, a firm must have enough quarterly earnings information available to make at least one updated naïve forecast. The final sample includes over 55,000 firm-year observations from 1985 through 2002. To evaluate trends, the 18-year sample period is sometimes split into six groups of three years or two groups of nine years. If a firm’s fiscal year ends on or before April 30, its fiscal year is assumed to end in the prior year when grouping by year end. For example, a firm with a January 31, 2002 fiscal year end is placed with firms having May 31, 2001 through December 31, 2001 (actually through April 30, 2002) fiscal year ends. The SEC presently requires quarterly earnings reports (or 10Qs) to be filed within 45 days of quarter end and annual earnings reports (or 10Ks) to be filed within 90 days of year end. (Under the Sarbanes-Oxley Act, these numbers will be reduced to 35 days and 60 days, respectively, for fiscal periods ending December 31, 2004 or later.) However, previous studies find that the vast majority of annual earnings are released within 45 days of fiscal year end (e.g., Givoly and Palmon, 1982). As IBES records analyst forecasts in 8 the middle of the month, virtually all quarterly earnings data and the vast majority of annual earnings data should be available to analysts by the second month after fiscal period end. Thus, analyst forecasts can be compared with the latest updated naïve forecast that has the necessary quarterly information available. These “Latest Available” updated naïve forecasts control for forecasting difficulty throughout the forecasting horizon and the sample period. A guide to these comparisons is below, the ⇒ signifying “compared with:” UNF Q0 ⇒ AF 2, AF 3, AF 4 UNF Q1 ⇒ AF 5, AF 6, AF 8 UNF Q2 ⇒ AF 8, AF 9, AF 10 UNF Q3 ⇒ AF 11, AF 12, AF Last Note that UNF Q1 can be compared with any analyst forecast made on or after the fifth month. However, UNF Q2 is likely to be more accurate than UNF Q1 once second quarter earnings are available in the eighth month. Similarly, UNF Q3 is likely to be more accurate than UNF Q2 or UNF Q1 when third quarter earnings are available in month 11. B. Theil’s Inequality Coefficient Theil (1966) recommends diagnosing forecast error by using a quadratic function to compute the mean squared forecast error (MSFE) for N forecasts at time t: MSFE = 1 N ∑ (AF i =1 N i ,t − EPS i ,t ) 2 (5) 9 where AFi,t is the forecast of earnings per share for firm i and EPSi,t is the corresponding actual earnings per share. Theil recommends deflating the MSFE by the sum of squared changes in earnings to obtain the Theil inequality coefficient (TIC) as below:4 TIC = ∑ (AF i =1 N i ,t − EPS i ,t ) 2 ∑ (EPS i =1 N i ,t − EPS i ,t −1 ) (6) 2 The TIC generates easily interpretable numbers and can be thought of as the ratio of analyst forecast error over naïve forecast error. A 0 indicates perfect analyst forecasts, while a 1 indicates equal accuracy between analyst forecasts and naïve forecasts. A number less than one indicates analyst forecast superiority; a number greater than 1 indicates naïve forecast superiority. The TIC has been used in many studies evaluating analyst forecast accuracy. For example, Elton, Gultekin, and Gruber (1984), demonstrate analyst forecasting superiority versus naïve forecasts and show TIC steadily decreases as the forecasting horizon shortens. Naïve forecasts can be improved by a simple adjustment. As the fiscal year progresses, quarterly earnings are released. Naive forecasts can easily be updated (as previously specified) to use this quarterly information implying a modification to the usual TIC. This “updated TIC” (UIC) compares analyst performance, not to the naïve forecast based solely on last year’s earnings, but to an updated naïve forecast incorporating the recent quarterly earnings releases. The change occurs in the denominator where naïve forecast error is replaced by the updated naïve forecast error. The new ratio is stated formally below: 4 Theil’s Inequality Coefficient, herein TIC, is often denoted as U2 in other studies. 10 Updated TIC = UIC = ∑ (AF i =1 N i =1 N i ,t − EPS i ,t ) 2 ∑ (EPS i ,t − UNFi ,t ) (7) 2 The UIC is interpreted in exactly the same manner as the original TIC. An advantage of using measures such as TIC or UIC is the clarity of the denominator. The alternative, forecast error, is usually computed by dividing AF–EPS by either EPS or price. The former is intuitively appealing and easily interpretable, but introduces the small denominator problem. The latter lacks intuitive appeal and is more difficult to interpret. However, using price in the denominator is often considered standard in the finance and accounting literature (see Richardson, Teoh, and Wysocki, 2004). C. Preliminary Statistics To gain an understanding of changes in forecasting difficulty throughout the time period studied, Table 1 presents the trends of two measures: quarterly earnings volatility and the percent of firms with only quarterly profits or only quarterly losses in a given fiscal year. Quarterly earnings volatility is computed as the standard deviation of the four quarterly earnings divided by the first available price on IBES during the fiscal year. Examining profitability first, over 80% of firms with annual profits report profits in each quarter. The percent of such firms remains stable over the time period. In contrast, the percent of all annual loss firms reporting losses in each quarter is on the rise. In 1985-1987, this percent was only 24.00%, but it increased each period, finally reaching 64.60% during 2000-2002. The table also shows that quarterly earnings volatility for non-loss firms decreased throughout the first ten years of the sample period before leveling off in the 11 1994-1996 sub-period. For loss firms, the volatility decreases considerably throughout the entire sample period, from 0.081 in 1985-1987 to 0.018 in 2000-2002. These preliminary statistics suggest that forecasting earnings has become easier over the sample period. Earnings became smoother and the quarterly sign of earnings became more consistent. IV. Results A. Forecast Error Table 2 presents correlations among EPS, selected AFs, and the UNFs. The selected AFs correspond to the release dates of quarterly earnings. For example, by the fifth month of the fiscal year, the first quarter earnings should have been released. Accordingly, AF 5 (and any subsequent month) can be directly compared to UNF Q1. AF 8 can be similarly compared to UNF Q2, and AF 11 can be compared to UNF Q3. Notably, the correlation between the UNFs and EPS increases over the forecasting horizon. UNF Q0 has a correlation of 0.71 with EPS increasing to 0.83 for UNF Q2 and 0.92 for UNF Q3. Thus, the updated naïve forecasts represent a considerable improvement versus the traditional naïve forecasts (UNF Q0) indicating that forecasting difficulty rapidly decreases near the end of the forecasting horizon. Indeed, UNF Q2 and UNF Q3 appear to be very accurate forecasts. The UNFs are also highly correlated with the AFs. For example, UNF Q3 has a 0.92 correlation with AF Last. Table 3 presents AFE and UNFE by month and time period. The table presents the updated naïve forecasts in the monthly column corresponding to when the information required to make such a forecast is likely available. The analyst forecasting trends uncovered in previous studies are clearly evident in this table. AFE decreases over 12 the forecasting horizon, with the “All Years” sample forecast error decreasing from 0.0450 in month 1 to 0.0172 in the last month. AFE also decreases over the sample period. For example, the last forecast decreases from 0.0269 in 1985-1987 to 0.0113 in 2000-2002. Similar decreases occur in every month. The same trends are evident in the UNFs. These forecasts also become more accurate over the forecasting horizon indicating that incorporating quarterly earnings considerably improves naïve forecasts. For example, in the “All Years” sample, error decreases from 0.0447 using UNF Q0 to 0.0191 using UNF Q3. The UNFs also exhibit the same decrease in error over the sample period. Furthermore, the updated naïve forecast errors are comparable to those of the analysts. For example, AFE Last is 0.0172 and UNFE Q3 is 0.0191 in the “All Years” sample. Table 4 presents the TICs and UICs by month of forecast. The table is useful for several purposes. It provides a direct comparison of analyst and naïve forecasts, a trend analysis over the forecasting horizon, and a trend analysis over the sample period. TIC (or UIC Q0) is the naïve forecast using last years’ earnings and is the usual TIC measure. “Latest UIC” is the latest UIC that can be computed during that forecast month, thus adjusting for forecasting difficulty through time. Panel A shows UICs pooled across all sample years. Panel B breaks down the TICs and Latest UICs by time period, and Panel C shows Latest UICs by profitability. The UICs themselves can be used for the direct comparison. It appears that the updated naïve forecasts are less accurate than the analysts, but they still perform admirably. For example, pooling all years, the Latest UIC Last is 0.91, a number that is close to 1 (recall 1 indicates equal forecasting ability). In addition, Panel C shows that 13 while analysts are clearly superior when forecasting earnings for non-loss firms, they are clearly inferior when forecasting earnings for loss firms. When examining the trends of Panel A, the UICs all steadily decrease during the forecast horizon. The correlations between the UICs and the forecast month are all -0.997, giving the appearance of steady analyst improvement over the forecasting horizon. However, this is not quite the case. In the “Latest UIC” row, which adjusts for forecasting difficulty, this trend vanishes. Rather, UICs increase when quarterly earnings are released resulting in a positive correlation of 0.307 between Latest UIC and time. Moreover, in month 11, the first month UIC Q3 is available, the analysts are inferior to the updated naïve forecasts (Latest UIC = 1.22). By the last month, the analysts are only slightly superior (Latest UIC = 0.91). Note that the Latest UIC Last of 0.91 is greater than seven of the 11 remaining monthly Latest UICs. For example, the Latest UIC in month 3 is 0.89. Overall, these results suggest that analyst improvement over the forecasting horizon is primarily attributable to quarterly earnings releases and not to an informational advantage. To examine trends over the sample period, Panel B presents the TIC and Latest UIC measures by time period. Regardless of the time period, the TICs steadily decrease during the forecast horizon. In all six time periods, the correlation between month and TIC is around –0.99. However, consistent with the results above, similar trends do not exist for the Latest UICs in any given time period. In three of the six time periods, the correlation between Latest UIC and month is actually positive. To gain a further understanding of the time series properties, the 72 Latest UICs are pooled together (from Table 4, Panel B) from month 2 to the last month. The 72 TICs 14 are similarly pooled. A regression is performed using either the Latest UICs or TICs as dependent variables. Two models are used. The first includes only one regressor, the month of the forecast. The second model includes the month and the UIC or TIC of the previous month.5 The latter model reduces the sample size to 66 as the first month of each time period is eliminated from the sample. The results of these regressions are presented on Table 5. When the month is the lone regressor, TIC displays a negative relation to time. When the lagged TIC is added, the time variable loses its significance. The coefficient of the lagged TIC is 0.9834, which is insignificantly different from 1.0000. The intercept term of -0.0745 is significant suggesting changes in TIC can be modeled as a random walk with a negative drift component. In contrast, the latest UICs do not demonstrate a powerful relation to time. The month variable is insignificant in both models and the second model includes a positive drift component. Overall, the analyses reveal that the updated naïve forecasts are quite accurate and that improvements in analyst forecasts over the forecast horizon are primarily attributable to quarterly earnings releases. In addition, with the exception of the 2000-2002 period, there appears to be little decrease in analyst error over the sample period. For example, the last latest available UIC is 0.86 in 1985-1987 and 0.83 in 1997-1999. The next tests examine this latter issue in more detail. Table 6 presents the results of regression models that regress AFE Last against control variables trend dummy variables. Although the results are presented using the AFE Last, the error in any month could be used and all provide similar results. The The included sample months in the second model are 2-13, where 13 is the Last month. However, the regression specifies the first month as 1 rather than 2, the second month as 2 rather than 3, etc. 5 15 control variables include size, E/P ratio, a dummy variable equal to 1 if the E/P ratio is negative, and a loss dummy variable (see Table for descriptions). The use of these control variables is based on an abundance of prior research finding that size, growth prospects, and profitability affect analyst forecasts (e.g., Richardson, Teoh, and Wysocki, 2004).6 The five trend dummy variables each represent three sample period years: 19881990, 1991-1993, 1994-1996, 1997-1999, and 2000-2002. The dummy variables coefficients are interpreted relative to the base time period of 1985-1987, whose effect is included in the intercept. Two additional variables are also included: quarterly earnings volatility and UNFE Q3. These two variables control for forecasting difficulty. For example, the decrease in forecast error might coincide with the reduction of earnings volatility as seen on Table 1. Model 1 includes size, E/P ratio, the E/P dummy, a loss dummy, and time period dummies as regressors. Model 2 adds quarterly earnings volatility to Model 1, while model 3 adds UNFE Q3 to Model 1. Model 4 includes both earnings volatility and UNFE Q3. Consistent with prior research, size is negatively related to forecast error and the loss dummy is positively related to forecast error in all the models. The E/P Ratio and E/P Loss Dummy coefficients are more ambiguous, changing sign depending on the regression. In Model 1, the trend dummy variables are negatively significant with the exception of 1988-1990, which is insignificant. Thus, as time increases, forecast error decreases, consistent with previous studies. 6 The results are similar if book-to-market ratio is used in place of E/P ratio. 16 The addition of quarterly earnings volatility in Model 2 has a profound effect on the trend dummy variable coefficients, causing the ones from 1991-1993 onward to decrease sharply. For example, the negative coefficient of the 1991-1993 dummy variable is now insignificant, and the magnitude of the 1994-1996 coefficient decreases about 65%, from -0.0116 to -0.0041. Model 3 adds UNFE Q3 to model 1. In this model, the trend dummy variables lose even magnitude versus model 2. For example, the 1994-1996 coefficient is now -0.0022. Finally, Model 4 includes both quarterly earnings volatility and UNFE Q3. In this model, the trend dummy variables lose most of their original magnitude. For example, the 1994-1996 and 1997-1999 coefficients are about a tenth of their Model 1 values. In addition, their values, both around -0.0010, are probably not economically significant. significance. Overall, the trends in forecast error over time nearly vanish when controlling for changes in forecasting difficulty. Importantly, however, analyst forecast errors do appear to decrease during the final sample period of 2000-2002. Whether the decrease in this period is due to Regulation FD, changing market conditions (i.e., bursting of the tech bubble), or improved forecasting remains an open question. As a final note, the The 2000-2002 coefficient value of -0.0045 does retain economic regression results are robust to deflating forecast error by absolute actual earnings rather than price. B. Forecast Optimism Table 7 presents the percent of firms with optimistic annual earnings forecasts pooled across all years. Analyst forecast optimism (AFO) is presented for each month, 17 while updated naïve forecast optimism (UNFO) is presented as follows: UNF0 Q0 in month 2, UNFO Q1 in month 5, UNFO Q2 in month 8, and UNFO Q3 in month 11. That table shows that the trend of decreasing optimism throughout the forecasting horizon exists, consistent with previous studies. In the “All Firms” sample, 63.07% of firms have optimistic forecasts in month 1, but only 42.07% have optimistic forecasts by the last month. The forecasts become pessimistically biased in month 11. When separating firms by profitability, optimism decreases over the forecast horizon for both non-loss and loss firms. However, forecasts remain optimistically biased for loss firms. Although not tabulated, the trend of decreased optimism over the sample period also exists. The updated naïve forecasts show different trends versus the analysts. In the “All Firms” sample, optimism increases slightly from UNFO Q0 through UNFO Q3. This same trend also prevails in the non-loss subsample. In the loss subsample, similar to the analysts, optimism decreases from UNFO Q0 through UNFO Q3. Table 8 presents an analyst superiority measure based on optimism. It is assumed that an unbiased 50% optimism percentage is the goal when forecasting. The measure is thus computed as follows: analyst superiority = |UNFO%–50% |–|AFO%–50%|. Positive numbers indicate analyst superiority; negative numbers indicate naïve forecast superiority. As an example, consider a month in which AFO is 45% and UNFO is 70%. The analyst superiority measure is 15% (|70–50|–|45–50|), the positive number indicating analyst superiority. Latest UNFs are used to compute UNFOs. The “All Firms” sample results suggest that analysts are superior for most of the forecasting horizon. However, AFO Last is actually more biased than that of the UNFO Last (Last superiority measure = -0.16). When forecasting non-loss firm earnings, 18 analysts are superior for most of the fiscal year, but their superiority decreases over the forecasting horizon. For loss firms, the opposite occurs. Analysts start with inferior bias, but their inferiority decreases over the forecasting horizon. The time period subsamples reveal the bias for analysts has improved over time for loss firms over time, but has worsened for non-loss firms. The results of Tables 7 and 8 suggest that updated naïve forecasts are less biased than the last analyst forecasts available prior to the earnings release. Analysts are less biased in all months when forecasting loss firm earnings. However, in contrast to forecast error, analyst forecast optimism does not appear to track naïve forecast optimism. The next test examines whether the optimism trends over time are related to changes in updated naïve forecasts. Table 9 reports the results of a logistic model using AFO Last (1 = optimistic forecast) as the dependent variable. The regressors, including control variables and trend dummy variables, are the same as those of Table 6 with the exception that UNFO Q3 replaces UNFE Q3. The logistic model is used because of the easy interpretability of the coefficients after computing their exponential function. The results are robust to the use of a probit model. Model 1 excludes quarterly earnings volatility and UNFO Q3, while Model 2 includes these variables. The trends of decreased forecast optimism is clearly evident in Model 1. The year dummy variables indicate that firms are much less likely to have optimistic forecasts in later time periods. For example, the odds ratio of 0.360 for the 2000-2002 trend variable implies that forecasts in that period are about 1/3 as likely to be optimistic as those of the base year, 1985-1987. In model 2, quarterly earnings volatility and UNFO Q3 are 19 significant. Both variables are significant and their inclusion increases regression model’s likelihood ratio. Firms with optimistic updated naïve forecasts are almost four times as likely to have optimistic analyst forecasts (odds ratio = 3.976). However, despite this significance, the trend variables remain as strong as in Model 1. Thus, trends in analyst forecast optimism appear to be unrelated to changes in updated naïve forecast properties or quarterly earnings volatility. V. Conclusions This study proposes a new method to evaluate analyst annual forecasts. Updated naïve forecasts that incorporate quarterly earnings releases are utilized. Despite their simplicity, these forecasts are far superior to forecasts using only last year’s earnings. In addition, the updated naïve forecasts compare favorably with analyst forecasts, actually outperforming analysts when forecasting for loss firms. When controlling for forecasting difficulty using updated naïve forecasts, the trends of increased analyst accuracy over the forecasting horizon and over the sample period are much weaker, although the trend of increased forecast pessimism remains in effect. This study is important because it suggests that, despite tremendous informational advantages, analyst forecast improvement is primarily attributable to quarterly earnings releases and quarterly earnings properties. Furthermore, although no search was conducted in this study, more accurate naïve forecasts might be found. For example, after third quarter earnings are released, a forecast can be made by adding third quarter earnings to the sum of first, second, and third quarter earnings (instead of adding the average of the first three quarter’s earnings to the sum). 20 This study can also be easily extended into a quarterly analysis (using quarterly naïve forecast models) and into an international sample. 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Chicago: Rand McNally. 23 Table 1 Quarterly Profits and Losses and Earnings Volatility Four Quarterly Profits (%) All Years 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 1985-1993 1994-2002 Difference 68.46 63.43 68.74 71.28 73.19 69.26 62.60 68.16 68.75 -0.59 Percent of All Profit Firms Panel A 82.95 75.23 80.39 84.11 85.75 85.21 83.70 Four Quarterly Losses (%) 8.50 3.66 3.91 6.50 7.26 10.31 16.13 4.82 10.89 -6.07*** Percent of All Loss Firms 49.42 24.00 27.54 43.25 50.59 55.73 64.60 All Years 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 1985-1993 1994-2002 Difference Panel B Quarterly Earnings Volatility All Firms Non-Loss Firms Loss Firms 0.015 0.010 0.038 0.027 0.023 0.018 0.011 0.010 0.011 0.021 0.010 0.011*** 0.016 0.013 0.010 0.008 0.007 0.008 0.013 0.008 0.005*** 0.081 0.076 0.048 0.024 0.022 0.018 0.067 0.021 0.046*** This table reports the percent of firms reporting only profits/only losses in every quarter and quarterly earnings volatility. A firm is considered to have four quarterly profits (losses) if its quarterly IBES earnings are greater (less) than zero in each quarter of the fiscal year. Quarterly earnings volatility is equal to the quarterly earnings standard deviation for a given fiscal year divided by the first available IBES price in that fiscal year. The price must be available in the first six months of the fiscal year. A non-loss firm has annual IBES earnings greater than or equal to zero. A loss firm has annual IBES earnings less than zero. The *** indicates the difference is significantly different from zero with 99% confidence. 24 Table 2 Correlations between Forecasted and Actual Earnings UNF Q0 1.00 UNF Q1 0.67 1.00 UNF Q2 0.72 0.87 1.00 UNF Q3 0.73 0.79 0.93 1.00 AF 5 0.83 0.71 0.79 0.81 1.00 AF 8 0.81 0.74 0.85 0.87 0.96 1.00 AF 11 0.78 0.73 0.86 0.92 0.90 0.96 1.00 AF Last 0.76 0.72 0.85 0.92 0.87 0.93 0.98 1.00 EPS 0.71 0.70 0.83 0.92 0.79 0.85 0.91 0.93 1.00 UNF Q0 UNF Q1 UNF Q2 UNF Q3 AF 5 AF 8 AF 11 AF Last EPS This table reports correlations among analyst annual forecasts, updated annual naïve forecasts, and actual annual earnings per share. AF i represents mean analyst forecasts in the ith month of the fiscal year, “1” being the first month and “12” being the month of fiscal year end. “Last” refers to the last forecasts are made prior to the earnings release. All correlations are significantly different from zero with 99% confidence. 25 Table 3 Annual Forecast Error: Analysts versus Updated Naïve Forecasts 1 0.0450 0.0596 0.0591 0.0493 0.0343 0.0385 0.0402 2 0.0429 0.0581 0.0576 0.0468 0.0329 0.0357 0.0372 Q0 0.0447 0.0547 0.0600 0.0496 0.0359 0.0379 0.0423 3 0.0409 0.0556 0.0557 0.0452 0.0314 0.0338 0.0350 Analyst Forecast Error by Month (12 = fiscal year end) 4 5 6 7 8 9 10 0.0389 0.0358 0.0337 0.0315 0.0278 0.0257 0.0235 0.0530 0.0539 0.0431 0.0295 0.0321 0.0323 0.0503 0.0511 0.0399 0.0271 0.0288 0.0284 0.0476 0.0483 0.0375 0.0255 0.0269 0.0269 0.0447 0.0463 0.0354 0.0234 0.0251 0.0243 0.0411 0.0425 0.0310 0.0204 0.0215 0.0204 0.0385 0.0402 0.0279 0.0186 0.0199 0.0187 0.0364 0.0371 0.0258 0.0166 0.0178 0.0166 11 0.0202 0.0327 0.0334 0.0222 0.0141 0.0148 0.0128 Q3 0.0191 0.0333 0.0263 0.0198 0.0140 0.0143 0.0149 12 0.0182 0.0295 0.0297 0.0198 0.0125 0.0139 0.0117 Last 0.0172 0.0269 0.0273 0.0190 0.0119 0.0133 0.0113 Corr. w/ Month All Years 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 -0.998 -0.999 -0.995 -0.997 -0.997 -0.996 -0.995 All Years 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 Updated Naïve Forecast Error by Quarter Q1 Q2 0.0415 0.0295 0.0622 0.0553 0.0445 0.0326 0.0325 0.0349 0.0470 0.0398 0.0309 0.0227 0.0228 0.0238 This table reports mean analyst forecast error by month and mean updated naïve forecast error by quarter. Forecast errors are computed as the absolute difference between actual annual EPS and forecasted EPS, and then deflated by the first available price in the corresponding fiscal year. The price must be available in the first six months of the fiscal year. Q1 updated earnings are equal to four times first quarter earnings. Q2 updated earnings are equal to two times to sum of first and second quarter earnings. Q3 updated earnings are equal to four times the average of first, second, and third quarter earnings. The correlations between analyst forecast error and month (Last = 13) are shown in the last column. 26 Table 4 Thiel’s Inequality Coefficients Month (12 = fiscal year end) Measure 1 2 3 4 5 6 Panel A 7 8 9 10 11 12 Last Corr w/ Month All Years TIC (UIC Q0) UIC Q1 UIC Q2 UIC Q3 Latest UIC 1.04 1.15 2.02 4.28 (Bold signifies quarterly earnings necessary for UIC computation were most likely available) 0.97 0.89 0.82 0.73 0.67 0.59 0.50 0.43 0.36 0.29 1.07 0.98 0.91 0.80 0.74 0.65 0.55 0.48 0.40 0.32 1.88 1.74 1.61 1.42 1.31 1.15 0.97 0.84 0.71 0.57 3.96 3.68 3.43 3.02 2.77 2.45 2.06 1.79 1.50 1.22 0.97 0.89 0.82 0.80 0.74 0.65 0.97 0.84 0.71 1.22 Panel B TIC (UIC Q0) Time Period 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 1 1.12 1.02 1.05 0.99 1.17 0.94 2 1.10 0.98 0.97 0.90 1.04 0.83 1.10 0.98 0.97 0.90 1.04 0.83 3 1.02 0.94 0.88 0.80 0.95 0.75 1.02 0.94 0.88 0.80 0.95 0.75 4 0.97 0.89 0.85 0.73 0.86 0.65 0.97 0.89 0.85 0.73 0.86 0.65 5 0.89 0.82 0.73 0.62 0.74 0.55 0.72 1.02 0.89 0.65 0.82 0.68 6 0.82 0.78 0.67 0.56 0.67 0.50 7 0.73 0.70 0.59 0.48 0.59 0.42 8 0.64 0.62 0.47 0.41 0.49 0.32 0.82 1.31 1.10 0.87 0.91 0.73 9 0.57 0.55 0.39 0.34 0.42 0.28 0.73 1.16 0.92 0.74 0.78 0.64 10 0.51 0.47 0.32 0.28 0.35 0.21 0.66 1.01 0.74 0.61 0.66 0.47 11 0.44 0.40 0.25 0.22 0.26 0.16 1.09 1.72 1.31 1.12 1.04 0.82 12 0.40 0.34 0.20 0.20 0.24 0.15 0.99 1.45 1.05 1.00 0.96 0.74 Last 0.35 0.28 0.17 0.17 0.20 0.13 0.86 1.22 0.91 0.85 0.83 0.64 Corr w/ Month 0.26 0.28 0.50 1.06 1.06 0.22 0.24 0.43 0.91 0.91 -0.997 -0.997 -0.997 -0.997 0.307 -0.997 -0.996 -0.996 -0.990 -0.993 -0.985 -0.138 0.685 0.308 0.324 -0.131 -0.203 Latest Available UIC 0.68 0.60 0.96 0.87 0.82 0.72 0.58 0.49 0.74 0.65 0.61 0.52 27 Table 4 (cont.) Thiel’s Inequality Coefficients Panel C Latest Available UICs Time Period Non-Loss All Years 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 Loss All Years 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 2 0.57 0.59 0.51 0.53 0.53 0.67 0.62 1.33 1.51 1.37 1.40 1.44 1.32 1.03 3 0.52 0.53 0.49 0.49 0.46 0.60 0.56 1.23 1.42 1.32 1.26 1.31 1.22 0.92 4 0.47 0.51 0.45 0.44 0.39 0.55 0.47 1.15 1.34 1.26 1.22 1.23 1.10 0.81 5 0.37 0.30 0.50 0.41 0.28 0.37 0.38 1.36 1.21 1.45 1.43 1.51 1.48 1.12 6 0.34 0.28 0.47 0.37 0.25 0.34 0.32 1.25 1.14 1.37 1.32 1.29 1.32 1.04 7 0.29 0.24 0.43 0.32 0.20 0.29 0.25 1.12 1.01 1.24 1.16 1.13 1.19 0.92 8 0.47 0.38 0.74 0.49 0.35 0.44 0.41 1.45 1.18 1.68 1.72 1.74 1.40 1.07 9 0.40 0.34 0.66 0.41 0.30 0.37 0.33 1.26 1.05 1.49 1.43 1.56 1.19 0.95 10 0.33 0.31 0.58 0.34 0.24 0.29 0.21 1.07 0.95 1.28 1.15 1.30 1.03 0.73 11 0.65 0.55 1.14 0.65 0.50 0.50 0.49 1.63 1.50 2.05 1.89 1.96 1.39 1.05 12 0.61 0.55 1.03 0.59 0.43 0.52 0.45 1.39 1.32 1.68 1.47 1.70 1.25 0.94 Last 0.59 0.53 1.03 0.54 0.41 0.50 0.40 1.15 1.11 1.33 1.23 1.37 1.07 0.81 Corr w/ Month 0.25 0.01 0.82 0.31 -0.10 -0.32 -0.41 0.14 -0.37 0.44 0.24 0.43 -0.26 -0.28 This table reports Thiel’s Inequality Coefficients (TIC) and updated TICs (UIC) by month of forecast. TIC (UIC Q0) is computed as the sum of squared forecast errors divided by the sum of squared change in earnings from current year’s earnings to last year’s earnings. UICs are computed by dividing the sum of squared forecast errors by the difference between earnings and an updated naïve forecast using quarterly earnings. Q1 updated earnings are equal to four times first quarter earnings. Q2 updated earnings are equal to two times to sum of first and second quarter earnings. Q3 updated earnings are equal to four times the average of first, second, and third quarter earnings. “Latest UIC” refers to the UIC using the most recently available quarterly information. The correlation between the ratios and the month is given, assigning a value of 13 to the “Last” forecast month. Panel A reports monthly TICs and UICs after pooling all observations. Panel B reports monthly TICs and Latest UICs by time period. Panel C reports monthly Latest UICs by loss/non-loss firms and time period. A loss occurs when IBES annual earnings are less than zero; a non-loss occurs otherwise. 28 Table 5 Pooled Regressions of TIC or UIC versus Lagged Values and Month Intercept 1.0220 (38.69)*** Month -0.0714 (-19.89)*** Yt-1 R2 F-statistic 0.85 395.50*** Yt = TIC Yt = TIC Yt = Latest UIC Yt = Latest UIC -0.0745 (2.72)*** 0.8028 (14.55)*** 0.3269 (3.37)*** 0.0026 (1.25) 0.0102 (1.37) 0.0122 (1.64) 0.9834 (37.92)*** 0.99 4102.05*** 0.03 1.86 0.5300 (5.03)*** 0.34 15.97*** This table reports the coefficients and t-values of a pooled regression model using either TIC or Latest UIC, each computed for six time periods, from Panel B of Table 4 as dependent variables. The independent variables are month (1-12) and the previous month’s TIC or Latest UIC. When lagged variables are used in the regression, the first month of each time period is dropped and each month’s numeric value is decreased by 1 (e.g., month 2 becomes month 1). The *** indicates the coefficient is significantly different from zero with 99% confidence. 29 Table 6 Regression of Analyst Forecast Errors versus Control Variables, Updated Naïve Forecasts, and Trend Dummies Model 1 AFE Last Coefficient (t-value) 0.0360 (32.6222)*** -0.0036 (-32.5697)*** 0.0194 (3.6950)*** 0.0024 (1.9957)** 0.0374 (31.0768)*** Model 2 AFE Last Coefficient (t-value) 0.0160 (7.7992)*** -0.0018 (-9.7156)*** -0.0188*** (-4.7874)*** -0.0019 (-1.7304)* 0.0232 (16.0883)*** 0.6844 (9.6431)*** 0.6207 (26.6545)*** 0.0012 (1.0960) -0.0065 (-6.5569)*** -0.0116 (-13.2438)*** -0.0118 (-13.2866)*** -0.0150 (-16.5518)*** 0.1511 1013.13*** 0.0031 (3.1374) *** -0.0015 (-1.5803) -0.0041 (-4.3424)*** -0.0042 (-4.2955)*** -0.0073 (-7.3455)*** 0.3701 3007.98*** 0.0042 (4.8603)*** 0.0002 (0.2972) -0.0022 (-2.9709)*** -0.0020 (-2.7432)*** -0.0054 (-7.3510)*** 0.4531 4237.66*** Model 3 AFE Last Coefficient (t-value) 0.0087 (9.0339)*** -0.0014 (-14.9272)*** 0.0103 (4.7656)*** 0.0007 (0.7174) 0.0193 (18.9046)*** Model 4 AFE Last Coefficient (t-value) 0.0068 (6.1964)*** -0.0012 (-9.9272)*** -0.0058 (-1.1495) -0.0008 (-0.8839) 0.0177 (15.6566)*** 0.3583 (3.8398)*** 0.4314 (8.9004)*** 0.0043 (5.0122)*** 0.0007 (0.8129) -0.0013 (-1.8631)** -0.0012 (-1.6651)* -0.0045 (-6.1165)*** 0.4679 4089.31*** Independent Variables Intercept Log (Size) EP Ratio EP Loss Dummy Loss Dummy Q EPS Volatility UNFE Q3 Year1988-1990 Year1991-1993 Year1994-1996 Year1997-1999 Year2000-2002 R2 F-statistic 30 Table 6 (cont.) Regression of Analyst Forecast Errors versus Control Variables, Updated Naïve Forecasts, and Trend Dummies This table reports the results of a regression using analyst forecast error as the dependent variable and independent variables related to firm characteristics, updated naïve forecast error, and time period. The dependent variable, AFE Last, is defined as the absolute value of forecasted annual earnings in the last available month prior to the earnings release less the corresponding actual earnings, divided by the first available price in the current fiscal year. The independent variables are defined as follows: log(size) is the logarithm of price times shares computed using the first available information in the current fiscal year; E/P ratio is IBES annual earnings in the previous fiscal year divided by the first available price in the current fiscal year if the ratio is positive and zero otherwise; E/P loss dummy is equal to one if IBES annual earnings in the previous fiscal year are zero or negative and zero otherwise; loss dummy equals one if IBES annual earnings in the current fiscal year are negative and zero otherwise; Q EPS Volatility is equal to the standard deviation of the four quarterly IBES earnings in the current fiscal year divided by the first available price in the fiscal year; and UNFE Q3 is the updated naïve forecast error using three quarters of earnings. Time period dummy variables are also included, equaling one if the forecast pertains to the time period and zero otherwise. The t-values are computed using White’s standard errors. The ***, **, * indicate the values are significantly different from zero with 99%, 95%, and 90% confidence, respectively. The full regression model follows for firm i in fiscal year t: AFE Last i,t = b1 + b2 Log(size)i,t + b3 EP Ratioi,t-1 + b4 EP Loss Dummyi,t-1 + b5 Loss Dummyi,t + b6 Q EPS VOLATILITY i,t + b7 UNF Q3i,t + b8 YEAR1988-1990 i,t + b9 YEAR1991-1993 i,t + b10 YEAR1994-1996 i,t+ b11 YEAR1996-1999 i,t + b12 YEAR2000-2002 i,t + ei,t 31 Table 7 Annual Forecast Optimism: Analysts versus Updated Naïve Forecasts 1 All Firms AFO UNFO Non-Loss AFO UNFO Loss AFO UNFO 63.07 2 62.16 36.78 56.91 30.27 88.30 70.26 3 61.37 Forecast Optimism Percent by Month (12 = fiscal year end) 4 5 6 7 8 9 10 60.34 59.98 36.60 55.03 31.59 84.52 60.23 59.24 58.09 56.64 39.04 52.00 34.87 79.38 58.90 55.25 52.33 11 48.42 42.23 44.37 38.85 71.22 58.21 12 45.69 Last 42.07 Corr w/ month -0.95 57.76 56.26 55.31 54.35 53.20 50.62 47.87 41.78 38.26 -0.94 89.37 87.18 85.89 83.23 82.01 77.49 74.96 68.89 65.97 -0.98 This table reports the percent of firms with optimistic annual earnings forecasts by month. A forecast is defined as optimistic if its mean monthly forecast is greater than the corresponding actual earnings. Analyst forecast optimism is presented for each month. Updated naïve forecast optimism (UNFO) is presented follows: UNF0 Q0 in month 2, UNFO Q1 in month 5, UNFO Q2 in month 8, and UNFO Q3 in month 11. The correlation with the month (Last = 13) for the AFOs is shown in the last column. 32 Table 8 Annual Forecast Optimism: Analyst Superiority Measure 2 1.06 12.82 -18.04 -9.68 -5.49 -0.61 11.01 5.27 -1.67 3.36 7.19 10.99 22.24 20.87 13.32 -20.71 -18.81 -21.06 -18.83 -16.95 -11.71 3 1.85 13.47 -16.92 -9.23 -4.91 -0.24 11.94 6.26 -0.53 3.86 7.80 11.47 23.30 21.78 14.01 -20.31 -18.46 -21.26 -18.15 -15.34 -9.16 Analyst Forecast Superiority by Month (12 = fiscal year end) 4 5 6 7 8 9 10 11 2.88 3.42 4.16 5.31 4.32 5.71 8.63 6.19 14.42 13.38 14.06 15.21 13.13 14.51 13.00 5.52 -15.63 -24.29 -23.00 -21.78 -20.48 -18.59 -16.06 -13.01 -8.73 -3.76 0.82 13.24 7.14 0.68 4.34 9.11 12.62 24.27 22.64 14.60 -20.04 -17.85 -20.61 -17.53 -14.16 -6.07 -11.32 -7.50 1.47 13.89 9.83 4.06 -0.10 3.52 12.05 22.95 22.32 13.91 -27.34 -22.84 -26.96 -26.51 -24.43 -18.48 -10.65 -7.38 2.58 14.43 10.84 4.89 0.67 3.69 13.06 22.47 21.38 14.68 -26.79 -22.68 -24.84 -25.50 -22.87 -17.40 -9.83 -6.50 3.63 15.48 12.24 6.40 1.56 4.60 14.22 21.36 20.04 16.07 -25.99 -22.50 -24.50 -25.28 -20.97 -15.22 -10.16 -8.30 3.09 14.07 11.10 5.79 -0.18 1.49 12.55 17.36 14.77 12.48 -29.85 -23.96 -26.25 -24.56 -17.41 -11.76 -9.13 -7.73 4.56 15.65 12.71 7.51 0.84 1.94 13.89 15.79 13.14 10.76 -28.36 -22.29 -24.55 -22.67 -15.63 -10.05 -7.63 -5.67 6.86 14.27 10.45 5.43 2.34 4.20 16.13 13.33 9.68 5.16 -27.00 -21.28 -21.80 -20.03 -12.40 -5.38 -7.72 -4.27 8.15 7.02 2.54 -3.31 1.30 4.25 8.52 5.67 0.87 -5.36 -27.47 -24.83 -18.83 -15.12 -7.10 -0.44 12 3.46 2.93 -10.68 -5.56 -1.69 7.19 4.32 -0.13 -6.38 3.56 4.64 5.30 2.94 -1.74 -8.77 -25.85 -21.68 -16.78 -12.89 -3.92 1.59 Last -0.16 -0.59 -7.76 -2.24 2.31 4.07 0.84 -3.77 -10.46 6.51 0.37 2.19 -0.93 -5.86 -13.68 -24.01 -18.38 -11.45 -8.98 -0.79 -1.64 Corr w/ month All Firms Non-Loss Loss All Firms 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 Non-Loss 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 Loss 1985-1987 1988-1990 1991-1993 1994-1996 1997-1999 2000-2002 0.28 -0.74 0.62 0.73 0.49 0.88 -0.58 -0.44 -0.36 0.13 -0.69 -0.51 -0.92 -0.92 -0.84 -0.55 -0.35 0.53 0.49 0.72 0.65 33 Table 8 (cont.) Annual Forecast Optimism: Analyst Superiority Measure This table reports the superiority of analyst forecast bias versus naïve forecast bias by month and time period. The superiority measure assumes 50% as the desired level of forecast optimism. Optimism is present when the forecasted annual earnings are greater than the corresponding actual IBES annual earnings. The percentage of optimistic is computed each month using analyst forecasts and latest updated naïve forecasts. The superiority measure is computed as follows: analyst superiority = |UNFO%–50% |–|AFO%–50%|. Positive numbers indicate analyst superiority; negative numbers indicate naïve forecast superiority. The correlation with the month (Last = 13) is shown in the last column. 34 Table 9 Logistic Model Predicting Forecast Optimism Model 1 Model 2 Dependent Variable: 1 if Optimistic AF Last, 0 Otherwise (e coefficient) Chi-square Odds Ratio Coefficient Chi-square 57.6151*** -0.1329 7.0515*** 148.4355*** 0.931 -0.0793 163.5541*** 9.9916** 2.110 -0.0941 1.8856 88.6902*** 0.707 -0.3034 71.7374*** 1886.6530*** 4.106 1.1592 1108.4799*** 2.3397 35.6349*** 1.3802 4777.1309*** 24.5559*** 0.822 -0.2363 32.1263*** 124.0551*** 0.649 -0.4033 96.6292*** 325.8357*** 0.508 -0.6247 246.6216*** 493.3436*** 0.436 -0.8255 435.2581*** 659.1712*** 0.360 -1.0696 645.5285*** Independent Variables Intercept Size E/P Ratio E/P Dummy Loss Dummy Q EPS Volatility UNFO Q3 Year1988-1990 Year1991-1993 Year1994-1996 Year1997-1999 Year2000-2002 Coefficient 0.3795 -0.0712 0.7469 -0.3474 1.4125 -0.1958 -0.4317 -0.6774 -0.8299 -1.0220 (e coefficient) Odds Ratio 0.924 0.910 0.738 3.188 10.378 3.976 0.790 0.668 0.535 0.438 0.343 Likelihood Ratio 3957.9741*** 9029.8442*** This table reports the results of a logistic regression using analyst forecast optimism as the dependent variable and independent variables related to firm characteristics, updated naïve forecast optimism, and time period. A forecast is optimistic when the mean forecast of annual earnings is greater than the corresponding actual annual IBES earnings. The presented results use AF Last and UNF Q3 to determine optimism (AFO Last and UNFO Q3, respectively). All other variables are as defined in Table 6. The Odds Ratio is computed as the exponential function of the coefficient. The ***, **, * indicate the values are significantly different from zero with 99%, 95%, and 90% confidence, respectively. The full regression model follows for firm i in fiscal year t: AFO Last i,t = b1 + b2 Log(size)i,t + b3 EP Ratioi,t-1 + b4 EP Loss Dummyi,t-1 + b5 Loss Dummyi,t + b6 Q EPS VOLATILITY i,t + b7 UNF Q3i,t + b8 YEAR1988-1990 i,t + b9 YEAR1991-1993 i,t + b10 YEAR1994-1996 i,t+ b11 YEAR1996-1999 i,t + b12 YEAR2000-2002 i,t + ei,t 35