A monthly contemporaneous analysis of the 11 months prior actual earnings forecasts is applied across a 20-year interval from 1 July 1988 through 30 June 2008. Contemporaneous macroeconomic factors which may impact earnings forecasts are controlled in the sample that arm of a brokerage firm is involved with the mergers or acquisition activity of the client firm.

spans over four economic cycles.7 Possible macroeconomic factors that are considered are fluctuations in interest rates, exchange rates, business spending, consumer sentiment, and fiscal policy changes.

Prior to the discussion of the statistical techniques pertaining to the testing of the hypothesis, it is important to refine measures of forecast bias that are used in the past forecast literature to obtain an appropriate benchmark to facilitate the study of analyst earnings forecast distribution characteristics. The main motivation of this study lies in our interest to evaluate the significance of non-normality in cross-sectional analyst earnings forecast distributions. In analyst earnings forecasts research, consensus point estimates of analyst earnings forecasts sample distributions are used in the calculation of two types of forecast error measures. These are (i) firm-based, which measures the deviation of the consensus estimate earnings away from the actual earnings, after dividing it by a deflator to achieve scaling and (ii) analyst-based, which measures the difference between an analyst’s forecast error and the per period consensus of all analysts’ forecast errors, again scaled by a deflator. This is termed the analyst’s relative forecast error measure (following Brown, 1999).

The latter error measure is altered in this study. An analyst earnings relative forecast (AERF) bias measure may is defined as:

analyst _ earnings _ forecast  analyst _ earnings _ consensus AERF _ BIAS  (1) deflator

The use of deflators in earnings forecast research has been scarce. When attempted, they are often not sufficiently detailed to yield a generalisation of result nor robustness of result. Thus, for completeness and for robustness of results, this study employs four deflators in relation (1). They are: (i) a firm’s share price at 11 months prior actual earnings are reported PRICEt=-11; (ii) a firm’s share price at each statistical period PRICEt; (iii) the period’s consensus analysts’ earnings forecast CONS; and (iv) a modified version of the mean absolute percentage error (MAPE) as suggested by Makridakis (1993).

The fourth measure, which is denoted by mPE hereafter, operates best in a majority of situations and at the same time satisfies theoretical and practical concerns. It is able to Artis et al. (1997) found average economic cycles to be 51 months in duration across a study of 12 countries (G7 and 5 European countries) from years 1961 through 1993. Thus, the data sample in this study covers 20 years x 12 months/ 51 months=4.7 economic cycles.

mitigate scaling problems, is robust from one data set to another, and is protected from the influence of outliers. The mPE measure improves upon the MAPE measure by avoiding scaling problems by dividing the error (Actual-Forecast) by the average of the Actual and Forecast, that is, (A+F)/2. Hence the mathematical form of the error measure mPE becomes:

A F mPE  (2) (A  F) / 2 where A is the actual reported earnings and F is the analyst earnings forecast.

For the purpose of this study, the per period analyst earnings forecast consensus item (CONS) replaces the actual reported earnings (A) to form the analyst earnings relative forecast (AERF) bias as included in equation (1).

Hypothesis 1 is tested with three goodness of fit tests using AERF_BIAS (relation 1) together with the deflators mPE, PRICEt=-11, PRICEt and CONS.

The goodness-of-fit tests are the Kolmogorov-Smirnov (K-S) test, the Anderson- Darling (A-D) test and the Cramér-von Mises (CVM) test (Siegel and Castellan, 1988). All were developed to examine whether a given distribution fits a specified distribution (a normal distribution in this study). The A-D test has been modified to overcome limitations8 of the K- S test but it is only available for a limited number of distribution types.

Mean Table 2 provides descriptive statistics on the effects of the IBES internal rules on the percentage matches between analyst estimates’ mean and the IBES consensus mean from the 1 July 1988 through 30 June 2008. Results suggest that the application of the IBES internal rules is necessary for specific analyst earnings forecasts to be identified and is, therefore, included in the sample distribution for goodness of fit tests to be carried out.

The skewness in sensitivity towards the centre of the distribution and the need for the theoretical distribution to be fully specified.

Panel A of Table 2 reports the mean, median and standard deviation of the cross sectional per Year End Period percentage matches of the analyst estimates’ mean and the IBES consensus mean both prior to and posterior to the application of IBES internal rules. Within each Year End Period, only those firms with analyst estimates and IBES consensus persisting from 11 statistical periods through reporting date are selected to control for sample size effects. For example, for the Year End Period 1994-1995, there were 2,160 (2,987) analysts’ forecasts for firms which published estimates for at least 1 statistical period prior each firms’ reporting date for prior (posterior) to the employment of the IBES internal rules. This was reduced significantly to 957 (2,508) when firms with at least 11 statistical periods prior reporting date were imposed for selection.

In the case of the posterior application of the IBES internal rules, the highest number of matches occurred in the financial fiscal year 1994-1995 (94.06 percent) and the lowest number of matches occurred in the financial fiscal year 1990-1991 (18.11 percent). Another result is the low matching percentage (<50 percent) in the earlier Year End Periods (1988- 1993) and the subsequent increase in matching percentage to a high of greater than 50 percent in the later Year End Periods (1993-2008). A possible explanation for both the high range value (94.51 percent-18.11 percent=76.4 percent) and increase in percentage of matches from below to over 50 percent is due to the changes to internal rules used by IBES, including the amendments, removal or addition of internal rules which existed in the earlier periods but not in the later periods or vice versa. Further, these changes in internal rules may be attributable to regulatory changes or the way multiple earnings forecasts are chosen and provided by brokerage firms to IBES.9 For example, regulatory changes include changes to the number of stoppage months placed upon a brokerage firm’s estimates from when a stop signal is initiated by IBES.

The greater number of statistical periods of the posterior as opposed to the prior application of IBES internal rules across all Year End Periods is attributable to the carry forward of analyst estimates into subsequent periods which initially did not have any existing estimate(s) made by the same analyst. This implies that some firms in the data set prior to being treated with the IBES internal rules will have some statistical periods without any estimates. Since the sample selection chooses only those firms with estimates from 11

Using the sample data selection process detailed in section 3, it is found that there are multiple earnings forecasts supplied by different analysts of the same brokerage firm in the same statistical period, only the most recent estimate is used by IBES in its consensus calculation.

statistical periods through reporting date, firm selection is carried out after the IBES internal rules are applied.

To maintain consistency and continuity in the analyses, the set of analyst detailed estimates data which have undergone the treatment of IBES internal rules in the previous section is now used to generate the set of contemporaneous distributional properties from 11 months prior through actual earnings reporting on a per month (statistical period) basis.

Table 3 provides the descriptive statistics of the analyst earnings forecast bias (AERF_BIAS) distributions using the four different deflators PRICEt=-11, PRICEt, CONS, and mPE, for all Australian IBES firms for the 20 test years. For example, the median of the fifth month prior reporting for AERF_BIAS_CONS is calculated as follows. The median of each firm-specific distribution of analyst earnings forecasts at five months prior to the firm’s actual reporting date is computed for all firms. The AERF_BIAS_CONS of each median is then determined, followed by averaging all median-AERF_BIAS_CONS with the resulting mean value being the required contemporaneous median relative forecast value.

By taking the averages of forecasts summarised per period, bias values are generated across all firms. For instance, the bias of the distribution of analysts’ earnings forecasts was first computed for each ASX firm at 11 months prior to actual earnings announcement. Then the mean of the bias across all these ASX firms was generated to produce a summary bias value at 11 months prior to actual earnings reporting.

Distortions to AERF_BIAS caused by zero deflator values 10 need to be addressed. Forecasts with zero deflators are removed to prevent the introduction of infinite values. For example, the deflator mPE when used with analysts’ earnings relative forecast bias, is by

Results for non-removal of zero deflators were found to be consistent with the case when zero denominators were removed. To avoid division by zero errors for the non-removal case, the relevant analyst estimates were assigned large relative forecast bias values of 100,000.

definition the analyst estimate plus period’s consensus. If the forecast earnings value is equal to the negative of the period consensus, then the resulting AERF_BIAS_mPE value will be infinite.

All firms' cross-sectional analyst forecast bias distribution parameters such as median and the first four moments (per statistical period) were grouped by the number of statistical periods up to 11 months prior the corresponding firm's reporting date. In this way the timing differences between the earnings reporting dates of different firms and their corresponding forecast bias distributions are controlled. This was employed to all firms with year end dates 1st July 1988 through 30th June 2008. b Skewness is equal to 0 for a standard normal distribution and values may range between negative infinity and positive infinity. c Excess kurtosis is used rather than kurtosis. Kurtosis omits the subtraction of 3 so that for a standard normal distribution, the excess kurtosis is equal to 0 and kurtosis is equal to -3. The excess kurtosis must lie between -2 and infinity. It is termed leptokurtic when it is greater than 0 and platykurtic when it is less than 0.

The results suggest a positive bias (median less than mean) in general, consistent with prior reported empirical evidence of optimistic analyst forecast bias (e.g., Brown, 1998 and Mande, Wohar and Ortman, 2003). The median, on average, is consistently negative across all error deflator types except for AERF_BIAS_mPE. The mean is consistent with the expectation that when distributions of analysts’ earnings estimates distributions are normalised to a mean of zero, the average across all firms will also be zero. The analysts optimism bias is corroborated by the other two distributional characteristics, i.e, skewness and kurtosis. These show that, on average, AERF_BIAS distributions are positively skewed and is leptokurtic in nature 11 months or less from the day of actual earnings release, suggesting that analyst earnings estimates distributions are fairly asymmetric. This result is exhibited by the positive mean skewness and excess kurtosis across the 4 deflators.

Table 4 reports the results for the goodness-of-fit tests and skewness/kurtosis location tests of cross-sectional AERF_BIAS distributions in each of the 11 months prior reporting for firm years. Panel A reports the statistics and p-values of the Kolmogorov-Smirnov test, the Anderson-Darling test and the Cramér-von Mises test while panel B reports the statistics and p-values of the Student's t test, the Sign test and the Wilcoxon Signed Rank test. In Panel A, AERF_BIAS distributions reveal a rejection of fit to a normal distribution, with the D-statistic (<0.01), A-Sq-statistic (<0.005) and the W-Sq-statistic (<0.005) significantly positive for all relative forecast metrics in all statistical periods prior to the releases of actual earnings.

Panel B reports the significance of analyst forecast bias distributions’ skewness and kurtosis from zero, the value expected from a normal distribution. For succinctness, only non- significant results are shown. They are relatively sparse given that there are 33 non-significant results of the 264 tests run (3 statistical tests for skewness and excess kurtosis each spread over 11 months and 4 deflators). Moreover, the 3 non-significant results for bias metrics AERF_BIAS_PRICEt=-11, AERF_BIAS_PRICEt and AERF_BIAS_CONS may be attributable to the decreasing power-efficiency of the Sign test for large samples, with the Wilcoxon Signed rank test and the Student’s t test been more power-efficient in large sample cases exhibiting opposing results.

Likewise, the overwhelmingly non-significant results (30/66*100=45%) for AERF_BIAS_mPE may have been caused by a metric dependent factor because the other 3 bias metrics have overwhelmingly reported polarised results.

All firms' cross-sectional analyst relative forecast bias distribution parameters such as median and the first four moments (per statistical period) were grouped by the number of statistical periods up to 11 months prior the corresponding firm's reporting date. In this way the timing differences between the earnings reporting dates of different firms and their corresponding relative forecast bias distributions are controlled. This was employed to all firms with year end dates 1 st July 1988 through 30th June 2008. c Only non-significant test statistics and probabilities are shown due to the scarcity of such evidence, indicating that it may have arisen due to reasons not related to the underlying characteristics of the distribution but rather on the method of analysis such as the sensitivity of the particular significance test used.

As such, the earnings forecast dependency of the mPE deflator may have introduced skewness into the underlying bias distribution. The other relative forecast bias metrics AERF_BIAS_PRICEt=-11, AERF_BIAS_PRICEt and AERF_BIAS_CONS depends on the constant deflators share price and actual reported earnings. Finally, those results not shown have significantly positive statistics (p-values<0.0001) suggesting that the skewness and excess kurtosis values are not of a normal distribution. This evidence is consistent with those previously presented.