Splat

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

Five error deflators are used between the two error metrics of IBES individual analysts’ earnings estimates (relative forecast bias91 _{AERF_BIAS and actual forecast accuracy}

AEAF_ACC) as follows:

(1) firm’s share price at statistical period t=-11 (PRICEt=-11);

(2) firm’s share price at t (PRICEt);

(3) consensus (CONS) for AERF_BIAS; (4) actual (ACTUAL) for AEAF_ACC; and

(5) average of forecast and consensus (mPE), for all Australian IBES firms for the 14 years from the 1st July 1988 through 30th June 2002.

The analysis commenced by addressing forecast distortions caused by zero deflator values. This led to the deliberate removal of AERF_BIAS with zero deflators, which prevents the introduction of infinite relative forecast values, and thus distortions, into the distributional properties of a specific statistical period. For example, the deflator mPE when used with AERF_BIAS, is by definition the analyst estimate plus period’s consensus (forecast+consensus). If the forecasted earnings value is equal to the negative of the period consensus, then the resulting AERF_BIAS_mPE value will be infinite. On the other hand, the two PRICE deflators do not possess a zero deflator because share prices have a lower bound of greater than zero. Hence this culling process resulted in a reduction of the sample sizes of individual analysts’ earnings forecasts for the AERF_BIAS_ACTUAL by 0.11% ([268,275-268,561]/268,561) but the sample sizes of the two other PRICE deflated measures, AERF_BIAS_PRICEt=-11 and AERF_BIAS_PRICEt were unaffected. The results of the

reduction in sample size are shown in Table 5-3.

Table 5-3. Effects on sample size after observations with zero deflators (PRICEt=-11,

PRICEt, CONS, ACTUAL and mPE) are removed. Error Deflator

PRICEt=-11 PRICEt CONS ACTUAL mPE

Individual analysts’ earnings forecasts Prior removal of zero deflators 261,575 268,561 268,561 268,561 268,561 Post removal of zero deflators 261,575 268,561 268,561 268,275 268,561 IBES consensus earnings forecasts Prior removal of zero deflators 35,554 39,106 39,106 39,106 39,106 Post removal of zero deflators 35,554 39,106 39,028 39,000 39,021

Table 5-4 provides the descriptive statistics, median and first four moments, of the distributions of individual analysts’ earnings relative forecast bias92 _{(AERF_BIAS) using the}

four deflators CONS, mPE, PRICEt=-11 and PRICEt. For completeness, the actual forecast

accuracy (AEAF_ACC) distributions using the four different deflators PRICEt=-11 and

PRICEt, have also been produced in Appendix A1. For instance, the median of the 5th month

prior to actual earnings reporting for AERF_BIAS_CONS is calculated as follows. The median of each firm’s specific distribution of analysts’ 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 value being the required median relative forecast value.

The notion of a combination of forecasts (see 3.4.8) was utilised to generate summarised bias and accuracy values on a per period basis across all firms. For instance, the bias of the distribution of individual 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.

Forecast distortions caused by zero deflator values93 _{have been addressed. This led to the}

deliberate removal of specific analyst’s earnings forecasts with zero denominators, which

92 _{The analysts’ earnings relative forecast bias metric is the shift in location of each analyst estimate}

about its consensus mean to bring about standardisation. Bias refers to the unsigned nature of this shift in location.

93 _{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.

prevents the introduction of infinite relative forecast values, and thus distortions, into the distributional properties of a specific statistical period. For example, the deflator mPE when used with AERF_BIAS, is by definition the analyst estimate plus period’s consensus (forecast+consensus). If the forecasted earnings value is equal to the negative of the period consensus, then the resulting AERF_BIAS_mPE value will be infinite. On the other hand, the two PRICE deflators do not possess a zero deflator because share prices have a lower bound of greater than zero. However, there may be newly listed firms for which share prices may not exist 11 months prior to actual. These firms are also filtered from the AERF_BIAS_PRICEt=-11 sample. Hence this culling process resulted in smaller per statistical period sample sizes for the AERF_BIAS_CONS (3550), the AERF_BIAS_mPE (3550) and the AERF_BIAS_PRICEt=-11 (3232) relative forecast measures but the sample size of the PRICE deflated measure AERF_BIAS_PRICEt (3555) remains unaffected.

Table 5-4 Panel A reports the properties of the distributions of AERF_BIAS. The analysts’ earnings estimates distribution median and mean suggests a positive bias (median < mean) in general, consistent with prior empirical evidence of optimistic analysts’ 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 optimistic bias is corroborated by the other two distributional characteristics skewness and kurtosis. They show that on average earnings estimates relative forecast distributions are positively skewed and leptokurtic94 _{in nature 11 months or less from the day of actual}

earnings release, suggesting that analysts’ earnings estimates distributions are fairly asymmetric. This result is exhibited by the positive mean skewness and excess kurtosis across the 4 deflators.

Appendix A1 reports the analysts’ actual forecast accuracy (AEAF_ACC) distributional properties. The analysts’ earnings forecast accuracy is shown to be positive (mean > 0) on average in the year approaching actual earnings announcement. However, the implications are distinctly different from the relative bias results. Rather, in this case the mean of the distributional properties through the 11 months prior to reporting is based on cross-sectional distributions of forecasts against the actual announced earnings and the accuracy of earnings

94 _{Positive kurtosis is defined as leptokurtic and describes the greater degree of peakedness of a}

analysts, on average, ranges from 5.72% (AEAF_ACC_PRICEt=-11) to 123.19%

(AEAF_ACC_mPE) across the 4 error deflators. Finally, the average median accuracy values are higher than the average median bias values in Table 5-4 Panel A. For example, AEAF_ACC_PRICEt=-11 median accuracy is greater than the AEAF_ACC_PRICEt=-11

median bias by 104.42% (100x(0.0543--0.0024)/0.0543). Specifically in relation to the results of AEAF_ACC_PRICEt=-11, the mean actual forecast accuracy is decreasing over time

until reporting, from 5.84% to 4.67% for median and 6.11% to 4.97% for mean respectively, consistent with the conclusion drawn by Brown (1996) that analysts’ forecast accuracy decreases over time using stock price as the deflator. This result is also supported by the two other measures AEAF_ACC_ACTUAL mean (126.88% decreased to 72.44%) and AEAF_ACC_mPE mean (141.85% to 80.05%).

In Table 5-4 panel B, I use the Kruskal-Wallis95 _{test to decide whether the 11 independent}

monthly samples of relative forecast distribution medians and 1st _{moment means are from}

different populations. Both bias and accuracy for all 4 deflators are examined with p-values <.0001 implying a significance and hence the rejection of the null hypothesis that the 11 monthly samples of relative forecast distribution mean or median come from the same population. In other words, p-values for all scenarios are <0.0001, corroborating the significance and non-rejection of the alternative hypothesis that the monthly independent samples of relative forecast distribution mean or median may in fact come from different populations, consistent with the results of Brown et al. (2004). Furthermore, by controlling for possible inter-month correlations caused by factors not under consideration, I substantiate the construct validity of both temporal and cross-sectional relationships amongst the variety of distributional properties. The next section looks at the further data partitioning applied as a result of the high actual forecast error found in the descriptive statistics of this section.

95 _{The Kruskal-Wallis (K-W) test utilises a nonparametric one-way analysis of variance by ranks}

technique to test the null hypothesis that the 11 monthly samples come from the same population or from identical populations with the same median. See Siegel and N. John Castellan (1988) for further details.

Table 5-4. Descriptive Statistics on Distributions of Analysts' Relative Forecast Bias (AERF_BIAS) Using Deflators PRICEt=-11, PRICEt, CONS and mPE - Months Prior Reporting for Year End Period 1/7/1988 Through 30/6/2002

Panel A: Analysts' Relative Forecast Bias Months (Statistical

Periods)

Prior to Reporting of Actual

(Forecast Indicator = 1)a

AERF_BIAS Deflated by Period Consensus

(AERF_BIAS_CONS d)

AERF_BIAS Deflated by Average of Consensus and Forecast

(AERF_BIAS_mPE d)

Sample Size Mediand

1st Moment Mean 2nd Moment Standard Deviation 3rd Moment Skewnessb 4th Moment Excess

Kurtosisc Sample _{Size Median} 1st Moment Mean 2nd Moment Standard

Deviation 3rd MomentSkewness Excess Kurtosis 4th Moment

11 3059 -0.0220 0.00 0.3611 0.2628 0.5886 3059 -0.0023 0.00 0.4390 0.0255 0.5881 10 3174 -0.0125 0.00 0.2522 0.2559 0.7011 3174 -0.0101 0.00 0.3725 0.0101 0.6548 9 3299 -0.0159 0.00 0.2512 0.2621 0.7304 3299 -0.0084 0.00 0.3793 0.0145 0.6897 8 3418 -0.0316 0.00 0.3467 0.2657 0.7929 3418 -0.0032 0.00 0.5213 0.0232 0.7508 7 3499 -0.0109 0.00 0.2695 0.2734 0.8291 3499 -0.0024 0.00 0.4004 0.0487 0.8045 6 3575 -0.0159 0.00 0.3154 0.2548 0.8674 3576 0.0469 0.00 0.7132 0.0210 0.8539 5 3661 0.0164 0.00 0.4844 0.2510 0.9490 3662 -0.0011 0.00 0.5103 0.0364 0.9219 4 3740 0.0309 0.00 0.4808 0.2572 1.0528 3740 -0.0092 0.00 1.0661 0.0528 1.0172 3 3807 -0.0024 0.00 0.4593 0.2575 1.1144 3807 -0.0024 0.00 0.4989 0.0473 1.0888 2 3874 0.0139 0.00 0.4723 0.2515 1.1785 3874 0.0019 0.00 0.4600 0.0548 1.1519 1 3945 -0.0179 0.00 0.4107 0.2680 1.1462 3946 -0.0005 0.00 0.3212 0.0843 1.1007 Mean 3550 -0.0062 0.00 0.3731 0.2600 0.9046 3550 0.0008 0.00 0.5166 0.0380 0.8748

…continuation of Table 5-4 from the previous page.

Months (Statistical Periods) Prior to Reporting of Actual (Forecast Indicator = 1)

AERF_BIAS Deflated by Firm’s Share Price at Statistical Period

t=-11 (AERF_BIAS_PRICEt=-11d)

AERF_BIAS Deflated by Firm’s Share Price at Statistical Period t

(AERF_BIAS_PRICEtd)

Sample

Size Median 1st MomentMean

2nd Moment Standard Deviation 3rd Moment Skewness 4th Moment Excess

Kurtosis Sample Size Median 1st Moment Mean 2nd Moment Standard

Deviation 3rd Moment Skewness

4th Moment Excess Kurtosis 11 3060 -0.0022 0.00 0.0209 0.2614 0.5886 3059 -0.0022 0.00 0.0208 0.2623 0.5886 10 3117 -0.0022 0.00 0.0199 0.2588 0.7016 3174 -0.0021 0.00 0.0199 0.2585 0.7011 9 3163 -0.0025 0.00 0.0200 0.2634 0.7280 3301 -0.0026 0.00 0.0214 0.2591 0.7304 8 3206 -0.0028 0.00 0.0210 0.2739 0.7899 3423 -0.0027 0.00 0.0223 0.2685 0.7929 7 3231 -0.0028 0.00 0.0204 0.2826 0.8259 3503 -0.0025 0.00 0.0218 0.2805 0.8291 6 3249 -0.0027 0.00 0.0213 0.2689 0.8561 3579 -0.0027 0.00 0.0242 0.2668 0.8674 5 3276 -0.0020 0.00 0.0205 0.2649 0.9489 3668 -0.0022 0.00 0.0245 0.2594 0.9490 4 3297 -0.0025 0.00 0.0199 0.2942 1.0465 3746 -0.0026 0.00 0.0246 0.2844 1.0528 3 3306 -0.0022 0.00 0.0193 0.2898 1.1166 3816 -0.0024 0.00 0.0256 0.2832 1.1144 2 3319 -0.0020 0.00 0.0184 0.2839 1.1820 3883 -0.0023 0.00 0.0261 0.2714 1.1785 1 3330 -0.0023 0.00 0.0185 0.3126 1.1603 3954 -0.0026 0.00 0.0282 0.3007 1.1468 Mean 3232 -0.0024 0.00 0.0200 0.2777 0.9040 3555 -0.0024 0.00 0.0236 0.2723 0.9046

…continuation of Table 5-4 from the previous page.

Panel B: Kruskal Wallis Teste _{of Difference Between All 11 Monthly Relative Forecast Distribution Mean/ Median Samples Prior Reporting - Bias}

AERF_BIAS_CONS AERF_BIAS_mPE AERF_BIAS_PRICEt=-11 AERF_BIAS_PRICEt

Mean Median Mean Median Mean Median Mean Median Average Sample Size Per Month

(Statistical Period) 3550 3550 3550 3550 3232 3232 3555 3555

Kruskal-Wallis H-Statistic 4.6665 9.0142 46.6987 8.572 4.6665 8.5718 4.6665 9.1765

(<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) (<.0001) ___________________________________

a _{All firms' parameters of the distributions of analysts’ earnings forecast bias such as median and the first four moments (per statistical period) were grouped by the number of statistical periods}

up to 11 months prior to the corresponding firm's reporting date. In this way I control for the timing differences between the earnings reporting dates of different firms and their corresponding

distributions of AERF_BIAS. This was employed to all firms with year end dates 1st _{July 1988 through 30}th _{June 2002.}

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.

d _{The median and first four moments of the analysts’ earnings relative forecasts bias (signed error) and accuracy (unsigned error) distribution is measured using the analysts’ earnings relative}

forecast (AERF) bias and analysts’ earnings forecast (AEAF) accuracy measure defined as:

_ _ _ _

_ analyst earnings forecast analyst earnings consensus

AERF BIAS

deflator  

| _ _ _ _ |

_ analyst earnings forecast acutal announced earnings

AEAF ACC

deflator  

The four deflators are:

(1) Firm’s Share Price at statistical period t=-11: PRICEt=-11

(2) Firm’s Share Price at t: PRICEt

(3) Period consensus: CONS

(4) Average of Consensus and Forecast: mPE

5.11 Further Data Partitioning Due to High Actual Forecast Error of