Bachelor Thesis:
Do EPS forecast error and EPS forecast dispersion vary
with scale for firms listed in the Netherlands?
Abstract
Cheong and Thomas (2010) found in their paper that forecast error and forecast
dispersion did not show variation with scale for some markets. The results in this paper show that firms listed in the Netherlands show a negative relation between forecast error and scale and a both positive and negative relation of forecast dispersion with scale. This is due to managerial, analyst and investor behaviour. The results could have impact on both previously published and future research conducted in the Netherlands. Forecast error and disagreement were always assumed to increase with scale and were therefore deflated. Deflating forecast error and dispersion by stock price could create a negative relation between scale and deflated variability and disagreement if these variables do not increase with scale, thereby causing spurious results.
Name: Hylke Schaaf Student number: 5870550
Program: Finance and Organisation Thesis supervisor: Shivesh Changoer
1. Introduction
Not so long ago it was presumed that deviation of actual earnings per share from the forecast consensus, or forecast error, and deviation of individual forecasts of earnings per share by analysts from the consensus, or forecast dispersion, varied with scale. This was because both actual earnings per share (EPS) and the consensus forecast do vary with scale across shares of different firms. However, Cheong and Thomas (2010) show that forecast error and forecast dispersion do not always vary with scale.
These results of Cheong and Thomas are surprising. Forecast error and dispersion are not reported as a percentage of the share price but in absolute cents. One would expect the forecast error measured in cents to be larger if the amount of earnings being
estimated is larger. The same goes for the forecast dispersion. As the consensus forecast increases, one would expect analysts to give a wider variety of individual forecasts. The counter intuitive findings of Cheong and Thomas call for further investigation, not only into the possible explanations of the findings but also in other markets than the ones looked at by Cheong and Thomas, since the result could have implications for prior research conducted in those markets.
In this paper it will be investigated whether forecast error and dispersion vary with scale for firms listed in the Netherlands. Cheong and Thomas have not looked at this market in their 2010 paper. Since Cheong and Thomas found different results for different markets it should be explained whether firms listed in the Netherlands show variation with scale for forecast error and forecast dispersion. In this paper the term variability will be used to describe the forecast error and the term disagreement will be used for the forecast dispersion.
The result of this research could be of value for investors investing in the Netherlands because investors often rely on the analysts’ forecasts of EPS. (Degeorge et al.,1999). Earnings estimates are important for equity valuation and have become an integral part of reporting in the financial press. If it is found that there is a lack of variation with scale
for forecast error this could indicate whether managers actively smooth earnings1 in the
Netherlands and this could influence investment decisions. This research could also further our understanding of managerial behaviour, as it is possible that managers suffer from behavioural bias that causes them to smooth their earnings. Investigating whether analysts do or do not show variation of forecast dispersion with scale could be helpful in our understanding of analyst (and possibly managerial) behaviour.
Another important implication of the findings in this paper could be that previous researches using data containing firms listed in the Netherlands and using measures of forecast error and forecast dispersion, need to be re-‐evaluated. Previous research has assumed that the magnitudes of forecast error and forecast dispersion vary with scale and it has deflated both variables accordingly. Deflating the variables of variability and disagreement could have caused biased estimates in previously published researches. Deflating by measures of scale can create a strong negative relation between scale and deflated variability or disagreement. This means that if deflated variability or
disagreement is used as a variable it could generate invalid results if the other variable is correlated with scale.
The 2010 paper of Cheong and Thomas will be used as a basis to build this thesis upon. The results of the Cheong and Thomas paper will be compared with the results that would be expected based on theories in previously published literature. These combined will provide a background to relate the result of this paper to. They will provide possible explanations for when our results differ from the findings of Cheong and Thomas. Since this paper investigates a different market and Thomas and Cheong did not find the same results for all markets it could be that our results are different from the Cheong and Thomas findings.
After this section the paper is structured as follows: In section 2, previously published literature will be investigated. In this section, first, the research of Cheong and Thomas (2010) and their findings will be briefly discussed. Their paper and other previously published literature will then be used to investigate why forecast error and dispersion
1 Smoothing of reported earnings can be defined as dampening the fluctuations about
would not vary with scale and what might be the rationale behind this. In section three the variability with scale will be investigated for firms listed in the Netherlands and the results of this research will be presented. In section four the results of our research will be summarized and discussed.
2. Background literature
2.1 The Cheong and Thomas research
In their investigation, Cheong and Thomas(2010) found that deviations of actual
earnings per share from analysts’ consensus forecast of EPS, as reported by I/B/E/S2, do
not vary with share price, or scale, for U.S. firms and a number of other markets. These markets did not show an increase in the variation of the forecasts dispersion with scale. The problem with drawing general conclusions from the findings in these markets is that Cheong and Thomas did not find the same result in all markets. Some markets did show variation with scale for variability and dispersion. The results of Cheong and Thomas further showed that variability and disagreement increase with scale for per share sales forecasts and operating cash flows per share, but this is covered by the scope of this paper.
2.2 Explanations proposed by Cheong and Thomas for the lack of variation of forecast error and dispersion with scale
Cheong and Thomas (2010) investigated three possible explanations for the found lack of variation of variability and disagreement with scale. The first explanation was that variability and disagreement do not vary with scale in nature because of subtle process and measurement issues associated with EPS forecasts that are missed the first instance. It could be that EPS variability and disagreement are determined more by analyst-‐
manager communication than by underlying uncertainty about EPS, since forecasts made before earnings announcements may have been prepared by managers who have observed the preliminary estimates of EPS. It seemed Cheong and Thomas unlikely that per share cash flows and accruals both vary with scale in nature in such a way that EPS,
2 I/B/E/S, or Institutional Brokers’ Estimate System, is a database containing earnings
whish is the sum of the two, does not show variation for variability and disagreement. They therefore rejected the first explanation.
The second explanation is that variability and disagreement do increase naturally with scale, but other factors cause the scale variation to be reversed on average. An example of this is that low price shares often have a relatively larger part of forecasts that are no longer up to date compared to high priced shares. This could counter the natural
variation with scale. Older shares are more likely to show a larger forecast error. Cheong and Thomas (2010).
Cheong and Thomas rejected this second explanation because they were unable to find factors that increase/decrease with scale and also decrease/increase with variability or disagreement. They think that the lack of variation with scale they observed is unlikely to be a coincidental consequence of the net effect of different factors, as suggested by their second explanation.
A third explanation that is suggested by Cheong and Thomas is that the outcome of their research is one that is desired by analysts. There might be incentives or behavioural biases that could cause analysts to suppress the natural variation with scale. These could explain why analysts focus on deviations from EPS in cents per share and not on a
percentage of price or EPS and explain why analysts target similar bounds for deviations across small and large shares. A possible explanation for this behavioural bias is that the financial press focus in reporting’s on cents per share and does not adjust for scale. This means that analysts following high price shares have an incentive to work harder to generate forecast error magnitudes and dispersion similar to those of low price shares. If they provide the same effort for high priced shares as their colleagues do for low priced shares their analyses would seem to be of lower quality than the ones made for low priced shares because the would be an equal percentage, but more cents, off target.
Some of the results found by Cheong and Thomas point them in the direction of the third explanation. But at a practical level, while increased analyst effort for firms with higher share prices can reduce disagreement to a level similar to low price firms, they found it difficult to see how increased analyst effort would result in a reduction in forecast error
for high priced firms. In order for the forecast error to be reduced, or show no variation with scale, the cooperation of managers has to be considered. If managers cooperate with analysts and smooth the EPS being forecasted, this would reduce forecast error. Managerial smoothing, combined with increased analyst effort, could cause means the forecast error and dispersion to be lower than what they would naturally be.
Theoretically, it is also possible that analysts are not involved at all in providing
managers with incentives to smooth their earnings. But from the results of Cheong and Thomas it appears that managers are less likely to engage in smoothing when their shares are not the subjected to the analysis by analysts. This correlation suggests that analysts are somehow involved. Cheong and Thomas also looked at cash flows and sales and did not observe the suppression of variation with scale by analysts in their data. This underlines the suggested relation between managerial smoothing and analysts.
Since the results of Cheong and Thomas show that managers that are not followed by analysts smooth less than firms that are not followed by analysts, managers do not seem to suffer from independent behavioural bias. Analysts on their turn do not seem to suffer from independent behavioural bias since variability and disagreement for cash flows and sales do vary with scale. This means that the findings of Cheong and Thomas suggest that both managers and analysts are taking the expectation of others, possibly investors, into account. Cheong and Thomas think that investors are, indirectly, the reason for the found lack of variation. Through market pressures, investors cause managers to
cooperate with analysts and smooth their reported EPS. If managers of firms with large shares smooth earnings more than managers of firms with small shares, the volatility of reported EPS could be relatively similar for both groups. Investors could also be the cause that analysts provide more effort for high price shares. The actions of managers and analyst’s that are incentivised by investors could have the combined effect of causing variability and disagreement not to show variation with scale.
2.3 Reasons for managerial smoothing
Managerial smoothing can be seen as an attempt on the part of a firm’s management to reduce abnormal variations in earnings to the extent that they are allowed under accounting and management principles. Firms generally manage earnings because they
hope to be rewarded by the market and their superiors for delivering earnings that are smoother and come in consistently above analyst estimates.
There are many reasons why managers would smooth their earnings. See Beidleman (1973). First of all, earnings are used inside de firm to measure and evaluate the past performance of a manager of the firm. This gives the manager an incentive to keep EPS volatility stable. Smoothing the EPS helps the manager to average out the high and low earnings. If the manager reports very high earnings the superiors, but also investors and other stakeholders, will probably expect the manager to perform just as good in the next period. This might not be realistic. The shareholders will then punish the manager by firing him. This gives the manager an incentive to create expectations with those involved that he thinks he can meet in the next period. By smoothing the manager can also prevent the reporting of very low earnings because he averages out the positive and negative periods. If the manager does not meet the expected high earnings or reports very low earnings the manager could be punished. The threat of punishment gives the manager individual incentives to smooth EPS and this could make the manager
behavioural biased. Beidleman (1973). This contradicts the results of Cheong and Thomas (2010) who showed that managers do not engage in managerial smoothing when analysts are not involved. Managers do seem to have incentives to smooth their income regardless of analysts being involved.
Besides the chances of being punished, managers have another personal incentive to smooth earnings and thereby increase share price. Future income is often related to the future share price. The uncertainty of his future income creates an idiosyncratic risk on the manager because his income will depend on a single share price. This risk is reduced if the share price is less volatile, which can be achieved by smoothing EPS. Most
employment contracts are designed in such a way that managers receive a higher salary if their share price is higher. Bouwman (2014). Managers who receive compensation that is more sensitive to their firms’ stock prices tent to smooth more. CEO option and stock ownership are examples of CEO compensation that is extra sensitive to stock prices. See Bouwman(2014). Again, analysts are not necessarily involved in providing managers with an incentive to smooth earnings.
Other internal reasons for managers to smooth their earnings are that the EPS is used as a factor in the formulation of plans and budgets in future income periods and for making capital acquisition decisions. Beidleman(1973). Fluctuating earnings make it harder for managers to coordinate these activities and to answer their investors if they question the feasibility of the plans. This also contradicts the results of Cheong and
Thomas(2010) who say that analysts necessarily have to be involved.
According to Beidleman, it is commonly accepted that the value of an asset can be treated as the discounted or present value of a stream of expected net cash flows where the rate of the discount is related to the uncertainty associated with the expected cash flow. The variability of earnings can therefore be seen as an important measure of the overall riskiness of a firm. Beidleman (1973). Less variation in the reported earnings has a positive effect on the value of shares. A study of Barnes (2001) on the relationship between price to book value ratios and earnings stability concludes that stocks with lower earnings volatility trade at higher values and finds that this is true even when the earnings stability reflects accounting choices rather than operating stability; firms where earnings are stable but cash flows remain volatile continue to trade at higher values. This means that investors have reasons to encourage earnings management. The involvement of analysts does not seem to be essential to give a manager an incentive to smooth. Again, this contradicts the result of Cheong and Thomas who suggested that managers do not engage in managerial smoothing when analysts are not involved.
Another way in which earnings management influences a firms stock price is
investigated by Payne and Robb (2000). They looked whether managers might aim to meet or beat analysts’ forecasts. Their results indicate that managers align earnings with market expectations as determined by analysts’ forecasts. Managers use earnings
management in order to protect a company’s stock price, which would fall if their earnings would deviate from the expectations of the market. Both managers and
analysts stand to gain if EPS forecasts are met. Managers will seem to have done a good job at managing the firm, which will bring rewards and/or reduce the chance of being fired. Analysts will seem to have cast a correct forecast and attract more funds. This supports the theory of Cheong and Thomas that managers have an incentive to
cooperate with analysts. This could cause the forecast error not to show variation with scale.
Managerial smoothing is also influenced by the ownership structure. See Carlson and Bathala (1997). Institutional ownership creates a pressure for current earnings and institutions tend to divest when a firm’s performance weakens. This gives managers an incentive to smooth earnings. Very dispersed ownership on its turn creates a better position for managers to adopt discretionary accounting practices that serve in their interest, in this case earnings management.
Another way in which ownership dispersion could influence the extent of EPS smoothing is because of the information asymmetry, which tends to be larger when ownership is more dispersed. Empirical results of Richardson (2000) suggest a
systematic relationship between the magnitude of information asymmetry and the level of earnings management. Management’s intent could be not to try to fool the market by smoothing income but to relate additional information to investors about the expected future cash flows. Barnea et al. (1976). This theory of information signalling by EPS smoothing is contradicted by the research of Ball (2013). In this paper Ball brings the argument forward that there are many competing information sources available to investors and stakeholders of the firm. Many of these sources are more frequent than periodic financial reporting. It is also shown in a paper by Ball and Shivakumar (2008) that because of the relatively low frequency of financial reporting by managers, it is unlikely to provide a lot of new information to stakeholders. Financial reports are issued independent of whether there is new information and they are primarily backward looking. Other information sources are often comparatively high frequency, released only when there is substantial information to report and both forward and backward looking. Ball (2013). There is no consensus in the literature regarding the influence of the information signalling effect of reported earnings. This weakens the argument that ownership dispersion has a positive effect on managerial smoothing but it could prove to be a helpful explanation for surprising results.
Analysts also stand to gain when managers smooth earnings. Analysts are happy with the smoothing of income because in makes their job easier. With the same amount of
effort analysts are now able to forecasts EPS with a lower forecast error. Low variation in EPS also increases the confidence of the market in the shares of a firm, thereby enlarging the market for these shares. See Beidleman (1973). Dechow’s (2012) empirical research found that analysts exert less effort forecasting earnings for firm’s that generate less brokerage or investment banking business since they create less value for the analysts. Cheong and Thomas suggested that the convergence of analysts forecast could be due to increased effort of the analysts. When analysts are not really interested in firms they are often less certain about the last digit of the forecast and round the number. This means there will be more disagreement among analysts when they are not really interested in firms. Since brokerage is influenced by the extend to which earnings are smoothened, analysts will be more interested in firms that smooth more. They would therefore be willing to exert more effort in their forecast and thereby reduce the variation of scale in forecast dispersion. This supports the theory of Cheong and Thomas that the combined effect of managerial smoothing and analysts effort could reduce the variation in forecast error and forecast dispersion.
What is interesting is that, according to Payne and Robb(2000), managers seem to have greater incentives to meet analysts forecasts when the dispersion in analysts’ forecasts is low. It looks like managerial smoothing and analysts lowering the dispersion have a positive effect on each other. Cheong and Thomas found that there was variation in forecast error to be found in markets that were not followed by analysts. According to the findings of Payne and Robb it could have been the case that in the research of Cheong and Thomas, firms followed by analysts smooth more than firms that are not followed by analysts. This does not mean that firms that are not followed by analysts do not smooth. It can be that these managers just smooth to a lesser extent, which is not able to counter the variation of the forecast error with scale completely.
In research of Farraghe et al.(1994) it appears that there is a significant inverse relationship between investor relations, measured by financial Analysts Federation Corporate Information Committee, and the dispersion of security analysts EPS forecasts. If large firms have better investor relationship programs than firms with lower priced shares this could converge the EPS Forecasts and dampen the variation of disagreement with scale of one of the groups compared to the other. This part of the
research of Farraghe supports the second explanation of Cheong and Thomas. It shows that the relation between analysts and managers has a positive effect on the negative forecast dispersion. It could reduce variation in disagreement with scale.
The literature reviewed suggests that managers have different kinds of incentives to smooth their earnings. The first are personal incentives, for example receiving a higher salary. Another category consists of incentives that are related to internal business matters and do not directly involve investors, for example budgeting. The last and
possibly the biggest incentives are provided by investors, for example the threat of being fired. This is not in completely in line with the results of Cheong and Thomas (2010), which suggested that managers smooth earnings because of investors and not because of personal behavioural bias.
The suggestion of Cheong and Thomas that analysts and management work together in reducing forecast error and dispersion is supported by the literature since analysts have reasons to work harder and thereby reduce dispersion when earnings per share are managed. If managers try to meet or beat the forecast consensus, each analyst has an incentive to get their analysis as close as possible to the consensus.
It was also found that managers seem to have greater incentives to increase income when the dispersion in analysts’ forecasts is low. It can therefore be said that there seems to be a positive relation between earnings management and lower dispersion in analysts’ forecasts that works both ways. This could explain the lack of variation
Thomas and Cheong(2010) found for forecast errors and forecast dispersion with scale.
3. Samples and evidence of the research 3.1 Data description
For the dataset the I/B/E/S unadjusted database is used and the dataset contains annual financial statements for firms listed in the Netherlands between 2008 and 2014. This period is chosen because 2007 counts as the beginning in the financial crisis. The
relation between pre-‐crisis earnings management and earnings management during the economic crises could cause unknown effects to this research and might lead to biased results. That a financial crisis can affect the way and extent to which managers smooth their earnings was shown by Chia et al. (1986). Their paper investigated the effect of the Asian financial crisis on managers and it showed that the earnings management culture had changed. This paper does not have the purpose to compare pre-‐crisis and in-‐crisis earnings management so therefore the period 2008 to 2014 is chosen.
Each calendar year the consensus forecast (FORECAST), that is the mean of individual forecasts, the standard deviation of individual forecasts surrounding the consensus (DISPERSION), the actual EPS value (IBESACTL), and the share price (BEGPRICE) are gathered in the sample. Share price, rather than EPS, is used as the measure of scale because it is less likely to be associated with measurement error. MEANSTALE will indicate the mean age of the forecasts.
Forecast error (FCSTERR) is measured as IBESACTL minus FORECAST. The last variable included in the research is COVERAGE, which is the number of forecasts on a particular EPS reporting. The BEGPRICE at the end of each year is used to form price deciles. The data was sorted on the BEGPRICE variable and than divided into deciles. Decile 1 represents the lowest 10 percent and decile 10 the largest 10 percent.
To allow for a meaningful measure of dispersion, EPS forecasts with fewer than three forecasts are deleted. Of course, if there is only one forecast the forecasts dispersion would automatically equal zero. This would trouble the analysis of the results. Another reason is that is also done in practise, by for example Thomson First Call3, in an attempt
3 Thomson First Call is a leading distributor of brokerage-‐firm research and analyst
to eliminate the possibility of one poor forecast skewing the consensus figure into exceptional earnings surprises. See Thomas and Cheong (2010).
“Unadjusted” values are used because of concerns about rounding off in “adjusted” I/B/E/S data. “Unadjusted” means that the data is not adjusted for stock splits. If the “adjusted” stock split data was used the analysts’ earnings per share estimates of a couple of years back would be based of the number of shares outstanding as of today, rather than the number of shares outstanding at the time the analyst did the forecast. The problem with this is that after dividing the analysts’ forecasts by a split adjustment factor, I/B/E/S rounds the estimate to the nearest cent. Diether et al.(2002) give an example: If a stock has split 10-‐fold, actual earnings per share estimates of 10 cents and 14 cents would be reported as 1 cent per share each. I/B/E/S would then include an adjustment factor of 10 in the Adjustment File, so that the earnings per share estimates would be assumed to be 10 cents each, rather than the correct values of 10 and 14 cents, respectively. This would make the variance of analysts’ forecasts equal to zero, when in fact is positive. See Diether et al. (2002). Using unadjusted data is recommended by the WRDS manual to work around this problem.
The unadjusted data is adjusted for dividends and stock splits which is important when analyzing forecasts over a long period of time as shown by Beaver et al. (2008). The I/B/E/S adjustment factor is used to adjust the actual values valid on the report date and unadjusting the then adjusted actual using the IBES adjustment factor valid on the estimate date. This is the first method suggested in the WRDS manual. It is still possible to have some problems when the I/B/E/S report date lies between the true split date and the effective split date, but this almost never happens according to Robinson and Glushkov(2006), working at Wharton Research Data Services.
3.2 Results
Table 1 reports means and medians of the primary I/B/E/S sample of Dutch firm years. There is considerable variation in scale across the price deciles: mean and median values of BEGPRICE are over twenty times the size in the tenth price decile then they are in the first decile. Variation with scale for share price is also reflected in the variation of the consensus EPS forecast (FORECAST) and actual EPS as reported by to I/B/E/S (IBESACTL). The remaining row indicates that there is no trend in the number of analysts following (COVERAGE)
Table 1: Variation across BEGPRICE Deciles in Means and Medians of selected variables Table 1 reports the mean and median of selected variables across deciles of BEGPRICE, which is the end of year share price. IBESACTL is the actual quarterly EPS as reported by I/B/E/S, and FORECST is the most recent consensus (mean) EPS forecast for that firm-‐year. COVERAGE displays the analysts following the shares. The sample contains 2730 firm-‐years derived from firms listed in the Netherlands on I/B/E/S with available data, between January 2008 and January 2014.
Variable Stats 1 2 3 4 5 6 7 8 9 10 All
BEGPRICE Mean 2.2 4.98 8.12 11.2 14.1 17.35 22.22 27.93 35.22 50.54 19.39 Median 2.27 4.9 8.18 11.34 14.1 17.07 22.49 27.72 34.88 48.35 15.56 FORECAST Mean 0.29 0.59 0.91 1.02 1.4 1.68 1.68 2.19 2.53 3.23 1.55 Median 0.25 0.6 0.86 1.02 1.39 1.48 1.58 1.93 2.41 3.14 1.42 IBESACTL Mean 0.17 0.13 0.63 0.67 1.16 1.55 1.62 2.12 2.46 3.18 1.37 Median 0.12 0.34 0.79 0.93 1.3 1.41 1.57 1.94 2.48 3.02 1.32 COVERAGE Mean 10.6 17.39 20.71 17.66 13.95 11.96 17.87 17.53 17.62 18.95 16.46 Median 9 14 21 13 10 10 12 12 16 16 13
Figure 1 and 2 give a graphical view of the across-‐price-‐decile distribution of the
forecast error and the forecast dispersion. Each vertical bar represents the distribution for one price decile. The marks identify the location of the median and the 5th, 25th, 75th and 95th percentiles of the pooled distributions. In table 2 and 3 the corresponding numerical values of the median, standard deviation and interquartile ranges can be found.
The results in figure 1 and table 2 and show that forecast error magnitudes do not increase with scale for share price for firms listed in the Netherlands. The spread
between the 25th and 75th percentiles in figure 1, represented by Qrange in table 2, does
not increase along with the deciles. Rather it shows a downward trend.
Figure 1
Table 2: Variation of forecast variability across BEGPRICE decile.
Table 3: Variation of forecast dispersion across BEGPRICE deciles
Table 2 and 3 report the mean, median, standard deviation(StdDev), interquartile range (Qrange), and the number of observation (N) for distributions across deciles of BEGPRICE, which is the end of year share price. FCSTERR is defined as IBESACTL minus FORECAST, where IBESACTL is the actual quarterly EPS as reported by I/B/E/S, and FORECST is the most recent consensus (mean) EPS forecast for that firm-‐year. DISPERSION is the standard deviation of the individual analyst forecasts around the consensus. The sample contains 2730 firm-‐years derived from firms listed in the Netherlands on I/B/E/S with available data, between January 2008 and January 2014. All prices and forecast/actual EPS are in Euro’s
The results in figure 2 and table 3 show that forecast dispersion magnitudes do not automatically increase with scale for firms listed in the Netherlands. The focus here is not on the spreads of these distributions, but on the mean and medians because the variable (DISPERSION) already measures spread across individual forecasts. The median value of DISPERSION shows a kind of a wave effect over the different deciles. Overall, the means and medians of DISPERSION seems to be increasing over the price deciles. 1 2 3 4 5 6 7 8 9 10 All FCSTERR Mean 0.43 0.51 0.44 0.37 0.36 0.25 0.24 0.21 0.25 0.18 0.32 Median 0.131 0.22 0.11 0.1 0.18 0.14 0.11 0.1 0.12 0.12 0.13 StdDev 0.72 0.69 0.8 0.89 0.52 0.3 0.33 0.31 0.4 0.17 0.57 Qrange 0.409 0.49 0.38 0.18 0.31 0.28 0.23 0.18 0.28 0.19 0.27 N 273 273 273 273 273 273 273 273 273 273 2730 1 2 3 4 5 6 7 8 9 10 All DISPERSION Mean 0.12 0.17 0.2 0.15 0.18 0.22 0.2 0.17 0.21 0.25 0.19 Median 0.07 0.13 0.14 0.1 0.12 0.16 0.17 0.15 0.18 0.22 14 StdDev 0.12 0.17 0.19 0.22 0.17 0.25 0.14 0.12 0.14 0.14 0.17 Qrange 0.12 0.14 0.17 0.08 0.19 0.16 0.13 0.12 0.14 0.18 0.16 N 273 273 273 273 273 273 273 273 273 273 2730
Figure 2
In previous literature investigating forecast errors, the forecast error was often divided by a scalar. This process is called forecast error scaling or deflating. Theory said, for example, that it was necessary to deflate forecast errors by stock prices because of the correlation between unexpected earnings and changes in stock prices. See Brown (2001).
As the results in figure 1 and 2 indicate that variability and disagreement show a
different variation with scale than always was presumed, deflating them by scale should have created a negative relation with scale, causing previous research to find biased results.
In figure 3 and 4, FCSTERR and DISPERSION are scaled by BEGPRICE and are called scfcsterr and scdisp respectively. These figures show that both variables now suddenly show a very strong downward trend. Which is to be expected if FCSTERR and
DISPERSION do not actually vary with scale.
Figure 3 and 4 offer a more detailed view of the distributions of dispersion and forecast error respectively. In this way unusual patters could be detected. The histograms show the fraction of the samples represented by a certain value of dispersion or forecast error. Only histograms of deciles 1, 5, and 10 are given. The represent low, medium and high priced shares
Figure 4: Histograms for FCSTERR for price deciles 1, 5, and 10
Figure 3a. distribution of scfcsterr (FCSTERR scaled by
BEGPRICE) over the price deciles Figure 3b. distribution of scdisp (DISPERSION scaled by BEGPRICE) over the price deciles
Figure 5: histograms for DISPERSION (for price deciles 1,5, and 10)
While these histograms show specific aspects that vary across price deciles, such as skewness and range, the also confirm our earlier conclusions. The variation of FCSTERR seems to be getting smaller as price increases. The mean and median of DISPERSION increase as price increases.
3.3 Other variables that could impact the variation of variability and disagreement with scale in our sample
The results of table 4, 5, and 6 indicate the variation of variability and disagreement with various variables that, based on the literature in section 2, could provide us with more insight into the relations of variability and dispersion with scale. There variables are considered: COVERAGE(table 4), DISPERSION(table 5) and MEANSTALE(table 6).
Coverage Decile Variable Stats 1 2 3 4 5 6 7 8 9 10 COVERAGE Median 5 8 9 10 12 14 20 24 29 34 BEGPRICE Median 11.93 14.72 13.07 14.10 20.38 33.13 12.16 18.32 17.47 13.60 FCSTERR Qrange 0.24 0.41 0.36 0.36 0.30 0.32 0.18 0.23 0.28 0.19 DISPERSION Median 0.08 0.14 0.14 0.14 0.16 0.18 0.16 0.14 0.17 0.11
Table 4. Variability and disagreement for EPS forecasts based on deciles of COVERAGE.
Figure 5c. Decile 10 Figure 5a. Decile 1 Figure 5b. Decile 5
The results in Table 4 indicate that while COVERAGE is positively related to the share price, it seems to be negatively correlated with forecast error and slightly positively correlated to disagreement. These results of table 4 support the earlier results that showed a negative relation of forecast error with scale and a both positive, decile 1 to 6, and negative, decile 6 to 10,relation of disagreement with scale.
According to Dechow’s (2012), interesting stocks with a higher COVERAGE should have lower DISPERSION because analysts are expected to work harder for important stocks, see Cheong and Thomas(2010). This can be seen from decile 6 to 10.
The negative relation between analyst coverage and forecast error is supported by Payne and Robb (2000). As stock are more interesting/profitable fore analysts, more analysts will cover the stock. The results of Payne and Robb state that there is a negative relation between analyst coverage and forecast error because FCSTERR and
DISPERSION are positively correlated.
Dispersion Decile Variable Stats 1 2 3 4 5 6 7 8 9 10 DISPERSION Median 0.03 0.06 0.08 0.11 0.13 0.16 0.19 0.24 0.3 0.5 COVERAGE Median 10 11 12 12 15 13 14 13 18 18 BEGPRICE Median 9.09 11.82 12.52 13.07 18.46 21.59 21.11 19.76 20.38 17 FCSTERR Qrange 0.10 0.13 0.15 0.24 0.26 0.35 0.37 0.44 0.56 0.93
Table 5. Variability and disagreement for EPS forecasts based on deciles of DISPERSIOM.
In table 5, there is a positive relation between DISPERSION and BEGPRICE, as is also found in our main results. There seems to be a strong positive relation between forecast error and disagreement. While this seems natural and is supported by our literature, it is not directly reflected in our main results, where forecast error and forecast dispersion seem to have separate relations with BEGPRICE.
According to the theory of Payne and Robb (2000), managers would have greater
incentives to meet analysts’ forecasts when the dispersion in their forecast is lower. This would lead to a lower forecast error. Table 5 supports the theory of Payne and
Robb(2000) and shows there is a strong positive relation between DISPERSION and FCSTERR in our sample.
Meanstale Decile Variable Stats 1 2 3 4 5 6 7 8 9 10 Meanstale Median 14 30.23 49.60 64.8 69.05 80.20 94.78 111 123.60 154.2 BEGPRICE Median 16.05 13.56 15.58 17.98 17.56 15.38 16.39 13.95 16.36 15.47 FCSTERR Qrange 0.19 0.42 0.41 0.77 0.38 0.21 0.21 0.31 0.26 0.35 DISPERSION Median 0.14 0.16 0.15 0.15 0.15 0.13 0.14 0.15 0.15 0.15
Table 6. Variability and disagreement for EPS forecasts based on deciles of MEANSTALE.
The deciles in table 6 for MEANSTALE do not show correlation with BEGPRICE and there is no evidence of a strong positive effect of MEANSTALE on FCSTERR and DISPERSION. This is surprising since one would expect older forecast to show, on average, a higher forecast error and a higher forecast dispersion. As table 6 shows a slightly negative relation between MEANSTALE and FCSTERR and no relation to BEGPRICE and DISPERSION it corresponds with our main results. It can be that the negative relationship between FCSTERR and BEGPRICE can be explained by the irregular relation between MEANSTALE and FCSTERR a in our sample.
3.4 Theoretic explanations of the results
In our main results, the variation of the forecast error seemed to get smaller as the share price increased. This is rather puzzling since it was always assumed that there was a positive relation with scale and Cheong and Thomas(2010) showed no variation with scale. This papers shows there is a third possible relation, a negative relation between variation of forecast error with scale.
An explanation for the variability-‐finding could be that the effect of managerial
smoothing on the forecast error is not only countering the effect of a natural increase in forecast errors with scale but even causes the forecast error to have a negative variation with scale for the share price. In other words, as share price increases, managers try harder to meet analysts’ forecasts consensus. It can be that managers of high priced
shares are, on average, more under pressure of investors. This is very well possible if, for example, ownership of larger shares is more dispersed and this creates pressures for current earnings. Carlson and Bathala(1997).
The findings concerning the disagreement across analyst’s varying with scale do show variance with scale but this relation is both positive and negative. Cheong and Thomas (2010) did not find any variation with scale for forecast dispersion. This result could mean that analysts do not always converge their forecasts, even if the managers smooth EPS.
The results reported concerning the variation of forecast dispersion could be explained if managerial smoothing and the amount of effort analysts exert are not always directly related. The literature reviewed in section 2 of this paper supports this possible
explanation. Managers have incentives of their own to smooth earnings. Analysts could choose to work harder if managers engage in smoothing but it is not always necessary. It was shown in the literature review that managerial smoothing and converging of
analysts’ forecasts could happen independent from each other since both managers and analysts have their own reasons to reduce forecast error and forecast dispersion. Although they also have incentives to work together, this does not always has to be the case.
4. Conclusion and discussion 4.1 Conclusion
The results show that the magnitudes of dispersion and forecast error vary with scale for firms listed in the Netherlands. This was not expected on the basis of the main findings of the paper of Cheong and Thomas(2010). Here it was suggested that no variation would be found. Managerial smoothing would counter the effect of increasing volatility and help incentivised analysts to keep the level of dispersion relatively
constant as the scale increases.
Not only did our results show variation, the variability and dispersion showed a
the literature review conducted in this research. Individual reasons for managers to engage in smoothing independent from analysts could be the reason for our results. Changing investor pressures could cause the negative relation of variability with scale. An uncertain relationship between managerial smoothing and analysts’’ reduction of dispersion could cause the changing variability of dispersion with scale.
In our sample there seemed to be an irregular relation between the age of the forecasts and the forecast error and forecast dispersion. Further investigation is needed to the reasons behind this irregular relation and its impact on the variation of the forecast error and forecast dispersion with scale.
The results in this paper offer a new view on the relationship between the variation of forecast error and forecast dispersion with scale than previous research. Future
research should extend our knowledge of this relationship and investigate the possible explanations for the puzzling findings offered in this paper.
4.2 Discussion
Further investigation into the nature of the firms contained in the sample might provide information about why the results are so different from the results that were expected and the possible role of ownership dispersion in this process. Ultimately, the existence of earnings management will be very difficult to prove because it can only be proven definitively by knowing the mindset of management.
Due to the limited scope of this research and because of the deleting of all samples with COVERAGE less than three the overall data sample has become somewhat small. This could have had influence on the results. The ability to detect scale variation could be hindered by small rounding errors inherent in I/B/E/S per share data reported to the nearest cent. See Ball (2012).
