COMBINING PREDICTIVE REGRESSION MODELS TO OUTPERFORM ANALYST QUARTERLY EPS ESTIMATE, EMPIRICAL ANALYSIS OF THE GERMAN INDUSTRIAL AND ELECTRONIC EQUIPMENT INDUSTRY

COMBINING PREDICTIVE REGRESSION MODELS TO

OUTPERFORM ANALYST QUARTERLY EPS ESTIMATE,

EMPIRICAL ANALYSIS OF THE GERMAN INDUSTRIAL

AND ELECTRONIC EQUIPMENT INDUSTRY

Dirk van den Belt1

Thesis MSc Finance January 2016 University of Groningen Faculty of Economics and Business

Supervisor: Dr. W.G. Bessler

Abstract Analyst have a conflict of interest which leads to biased earnings estimates. This

research uses a combination of 23 bivariate predictive regressions to predict quarterly EPS. With data, starting in 2003, earnings are predicted between 2011 Q4 and 2015 Q2.The sample consists of 17 German firms in, the industrial and electronic equipment industry and they are all covered by analyst. The combination forecast fails to consistently outperform analyst in their EPS estimates. Although a positive bias from analyst is proven. Additionally the forecast combination does outperform for firms with low coverage and could also be used for firms that are not covered by analyst. The current combination forecast should be improved to disrupt analyst superiority completely.

Keywords Quarterly EPS forecast, Analyst performance, Predictive regression,

Combination forecast JEL-classification G17, G10, C53

Words 9,760

1.

I

NTRODUCTION

Future earnings estimates are an important instrument in the financial world. Forecasts are used internally by manager and externally by investors to value or to measure performance. These forecasts are often based on earnings estimates of research analysts. Also the academic world uses the estimates from analyst as earnings forecast. The problem is that these “research analyst are subject to a number of well-known conflict of interest that can result in biased or inaccurate forecasts”2 _{(Bradshaw, Drake and Myers, 2012, p.945). Academic researchers have therefore} always studied this conflict of interest and tried to build models that could outperform analyst earnings estimate. There are examples of models that might outperform analyst forecast on longer horizons. Bradshaw et al. (2012) were able to outperform analyst earnings on 2 and 3 years horizon. However the largest challenge is to outperform analyst on shorter horizon, as the advantage of analyst over models is the greatest on shorter horizons3_.

This research attempts to beat analyst there were their advantage is the greatest, on the short horizon. It incorporates 23 variables from different origin that were proven relevant in previous studies by forecasting firms earnings. Whereas most empirical research on forecasting earnings is focused on the US, this study tries to predict firm earnings in the German market. Due to systematic inter industry differences forecasting might be industry specific. Therefore, but also to limit the scale of this research, one specific industry within Germany is being studied; the industrial and electronic equipment industry. This industry is chosen for several reasons; its large presence in the German market (17% of all listed German firms), enough volatility to be interesting for modelling and the availability of historical quarterly earnings figures.

Future earnings are an input in firm valuation and the potential improvement in the predictability of earnings could influence valuations. The predictability of earnings could therefore questions the efficient market hypothesis as well (Seng and Hancock, 2012). The efficient market hypothesis in its weakest form states that (stock) prices reflects all past public available information (Fama, 1978). If earnings predictions can be improved than they could be used to determine the firms value and so predict future returns. This would reject the efficiency of markets. These questions however are not part of this study. For now the research is limited to the potential improvement of quarterly earnings forecast as they are given by analyst. What these improved forecast would imply for valuations and/or stock returns is not incorporated.

2 _{Bradshaw et al. (2012) refer to work of several authors to support this claim. (p. 945)}

3 _{For other European countries (e.g. UK and The Netherlands) historical quarterly earnings were not available over}

Section 2 focus on a literature review which elaborates previous research on earnings prediction and the conflict analyst have in this. Section 3 describes the data and the sample, chapter 4 is about the methodology that is being used in the model. Section 5 presents the results and section 6 concludes.

2. LITERATURE

This section discusses: (2.1) the bias analyst have in estimating earnings, (2.2) an overview of models that have been proposed to outperform analyst and (2.3) variables that have been used in previous studies.

2.1

A

Analyst predict earnings and future returns and use these in their recommendations. Earnings estimates are an input in their own valuation but are also used by others. The problem is that analyst have conflicting interest that lead to biased or inaccurate forecast. There are several ways in which analyst can have conflicting interest. A well-known conflict of interest is the earnings-guidance game (Richardson, Teoh and Wysocki, 2001). Analyst who write recommendation and valuate firms are in need of private information that is not available to other market participants. Managers of the firms, that are being covered by a research analyst, have this information and therefore the analyst keeps up a good relationship with the management of the covered firm (Lim, 2001). Managers have certain interests as well (personally as well as on their firms behalf) which lead to an earnings-guidance game. Richardson et al. (2001) describe in the ‘walk-down’ to beatable analyst targets, how managers and analyst utilize this mutual dependency. After an earnings announcement, managers have the incentive to sell stocks. This can be on the firms behalf, by an equity issuance, or by selling their personal shares. Therefore managers have the incentive to motivate analyst to overestimate future earnings. However after the first earnings announcement the game starts and managers walk down analyst forecast to a ‘beatable’ level. Managers pressure analyst to adjust their estimates downwards so that the management of covered firms can present that they have beaten the latest analyst estimates. “Similar to the results for the annual window, we document a pattern of increasing pessimism as the quarterly earnings announcement approaches. The forecast errors are either close to zero or optimistic initially, and then become pessimistic in the two weeks preceding a quarterly earnings announcement” (Richardson et al., 2001, p.21). The earnings-guidance game suggests that analyst have the incentive to overestimate earnings on longer horizons but under estimate earnings on short horizons.

investment banking department that would like to offer M&A services or facilitate an equity issuance. Dechow, Hutton and Sloan (2000) state that analyst who work in an institution that operates as well as sell-side advisers in equity issues, tend to systematically overestimate long-term growth rates. Another conflict of interest is that analyst often work for a brokerage department. Brokers earn something when a trading takes place. Therefore analyst are incentivized to break the current market valuation by over- or underestimating the earnings forecast. In this way they can say that the current market price is under- or overvalued, and convince their client to sell or buy stocks. Besides all conflicting interest the analyst also has a personal reputation to keep up. A good reputation might also increase the ability for a analyst to generate trade for the brokerage firm (Jackson, 2005). This incentives analyst to produce accurate and correct estimates. Furthermore a good reputation is also important for the personal career of an analyst. (Leone & Wu, 2007)

2.2

S

,

VS

Due to the possible conflict of interest of analyst, academics have always been searching for other ways to predict earnings. Many studies have, from the seventies on, compared analyst forecast with the outcome of univariate time series models in order to outperform the analyst. Brown, Griffin and Zmijewski (1986) found that univariate time-series models were not able to outperform analyst quarterly earnings estimates because of the better utilization of information by analyst and their timing advantage. This conclusion hold for a long time4 _{until more recent research of Bradshaw et}

al. (2012) stated that this previous research on analyst superiority was incomplete, misleading, or

both. Bradshaw found that on longer forecast horizons (2 and 3 years ahead) random walk time series models could outperform the forecast of analyst. For shorter horizons however, time-series models are not able to outperform analyst as the advantages of analyst are the greatest on shorter horizons.

Studies comparing analyst to time series distinguish two sources of superiority. The first is the timing advantages of analyst, which enables them to include information released after the moment the model makes a forecast. The second is the information advantage of analyst, which is their access to a broader information set (Fried and Givoly,1982). This is non-public company information that they gains from their good relationship with the management of covered firms (Lim, 2001). This information is very valuable to the analyst and in forecasting earnings and could start the earnings-guidance game between managers and analyst. However for Lim this doesn’t mean that analyst do not give the most accurate forecast. “Rational analysts who aim to produce accurate forecasts may optimally report optimistically biased forecasts. By trading off bias to

improve management access and forecast” (Lim, 2001, p.383). Only rational (human) agents could make a trade off like that and gain private information. Graves, Davis and Mendenhall (1990) discuss a possible third source of analyst superiority, which also related to rationality of humans. They claim that the superiority is also caused by the use of judgemental heuristics from analyst. “The possibility that humans can use past earnings data to predict future earnings more accurately than can mechanical time-series models” (p.501)

Not all academic researchers have accepted these biases and a lot have kept on searching for better alternatives. Recent research focuses on models that included larger sets of information that could potentially predict firms earnings. Earnings are effected in a lot of ways by internal and external forces. The exact working of these forces might not be known or at least changes over time. These structural instabilities make one single model not sufficient for forecasting EPS. “.. it is not possible to anticipate ex-ante the precise variables that foretells future earnings” (Bansal, Strauss and Nasseh, 2015, p.3). Predicting could therefore be improved by combining the results from different predictors. There is a large set of data available that can potential predict changes in EPS. The challenge is to select ex-ante (1) which (weighting) and (2) how (coefficient) these predictors are influencing EPS. Besides linear relations Zhang, Cao and Schniederjans (2004) present an example of the usefulness of neural networks in predicting earnings. Neural networks could also capture the possible third source of superiority, the judgemental heuristics as discussed by Graves et al. (1990). However the working of neural networks is a black box (Brooks, 2014) and the econometric methodology goes beyond the scope of this research.

2.3

Earnings could potential be effected in a lot of ways. A combination forecast allows for a larger set of potential explanatory variables. This section is an overview of variables that were found to be relevant in previous studies by predicting EPS. All these variables could be used in the model. This research does not focus on how this relation work, but it deals with the question if a variable has potential predictive ability.

An important aspect in the predicting of earnings is a mean reverting process. “There is also predictable variation in earnings. Much of it traces to the mean reversion of profitability. An important practical implication of this result is that forecasts of earnings (e.g., by security analysts) should exploit the mean reversion in profitability” (Fama & French, 2000, p.174). Mean reversion in finance is a process in which firms profitability revert back to a certain mean. This due to competitive environment in which firms operate (Canarella, Miller and Nourayi, 2013). If earnings grow, than profitability grows and so excess returns are created. These excess returns attracted competitors and this increases competition which thereby erodes the excess returns (and earnings) again. Fama et al. (2000) also finds that mean reversion for earnings is faster when earnings are further from its mean. Studies that predict earnings incorporate the potential effect that mean reversion has. Example are Zhang et al. (2004), Ball, Ghysels & Zhou (2015) and Bansal et al. (2015) who include a autoregressive parameter in their linear model.

Seasonality is specifically effecting quarterly reporting’s and quarterly forecast. To account for the seasonal effect Ball et al. (2015) predict seasonally-adjusted earnings. Zhang et al. (2004) include the change in EPS lagged by 4 quarters in their linear model to incorporate the effect of seasonality and Bansal et al. (2015) included EPS lagged by 4 and 8 quarters.

and labour force. Abarbanell et al. (1997) also studied the relation between these signals and analyst earnings reversions and conclude that analyst are not fully including the value relevant information of these fundamental signals in their estimates. Seng et al. (2012), Ball et al. (2015), Bansal et al. (2015) are examples of recent studies that use fundamental variables in predicting earnings. They all refer to the work of Lev et al. (1993) and Abarbanell et al. (1993) and included some of these variables in their models. The measurement of these variables by Lev et al. (1993) was in a way that they would signal negative returns. However Abarbanell et al. (1997) have already state that this relationship could also be positive.5 _{This finding furthermore indicates the} instable relationship that these variables could have on earnings. Next to the variables form Lev et

al. (1993), Bansal et al. (2015) found that book value of equity per share also has substantial

predictive ability in forecasting earnings.

There is a large range of macroeconomic forces that could potentially influence firm earnings. What is specific for the industry in this study is that it is ahead of economic cycles. Whenever the economy peaks and producers are less certain about the future they will stop ordering new equipment. Therefore early and leading indicators of economic cycles needed to be included in the model so these cycles can be predicted. Based upon previous studies from Welch (1984), Abarbanell et al. (1997), Hess & Kreutzmann (2010), Ball et al. (2015) and Bansal et al. (2015), several industry wide variables have been chosen as potential predictors: general indicators about the German economy and indicators about inflation, interest, commodity prices and currency effects.

Stock price reflect future earnings. Because the current value of a company is discount of its future cash flows and earnings are future cash flows. An increase in stock price could indicate that investors expect higher future earnings. Therefore Bansal et al. (2015) included stock return and price-earnings ratio as variable to predict future earnings, Ball et al. (2015) included excess stock returns and stock return volatility as explanatory variable.

3. DATA

This section; (3.1) presents the sample, (3.2) gives an overview of how and where the data is collected and (3.3) describes the all data till the first quarterly estimate.

3.1

S

:

In order to predict quarterly earnings by using predictive regression historical quarterly earnings needed to be available. The aim of this research is to predict quarterly EPS in a non-US market. Unfortunately for many countries outside the US it was not possible to collect historical quarterly EPS figures on a longer horizon. Within Germany most listed companies started to report on a quarterly basis around 2003. Therefore the data covers a period from 2003 Q3 till 2015 Q2. Before 2003 there are a very few firms that report on a quarterly basis.

The sample is constructed by including all listed German firms that generated the most revenue in industry with two digit SIC code 35 or 366_{. The sample is narrowed based upon the following} criteria; firm has to report on a quarterly basis for at least 7 consecutive years from 2004 till 2014, at least 8 earnings estimates from analyst needed to be available in the out-of-sample period (2011 Q4 – 2015 Q2) and at least 20 quarterly reportings needed to be available. These criteria shrink the sample size to 17 firms. Table 7 presents all firms incorporated in the sample.

3.2

D

Quarterly EPS figures are collected from Datastream using code WSC05221, WSC05222, WSC05223, WSC05224. These EPS figure exclude extraordinary items after tax. The data is corrected for companies that reported on another frequency then calendar years. Missing data points are corrected manually using data from Thomson One or using annual EPS and deduct the other three quarters. Table 8 presents the measurement of EPS as being used in the model. EPS is measured as absolute increase instead of a growth rate. This because EPS often is negative, exactly zero or close to zero. Calculating a constant growth rate is not possible when EPS is negative or zero. Calculating quarterly growth is not possible when EPS is exactly zero and the growth rate will explode when it is close to zero.

Table 9 and 10 in the appendix give an overview of all variables that are included as predictive variables in the model. Section 2 gives an overview of variables used in the previous studies to predict EPS. This study divides the predictive variables in two groups. The predictive variable that differ across firms and are therefore ‘firm specific’ and the variables that are the same for all firms in the sample and are therefore ‘industry wide’.

There are 11 firm specific predictive variables included. The change of quarterly EPS lagged by one quarter to account for the potential effect of mean reversion. The change in quarterly EPS

6 _{SIC code 35 is ‘Industrial and Commercial Machinery and Computer equipment’ and code 36 is ‘Electronic and other}

lagged by 4 quarters to include potential seasonality. The trailing firm specific PE ratio is included to capture investor’s expectation of future earnings. Trailing PE is calculated as the market capitalization divided by the sum of the earnings from the last 4 quarters. The other firm specific predictive variables consist of fundamental accounting-related variables and are collected using quarterly reporting data from Thomson One. Not all 9 variables from the study of Abarbanell and Bushee could be collected, only 7 variables are included. These are also the more important variables of which other studies have shown the predictive ability. Book value of equity per share is also included. Due to restatements detailed quarterly accounting items are sometimes missing. Not all accounting items are available (or updated) in the database after a restatement. These missing data points were corrected manually by interpolating the original accounting items linearly between the last known and next known value. ‘Sales & administrative expense’ is recognized as separate item after 2007 and therefore not available during the full sample period. Most firm specific variables are measured as the change in the growth rate, table 9 in the appendix presents exact measurement of all included variables.

Industry wide variables are collected from several sources and imported using Datastream. General German economy is measured by 5 different predicting variables; growth in industrial production, growth in trailing price earnings ratio of DAX30 (to capture investor’s expectation), growth in unemployment, growth in vacancies and change in business climate in Germany. The business climate is measured by a survey related to current business situation and business expectations for firms within industrial production and trade sector. Inflation is measured as the producers price index (PPI). For interest three aspects are included the; default spread, yield spread and short term interest. Oil and industrial metals are included as potentially relevant commodities. Currency effects are measured by the traded weighted Euro index. Inflation is included to capture price increase, therefore other industry wide predictors are on constant prices and/or volume. Table 10 presents all industry wide predicting variables their measurement and source.

11 present an overview of the total number of estimates and the average number of estimates per company that are used in the consensus forecast during the out-of-sample period.

3.3

D

For this research the sample period is divided into an in-sample and out-of-sample period. The descriptive statistics describe the data during the in-sample period. The out-of-sample period is to compare the performance of the forecast from the model of this study to the forecast of analyst. Table 12 presents the summary statistics for the dependent variable (ΔEPS) during the in-sample period. ∆𝐸𝐸𝐸𝐸𝐸𝐸 is measured as absolute increase instead of a growth ratio. Because ΔEPS is not scaled the standard deviation does not give a good measurement to comparing the volatility of the earnings between companies. To give a better indication of volatility across companies in the sample also the mean absolute EPS and the standard deviation of absolute EPS is published in the table. Not many firms have changes in EPS that are statistically correlated. Changes in EPS do not often move in the same direction suggesting that industry wide predictors might differently influence EPS across companies.

Table 13 and 14 present the summary statistics for the predictors included in this study during the in-sample period. For the firm specific predictors this is the total of all firms. Remarkable is that the ‘effective tax rate’ (ETR) is relatively volatile with a standard deviation of 404%. This has to do with reporting standards. ETR is calculated as reported taxes divided by reported earnings before tax. Only the reported taxes are often above the reported earnings which makes the effective tax higher than 100%. The number of observations differs for the firm specific predictors and is especially low for ‘Sales & Administrative expenses’ (S&A) and ‘Price-earnings ratio’ (PE). Some firm specific items only started to be reported separately in quarterly results after some time and PE cannot be calculated when earnings are negative.

The correlation among different predictors included in this model is relatively low with some peaks of having a correlation around 0.8. Highly correlated predictors could mean that those predictors are measuring the same process on-going in the economy. This could lead to collinearity in a multiple regression forecast. An advantage of the combination forecast with bivariate regressions over a multiple regression forecast is that we do not have to deal with potential over fitting in the model caused by collinearity of explanatory variables.

4. METHODOLOGY

Welch et al. (2008) demonstrate that it has an exceptionally poor out-of-sample performance in prediction the equity premium. EPS has the same structural instabilities and the complexity of predictors as equity premium, which makes that one single model will not be sufficient (Bansal et

al., 2015). “Our evidence suggests that the usefulness of forecast combining methods ultimately

stems from the highly uncertain, complex, and constantly evolving data-generating process underlying expected equity returns, which are related to a similar process in the real economy. This type of process will be difficult to approximate with a single, relatively parsimonious predictive regression model, while forecast combination reduces the uncertainty/instability risk associated with reliance on a single model” (Rapach et al., 2010, p.858).

Analyst are able to constantly adjust the way that predictors influence EPS. To beat analyst in their forecast the model should have this flexibility as well. This is accomplished by using a performance based weighting scheme that gives more weight to the forecast of predictors that accurately forecast. It is not possible to ex-ante determine which predictors would be the best. Therefore the weight of a single predictor is based upon the historical performance of this predictor. This weighted combination forecast is than compared against the forecast of analyst.

4.1

P

The linear relation of the change in EPS for firm (i) and predictors (j) in quarter (q) is;

∆𝐸𝐸𝐸𝐸𝐸𝐸_{𝑞𝑞,𝑖𝑖𝑖𝑖} = 𝛼𝛼_{𝑞𝑞,𝑖𝑖𝑖𝑖}+ 𝛽𝛽_{𝑞𝑞,𝑖𝑖𝑖𝑖}𝐸𝐸𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃_{𝑞𝑞−1,𝑖𝑖} + 𝜇𝜇_{𝑞𝑞,𝑖𝑖} (1) Nearly all predictors are in growth rates and therefore the depend variable in the regression should preferably be in the same measurement. However EPS is often zero, close to zero or negative. This makes the growth rate impossible to calculated and/or let growth rates explode. Therefore this models uses the real absolute change in EPS as dependent variable.

∆𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞+1,𝑖𝑖𝑖𝑖 = 𝛼𝛼� + 𝛽𝛽𝑞𝑞,𝚤𝚤𝚤𝚤 � 𝐸𝐸𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑞𝑞,𝚤𝚤𝚤𝚤 𝑞𝑞,𝑖𝑖 (2) Estimating 𝛼𝛼� and 𝛽𝛽̂ using OLS for every company (17), every predictor (23) and all quarters (15). In this way the change in EPS (ΔEPS) can be predicted. The information that is used, the predictors, are all lagged 1 quarter so that all information that is being used is also available to the analyst at the time of his estimate. This prevents a forward looking bias in the model.

4.2

R

W

makes the OLS estimates more accurate. However the combination forecast is used because of the complexity of forces that influence EPS and the uncertain and changing parameters which have to be included. The parameters of the model change over time. Including more observations means including less recent observations. Whereas the relationship between the variables might already be changed.

The rolling window includes only the most recent quarters. Therefore a predictive regression uses a rolling window of 8 years and incorporation 32 observations is set as base model. A regression with a recursive windows is also tested as a robustness check. The first estimated EPS is for 2011 Q4. It uses lagged predictors (as independent variable) from 2003 Q3 till 2011 Q2 and historical EPS (as dependent variable) from 2003 Q4 till 20011 Q3. The rolling window is set to 8 year to have a sufficient number of observations for estimating OLS. This creates an out-of-sample period which is still large enough to have a sufficient number of predictions to compare the outcome of analyst to the outcome of the model. Expanding the regression window would not only include potentially less relevant historical estimates it would also expand the in-sample period. This would shrink the sample period and limit the number of forecast to compare. Expanding the out-of-sample period would decrease the regression window and would make the OLS estimates less accurate. As a robustness test a regression using a rolling window of 9.5 years and 6.5 years is also tested. Table 1 gives an overview of the different regression windows and the number of out-of-sample predictions. Note that the RW9.5Y does not have the same out-out-of-sample period as the other regression windows have.

Table 1 Regression windows

Frist regression window First estimate Out-of-sample

predictions Rolling window 8 year

(RW8Y)

2003Q4 – 2011Q3

(32 observations) 2011Q4

2011Q4 – 2015Q2 (15 quarters) Rolling window 9.5 year

(RW9.5Y)

2003Q4 – 2013Q1

(38 observations) 2013Q2

2013Q2 – 2015Q2 (9 quarters) Rolling window 6.5 year

(RW6.5Y) 2005Q2 – 2014Q3 (26 observations) 2011Q4 2011Q4 – 2015Q2 (15 quarters) Recursive window (RCW) 2003Q4 – 2011Q3 (≥32 observations)7 2011Q4 2011Q4 – 2015Q2 (15 quarters)

4.3

C

The weighting is based upon the historical performance of a single predictor. Rapach et al. (2010) discusses two classes of weightings in combinations forecast (p. 827). One class is using a simple average or mean to combine the individual forecast. The second class is based on historical forecasting performance. This often uses a holdout out-of-sample period in which the weights are determined. The current out-of-sample period is only 15 quarters long, reducing this by introducing an hold-out period could improve the weighting. However it would furthermore reduce the number of quarters in the out-of-sample forecast evaluation. Therefore this model does not use an holdout period but performance depends on the performance in the last quarters, and first estimate in the out-of-sample period is based upon an equally weighted (mean) combination forecast. This allows the weights to change over time, well at the same time there are still 15 quarters to compare performance of the combination forecast to analyst. The weighting may accurately be simulating the real world situation where sensitivities and predictive power of individual predictors change over time (Bansal et al. , 2015, p.3). Forecasting performance of a single variable is measured by the Squared Forecast Error (SFE), which is calculated by:

𝐸𝐸𝑆𝑆𝐸𝐸_{𝑞𝑞,𝑖𝑖𝑖𝑖} = �𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞,𝑖𝑖𝑖𝑖𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹− 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞,𝑖𝑖𝑖𝑖𝐴𝐴𝐴𝐴𝐹𝐹𝐴𝐴𝐹𝐹𝐴𝐴� 2

(3) The dependent variable in the current model is the real change is EPS (ΔEPS) and therefore SFE cannot be compared across companies or quarters. For the weighting the scaling is captured by the denominator in the weight calculation. Weight for predictor (j) at quarter (q) for company (i) is calculated by; 𝑤𝑤_{𝑞𝑞,𝑖𝑖𝑖𝑖} = 1 𝐸𝐸𝑆𝑆𝐸𝐸_{(𝑞𝑞−1),𝑖𝑖𝑖𝑖} � ∑ _{�1 𝐸𝐸𝑆𝑆𝐸𝐸} (𝑞𝑞−1),𝑖𝑖𝑖𝑖 � � 𝑛𝑛 𝑖𝑖=1 (4) and the expected EPS from the performance weighted (PW) combination forecast is8_:

𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞,𝑖𝑖 = ��𝑤𝑤𝑞𝑞,𝑖𝑖𝑖𝑖∙ 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞,𝑖𝑖𝑖𝑖� 𝑛𝑛

𝑖𝑖=1

(5) The performance weighted (PW) combination forecast assumes that the performance in last quarter is a indicator for the performance in the next quarter. As a robustness check the outcome of the PW forecast is compared to the outcome were all predictors get the same weight in the combination. This is the equally weighted combination forecast (EW). Which falls into the first class of weighting scheme as recognized by Rapach et al. (2010).

8 _{Some observations are missing as discussed in section 3.3 the weight for predictors with less than 20 observations in}

4.4

F

The dependent variable (ΔEPS) is not scaled and therefore ordinary forecast errors can not be compared across companies. Others studies chose to scale the squared forecast error in order to compare. Zhang et al. (2004) does this by dividing the difference (model and actual) by actual EPS value. Bradshaw et al. (2012) by dividing the difference (model and benchmark) by stock price. In this research a ratio is calculated that can be compared across companies.

Depending on the availability of analyst forecast at maximum 15 different quarters can be compared. Outperformance in a specific quarter is achieved if the SFE of the model is lower than the SFE of analyst. Ball et al. (2015) evaluated earnings prediction by the median absolute scaled error ratio (MASER)9_{. For this research the MASER is adjusted to the mean squared forecast error} ratio (MSFER). The mean is used instead of the median because extreme incorrect predictions matter and that needs to be included in the evaluation.

𝑀𝑀𝐸𝐸𝑆𝑆𝐸𝐸𝑀𝑀 = 𝑀𝑀𝑃𝑃𝑀𝑀𝑀𝑀 �𝐸𝐸𝑆𝑆𝐸𝐸𝑀𝑀𝐹𝐹𝑀𝑀𝐹𝐹𝐴𝐴�

𝑀𝑀𝑃𝑃𝑀𝑀𝑀𝑀 (𝐸𝐸𝑆𝑆𝐸𝐸𝐴𝐴𝑛𝑛𝐹𝐹𝐴𝐴𝐴𝐴𝐹𝐹𝐹𝐹₎ (6)

If the MSFER value is below (above) one then the model outperformed (underperformed) the analyst for that specific firm. If in a specific quarter for a specific firm no analyst estimate is available than this quarter is not incorporated in the evaluation and not included in the mean. The complete sample is evaluated by the overall MSFER. As not all firms have analyst estimates available for all quarters, weight of the MSFER of a single firm in the overall MSFER depends on the number of quarters which it has analyst estimates available.

5. RESULTS

This chapter presents the empirical findings. First section is an in-sample analysis of the different predictors. The in-sample analysis presents the coefficient and statistical significance of the different variables that are included. The next section (5.2) is an out-of-sample prediction in which the performance of the model is compared to the estimates of analyst. Also the out-of-sample prediction performance of individual predictors is evaluated.

5.1

I

-

Table 15 and 16 presents coefficients and the R2 _{for all firms using a bivariate regression in which} the predictors lagged one quarter on the change in EPS. The in-sample analysis covers the period

9 _{𝑀𝑀𝑀𝑀𝐸𝐸𝐸𝐸𝑀𝑀 ≡} 𝑀𝑀𝐹𝐹𝑀𝑀𝑖𝑖𝐹𝐹𝑛𝑛 ��𝐹𝐹𝐹𝐹𝑞𝑞𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀�∆𝐹𝐹𝑞𝑞��

of the first regression window (2003Q3 till 2011Q3). Certain regressions could not be calculated during the first in-sample period because the number of observations was not enough to run a regression.10 _{The in-sample analysis also includes a statistical significance test for the coefficient} (𝐻𝐻0: 𝛽𝛽 = 0). It test whether a predictor statistically significantly predicts future changes in earnings. To account for heteroscedasticity and autocorrelation in the error term this test is based on robust Newey-West standard errors.11

In-sample R2 _{are low, but predictive regressions with small R}2 _{can already be economically} meaningful (Campbell and Thompson, 2008). In-sample fit is not a good measurement for the out-of-sample prediction. “We considered other methods, where combining weights are selected more elaborately using in-sample model fit, they performed poorly compared to the simpler schemes. This agrees with the forecasting literature” (Rapach et al. , 2010, p.827). The in-sample analysis is included however to present the relation and the statistical significance between predictors and EPS. During the out-of-sample prediction only forecasting results are evaluated and the coefficient is not discussed.

All firms have a negative coefficient on ‘EPS-1’, the change in EPS is negatively related to the change of EPS in last quarter. This implies that EPS is mean reverting. ‘EPS-1’ also has on average the highest R2 _{of all predictors included in this study. ‘EPS-4’ should capture the} seasonality effect. This however seems not to have large impact for the industry studied in this research. Coefficient of ‘EPS-4’ should be positive when seasonality would be an issue, but even statistically significant negative coefficient are found. Remarkable is the coefficient on ‘PE’, all statistically significant coefficients are negative. Economical intuition would say that an increase in the trailing PE ratio indicates an increase in future earnings. Investors are willing to pay more for every Euro a firm currently earns if they expected future earnings to increase. However ‘PE’ might not be a good predictor for short term earnings. Because the trailing PE ratio also captured the same effect that is measured by ‘EPS-1’. If the earnings in the last quarter are high the PE ratio decreases but due to mean reversion the earnings in the next quarter will decrease.

Lev et al. (1993) have formulated their measurement of fundamental signals in a way that they would signal negative earnings. This would mean that all coefficient would be negative, but the results also find statistically significant positive coefficient for these fundamental signals. For example ‘inventory’ (INV) and ‘effective tax rate’ (ETR) both have 3 statically significant positive coefficients. The ‘effective tax rate’ (ETR) is statistically the best fundamental signal that is

10 _{In some cases observations in the in-sample period are missing but the regression can still be estimated. The lower}

number of observations is taken into account by the standard errors. Quarterly reporting of S&A started in 2007 and PFE were founded after 2006. Therefore not enough data is available on these variables and this firms.

11 _{“the Newey-West procedure in fact produces ‘HAC’ (Heteroscedasticity and Autocorrelation Consistent) standard}

included in this model and is significant for 7 firms. Short term interest (EB3M), the oil price (OIL) and industrial production (INDP) are statistically good industry wide predictors for future earnings. ‘CAPX’, ‘PEDX’ and ‘VACA’ are not significant for any firm and thereby statistically the worst predictors.

The results differ also across firms. ‘AIX’ and ‘WAC’ only have one significant coefficient across all predictors. All macroeconomic variables measure the Germany economy, ‘ADV’ and ‘SIE’ both have most operations outside of Germany12 _{. Not surprisingly they both have no significant relation} with any of the macroeconomic variables.

5.2

O

-

-

Table 2 presents the out-of-sample predictions results. The ‘% quarters’ refers to the percentage of quarters that the model outperformance the analyst forecast. The model performs poorly with generating an overall MSFER of 1.7. However in 46% of the quarters the model (PW RW8Y) outperforms the analyst forecast. This is about half of the quarters in the out-of-sample period. But due to some large forecast error the model heavily underperformed compared to analyst and generates a MSFER far above 1. KON and PFE are good examples of what happens, both companies have a MSFER far above 1 (1.9 and 1.7 respectively) but for both firm the model was more accurate in most of the quarters (80% and 71% respectively). For both firms one extreme incorrect forecast lead to a high MSFER.

Table 2 Results

Overall ADV AIX DEU DUE GEA HEI INF KON KRO KUK NOR PFE RHE SGL SIE WAC WIN MFSER 1.70 0.8 0.8 1.1 1.5 1.8 1.1 4.2 1.9 2.4 1.8 2.2 1.6 0.7 1.7 2.1 0.4 2.2

% quarters 46.2 50 67 50 31 33 50 33 80 33 47 33 71 47 54 60 67 20

The forecast from the model is based on ∆𝐸𝐸𝐸𝐸𝐸𝐸 and 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞−1. In some quarters EPS is extremely high or low and will return to a normal level in the next quarter. This is the mean reversion of earnings. The current model does not ex-ante know when an outcome is extreme and it does not give enough weight to the predictor that has to capture the mean reversion (EPS-1) in the next forecast. The forecast for EPS from the current model in a quarter after an extreme outcome is somewhere close to the value of that extreme outcome. The model only foresees minor changes in EPS, where as it should give a high to the mean reversion. Mean reversion is faster when earnings are further from its mean. (Fama et al., 2000) Analyst incorporate the large effect of mean reversion after extreme outcomes. The current combination forecast model does not and estimate

an outcome close to the extreme value (∆𝐸𝐸𝐸𝐸𝐸𝐸 + 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞−1). This will result in a large SFE for the model, much larger than the SFE for analyst and the MSFER rapidly increases.

5.2.1

A

To overcome this problem the combination forecast has to be adjusted in a way that it will account for these extreme outcomes on EPS. A first solution that has been tested to overcome this problem is to include more predictive regression that measured the mean reversion13_{. This did however} only improve the overall MSFER by 0.01. Another solution is to change the dependent variable in all regressions. The dependent variable in all regressions is adjusted to the difference of the last known value of EPS (𝐸𝐸𝐸𝐸𝐸𝐸_𝑞𝑞−1) and a Simple Moving Average (SMA) of EPS. Were SMA is calculated as;

𝐸𝐸𝑀𝑀𝑀𝑀(𝐸𝐸𝐸𝐸𝐸𝐸_𝑞𝑞) = 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞+ 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞−1+ ⋯ + 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞−𝑛𝑛

𝑀𝑀 (7)

With the dependent variable in the regression being;

∆𝐸𝐸𝐸𝐸𝐸𝐸_𝑞𝑞 = 𝐸𝐸𝐸𝐸𝐸𝐸_𝑞𝑞− 𝐸𝐸𝑀𝑀𝑀𝑀(𝐸𝐸𝐸𝐸𝐸𝐸_𝑞𝑞−1) (8)

The out-of-sample forecast is tested with a moving average of 1 year (n=4) and a moving average of 2 years (n=8). Both did improve the MSFER remarkably whereas the number of quarters that the model outperformed only slightly improved. The moving average with 1 year resulted in the best out-of-sample predicting results and these are presented in table 3.

Table 3 Results adjusted dependent variable

Overall ADV AIX DEU DUE GEA HEI INF KON KRO KUK NOR PFE RHE SGL SIE WAC WIN MFSER 1.18 1.0 1.0 1.0 0.7 1.0 0.7 3.1 0.6 1.4 1.3 2.6 0.9 0.4 0.9 1.1 0.7 1.7

% quarters 48.7 50 53 50 69 33 60 33 80 40 47 17 43 53 54 53 50 47

Figure 1 shows average real EPS and average forecast in every quarter. To compare EPS across firms in one single graph EPS is expressed in standard deviation14 _{from the mean}15 _{for each firm.} This implies that in the first quarter (2011Q4) the real EPS (green) of all firms in the sample is on average 0.1 standard deviation above the mean EPS. Also the prediction of analyst (blue), the forecast from the model with adjusted (red) and unadjusted dependent variable (purple) is included. In the averages only the overlapping16 _{quarters are used.}

13 _{The regression that were added are EPS lagged by 2 and 3 quarters.}

14 _{The figure expresses in standard deviation to overcome the scaling problem of EPS. Standard deviation is the}

standard deviation of real EPS during the whole out-of-sample period.

Figure 1 Forecast and real EPS over time

This graph shows the problem of the model with an unadjusted dependent variable. It has the tendency to forecast EPS somewhere close to the last know value of real EPS. Another finding is that analyst on average are always positively biased. For all quarters analyst are above real EPS and therefore too optimistic in their estimate. Figure 2 shows a histogram of the distribution of individual forecast errors17 _{from analyst and the model which are divided by the standard deviation.} Table 4 shows how these forecast errors divided by standard deviation are distributed.

Figure 2 Table 4 Distribution Analyst Model Mean 0.48 0.16 Skewness 0.45 0.31 Kurtosis 5.13 3.86 Jarque-Bera 44.89 9.47 P-value 0.000 0.009

forecast has a positive bias. The mean is calculated using only overlapping quarters for which an analyst estimate is available. The mean from the model reduces from 0.16 to 0.08 when all quarters are included. The positive bias of analyst is much larger than the positive bias of the model.

The number of analyst estimates included in the analyst consensus forecast should increase the accuracy of the consensus forecast. Figure 3 is a plot of the MSFER of every firm to the average number of analyst included in the consensus forecast for that firm. This indicates a positive relationship between the MSFER and the number of analyst estimates included in the consensus forecast. If there are more analyst estimates included in a forecast then this forecast is more accurate. Therefore the overall MSFER is calculated for half of the firms with the lowest analyst coverage and half of the firms with the highest analyst coverage. The MSFER for the lower half is 0.98 whereas the firms with more coverage have an overall MSFER of 1.35. The model is able to outperform analyst for firm with a lower analyst coverage.

Figure 3 Average number of analyst estimates in consensus forecast and MSFER per firm

5.2.2

The base model is a rolling regression of 8 years and as variation on the base model other regression window, as well as an equally weighted combination forecast, is tested. Table 5 presents the MSFER for al variations of the model. The regression using a window of 9.5 years has a shorter out-of-sample period as the first in-sample regression window is longer. To compare the results from the RW9.5Y with other regression windows the MSFER is separately calculated for this period.

Table 5 weighted average MSFER for model variations

The rolling window of 8 year performs the best compared to all other regression windows. Including more observations as is been done by the recursive window and the rolling window of 9.5 years, does not improve the results. Including less observations, but thereby only more recent observations doesn’t either improve the results. Deciding on the regression window is a consideration between (1) enough observations for reliable OLS estimates and (2) not to many so that only the most relevant recent observations are included. In this empirical example 8 years and 32 observations is the right choice.

5.2.3

W

The performance weighting is not successful as the equally weighted combination forecast performs comparable or even outperformers. Analysing the individual weights assigned to predictors clarifies why the weighting system fails. In 24% of the combinations a single predictor get more than half of the weight and in 7% of the combinations a single predictor get even more than 90% of the weight in the combination18_{. If so much weight is placed on one single variable,} the combination effect is cancelled out. The philosophy behind the combination method is that it is not possible to ex-ante determine what the sensitivities in the next quarter are. This does not imply that weighting is not possible and that the naïve method of equally weighting is the best. Certain forces could in general and over time effect the firms earnings more than others. Predictors that measure those forces should be assigned a higher weight. But performing well in one quarter does not imply that one predictor should get half of all weight or even more. In addition “it is typically desirable to have relatively stable combining weights over time” (Rapah et al., 2010, p.827). Therefore the performance weighting has to be adjusted in a way that the weights will be more equally distributed among the predictors.

A first possible adjustment to improve the weighting is to determine historical performance on more than one quarter. Other studies implement a holdout out-of-sample period after the first in-sample period. However it would further reduce the out-of-sample evaluation period. A solution is to measure performance of predictors at first by using the rolling window of 6.5 years. Using this regression window it is possible to forecast 1.5 year before the out-of-sample period of RW8Y starts. The performance of individual predictors are measured in the original way (equation 4) but

18 _{A total of 255 combinations (17x15) and 60 combinations a weight is above 0.5, in 18 combinations the weights is}

the weight depends on performance over multiple quarters. This indeed resulted in more stable weights but it increased the overall MSFER19_.

Another adjustment is to compress the weights using the natural logarithm20_{. This results in more} equally distributed weights among predictors and it reduces the overall MSFER from 1.18 to 1.11. Though it also assigns negative weights to certain predictors when the SFE is above 1. Using the last adjustment it is possible to create a weighting that outperformed equal weighting. However this outperformance, was only after several different weighting schemes have ex-ante been tested on the sample.

5.2.4

I/B/E/S

The analyst EPS estimates used in this research are download in November 2015. The same data21 _{is downloaded in the beginning of January 2016. During two months that past there are at} least a 38 additional analyst estimates added and 47 analyst estimates removed. Ljungqvist et al. (2009) found evidence that change in the I/B/E/S database are non-random. To see the effect on the overall MSFER it is recalculated using the newest (January 2016) available analyst estimates. The MSFER would increase from 1.18 to 1.55. Which indicated that especially incorrect analyst estimates are deleted from the I/B/E/S database.

5.2.5

The original weighting is a good way to visually present how the individual predictors perform relative to each other. If a predictor preforms well then it produces a low SFE and so its weight in the next quarter will be high. Figure 4 shows the weight over time given to industry wide and firm specific predictors.

19 _{Several different methods are tested. Using discount weights were recent quarters get more weight let to a MSFER of}

1.24, using the average weight of the last six quarters generates a MSFER of 1.22 and by using the average of two quarters to MSFER is 1.23.

20

Weights in this adjustment are calculated by: 𝑤𝑤𝑞𝑞,𝑖𝑖𝑖𝑖 = ln�1 𝑆𝑆𝐹𝐹𝐹𝐹(𝑞𝑞−1),𝑖𝑖𝑖𝑖

� � ∑ _{ln�1 𝑆𝑆𝐹𝐹𝐹𝐹} (𝑞𝑞−1),𝑖𝑖𝑖𝑖 � � 𝐵𝐵 𝑖𝑖=1

Figure 4 Weights of predictors over time

Ball et al. (2015) discovered that in his earnings prediction model more weight was applied to macroeconomic predictors during the financial crisis. The German economy was at the start of the out-of-sample period in a recession. With negative growth rate for economic indicators like production and GDP. Somewhere in the end of 2012 there was a turning point were growth started to become positive22_{. This change in the economic cycle seems to have small effect on the} performance of industry wide indicators. The weight of industry wide predictors which consist of macroeconomic variables is 8% higher in the first 5 quarters then in the last 10 quarters. However this is also effected by two peaks in performance of firm specific predictors in 2013 Q3 and 2014 Q1 which both are caused by extreme over performance of outliers23_.

Figure 5 Industry wide predictors

22 _{German industrial production started to grow after 2012Q4 and German GDP started to grow after 2013Q1.}

23 _{As described in section 5.2.2 certain predictors can get weights over 0.9 this happened in Q3 2013 and Q1 2014 for}

‘BVEps’, ‘S&A’ and ‘GM’, this effect can also been seen in figure 6. 0% 20% 40% 60% 80% 100% Q4 2011 Q1 2012 Q2 2012 Q3 2012 Q4 2012 Q1 2013 Q2 2013 Q3 2013 Q4 2013 Q1 2014 Q2 2014 Q3 2014 Q4 2014 Q1 2015 Q2 2015 We ig h t

Industry wide Firm specific

0% 10% 20% 30% 40% 50% 60% 70% Q4 2011 Q1 2012 Q2 2012 Q3 2012 Q4 2012 Q1 2013 Q2 2013 Q3 2013 Q4 2013 Q1 2014 Q2 2014 Q3 2014 Q4 2014 Q1 2015 Q2 2015 We ig h t

Figure 6 Firm specific predictors

Table 6 Average weight on individual predictors assigned during the out-of-sample period

DESP VACA TWEU PERA SURV YISP PPI UNEM IMET OIL INDP EB3M

Average 5.2% 5.0% 4.9% 4.3% 4.2% 4.2% 4.0% 4.0% 4.0% 4.0% 3.7% 3.6%

Min. 2.0% 2.2% 2.9% 2.2% 2.1% 2.2% 2.2% 2.6% 2.5% 2.5% 2.4% 2.3%

Max. 10.6% 12.1% 9.1% 8.5% 10.8% 12.7% 15.3% 8.5% 9.7% 8.7% 5.9% 7.6%

S&A LF BVEps ETR EPS-4 PE GM AR INV EPS-1 CAPX

Average 4.9% 4.7% 4.7% 4.7% 4.6% 4.6% 4.4% 4.3% 4.2% 4.0% 3.9%

Min. 1.4% 2.1% 2.5% 1.7% 2.4% 2.1% 1.8% 1.6% 1.9% 2.0% 2.2%

Max. 16.3% 8.8% 10.6% 9.0% 9.4% 11.3% 11.0% 7.5% 11.0% 10.8% 8.1%

Figure 5 and 6 show the average performance of individual predictors over time. This is the average weight that is assigned in one quarter to all firms in the sample. Table 6 presents the minimum, maximum and average weight over all quarters.

Overall predictors perform relatively equivalent, the difference between the worst ‘EB3M’ and the best predictors ‘DESP’ is only 50%. To test the additional value of the combination forecast the MSFER is calculated using only one predictive regression with ‘DESP’ as independent variable. It does improve the MSFER for some individual firms but the overall MSFER is increased to 1.33. Even when ex-post the best predictor is known, the combination forecast still outperforms. When comparing the out-of-sample predictions with the in-sample results the finding of Rapach et al. (2010) that; is-sample model fit poorly indicates out-of-sample prediction, is confirmed. The regression using ‘EPS-1’ resulted in the highest R-squared but it is one of the worst predictors included.

Comparing the performance of individual predictors to the result of other studies we cannot confirm their findings. The fundamental signals originated from the work of Lev and Thiagarajan and ‘INV’, ‘AR’ and ‘CAPX’ are the three most important. Nevertheless these three have the poorest performance of all included fundamental variables. Bansal et al. (2015) found that ‘BVEps’ and

0% 10% 20% 30% 40% 50% 60% 70% Q4 2011 Q1 2012 Q2 2012 Q3 2012 Q4 2012 Q1 2013 Q2 2013 Q3 2013 Q4 2013 Q1 2014 Q2 2014 Q3 2014 Q4 2014 Q1 2015 Q2 2015 We ig h t

inflation (here measured as ‘PPI’) are the best predictors but they only perform on average in this study.

6.

C

ONCLUSION

The current model is not sufficient to replace analyst estimates in the prediction of EPS. Although a positive bias of analyst is demonstrated, the current model is not able to outperform analyst in forecasting EPS. The current model cannot outperform analyst estimates for all firms. The performance of the current model is comparable to analyst and might be useful for firms on which no analyst estimate is available. It could also be an important addition for firms with a lower analyst coverage, as for these firms the model does outperform analyst. The inputs used are all commonly and publicly available and the same set inputs are used for all firms. Analyst can incorporate private information and add specific inputs for individual firms. For example Adva AG and Siemens have most operations outside of Germany and all macroeconomic variables included in this study only measure the Germany economy. Therefore there is still room for improving the combination forecast with predictive regression. That besides these limitations and potential improvement the current model already outperforms firms with low coverage shows that analyst do not optimally use all information for the most accurate forecast. The positive bias from analyst is in line with the findings of the literature. Richardson et al. (2001) found that the forecast error for quarterly earnings for analyst becomes too pessimistic two week preceding a quarterly earnings announcement. The quarterly earnings estimates used in this research are from one quarter prior to the earnings announcement.

Two important findings for the combination forecast with bivariate predictive regressions are: (1) it seems not possible to ex-ante determine which predictor will have more influence. Nearly all version of weighting have failed to outperform the equally weighted forecast. (2) The regression window should be a consideration between only using recent observation and including enough observations for reliable OLS estimates. During this research there are adjustments made to the original model to improve out-of-sample results. These adjustments are presented during the results section. In a pure out-of-sample test a model would not be adjusted depending on how well the model fits the out-of-sample data.

There are important influence to his research that have not been studied. One is the industry classification (Krishnan & Press, 2003). The current industry being studied is composed of firms within two double digit SIC industries. It might be however the SIC classification does not make sense or that merging the two is inaccurate. Also the recognition of earnings, change in accounting standard and the restatement of quarterly figures might have influenced this research. An example is that the distribution of earnings seems non-random. Relatively often the quarterly earnings are exactly zero. Logical explanation for this could be that managers do not want to have negative earnings in their quarterly results. They therefore play around with the recognition of earnings in quarterly figures to prevent this from happening. Analyst could incorporate this behavioural influence in their estimates whereas the current model does not.

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A

PPENDIX

Table 7 Firms in the sample

Abbreviation Company SIC code Main product segment ADV Adva Ag 36 Telecom equipment AIX Aixtron Se 35 Semiconductors

DEU Deutz Ag 35 Commercial vehicles and trucks DUE Duerr Ag 35 Industrial machinery

GEA Gea Group Ag 35 Industrial machinery HEI Heidelberger Druck 35 Industrial machinery INF Infineon Technologie 36 Semiconductors KON Kontron Ag 35 Electrical equipment KRO Krones Ag 35 Industrial machinery KUK Kuka Ag 35 Industrial machinery

NOR Nordex Se 35 Renewable energy Equipment PFE Pfeiffer Vacuum Tech 35 Industrial machinery

RHE Rhein Ag 35 Auto parts

SGL Sgl Carbon Se 36 Industrial machinery SIE Siemens Ag 36 Diverse industrials

WAC Wacker Neuson Se 35 Commercial vehicles and trucks WIN Wincor Nixdorf Ag 35 Computer services

Table 8 Dependent variable

Table 9 Independent - Firm specific predictors

Abbreviation Variable Measurement Economic intuition (LT)24 AR Receivables

ln � 𝑀𝑀𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑅𝑅𝑀𝑀𝑏𝑏𝑏𝑏𝑃𝑃𝐹𝐹𝑞𝑞 𝑀𝑀𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑅𝑅𝑀𝑀𝑏𝑏𝑏𝑏𝑃𝑃𝐹𝐹𝑞𝑞−1�

Disproportionate accounts receivable increase may suggest difficulties in selling

BVEps Book value of

equity per share ln �

𝐵𝐵𝐵𝐵𝐸𝐸𝐵𝐵𝐹𝐹𝑞𝑞

𝐵𝐵𝐵𝐵𝐸𝐸𝐵𝐵𝐹𝐹𝑞𝑞−1�

Not applicable, this variable is not part of Lev and Thiagarajan.

CAPX Capital

expenditure 25 Industry CAPX − ln �

𝐶𝐶𝑀𝑀𝐸𝐸𝐶𝐶𝑞𝑞

𝐶𝐶𝑀𝑀𝐸𝐸𝐶𝐶𝑞𝑞−1�

A decrease in CAPX may indicate managers’ concerns with the adequacy of current and future cash flows. EPS-1 Change in EPS

lagged by 1 quarter26

∆𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞,𝑖𝑖 = 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞,𝑖𝑖− 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞−1,𝑖𝑖 Not applicable, this variable is not part

of Lev and Thiagarajan.

EPS-4 Change of EPS lagged by 4 quarters27

∆𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞−3,𝑖𝑖 = 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞−3,𝑖𝑖− 𝐸𝐸𝐸𝐸𝐸𝐸𝑞𝑞−4,𝑖𝑖 Not applicable, this variable is not part

of Lev and Thiagarajan.

ETR Effective tax rate _�𝐸𝐸𝐸𝐸𝑀𝑀𝑞𝑞−3+ 𝐸𝐸𝐸𝐸𝑀𝑀𝑞𝑞−2+ 𝐸𝐸𝐸𝐸𝑀𝑀𝑞𝑞−1

3 � − 𝐸𝐸𝐸𝐸𝑀𝑀𝑞𝑞 𝐸𝐸𝐸𝐸𝑀𝑀 = 𝐵𝐵𝑃𝑃𝑃𝑃𝑃𝑃𝑀𝑀𝑝𝑝 𝑃𝑃𝑀𝑀𝑃𝑃𝑀𝑀𝑃𝑃𝑀𝑀𝑒𝑒𝐹𝐹 𝑃𝑃𝑀𝑀𝑝𝑝�

Reduction of ETR reflects less persistent earnings. GM Gross margin28 ln � 𝐸𝐸𝑀𝑀𝑏𝑏𝑃𝑃𝐹𝐹𝑞𝑞 𝐸𝐸𝑀𝑀𝑏𝑏𝑃𝑃𝐹𝐹𝑞𝑞−1� − ln � 𝐺𝐺𝑀𝑀𝑞𝑞 𝐺𝐺𝑀𝑀𝑞𝑞−1�

Affect the long-term performance of the firm and are therefore informative with respect to earnings persistence. INV Inventory

ln � 𝐼𝐼𝑀𝑀𝑅𝑅𝑞𝑞

𝐼𝐼𝑀𝑀𝑅𝑅𝑞𝑞−1� − ln �

𝐸𝐸𝑀𝑀𝑏𝑏𝑃𝑃𝐹𝐹𝑞𝑞

𝐸𝐸𝑀𝑀𝑏𝑏𝑃𝑃𝐹𝐹𝑞𝑞−1�

Inventory increases that outrun sales suggest difficulties in generating sales.

LV Labour force 𝐸𝐸𝑀𝑀𝑏𝑏𝑃𝑃𝐹𝐹 𝐵𝐵𝑃𝑃𝑃𝑃 𝑃𝑃𝑒𝑒𝐵𝐵𝑏𝑏𝑃𝑃𝑒𝑒𝑃𝑃𝑃𝑃𝑞𝑞−1− 𝐸𝐸𝑀𝑀𝑏𝑏𝑃𝑃𝐹𝐹 𝐵𝐵𝑃𝑃𝑃𝑃 𝑃𝑃𝑒𝑒𝐵𝐵𝑏𝑏𝑃𝑃𝑒𝑒𝑃𝑃𝑃𝑃𝑞𝑞

𝐸𝐸𝑀𝑀𝑏𝑏𝑃𝑃𝐹𝐹 𝐵𝐵𝑃𝑃𝑃𝑃 𝑃𝑃𝑒𝑒𝐵𝐵𝑏𝑏𝑃𝑃𝑒𝑒𝑃𝑃𝑃𝑃𝑞𝑞−1

More efficient labour force signals increase in future earnings.

PE 12 months trailing price-earnings ratio29

ln � 𝐸𝐸𝐸𝐸𝑞𝑞 𝐸𝐸𝐸𝐸𝑞𝑞−1�

Not applicable, this variable is not part of Lev and Thiagarajan.

S&A Sales and administrative expenses ln � 𝐸𝐸&𝐺𝐺𝑞𝑞 𝐸𝐸&𝐺𝐺𝑞𝑞−1� − ln � 𝐸𝐸𝑀𝑀𝑏𝑏𝑃𝑃𝐹𝐹𝑞𝑞 𝐸𝐸𝑀𝑀𝑏𝑏𝑃𝑃𝐹𝐹𝑞𝑞−1�

Administrative sales are approximately fixed, therefore increase is considered negative suggestion a loss of

managerial cost control.

24 _{The economic intuition or interpretation as given by Lev and Thiagarajan (1993)} 25 _{Industry CAPX is calculated by the average CAPX of all companies in the sample.}

26 _{All predictors are lagged by one quarter in the bivariate regression, therefore the measurement this not included this}

lag.

27 _{All predictors are lagged by one quarter in the bivariate regression, therefore the measurement only includes a lag of 3}

quarters.

28 _{𝐺𝐺𝑀𝑀}

𝑞𝑞= 𝐸𝐸𝑀𝑀𝑏𝑏𝑃𝑃𝐹𝐹 − 𝐶𝐶𝐶𝐶𝐺𝐺𝐸𝐸