The distribution of the Return on Capital Employed (ROCE)

Transcription

1 Appendix A The historical distribution of Return on Capital Employed (ROCE) was studied between 2003 and 2012 for a sample of Italian firms with revenues between euro 10 million and euro 50 million. 1 As well as observing the behaviour of ROCE for different sectors, we studied the distribution behaviour changes along with changes in some determining factors of the ROCE such as profitability ratios and turnover ratios. Descriptive analysis: definition of the sample of reference. To make the analysis as robust as possible, we will immediately eliminate firms with missing data, maintaining only those with complete data. In particular, the cleaning of the data has the following steps: The number of values missing is: 53,296 for Return on Capital Employed; 53,616 for Return on Sales; 87,207 for Monetary cycle; 50,135 for Lease to Sales; 48,026 for Fixed Assets to Total Assets; 48,800 for Fixed Asset Turnover; 17,140 for type of company (in this case the missing data is due to the difficulty of automatically identifying the company organisation from the name provided in the archive); 550 for the Ateco code; The total number of lost observations due to missing values is 102, As well as eliminating the missing data, we have considered the presence of irregular values below. In particular, we have observed: 214 values of the variable costs for leasing of assets (rents and so on) less than 0 or greater than 1 (limits placed to eliminate values such as 12,000 and 2,389,000 respectively the minimum and maximum observed); 953 values of the variable Fixed Asset Turnover less than 0 or greater than 25,000 (also in this case these limits are placed to eliminate values that are obviously incorrect); 167

2 168 Appendix A 5 observations of the variable Fixed Assets to Total Assets greater than 1. The overall effect of the data cleaning provides a dataset of 134,139 observations (more than sufficient to be able to evaluate the distributive ownership of the index we are interested in). The distribution of the Return on Capital Employed (ROCE) ROCE distribution is asymmetrical with a very high proportion of irregular observations (Figure A.1). In particular we observe a very high number of positive as opposed to negative irregular values. Figure A.2 provides the ROCE box and whiskers plot diagrams for the Ateco sectors. The graphs indicate that the individual Ateco categories have distributions that can be significantly different in terms of average. In general, all the conditional (and unconditional) distributions are asymmetrical with a significant number of irregular values, mainly positive. An alternative representation of the distributions of conditional frequency is based on violin plots. Figure A.3 provides an example of Histogram of ROCE Frequency ROCE values Figure A.1 Historical distribution of ROCE Source : Aida Amadeus data.

3 Figure A. 2 code Distributions of the conditional ROCE observed on the Ateco Source: Aida Amadeus data ROCE distribution by observed industry classification Figure A. 3 Distributions of frequency of the conditional ROCE for the five Ateco codes chosen. Source: Aida Amadeus data. the distributions of frequency for some sectors of interest for which we analysed three firms in the Chapter 5. The width of the graphs represents the numbers of the sub-groups whereas the thin shape identifies the ROCE distribution asymmetry. The same solution has also been adopted to represent conditional ROCE distribution according to the type of company: cooperatives (COOP), limited companies with Account Equity greater than euro

4 170 Appendix A 120,000 (SPA) and limited companies with Account Equity greater than euro 10,000 (SRL) (see Figure A.4). Nonetheless, we can observe that the difference between the average levels of the ratio in the three sub-groups for the distributions of frequency observed are not significantly different. The same investigation has also been undertaken for years of observation (see Figure A.5). Also in this case the distributions are ROCE distribution by observed legal types COOP SPA SRL Figure A.4 Distributions of frequency of the conditional ROCE for the three types of companies identified in the dataset. Source : Aida Amadeus data Figure A.5 Distribution of the conditional ROCE for the year of observation. Source : Aida Amadeus data.

5 Appendix A 171 not significantly different. Nonetheless, we can identify an average negative trend for the beginning of the current period of economic crisis that carries on until the latest data available to us. The formalisation of this graph is summarised in Table A.1 where the principal indices of position (minimum, first quartile, medium, average, second quartile and maximum) are provided together with the indices of variability (standard deviation and interquartile range). The analysis of the descriptive statistics provided in Tables A.1 and A.2 allows us to identify a certain difference in the distribution of the economic ratio compared to the three classifications considered. In particular, we can observe an average difference between the values observed in the three types of company. The analysis of the indices of variability (standard deviation and interquartile difference) allows us to identify the presence of heteroscedasticity in the dataset. The maximum average value and the maximum variability are observed for the SRLs whereas the minimum values of average and variability correspond to the COOP. The analysis conditional on the Ateco classification allows us to identify by business sectors (46 and 47) the average values and also the variability greater than that of the industrial production sectors (22, 25 and 31). With regard to the analysis of the phenomenon conditional on the year of observation, we can see that the average values have a performance which could plausibly be associated with the general climate of economic deterioration. The study of ROCE determining factors When describing the context of analysis, we must also investigate the distribution of the co-variables or control variables for the system. In particular, we can identify the following variables in this dataset: Profitability ratios: Return on Sales and Lease to Sales (ROS and MC): the first is the relationship between EBIT and sales and allows us to understand the firm s unitary margin; the second identifies the incidence of the costs of rent and of leasing on sales, profit achieved if comparable firms have some productive units rented; Turnover and incidence ratios: Monetary cycle, Fixed Asset Turnover and Fixed Assets to Total Assets (LOS, FA% and FAT). The first represents the space of time between payments and

6 Table A.1 Conditional descriptive statistics for the ROCE Mean Minimum 1st quartile Average 3rd quartile Maximum Standard deviation Interquartile difference Kurtosis Skewness ROCE Legal type COOP SPA SRL Ateco Industry Classification Year of observation Source : Aida Amadeus data.

7 Table A.2 Conditional empirical quartiles for the ROCE Empirical quantiles 0% 0.10% 1% 5% 10% 90% 95% 99% 99.90% 100% ROCE COOP SPA SRL Ateco Ateco Ateco Ateco Ateco Year Year Year Year Year Year Year Year Year Year Source : Aida Amadeus data.

8 174 Appendix A collections and calculated as sale times plus collection times less payment times; the second is the relationship between sales and total assets, expressing how many times the fixed investments are recovered through sales, the last is the relationship between the assets and the total assets, profit to be determined based on the weight of the multi-year costs compared to the needs of working capital; Basic details: company organisation, Ateco code of activity and year of observation (LType, IndClass and Year respectively); Whereas the last three variables can easily be studied with the tables of frequency (Tables A.3 and A.4) the other variables are numerical and require a numerical synthesis (similar to that observed in Table A.1 see the results provided in Table A.5). With regard to the results in Tables A.3 and A.4, we observe that the distributions of frequency of the observations are not strongly conditioned by the year of observation. The analysis of the results provided in Tables A.5 and A.6 mainly allows us to identify the presence of outliers in the data and in particular for the FAT and MC variables. After having studied the summary descriptive indices of ROCE distribution and of the other quantitative variables we must study the relationship between these variables. To this end, in Tables A.6 and A.7 respectively we provide the matrixes of the Spearman and Pearson indexes of co-relationship and the results of the theoretical test on the linear independence between variables. We can note that all the linear co-relationships studied are statistically significant. However, this result is associated more with the many samples considered than the real relationship existing between variables. Empirical evidence in confirmation of this statement is given by the results provided in Figure A.5. We can see that relationships existing between the variables (the results of the non-linear regressions obtained using the generalised additional model based on the spline are provided in red) are not very evident from the dispersion graphs. In Table A.6, the co-relationships between the variables have been calculated both through Pearson s index of linear co-relationship and considering the index of co-relationship between Spearman s levels. In both cases, we can see that there is no cause for concern regarding the co-linear variables as we do not see any high co-relationships between the

9 Appendix A 175 Table A.3 Distribution of frequency of the observations for years ( ), type of company and Ateco code (to simplify reading of the results, we have provided in this table only the frequencies of the categories most represented in the dataset) Year of observation COOP % % % % % SPA % % % % % SRL % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % Totals % % % % % Source : Aida Amadeus data.

10 176 Appendix A Table A.4 Distribution of frequency of the observations for years ( ), type of company and Ateco code (to simplify reading of the results we have provided in this table only the frequencies of the Ateco categories most represented in the dataset) Year of observation COOP % % % % % SPA % % % % % SRL % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % Totals % % % % % Source : Aida Amadeus data

11 Table A. 5 Statistics describing the explanation variables Mean Minimum 1st quartile Average 3rd quartile Maximum Standard deviation Interquartile difference Kurtosis Skewness ROS MC LOS FA% FAT Source: Aida Amadeus data. Table A.6 Empirical quantiles of the explanation variables Empirical quantiles 0.10% 1% 5% 10% 90% 95% 99% 99.90% ROS MC LOS FA% FAT Source: Aida Amadeus data.

12 178 Appendix A Table A.7 Co-relationships between variables considered in the study ROCE ROS MC LOS FA% FAT Table A.8 Test for the absence of linear co-relationship Relationship Correlation P.value ROCE ROS ROCE-MC ROCE-LOS ROCE-FA% ROCE-FAT Source : Aida Amadeus data. Spearman correlation indexes ROCE ROS MS LOS FA% FAT Pearson correlation indexes ROCE ROS MS LOS FA% FAT Source: Aida Amadeus data explanation variables (except for the relationship between fixed asset to total assets and fixed asset to turnover identified with the co-relationship coefficient between levels). The only co-relationships worthy of note are those that can be observed between the ROCE and the other variables included in the study. The results provided in Table A.8 allow us to state that there is a statistically significant linear relationship between the ROCE and the other ratios. This relationship will also be investigated with the

13 Appendix A 179 help of the models of regression for panel data as it is possible to see in the next section. The significance of the relationship (that it is not very intense) presents a maximum value of the index of co-relationship The same relationships can be studied with the help of the dispersion graphs provided in Figure A.6 (where we also find the non-linear regressions obtained through smoothing). ROCE Local polynomial smooth ROS kernel = epanechnikov, degree = 0, bandwidth = ROCE Local polynomial smooth MC kernel = epanechnikov, degree = 0, bandwidth = Figure A.6 Continued

14 180 Appendix A Local polynomial smooth 0 ROCE LOS kernel = epanechnikov, degree = 0, bandwidth = ROCE Local polynomial smooth FA% kernel = epanechnikov, degree = 0, bandwidth =

15 Appendix A 181 ROCE Local polynomial smooth FAT kernel = epanechnikov, degree = 0, bandwidth = Figure A.6 Study of the relationship between quantitative variables Source : Aida Amadeus data. Models of regression dynamic panels and regression with autoregressive residuals To study the relationship between the ROCE and the variables that we have already listed in the previous section, we have used specific models for the data structure. Therefore, the models used in this context consider all the presence of temporal self-relationship of the residuals (see Baltagi, 2008 for more details on the models adopted) and to take into account this self-relationship we have used dynamic panel models in which the variable response becomes a delayed part of the regressors (using a logic similar to that of the models for simple time sequences, see Arellano and Bover, 1995; and Arrelano and Bond, 1991 for more details). The estimated results provided in Table A.9 allow us to confirm that, except for the variable fixed assets turnover, we can identify a relationship between the ROCE values and the context variables chosen for the study. The estimated coefficients of the regressions represent the net effect of each variable on the value of the ROCE and given the substantial coherency of the results between the various models estimated, we can state that: the increase of the fixed assets to total assets and the monetary cycle has negative effects on the estimated value of the ROCE;

16 Table A.9 Results of linear regression on the panel data (considering both static first model and dynamic models) Random Effects GLS regression with AR(1) Arellano-Bond dynamic disturbances System dynamic panel-data panel-data Dynamic Random Effects GLS regression with AR(1) disturbances Full model Full model Null model Full model Null model Full model Null model Explicative variables Est. values Std. Errors Est. Values Std. Errors Est. values Std. Errors Est. Values Std. Errors Est. values Std. Errors Est. values Std. Errors Est. values Std. Errors Constant Lagged ROCE FA% FAT MC ROS LOS SRL Dummy COOP Dummy Autocorrelation Index RE standard deviation Errors standard deviation Goodness of fit index > >0.001 >0.001 >0.001 >0.001 >0.001 >0.001 > Sign. AR(1) Sign. AR(1) Sign. AR(1) Sign. AR(1) Source: Author s analysis of Aida Amadeus data.

17 Table A.10 Statistics describing regression residuals for dynamic models (these residuals must be interpreted as measuring the purely irregular component of the ROCE) Mean Minimum 1st quartile Average 3rd quartile Maximum Standard deviation Interquartile difference Kurtosis Skewness System Dynamic Full Model System Dynamic Null Model A-B Dynamic Full Model A-B Dynamic Null Model RE model with AR(1) residuals Full Model RE model with AR(1) residuals Null Model Source: Author s analysis of Aida Amadeus data.

18 184 Appendix A however, there is a positive correspondence between the ROS and the identification variables of the SRL and of the COOP; the lagged ROCE delayed variable has a positive value and indeed its inclusion in the model allows us to explain the residual self-relationship present in the first model (the only non-dynamic). This is highlighted by the very reduced value assumed by the self-relationship coefficient of the residuals in the last model estimated. For all the dynamic models, we have attempted to verify the actual weight of the explanation variables by estimating the complete models (full model) and the void models (null model) and comparing the estimated results. These comparisons have been made for all three specifications adopted but from a purely descriptive point of view, it is much simpler to stop at the comparison between the coefficients of linear determination calculated automatically by the Stata software for the latest model. By comparing two values of R 2 it is reasonable to conclude that the support for the explanation variables (7 variables) at the model s explanation capacity is very limited. The objective of this analysis is to clean the phenomenon observed (ROCE) by removing the co-variation effects and taking into account their temporal dependence. The residuals of the regressions considered can be studied to understand if, net of the variables considered, the phenomenon assumes more regular performance specifics, compared to the pure phenomenon. As we can observe, also after having considered the dynamic component in the model, the self-relationship of the residuals is still significant from a statistical point of view even if its size is significantly reduced. Table A.9 provides statistics describing the residuals of the models. The best indices of asymmetry and kurtosis correspond to the first complete dynamic model but this has a higher standard deviation and interquartile difference. The model with the least residual variation is the complete model with casual effects, variable delayed response and self-regressive residuals. In general, all the models have a very high index of kurtosis (that corresponds to the presence of very irregular values already in the original data) and a positive asymmetry. The diagnostics of the models and the descriptions of the distributions of the regression residuals are very similar between the models considered. Therefore, we provide below analysis of only the residuals of the GLS random effects regression with AR(1) disturbances model.

19 Residuals 0 Distance above median Distance below median Residuals Inverse Normal 100 Empirical distribution of model residuals Density Residuals Figure A.7 Diagnostic plot for model residuals. Source : Author s analysis of Aida Amadeus data.

20 Appendix B With reference to the statistical analysis, other descriptive analysis can be used considering the various classifications examined together. Table B.1 Empirical quantiles for the context variables according to Ateco code Empirical quantiles 0.10% 1% 5% 10% 90% 95% 99% 99.90% ROS Ateco MC Ateco LOS Ateco FA% Ateco FAT Ateco ROS Ateco MC Ateco LOS Ateco FA% Ateco FAT Ateco ROS Ateco MC Ateco LOS Ateco FA% Ateco FAT Ateco ROS Ateco MC Ateco LOS Ateco FA% Ateco FAT Ateco ROS Ateco MC Ateco LOS Ateco FA% Ateco FAT Ateco Source : Dati Aida Amadeus. 186

21 Table B.2 Empirical quantiles for the ROI for year and type of company (at the same time) Empirical quantiles 0% 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% 100% Year 2003 ROCE Year 2003 COOP Year 2003 SPA Year 2003 SRL Year 2004 ROCE Year 2004 COOP Year 2004 SPA Year 2004 SRL Year 2005 ROCE Year 2005 COOP Year 2005 SPA Year 2005 SRL Year 2006 ROCE Year 2006 COOP Year 2006 SPA Year 2006 SRL Year 2007 ROCE Year 2007 COOP Year 2007 SPA Year 2007 SRL Year 2008 ROCE Year 2008 COOP Year 2008 SPA Continued

22 Table B.2 Continued Empirical quantiles 0% 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% 100% Year 2008 SRL Year 2009 ROCE Year 2009 COOP Year 2009 SPA Year 2009 SRL Year 2010 ROCE Year 2010 COOP Year 2010 SPA Year 2010 SRL Year 2011 ROCE Year 2011 COOP Year 2011 SPA Year 2011 SRL Year 2012 ROCE Year 2012 COOP Year 2012 SPA Year 2012 SRL Source : Aida Amadeus data.

23 Table B.3 Empirical quantiles for the variables of context by year Empirical quantiles 0.10% 1% 5% 10% 90% 95% 99% 99.90% Year 2003 ROS Year 2003 MC Year 2003 LOS Year 2003 FA% Year 2003 FAT Year 2004 ROS Year 2004 MC Year 2004 LOS Year 2004 FA% Year 2004 FAT Year 2005 ROS Year 2005 MC Year 2005 LOS Year 2005 FA% Year 2005 FAT Year 2006 ROS Year 2006 MC Year 2006 LOS Year 2006 FA% Year 2006 FAT Year 2007 ROS Year 2007 MC Year 2007 LOS Year 2007 FA% Year 2007 FAT Continued

24 Table B.3 Continued Empirical quantiles 0.10% 1% 5% 10% 90% 95% 99% 99.90% Year 2008 ROS Year 2008 MC Year 2008 LOS Year 2008 FA% Year 2008 FAT Year 2009 ROS Year 2009 MC Year 2009 LOS Year 2009 FA% Year 2009 FAT Year 2010 ROS Year 2010 MC Year 2010 LOS Year 2010 FA% Year 2010 FAT Year 2011 ROS Year 2011 MC Year 2011 LOS Year 2011 FA% Year 2011 FAT Year 2012 ROS Year 2012 MC Year 2012 LOS Year 2012 FA% Year 2012 FAT Source : Aida Amadeus data.

25 Table B.4 Empirical quantiles of the ROCE for year and Ateco code Empirical Quantiles 0% 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% 100% Year 2003 ATECO Year 2003 ATECO Year 2003 ATECO Year 2003 ATECO Year 2003 ATECO Year 2004 ATECO Year 2004 ATECO Year 2004 ATECO Year 2004 ATECO Year 2004 ATECO Year 2005 ATECO Year 2005 ATECO Year 2005 ATECO Year 2005 ATECO Year 2005 ATECO Year 2006 ATECO Year 2006 ATECO Year 2006 ATECO Year 2006 ATECO Year 2006 ATECO Year 2007 ATECO Year 2007 ATECO Year 2007 ATECO Year 2007 ATECO Year 2007 ATECO Year 2008 ATECO Year 2008 ATECO Year 2008 ATECO Continued

26 Table B.4 Continued Empirical Quantiles 0% 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% 100% Year 2008 ATECO Year 2008 ATECO Year 2009 ATECO Year 2009 ATECO Year 2009 ATECO Year 2009 ATECO Year 2009 ATECO Year 2010 ATECO Year 2010 ATECO Year 2010 ATECO Year 2010 ATECO Year 2010 ATECO Year 2011 ATECO Year 2011 ATECO Year 2011 ATECO Year 2011 ATECO Year 2011 ATECO Year 2012 ATECO Year 2012 ATECO Year 2012 ATECO Year 2012 ATECO Year 2012 ATECO Source : Aida Amadeus data.

27 Table B.5 Descriptive statistics for the conditional ROCE at the Ateco codes observed Ateco Classification Mean Standard deviation Empirical quantiles 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90% Continued

28 Table B.5 Continued Ateco Classification Mean Standard deviation Empirical quantiles 0.10% 1% 5% 10% 25% 50% 75% 90% 95% 99% 99.90%

29 Source : Aida Amadeus data.