The relationship between the value of voting rights and the concentration of ownership of companies on the German stock market

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The relationship between the value of voting rights and the concentration of

ownership of companies on the German stock market

Tim de Boer 11035056

Bachelor’s Thesis Finance and Organisation

2017/2018

Supervisor P.R. Stastra

Abstract

With the new discovered method of Kalay et al. (2014), the value of voting right of stocks can now be calculated for almost every company. This new method should make a more precise estimation of the value of voting rights. It is therefore interesting to see what the determinants of these voting rights are. This research examines whether the concentration of ownership of the company is one of the determinants. The scope of this research focusses on companies on the German DAX and MDAX. This research concludes that the effect of the concentration of ownership is not significant.

2 Statement of Originality

This document is written by Tim de Boer who declares to take full responsibility for the content of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Table of content

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1. Introduction

The right to vote can be valuable for shareholders (Karakas 2014). But when there is a major shareholder or a lot of investors with more shares, voting power of a single vote becomes relatively smaller. One can suggest that the vote becomes less valuable. But is there a significant relation between the concentration of ownership and the value of the voting right? Furthermore, to what extend does the degree of concentration have an effect on the value of voting rights? This research examines this effect.

The outcome can be interesting for investors. This right to vote gives shareholders the change to vote at shareholder meetings and therefore gives them influence at the strategy of the firm (Bodie et al. 2011). But not every investor visits shareholder meetings which means they do not use the value of the voting right. If there is a negative relationship, investors can invest in companies with high concentration of ownership. A high concentration could lead to a relatively smaller value of the voting rights and therefore the stock could become relatively cheaper compared to stocks with a high value of voting rights. Or alternatively, for shareholder activists, who buy shares so they can influence the strategy of the firm, to invest in firms with low concentration (Bodie et al 2011). This result would be the same as the findings with the valuation of dual-class shares, where one type of shares has more voting rights then the other and therefore becomes more valuable (Nicodano, 1998). Or with the research of Hauser and Lauterbach in 2004. They investigated the change in voting right with the loss of a blockholder, which implies a high concentration of ownership.

Kalay and Karakas (2014) researched the value of voting rights and discovered a new valuation method. The advantage of this method is that it has the ability to calculate the value of voting rights of every company, as long as there are option prices on the stock of the company available. They looked at the change in value of voting right during the time and found that it increases around events where the voting right can be executed, for example shareholder meeting events.

The second topic of this research is the concentration of ownership. Overland et al. (2012) compared twenty different methods for measuring the concentration of ownership. They concluded that there is not a perfect way to measure ownership, but most methods have strong correlations. Not all the method can be used all the time. One problem for measuring the concentration of ownership is that a report of the shareholder distribution is not mandatory. This could lead to data constraints (Overland et al, 2012). The connection between ownership and value of voting rights has been made before by Hauser and Lauterbach (2004) using dual-class shares. The problem is that not all companies have dual-class shares. This research will use the method discovered by Kalay et al. (2014) and will make a more precise estimate of the statistic relation between the concentration of ownership and the value of voting rights.

5 However, contrary to other research this research did not find any relation between the value of voting rights and the concentration of ownership. The research was based on companies on the German DAX and the MDAX. Even the effect of an ultimate owner (blockholder) turned out to be insignificant. This could mean that the new discovered method is not the perfect way of measuring voting rights yet. Further research should point out if these results are a consequence of the valuation method of voting rights or that, with the data used in this research, no effect exists.

First there will be a description of the existing literature on the topic of the valuation of voting rights and what their relation is with options. After that, theory about the different methods of concentration of ownership. This is stated in the literature review section. Next, the research method is clarified and the formulas that are used will be explained in the methodology section. After that, the result are presented and discussed. They are also linked to the existing literature about these topics. In the end, a conclusion will be made, and the possible limitations of this research are discussed. Finally, recommendations are given for further research on the topic of valuation of voting right and the possible determinants of it.

2. Literature Review

2.1 Voting rights

Shareholders who own one or more shares have a right on a share in the financial outcome in the form of a dividend and the right to vote at shareholder meetings. This right to vote can be valuable for investors. These shareholder meetings are at least once year. The shareholders have, for example, the authority to elect the members of the board. The board then makes sure that the management team acts in the interest of the shareholders. In this way the shareholders can influence the decisions in the organisation of the firm (Bodie et al. p41).

Most of the research done on the value of these votes has been done with the use of dual-class shares (Hauser and Lauterbach, 2004). With dual-dual-class shares the companies issues two different shares, A-class and B-class shares. They have the same right on dividend but instead of ‘one-share-one-vote’, A-class shares have, for example, 10 votes per share. The difference in price should then show the value of voting rights (Hauser & Lauterbach 2004). A problem with this method is that a lot of companies do not have this kind of shares so that would make it impossible to have an adequate measure of the voting rights of other companies.

A second way of determining the value of voting rights is by looking at the value of stocks before and after the sale of the shares of a blockholder. If there is one major shareholder with more

6 than half of the voting rights, and therefore all the voting power, the rest of the voting rights become worthless. If a blockholder sells his shares on the open market the value of voting rights should go up. The right on dividend remains the same so the difference in stock price should capture the increase in value of voting right (Dyck and Zingales, 2004). According to their research there is a high concentration has a negative effect on the value of voting rights. However, they only investigated companies with a blockholder. This research will also take companies with lower concentration of ownership into account.

A third method uses the increase in value of the voting right around shareholder meetings. The method looks at the extra costs of borrowing a share around shareholder meetings (Aggarwal et al., 2012).

All these methods find positive values for voting rights. Problem with all these methods is that they either have restricted data due to a relatively small sample (not all firms have dual-class shares or a blockholder) or they look at one specific point in time (shareholder meetings).

The latest method of Kalay et al. (2014) shows a method for every company at any point in time. As long as there are option and stock prices of the company available. They used the put call parity to create a synthetic stock that creates the same cash flows as the underlying stock. The difference in value between the underlying stock and the synthetic stock should capture the right on dividend and the right to vote. The direct method does not take possible dividend payments into account. The lower bound method adds the present value of the dividend payment to the value of the synthetic stock (Kalay et al. 2014). Their method will be explained precisely in the methodology section since this is the method used in this research. This method has three main advantages in comparison to the other methods. First, the value of the voting rights can be calculated for every stock that has data of the price of option pairs available. An option pair consists of a call and a put option with the same strike price and the same time to maturity. This means the value of the voting rights can be estimated for large numbers of stock for almost every company. Second, the option prices are exogenously determined. This means the data is widely available so the research will not have a large selection bias. This bias exists for example with the use dual-class shares where the sample size is dependent of the companies that use such shares. Third, this method can estimate the value of voting rights at any point in time (Kalay et al. 2014).

To understand the method of Kalay et al. (2014), some theory about how options work is needed. An option gives investors the right to buy or sell an asset at a specified price, the strike price. A call option gives investors the rights to buy and a put option gives investors the right to sell. Important to notice is that an option is not an obligation (Bodie et al. p678). This research will look at European options. European options can only be exercised at the expiration date. So at the expiration

7 date of the option investors can decide whether or not to exercise the option. Options can be used to hedge risk in volatile markets but can also generate very large pay-offs. Just as with normal stocks investors can go long on an option (buyer) or go short (seller) (Bodie et al. p678).

2.2 concentration of ownership

The concentration of ownership describes the distribution of shareholders and therefore the distribution of voting power. Because the voting power of shareholders can influence the strategy and decisions of a firm, the concentration of ownership is an important aspect of the characteristics of a firm (La Porta et al., 1999). Although some research points out that it does have an effect on firm performance (McEachern, 1975), there is also research that shows that there is no significant effect (Scherer, 1988) or even a negative relation between concentration of ownership and firm performance (Leech and Leahy, 1991). According to Overland et al. (2012) there are three major reasons for the difference in outcomes between research on concentration of ownership: difference in context, difference in quality of the data and difference in methodology used. Possible difference in outcomes with this research are discussed in the conclusion.

On the question how to measure ownership, Overland et al. (2012) compared twenty different methods. The different measures range from easy methods, for example looking a the percentage the largest shareholder holds, to complicated measures which used advanced indices that are used in game theory. All methods strongly correlate and it depends on the context which method is the best. the Herfindahl-Hirschman index is the most common way to measure market concentration but it can be used to measure other concentrations as well (Onderstal, p36). The Herfindahl-Hirschman index reflects the sum of the squared percentages. It will be further explained in the methodology since this is the method used in this research. This method is also used in other research, among them Leech & Leahy, 1991; Renneboog, 2000; Goergen & Renneboog (2001). The main advantage of this method is an increase in shares of a large shareholder has more weight on the index than an increase in shares of a smaller shareholder. Even if the increase is with the same number of shares. This is useful because the size of the largest shareholder is the biggest determinant of the concentration.

3. Methodology

3.1 Value of voting rights

This research investigates what the relation between the value of voting rights and the concentration of ownership, of companies on the DAX and the MDAX in Germany is. Therefore, two datasets are needed. The German DAX and MDAX are indexes which consists of 30 and 53 companies respectively. This leads to a possible dataset of 83 companies. To construct the value of voting rights

8 the same method as Kalay et al. (2014) is used. They constructed a synthetic stock with the put-call parity and compared the value of that synthetic stock with the underlying stock. To construct a synthetic stock, the put-call parity is needed:

𝑆 + 𝑝 = 𝑐 + 𝑃𝑉(𝑋) (1)

Where S is the stock price of the company, p the price of a put option with strike price X and time to maturity t, c the price of a call option with strike price X and time to maturity t and PV(X) the present value of investing X in a risk-free asset with time to maturity t. The strike price for the put and the call must therefore be the same. By rewriting the formula investors can construct a synthetic by going long on a call option, short on a put option and investing the strike price in a risk-free asset with the same expiration date. Important is that the options have the same strike price and time till maturity.

Ŝ(𝑡) = 𝑐 − 𝑝 + 𝑃𝑉(𝑋) (2)

Here Ŝ(𝑡) is the value of the synthetic stock. This synthetic stock has the same pay-off as the underlying stock but does not have the right to vote on shareholder meetings. The difference should therefore capture the value of the right to vote:

𝑃𝑉(𝑉𝑜𝑡𝑒(𝑡)) = 𝑆 − Ŝ(𝑡) + ɛ (3)

Kalay et al. (2014) called this the direct method. The other method is the lower bound method where the present value of the dividend payment, if there is one in the time till expiration, is subtracted.

𝑃𝑉(𝑉𝑜𝑡𝑒(𝑡)) = 𝑆 − Ŝ(𝑡) + 𝑃𝑉(𝐷𝑖𝑣) + ɛ (4)

This method is more complete then the direct method. Problem with the lower bound method is that most of the outcomes can become negative. Since the right to vote cannot be negative, these

9 outcomes would become zero. In the research of Kalay et al. 88% of the outcomes became negative and turning them all to zero would give the results a higher outcome. Another way of solving this problem is by only looking at the positive values of voting rights. This thesis will only look at the direct method. If there are negative outcomes in the direct method, this thesis will only take the positive outcomes into account. One bias of Kalay et al. is the value of early exercise of the options. This thesis doesn’t have that bias because it uses European style options which can only be exercised at the expiration date of 19-03-2019.

The data is retrieved from database DATASTREAM. The period used is 27-3-2018 till 22-5-2018 and the daily value of the voting rights is calculated. This time period is used because earlier data is not available. The data will be regressed at three separate dates. The 29th _{of March, 25}th _{of April and}

the 22th _{of May. As a risk-free rate this research will use the yield on a German 10 year government}

bond. The current yield, 23th _{of May 2018, is used because the research looks at a recent point the bias}

will be nihil. The TNX rate was available for all the days but there was no large difference in value. And because this research looks at German companies the German bonds were chosen as a risk rate.

3.2 Concentration of ownership

Next, the data for the concentration of ownership is needed. Overland et al. (2012) compared 30 different methods. The most commonly used method is the Herfindahl-Hirschman index (Overland, 2012). This method is mostly used to measure market concentration but can also be used to measure other concentrations (Herfindahl, 1950). What is does is that it sums up the squared sums of the percentage of voting rights of each shareholder:

𝐻 = ∑ 𝑝2_𝑖 𝑁

𝑖=1

(5)

Where p is the percentage of voting right of one shareholder. Other studies that used this method only used the largest shareholder to calculate this index (Leech & Leahy, 1991; Renneboog, 2000; Goergen & Renneboog, 2001). They did this because of unavailability of the data that can arise because transparency of shareholder distribution in not mandatory. This research will look at the five largest shareholders. This should give a better view of the total concentration. The data is available at the Orbis database.

10 3.3 regression and control variables

This research will regress the data on three separate dates: 27th _{of March, 25}th _{of April and the 22}th _of

May. The dates are at the beginning, middle and end of the dataset. This is because the value of the vote changes during the year so different dates could result in different results (Kalay et al. 2014). The dependent variable (Y) in this research is the value of voting rights. To make the regression more significant some control variables are added. The regression formula will look like this:

𝑌 = 𝐵0+ 𝐵1∗ 𝐻 + 𝐵2∗ 𝑆𝑖𝑧𝑒 + 𝐵3∗ 𝑈𝑙𝑡𝑖𝑚𝑎𝑡𝑒𝑜𝑤𝑛𝑒𝑟 + 𝐵4∗ 𝑀𝑎𝑐ℎ𝑖𝑛𝑒𝑟𝑦 + 𝐵5∗ 𝐶ℎ𝑒𝑚𝑖𝑐𝑎𝑙𝑠 + 𝐵6∗ 𝐵𝑎𝑛𝑘𝑠 + 𝜀.

(6)

Where 𝐵0 is a constant and 𝐻 is the Herfindahl-Hirschman index which represents the concentration of ownership. The variable 𝑆𝑖𝑧𝑒 indicates the size of the firms. It represents the natural logarithm of the revenue of the companies. The yearly revenue over 2017 was used in this research. Which is available in the Oribis database. Another proxy for size could be the number of employees that work for the company. However, this data was not available for every company. The 𝑈𝑙𝑡𝑖𝑚𝑎𝑡𝑒 𝑂𝑤𝑛𝑒𝑟 is a dummy control variable if there is one shareholder with more then 50% of the shares. When one shareholder has all the voting power, the value of one single vote could possibly become zero. This data comes from the same database as the shareholder distribution. The third control variables are dummies for industries. The four industries used are machinery, chemicals, banks and others. The industry description is downloaded from the Orbis database.

Not all the data was available for every company on the DAX and the MDAX. The stock prices were available for every company. The biggest problem was finding option prices with the same strike price and time to maturity. In the chosen time period of 27-3-2018 till 22-5-2018 there were 57 option pairs available. With that data 57 values of voting right were calculated. There was one outlier that was excluded from the dataset. The value of the voting right of MTU deviated more than two standard deviations of the mean and was therefore excluded from the dataset. The data of shareholder distribution was available for 55 of the 56 left companies. For all these companies the revenue of 2017 was available. On the three dates, where the data was regressed, not all the values of voting right were positive. Since the value of a vote can not be smaller than zero, the negative outcomes were excluded of the dataset. Therefore, there were 49, 45 and 42 companies left to investigate on the three chosen dates.

11 3.4 Hypotheses

The main interest in this research is 𝐵1. This reflects the effect of H on the dependent variable Y. The hypotheses are:

H0: 𝐵1=0 H1: 𝐵1≠0

The regression will test whether the coefficients of the regression formula are significantly different from zero. This means there will be a two-sided test with a significance level of 5% (α=0.05). 𝐵1 is expected to be smaller than zero. A higher degree of concentration of ownership should decrease the voting power. This would be in line with Nicodano’s (1998) finding that the value of a single vote is less valuable at companies with a blockholder. Hauser & Lauterbach (2004) also found that the price of the vote increases whit the loss of a blockholder. Their finding is therefore in line with the hypotheses of this research. The research of Nicodano and Hauser & Lauterbach only focusses on companies with a Blockholder, and therefore high concentration of ownership. This research will also look at companies with low concentration of ownership. The effect could therefore be smaller. Based on their research the control variable ultimate owner is expected to be significantly smaller than zero.

4. Results

Now the results of this research are discussed. The correlation tables of the variables in the regression formula are shown in the appendix. The correlation between the concentration of ownership and the value of voting rights is positive in the first two regressions and negative in the last regression. The negative correlation was expected since high concentration should lead to relatively low voting power per share. A change in correlation was expected because the value of voting right changes during the year (Kalay et al. 2014). Since the concentration of ownership remains the same, a change in correlation was expected. Next the results of the regression are

shown in table 1. The full regression tables are shown in the appendix. The table show the value of the coefficients of the regression formula that should capture the determinants of the dependent variable vote. Beneath the coefficient, the standard errors (heteroskedastic) is shown between the brackets.

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Table 1: Table 1 shows the results of the regression analysis on the three different dates. P*<0.2; P**<0.1;

P***<0.05

Regression 1 Regression 2 Regression 3

Dependent variable: Dependent variable: Dependent variable:

Vote Vote Vote

Constant -4,9983230 -2,717798 -0,9128461 (2,321042) (2,642912) (-1,84464) Concentration of -0,4970523 -1,429551 -1,2590410 ownership (H) (-2,824133) (-3,292628) (-1,623774) Size (lnrev) 0,38295030*** -0,2423087* 0,1179415* (-0,1604287) (-0,1839023) (-0,1167747) Ultimate Owner 0,5646771 1,046793 0,3197428 (-1,18336) (-1,620159) (-0,7170965) Machinery 0,112823 -0,062117 0,7469025 (-0,6414283) (-0,8270988) (-0,4798805) Chemicals 0,3592955 0,454924 0,9940856 (0,8429715) (0,8015163) (-0,6626908) Banks 1,0296300 0,754743 -0,2708563 (1,504123) (1,338795) (-0,3951183) N 49 45 42 Adjusted R-square 0,0309 0,0921 0,1453 Root MSE 1,9259 2,0059 1,8456

The results show that there is no significant relation between the concentration of ownership and the value of voting rights. In all the regressions, on the three different dates, the p-value of the coefficient H was higher than 0.05. Therefore, this research concludes that there is no effect. This is, however, in

13 contrary to other research. Although no research looked at randomly chosen companies but at companies with on specific characteristic like dual-class shares (Hauser & Lauterbach, 2004). Hauser & Lauterbach found a rise in the value of voting rights of a firm when a blockholder sold his shares. This implies a negative relationship between the existence of a blockholder and the value of voting rights. This research also looked at the concentration of ownership with companies without a blockholder. That could be a possible reason that no effect is found in this research. Perhaps the effect is only feasible with companies with a certain degree of concentration of ownership and the low concentrated companies could therefore be a bias in this research. This bias is however unlikely. The results show that the existence of an ultimate owner is insignificant as well. This was also not expected. An ultimate owner reflects a high concentration of ownership so according to the hypotheses of this research and that of Hauser and Lauterbach (2004) the effect should be even stronger than the effect of coefficient H. It is therefore prominent that in this research no effect was found. One possible cause of the absence of an effect may be the country used in this thesis. The value of voting rights differs across countries (Nenova, 2003).

The only significant effect was the size of the firm. The effect was positive which implies that companies with more revenue have higher value of voting rights. This effect was only found in regression one. However earlier research pointed out that firm size does not have an effect on the value of the vote (Kalay et al. 2014). None of the industries used as dummy variable has an effect in this research. There is no research on the difference in value of voting rights across industries with this method yet.

5. Conclusion

This research investigates the effect of the concentration of ownership on the value of voting rights. The research is done by constructing a synthetic, nonvoting, stock with the put-call parity and comparing the value of it with the underlying, voting, stock. The degree of concentration of ownership was computed with the Herfindahl-Hirschman index. The results show that there is no significant relation between the value of voting rights and the concentration of ownership in the German market. This is in contrary with the expectations and the findings of other research. Next the possible causes of this result are reviewed. After that, the implications for the existing literature are discussed. Finally, recommendations for further research on this topic are given.

One of the causes of the absence of an effect may be some research limitations. First of all was the data set with 49, 45 and 42 observations relatively small compared to other research. A larger sample could give a better view of the population. Furthermore, this research examines a short time

14 period. This was due to data problems. The option prices were only available in the last three months. This could have caused a bias in this research. This is because the value of voting rights changes during the year (Kalay et al. 2014). In their research, Kalay et al. found that the vote becomes more valuable around shareholder meetings, mergers and acquisitions, and when there is hedge fund activism. This research does not take these possible events into account. Also, the use of the direct method may influence the result. The lower-bound method is a more accurate way of measuring the value of the voting right (Kalay et al. 2014). Problem with this method is that the subtraction of the dividend payment made too many values negative. Since this research only looked at companies with a positive value the sample would be too small. The number of companies with a positive value was smaller than 30. Furthermore, this research assumed that the concentration of ownership represents the concentration of voting rights. It could be possible that companies have different structures of voting power than the standard ‘one share one vote’. This assumption was made data on voting is not available for every company. This assumption could be a bias if companies different kind of shares with different degrees of voting power.

The results of this research could imply that or, the method of constructing the value of voting rights is not a good measure after all and that it needs be more specific. Or that the concentration of ownership does not have any effect of value on voting rights. The method of Kalay (2014) is relatively new so more research should find out whether the results of this research can be seen as an incident. Another finding in this research is that even the existence of a blockholder has no effect on the value of voting rights. The expectation was that there was a negative effect. Since a blockholder has more than half of the voting power, the blockholder has enough voting power to make all the decisions that require the most votes. From this fact follows that the value of one single votes could become nihil. Although in the research of Hauser & Lauterbach (2004) the value of the vote was positive, even with the existence of a blockholder. Nevertheless was the value very close to zero and the absence of an effect is therefore surprising. Possible reason for the absence of an effect could be that there was a different between shareholder distribution and voting power distribution. For example, with dual-class shares. In that case a shareholder can own 30% of the shares but 51% of the voting power. This research does not take the possibility of dual-class shares or other construction to distribute voting power into account.

Further research is needed to test whether the results of this research can be seen as a coincidence, maybe the several limitations created a large bias. Or that the effect on the German simply does not exist. The method of Kalay et al. (2014) is relatively new so there are a lot of research opportunities left. The advantage of this method is that it can calculate the value of the voting rights for every company. Most of the earlier research used either the method of dual-class shares or the

15 sale of controlling blocks (Kalay et al. 2014). The limitations of these methods are that the specific characteristics must be available at the investigated companies. It is therefore interesting to see how the value of the votes differ between companies and what the determinants are of these, possible, different values. This research examined one possible determinant, the concentration of ownership. In Germany the effect was insignificant but it is a possible effect in other countries. The result of this research can be used in the discussion around corporate governance and control. The degree of shareholder control has, according to this research, no effect on the value of that control. More research is needed to see what the different determinants of the value of voting rights are.

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6. Literature

Demzets, H., Lehn, K., (1985). The structure of corporate ownership: causes and consequences. Journal of Political Economy, 93(6). 1155-1177

Gurun, U., Karakas, O. (2016). Earnings and the value of voting rights. SSRN electric journal

Hauser, S., Lauterbach, B. (2004). The value of voting rights to majority shareholders: evidence from dual-class stock unifications. The Review of Financial Studies, 17(4), 1167-1184.

Kalay, A., Karakas, O. & Pant, S. (2014). The marked value of corporate votes: theory and evidence of option prices. Journal of Finance, 69(3), 1235-1271.

La Porta, R., Lopez-De-Silanes, F., Shleifer, A., (1999). Corporate Ownership around the world. Journal of Finance, 54(2), 471-517.

Nenova, T., (2003). The value of voting rights and control: a cross country analysis. Journal of Financial Economics, 68, 325-351.

Overland, C., Mavruk, T., & Sjogren, S. (2012). Keeping it real or keeping it simple? Ownership Measures compared.

Leahy, J., Leech, D., (1991). Ownership structure, control type classifications and the performance of large British companies. The Economic Journal, 409(101), 1418-1437.

Nicodano, G., (1998). Corporate groups, dual-class shares and the value of voting rights. Journal of Banking-Finance, 22, 1117-1137.

Goergen, M., Renneboog, L. (2001). Investment policy, internal financing and ownership concentration in the UK. Journal of corporate finance, 7(3), 257-284.

Berk, J., & DeMarzo, P. (2014). Corporate Finance. Oxford: Pearson Education. Bodie, Z., Kane, A., & Marcus, A. J. (2011). Investments. New York: McGraw-Hill/Irwin. Onderstal, S. (2014). Economics of Markets and Organisations. Pearson Benelux

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7. Appendix

This is an overview of the different data output. First the correlation tables of the three regressions are shown. The correlations are calculated in Microsoft Excel.

Next the regression output on the three different dates. For the regression calculations, the statistical program STATA was used.

29-mrt vote H lnrev ultima~r Machin~y chemic~s banks

vote 1,00 H 0.1888 1,00 lnrev 0.3496 0.3167 1,00 ultimateow~r0.1931 0.8452 0.2833 1,00 Machinery 0.0299 0.0268 0.1196 0.1293 1,00 chemicals 0.0586 0.0868 0.0470 0.0311 0.3203 1,00 banks 0.1360 0.1243 0.0361 0.0183 0.1886 0.1510 1,00

24-apr vote H lnrev ultima~r Machin~y chemic~s banks

vote 1 H 0.1508 1 lnrev 0.2422 0.3959 1 ultimateow~r0.1931 0.8504 0.3734 1 Machinery -0.0108 0.1071 0.0305 0.2417 1 chemicals 0.0783 0.0513 0.0616 -0.0223 -0.3015 1 banks 0.0949 0.1180 0.0540 0.0209 -0.1884 -0.1562 1

22-mei vote H lnrev ultima~r Machin~y chemic~s banks

vote 1,00 H -0.0063 1,00 lnrev 0.1385 0.3759 1,00 ultimateow~r0.0425 0.8610 0.3171 1,00 Machinery 0.1685 0.1222 -0.0047 0.2408 1,00 chemicals 0.2512 0.0781 0.1280 0.0058 -0.3211 1,00 banks -0.1474 -0.0497 -0.0159 -0.0598 -0.1701 -0.1490 1,00 _cons -4.998323 2.941718 -1.70 0.097 -10.93495 .9383043 banks 1.02963 1.075364 0.96 0.344 -1.140542 3.199802 chemicals .3592955 .749583 0.48 0.634 -1.153424 1.872015 Machinery .112823 .6807494 0.17 0.869 -1.260985 1.486631 ultimateow~r .5646771 1.063021 0.53 0.598 -1.580586 2.709941 lnrev .3829503 .1837674 2.08 0.043 .0120927 .7538079 H -.4970523 2.3369 -0.21 0.833 -5.213107 4.219002 vote Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 183.724388 48 3.82759142 Root MSE = 1.9259 Adj R-squared = 0.0309 Residual 155.787441 42 3.70922479 R-squared = 0.1521 Model 27.9369468 6 4.65615781 Prob > F = 0.2985 F(6, 42) = 1.26 Source SS df MS Number of obs = 49 . reg vote H lnrev ultimateowner Machinery chemicals banks

18 _cons -2.717798 2.642912 -1.03 0.310 -8.068092 2.632497 banks .7547426 1.338795 0.56 0.576 -1.955507 3.464992 chemicals .4549243 .8015163 0.57 0.574 -1.167661 2.077509 Machinery -.0621174 .8270988 -0.08 0.941 -1.736491 1.612257 ultimateow~r 1.046793 1.620159 0.65 0.522 -2.233048 4.326634 lnrev .2423087 .1839023 1.32 0.196 -.1299821 .6145995 H -1.429551 3.292628 -0.43 0.667 -8.095128 5.236027 vote Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = 2.0059 R-squared = 0.0921 Prob > F = 0.5025 F(6, 38) = 0.90 Linear regression Number of obs = 45 . regress vote H lnrev ultimateowner Machinery chemicals banks, vce(robust)

_cons -2.903774 2.750984 -1.06 0.298 -8.488568 2.68102 banks -.6958414 .6442917 -1.08 0.288 -2.003823 .6121403 chemicals .5395396 .7958126 0.68 0.502 -1.076046 2.155125 Machinery .0999361 .7897795 0.13 0.900 -1.503402 1.703274 ultimateow~r 1.818256 1.6266 1.12 0.271 -1.483916 5.120429 lnrev .2748151 .1990174 1.38 0.176 -.1292117 .6788419 H -4.067299 3.197124 -1.27 0.212 -10.55781 2.423208 vote Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust Root MSE = 1.8456 R-squared = 0.1453 Prob > F = 0.3314 F(6, 35) = 1.20 Linear regression Number of obs = 42 . regress vote H lnrev ultimateowner Machinery chemicals banks, vce(robust)

19 This is an overview of the OLS assumptions. The data used for this analysis is from the last regression. This regression is randomly chosen of the three regressions

Assumption 1: linearity of the model

The next graph is a visual presentation of the linearity of the model.

Assumption 2: The sample is randomly drawn of the population.

The data from this research is randomly downloaded from the days that were available. The three dates of the regression were randomly chosen of the available dates. Furthermore, the companies used in this research are cross industries. In contrary to other research on this topic, this research did not use companies with one common characteristic. For example, dual-class shares or a blockholder selling his shares.

0 2 4 6 8 1 0 0 .2 .4 .6 .8 H

20 Assumption 3: The mean of the residuals should be zero.

The next graph gives the spread of the residuals.

Assumption 4: homoskedasticity

The test for homoskedasticity gives a P-value higher than 0.05. This means homoskedasticity cannot be rejected. In other words, homoskedasticity can be assumed.

-2 0 2 4 R e s id u a ls .5 1 1.5 2 Fitted values Total 21.00 21 0.4587 Kurtosis 1.58 1 0.2088 Skewness 10.72 5 0.0571 Heteroskedasticity 8.70 15 0.8927 Source chi2 df p Cameron & Trivedi's decomposition of IM-test

21 Assumption 5: Normality of the residuals

-2 0 2 4 R e s id u a ls 0 2 4 6 vote 0 .2 .4 .6 D e n s it y -2 0 2 4 Residuals

22 The graph shows a histogram of the residuals with a density line. For normality the P value should be higher than 0.05. The p-value is smaller, so normality of the residuals is rejected.

residual 41 0.84654 6.183 3.839 0.00006 Variable Obs W V z Prob>z Shapiro-Wilk W test for normal data