Do M&A Rumors and Announcements Create Value in the Acquirer Stock?
– Insights From Extended CAR Analysis and Markov Switching
Abstract:
This paper studies the existence of both M&A rumor and M&A announcement returns with the cumulative abnormal return analysis, using several breakdowns to find factors that influence the abnormal returns. As extension, the Markov switching model is tested to see whether it is able to predict regime switches around the M&A rumor and announcement dates. The sample includes over 6,000 observations and focuses on M&A’s in the Euronext markets in the period from 2003-2015. M&A waves are also taken into account to search for differences in stock price movements between the M&A wave periods and the control period. This study finds positive significant cumulative abnormal returns on M&A announcements. Furthermore it finds that the Markov switching model is able to predict regime switches for M&A announcements due to an increased volatility. These are found to be significantly present. For the M&A rumors however, no significant volatility switches are found.
Student: Hylke G. Heeres Student number: 1910221
Program: MSc Finance (University of Groningen) Thesis supervisor: Dr. T.M. Katzur
Date: 13-06-2016
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I. Introduction
Merger and acquisition (referred to as M&A) rumors and announcements are expected to cause a price change in the acquirer company’s stock. A merger is defined as a process of combining the assets, cultural values and management practices of two separate organizations into a new entity and an acquisition is a business takeover, which is the process of buying out another business by taking over the ownership of the entity’s stock, equity interests or assets (Javidan, Pablo, Sing, Hitt and Jemison, 2004).
A share price is initially determined by supply and demand, which in their turn are determined by factors such as dividends, market movements and future economic prospects. The supply and demand of a share is also influenced by unexpected events, like M&A rumors and announcements which influence the future prospects of the firm. Since the post-transaction objective of M&A’s is that the new formed company is more competitive, more efficient and more profitable than either of the companies alone could have become (McBeath and Bacha, 2001), future prospects are expected to be improved. The information regarding the M&A rumor or announcement is becoming publicly available at a non-pre-specified moment, which makes it an unexpected event. This element of surprise forms the basis of the expected abnormal returns in the stock prices of the acquirer firm. In the current markets many hedge fund strategies are “event driven”, meaning that they intend to benefit from price movements caused by for example M&A’s (Jorion, 2008). This type of investors is speculating on whether M&A rumors will be converted into announcements or not and in what way they can benefit from this event.
3 Many previous studies on M&A announcement returns have the same starting point for the cumulative abnormal return analysis: known announcement dates which are tested for abnormal returns around these dates. However, the existence of M&A rumor returns is not extensively studied. Studies on M&A rumor and announcement returns focus on a pre-set period in which the returns are calculated and explained. But in these studies major changes of M&A activity over time are hardly taken into account. M&A activity changes over time, periods with more than normal M&A activity are called M&A waves. The economic history has been divided into these M&A waves (Vazirani, 2015). These waves typically follow cyclical patterns with at the beginning an intense activity of M&A’s and thereafter a period of fewer M&A’s. Vancea (2013) and Vazirani (2015) show that the last M&A waves of the European economy does not differ much from the last M&A waves in the United States of America (US). The last confirmed M&A wave was in the period of 2003-2007. After that wave a period of low M&A activity started, which ends in 2014 since the year 2015 shows highly increased M&A activity and is stated to be the start of a new M&A wave (Baigorri, 2016).
Andrade et al. (2001) used a restrained sample of acquisitions of public companies. They found insignificant negative abnormal returns for the acquirer firms around the announcement date of M&A’s. Although these results are insignificant, they point out that the sector of the acquiring company may be of influence on the abnormal returns. Moeller, Schlingemann and Stulz (2004) use other breakdowns, as they find positive significant abnormal returns over their entire sample. They find that abnormal returns for large firms tend to negative abnormal returns, in which small firms create positive abnormal returns. Following Moeller et al. (2004), the size of the company is a legitimate concern for the rumor and the announcement effect, they state that the event is less unexpected for large firms as for small firms. They also test for a breakdown on whether the targets are private or public, and find that private targets create higher abnormal returns than public targets.
4 that there are external (unexpected) events influencing the stock price, for example the M&A rumor or announcement. Gelman and Wilfling (2009) find, based on a sample of five large target companies, that the model is able to predict volatility switches.
I will study over 6,000 M&A rumors and announcements within the Euronext markets. A similar study, with both a cumulative abnormal return analysis on M&A rumors and on M&A announcements, plus the extension with the Markov switching model has not yet been done before. The extensions to the M&A rumor effects and with the Markov switching model may provide new insights for shareholders and investors. It can also provide extended motives and support for “event driven” hedge funds.
The cumulative abnormal return analysis will be performed over data from the period 2003 to 2015 and examines the M&A rumor and announcement returns. I have divided the sample into three different periods, of which two M&A waves (the years 2003-2007 and 2015) and a control period (the years 2004-2008). The control period is a period with normal M&A activity. The number of rumored and announced M&A’s is significantly higher in the M&A wave periods than in the control period. The increased M&A activity suggests that abnormal returns differ between the M&A waves and the control period. I make several breakdowns based on the findings of Andrade et al. (2001) and Moeller et al. (2004), which provides more insight on why M&A announcement returns differ so often between different M&A announcements. The breakdowns that I use are: on the acquirer’s market capitalization (size); on the capital intensity of the acquirers main operating sector; and on the acquirers main operating sector.
5 In this study, I find significant positive M&A announcement returns between 0.67% and 1.19% over the different time periods. I also find positive M&A rumor returns between 0.36% and 1.12%, but these returns are not significant. I do not find proof to conclude M&A rumor and announcement returns differ between M&A waves and the control period. However, I do find significant proof that firms with a smaller market capitalization (firm size) gain higher M&A announcement returns. For the breakdowns on different sectors and the capital intensity of sectors, I do not find significant results. With the Markov switching model I find significant volatility switches for the event window of M&A announcements. In the event window of M&A rumors, I do find some volatility switches, but not for enough events to claim that they are significantly present. The moment of the volatility switch proves to appear both before and after the known event date.
This thesis is organized into six sections. Following the introduction, in Section II existing literature and empirical evidence on this subject are discussed and reviewed in the search of a theoretical answer to this study. In Section III the used methodology is introduced as well as an elaboration of how the models are tested. Next, the used data and some descriptive statistics are shown, as well as the conducted analysis, after which the results are presented in Section V. Finally section VI provides a detailed discussion of the results and a conclusion to this study.
II. Literature review
6 Many studies focus only on the aspect of the existence of abnormal returns and their origin and little research is conducted with models that can find these abnormal returns themselves, like for example the Markov switching model. The basis often lies in an event study, for which detailed reviews are provided by MacKinlay (1997) and Binder (1998). Large amounts of literature (e.g. Andrade et al., 2001; Borges & Gairifo, 2013; Moeller et al., 2004; Rani, Yadav & Jain, 2013; Rani, Yadav & Jain, 2015; Savor & Lu, 2009) on the effects of M&A announcements on the stock prices of both the target and bidder firm is available, and limited literature (e.g. Gao and Oler, 2012) is available on the effects of M&A rumors on the stock price of target and bidder firms.
For M&A’s, the post-transaction objective is that the new formed company is more competitive, more efficient and more profitable than either of the companies alone could have become (McBeath and Bacha, 2001). This refers directly to the incentive of the M&A. Economic theory has provided many possible reasons, such as: increasing profitability, competitiveness, and efficiency, improving economies of scale or by taking advantage of opportunities for diversification. Campbell, Sirmon and Schijven (2016) argue that M&A’s represent one of the key strategic actions that managers can undertake to improve or sustain their firm’s performance. The main driver of M&A’s may not be exactly the same over several industries, but part of it always remains as mentioned above, that the acquiring company together with the acquired company, or the both of them in a merger, are to achieve more competiveness in the market. If this target is achieved, their position in the market is expected to improve and with that, they probably reach the goal of realizing earnings growth (McBeath and Bacha, 2001).
7 around the announcement date of an M&A. It is possible to expect the abnormal returns both before and after the actual announcement date.
In the past decades the number of M&A’s has been increasing. This fact together with the expected value creation makes M&A’s the main subject in many papers. In the previous paragraph I described the incentive and goals of M&A’s which result in expected abnormal returns on the acquirer company’s stock around both the M&A’s rumor and announcement dates. The expected abnormal returns around the announcement date of M&A’s are widely studied, but there are differences in the outcomes.
Rani et al. (2013) studied whether there are abnormal returns around the announcement date of a M&A for 623 Indian companies in the period of 2003-2008, and Bassen, Schiereck and Wübben (2010) studied a sample of cross border M&A’s in which German firms takeover firms from the US. In contradiction to the results of Andrade et al. (2001), Rani et al. (2013) find that shareholders of acquiring Indian corporations experience a significant positive abnormal return on the announcement day. They also find a significant cumulative average abnormal return on a multi-day event window for the one percent level. For the five day event window they find a cumulative average abnormal return of 2.07%. Rani et al. (2013) have used different event windows to find which event window yields the highest cumulative abnormal returns. They find that an event window of five days provides the highest significant result. This five day event window accounts for two days prior to the event, the event date, and two days after the event. Bassen et al. (2010) however, find only in a three day event window a significant positive abnormal return of 1.16%. During this period the sample still consists of extreme values of positive and negative cumulative abnormal returns. The difference may be explained by the fact that Bassen et al. (2010) use a dataset of cross border M&A’s. In most cases still an abnormal return is generated but the successes are more scattered and might even create significant negative abnormal returns.
8 total abnormal returns that are realized before the actual announcement date. Borges and Gairifo (2013) find that there are significant cumulative abnormal returns in advance of the acquisition announcement, and that they account for 29.39% of the total abnormal returns resulting from the announcement. These data are suggesting that there may be an impact on the returns already from a rumor or information leakage in advance of the announcement.
Gao and Oler (2012) studied the rumors and the incentives to sell target stocks before the actual announcement of an acquisition. They state that selling stocks before the takeover announcement exposes traders to a considerable risk, rational investors therefore will engage in selling only if there is a compensation for this risk. The risk is that a rumor increases the price of a share, but this price may further increase when the rumor converts in an actual announcement. However, when the rumor does not convert into an announcement, the price is expected to be back at its pre-rumor level over a 70-trading day period after the initial price jump (Gao and Oler, 2012). This suggests that selling just after a rumor may be profitable. However, the investors then risk not gaining the extra abnormal return that may be realized if the rumor is converted into an actual announcement. Gao and Oler (2012) find that it is profitable for sellers to short the target stock right after the rumor, for this reason the seller can benefit from both a conversion into an actual announcement as if no announcement follows up the rumor. These results of Gao and Oler (2012) provide a theoretical and empirical backing to test for abnormal returns around the rumor date.
During the economic history, M&A’s have shown to follow a trend in the form of so-called M&A waves. Following Vancea (2013) and Vazirani (2015), economic history can be divided in M&A waves. Vazirani (2015) puts emphasis on the US economy and Vancea (2013) on the European economy. The last M&A wave that created economic expansion according to Vancea (2013) and Vazirani (2015) took place from the year 2003 up to and including 2007. This wave occurred simultaneously in the US economy and the European economy. In Europe the M&A waves only started after 1960, when increasing interdependence of economies favored the concentration movement (Vancea, 2013).
9 wave period. According to the findings of Vazirani (2015) and Vancea (2013) the M&A waves show different perspectives for M&A’s. The suggestion of different perspectives provides a set-up for this study, to test for differences in M&A rumor and announcement returns between the M&A waves and a control period.
Savor and Lu (2009) limited their sample to public companies only. Their results show significant negative abnormal returns, which is more in line with the results of Andrade et al. (2001). The results of Andrade et al. (2001) are backed by Moeller et al. (2003), and they find through a breakdown of their sample that on average public companies are more likely to generate negative abnormal returns around the announcement date of M&A’s. But not only is the origin of the company an important factor, Moeller et al. (2003) find that firm size also has a major influence on the abnormal returns of M&A announcements. Their study suggests that larger firms on average generate negative abnormal returns and smaller firms generate positive abnormal returns.
10 The empirical results, as described in this section, are the initiative for the hypotheses that I will be testing in this study. The hypotheses are divided into two parts, firstly the hypotheses to the standard cumulative abnormal return analysis and thereafter the hypotheses to the breakdowns and Markov switching model.
1a/b. An abnormal return in the acquirer stock is realized around the rumor/announcement
date of an M&A.
2a/b. During M&A waves, the realized abnormal returns created by M&A
rumors/announcements differ from the realized abnormal returns in the control period.
The following null hypotheses are for the breakdowns of the standard cumulative abnormal return analysis and the Markov switching model:
3. Realized abnormal returns due to M&A announcements differ between acquirer companies operating in different sectors.
4. Realized abnormal returns due to M&A announcements differ between acquirer companies due to the size of their market capitalization.
5. Realized abnormal returns due to M&A announcements differ between acquirer companies that are grouped for the capital intensity of the sector they operate in. 6a/b. The Markov switching model predicts a regime switch to a high volatility state around
the rumor/announcement date of M&A’s
7. The regime switch predicted by the Markov switching model, occurs directly after the event.
III. Methodology
11 returns in the form of an event study is discussed, next the econometrics of the Markov-switching model are discussed.
Event study method
MacKinlay (1997) discusses the most common models used in event studies to calculate abnormal returns in stock prices, these are the Constant mean return model and the Market return model. I will be using the Market return model in the event study part of this study. The advantage over the Constant mean return model is the adjustment for market returns by removing the market related share of return, this reduces the variations in abnormal returns (MacKinlay, 1997). The abnormal returns are expected to be normally distributed with a zero mean. Since the market return model assumes a “stable linear relation between the market return and the security return” (MacKinlay, 1997, p.15), I can test whether there are abnormal returns around the announcement or rumor date of M&A’s. The Market return model calculates the abnormal return for security i at time τ, ARiτ,
as
ARiτ = Riτ – α̂i – β̂iRmτ, (1)
where Rmτ is the market return at time τ, Riτ is the return of security i at time τ with the
calculation for returns as 𝑅τ = 𝑃τ
𝑃τ−1− 1, (2)
where 𝑃τ is the stock price at τ and 𝑃τ−1 is the stock price at τ-1. The abnormal return is
further dependent of two parameters, the beta of security i with the market return and alpha. The parameter alpha, α̂I, is calculated as
α
̂i = µ̂i – 𝛽̂i µ̂m, (3)
and the parameter beta, 𝛽̂i, is calculated as
𝛽̂𝑖 =∑ (𝑅𝑖𝜏−µ̂𝑖)(𝑅𝑚𝜏−µ̂𝑚)
𝑇1 𝜏=𝑇0+1
12 where µ̂𝑖 is the mean return of security i calculated over the estimation window and µ̂𝑚 is
the mean return of the market measured in the estimation window. The mean return of the security, µ̂𝑖, and the mean return of the market, µ̂𝑚, are calculated as
µ̂𝑖 = 1/𝐿1∑𝑇1 𝑅𝑖𝜏
𝜏=𝑇0+1 , (5)
and
µ̂𝑚 = 1/𝐿1∑𝑇1 𝑅𝑚𝜏
𝜏=𝑇0+1 , (6)
where L1 represents the number of days that are in the estimation window, which is 244.
Formula’s (1) up to and including (5) represent the Market return model for the purpose of calculating abnormal returns. With the abnormal returns calculated for the event windows, the cumulative abnormal return (CAR) can be calculated as
𝐶𝐴𝑅𝑖(𝜏1, 𝜏2) = ∑𝜏2 𝐴𝑅𝑖𝜏
𝜏=𝜏1 , (7)
which shows that the CAR is the sum of the abnormal returns in the event window for security i. With the calculation of the CAR’s per security, the cumulative average abnormal return (CAAR) can be calculated as
𝐶𝐴𝐴𝑅𝜏1,𝜏2 = 1
𝑁∑ 𝐶𝐴𝑅𝑖 𝑁
𝑖=1 , (8)
which is the weighted average of the CAR’s.
When arriving at the CAR and CAAR values, the hypotheses still have to be tested. In order to define which statistical test is appropriate to test for significance of the results, first the CAR’s have to be tested for normality. To test for the normality of the CAR’s the Shapiro Francia test will be used in this study, since the number of observations of four out of the twelve variables are larger than 2,000. The Shapiro Francia test with the log transformation is a suitable test for normality, since it is valid for sample sizes from 10 ≤ n ≤ 5000 with n as the number of observations.
Markov switching model
13 with i as the state, of which follows that there are m regimes. This assumption states that the depending variable, 𝑦𝑡, switches regime due to an unobserved external event at time t
which is denoted by 𝑠𝑡. The model is built in such a way, that the probability distribution of
the state at any time t, depends only on the state in time t-1 (Brooks, 2014). The model allows for multiple switches over time. A switch shows a noticeable change in the volatility of the stock price, which is assumed to be caused by an external event. The stock returns are adjusted for the market movements and are calculated with formulas (1), (2) and (3). The same calculations as for the event method, but in this case the returns are calculated for the whole sample instead of the estimation and event windows.
The Markov switching model is applied to the daily stock returns adjusted for market movements, the model is expected to predict the moment when the volatility switches occur. These switches may be caused by for instance the rumor or announcement of a M&A. The Markov switching model uses an estimation specification for the calculation, which is
𝑦𝑡 = 𝜇𝑠𝑡+ 𝜖𝑡, (9)
where 𝑦𝑡 is the adjusted stock return, 𝜇𝑠𝑡 is the mean for 𝑠𝑡, (𝑠𝑡 = 1, 2), which are the two
states that follow a standard 2-regime Markov process. And 𝜖𝑡 indicates the standard deviation or sigma, which indicates the low and high volatility states. The outcome of the sigma provides information to distinguish whether state 1 or state 2 is the high volatility state, which can differ between each stock. The Markov switching model also provides information about the expectations of switches, which is the probability of being in state 𝑠𝑡
provided that the system was in state 𝑠𝑡−1 in the previous period. This is econometrically
shown by
𝑝𝑟𝑜𝑏[𝑧𝑡 = 1|𝑧𝑡−1 = 1] = 𝑝11 (10)
𝑝𝑟𝑜𝑏[𝑧𝑡 = 2|𝑧𝑡−1 = 1] = 1 − 𝑝11 (11)
𝑝𝑟𝑜𝑏[𝑧𝑡 = 2|𝑧𝑡−1 = 2] = 𝑝22 (12)
𝑝𝑟𝑜𝑏[𝑧𝑡 = 1|𝑧𝑡−1 = 2] = 1 − 𝑝22 (13)
where 𝑝11 and 𝑝22 are the probabilities of being in state 1, respectively 2, given that the
14 being in state 2, given that the system was in state 1 in the previous period and 1-𝑝22 is the
probability of being in state 1, given that the system was in state 2 in the previous period. Stock returns are expected to remain in the low volatility state until the stock is influenced by an unexpected event, then a temporary switch to the high volatility switch is expected
IV. Data
This section describes the data that I used in this study. Firstly I discuss the sample and the requirements that are used to delimit the sample. Thereafter a further analysis of the data is given, in which I show how limitations of the dataset are solved and finally I provide the descriptive statistics. In this analysis I have used two different data sources: Zephyr for the necessary company information, the historical information on M&A’s and the M&A rumor and announcement dates; and Datastream for the daily stock returns of the acquirer stocks in the defined time periods.
The central dependent variable in this study is the return in excess of the normal returns adjusted for market movements, called the abnormal return, around the rumor and the announcement date of M&A’s. The basis for the calculation of these abnormal returns are the day-to-day closing stock prices and the day-to-day closing prices of the indices. In this study, MacKinlay (1997) is followed for the event study regarding the abnormal returns. The Markov switching model is executed in accordance with Gelman and Wilfling (2009) and Brooks (2014).
15 period. For the selection of data only mergers and acquisitions were included in the sample with the requirement that they were announced officially. But after the announcement the M&A may have been a success, failure or not yet been executed. For further selection of the sample, I focused on the four Euronext markets, being the Belgian, Dutch, French and the Portuguese stock markets. The largest stock indices from these countries are respectively the BEL 20, the AEX, the CAC 40 and the PSI 20. I selected M&A with the requirement that the acquirer stock is listed on one of the Euronext markets to ensure that they are following the M&A waves as Vancea (2013) and Vazirani (2015) describe.
For each selected firm, I extracted the daily closing stock prices regarding the corresponding time period. Subsequently I collected the daily closing prices of the AEX, CAC 40, BEL 20 and the PSI 20. These indices are being used to calculate the beta to adjust the daily returns for market movements. The event date is the identified date of the rumor or announcement in either of the cases. In those cases that this date was on a non-trading day, the first following trading day is allocated as the event date. I use two different event windows to find out whether abnormal returns are present and if it influences the significance of the results. These event windows, backed by the results of Borges and Gairifo (2013) for the use of both days prior and after the event, are an eleven-day event window, five days prior and five days after the event date, and a five-day event window, two days prior and two days after the event date. For the calculation of abnormal returns, an estimation window is necessary to calculate the mean return on each stock. The estimation window I used is from 250 trading days prior to the event until 6 trading days prior to the event, which sums up to 244 trading days that form the estimation window.
16 the event window of the rumor, overlapped with the event window of the announcement. For these cases I removed the stocks from the rumor sample in order to avoid biased results.
The final samples, after adjusting them for errors and inconsistencies, are shown in Table 1 in numbers of observations, where they are shown for six combinations of time periods and event. The samples of the three time periods total up to 6,298 M&A’s that are included in the samples.
Table 1 - Overview of the main subsamples for the event study
This table represents the subsamples for the event study, the number of observations of each subsample is shown. Further it is shown how the subsamples are divided over the different events and time periods with the number of observations.
Event Time period Number of observations
Announcement 2003-2007 2,784 Announcement 2008-2014 3,120 Announcement 2015 394 Rumor 2003-2007 560 Rumor 2008-2014 660 Rumor 2015 68
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Table 2 – Descriptive statistics based on the main sector of the acquirer company
This table contains the descriptive statistics based on the main sectors of the acquiring company for the three time periods: 2003-2007, 2008-2014 and 2015. The frequency is the number of companies operating in that sector and percent is the percentage for which the sector is represented in the subsample.
2003-2007 2008-2014 2015
Acquirer main sector Frequency Percent Frequency Percent Frequency Percent
Banks 163 5.85% 123 3.94% 9 2.28%
Chemicals, rubber, plastics,
non-metallic products 214 7.69% 225 7.21% 40 10.15%
Construction 119 4.27% 95 3.04% 10 2.54%
Education, Health 17 0.61% 19 0.61% 4 1.02%
Food, beverages, tobacco 143 5.14% 131 4.20% 17 4.31% Gas, Water, Electricity 82 2.95% 71 2.28% 18 4.57% Hotels & restaurants 30 1.08% 16 0.51% 4 1.02%
Insurance companies 70 2.51% 63 2.02% 8 2.03%
Machinery, equipment,
furniture, recycling 474 17.03% 618 19.81% 58 14.72% Metals & metal products 78 2.80% 66 2.12% 10 2.54% Other services 839 30.14% 1,111 35.61% 139 35.28% Post and telecommunications 133 4.78% 119 3.81% 12 3.05% Primary Sector (agriculture,
mining, etc.) 61 2.19% 67 2.15% 9 2.28%
Publishing, printing 144 5.17% 131 4.20% 25 6.35% Textiles, wearing apparel, leather 13 0.47% 19 0.61% 1 0.25%
Transport 26 0.93% 31 0.99% 6 1.52%
Wholesale & retail trade 153 5.50% 189 6.06% 21 5.33%
Wood, cork, paper 25 0.90% 26 0.83% 3 0.76%
Total 2,784 100% 3,120 100% 394 100%
Table 3 – Descriptive statistics based on the market capitalization of the acquirer company
This table provides the descriptive statistics based on the market capitalization of the acquiring company for the three time periods: 2003-2007, 2008-2014 and 2015. The mean is the average size of the acquirers market capitalization, the median is the mid-point acquirers’ market capitalization. The minimum and maximum are respectively the smallest and the largest acquirers’ market capitalization.
2003-2007 2008-2014 2015
Mean € 24,252,922.54 € 24,172,357.91 € 31,723,943.06 Median € 2,713,082.79 € 3,300,652.09 € 2,913,154.71 Maximum € 328,046,647.82 € 328,046,647.82 € 328,046,647.82 Minimum € 640.02 € 450.00 € 4,545.62
18 of the size of market capitalization on the abnormal returns will be tested. The main statistics for the samples regarding the market capitalization of the acquirer firms are shown in Table 3. The mean of the market capitalization is clearly higher than the median, this observation indicates that the number of firms with a smaller market capitalization in the sample is higher than the number of firms with a larger market capitalization. This observation can also be interpreted as that the possible abnormal returns of smaller firms are of a higher influence on the abnormal returns of the entire dataset. The actual influence of the size of the market capitalization to the abnormal returns is tested in this study.
For the use of the data in the Markov switching model however, the data is not selected for the rumor and announcement date, but a subsample is taken from the main sample based on the time period. This subsample contains 55 entities, as shown in Table 1 Appendix A, which are selected for having at least one rumor and announcement in 2015 with at least 30 days between the rumor and announcement date. I made this distinction to ensure that the official rumor and announcement date cannot influence each other in the Markov switching model, or that the switch of both the events overlaps causing biased results. I have chosen to perform the Markov switching model on the most recent M&A rumors and announcements to decrease the possibility of earlier research on the same dataset with the same econometric model. Also the Markov switching model is showing the best results if it is carried out on one entity at a time, in this case for the 55 entities with an M&A rumor and announcement in the year 2015.
V. Results
19 Further the results of the Markov switching model will be tested and shown to find out whether the model is capable of predicting the rumor and announcement dates of M&A’s.
Event study
For the event study, the returns and abnormal returns are calculated following formulas (1) and (2), after which the cumulative abnormal returns are calculated using formula (7). The Shapiro Francia test for normality, tests whether the data are normally distributed. The results for all sample variables concerning the cumulative abnormal returns show significant results rejecting the null hypothesis, therefore the CAR’s are non-normally distributed. In further testing, models that do not assume normality are used on the samples. The daily CAAR’s (means) of the cumulative abnormal returns per period and for both the rumor date and announcement date are shown in Table 4. They show positive CAAR’s for all twelve variables, which suggests that both the rumor and announcement of a M&A have a positive effect on the stock return.
Table 4 – Cumulative average abnormal returns for subsamples
This table reports the daily CAAR (mean) of each subsample regarding both the five and the eleven day event windows. The mean is calculated with formula’s (1) up to and including (8) as described in the methodology section. The min and max are the minimum and maximum values of the CAR’s for each event window and time period. In this table the seventh column represents the z value of the Wilcoxon sign rank test that is used as the appropriate test, assuming non-normally distributed data, the last column shows the corresponding probabilities. The significance of the CAAR’s is denoted as follows: * significant at the 10% level, ** significant at the 5% level, *** significant at the 1% level.
Variable Number of obs. Mean Std. Err. Min Max z Prob > |z|
20 The positive CAAR’s are significant for most of the announcements of which four at the 1% level. This means that M&A announcements indeed are an unexpected event that influence the stock returns creating positive abnormal returns. This result is in line with the findings of Rani et al. (2013), Borges and Gairifo (2013) and Bassen et al. (2010), who also find positive and significant CAAR’s around the announcement date of M&A’s. For the rumor of M&A’s the CAAR’s are positive as well, but the results are only significant for the sample of 2015. This result suggests that the impact of M&A rumors is not similar to the impact of M&A announcements, which is in line with the minimum and maximum values of both events. The minimum values are in a similar fashion for both the announcements and rumors, the maximum values of the announcements are higher for all time periods and event windows. With these results hypothesis 1b is accepted, since the majority of the results show significant CAAR’s for the event window of the M&A announcement. Hypothesis 1a has to be rejected. I expected a positive and significant CAAR for the event window of the M&A rumor, but the results are insignificant. Therefore I cannot accept the hypothesis that M&A rumors cause positive abnormal returns. The conclusion using the cumulative abnormal return model is that M&A announcements do and M&A rumors do not have (positive) impact on the stock returns.
21 and 2b are rejected since there is sufficient evidence to proof that there are no differences in the abnormal returns of M&A rumors and announcements between the M&A wave periods and the control period. This result indicates that the M&A waves are only increased M&A activity, which does not have influence on the abnormal returns that appear around the announcement of M&A’s. This result is an interesting addition to the studies of Vazirani (2013) and Vancea (2015).
Table 5 – Results of the test for differences in the CAR’s between the M&A waves and control period.
This table reports the results of the Wilcoxon rank sum test in comparing the CAR’s of the M&A waves with the control periods for both the M&A rumors and announcements. The means of each subsample represent the daily means where mean 1 represents the mean of variable 1 and mean 2 represents de mean of variable 2. The sixth column represents the z value of the Wilcoxon rank sum test after which the probabilities are shown in column seven. The input for this test was that the CAR’s of variable one are equal to the CAR’s of variable two. The significance is denoted as follows: * significant at the 10% level, ** significant at the 5% level, *** significant at the 1% level.
Variable comparison Variable 1 Variable 2 mean 1 mean 2 z Prob > |z|
Rumors 5day 2003-2007 to 2008-2014 2003-2007 2008-20014 0.36% 0.60% 0.158 0.8748 5day 2008-2014 to 2015 2008-2014 2015 0.60% 0.97% -0.347 0.7288 11day 2003-2007 to 2008-2014* 2003-2007 2008-20014 0.45% 0.70% 1.696 0.0899 11day 2008-2014 to 2015 2008-2014 2015 0.70% 1.12% 1.310 0.1902 Announcements 5day 2003-2007 to 2008-2014 2003-2007 2008-20014 0.72% 0.82% 0.088 0.9299 5day 2008-2014 to 2015 2008-2014 2015 0.82% 0.94% -0.839 0.4015 11day 2003-2007 to 2008-2014 2003-2007 2008-20014 0.67% 1.19% 0.190 0.8494 11day 2008-2014 to 2015 2008-2014 2015 1.19% 0.71% -0.317 0.7514
22 At first I have divided the subsample in four quartiles as shown in Table 6, each quartile represents approximately 25% of the sample’s companies. The results show significant results for the differences between the first and fourth quartile, the second and fourth quartile and the third and fourth quartile. This means that the CAR’s of companies with a market capitalization below 15 million differ significantly from the CAR’s of companies with a market capitalization larger than 15 million. Therefore hypothesis four is accepted, which is in line with the results of Andrade et al. (2001) and Moeller et al. (2004). The conclusion to this result is that smaller firms on average have higher CAR’s than larger firms, which suggests that the event is less unexpected for larger firms than for smaller firms.
Table 6 – Test results on differences between the CAR’s for the size of acquirer market capitalization
This table presents the test results for the Wilcoxon rank sum test, in which the companies with M&A announcements in the time period 2015 are grouped into four quartiles of the subsample, each quartile is compared to the other quartiles. The quartiles are created as such that each quartile represents approximately 25% of the number of companies in the subsample. The mean represents the daily CAAR’s for each market capitalization group and the probabilities represent the probability that the groups have similar CAR’s. The significance of mean shows the probability of the means. The significance is denoted as follows: * significant at the 10% level, ** significant at the 5% level, *** significant at the 1% level.
Prob > |z| Prob > |z| Prob > |z|
Significance of mean 2015 Market Cap group (quartiles) mean Second Third Fourth Prob > |z| First: < 0.3 mln 1.58%*** 0.4751 0.1117 0.0006*** 0.0052 Second: > 0.3 mln and < 2.5 mln 1.79% 0.7374 0.0560* 0.1826 Third: > 2.5 mln and < 15 mln 0.75% 0.0873* 0.1952
Fourth: > 15 mln -0.56% 0.1406
23
Table 7 – Test results on differences in the CAR’s of various sectors
This table reports the results of the Wilcoxon rank sum test of comparing the CAR’s of the different sector groups for the M&A announcements for the time period of 2015. The classification of the sectors into groups is shown in Appendix A Table 2. The daily means of each subsample are denoted after which the probabilities are shown, the input for this test was that the CAR’s of group # are equal to the CAR’s of group #. The significance of mean shows the probability of the means. The significance is denoted as follows: * significant at the 10% level, ** significant at the 5% level, *** significant at the 1% level. Prob > |z| Prob > |z| Prob > |z| Significance of mean
2015 Sector group mean 2 3 4 Prob > |z|
1 1.06%** 0.0987* 0.5073 0.2983 0.0126
2 0.90% 0.0917* 0.6595 0.9339
3 1.23%* 0.1513 0.0577
4 0.02% 0.5382
For the third case, the subsample is divided into two sector groups, one with high capital intensity (group 1) and one with low capital intensity (group 2). The positive CAAR of the sector group with low capital intensity is significant, but the CAAR of the sector group with high capital intensity is not, the results are presented in Table 8. The comparison does not provide significant results, therefore hypothesis five must be rejected and I assume that the capital intensity of the operating sector does not influence the CAR’s of the announcement of M&A’s.
Table 8 – Results of the test for differences in the CAR’s of sectors classified for capital intensity
This table reports the results of the Wilcoxon rank sum test in comparing the CAR’s of the companies classified into groups based on their main sectors’ capital intensity for the M&A announcements of the time period 2015. The daily means of each subsample are shown, as well are their probabilities in the last column. The calculated probability of the Wilcoxon rank sum test is shown in the third column. The significance of mean shows the probability of the means. The significance is denoted as follows: * significant at the 10% level, ** significant at the 5% level, *** significant at the 1% level.
Prob > |z|
significance of mean 2015 Sector capital intensity mean 2 Prob > |z| 1: High capital intensity 0.86% 0.1958 0.6187 2: Low capital intensity 0.85%** 0.0123
Markov switching
24 market returns. The adjusted returns are calculated over the stock data of 55 companies that rumored and announced M&A’s in the year 2015, using formula’s (1) up to and including (6). The adjusted returns are tested with the Markov switching model for regime switches in the year 2015.
The Markov switching model generates for each stock the mean and sigma for the two states that the stock can persist in, as econometrically shown in formula (9), 𝑦𝑡 = 𝜇𝑠𝑡+ 𝜖𝑡. The states are a high and a low volatility state which I determine using the sigma of the
Markov switching model. A stock that is in the state of the low sigma, is in a low volatility state. This low volatility state is known as the state of normal activity in which there are small fluctuations in the stock price that are not caused by unexpected (external) events. The model also predicts the probability of the stock remaining in the current state the next period or expecting a switch, as shown in formula’s (10) up to and including (13) in the methodology section. The coefficients per stock are shown in Appendix B Table 1. With the test I generated a data string per stock for each day of the probability that the stock is in state one. This data string shows the probabilities, rounded to a whole number, of either being in state one with probability one or probability zero. A plot of these probabilities provides a better view of the regime switches, therefore I added as an illustration the data of two companies, both in the form of a table and in two figures (Figure 1 and figure 2).
25
Table 10 – Results of the Markov switching model for Microsoft and Cisco Systems
This table presents an example of the results of the Markov switching model for two out of the 55 companies, this example
is to provide an illustration of the test results over the whole sample. The model uses formula (10): 𝑦𝑡= 𝜇𝑠𝑡+ 𝜖𝑡, the daily
mean return in this table is represented by 𝜇𝑠𝑡 in the formula and is shown in column two and three. The sigma is
represented by 𝜖𝑡, in which state one is the low volatility state and state two is the high volatility state. P11 and P21
represent respectively the chance of being in state one given that the stock was in state one in the previous period and the chance of being in state one given that the stock was in state two in the previous period. The last four columns represent the test results of the Wald test, which tests whether the means and sigma’s of state one and state two are significantly different from each other. The level of significance is denoted as follows: * significant at the 10% level, ** significant at the 5% level, *** significant at the 1% level.
Mean Sigma Mean state 1 = mean state 2 Sigma state 1 = sigma state 2 Company
name State 1 State 2 State 1 State 2 P11 P21 Chi^2 p Chi^2 p
Microsoft -0.04% 0.40% 1.03% 43.43% 0.9608 0.4027 0.22 0.6417 64.49 0.0000*** Cisco
Systems 0.01% -0.06% 0.95% 2.59% 0.9720 0.1733 0.02 0.8801 25.37 0.0000***
In Figure 1 and Figure 2 the probabilities of being in state one are plotted for the same entities as that are shown in table 10, respectively Microsoft and Cisco systems. As Table 10 proves, state one is the low volatility state.
26
Figure 1 – Plotted probabilities of being in state 1 for Microsoft
This figure shows the plotted probabilities of being in state one, the low volatility state for Microsoft. The magenta colored vertical line (the first straight vertical line), represents the event date of the M&A rumor, the red colored vertical line (the second straight vertical line), represents the event date of the M&A announcement.
In Figure 2, the red vertical lines (last two straight vertical lines) are the two dates of two different M&A announcements, the magenta colored vertical lines (first two straight vertical lines) are the two dates of two different M&A rumors for two different M&A’s. For both the M&A rumors no clear switch is visible in the plotted probabilities, but for both M&A announcements a clear switch is visible. The first M&A announcement already shows a clear switch before the actual announcement, and the second switch appears on the event date. The plot shows more possible switches which cannot be explicitly attributed to this M&A rumor or announcement, these switches are expected to be occurring due to other unexpected external events influencing the stock price of Cisco systems.
27
Figure 2 – Plotted probabilities of being in state 1 for Cisco systems.
This figure shows the plotted probabilities of two different M&A rumors and announcements of being in state one for Cisco systems. In this plot, state one is the low volatility state. The magenta colored vertical lines (the first two straight vertical lines), represent the event date of the two M&A rumors, the red colored vertical lines (the last two straight vertical lines), represent the event dates of the two M&A announcements.
The outcomes of the Markov switching model show various results in the prediction of both the rumor and the announcement of M&A’s. In addition to Table 1 Appendix B, Table 2 Appendix B provides the probabilities of whether state one differs significantly from state two for both the means and volatilities. These results are generated using the Wald test and they are used to test for hypotheses 6a and 6b. For 30 of the 55 M&A rumors, a clear switch is recorded in a five day event window, whereas for 25 M&A rumors no clear switch is visible in a five day event window around the rumor date. Therefore I cannot accept hypothesis 6a that the Markov switching model shows a clear regime switch from low to high volatility around the rumor date of M&A’s. On the other hand, for 41 out of the 55 M&A announcements a clear switch to a high volatility state is recorded in a five day event window. This result provides enough evidence to accept hypothesis 6b that the Markov
28 switching model is able to predict the announcement date of M&A’s with showing a volatility switch in the results. With the results to hypotheses 6a and 6b, I will be testing hypothesis seven only for the significantly present switches of both the rumor and announcement dates.
To test for hypothesis seven, I have studied the outcomes of the Markov switching model for whether the switches that the model did show appeared before the actual event date, or directly after the event date. Out of the 71 observations that show a switch around the event date, there are 41 around the announcement and 30 around the rumor date. Of the totals, 27 switches appear directly after the event date and 44 switches appear before the event date. These results do not provide enough evidence to give a conclusive answer to hypothesis seven, but they do suggest that using an event window with days prior and post the event date for the cumulative abnormal return analysis is correct.
The results of the Markov switching model can also be interpreted in a broader way, by not limiting the results to the event window. In some occasions, the results show a switch on a different date close to the assumed event date when there is no switch in the event window. In my opinion, these findings suggest that the known dates, especially for the M&A rumors, may be provided incorrectly by Zephyr. The moment that a rumor comes out may be documented incorrectly, and it may be very difficult to set the rumor at a specific date. This result is particularly important for the cumulative abnormal return model, since a set event window based on the provided event date is used. The results also show that since the switch appears in some cases before the event date, in quite some cases information is leaked right before the official M&A announcement. Assuming the official announcement date is documented correctly.
VI. Conclusion
29 announcements of M&A’s are successfully predicted with the Markov switching model. The announcements and rumors of M&A’s are tested with the standard cumulative abnormal return analysis for abnormal returns within M&A waves and a control period. In the M&A waves significantly more M&A’s occur per year than in the control period, and this study has tested whether there are different rumor and announcement returns on the stocks between those periods. Further tests are performed to test for differences in the announcement returns between sectors, the capital intensity of sectors (high or low) and for the size of the market capitalization of the acquirer company. For these tests a subsample is used, concerning the financial data of M&A’s in the year 2015 as the most recent data. A subsample of 55 of the most recent M&A rumors and announcements is used for the Markov switching model to ensure that the rumor and announcement do not influence each other.
I find that there are significant CAAR’s around the announcement of M&A’s between 0.67% and 1.19%. These findings are backed by the results of the tests with the Markov switching model, this model is proved to be able to predict volatility switches around the majority of the M&A announcements.
For the rumors of M&A’s however, positive insignificant CAR’s are found, which is in line with the results from the Markov switching model. In the Markov switching model, volatility switches around the rumor date of M&A’s were found for just over half of the subsample. This finding suggests that in some cases the stock prices react to M&A rumors, but this result is not significant. There are two possible conclusions for this result: either the M&A rumor has not a significant impact on the stock price, or the available rumor dates are incorrect. Since the determination of the exact rumor date can be very difficult, my opinion is that there may be flaws in these available dates, also since there are other volatility switches in the stock data which may be caused by a rumor about the M&A.
30 results are found to state that the CAR’s between sectors differ, both divided in sector groups and for another test grouped by capital intensity of the sectors. Finally, since the size of the market capitalization does have influence on CAR’s of the M&A announcements, I can conclude that the CAR’s of the companies with a market capitalization of under 15 million euro differ from the CAR’s of companies with a market capitalization of over 15 million euro. With this result, I can state that information on M&A’s for larger companies is less unexpected than information on M&A’s of smaller companies. This result is also supported by the fact that larger companies are tracked more closely by both media and shareholders.
The results that I have found are mostly in line with existing literature on these subjects, as most studies find abnormal returns around the announcement of M&A’s. In previous literature however, studies on different sectors show differences in the percentage of the CAAR’s. This observation is not confirmed in this study since no significant differences between the CAR’s of the sectors are found. In previous literature the Markov switching model has proven to predict the volatility switch of large M&A’s. I confirm these findings and extended it to smaller firms and a larger sample. The Markov switching model can be used as a statistical tool to find volatility switches in stock prices, but unfortunately the model itself cannot assign these switches to a specific event at all time.
31 A different approach is a follow-up study in finding the effects of M&A rumors and announcements on option trading of those stocks. Since the results of the Markov switching model show significant volatility switches around some rumor dates and most of the announcement dates, this increased volatility of the stock prices is interesting for trading with derivatives like options and for “event driven” hedge funds. A combination of testing with the Markov switching model and using a similar approach as Gao and Oler (2012), may result in interesting results regarding option trading around M&A rumors and acquisitions.
References
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32 Gao, Y., Oler, D., 2012. Rumors and pre-announcement trading: why sell target stocks before acquisition announcements? Review of Quantitative Finance & Accounting 39, 485-508.
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Appendix A – ‘Descriptive statistics’
Table 1 – Descriptive statistics Markov sample
This table shows the descriptive statistics for the subsample of 55 companies that are used in the Markov switching model, the statistics contain the frequencies of the industries that are represented in this subsample, as well as the percentage of the total each sector is. After that, the average, median, minimum and maximum values are shown for the market capitalization of the companies in this subsample.
Industry Frequency Percent
Banks 3 5.45%
Chemicals, rubber, plastics, non-metallic products 3 5.45%
Food, beverages, tobacco 6 10.91%
Gas, Water, Electricity 2 3.64%
Hotels & restaurants 2 3.64%
Insurance companies 4 7.27%
Machinery, equipment, furniture, recycling 10 18.18%
Metals & metal products 2 3.64%
Other services 12 21.82%
Post and telecommunications 2 3.64%
Primary Sector (agriculture, mining, etc.) 1 1.82%
Publishing, printing 1 1.82%
Transport 4 7.27%
Wholesale & retail trade 2 3.64%
Wood, cork, paper 1 1.82%
34
Table 2 – Classification of the sectors into sector groups
This table shows the classification of the sectors into four sector groups for the test whether the CAR’s differ amongst different sectors. Each column represents a sector group in which each row is a sector that is assigned to that sector group.
Sector group 1 2 3 4 Construction Chemicals, rubber, plastics, non-metallic products Hotels & restaurants Banks Education, health Food, beverages, tobacco Publishing,
printing Insurance companies Gas, water, electricity Machinery, equipment, furniture, recycling Post and telecommunications Other services
Metals & metal products
Primary sector
(agriculture, mining, etc.)
Transport
Textiles, wearing
35
Appendix B – ‘Test results for Markov Switching model’
Table 1 – Test results of the Markov Switching model summarizedThis table shows the test results of the Markov switching model, the results are summarized. For these results the model uses formula (9): 𝑦𝑡= 𝜇𝑠𝑡+ 𝜖𝑡. The regime mean in this table is
represented by 𝜇𝑠𝑡 in the formula, and the sigma is represented by 𝜖𝑡 which shows which regime is the high volatility state, regime 1 is the low volatility state and regime 2 is the high volatility
state. P11 and P21 represent respectively the chance of being in state one given that the stock was in state one in the previous period and the chance of being in state one given that the stock was in state two in the previous period. The last four columns show for both the M&A rumor and announcement whether there was a regime switch in the event window, and if there was whether it was before or on/after the known event date. The used event window for the switches to occur is a 5-day event window as used in the CAR analysis.
Mean Sigma Rumor Announcement
Company name Rumor date
Announced
date State 1 State 2 State 1 State 2 P11 P21
Switch around event Switch before or after event Switch around event Switch before or after event R&S RETAIL GROUP 31-8-2015 18-11-2015 -0.23% 0.47% 0.05% 10.35% 0.7000 0.6221 yes after yes after OCI 19-2-2015 13-11-2015 -0.16% 0.59% 1.07% 4.21% 0.8925 0.4016 yes after yes after UNILEVER CERTS. 29-5-2015 1-10-2015 -0.03% 0.04% 0.44% 1.07% 0.7920 0.3036 yes after yes before CISCO SYSTEMS 13-7-2015 30-9-2015 0.01% -0.06% 0.95% 2.59% 0.9720 0.1733 no - yes after RANDSTAD HOLDING 19-5-2015 24-9-2015 -0.08% 0.37% 0.94% 22.47% 0.8820 0.5644 no - yes after MICROSOFT 19-7-2015 8-9-2015 -0.04% 0.40% 1.03% 43.43% 0.9608 0.4027 no - yes before HEINEKEN 4-8-2015 8-9-2015 -0.08% 0.12% 0.69% 1.37% 0.9671 0.5315 yes before yes after ING GROEP 13-4-2015 7-9-2015 0.04% -0.91% 0.66% 1.40% 0.7924 0.4704 no - no - CISCO SYSTEMS 30-6-2015 27-8-2015 0.01% -0.06% 0.95% 2.59% 0.9720 0.1733 no - yes before HYDRATEC INDUSTRIES 20-5-2015 9-7-2015 -0.01% 0.01% 0.28% 3.45% 0.7025 0.6795 yes before yes before XPO LOGISTICS 28-4-2015 11-6-2015 0.12% -0.07% 4.55% 16.51% 0.8705 0.0767 yes after no - MUENCHENER RUCK. 26-3-2015 3-6-2015 0.05% -0.63% 0.73% 17.50% 0.8360 0.2128 no - no - INTEL 27-3-2015 1-6-2015 -0.06% 0.43% 1.14% 2.68% 0.9037 0.7342 yes after no - DPA GROUP 10-3-2015 22-4-2015 -0.08% 0.10% 0.99% 2.52% 0.9273 0.0946 yes before yes after ANHEUSER-BUSCH
36
Table 1 (continued)
Mean Sigma Rumor Announcement
Company name Rumor date
Announced
date State 1 State 2 State 1 State 2 P11 P21
37
Table 1 (continued)
Mean Sigma Rumor Announcement
Company name Rumor date
Announced
date State 1 State 2 State 1 State 2 P11 P21
Switch around event Switch before or after event Switch around event Switch before or after event VEOLIA
ENVIRONNEMENT 6-5-2015 5-6-2015 -0.07% 0.42% 0.86% 2.21% 0.9032 0.5641 yes before yes after EDF 30-1-2015 22-4-2015 0.04% -0.13% 0.80% 2.51% 0.8103 0.6510 no - yes after ESSILOR INTL. 31-1-2015 20-4-2015 0.01% -0.05% 0.59% 1.46% 0.8830 0.4865 yes after yes before ACCOR 9-3-2015 17-4-2015 0.04% -0.27% 1.05% 1.80% 0.9938 0.0456 yes before yes after CLASQUIN 19-1-2015 31-3-2015 -0.20% 0.10% 0.02% 1.74% 0.5466 0.2203 no - no - ORANGE 11-1-2015 20-3-2015 0.05% 0.24% 0.85% 2.16% 0.8722 0.6536 yes after yes before GROUPE
CONCOURSMANIA 20-1-2015 17-3-2015 0.33% -0.17% 0.07% 2.85% 0.5281 0.2632 yes after yes after VISA 'A' 8-5-2015 2-11-2015 -0.07% 0.26% 0.87% 2.16% 0.8781 0.4470 yes after yes after WILLIAM DEMANT
HLDG. 17-2-2015 30-9-2015 -0.10% 0.65% 1.03% 2.21% 0.9296 0.4506 no - yes after LANNETT 1-6-2015 2-9-2015 0.16% -0.19% 1.67% 4.30% 0.9245 0.0916 no - yes before CAPITAL ONE FINL. 3-6-2015 11-8-2015 0.03% -0.52% 1.03% 4.71% 0.9653 0.6301 no - no - AUDI 10-4-2015 3-8-2015 -0.03% 0.16% 1.05% 3.71% 0.9627 0.1846 no - yes before ABENGOA 26-3-2015 25-6-2015 -0.34% 0.14% 2.45% 17.70% 0.9579 0.1650 yes after no - XPO LOGISTICS 20-2-2015 28-4-2015 -0.10% 0.37% 1.97% 5.47% 0.9458 0.2073 yes after yes after WILLIAM DEMANT
HLDG. 17-2-2015 2-4-2015 -0.10% 0.65% 1.03% 2.21% 0.9296 0.4505 yes before yes before
Totals and counts number of switches on/after the event 12 15
number of switches before the event 18 26 Number of event without regime switch
around the event 25 14
Number of events with regime switch
38
Table 2 – Test results of testing for significant differences between the means and sigma’s of the Markov switching model results
This table shows the results of the Wald test for testing whether the means and sigma’s for the high volatility state differ significantly from the means and sigma’s of the low volatility state, state 1 represents the low volatility state and state 2 the high volatility state. In parentheses, behind the values of the means and sigma’s, there are the standard errors of the means and sigma’s. The chi squared column shows the Chi square statistic of the Wald test for both the mean and the sigma, where after the p-value is generated which is used to check whether the result is significant. The significance is denoted as follows: * significant at the 10% level, ** significant at the 5% level, *** significant at the 1% level.
Mean Sigma Mean state 1 = mean state 2 Sigma state 1 = sigma state 2
Company name State 1 State 2 State 1 State 2 Chi^2 p Chi^2 p
39
Table 2 (continued)
Mean Sigma Mean state 1 = mean state 2 Sigma state 1 = sigma state 2
Company name State 1 State 2 State 1 State 2 Chi^2 P Chi^2 p
