Analysis of the estimation windows 71

For the analysis of the estimation windows, only eight estimation windows, each consisting of 250 trading days, were considered. The eight estimation windows were established based on the fact that this study considers two event dates, namely sponsorship announcement date and hosting date (start date) of a FIFA World Cup™ soccer tournament, for each of the four home-based sponsor companies chosen for this study. It is of great importance to highlight the fact that all eight estimation windows which were analysed in this section were based on a [–40, 40] event window. The longest event window that was considered in this research study was [–40, 40] and thus it was deemed appropriate to analyse all the estimation windows for both event dates for each home-based sponsor company based on a [–40, 40] event window.

The estimation windows were analysed to support or refute the assumption that calculated ARs for the estimation windows are normally distributed. Two methods were used to support or refute this assumption. Firstly, graphical representations of the calculated ARs of the eight estimation windows are presented in sections 4.3.1.1 and 4.3.1.2, and based on simple observations of the distribution of the calculated ARs, a conclusion was made. Saunders et al. (2009) explains that data is normally distributed when it can be plotted as a bell-shaped curve. A bell-shaped curve is a graph where the data is symmetrical and has a single peak which represents the median (mid-point) of the data (DeFusco, McLeavey, Pinto & Runkle, 2007). An example of a normally distributed bell-shaped curve is represented in Figure 4.1 below. Secondly, this study used descriptive statistics to further evaluate the distribution of the calculated ARs of the eight estimation windows. Four of the seven descriptive statistics which were examined, namely the mean, standard deviation, skewness and kurtosis, represent four statistical figures which indicate defining characteristics of a normal distribution in academic research (DeFusco et al., 2007). Further discussion of what values,

- 72 - in terms of descriptive statistics, represent a normal distribution will be given in sections 4.3.1.1 and 4.3.1.2.

FIGURE 4.1: Example of a normally distributed bell-shaped curve

Source: DeFusco et al. (2007)

4.3.1.1 Analysis of abnormal returns during sponsorship announcement estimation window (estimation window based on the [–40, 40] event window)

Histograms

The distribution of the ARs during the estimation window for each home-based sponsor company is represented in the histograms in Figure 4.2 below:

- 73 - TOSHIBA DEUTSCHE TELEKOM

MTN GROUP LIMITED Oi SA

FIGURE 4.2: Frequency of the distribution of the home-based sponsor company’s abnormal returns during the estimation window at sponsorship announcement (estimation window based on [–40, 40] event window)

The ARs appear to be spread out for all the home-based sponsor companies, except for Oi SA. In addition, the histograms of Toshiba, Deutsche Telekom, MTN Group Limited and Oi SA all depict a shape which roughly resembles a symmetrical bell-shaped curve. Based on visual observation alone, one can conclude that the distribution of ARs for all four home- based companies appear to somewhat represent a symmetrical bell-shaped curve. That being said, a conclusion that ARs are somewhat normally distributed based solely on visual observation is not sufficient evidence to conclude that the ARs are normally distributed.

- 74 - Therefore, to further support the assumption that the ARs are normally distributed, an analysis of the descriptive statistics is required.

Descriptive statistics

The descriptive statistics of ARs during the estimation window (based on the [–40, 40] event window) during the sponsorship announcement stages are presented in Table 4.2 below:

TABLE 4.2: Descriptive statistics of ARs during the estimation window at sponsorship announcement (estimation window based on [–40, 40] event window)

TOSHIBA DEUTSCHE TELEKOM MTN GROUP LIMITED Oi SA Mean 0.00% 0.00% 0.00% 0.00% Median –0.09% –0.15% –0.08% 0.41% Maximum 9.78% 9.68% 9.93% 10.91% Minimum –8.20% –8.44% –6.17% –44.28% Standard Deviation 2.74% 3.23% 2.26% 3.87% Skewness 0.20 0.43 0.40 –6.61 Kurtosis 3.62 3.34 4.21 73.37 Observations 250 250 250 250

Mean: All four home-based sponsor companies’ ARs during the estimation window have sample means that are very close to 0%. One of the properties of a standard normal distribution is that the sample data has a mean of 0 (DeFusco et al., 2007).

Standard deviation: Another characteristic of a standard normal distribution is that sample data has a standard deviation value close to 1 (DeFusco et al., 2007). Unfortunately, the standard deviation for Toshiba (2.74%), Deutsche Telekom (3.23%), MTN Group Limited (2.26%) and Oi SA (3.87%) are not close enough to 1 in order for the sample data, solely based on the standard deviation figure, to be considered normally distributed. However, the large difference between the maximum AR and the minimum AR for all four home-based sponsor companies does provide

- 75 - a mathematical reason for such high standard deviation figures for all four home-based sponsor companies’ ARs during the estimation window.

Skewness: A standard normal distribution should have a skewness value of 0 (DeFusco et al., 2007). The skewness figure for Toshiba, MTN Group Limited and Deutsche Telekom are 0.20, 0.40 and 0.43, respectively. These figures are a clear indication of a small positive skewness as these figures do not stray too far away from the value of 0. The skewness figure for Oi SA is –6.61, which indicates that the sample data for Oi SA is strongly negatively skewed.

Kurtosis: The kurtosis values for Toshiba and Deutsche Telekom are 3.62 and 3.34, respectively. DeFusco et al. (2007) explain that a standard normal distribution has a kurtosis value of 3. Thus, the kurtosis values for Toshiba and Deutsche Telekom are close enough to the critical kurtosis value of 3. The kurtosis figures for MTN Group Limited (4.21) and Oi SA (73.37) are not close enough to the critical kurtosis value of 3 and thus based solely on a kurtosis value perspective, MTN Group Limited and Oi SA are not indicative of a standard normal distribution.

4.3.1.2 Analysis of abnormal returns around the start date of a FIFA World Cup™ soccer tournament estimation window (estimation window based on the [–40, 40] event window)

Histograms

The distribution of the ARs for the estimation window for each home-based sponsor company, for each specific FIFA World Cup™ soccer tournament, is represented in the histograms in Figure 4.3 below:

- 76 - TOSHIBA DEUTSCHE TELEKOM

MTN GROUP LIMITED Oi SA

FIGURE 4.3: Frequency of the distribution of the home-based sponsor company’s abnormal returns during the estimation window for the different FIFA World Cup™ soccer tournament start dates (estimation window based on [–40, 40] event window)

The histograms for Toshiba, Deutsche Telekom, MTN Group Limited and Oi SA appear to roughly represent bell-shaped curves. Each histogram is roughly symmetrical and each histogram has a peak which represents the median of the sample data. As previously mentioned in section 4.3.1, in order for sample data to be considered bell-shaped, the data, when plotted as a histogram, needs to look symmetrical and it needs to have a peak. Thus, based on visual observation, one can conclude that the ARs during the estimation window for each home-based sponsor company are normally distributed.

- 77 - Descriptive statistics

The descriptive statistics of ARs during the estimation window (based on the [–40, 40] event window) for the different FIFA World Cup™ soccer tournament start dates are presented in Table 4.3 below:

TABLE 4.3: Descriptive statistics of ARs during the estimation window for the different FIFA World Cup™ soccer tournament start dates (estimation window based on [–40, 40] event window) TOSHIBA DEUTSCHE TELEKOM MTN GROUP LIMITED Oi SA Mean 0.00% 0.00% 0.00% 0.00% Median –0.27% –0.02% –0.03% 0.32% Maximum 11.09% 2.70% 8.74% 22.46% Minimum –8.80% –4.51% –5.40% –13.67% Standard Deviation 3.21% 0.89% 1.95% 4.22% Skewness 0.33 –0.39 0.55 0.60 Kurtosis 3.30 5.68 4.79 6.80 Observations 250 250 250 250

Mean: The mean values for all four home-based sponsor companies are 0. As

previously mentioned, a mean value of 0 is indicative of data being normally distributed (DeFusco et al., 2007).

Standard deviation: Deutsche Telekom (0.89%) is the only one with a standard deviation that is close to 1. Thus, based on the standard deviation figure of 0.89%, the sample data would be considered normally distributed as it is close to 1. The standard deviation figures for Toshiba (3.21%), MTN Group Limited (1.95%) and Oi SA (4.22%) are vastly different from 1 and thus one cannot conclude that the ARs during the estimation windows for Toshiba, MTN Group Limited and Oi SA are normally distributed based on standard deviation alone.

- 78 - Skewness: The skewness value of Toshiba (0.33) which indicates a skewness that is slightly positive and that of Deutsche Telekom (–0.39) which indicates a skewness that is slightly negative are close enough to the value of 0, which, according to DeFusco et al. (2007), indicates a standard normal distribution. The distribution of ARs during the estimation window for MTN Group Limited and Oi SA are said to be positively skewed with skewness values of 0.55 and 0.60, respectively.

Kurtosis: The kurtosis values for MTN Group Limited (4.79), Deutsche Telekom (5.68) and Oi SA (6.80) are not close enough to the critical value of 3 for a standard normal distribution (DeFusco et al., 2007). However, the kurtosis value of Toshiba (3.30) is close enough to the critical kurtosis value of 3 for a standard normal distribution.

Based on the analysis (visual observation of the above histograms and the descriptive statistics) of the distribution of the ARs during the estimation window for the sponsorship announcement date as well as the hosting stage (start date) of a FIFA World Cup™ soccer tournament, one can conclude that the samples under examination display characteristics which reflect a normal distribution of ARs. For example, all eight histograms (four around the sponsorship announcement date and four during the hosting stages (start date) of a FIFA World Cup™ soccer tournament) depict a shape which roughly resembles a symmetrical bell-shaped curve. Furthermore, all eight histograms have a single peak, which supports the statement that all eight histograms roughly resemble a bell-shaped curve. From a descriptive statistics point of view, all eight samples under examination have sample means equal to zero, a characteristic which indicates normal distribution. Around both the sponsorship announcement date and the hosting stage (start date) of a FIFA World Cup™ soccer tournament, 5 out of 8 data samples had skewness values close to 0, while 3 out of 8 data samples had a kurtosis value close to the critical kurtosis value of 3.

4.3.1.3 Implications of the findings from sections 4.3.1.1 and 4.3.1.2

In section 4.3.1.2 a conclusion was made, based on the analysis of histograms and descriptive statistics, that the distribution of ARs during the respective estimation windows are normally distributed. Hauswald (2003) explains that ARs during an estimation window

- 79 - are normally distributed when event studies implement a large enough estimation window (i.e. an estimation window larger than 100 days). In this study, each estimation window consisted of 250 trading days, which automatically allowed one to assume that the ARs during the estimation windows were normally distributed.

Furthermore, the results from the analysis of the histograms and the descriptive statistics provided evidence that the ARs during the respective estimation windows were normally distributed, which allowed one to accept the assumption made in section 3.3.10 that the ARs during the estimation windows for this study will be normally distributed. Thus, since the ARs during each respective estimation window are normally distributed, the standard student’s t-test, which is a parametric test, will be implemented to test the significance of CARs.