In both the event study and the long-run stock performance study, the main purpose is to determine whether SEOs have an effect on short- and long-term returns for issuing firms. In addition to this, and to help answer our research question, it is useful to analyze firm-specific characteristics and their respective relations with the firms’ short- and long-run stock returns. The most straightforward and common way to do this is through a multiple regression analysis.
Ideally, one should use an entire population in order to derive the real regression function. When using a sample of a population, the regression function will only be an approximation of the real function.
However, by using the Ordinary Least Squares (OLS) method, one can make the approximation as close as possible. However, when conducting a multiple regression analysis, it is important to ensure the validity of the model. Therefore, one should ensure to satisfy a number of assumptions underlying the linear OLS regression model (Brooks, 2008; Gujarati & Porter, 2009).
1. The linearity assumption
All variables should be relevant and the relation between the dependent variable and the independent variables should be linear (Brooks, 2008). Extreme values might cause this assumption to be violated, meaning that they may need to be excluded or transformed (Lewis, Thornhill & Saunders, 2007). The most common way to mitigate such issues is to transform the variables by for instance using their natural logarithm (Brooks, 2008).
2. The mean of the error terms is zero
The average value of the error terms in the regression model should be zero. However, Brooks (2008) argue that this assumption is satisfied automatically as long as a constant is included in the model.
3. The variance of the error terms is constant
When the variance of the error terms is constant, the assumption of homoscedasticity is fulfilled; meaning that variance of the residuals is equal for any given value of the independent variables (Gujarati & Porter, 2009). The most common test to control for heteroscedasticity is White’s test (Brooks, 2008). If heteroscedasticity is found, the coefficient estimates will not be best linear unbiased estimators, and conclusions drawn from the model could potentially be misleading (Brooks, 2008).
4. The error terms are uncorrelated with each other
The error terms should be random and cannot display autocorrelation between each other (Gujarati & Porter, 2009). The consequences of autocorrelation are similar to the consequences of heteroscedasticity. The most common test to control for autocorrelation is the Durbin-Watson’s test (Brooks, 2008).
5. The error terms are normally distributed
The error terms should be symmetric around the mean with no evidence of kurtosis (Gujarati &
Porter, 2009). An outlier might cause the error terms to be non-normally distributed and thereby, violate the assumption. Brooks (2008) argues that large sample sizes mitigate this issue. The reason for this is based on the central limit theorem, which states that larger samples will cause the sample mean to converge towards the population mean.
6. The explanatory variables are not correlated with one another
The CLMR assumes no multicollinearity, i.e. no correlation between any of the independent variables. If multicollinearity is found, it will be different to separate the individual effects of the independent variables on the dependent variable (Brooks, 2008). Gujarati & Porter (2009) argue that any correlations less than 0.8 are non-problematic.
In accordance with reporting equally- and value-weighted averages, which is conducted to demonstrate differences between smaller and larger companies and the corresponding return results, we will also perform a weighted least square regression (WLS) for each dataset in addition to the OLS regression.
This simultaneous application of the two regression methods should enable us to disclose differences of the respective factors on smaller and larger companies and consequently give the possibility to draw more refined findings from the regression set with respect to potential predictable paradigms.
Therefore, the market capitalization is used as weights and the WLS regression should better reflect the contribution of the individual observation to the final regression parameters.
4.6.1 Regression Diagnostics
As explained above, all assumptions should be met to ensure a significant regression model. The first assumption of a linear relationship between the dependent and the independent variables should be fulfilled because the variables included are anchored in previous research, as discussed in section 3.3
“Independent Variables”. Furthermore, the natural logarithm is incorporated for variables that are scattered more broadly, in our case market value, to mitigate potential outliers. The second assumption is fulfilled since all regressions include a constant and hence the average of the residuals is zero. IBM’s SPSS program, which is used to run the respective regressions, is capable of performing the Watson’s t-test. The Watson results for all regressions can be found in Appendix 2. A Durbin-Watson test statistics of 2 indicates that no autocorrelation is prevailing. The results from our
regressions display scatter in close proximity to 2, except for the WLS regression for the CAR results..
Consequently, autocorrelation seems to be highly unlikely in the majority of the regression sets, and therefore deemed as rather unproblematic for this study’s results, resulting in assumption 4 to be fulfilled. Furthermore, multicollinearity can be tested by checking the correlation between the independent variables. A correlation matrix, which is obtained from SPSS, is reported in Appendix 3. It displays that none of the variables features a correlation close to the critical value of 0.8, and hence the problem of multicollinearity can be considered of little influence on the results. We forego testing for normally distributed error terms as Brooks (2008) explains that a large sample size will mitigate a problem arising from non-normally distributed error terms. Building upon the central limit theorem, we consider this thesis’ sample size as sufficiently large to mitigate a potential problem.
Based on this discussion, it becomes evident that 5 out of the 6 assumptions appear to be met to a suitable degree with the exception of assumption 3 concerning the heteroscedasticity. Therefore, it is important to keep in mind that the regression results might be biased to some degree, which has to be considered in the analysis and the corresponding conclusions.
4.6.2 Definition of Variables
The following section will account for the definition and measurement of the dependent and independent variables employed in this thesis. The independent variables are chosen based on previous research that has previously been discussed in the literature review. This thesis will test all independent variables on both the announcement returns and long-run returns.
Dependent Variables
CAR: The dependent variable in the first set of regressions is the cumulative abnormal return of the equity issuer surrounding the SEO announcement [-1,1], as described in section 4.4.5
‘Calculation of Abnormal Returns’. The CAR will also be included as an explanatory variable in our second set of regressions where we examine the variation in long-run stock performance for issuing firms.
BHAR: The dependent variable in the second set of regressions is the BHAR for the equity issuers, as described in section 4.5.2 ‘Buy-and-Hold Abnormal Return’.
Independent Variables
Relative size of the issue: The relative size of the equity issue (RelSize) regards the actual issue proceeds divided by the market value 5 days prior to the issue. The proceeds of the SEO are obtained from Thomson One Banker, while the market value is extracted from Datastream.
As Thomson One Banker only reports the dollar value, the respective issue sizes are converted to euros by the application of the exchange rate on the announcement date.
Market capitalization: The natural logarithm of the market capitalization (MarketCap) in million euros. The market capitalization is extracted from Datastream and the observation is 5 days prior to the SEO announcement.
Book-to-Market Ratio: The book-to-market ratios (B2M), which is the book value of equity divided by the market value of equity, is extracted from Datastream by dividing common equity by the market value and the observation is 5 days prior to the SEO announcement.
Momentum: As momentum factor (MOM) serves the return over the eleven months prior to the announcement for each event company. The stock price data is extracted once again from Datastream.’
Frequent Issuer: As frequent issuer (FreqIssuer), companies, which issue equity more than once in the period between 1990 and 2012, are denoted. The frequent issuer variable will be used as a dummy. Every issuance event, but the first for each event company, will receive a 1 for being a frequent issuer, while the first issue of a company within the period will be identified by a 0.
Industry: The sample companies are divided into four industries – utilities, financials (FIN), industrials and IT – according to the ‘Industry Classification Benchmark’ in Datastream.
Companies that were assigned a differential industry classification are combined in the industrials dummy. Furthermore, the industrials dummy serves as the benchmark for the other three and hence will not be used in the regression as every company is assigned a 0. For the other three, the company is assigned a 1 when they are included in the industry and a 0 if not.
5 Data, Empirical Results & Analysis
The chapter commences by presenting a brief summary of the characteristics of the final sample.
Subsequently, the results of the announcement effects, the long-run stock performance and the multivariate analysis are presented and analyzed. Lastly, we analyze the long-run stock performance based on the market reactions and discuss predictable patterns while trying to establish a potential trading strategy.