The Goofy

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The equation is (MacKinlay, 1997):

!"!" =!! +!!×!!" +!!" Equation 1. The Market Model

Where:

!"!" = Expected return for stock ! on day τ !! = Alfavalue (constant) for stock ! !! = Systematic risk, betavalue for stock !13

!!" = The market return on day τ !!" = Zero mean disturbance term in the model on day τ

There are many different models for calculating the abnormal returns of a firm, the most commonly used are the market model and constant mean return model (Mackinlay,1997). the constant mean return model uses a constant mean to calculate the abnormal returns of the individual firms. The constant mean is usually in the form of a risk-free security such the u.s treasury bill with one-month maturity.

The market model

Is an ordinary least square (old) regression of the individual stock in regards to market index with the daily returns as an independent variable the stocks beta value as an explanatory variable a broad-based stock index like the FTSE all share, s& p 500. According to Benninga ( 2008), the most common criteria for choosing market index should either be a floating weighted index or broad-based value weighted index.

“The market model gives a potential improvement over the constant mean return model. By removing the part of the return that is related to variation in the market’s return, the variance is reduced. This, in turn, can lead to increased ability to detect event effects” (Mackinlay, 1997).

This thesis uses the fast all share index as the broad-based index follows the suggestion by Mackinlay and uses the market model to calculated the abnormal returns. The historical price data downloaded from datastream is shown as the actual stock prices . The prices are then converted to returns which is used in the statistical test . Below is the formula applied.

Daily returns on the index are calculated with the formula below:

When using the market model the expected- and abnormal returns are calculated as for- lows: The equation is (MacKinlay, 1997):

The beta coefficient is calculated with the formula below:

The Alfa value is calculated according to the formula below:

The normal returns of the stock are calculated using the estimation window. Following Benninga 2008) suggestion t he length of the estimation window is 250 trading days. The main reason for using a longer trading window is to avoid bias in the results .(Benninga,2008)

Below is the choice of estimation window and event window.

The abnormal returns are computed as the difference between the actual returns of the acquiring company’s stock and the expected returns.The abnormal return is the estimated effect of the event that cannot be explained by the market's general development (MacKinlay, 1997).

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Aggregating abnormal returns

In a nutshell, Any variation in the stocks actual returns from the expected return will result in either a negative or a positive abnormal return. The effects on the stock are analyzed by the calculation of the abnormal return where each stock for every trading day in the estimation period computed.

next step

When AAR, CAR, and CAAR are calculated, hypotheses can be formed and tested statistically to verify the significance of the results (MacKinlay, 1997).

3.3 Statistical tests

When conducting an event study, a significant part is draw general conclusions about the population based on the results of the sample using a statistical test. This section will, therefore, explain why these specific tests are included, and how they supplement each other regarding they are used to treat the problems in the data set.

The method used in similar event studies for testing whether the abnormal returns (AR) surrounding the M&A announcement is statistically significant fall into two categories and these are parametric and non-parametric tests. The parametric tests have stronger requirements but however considered as reliable tests when the requirements are satisfied (Westerlund, 2005).

The primary requirement is that the sample follows a normal distribution, hence why a normality test is needed for the cross- sectional average abnormal returns (AAR) for each day over the event window as well as for the cumulative average abnormal returns, (see Appendix 9).

These stronger requirements can be difficult for the data to meet, which is also the case in this thesis and that the parametric test statistics will, therefore, lose some statistical power. Going by Brooks(2010) suggestion, the series are controlled for extreme values, before the normality test is performed, which not controlled can distort the normality.Going by Korner & Wahlgren (2010) suggestions the AR AND CAR for every cross-sectional is tested boxplot diagrams to check for the extreme values. These outliers can either be eliminated from the observations or winsorised.

The separation of outliers is done in (EViews) where observations below the fifth percentile and above the ninety-fifth percentile are removed for abnormal returns and cumulative abnormal returns

. The chosen significance test is the Students t-test(Westerlund, 2005) for which the cumulative abnormal returns and abnormal returns for samples of private and public targets are tested for throughout the event window. The hypotheses which are tested are stated as follows: