• Merger events
Merger events are considered very important from the market point of view as there is a great deal of attention when a merger occurs. All the investors and analysts are very keen on knowing the after effects of a merger as the share prices fluctuate greatly . The prices could go up steeply or could even drop. These fluctuations in the stock prices around the merger event are estimated by the event study methodlogy.

Efficient market
An investment theory developed by Professor Eugene Fama stating that it is impossible to “beat the market” because stock market efficiency causes existing share prices to always incorporate and reflect all relevant information. According to the EMH, stocks always trade at their fair value on stock exchanges, making it impossible for investors to either purchase undervalued stocks or sell stocks for inflated prices. The following are the three forms of efficient market.

• Weak form
According to Bodie et al (2008) “ the weak form of market efficiency asserts that stock prices already reflect all information that can be derived by examining market trading data such as the history of past prices or trading volume. The weak form theory states that it is impossible for an investor to achieve a positive abnormal return by using these past information.

• Semi strong form
According to Bodie et al ( 2008 ) the semistrong form hypothesis states that all publicly available information regarding the prospects of a firm must be reflected already in the stock price. For eg. past prices, balance sheet composition, accounting practices. If the investors have access to such information then one would expect it to be reflected in stock prices.

• Strong form
According to Bodie et al ( 2008 ) the strong-form efficient market hypothesis states that stock prices reflect all information relevant to the firm , even including information available only to company insiders.

D?t? ?nd T?st?ng M?thodology
The data used for the study consists of a sample of 50 companies either a target or an acquiring company between the period January 11’ and July 12’ and were collected using Thompson one banker . Event study is the best way to study the abnormal returns and the changes in the stock prices around a merger event and hence we will use this method to explain the results of the output we received after processing the collected data.

Identifying the event window and the event day
We need to establish exactly what the event is (e.g., the announcement of quarterly earnings for a firm) and determine the period during which security prices will be affected by this event. In our case the event is most likely to be a merger announcement and for this purpose we chose an event window of 31 days which will be 15 days before the event date and 15 days after the event date .In event studies identifying the event window and the event date is very important . Estimation period is also very important for event studies and in our case we have taken an estimation period of 300 days .

Estimation of abnormal returns within the event window
In order to calculate the abnormal returns we need to first calculate the log returns on the share prices of each of the 50 companies and then regress the results to find the expected returns , the abnormal returns and the cumulative abnormal returns. They are explained in brief below.
• Expected returns
The expected return is the return on a risky asset, given a probability distribution for the
possible rate of return. Expected return equals some risk-free rate plus a risk premium (
difference between the historic market return, based upon a well diversified index such as
the FTSE 100 and the historic U.K. Treasury bond) multiplied by the asset’s beta. The
conditional expected return varies through time as a function of current market
information. The expected returns can be mathematically represented by the following
formulae which we have used in our data to calculate the expected returns which will be
further used to calculate the abnormal returns.
• Abnormal returns
Abnormal returns is the returns generated by a security or a portfolio over a period of time which is different from the expected rate of return . It is the return in excess of the
return to a market portfolio and can be denoted by the following formulae.
ARj,t = Rj,t – E(Rj,t)
The abnormal return could also be negative at times.

• Cumilative abnormal returns
Cumulative abnormal returns is the sum of all abnormal returns in a certain period of time and can be denote by the below formulae.
CARit,;t+K = Sk ARi,,t+k
• Cumilative average abnormal returns
The cumulative average abnormal returns is the average of all the 50 cumilative abnormal returns in our data and the CAAR is used to calculate the t-statistic values during the event window. The cumulative average abnormal returns is denoted by the following formulae.
Hypothesis testing
In our assignement we are examining whether the market is efficient or not. As stated earlier the semi-strong form of efficiency refers to a market in which prices efficiently adjust to other information that is obviously publicly available (e.g., announcements of annual earnings, stock splits, etc). Therefore, at any point in time, the information set is fully reflected by prices i.e. prices are always equal to their fair values. It is then impossible to have abnormal return.
In order to test the semi-strong form of efficiency in relation to the merger and acquisition announcement, the following hypothesis is formulated: H0: the abnormal returns on the event day and throughout the event window are equals to 0.
Equivalent to
H0: against H1

Where is the standard deviation of the cumulative abnormal return of the 50 companies, n is the number of companies.
The decision rule is: Accept H0 if = t0.05
Reject H0 if > t0.05
For a sample of 50 target companies, and with a significance level of 5%, the critical value t0.05 is equal to 1.676.

Results
The below table helps us in explaining if the market is semi strong or not semi strong and thereby assists us in understanding the market reaction to an announcement. In the below table the t-statistic value is at an average level and increases slowly until day -2 . Based on the critical value from the t distribution table, all the values until day -2 are accepted which means that the market is semi strong or efficient and that all publicly available information are reflected in the stock prices. After day -2 there is an increase in the values as the announcement is made. The t-statistic values until day 15 are rejected which is a proof that the market is inefficient and the stock prices do not reflect information which are publicly available.
AVERAGE ABNORMAL RETURNS
CAR t-stat
-15 0.005669 0.18
-14 0.007219 0.23
-13 0.015317 0.49
-12 0.017305 0.55
-11 0.019941 0.64
-10 0.024717 0.79
-9 0.023335 0.75
-8 0.024532 0.78
-7 0.049406 1.58
-6 0.035482 1.13
-5 0.041562 1.33
-4 0.030616 0.98
-3 0.039618 1.27
-2 0.043967 1.41
-1 0.072314 2.31
0 0.062873 2.01
1 0.069642 2.23
2 0.068720 2.20
3 0.068385 2.19
4 0.074202 2.37
5 0.070022 2.24
6 0.071609 2.29
7 0.069610 2.22
8 0.064817 2.07
9 0.065765 2.10
10 0.067135 2.15
11 0.067027 2.14
12 0.068563 2.19
13 0.074343 2.38
14 0.067968 2.17
15 0.073326 2.34

However the overall picture as shown by the above table and the graph below shows evidence of an inefficient market and shows an increasing abnormal returns which explains that the market is not semi strong and that there is an upward trend in the prices due to the announcement and that the security prices do not reflect all publicly available information.

Graph 1 – Average cumilative abnormal returns

Conclusion
We can conclude by saying the market in United Kingdom is not efficient or semi-strong as there is an abnormal returns in the value of the stocks. The price of the stocks increase rapidly as the merger event approaches causing inefficiency in the market. The stock prices tend to be overpriced or underpriced and they tend to remain like that for quite a long time.

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