5. Cumulative Average Abnormal Returns Study
5.2. Event Study Methodology and Abnormal Returns
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(TAIEX) includes stocks with several market capitalizations (small, medium, big) and is not as specific as the CAC 40 in France. This is the reason why we will take an additional index in Taiwan: the FTSE TWSE Taiwan 50 index which will allows us to compare more specifically big capitalization index between France and Taiwan as it would not have been possible to do it with the TAIEX. The main index of Taiwan will however be used for another comparison between the two main indices of each country.
The data that has been extracted to conduct our event study methodology is the daily data of each indices described above for a period that will match the requirements of our methodology.
This period will be explained in detail in the next part directly related to the methodology used for our research. The choice of the daily data for this part of the study relies on the fact that it will allow us to work on a short time period before and after the presidential election.
5.2. Event Study Methodology and Abnormal Returns
The event study methodology can be used to measure the impacts of a specific event on a dependent variable, most commonly common equities (stocks) in order to assess the event’s effect on the value of the company. Event study can be commonly conducted to measure the effects of events such as earnings announcements, mergers, acquisitions, Initial Public offering, debt issue, stock split announcements (studied by James Dolley in 1933), change of the regulatory environment (legislation, law) and macro-economic variables such as unemployment rate or trade deficit. This list is not exhaustive but we can think that economic, corporate and law-related events are the one very likely to impact a company’s valuation and its stock price. A strong underlying assumption regarding the use of an event study is the market efficiency. Given this, we can expect that the effect(s) of the event of our study will have an
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immediate reflection on the market. It will be then possible for us to measure the impact of the event in a short period of time as the market processes the information in an unbiased way and efficiently. In our case, we will calculate the CAAR (cumulative average abnormal returns) at different period of time around the presidential elections dates we selected. The presence of significant value for the CAAR would then help us to interpret the impact of presidential elections (the event) on the market indices we are working with; as in our case we do not work with firms’ equities. The event study methodology has been used to answer different political-related question among time. In their study Political elections and the resolution of uncertainty: The international evidence for example, Pantzalis, Stovall and Turtle (2000) used this methodology to provide the most complete study realized regarding the analysis of stock market indices around presidential elections dates with more than 33 countries analyzed. A research paper published by MacKinlay in 1997 called Event studies in Economics and Finance attempts to give a step-by-step accurate methodology for the conduct of event studies. Even if there is not one most accurate way to conduct an event study, this research remains a reference and will serve as a departure point to conduct the event study we want to answer out research question.
Defining the event of interest
The first step in doing an event study is to determine the “event of interest” as MacKinlay called it, which means in our case, the event that will possibly impact the stock market indices chosen for both France and Taiwan. In this study, we want to assess the impact of presidential election for the two countries of our study. We can then deduct that our event of interest will be the date of presidential election for France and Taiwan, when the new president is elected. In the case of Taiwan, the presidential election happens in one round, so there are no difficulties stating that
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the event of interest will be the day of the presidential election. For France however, the presidential elections happen in two rounds, separated by 15 days. The event of interest for us will be the second round date, as at its end, the new president will be elected, known and all the uncertainty linked to the event will end. We will then be taking for both countries the official presidential election date as event of interest. This date will be T=0.
Defining the event window
The event window is defined by MacKinley as “the period over which the security prices of the firms involved in this event will be examined”. The author gives as example the situation of an earnings announcement by a company: the event of interest will be the day of the announcement while the event window will have to include the event of interest plus periods prior and after the event so that it is possible to study the surroundings of the event. Again, the definition given by the author is for security prices but we will be working with indices so we will adapt this definition to indices. Nevertheless, in the case of presidential election, the elections dates decided by both the governments of France and Taiwan happen to be during the weekend. In France, presidential elections are organized Sundays while in Taiwan it happens to be Saturdays. Concretely, it means that the Stock Exchange of the two countries does not open the day of presidential election so it is not possible to define an event window which includes the day of the elections. We will have to propose an alternative to this situation and the best solution seems to consider the two weeks prior the election date as two different event windows.
Indeed, as we want to analyze the impact of elections on stock market, we need to assess the impact before and after the election date as it is not possible to include the event of interest in the event window. The choice of defining the event window as the two week before relies on the fact that a specifically called post-event window will be chosen and explained later, in the
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following parts. A one week period defined as (-7,-1) will then be our first event window for this event study. It is the period starting at T= -7 days before the presidential election date and ending at T= -1 days before the presidential election date. Another event window will be defined as the following (-14,-8), starting at T= -14 days before the presidential election date and ending at T= -8 before the presidential election date. To summarize, we will have two “one week event window”, prior to the presidential election date. The reason of the choice of this specific period relies on different factors. The first ones are the fact that the first round of the presidential election happens in France two weeks before the second round date and for both countries, this period concords with the second half of the presidential campaign. Therefore, this period between the two rounds in France is short (this is the closest to the event of interest) and happens to be the moment when the electors will make their final choice between the two remaining candidates if it is not already made. Nevertheless, we can expect the fact the two last week before the date of elections, citizens have, at the majority, made their choice regarding the candidate they want to choose. In fact, in both countries the campaign has already started and has been really intense for two weeks already. In France, the outcome of the first election round has just been released so we can expect the citizens to have already thought about the different possibilities of outcomes and make their final choice according to that. Even if people can still change their vote until the last day of the presidential campaign, it is safe to say that the closer we are from the presidential election date, the more important the number of person having made their final decision will be. The decisions made by the citizens can be reflected in the stocks prices or the value of indices as they will associate different probabilities to the two possible outcomes and set the new price on the market according to the different probabilities they estimate. In their research paper, Pantzalis, Stovall and Turtle (2000) worked with a weekly data and defined an event window as (-2,0), the three weeks period prior to the election
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day, starting at T= -2 and ending at T= 0 (week of the presidential election). The reason of this choice for the authors relies on the fact that this window “includes the periods with the most potential for uncertainty resolution leading up to election”. According to them, the more resolved the uncertainty is, the closer we are from the election date. Concretely, it means for them that we have better chances to observe positive abnormal returns during the period close to the event as the risk directly linked to the outcome uncertainty will be reduced (which will have the effect to increase the indices value). In their research paper called Risk aversion, uncertain information and market efficiency, Brown and Al. (1988) state that “investors often set stock prices before the full ramifications of a dramatic financial event are known” (p.356). It means that investors will try to determine and set the value of the indices (according to the stock prices listed on them) before the day of the election that will provide the final outcome. This information supports our reasoning as it seems that the month before the election will have the highest probability to show abnormal returns as the presidential campaign will be active. This probability will increase as we come closer to the presidential date. This is the reason why, we have chosen the two event windows (-14,-8) and (-7,-1) to complete our event study. The second week and the week before the presidential election date have been separated to see whether or not it is possible to have more specific and precise results the closer we are from our event of interest. We reduced the period of study chosen by Pantzalis, Stovall and Turtle to two weeks instead of three as it comes in the middle of the presidential campaign for both countries and the first round has been done in France. We believe then that this period of two weeks will give us more probability to observe abnormal returns as the uncertainty has more chance to be solved.
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Defining the pre-event window
MacKinley also states in his research paper that the “periods prior and after the event may also be of interest”. In our case, we consider that those periods are “of interest” and we will define them to include them in our study to have a broad vision of the different elements and periods surrounding the presidential elections. The pre-event window will be defined for both countries as the first two weeks of the month prior to the election date: (-28,-15). Again, it is important to mention that in France the pre-event and event window will be separated by the first round of presidential elections. Nevertheless, this is not the case for Taiwan as presidential elections are only organized with a unique round. Then, what justify the choice of a pre-event window defined by (-28,-15)? The main reason is the beginning of the presidential campaign about a month before in the two countries of our study. There are official rules defining the way presidential campaign has to be organized in both France and Taiwan. Even if these ones are not totally identical and their regulations have changed over time, we have come out with an average between France and Taiwan for the period of our study. This average showed that the presidential campaign starts around 1 month, that is to say 4 weeks, before the actual date of elections in the two respective countries of our study. This is nevertheless during the first two weeks of the campaign that we can expect all the candidates to be the more active and the voters be influenced by the media coverage and make their choice according to this.
Defining the post-event window
The post-event event window will be set with the goal to analyze the impact(s) of the presidential election on the market indices after the presidential election day, when the final outcome is known. We can naturally set up the fact that it will start the day after the election
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date. The new president will then be known by the public and the market might react to the outcome of the elections. The post-event window will be defined as (+1,+28) so that it will stop four weeks exactly after the date of the election date. The reason of this choice relies on the findings made by, who found that abnormal returns are significant the first week after the presidential election but this result can be extended to 1 month after. We will then take the larger period to see whether or not it is possible to find actual abnormal results over a longer period than one or two weeks after the presidential election outcome, which is in our opinion, more likely to happen as the market may react easily on the short-term after this type of event.
Defining the estimate window and the method to calculate expected or normal returns
The estimate window is an important part of our methodology to conduct this event study. In fact, this is the window that will help us to determine the normal or expected daily returns for the indices we are working with. We will explain later that the expected daily returns for each index before a presidential election will contribute to the calculation of abnormal returns, what we want to work with for this study. The estimate window will be defined before the pre-event window. We decided to pick the period (-149,-29) to define this specific window. It is equivalent to a four month period before the pre-event window and the official beginning of the presidential campaign. We believe that this period will be long enough to determine an accurate average daily return for each index before the elections we defined in our study. We will be able to determine the normal/expected returns on each index during this period by the following formula:
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Where:
2- T1 is the estimate period : 120 days (4 months)
3- Rt is the index daily rate of return for t days during the estimate window.
Nevertheless, we have to justify this way to calculate the expected return for each index because it differs from what is commonly used for this part of the event study. In his research paper MacKinley gives two “common” choices in the conduct of event study to calculate the expected return of the securities we want to work with. The first one is called constant mean return model, also called mean-adjusted return model while the name of the second is the market model. The author reminds that the constant mean return model “assumes that the mean return of a given security is constant over time”. This model can be defined as an “economic”
one and considered as the most simple. Nevertheless, the results found using it are often very similar to the more complex models, according to Brown and Warner (1980,1985). On another hand, the Market Model (MM) “assumes a stable relation between the market return and the security return”. This is a statistical (different from the economic) model that can be expressed as the following:
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Where:
- Rit is the period-t return on the security i - Rmt is the market portfolio
- α,β and the variance are the parameters of the market model
As we can see, the market model establishes a link between the market portfolio and any given securities. Main indices such as the S&P 500 are often chosen as market portfolios in this model because they are references to work with. With the market model, it is possible to find the abnormal returns of the securities by performing a regression on the chosen market portfolio.
Cable and Holland stated in their paper Modelling Normal Returns in Event Studies: A Model-Selection Approach and Pilot Study, published in 1999, that the two others common models to conduct an event study were the CAPM and the IM (‘index’ model). The CAPM differs from the market model in the sense that it includes the risk-free rate. The index model differs from the mean-adjusted return model (first one explained) from the point that the returns are not systematically constant for a security but that they are equal across securities. It implies that α =0 and β= 1 so we can obtain the following expression (replacing in the MM):
So that the expected returns across securities E(Rit) is equal to the expected returns of the market portfolio E(Rmt).
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The different possibilities to determine the normal return explained above led us to consider using a constant mean return model/mean-adjusted return model for our study. Nevertheless, we don’t work in our case with securities but with stock market indices. This is the reason why we extended the methodology for securities explained by MacKinlay to indices so that we can conduct our research. The estimate window will then belong to the same index we want to perform the analysis on. This model will be the only way for us to determine the normal return of our estimate window without performing a regression. In fact, it is not possible to perform regression of a market index on itself and using a regression-based model such as the Market Model would have implied using an index of reference for the indices we are working with, which was, in our opinion not relevant as we will explain in the part related to the “alternative way to process” of our thesis.
In his research paper, MacKinley summarize the time line for an event study as the following:
When we adapt this time line to our event study and the different windows of interest that have been selected for the reasons explained above, we can express the following one:
Post‐event window Event windows
Pre‐event
+28
‐1 +1
‐28 ‐15 ‐14 ‐8 ‐7
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The estimation window comes before this representation and can be represented as it is in
The estimation window comes before this representation and can be represented as it is in