4. Market Cycles Study
4.2. Methodology
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Stock Exchange (launched in 2002), the FTSE TWSE Mid-Cap 100 index, as its name suggests, includes the 100 next market capitalizations which can be described as “Mid-Caps” (released in 2004) and for France the CAC mid-60 which includes 60 stocks with middle capitalization .The collect of our data started with determining the presidential election dates for both France and Taiwan. For this analysis we will need a full presidential term so we cannot include the elections of 2012 in both countries and the period after that. We will take for the TAIEX 1996 as a starting point because this is the first direct election that was hold in Taiwan. Regarding the CAC 40 in France, the system was implemented in 1987 so that it is possible for us to start with the election of 1988. For the other indices from France and Taiwan the study will take into account the possible elections according to the date those indices have been released on the market. Finally, we ended up collecting the weekly data for each index relevant for our study and this, for the period of our interest. The reason using weekly data rather than daily data comes from the fact that we want to calculate yearly returns so we do not need to work on a daily basis. Plus, the use of yearly data could not let us be as accurate as the use of weekly data to precisely determine yearly returns according to the presidential election dates. In fact, for example, the elections are not organized the exact same date every four years in Taiwan. The last election of 2012 happened in January while the previous ones used to happen in March. The use of weekly data allows us to adapt our study to this kind of change, which otherwise would bring bias in our results.
4.2. Methodology
We first thought about doing a “peak-trough’ analysis, using the same methodology that Marshall Nickles used in his research paper we introduced in our literature review. A
“peak-trough” analysis would have supposed to present first the graphs of the indices we are
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going to work with and this, for the period of our study. This would have been the way to find out the peaks and troughs of every index and observe graphically if yes or not a cycle can be identified before confirming it with relevant calculations. We are here working with a four-year period for Taiwan and between 5 and 7 for France (as the presidential term changed at some point of time). We have seen already that financial institutions and financial press commonly take “two successive quarter of decline in real GDP” to declare the economy in the state of recession. The NBER, in the United States, defines a recession as “a significant decline in economic activity spread across the economy, lasting more than a few months […]”. The study of Stovall in 1995 helped us to understand market cycles generally reproduce and anticipate business/economic cycles. In addition to that, we know already that many different market cycles have been identified throughout times (from weekly to 40 years). All those information are relevant and seem sufficient to know how to determine the different peaks and troughs for each index we are working with. Nevertheless, in his analysis, Marshall Nickles did not exactly respect the definition of recession period given by the NBER or the common press, using for example periods of 0.08 years or 0.17 years to define a “bear” market. Can we say that these periods are long enough to consider them as recessions or “bear” period of a market cycle? It seems difficult to know with certainty how to proceed to find the peaks and troughs graphically for an index and this type of study may more rely on personal appreciation than using a specific scientific method. This is the reason why we won’t use this method to conduct our research about market cycles but we will instead; present a method involving the analysis of yearly returns.
Our methodology consists in calculating for each full presidential term with our available data (4 years for Taiwan; 5 or 7 years for France) the yearly returns for the index we introduced
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above. It is important to mention that the weekly values of each index, extracted from Bloomberg, represent their value at the end of the week (once the stock exchange closes on Friday). Plus, to be as precise as possible, the calculations of the yearly returns are done to last exactly 52 weeks, unless it is not possible (earlier date of election than before for example).
Once the yearly returns have been calculated, it will lead us to conduct two different types of analysis:
- A “market cycle” analysis - A “comparative” analysis
The “market cycle” analysis aims to determine with the data selected for this study the average yearly returns for each year of the presidential term (for every index) and see whether or not it is possible to find similarities with the findings previously made in the United States, exposed in our literature review. A t-test will be conducted on each average to see if the results found are significant for an interval of significance of our interest. The calculation made to determine the t-test value is the following:
With:
3- x the sample mean
4- Delta the specified value to be tested, in this case 0 5- s the standard deviation of the sample
6- n the sample size
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It is important to mention that the analysis is already broaden compared to what have been previously conducted in the United States as we do not work only with the main indices from France and Taiwan but we also include indices to take into account the market capitalization factor. Once this first analysis conducted, we will focus more on this factor by doing a
“comparative” analysis between the big and mid-caps for France and between the big and mid-caps for Taiwan. The purpose of this analysis will be to see whether it is possible to see significant differences between indices according to the market capitalization of the stocks listed on them. Another type of t-test will be conducted, to compare two means and see whether they are significantly different from each other or not. The formula for this t-test is:
With:
7- x1 and x2 the two sample means
8- s1 and s2 the standard deviation of the two samples 9- n1and n2 the sample size
10- Delta the specified value to be tested, in this case 0