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Friday the 13th Statistical Analysis Featured

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Introduction
Superstitions can have a significant impact on the conduct of some people. It is the belief of many people that bad luck can result from such trivial things as walking under the ladder, spilling salt, breaking a mirror, or having a black cat cross your path. A self-help book entitled “The Secret” by Rhonda Byrne has a similar basis on the premise that one’s thinking can be impactful in that the positive thinking brings improvements in one’s life while the negative thoughts can have adverse results in one’s life. Astrology is also based on the tenet that one’s date of birth can have a powerful and a lasting impact on a person’s personal traits, love life, success at work and much more. Also, numbers are believed to be crucial. Some numbers can have their luck or unlucky members depending on how they conceive those numbers or what they have been made to believe about them. One of such numbers is 13 that are almost universally considered as an unlucky number in the European culture. Also, the Friday 13th is considered universally as being inauspicious.



Background
It is hard to imagine the rational foundation of superstition. There are many researchers that have tried to formulate models to help in understands about the persistence of superstition. For instance, Fundenberg and Levine (2006) came up with the game-theoretical model to show how superstition persists even when people are rational, and it discusses the types of superstitious that have a high likelihood of persisting. Two essential conclusions are that people shape their beliefs in the superstitions and that superstitions are possible under rationality. The superstitions develop when the occurrence of the trigger event has an occasional association with the correct outcome, but the payoff to that outcome needs to be sufficiently large.
Whether they are rational or not, superstitions can result in vital consequences. For that reason, some people have been known to consult horoscopes ahead to making important decisions, and a common example among these people is President Reagan that sought for advice from his astrologist concerning many issues such as, how to approach Mikhail Gorbachev in the discussion on how to end the Cold War in 1985. The tenets in unlucky numbers are widespread. In the United Kingdom, it has been reported that around 28 percent of the streets do not have number 13. Some people also refuse to commence new projects or avoid making major purchase decisions on Friday 13th. There is an estimate that puts business losses in the United States at $1 billion. Another recent report also found out that the flights taking place on Friday 13th are cheaper as compared to the flights taking place on other days in France, Sweden, Australia, and the UK. In contrast, Friday the 13th impact on the stock market has nil, or it may be positive even though it is small (Lucey, 2001; Chung, Darrat & Li, 2014).



In this research paper, we undertake a search he evidence that superstitions can have by looking at the stock market index of some countries. More specifically there will be an analysis and a calculation of the percentage change in the stock market index of 62 countries between the years 2008 and 2009 and the results will be useful in concluding if the average percentage is substantial for the Friday the 13th. There is the usage of the panel regression model with the corrected standard errors. The other aspect that will have examination is the turn of the month effect on Fridays. Three crucial results are associated with the Friday the 13th are observed. The first thing is that the depressed Friday the 13th impact is present when there is a negative return on the previous day. Secondly, when there is a positive return on the previous day, there is no depressed Friday the 13th impact. Thirdly, it is found that Friday the 13th effect does not depend on the growth domestic production of a country when the returns on otehr4 Fridays are leveraged as the yardstick.

Data Summary
The background material that needs to be known for this research is the international stock indices’ unequivocal results found out by Lucey (2000) for the period of 2008 to 2009. The model specified in this paper takes into account some points that help in the analysis of the data at validating the results. The first thing is that Friday the '13th only applies to Fridays. Therefore, as adopted in the previous results, the paper focuses on the daily returns on Fridays. The paper does not incorporate the analysis of the non-Friday days in the analysis. Secondly, the presence of the turn of the Friday’s month effect has to be taken into consideration. One of the choices that will be taken into account is the deletion of the returns at the turn of the month, and the other choice is the addition of a dummy variable to those days. However, the latter is adopted because it enables a convenient distinction of the controversial Friday the 13th impact with the turn of the month effect established. The returns of the days that do not fall in Friday the 13th are used as a control for the assessment.

Thirdly, we use the same data from the DataStream to find out the prior day effect by examining the returns on Mondays. Dummy variables are used to be based on the sign of prior day’s returns. The importance of the dummy variable is that it helps to capture the impacts of the one-day serial correlation. Fourth, previous research work into the area of Friday 13th effect examined the results for the individual stock exchange by country-to-country. We make use of the per capita GDP as a variable to explain the between-country variable. The effects are examined using the panel model. The fifth thing is that the data follows on the one for Lucey. That is because the decision constraints the time we are interested in studying.

Analysis
We obtain the time series of the daily stock index prices for 62 countries from the DataStream. It covers the period between June 1, 2000, And August 31, 2008. The calculation is then done for the daily returns (Ri,t) for the day t of the country I as percentages using the panel regression model below.
Ri,t = ln(Ii,t / Ii,t-1) * 100,
Ii,t-1 is the closing value of the day representing the index on the day t for the country designated i. The theoretical sample, the size used shows that there are 26,722 Fridays whereby there are 431 per country; the bad Thursdays are 11,694; and the turn of the month days are 3,595; while Friday the 13th. These days, of course, may be occasioned by unpredictable events such as holidays, and unexpected closures. Therefore, in case one of the indexes in the equation is missing, it also means that the day t is missing. From the theoretical sample size where Fridays are 26,722, the missing returns on prior Thursdays or Fridays reduce sample size to 25,101 which is a loss of 6 percent. The number of values that are missing on Fridays the 13th and the turn of the Fridays of the month is the same but higher as compared to the number that is missing on the control Fridays. Even though the explanations for the latter results do not offer the concrete grounds for making conclusions, it appears that Fridays the 13th, as well as the turn of the month Fridays, are unlucky days.
The first step in the data analysis is to leverage the conventional approach to finding out the magnitude of the Friday 13th effect. Below is the model that is used:
Ri,t = α0 + α1F13t + β0GDP + β1 (F13t * GDPi)+ δi + Ƹi,t

The model is used to the pooled data of 62 countries with the panel regression approach that as outlined earlier. The purpose of the GDPi expression is to make sure that the estimated coefficient α0 effectively measures the average of the intercepts for the countries if each of the countries is individually applied to the above equation. The same sentiments are also applied to the F13t * GDPi variable and the estimated coefficient designated by α1. The results demonstrate that the presence the depressed Friday the 13th impact (P = 0.009, α1 = -0.103) as compared to the other Fridays. It is shown below that these results are biased towards the determination of a significant effect of Friday the 13th because returns on the used control Fridays have enhancement by the effect of the turn of the month.
According to Chamberlain and his colleagues (1991), adding dummy variable for the turn of the month, TOMt produces the model
Ri,t = α’0 + α’1F13t + α’2TOMt + β’0GDPi + β’1 (F13t * GDPi)+ β’2 (TOMt * GDPi ) + δ’i + Ƹ’i,t

The three variables that contain the GDPi term have addition to the formula due to the reasons explained earlier. The results show that there is a turn of the month effect on the Fridays (α’2 = 0.283, P<0.001) when it if referenced against the other Fridays acting as the control. The findings are consistent with the turn of the month effect contained in some earlier literature such as the one for Kunkel et al., 2003 and McConnel & Xu, 2008. Thus, the addition of the dummy variable to the model reduces the magnitude of the effect of the Friday the 13th (P – 0.10, α’1= -0.064).
The GDP for the unlucky Fridays the 13th, that is, Bt i = 1 and F13t = 1. That shows the average return on the unlucky Fridays the 13th is persistently lower as compared to the average return on the control Fridays across all the 62 countries. The results clearly imply that the depressed effect of Friday the 13th is brought about by the bad day impact. Also, the parallelism shows that the impact is independent of the country as evidenced by their GDP per capita considering the bad control Friday effect.

Conclusion and Remarks
There are three conclusions possible from this study. The first one is that the enhanced good effect of the prior day and the depressed bad effect of the prior day as seen on the control Fridays are part of the GDP function. Those effects are attributed to the variation in the market efficiency. Cognate gross domestic production impacts are exhibited by Fridays the 13th as well as the turn of the Fridays of the month. The differences in the market efficiency also influence the effects. Secondly, it can be observable that there is an enhanced effect of the ‘turn of the month’ on Fridays. If we consider the effect of the prior day control Friday, there is a uniform month effect on Fridays across all the countries examined. The third concussion is that a depressed Friday the 13th effect is also valid. The results, however, shows that a depressed Friday the 13th impact is possible when there is a negative return on the Thursdays the 12th.

It is not easy to satisfactorily explain the reasons for the differences in the results from the findings of Lucey (2000). We can tentatively suggest that earlier findings, such as the one for Agrawal and Tandon (1994) are equivocal. One of the explanations possible might be due the impact of the prior Thursday the 12th. The prior research does not acknowledge the prior effect as they only focus on the returns. The degree that the average returns are negative will depend on the weighted mean of the good and the bad days’ impact. It is paramount that the effects of the Thursday the 12th be put into consideration. It is observed that the returns on good days of Friday the thirteenth are not very different Friday from the returns of the good control Fridays. The bad Fridays the thirteenth are the only days that experience the frightening effect. When the returns from the prior day are positive, the results of Friday the thirteenth are also positive. The reason for that is that on Thursdays the thirteenth, stock markets around the globe persistently assess the Friday the thirteenth as they do to the other Fridays.

Results
Agrawal, A., & Tandon, K. (1994). Anomalies or illusions? Evidence from stock markets in eighteen countries. Journal of international Money and Finance, 13(1), 83-106.
Chamberlain, T. W., Cheung, C. S., & Kwan, C. C. (1991). The Friday the thirteenth effect: Myth or reality?. Quarterly Journal of Business and Economics, 111-117.
Lucey, B. M. (2000). Friday the 13th and the philosophical basis of financial economics. Journal of Economics and Finance, 24(3), 294-301.
McConnell, J. J., & Xu, W. (2008). Equity Returns at the Turn of the Month. Financial Analysts Journal, 64(2), 49-64.
Fudenberg, D., & Levine, D. K. (2006). Superstition and rational learning. Harvard Institute of Economic Research Discussion Paper, (2114).
Chung, R., Darrat, A. F., & Li, B. (2014). Superstitions and stock trading: some new evidence. Journal of the Asia Pacific Economy, 19(4), 527-538.

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