Should Investors on Equity Markets Be Superstitious (on the Example of 52 World Stock Indices)?

The problem of efficiency of financial markets, especially the weekend effect, has always fascinated scientists. The issue is significant from the point of view of assessing the portfolio management effectiveness and behavioral finance. This paper tests the hypothesis of the unfortunate dates effect upon52 equity indices in relation to the following four approaches: close - close, overnight, open-open, open-close calculated for the sessions falling on the 13th and 4th day of the month, Friday the 13th, Tuesday the 13th. In the following part of the paper, the statistical equality of one-session average rates of return (close-close) for sessions falling on Friday 13th and sessions falling on other Friday sessions will be compared, as well as for sessions falling on Tuesday the 13th and sessions falling on other Tuesdays. The last part of the paper consists of the analysis of the correlation coefficients of Friday the 13th (close-close) rates of return calculated for the analyzed equity indices’ pairs.


Introduction
The

Literaturę Review
B elief in the ill-fortune that supposedly accompanies the o f 13th as well as the date o f Friday the 13th is widespread across the W estern world and has ancient and somewhat uncertain origins7. Both num ber 13 and Friday are characterized by long and separate histories associated with "bad luck". It is believed that these two were com bined in order to create an unfortunate date at the beginning o f the 20th century8.
In literature there are a lot o f explanations for these two lines o f superstitions: Christ was crucified on Friday, and the num ber o f people seated at the table for the Last Supper was 13. Even in advanced countries, people are prone to superstitions such as daily newspapers publishing horoscopes to guide their readers. Nowadays many buildings skip the thirteenth floor, streets lack num ber 13th and hospitals decline to label their operating theatres with that num ber9. Fudenberg and Levine theorize that superstitious beliefs can persist if the probability o f being exposed as untrue is sufficiently low10. If there is always any chance o f a bad outcome when following the superstition and some chance of a good outcome when not following the superstition, any person might not realize that the belief is untrue, and, persists in the superstition11.
Psychology and anthropology researchers suggest that people rely on superstition as a way to cope with misfortune and uncertainty, and to rationalize a complex world12. 7

Data and Methods
The research is divided into six parts. The calculations were proceeded concerning where: In the case when the population variances are unknown and cannot be assumed that they are equal, the num ber o f degrees o f freedom will be expressed according to the following form ula34:  (4) where: N -total number of observations across all the groups; _ ri = --average rank of all the observations in group i; ni ni -number of observations in group i; ri j -the rank (among all the observations) of observation j from group i. In all the analyzed cases, the p-values will be calculated. If the p-value is less than or equal to 0.05, then hypothesis H 0 is rejected in favor of hypothesis H 1. Otherwise,there is no reason to reject hypothesis H 0.
For each of the analyzed indices the following rates of return will be calculated: Ot-i -open price in period t-1. The paper consists of six parts: In the first part, the test for equality of two average rates of return will be exemplified for the rates of return in two populations. Assuming that if the first population is composed of the rates of return calculated for the session on the 13th day of the month, then the second population determines the rates of return for all the remaining sessions.
In the second part, the test for equality of two one-session average rates of return will be exemplified for the rates of return in two populations. Assuming that if the first population is composed of the rates of return calculated for the session falling

The analysis of the calendar effect -13th day of the month
The results of testing the zero hypothesis with the use of average rates of return for two different populations permit to draw the following conclusions (see also Table 1

The analysis of the calendar effect -13th day of the month falling on Friday
The results of testing the zero hypothesis with the use of average rates of return for two different populations perm it to draw the following conclusions (see also

The analysis of the calendar effect -13th day of the month falling on Tuesday
The results of testing the zero hypothesis with the use of average rates of return for two different populations permit to draw the following conclusions (see also

The analysis of the calendar effect -4th day of the month
The results of testing the zero hypothesis with the use of average rates of return for two different populations permit to draw the following conclusions (see also    Source: the author's own calculation.

The analysis of the calendar effect -the 13th day of the month falling on Friday vs other Fridays with the use of close-close rates of return
The  Table 5.

T ab le 5. P e rcentag e o f positive rates o f re tu rn , one-session a verag e rates o f retu rn fo r sessions fa llin g on Friday th e 1 3 th a n d fo r o th e r sessions fa llin g on Friday.
Shaded boxes indicate the equity indices for which the difference between the average rates of return in two populations of rates of return was statistically significant regarding eguality of two average rates of return. Source: the author's own calculation.

The correlation coefficients for the rates of return (close-close) falling on Friday the 13th
The  Source: the authors own calculation.
The highest value o f positive correlation coefficients was registered for OSE (50), and the lowest one for SO FIX index (23) -see Table 6.