Dummy Variable Regression Function On Spss

Published Date: 02 Nov 2017

CHAPTER 7

Firstly after computing our daily returns, we run our dummy variable regression function on SPSS 19.0 to test the presence of the Day of the week effect. We applied a descriptive analysis in order to view whether there are extreme values in our data set and if so, we will need to amend our data to remove any figure from our distribution.

Table 1.0

Descriptives

Statistic

Std. Error

Returns

Mean

.059106

.0147438

95% Confidence Interval for Mean

Lower Bound

.030196

Upper Bound

.088016

5% Trimmed Mean

.056222

Median

.043203

Variance

.598

Std. Deviation

.7731737

Minimum

-6.3827

Maximum

7.6546

Range

14.0372

Interquartile Range

.5200

Skewness

.196

.047

Kurtosis

17.254

.093

We compare the 5% trimmed mean and mean figures to know if there are extreme values in our distribution. Since the difference between the two figures is not significant (within 2 SD), we conclude that we do not expect outliers to significantly affect our results and hence no need to amend our data.

Moreover we observed that the distribution is non-normal as the kurtosis value is above 3 (kurtosis value = 17.254). It is a leptokurtic distribution as the level of peakedness is relatively high. Normality test is also applied to the distribution

The hypotheses testes are as follows:

Ho: The distribution follows a normal distribution

H1: The distribution does not follow a normal distribution.

Table 1.1

Tests of Normality

Kolmogorov-Smirnova

Shapiro-Wilk

Statistic

df

Sig.

Statistic

df

Sig.

Returns

.135

2750

.000

.791

2750

.000

a. Lilliefors Significance Correction

The statistics are 0.135 and 0.791 for Kolmogorov Smirnov and Shapiro Wilk tests respectively. The p-values are 0.000 <0.05 in both cases implying that we have enough evidence at 5% level of significance to reject Ho. Both normality tests confirm that the distributions were not normal.

To begin with, we make use of a descriptive statistic which will enable us to know whether Monday effect is present in Mauritius and to find out which day has the lowest and highest mean returns.

Descriptive Statistics

N

Mean

Std. Deviation

Monday Returns

550

.039283

.8132669

Tuesday Returns

551

.027862

.6939717

Wednesday Returns

550

.064024

.8146512

Thursday Returns

552

.048454

.7843253

Friday Returns

547

.116316

.7528124

Valid N (listwise)

547

The above table displays the mean return percent and the standard deviation for different trading days. We can clearly observed that the mean value of stock return is lowest on Tuesdays and highest on Fridays with a mean return of (0.027862) and (0.116316) respectively. We may rank the days of week starting form the lowest return to the highest as follows; Tuesday, Monday, Thursday ,Wednesday, and Friday. We found that there is a clear violation of the EMH hypothesis as the mean returns are not equal; however nothing is said about the significance level. Moreover the Standard deviation is larger on Wednesdays and smaller on Tuesdays. This implies that Wednesday’s returns are more volatile.

We will now have a more detail analysis of the day of the week effect for the 11 year periods starting from 2002 until 2012. Since stocks are traded five days a week on the Stock exchange of Mauritius, we tested the day of the week effect by taking a weekday as the benchmark and carried this operation for each of the 5 days. The benchmark day is the day against which the returns of the other weekdays are being compared.

Table 2.0

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Collinearity Statistics

B

Std. Error

Beta

Tolerance

VIF

1

(Constant)

.040

.033

1.198

.231

B2 TUES

-.011

.047

-.006

-.237

.813

.624

1.603

B3 WED

.024

.047

.012

.506

.613

.624

1.601

B4 THURS

.009

.047

.005

.189

.850

.624

1.603

B5 FRI

.077

.047

.040

1.647

.100

.625

1.599

a. Dependent Variable: Returns

The above table shows a multiple regression coefficient output. The error terms in the multiple regression models measure the difference between the regressors. According to the regression model, the more variable the error term, the larger the absolute difference will be expected.

The coefficient B1 is the mean Monday returns while the other coefficients, B2 to B5 represent the differences between the mean returns of Monday and returns from Tuesday to Friday. The differential intercept coefficients B3 to B5 are positive showing that Monday still yields lesser returns that Wednesday, Thursday and Friday. The average value of Rt, the regressand in our model, will tend rise as the values of the regressors are plugged in. However we also noticed that Tuesdays` values was negative implying a lower return than that of Mondays.

[ Insert table 2.1-2.4 about here ]

When we regarded Tuesday as the reference group we observed that the coefficients were positive for all the days of the week. This clearly shows that Tuesdays returns had the lowest coefficient values (B2=0.028) compared to the coefficients of the other remaining days with a higher positive deviations. In fact the results depart from the traditional Monday effect which postulates that Monday returns are lower than the average returns of the other weekdays.

In addition by just observing the coefficients, we may deduce that investors may buys shares at a lower price on Tuesday and sell them at a higher price on other days. Only Friday registered the best returns as it had the highest deviations from the coefficients of the remaining days.

Furthermore taking Wednesday as the benchmark, we found negative values of B1, B2 and B4 thereby showing that Wednesdays` returns was the second highest returns after Fridays. Wednesday had a mean return of (0.063) compared to Monday with a mean return of (0.40), implying a deviation of (- 0.024).

Taking Thursday as a benchmark we observed that both Mondays and Tuesdays had negative beta values with (-0.009) and (-0.020) respectively. On the contrary both Wednesday and Fridays had positive beta values with (0.015) and (0.068) respectively.

Finally considering Friday as the omitted group we observed that all the remaining betas were negative. Only Friday registered the best returns with a mean return of (0.116). Friday had the highest deviations from the coefficients of the remaining days. B5 (0.077) shows by how much Friday returns on average deviated from the Monday returns. Moreover this day of the week appears interesting for many investors as they may sell high on that particular day.

However before arriving at such conclusion, we must first of all analyse whether these results are significant or not. Nonetheless we must draw attention to the fact that the p-value is not significant in any case as the p-values are greater than 0.05. This implies that there is no evidence at 5% level to recognize that the daily means returns are significantly different.

Kruskal- Wallis Test

Table 3

Ranks

DAYS

N

Mean Rank

RETURNS

MONDAY

550

1321.35

TUESDAY

551

1326.04

WEDNESDAY

550

1386.43

THURSDAY

552

1396.05

FRIDAY

547

1448.04

Total

2750

Test Statisticsa,b

RETURNS

Chi-Square

9.736

df

4

Asymp. Sig.

.045

a. Kruskal Wallis Test

b. Grouping Variable: DAYS

The Hypotheses tested are:

Ho: The mean ranks are equal for all categories

H1: The mean ranks are different

The results in table 3 illustrates that the mean ranks are lower on Mondays and highest on Fridays. This result is different from the previous one and here we find that there is a sign of the possible Monday effect. In the test statistic table 3 we note that the returns are distributed as Chi square with 4 degrees of freedom. The probability of the kruskal Wallis statistic is 0.045 which is less than the 5% significance level. Therefore we cannot reject H1 and we deduce that the mean ranks are statistically different from each other. According Kruskal Wallis test, the Mauritian stock market is not efficient. Consequently to have more concrete results, the Mann Whitney pair – wise test is applied.

Mann-Whitney test

We make use of the Mann Whitney test in order to find out whether Monday effect is present on the stock exchange of Mauritius. We also make a pair-wise comparison between the other weekdays, so that we can have a more comprehensible result.

Table 3

Ranks

DAYS

N

Mean Rank

Sum of Ranks

RETURNS

MONDAY

550

550.23

302627.00

TUESDAY

551

551.77

304024.00

Total

1101

Test Statisticsa

RETURNS

Mann-Whitney U

151102.000

Wilcoxon W

302627.000

Z

-.080

Asymp. Sig. (2-tailed)

.936

a. Grouping Variable: DAYS

The hypotheses tested are:

Ho: mean returns are equal

H1: mean returns are different in the 2 categories.

In the "Ranks" table, the sample with the higher mean rank is the group with the greater number of high scores within it. Contrary to the above observations; here we find out that Monday’s returns were lower compared to Tuesdays` mean returns. We can clearly observes that Z =-0.08 and p = 0.936. Since p value is greater than 0.05, we have to accept Ho. This implies that the mean returns are not statistically different. As such we conclude that there is no evidence at 5 % significance level to say that Monday returns were indeed lower than Tuesday returns over the study period.

[Insert Table 3.1-3.8]

Progressing with the Mann Whitney pair wise test, we observed that the mean ranks for Monday were lower than those of the remaining weekdays. Moreover this test allows us to confirm that on average, returns were higher on Fridays that on the rest of the weekdays. Further examination of the analytic values showed than the mean ranks were lower for Tuesday compared to Wednesday, Thursday, and Friday. More over when comparing Wednesdays with the remaining days, we demonstrated that the returns of Thursdays and Fridays were relatively higher. Trying again to rank the days of the week starting with the lowest returns, we arrived at the conclusion that Mondays was the lowest followed by Tuesday, Wednesday, Thursday and then Fridays. Nevertheless we could not reject Ho in any case since the p values were greater than 5%. These p-values allow us to conclude that the mean returns are almost the same and that there is no significant difference.

Statistical Results- Monthly Anomaly

Descriptive Statistics

N

Minimum

Maximum

Mean

Std. Deviation

Jan

11

-.2037

.5522

.191700

.2304152

Feb

11

-1.0824

.1898

-.112638

.3657501

Mar

11

-.3587

.7303

.069368

.2580297

Apr

11

-.2475

.3155

.048306

.1906705

May

11

-.2345

.7013

.056485

.2427340

Jun

11

-.0863

.4079

.105571

.1488748

Jul

11

-.2704

.1956

.017686

.1541361

Aug

11

-.2221

.2360

-.012635

.1491885

Sep

11

-.2669

.4875

.146556

.2183778

Oct

11

-.7835

.4997

.056929

.3525668

Nov

11

-.6290

.7324

.077114

.3288296

Dec

11

-.1889

.1724

.051514

.1061901

Valid N (listwise)

11

The above table shows the Mean and Standard deviation for the 12 months. It also provides us with the maximum and minimum values of the returns for each month. It seems that almost all months with the exception of February and August, are actually having positive mean returns. Further observation allows us to confirm that January was eventually carrying the highest mean returns and that February was the lowest. January was in fact offering an opportunity for investors to reap abnormal returns. Moving to the standard deviation, we find out that February which obtains the lowest mean returns was actually having the highest deviation in its returns. This is shown clearly by the negative minimum value (-1.0824) and the maximum positive value (0.1898). October obtains the second best deviations (0.3525) compare to June with the lowest deviations (0.1488). However this table is incomplete as nothing is said about the significant level. So, we proceed again with the model summary table which will provides us with the multiple regression coefficient outputs.

Table 6

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1

(Constant)

.192

.073

2.617

.010

B2 FEB

-.304

.104

-.346

-2.938

.004

B3 MAR

-.122

.104

-.139

-1.181

.240

B4 APR

-.143

.104

-.163

-1.384

.169

B5 MAY

-.135

.104

-.154

-1.305

.194

B6 JUN

-.086

.104

-.098

-.831

.407

B7 JUL

-.174

.104

-.198

-1.680

.096

B8 AUG

-.204

.104

-.232

-1.972

.051

B9 SEP

-.045

.104

-.051

-.436

.664

B10 OCT

-.135

.104

-.153

-1.301

.196

B11 NOV

-.115

.104

-.130

-1.106

.271

B12 DEC

-.140

.104

-.159

-1.353

.179

a. Dependent Variable: Returns

The Table above shows the results of our regression. The mean returns for January starting from 2002 until 2012 is shown by (0.192). B2 to B12 show by how much mean returns of each respective month diverges from January returns. The betas in fact represent the difference of remaining returns from the January return. Here January is the benchmark category and the negative return implies that January returns are superior to non January returns. Since the P-value is 0.01 which is less than 0.05, we conclude that January mean returns were significantly different from the other average returns.

[Insert table 6-6.11]

The same test is being done by taking all the rest of the months as benchmark each time so that we can have a better observation and may be able to rank them according their average returns. Taking February as the omitted category, we examine that all the deviations of the non February returns was positive. Contrary to January which was reaping the highest returns, February was in fact having the slimmest returns. This incites us to declare that February produced the poorest returns and hence might be wise for investors to buy stocks in February and sell them in January. This trade of stocks can eventually be done since the p values are statistically significant. Moreover taking march as the comparison group , we observed that the betas (B2,B4,B5,B7,B8,B10,B12) were negative. This implies that March return was higher than those monthly mean returns. In this continuous process, picking April as the benchmark we found that almost all betas were positive except for B2, B7 and B8. We done this same exercise for the rest of the month until December and kept on observing the deviations. Finally we arrived at the conclusion that February was the lowest bearing returns followed by August, July, April, December, May, October, March, November, June, September and January. However we can clearly notice that all the rest p values are not significant except for Januarys and Februarys. More over since all T statistic are negative, this means that we cannot reject Ho (equality in mean monthly returns).

Kruskal Wallis Test

Ranks

MONTHS

N

Mean Rank

RETURNS

JANUARY

11

92.18

FEBRUARY

11

49.73

MARCH

11

61.45

APRIL

11

66.09

MAY

11

55.45

JUNE

11

73.36

JULY

11

60.36

AUGUST

11

49.91

SEPTEMBER

11

83.09

OCTOBER

11

69.00

NOVEMBER

11

71.00

DECEMBER

11

66.36

Total

132

Test Statisticsa,b

RETURNS

Chi-Square

13.160

df

11

Asymp. Sig.

.283

a. Kruskal Wallis Test

b. Grouping Variable: MONTHS

The Kruskal Wallis test is also applied to check if the monthly anomalies do exist in Mauritius.

The hypotheses tested are:

Ho: mean returns for all months are equal.

H1: Mean returns are different.

Here our result goes in line with the previous results showing that January is the month yielding the highest abnormal returns. This is shown by the mean rank (92.18) which is above all the remaining ranks. Furthermore we also identified that September was the next best highest mean ranks and February was the lowest. However we are required to reject H1 as the p-value exceeds the 5% significance level. Overall, the Kruskal Wallis test does not confirm the presence of anomalies in the stock market since statistics goad us to accept the null hypothesis. So, to have a better overview of the mean returns, we make use of Mann Whitney test (pair wise comparison).

Mann Whitney Test

Ranks

MONTHS

N

Mean Rank

Sum of Ranks

RETURNS

JANUARY

11

15.27

168.00

FEBRUARY

11

7.73

85.00

Total

22

Test Statisticsb

RETURNS

Mann-Whitney U

19.000

Wilcoxon W

85.000

Z

-2.725

Asymp. Sig. (2-tailed)

.006

Exact Sig. [2*(1-tailed Sig.)]

.005a

a. Not corrected for ties.

b. Grouping Variable: MONTHS

The Output gives the mean rank for each group. The mean rank is 15.27 for January compared to 7.73 for February. There are two p values labelled Asymp.sig(2tailed) and Exact Sig.[2*(1- tailed Sig.)]. To decide whether to reject Ho we make use of the asymptotic significance. The null hypothesis denotes equal mean ranks while the alternative hypothesis states unequal means. Since the p value is less than 5% we can affirm that there is a significance difference and hence reject the null hypothesis.

Insert table 8.1-8.11

Moving ahead with the Mann Whitney pair wise test of January with the rest of the months, we notice that there is a significance difference for 4 pair wise tests [(Jan-feb), (Jan-Jul), (Jan-Aug), (Jan-Dec)]. While for the other pair test we have to accept the null hypotheses. These results supports our previous findings namely the model summary table.

Insert table 8.12-8…..

The same comparison process is being done again and again for all the months of the year. Taking February as the comparison group we found that there is a significant difference in only (Feb-sep). Since September is the next best reaping highest mean returns and February is the lowest one, this implies that investor can still buy on February and sell it on September. However the mean returns are almost the same when taking March, April, May, June, July, August, September, October , November, December as the comparison group except for (June –Sept) where p value is lower than 5%.

Statistical Result – Turn of month anomaly

For the purpose of our research, we compare the ROM and TOM for the 11 years ranging form 2002 to 2012. We shall use the Mann Whitney pair wise test to make the comparison among the returns of the Tom [event window (-1, 4)] to the returns of the rest of the months. The result is as follows:

Ranks

MONTHS

N

Mean Rank

Sum of Ranks

RETURNS

TOM

132

138.11

18230.00

ROM

132

126.89

16750.00

Total

264

Test Statisticsa

RETURNS

Mann-Whitney U

7972.000

Wilcoxon W

16750.000

Z

-1.193

Asymp. Sig. (2-tailed)

.233

a. Grouping Variable: MONTHS

The Mann Whitney provided us with an overview of the mean returns for both groups. From the above table we find that the mean returns for TOM is actually greater than that of the ROM. TOM`s mean ranks is given by (138.11) compare to ROM`s mean ranks (126.89). This in fact shows us that in reality turn of the month anomaly do exist. Nevertheless when analyzing the p value, we observe that the result is statistically insignificant since (0.233) > (0.05). However this test does not provides us information about the mean ranks for each of the 11 years. In this specific case, we shall use divide the data into 3 sub periods and shall use the Wilcoxon Signed rank test. The 3 sub periods are as follows: 1st (2002-2005), 2nd (2006-2009) and 3rd (2010-2012).

Wilcoxon signed rank test

Ranks

N

Mean Rank

Sum of Ranks

TOM(02) - ROM(02)

Negative Ranks

8a

5.88

47.00

Positive Ranks

4b

7.75

31.00

Ties

0c

Total

12

TOM(03) - ROM(03)

Negative Ranks

6d

6.17

37.00

Positive Ranks

6e

6.83

41.00

Ties

0f

Total

12

TOM(04) - ROM(04)

Negative Ranks

4g

4.50

18.00

Positive Ranks

8h

7.50

60.00

Ties

0i

Total

12

TOM(05) - ROM(05)

Negative Ranks

6j

6.17

37.00

Positive Ranks

6k

6.83

41.00

Ties

0l

Total

12

a. TOM(02) < ROM(02)

b. TOM(02) > ROM(02)

c. TOM(02) = ROM(02)

d. TOM(03) < ROM(03)

e. TOM(03) > ROM(03)

f. TOM(03) = ROM(03)

g. TOM(04) < ROM(04)

h. TOM(04) > ROM(04)

i. TOM(04) = ROM(04)

j. TOM(05) < ROM(05)

k. TOM(05) > ROM(05)

l. TOM(05) = ROM(05)

Test Statisticsc

TOM(02) - ROM(02)

TOM(03) - ROM(03)

TOM(04) - ROM(04)

TOM(05) - ROM(05)

Z

-.628a

-.157b

-1.647b

-.157b

Asymp. Sig. (2-tailed)

.530

.875

.099

.875

a. Based on positive ranks.

b. Based on negative ranks.

c. Wilcoxon Signed Ranks Test

The first part of Wilcoxon test gives the number of observation (N) for the monthly returns in the year 2002 until 2005. We find that in 2002 there were 8 negative ranks which explain that returns of TOM were lesser than returns of ROM. However in 2004 a reverse result was found showing 8 positive ranks for TOM. This result goes in line with Turn of the month anomaly which states that TOM are always greater than ROM. Contrary to the above results, year 2003and 2005 had equal number of positive and negative ranks with a slightly larger positive mean(6.83) compare to (6.17) for both years. Analyzing the T statistic, we notice that for all the 4 years, the p value is greater than 0.05. This implies that the above results are insignificant.

Ranks

N

Mean Rank

Sum of Ranks

TOM(06) - ROM(06)

Negative Ranks

8a

6.13

49.00

Positive Ranks

4b

7.25

29.00

Ties

0c

Total

12

TOM(07) - ROM(07)

Negative Ranks

6d

5.17

31.00

Positive Ranks

6e

7.83

47.00

Ties

0f

Total

12

TOM(08) - ROM(08)

Negative Ranks

6g

5.50

33.00

Positive Ranks

6h

7.50

45.00

Ties

0i

Total

12

TOM(09) - ROM(09)

Negative Ranks

5j

6.20

31.00

Positive Ranks

7k

6.71

47.00

Ties

0l

Total

12

a. TOM(06) < ROM(06)

b. TOM(06) > ROM(06)

c. TOM(06) = ROM(06)

d. TOM(07) < ROM(07)

e. TOM(07) > ROM(07)

f. TOM(07) = ROM(07)

g. TOM(08) < ROM(08)

h. TOM(08) > ROM(08)

i. TOM(08) = ROM(08)

j. TOM(09) < ROM(09)

k. TOM(09) > ROM(09)

l. TOM(09) = ROM(09)

Test statistic

TOM(06) - ROM(06)

TOM(07) - ROM(07)

TOM(08) - ROM(08)

TOM(09) - ROM(09)

Z

-.784a

-.628b

-.471b

-.628b

Asymp. Sig. (2-tailed)

.433

.530

.638

.530

a. Based on positive ranks.

b. Based on negative ranks.

c. Wilcoxon Signed Ranks Test

Now using the Wilcoxon test for the years 2006 to 2009, we find most of the result is showing that the Turn of the month effect is not convincing except for the last year. The mean ranks and Sum of ranks for TOM are always greater than that of ROM. This is because Wilcoxon test makes an average of the TOM`s returns and compares it with ROM`s average returns for each month. However this Mean ranks doesn’t help us in our analysis and hence we are more concern with the number of time TOM exceeds ROM. Observing the years 2007 and 2008, we find that there were an equal number of positive and negative ranks. Moving to the T statistic, we arrived at the conclusion that once more the result was not statistically significant.

Ranks

N

Mean Rank

Sum of Ranks

TOM(10) - ROM(10)

Negative Ranks

5a

7.00

35.00

Positive Ranks

7b

6.14

43.00

Ties

0c

Total

12

TOM(11) - ROM(11)

Negative Ranks

6d

5.83

35.00

Positive Ranks

6e

7.17

43.00

Ties

0f

Total

12

TOM(12) - ROM(12)

Negative Ranks

4g

4.75

19.00

Positive Ranks

8h

7.38

59.00

Ties

0i

Total

12

a. TOM(10) < ROM(10)

b. TOM(10) > ROM(10)

c. TOM(10) = ROM(10)

d. TOM(11) < ROM(11)

e. TOM(11) > ROM(11)

f. TOM(11) = ROM(11)

g. TOM(12) < ROM(12)

h. TOM(12) > ROM(12)

i. TOM(12) = ROM(12)

Test Statisticsb

TOM(10) - ROM(10)

TOM(11) - ROM(11)

TOM(12) - ROM(12)

Z

-.314a

-.314a

-1.569a

Asymp. Sig. (2-tailed)

.754

.754

.117

a. Based on negative ranks.

b. Wilcoxon Signed Ranks Test

Based on the above table, the results obtained are more favorable for TOM rather than for the rest of the months. More positive TOM`s ranks was observed for the year 2010 and 2012 compare with that of year 2011, which had equal number of TOM and ROM ranks. For the year 2010, there were 7 occasions out of 12 when TOM was greater than ROM. TOM again exceeds ROM on 8 occasions in 2012. However when looking at the p values, we concluded that the results were not significant.

INTER TEMPORAL COMPARISON

Ranks

Mean Rank

2002

6.25

2003

6.79

2004

6.31

2005

5.79

2006

7.04

2007

5.90

2008

5.58

2009

6.13

2010

5.54

2011

5.06

2012

5.60

The purpose for making an inter temporal analysis is to identify in which years was the returns of each day of the week was the lowest and highest. The analysis is made for the last 11 years taking each day of the week as the observed value. We therefore applied both the kruskal wallis test and the Friedman test to make the comparison. The null hypothesis states that returns are equal overtime while H1 states unequal returns. We first of all we starts our analysis with Monday returns.

Kruskal- Wallis Test Friedman Test

Ranks

Years

N

Mean Rank

Monday Returns

2002

50

290.00

2003

51

315.22

2004

52

292.29

2005

49

268.12

2006

48

320.15

2007

51

288.49

2008

51

248.75

2009

49

285.90

2010

51

241.08

2011

50

227.00

2012

48

254.00

Total

550

Test Statisticsa,b

Monday Returns

Chi-Square

18.001

df

10

Asymp. Sig.

.055

a. Kruskal Wallis Test

b. Grouping Variable: Years

Test Statisticsa

N

48

Chi-Square

14.667

df

10

Asymp. Sig.

.145

a. Friedman Test

From the above tables, we find that both kruskal wallis and Friedman test gives the same results. Returns on Monday was fairly high in 2002 and 2003 but it drop for the following 2 years till 2005. In general, it became apparent that averages Monday returns was better in 2006, 2003, 2004 consecutively and that the lowest returns were in the years 2011, 2010 and 2008. Taking a close watch at Kruskal wallis test, the highest mean returns was given by a mean rank of (320.15) and lowest rank by (227.00). Nevertheless since both test p values are greater than the 5% significance level, we conclude that the results were not statistically significant.

Insert table

Taking Tuesday as the observed value,we find the highest mean rank given by Kruskal Wallis test was in 2007 given by (315.65) and the lowest in 2008 by (225.84). Further, we assess that the three highest returns was in the year 2007,2004 and 2010 whereas the lowest three mean rank were in the years 2008,2012 and 2009. The Friedman test displayed more or less the same result. Here again since the p value is (0.106), we have to accept the null hypothesis.

Moving to Wednesday, we observed that 2003, 2004 and 2006 were the highest producing returns compare to Thursdays, where the rankings was different. In fact 2006, 2007 and 2003 topped the list for Thursdays. However for both Wednesdays and Thursdays, the slimmest returns were observed in the years 2008, 2012 and 2011.The same result was obtained using the Friedman test.

We witnessed almost the same scenario with Friday returns as the lowest returns were observed in the same years, which are 2012, 2008 and 2011.On the whole it seems that the abovementioned 3 years continued on the same trend though the highest mean returns were observed in different years. The highest returns were observed in the years 2009, 2002 and 2006.

In addition to confirm our findings; we made another inter temporal analysis for daily returns. We tried to assess the behaviour of daily returns across the research interlude, i.e. over the 11years.

Kruskal Wallis Test Friedman Test

Ranks

Years

N

Mean Rank

Daily Returns

2002

248

1378.90

2003

252

1483.42

2004

254

1473.37

2005

249

1360.34

2006

251

1495.93

2007

250

1466.51

2008

248

1170.42

2009

250

1441.11

2010

252

1396.65

2011

249

1269.78

2012

247

1186.62

Total

2750

Ranks

Mean Rank

2002

6.09

2003

6.56

2004

6.32

2005

6.06

2006

6.45

2007

6.31

2008

5.15

2009

6.27

2010

6.04

2011

5.53

2012

5.23

Test Statisticsa,b

Daily Returns

Chi-Square

54.493

df

10

Asymp. Sig.

.000

a. Kruskal Wallis Test

b. Grouping Variable: Years

Test Statisticsa

N

247

Chi-Square

52.693

df

10

Asymp. Sig.

.000

a. Friedman Test

When we took daily returns as a whole population, we found out that 2003, 2004 and 2006 were among the 3 highest mean returns for both test. Moreover starting from the slimmest returns, we found that 2012 got the lowest mean returns followed by 2008 and lastly by 2011. The same rankings were observed in both tests and the results were statistically significant.