«Published Annually Vol. 6, No. 1 ISBN 978-0-979-7593-3-8 CONFERENCE PROCEEDINGS Sawyer School of Business, Suffolk University, Boston, Massachusetts ...»

As Table 9 shows, the mean monthly change of the last subperiod (0.60%) was significantly different from zero at 1% level, and higher than for the previous subperiod. The mean monthly change of April (2.09%) and December (1.53%) were significantly higher than zero. Whereas in the previous subperiod four months suffered negative mean monthly changes, in this subperiod it was two months: August (-0.32% -- not significant), and September (-1.41%) which was significantly different from zero at 6.9% level, and significantly different from the mean changes of the other months at 1% level. The mean changes of April and December are different from the other months at 3% level and 7% level.

The standard deviation for this subperiod (4.48%) was higher than that of the previous subperiod (3.57%). This may be attributable to the breakdown of the Breton Woods system, as well the effect of great volatility in oil prices, commodity prices, interest rates, and technological innovations which caused greater and speedier information flows. It is also partly attributable to the ‘dot-com’ mania, the stock market bubble, and the subsequent burst, which affected smaller stocks more than it affected larger stocks. March, May, June and December saw lower variances, and October exhibited higher variance compared to the other months. So for three subsequent subperiods December saw lower variances compared to the other months. It appears from the positive mean changes for December (specially for the last two subperiods) there was less end-of-year selling of DJIA stocks which are large and stable. The other aspect to note is that only in the last subperiod October saw highest standard deviation of monthly changes (6.57%). The highest standard deviation of monthly changes that a month went through was in April during 1929 to 1945 (13.14%).

The month effect for the various sub-periods in terms of mean of a month being different from the means of the other months

shows the following patterns:

1896-2008: Positive December (p=0.01), Negative September (p = 0.002) and February (p = 0.06) Conference papers © Knowledge Globalization Institute, Pune, India, 2012 1896-1928: Positive August (p = 0.051), and negative February (p = 0.03) 1929-1945: mean change of none of the months is significantly different from those of the other months even at 10% level 1946-1972: Positive December (p = 0.01), negative February (p = 0.03) and June (p = 0.05) 1973-2008: Positive April (p=0.03) and December (p=0.07), and negative September (p = 0.01) The mean monthly change of September was negative for the entire period as well as for each subperiod. However, the negative September effect was not significant in the first three subperiods, rather in the last subperiod, as well as for the entire period. Two of the subperiods exhibited negative February effect at 3% level. For the entire period, negative February effect was at a level of significance of 5.7%. In the third subperiod, positive December effect was at 1% significance level, whereas it was significant at 1.3% level in the entire period.

Comparisons of mean of monthly changes over four subperiods

Figure 3 graphically contrasts the means of monthly changes over the four subperiods. At least for 8 months of the 1929-1945 subperiod, means of monthly changes were way off the rest of the means (three in the positive territory and five in the negative territory). The Depression years caused the overall mean of this subperiod to be the lowest of all subperiods. The mean monthly changes underwent wild swings. For example, from a high of 4.05% in August, it went to a low of -2.81% in September. That had a significant impact on the mean changes of August and September when we consider the entire period.

The means of monthly changes of the other three subperiods were rather close.

Figure 3: Comparisons of means of monthly percentage changes of DJIA:1896-1928 vs. 1929-1945 vs. 1946-1972 vs. 1973

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-4 1896-1928 1929-1945 1946-1972 1973-2005 Conference papers © Knowledge Globalization Institute, Pune, India, 2012 As Table 10 shows, Kruskal-Wallis test of the medians of monthly changes of the four subperiods do not show any significant difference (H-statistic = 0.37; p = 0.95). Though not significantly different, the third subperiod has the highest median followed by the first.

Table 10: Results of Kruskal-Wallis Test of Difference in Medians of Monthly Changes of Four Subperiods

Similar is the result from Mood’s Median test (Chisquare = 0.99; p = 0.80).

We used t- tests to find differences in the means of the six pairs that can be formed with the four subperiods. No significant difference was revealed. We used nonparametric Mann-Whitney tests to find differences in the medians of the six pairs. Again, no significant difference was revealed.

We used F-test to detect differences in the standard deviations of the six pairs obtained from the four subperiods. Interestingly we find the variances of each subperiod to be highly significantly different at levels of significance of 0.00 in each case. The second subperiod has the highest standard deviation, then the first, then the last, and the third subperiod has the lowest standard deviation. From 8.62% standard deviation of monthly changes that we found for the second subperiod, it came down to 3.57% (a fall of about 59%). In the last subperiod, it increased to 4.51% (an increase of over 26%).

Month Effect Sans Outliers

We wanted to see how the results would change if we excluded months in which the change was larger than 15% (Case 1) or 10% (Case 2). Specifically, we wanted to see if the negative September effect for the entire data set may have been significant because of few large drops in that month. On reviewing the results of this line of analysis, we find that the mean percentage change was 0.63% for Case 1 (excluding 15%) and 0.67% Case 2 (excluding 10%) as compared to 0.55% for the entire data set (1896-2008), which shows the larger monthly changes were more negative than positive.

For the entire period (1896-2008) without removing any outliers, we have found that September had the most negative monthly average decline of 1.19%, which was significantly different from the remaining months. When we remove the months with changes larger than 15% (20 instances), we find that the month of December with the largest mean positive increase of 1.56% also becomes significantly different than the remaining months (Table 11).

8 Results are not reported for brevity.

9 Results are not reported for brevity.

When we remove the months with changes larger than 10% (90 instances), we find that the month of February with a small mean decline of 0.04% also becomes significantly different from the remaining months (Table 12). Whereas, September and December are significantly different than the remaining months with p-values under 0.01, February is different with a higher pvalue of 0.06. The September effect does not go away when outliers are excluded, but we find a very significant positive December effect and a less significant February effect.

Conference papers © Knowledge Globalization Institute, Pune, India, 2012 During the first period (1896-1928), there were three months with changes larger than 15% and 35 months with changes larger than 10%. We observe a negative month effect in February before removing outliers. On removing the three months with changes over 15%, we see a positive month effect in August in addition to the negative month effect in February. On removing 35 months with changes in excess of 10%, we see a complete change to a negative month effect in September and positive month effect in December.

During the second period (1929-1945), there were 15 months with changes in excess 15% and 36 months with changes larger than 10%. Incidentally, there have been only five other months with changes in excess of 15% in all of the remaining periods.

This period had the largest ever decline of 30.70% and the largest ever increase of 40.18%. In spite of such large fluctuations, there was no month effect whatsoever during this period even when the outliers are removed.

During the third period (1946-1972), there was no month with percentage change larger than 15% and only one month with change larger than 10%. As a result, the negative month effects observed in February and June and positive month effect in December remained unchanged when the lone outlier was removed. Significantly, no month effect was observed for September during this period.

In the last period (1973-2008), there were only two months with changes larger than 15% (both negative) and 18 months with changes larger than 10%. During this period, only a negative September effect was observed, which remained unchanged when the outliers are removed.

We also looked at the variances of monthly percentage changes for the entire period. Before removing any outliers, April’s variance was higher compared to that of the other months and the variances of January, February and December were lower. On excluding the 20 months with changes larger than ± 15%, the variances of September and November were found higher and the variances of February and December were lower (Table 11). On excluding 90 months with changes larger than ±10%, only July’s variance was larger than that of the other months and the variances of February and December were lower than those of the other months (Table 12).

Half-Monthly Effect

Continuing our search for anomalies, we divided each month into two parts – first half and second half. This gave us 24 halfmonthly periods. We then tested the previous three hypotheses for 1896-2008:

We summarize our findings below (from Tables 13 A and B) with I indicating the first-half of the month and II the second half of

the month:

The mean of percentage changes for the half-monthly periods during 1896-2008 was 0.28%, which was statistically significant with a p-value of less than 0.03.

The means of percentage changes for January I, March I, April I, July I, November I, and December II were significantly greater than zero. Mean of percentage changes for September II was significantly lower than zero.

10 Tables for the rest of this section will be provided on request.

The means of percentage changes for February II and September II were significantly lower (and negative) than the means of percentage changes for the remaining 23 half-monthly periods. April I and December II experienced significantly higher means than the remaining 23 half-monthly periods.

Standard deviations of the percentage changes for February I, February II, and December II were significantly lower than the remaining 23 half-monthly periods. In other words, the mean percentage changes for these half-monthly periods were significantly more consistent than the other half-monthly periods. October II, November I and December I experienced significantly higher standard deviations.

Considering whole months, as we did earlier, we found that in descending order, July, August and December experienced the highest mean changes. We now find that the higher means of July was attributed to the first halves of the months and for December, the second half. The second half of December experienced the highest mean change (1.47%) which was significantly Conference papers © Knowledge Globalization Institute, Pune, India, 2012 higher than for the other 23 half-month periods, and the standard deviation was significantly lower compared to the other periods.

We have explored three types of anomalies in the DJIA – if the mean of monthly percentage changes of each month over a period was different from zero, if the mean of monthly percentage changes for a month during a period is different from the means of all the other months in the period, and if the variance of monthly percentage changes for a month during a period is different from the variances of all the other months in the period. For the 1,347 monthly changes in our study, we find that the mean of monthly percentage changes was a significant 0.55% or 6.60% annualized. We find that the only significant month effect occurred in September (mean of monthly percentage changes being negative and significantly less than for the other eleven months) with a mean decline of -1.19%. It is hard to explain the significant negative returns for September. One possible reason might be that the volatility of daily percentage changes of October is high (this is our next area of investigation); if that is the case, we would expect significant number of investors to sell in September and stay away from stocks until October is over.

Another possible reason might be higher number of home closings in September which would possibly cause some sell-offs in the month to make down payments. August experienced the largest mean increase of 1.26%, followed by July (1.25%), December (1.17%) and January (1.05%). These means are significantly greater than zero. But none of these means are significantly different from the mean changes of the other months.

The mean monthly change of September was negative for the entire data set as well as for each subperiod. However, the negative September effect was significant not in the first three subperiods, rather in the last subperiod, as well as for the entire data set. Two of the subperiods exhibited negative February effect at 3% level. For the entire data set, negative February effect was at a level of significance of 5.7% level. In the third subperiod, positive December effect was significant at 1% level, whereas it was significant at 1.3% level in the last subperiod.

We investigated if the negative September effect may have been because of some large outliers. We deleted monthly changes of 15% and 10%. The negative September effect does not go away. We also find that the negative September effect is more a result of the second half of September than first half. The second half of December experienced the highest mean change (1.47%) which was significantly higher than for the other 23 half-month periods, and the standard deviation was significantly lower compared to the other periods.