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

Agrawal and Tandon (1994) find for nineteen countries covering data for 1970’s and 1980’s that the mean January returns are high – significantly high for eleven countries. Hawawini and Keim (2000) survey international findings and show that the high returns for January relative to other months, if used as explanatory variable, better accounts for cross-sectional returns of stocks than the CAPM beta or some other data-driven models proposed in recent times.

We intend to contribute to this growing literature by exploring month effect in the Dow Jones Industrial Average – the most popular stock index in the world. The stocks in the DJIA being among the most closely followed should render them efficiently priced. Hence, one would not expect anomalies like month effect to be exhibited by the DJIA.

An earlier work using the same index is by Lakonishok and Smidt (1988). It uses data from 1897 to 1986. Not only do we use a longer data set, but we also use different statistical tests to analyze month effect. Lakonishok and Smidt’s primary concern is to explore anomalies in returns around the turn of the week, around the turn of the month, around the turn of the year, and around holidays. They do not rigorously explore month effects as we do. They test if the means of monthly percentage changes are significantly different from zero and also do a sign test on the percentage of positive returns. We explore month effect from May 1896 to December 2008 from two perspectives: (a) for a given period, if the mean of monthly percentage changes of each month was different from zero, and (b) for a given period, if the mean of monthly percentage changes for a month was different from the means of all the other months. We also explore month effect over four subperiods during which the economy underwent structural changes over the last century. For the entire data set of 1,348 months, January mean return was 6 Wachtel introduced the concept of January effect in 1942, but Rozeff and Kinney’s article in the widely respected Journal of Financial Economics was the first evidence of January effect that attracted widespread attention.

Conference papers © Knowledge Globalization Institute, Pune, India, 2012 the fourth highest after July, August and December. This finding is similar to that of Lakonishok and Smidt who used data from 1897 to 1986. These findings reinforce the conclusions that the January effect is pronounced in the case of small firms and not in the case of large firms.

The next section describes the methodology used, description of data and descriptive statistics, analysis of results, and finally we summarize and conclude.

Our data consists of the percentage changes in the monthly closing values of the Dow Jones Industrial Average (DJIA) from May 1896 until December 2008. The DJIA is stock-price weighted and hence does not include dividends. It may seem that analysis of month effect will be affected by the omission of dividends. Lakonishok and Smidt (1988) find that this omission does not seem to affect their results with respect to month effect. Hence we do not include dividends.

In addition to analyzing the data for the entire period (May 1896 to December 2008), we divide the entire period into the

**following subperiods to gain deeper insight into the performance of DJIA:**

1896 to 1928 (which includes the World War I);

1929 to 1945 (Great Depression years, and World War II);

1946 to 1972 (which includes the stable period after World War II and the Breton Woods fixed exchange rate era, and the break down of that era in 1972);

1973 to 2008 (which includes the volatile world we have lived in since the first oil crisis of 1973).

We hope to show that the month effect is sensitive to the time period under study.

Many studies have used the dummy variable methodology to detect market seasonality. Chien, Lee and Wang (2002) provide statistical analysis and empirical evidence that the methodology may provide misleading results. We avoid this methodology.

**We study the month effect in terms of monthly percentage changes in three different ways:**

If the mean of monthly percentage changes is different from zero for the sample as well as for each month within the sample.

We subject the mean percentage change for a given month i to the following hypothesis test: Ho: i = 0 vs. Ho: i 0. Unless otherwise stated, significance in all cases is tested at 5% level.

If the means of the monthly percentage changes for a month is different from the other eleven months. We conduct the following hypothesis test for a given month i: Ho: i = j vs. Ho: i j, where j = {1, 2, …, i-1, i+1,,,,,, 11, 12}. Since we found the variances for the periods i and j to be unequal in many cases, we decided to use the more conservative t-test assuming unequal variances.

If the variability of the percentage changes for a given month is significantly different from the remaining eleven months. We conduct the following hypothesis test for a given month i: Ho: i = j vs. Ho: i j, where j = {1, 2, …, i-1, i+1,,,,,, 11, 12}.

Conference papers © Knowledge Globalization Institute, Pune, India, 2012 In addition to standard t-test which assumes normal distribution of the data, we also use Kruskal-Wallis non-parametric test which tests for differences among several population medians, and does not depend on normal distribution of data. We also use Mood’s Median Test which performs a nonparametric analysis of a one-way layout. It is highly robust against outliers and errors in data. Further, we use Mann-Whitney test which performs a two-sample rank test for the difference between two population medians.

The data consists of 1,348 end-of-month DJIA values and hence 1,347 values of monthly percentage changes. Data for August through November of 1914 is not included in the data set as the stock market was closed because of the First World War.

Over this period, the value of DJIA increased from 40.63 at the end of May 1896 to 8,776.39 at the end of December 2008 a 21,501% increase – with an average percentage change of 0.55% per month or 6.60% per year. The mean monthly percentage change in the DJIA for the total period is highly significant (p = 0.00). The standard deviation of the monthly percentage changes is 5.45% or 18.88% annualized, which is close to the approximately 20.50% standard deviation of the annual returns of the S&P 500 Index for 1926 to 2008. The summary statistics of the monthly percentage changes for period 1896 to 2008 are given in Table 1.

As we can see in the histogram below of the monthly percentage changes in the DJIA for the entire period, the distribution is slightly skewed to the left as the mean of 0.55% is smaller than the median of 0.83% per month. The skewness equals –0.05 and the kurtosis equals 5.86. The Jarque-Bera statistic equals 459.91 for p-value of less than 0.01. Since the p-value is less than 0.05, the normality assumption is violated. When sample size is large, as is in our case, even unimportant deviations from normality become technically significant. For this reason, we need to use other bases of judgment such as histogram. If we examine, the histogram in Figure 1, the distribution appears quite normal in shape. Assuming normal distribution, the probability that DJIA would increase in any month is 54.01% and the probability for the decrease is 45.99%.

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Table 2 shows the frequency of monthly increases every decade that were more than 10% and Table 3 shows the frequency of monthly decreases that were larger than -10%.

There were a total of 90 such instances from 1896 to 2008. Of those, 35 occurred during 1896-1928 (in 32 ½ years), 36 occurred during 1929-1945 (in 17 years), just one occurred during 1946-1972 period and the remaining 18 occurred during 1973-2008.

Over the entire period, August experienced 7 increases larger than 10% followed by 5 each in April, June and November. Over the entire period, September and October have suffered 8 decreases larger than 10%, followed by November with 6 decreases, and December with 5 decreases.

**Conference papers © Knowledge Globalization Institute, Pune, India, 2012 **

Looking at individual values of the monthly percentage changes, the DJIA increased by as much as 40.18% during April 1933 and declined by as much as 30.70% in September 1931 (Table 4). In the post-Second World War period, the biggest increase was 14.41% in January 1976 and the biggest decline was 23.22% in October 1987 (the month that included “Black Monday”).

Analysis of 1896 to 2008 Table 4 shows that the months with significant mean percentage increases in the DJIA are August with 1.26%, followed by July with 1.25%, December with 1.17% and January with 1.05%.

July and August have experienced the most mean percentage increases of any two consecutive months. September experienced the most negative mean percentage change (-1.19%), which is significant at 4% level, and also significantly lower than the mean of the other eleven months stacked together. The variances of January, February and December are lower than those of the other months (the standard deviation of monthly changes of all three are below 5%); April’s variance is higher than those of the other months (corresponds to its widest range between maximum and minimum monthly changes.) Figure 2 shows the cyclical pattern of the means of monthly percentage changes for the entire period. On average, there has been a big drop from August to September and then an increasing trend until December. For short-term traders, on average August is the month for short selling DJIA stocks, and September is the month to close the position. On average, a short-term trader stands to gain significantly by buying at the end of September, and selling at the end of December.

Conference papers © Knowledge Globalization Institute, Pune, India, 2012 Figure 2: Means of monthly percentage changes in DJIA: 1896-2008

Kruskal-Wallis test of difference in medians (Table 5) of monthly changes shows significant difference in the medians (H-statistic = 29.37; p = 0.002). December has the highest median followed by July and August. September has the lowest (negative) median.

Mood’s Median test also shows significant difference in the medians of the twelve months (Chisquare = 28.45; p = 0.00). So the negative September effect is also supported by two nonparametric test.

Analysis of 1896 to 1928 Table 6 shows the mean change of 0.68% per month for 1896 to 1928 is significantly different from zero.

7 Output is not shown for brevity.

The means of month-wise changes show significant positive mean for only August (2.46%) – which is significant at 1% level – but it is significantly different from the mean changes of the other eleven months at 5.1% level. The mean monthly change of February (-0.93%) is significantly lower than the mean changes of the other 11 months at 3% level. On average, there is a rebound in March (mean monthly change is 1.86%). As we found for the entire sample, for this subperiod also we find January and February exhibited variances of monthly changes which were lower than the variances of the other months. The standard deviation was highest for September (6.33%), but not significantly different than for other months.

**Analysis of 1929 to 1945**

Table 7 shows the mean monthly change for the second subperiod (0.16%) is not significantly different from zero. This was the result of the turmoil of the Depression years and the Second World War. June, July and August generated mean changes between 2.78% and 4.05%, and for five months, the mean changes were negative. But none of them were significantly greater than zero at 5% level. Only the mean of August (4.05%) was significantly different from zero at 9% level. It was different from the mean changes of the other months at 8% level.

The variance effect is exactly similar to what we found for the entire data: lower variances for January, February and December, and higher variance for April compared to the other months. But the standard deviations for different months ranged from 4.25% (January) to 13.14% (April), compared to 4.10% (February) to 6.10% (September) for the entire period.

**Analysis of 1946 to 1972**

The mean monthly change of the third subperiod (0.58%) was significantly different from zero at 0.00% level (Table 8). The mean monthly change of March (1.40%), July (1.53%) and December (2.11%) were significantly different from zero. The mean changes of three months were negative of which the mean changes of February (-0.64%) and June (-0.81%) were significantly lower than the means of other months at 5% level. The mean change of December was significantly higher than those of the other months.

Conference papers © Knowledge Globalization Institute, Pune, India, 2012 But the variance of December was significantly lower than for other months; so was the variance of March. Standard deviations of monthly changes were greatly subdued during this period of fixed exchange rate system ranging from 2.39% (March) to 4.17% (January). The lull in the aftermath of the Second World War, massive international reconstruction efforts, and the Breton Woods fixed exchange rate system brought a stabilizing influence in the DJIA.

**Analysis of 1973 to 2008**