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# Monthly Patterns In The DAX 30 Index?

Having identified March, April, November and December as the best months to hold the S&P500 index in my first post, I use the same statistical approach to see if such pattern manifests itself in the DAX 30 index. The DAX 30 consists of 30 major German companied trading on the Frankfurt Stock Exchange.

Methodology

Using data from Yahoo finance (finance.yahoo.com/q/hp?a=00&b=3&...), I examined the month returns of the DAX30 (^GSPC) from 1991 to 2010 to test the hypothesis that for certain months, the index returns are statistically significantly more than zero (H0 : r = 0; H1 : x > 0). The sample size for DAX is comparatively smaller than the one I used for S&P500 (20 instead of 61 due to DAX being a "younger" index than the S&P and therefore has fewer data) I computed the average monthly returns by dividing the sum of the returns for the same month by the sample size (n = 20). I then computed the sample standard deviation using the excel formula "STDEV(range of same month returns)/SQRT(20) ". Dividing the average monthly returns by the sample standard deviation obtains the test statistic.

For more on hypothesis testing, see http://statistics.about.com/od/Inferential-Statistics/a/An-Example-Of-A-Hypothesis-Test.htm

Results and Analysis

 Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec % positive 55.0% 55.0% 45.0% 75.0% 60.0% 55.0% 55.0% 60.0% 40.0% 70.0% 70.0% 85.0% average returns -0.01% 0.25% 0.58% 3.67% 0.54% -0.20% 0.97% -1.40% -3.38% 1.83% 2.04% 2.87% sample std dev 1.38% 1.33% 1.10% 1.43% 0.95% 1.11% 1.63% 1.40% 1.92% 1.54% 1.09% 1.23% t stat -0.01 0.19 0.53 2.57 0.57 -0.18 0.59 -0.99 -1.76 1.19 1.88 2.34

Using a one tail t test at the 1 % level of significance, a t statistic more than 2.528 (please see www.sjsu.edu/faculty/gerstman/StatPrimer... on the 20th row and column = 0.01 under one tail) indicates the DAX returns are significantly greater than zero on a statistical sense for that particular month. Note that the t stat is higher than the one used in my previous post on the S&P500. Intuitively, a smaller sample size requires a more restrictive test statistic to prove the case.

Looking at the above test results, only month of April seem to be a good month for holding the index. e.g. the DAX 30 averaged 3.67% with a 1.43% volatility for the months of March in the sample period for a t statistic of 2.57

In the above table once again the second row indicates the percentage of time the index returns more than zero. E.g. for 75% of the months of April (15 out of 20 times) in the sample period, the DAX returned more than zero. As can be seen from the table the indexes made positive returns more frequently in months where the t statistic are close to being statistically significant e.g. the months of April, November and December

Conclusion

From the above results, we can conclude that statistically speaking, April is the best month to hold the index on average. In terms of frequently generating a positive returns, April, November and December are the months with the highest probability.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

Additional disclosure: I intend to go long on the DAX in april if there is a suitable entry point in late March