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# Jieming See's  Instablog

Jieming See
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Jieming graduated from the National University of Singapore Business School in 2008. In his spare time, he follow news and analysis on the monetary and fiscal development in major economies like US, Japan and China. By following and understanding global macro-economic developments, Jieming... More
• ##### 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

Feb 28 11:00 AM | Link | Comment!
• ##### Monthly Patterns In SP500 Returns?

I have always been interested to find out if there is a monthly pattern in major stock indices return. Are there particular months when the index perform better or worse than average? What are the months when the index outperform or underperforms? Do all major indices share the same monthly pattern?

Methodology

Using data from Yahoo finance (finance.yahoo.com/q/hp?s=%5EGSPC&a=0...), I examined the month returns of the S&P500 (^GSPC) from 1950 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).I computed the average monthly returns by dividing the sum of the returns for the same month by the sample size (n = 61). I then computed the sample standard deviation using the excel formula "STDEV(range of same month returns)/SQRT(61) ". 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 59.02% 54.10% 63.93% 67.21% 57.38% 50.00% 54.10% 57.38% 43.33% 60.66% 65.57% 75.41% 0.87% -0.34% 1.06% 1.35% 0.19% -0.11% 0.84% -0.13% -0.63% 0.48% 1.37% 1.62% 0.61% 0.45% 0.44% 0.49% 0.48% 0.45% 0.52% 0.60% 0.58% 0.73% 0.57% 0.39% test statistic 1.42 -0.76 2.42 2.76 0.39 -0.24 1.62 -0.22 -1.08 0.66 2.40 4.10

Using a one tail t test at the 1 % level of significance, a t statistic more than 2.39 (please see www.sjsu.edu/faculty/gerstman/StatPrimer... on the 60th row and column = 0.01 under one tail) indicates the S&P500 returns are significantly greater than zero on a statistical sense for that particular month. Looking at the above test results, the months of March, April, November and especially December seems very good for holding the index! e.g. the S&P500 averaged 1.06% with only a 0.44% volatility for the months of March in the sample period for a t statistic of 2.42

In the above table I have also added the second row which indicate the percentage of time the index returns more than zero. E.g. for 63.93% of the months of March in the sample period, the S&P500 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 statistically significant.

Conclusion

From the above results, we can conclude that statistically speaking, March, April, November and December are the best months to hold the index on average. In my next analysis, I will use the same hypothesis testing methodology to see if the same month effect impacts other indices like the Nikkei 225, DAX 30 and CAC 40.

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

Tags: SPY
Feb 28 11:00 AM | Link | Comment!

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