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# Monthly Patterns In SP500 Returns?

|Includes:SPDR S&P 500 Trust ETF (SPY)

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
Click to enlarge

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.

Stocks: SPY