08-Feb-2006
An In Depth Look at January Barometers, from Vince Fulco
Spearman’s Rank Order Correlation of Dow Jones Index Members:
1st Month Performance vs. Subsequent 11 Months Performance
February 3, 2006
Extending the previously mentioned work on the January barometer, we chose to look at the data from a second vantage point. Spearman’s rank order correlation is a technique for determining the correlation between ordinal variables. In our application, the correlation’s inputs take into account the “standing” of each member in the performance table vs. its actual return results. For example, looking at the top five best performers in the Dow Jones Industrial index for two periods; January 2005 and the subsequent 11 months, we find:
2005
Starting Starting Next 11 Next 11
Company Month Month Months Months
Name Rank Performance Rank Performance
Altria Group 1 4.42% 4 17.06%
Disney 2 2.69% 29 -16.28%
Citigroup 3 2.12% 18 -1.06%
3M Co. 4 1.95% 24 -8.13%
Johnson & Johnson 5 1.81% 23 -7.11%
Using only the ranks of these companies (and the other index members), we perform a correlation calculation with R project’s cor.test() function. Due to the nature of the inputs, the significance measures in a typical Pearson’s correlation is not appropriate for this type of analysis. Instead, studying the p-values gives us an idea as to whether there is statistical significance between the two time periods in question.
For the full set of data, 2000-2005, the results of the study were:
Ranked Returns Study- 1st Month vs. Subsequent 11 Months
Dow Jones Index Members Starting Period: 12/31/1999 Ending Period: 12/31/2005
Results of Spearman's Rank Order Test
Spearman's P Year Rho Value 2000 -0.060 0.751 2001 -0.012 0.9494 2002 -0.022 0.9084 2003 -0.083 0.6618 2004 -0.019 0.9195 2005 -0.118 0.5326