Correlation – it’s a term most everyone is familiar with, especially when it comes to their investments. When aiSource speaks with investors, it seems that a vast majority of people put a strong emphasis on correlation, ultimately altering their decision to include/exclude a CTA from their CTA portfolio. The real question is, how much emphasis should an investor put on correlation?
Correlation is defined as a relationship between two or more variables measuring the tendency in which they vary together over a period of time. Correlation is measured through a coefficient, ranging from 1 to -1. A correlation coefficient of positive 1, simply means the variables have a perfect positive correlation to one another, a correlation coefficient of -1 means the variables are perfectly negatively correlated. A correlation coefficient of 0, means the variables have no tendency to relate over time. Refer to the illustration below:
If you reference the illustration above, you notice that a correlation coefficient lower than +0.50 and higher than -0.50 has a fairly weak relationship between the two variables and should carry little to no significance. On the other hand, a correlation coefficient greater than +0.50 and lower than -0.50 shows a strong correlation between the variables and should be considered significant.
How it Relates to Managed Futures
In managed futures, correlation is used to compare one CTA to another, a portfolio of CTAs to another portfolio of CTAs, and to compare a CTA/portfolio of CTAs to an index (like the S&P 500 or Newedge CTA index). Although the correlation coefficient can be calculated on daily returns, it is often looked at based on monthly performance returns.
Let’s look at a few examples to assess whether or not the correlation coefficient is significant and should be used in overall analysis. Let’s assume CTA X has a track record going back to 2011 and only invests in the e-mini S&P 500 (intra-day only), see below their track record:
Since CTA X only invests in the e-mini S&P 500 contract, analyzing the correlation coefficient to ensure the CTA X is not highly correlated to the S&P 500 index would make sense. Now let’s compare the above track record to the track record of the S&P 500 over the same time period, see below:
By calculating the correlation coefficient based on the monthly returns of the above two track records, you notice that CTA X has a -0.13 correlation to the S&P 500 index. Based on the scale above, we can assess that there is no significant correlation between CTA X and the S&P 500 even though CTA X invests in the exact same market. The reason why CTA X has no correlation is because even through its investing in the same market, its investment horizon is much shorter term. The S&P 500 index assumes you buy the index from the start of the year and hold it all the way through the end of the year without ever getting in or out. CTA X invests in the same underlying market, however is in and out of the market on a frequent basis making its correlation to the index insignificant.
Now, let’s look at another CTA that invests in the e-mini S&P 500 futures and options market. To keep things consistent, we will analyze CTA Y’s track record over the same time period (Jan 2011 to Dec 2015). See track record below:
Calculating the correlation coefficient of CTA Y’s track versus the S&P 500, we get 0.76. Based on the scale above, this CTA strategy has a very strong correlation to the S&P 500 index. One may ask, how is it possible that CTA X has a very low correlation to the S&P 500, where CTA Y has a high correlation when trading the exact same market. The answer is quite simple, the difference in strategy type is what separates CTA X from CTA Y. CTA X is in and out of the market on a daily basis looking to capture profits on short price movement in the e-mini S&P 500, whereas CTA Y has a longer term outlook on the e-mini S&P 500 which is also why it has a higher correlation to the market.
Correlation measures the tendency of how two or more variables fluctuate overtime. It allows investors the ability to clearly identify whether or not a CTA is interrelated to another CTA or strategy. A common misconception throughout managed futures is that if multiple CTAs trade the same market, they will be highly correlated to one another and this is not the case. When considering the significance of the correlation coefficient it is important to look at not only the markets traded, however the strategy type of the CTA as well.