I got the following inquiry from the ever-curious Trader Rod.
A few questions concerning correlation between two instruments for the purpose of diversification:
1. When calculating the correlation coefficient, given my time frame is daily, should I focus on daily closing prices or daily returns?
2. If the answer to previous question is to focus on returns, and the average holding period for a position is one week, should I calculate the coefficient using series of weekly returns?
3. What is a good threshold for diversification, i.e. at which point do I decide the two instruments are too highly correlated, e.g. anything below 0.7 is acceptable ?
Correlations have been gaining in focus of late, no doubt in large part due to the very obvious and public linkages between the dollar and stocks. It’s hardly a new thing, though. It’s been used in the type of work Rod is describing here for decades. Modern Portfolio Theory, for example, is heavily involved with correlation analysis. In other words, this isn’t a new field of analysis, so if it’s something you have a mind to explore there’s plenty of reading you can find on the subject. Make sure you do take a half approach, though. Using correlations without understanding what they are, what they mean, and how they can change can be extremely dangerous. Just ask the blown up banks and hedge funds who didn’t make it through the credit crisis.
As for Rod’s specific questions:
1) You should always use returns. They are how you can compare two instruments in a standardized fashion. Otherwise, differences in the prices of the securities can create comparison problems.
2) A holding period of only a week makes correlation application challenging. They tend not to be that stable in the short time frames. At best I’d say look at a rolling 5-week correlation and use it as a rough guideline. But realize that it’s only rough. There’s likely to be considerable deviation.
3) To achieve true diversification between two securities you need to have a near zero or negative correlation.