Am I the only one tired of hearing about the correlation between Oil and US Equities? Certainly that has been quite the trade, and there is obviously a fundamental connection between the two that goes beyond the US Dollar, but all the TV talk and loose use of the term "correlation" had me wondering just how strong the relationship has been from a bar-to-bar statistical standpoint. As this article will point out, over the long run the relationship has been less than one might assume from all of the talk.
Causal or Casual Relationship?
The inverse relationship between Oil and the S&P 500 certainly seems readily apparent, just look at the chart of the United States Oil (USO) versus S&P500 Spider (SPY) ETFs over the last ten-days:
But, statistically, are we being fooled by the recency effect of this fresh observation? Take a look at the longer-term six-month chart of the same ETFs below:
The market is clearly sensitive to oil, and suffered as it posted its sixty percent gain, but did the market decline sixty percent? How about forty? Has it recovered twenty percent as oil has fallen by the same relative amount? Clearly not. Even after considering the moderating energy component of the index, the statistical relationship on the broader market is considerably weaker than some may lead us to believe from their casual commentary. But how much so?
Just the Stats Ma'am
As shown in the chart below entitled 1-Day Rolling Correlation, over the last ten days, while there was obviously an inverse directional relationship between the indices, there was really only one when when the rolling correlation exceeded 70%:
(Note: One would minimally like to see closer to 80%-plus against at least 30 data points to consider the relationship statistically "strong".)
In fact, over the 790 five-minute bars constituting that ten-day period, there was only a -31.6% bar-to-bar correlation. Furthermore, over a longer two-year period using 20-day rolling correlations (20-Day Rolling Correlation), there was actually only one brief period late last July when such a significant statistical correlation occurred. Over the entirety of that period there was no measurable correlation (r=-0.8%). If anything, historically there appears to have been a positive regime bias to the relationship!
So what's all the hoopla about! Well, again there is the recency effect of the last several weeks, and crude oil near USD $150 per barrel will undoubtedly be etched in our collective conscious for some time to come.
More significantly, while the relationship may be dicey on a bar-to-bar statistical basis, during the last 20-days, 70% of the time the two indices did indeed close in opposite directions (Ratio of Inverse Closing Changes), confirming our intuitive reaction to the current regime.
The real question going forward, of course, is how much longer this connection will play out? Tracking the rolling correlation and ratio of inverse closes between the two may help you to answer this question.