The S&P 500's Historical Relationship With The Price Of Oil

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Includes: SPY
by: Paul Boland

Summary

There is prior research in the area of measuring how a commodities pricing might impact the pricing of equity markets - specifically oil and the S&P 500.

A regression model is constructed to measure the relationship between oil over the last ten years (2004-2014) and is presented here.

It would appear that roughly 30% of the change in oil can in part explain the change in the S&P 500.

Based on this model, the current pricing of the market (or the S&P 500) appears higher then the level that the current price of oil might suggest is normal.

There has been a long history of research in the area of oil prices and their connection with respect to equity market performance. The US Energy Information Agency (or EIA) has had its fair share of research done in this area as we can see from this chart here:

More recently in late 2012 the EIA came out with a paper that explored the ever increasing correlation between oil and the S&P 500's (NYSEARCA:SPY) performance.

Since expectations for future economic growth also impact demand for crude oil, it is expected that there would be a positive relationship between the price of oil and the value of the S&P 500. In fact, there has been a statistically significant positive correlation between daily percent changes of the WTI futures contract and daily returns on the S&P 500 U.S. equity index in 14 out of 15 quarters since 2008 (see chart below).

The research paper admits that some assumptions underlying the attempt to connect both the S&P 500 and the price of oil are somewhat infringed. With respect to the two tail test for significance of the correlation the study indicated the following:

Testing if the correlation of two sets of observations is different requires that the observations within each sample be independent and normally distributed. This is not necessarily true for returns on futures prices, which can show dependence on previous price movement over short time periods of time. Also noted in previous academic research, the historical distribution of returns on futures prices does not precisely fit a normal distribution, most notably exhibiting leptokurtosis, or an increase in the probability of extreme downside movements than would otherwise be expected in a normal distribution. For these reasons, the tests of significance are suggestive, but not definitive.

Recently we have seen that there is a decline in the price per barrel of oil and there is some concern among analysts of the price dropping below $90 per barrel. Oil related stocks have taken a significant hit from recent high's during the months of June and July of this year. Stocks that have been hit particularly by this recent drop in oil prices are the Offshore Drilling companies such as Transocean LTD (NYSE:RIG), Rowan Companies PLC (NYSE:RDC), and SeaDrill LTD (NYSE:SDRL) just to name a few. With their high cost of operation, they are going to be hit hardest if the price of oil continues to decline. Recently Rowan Companies was dropped from the S&P 500 but Transocean has remained. Both of these companies inclusion on the S&P 500 would be one of the reasons noted above to have an issue with the independence assumption with regard to any statistical analysis attempting to link the price of oil with the S&P 500's performance.

The study indicates that there was an increasing level of correlation from the years 2008 through 2012 when the research paper was released. Prior to 2008 there was a measurable correlation but it was not increasing. While the pricing of oil has remained relatively consistent and even experiencing some brief falls, the overall S&P 500 has continued to increase despite some of the stocks on the index having large exposure to the pricing of the commodity.

There has been a flurry of articles exploring the idea that the market might fall or experience a sort of correction. Naturally there are many reasons to speculate that this might be the case. However it might be interesting to once again explore the idea of the price per barrel and the correlation it has with the S&P 500's overall pricing. Not on a per quarter basis; but rather, to utilize the price of oil and its historical relationship with the S&P 500 as a means to project future S&P 500 levels or what the current level ought to be based on the relationship.

We took the pricing data for oil from 1986 through the current date. We took this data from the EIA and you can find this data in Excel right here. Then, we utilized data on the S&P 500 for the last ten years which can be found here.

A linear regression model was created to see what the connection was in aggregate over the last 10 years. A linear regression model run between the years of 2004 through the current day yields an R^2 of roughly 0.295 which shows a roughly 30% level of accuracy in the usefulness of utilizing the price of oil as an indicator for the price of the S&P 500.

Here are the summary statistics from the analysis:

So we can see from this that if the historical relationship between the price of oil and the S&P 500 were to hold, then we could do the following to see what the S&P 500's value should be per the price of oil today. Based on y = mx + b we have the following:

Price of S&P 500 = (Current Price of Oil*6.786) + 779.57

With oil at roughly $91.46 we can find that the projected S&P 500 price would be roughly 1,400. This is however with an R^2 suggesting 30% accuracy which means that the current level of the S&P 500 is also explained by many other factors which contribute to the remaining 70% within the model.

Interestingly, during 2011, 2012 and the early part of 2013 the price of oil as a predictor of the S&P 500's pricing seemed to be spot on whereas the price of the S&P 500 plummeted below the regression line during 2008 and 2009. With the continued success of the S&P 500 versus the relatively stable oil price, the S&P 500 is now at prices that are above what would simply be explained through the pricing of oil.

The reason for a potentially overvalued market versus the commodity pricing of oil is naturally much more complicated then this simple analysis can really measure. As the EIA paper suggested, to assume independence between the S&P 500 and the price of oil is unwise when we know that there are many companies in the oil industry directly listed on the Index. It would possibly be better to form a percentage of oil-related stocks versus the overall S&P 500 and use this as a control in the analysis.

In any case, it can certainly be stated that to the extent that oil is correlated with the price of the S&P 500 (which appears to be about 30%), the market is currently trading at a higher level than the past historical 10 year pattern. Whether this is a good thing, a bad thing, or an easily explained difference is an entirely more complex issue.

Disclosure: The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.

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