Sunday, February 04, 2007

Cointegration between oil and bond yield? Not!

An article in the Feb 1 issue of the Economist magazine suggested that there may be a link between crude oil price and long-dated US treasuries. Their reasoning is that if oil price is high, OPEC will need to re-invest the pile of cash that they generate, and eventually a lot of this ended up invested in US 10-year bond. Therefore, when crude prices go up, 10-year yield should go down. As I explained before, the fact that these 2 numbers are anti-correlated do not prevent them from being cointegrated. And in fact, the Economist article plotted the crude oil prices together with bond yield over the last year together, and they seem tantalizingly close to being cointegrated.

My curiosity piqued, I proceeded to get a longer history of these data to examine.

In the graph above, I plotted the (normalized) difference between the 10-year treasury yield and oil price. One can see that over the last year and a half, they are indeed cointegrated to a good degree. (To see that, notice the spread is range-bound, or mean-reverting, from mid-2005 to the present.) But this relationship breaks down completely over the longer history.

Though I think that the Economist magazine is doing a disservice to its readers for plotting this graph over just one year and making innuendos of linkage, it is a nice illustration of the danger of studying cointegration over a short window.


aka_ces said...


In the article you refer to, "The Economist" is not making a chart interpretation as simple as your entry suggests:

"But pinning down a direct correlation is tricky. Barclays Capital points to a clear connection between oil prices and holdings of Treasury bonds by the Organisation of the Petroleum Exporting Countries (OPEC). But an IMF study* has found few links between oil prices and ten-year Treasury yields, and a paper** by Raman Toloui of PIMCO, the fund management group, suggests an indirect relationship at best. He shows how oil exporters have recently been amassing reserves faster than Asian governments have—last year, he estimates that they generated some $500 billion of reserves, against $284 billion in Asia. Much of this surplus ends up in central banks, or in government outfits like the Kuwait Investment Authority. Mr Toloui reckons that every $10 rise in the price of crude brings oil exporters an extra $90 billion-100 billion a year. Their assets add up to at least $1.5 trillion.

It is not possible to get accurate data on where all this money has been invested. But Mr Toloui reckons that some 40% can be pinned down. The vast bulk (two-thirds) is invested in bank deposits and short-term securities. Only 3% is put into long-dated American Treasuries.

So that would not, at first sight, seem to suggest that oil money has been driving bond yields up and down. Consequently, there should be little reason to fear that lower oil prices will remove a big buyer from the Treasury-bond market.

However, it may be that oil money flows into Treasuries via an indirect route, for example through fund managers acting on the oil nations' behalf. And even if an OPEC country invests its reserves in, say, Japan, that only gives the Japanese more money with which to finance the American current-account deficit."


Americans may, therefore, have just cause for some concern about their bond markets. The oil exporters do not appear to be as keen to buy dollars as do Asian central banks—which want to control their exchange rates to ensure their exports remain competitive. And even Asian nations, such as China, are talking about finding new ways of investing reserves.

In the long run, this could mean that Americans would have to pay more to finance their current-account deficit—a bearish sign. The recent rise in bond yields could be a first step in that reckoning."

Anonymous said...

You say that a longer term chart shows that the two price series are not really cointegrated. But don't relationships change over time?
Couldn't two price series that are strongly cointegrated over a long period of time just cease to be cointegrated in the future? How do we know the relationship is likely to hold in the future. Does just going back further and getting more data solve the problem?

Ernie Chan said...

Thanks, Charles, for your elaboration. No, I didn't mean to suggest that the Economist based its entire article on one chart. I just wished they would plot more than 1 year of data to indicate the uncertainty of this link.

Ernie Chan said...

Dear Anonymous,
You are right that cointegration relationship do change over time. But you definitely cannot claim such a relationship if it holds for only 1 year. Depending on the horizon of your trading, if you intend to hold positions for several months, then the relationship better hold over, say, 5 or more years. If on the other hand, your trading horizon is a few hours, it may be ok to find a relationship that just held for the last year: but you got to be ready to abandon the relationship pretty quickly when it looks like it is breaking down.

Anonymous said...

Wonderful to see further explanations concerning correlation and cointegration with real world examples.

My only comment is that you always post a graph, which is necessary to visualize the data for yourself and to publish, but what would have been your criteria basing this over a five year period, and only looking at raw unplotted data to draw the same conclusions?

In other words, with a large pool of possible tested stocks or indices it would be impractical to visualize and plot each pair. What statistical criteria would you use to screen and scan on just raw data for possible candidates without having to visualize and plot the results?

Ernie Chan said...

I mentioned in a previous article that the statistical test for cointegration can be found in a University of Toledo econometric Matlab package. The explanation of this so-called Dickey-Fuller test can be found in the Market Models book by Carol Alexander.

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