Hi Christopher, Peter, Dan, as well as Ernesto,
I'm sort of a "new kid on the block", with a background and some perspectives rather different from most people here. In addition to my former "day job" in O&G E&P (if you don't know what that means or how it might be relevant, please feel welcome to check out my 3 posts on Joao's thread entitled "Trading algo: how to interpret results", I have also been trading for about 30 years. I looked at this issue of stock-commodity relationships some years back and decided, as Christopher has, that it was definitely likely to be fruitful for further research, but I didn't have the tools available to explore it further at that time. I would like to pick it up again here, if there is sufficient interest.
Here are some things I found in my previous informal research:
1) Many companies, and their fortunes and stock prices, have very clear relationships with the prices of commodities which those companies either produce (and hence represent a profit centre for them) or consume, and hence represent a COB (cost of business) to them. In the latter case, think for example of any of the airlines and CL futures because jet fuel is a refined hydrocarbon product derived from crude oil . In the former case, think for example of ABX & GC futures or of FCX & HG futures, or XOM & CL & NatGas futures. An interesting one is ADM. Are soybeans / bean meal / bean oil predominantly a cost or a source of profit for that company? Actually I'm not sure which predominates, but those commodities and that stock are certainly related.
2) In some cases the relationships are either less clear or possibly even spurious. See Max & Delaney's Lecture 16 on p-Hacking & multiple comparison bias. Actually, from a practical perspective though, this is usually less of a problem than it might appear to a statistician, and even a quick look at the company's annual report on its website will usually be enough to provide reasonable insight into whether the relationship is real or not.
3) There are some relationships which may be real and strong but are not necessarily obvious. In particular, ALL international commodities that have their prices denominated in USD are related because of that link via their base currency. This leads to some interesting and non-obvious relationships between commodities, such as for example between wheat & silver. Its not a spurious relationship, it is a real one and it's because if the value of the USD goes down relative to a basket of international currencies (think DX futures), then clearly both wheat & silver (as well as other commodities) prices are correspondingly driven up in dollar terms.
4) One possible exception to this is Natural Gas, which is denominated in USD but (and this is something which may not be obvious to people outside the oil & gas industry) Nat Gas is generally NOT an international commodity, for reasons as explained on the "Trading algo: how to interpret results" thread.
Talk more later if you are interested.
Cheers, best wishes,