Commodities Complex

In my last post, I said I would try to confront the problems presented by the similarities and differences between the gold/copper ratio and the silver/oil ratio, especially considering that we believed we had found an excellent way to model gold/copper, and yet silver/oil, despite its multiple similarities, never quite seemed to fit into anything. Moreover, any partial solutions that suggested themselves often seemed to violate other relationships that we had modeled and appeared more satisfactory, especially those involving the oil/copper ratio, which seems to be somewhere between the dollar/yield ratio and the yield curve spread.

In any case, we have decided, somewhat reluctantly, to try to address the commodities complex as a whole (except for agriculture), which is just as well, since any solution to silver/oil will inevitably require a kind of universal system. And, we have, for the time being, settled on such a model, although parts of it are untested and tentative, partly because we have yet to think through all the implications and partly because we do not have all the necessary data to do the job justice. Nevertheless, there is a certain symmetry which we think makes up for this lack of certainty. And in any case, presenting a general structure for the commodities complex, even if that complex is flawed, will help us to structure our future considerations of the problem and ideally contribute to a solution. I will try to make clear which parts of the system are more tentative than others.

That being said, let me also say that by attempting to model the commodities complex “as a whole”, I won’t be talking about palladium or cocoa or natural gas or aluminum, etc. Although these are both important and interesting, my preliminary consideration of these kinds of commodities suggests that they are largely functions of the generalized commodity structure represented by the quadrumvirate of gold, silver, copper, and oil.

The keystone of the system is the gold/copper equation, because it is so inclusive of fundamental elements and appears to resemble a number of other ratios, but mostly because it seems to be so effective. But, let’s begin with the simplest statements and work our way to the more complex.


Commodities as a whole have a strong inverse relationship with the dollar/10-year yield ratio. This appears to be a by-product of the phenomenon known as Gibson’s Paradox, which we have commented on before in a slightly different context. Another way of stating this is,

  • commodities = yields/dollar

GSCI commodity index

10-year yield/dollar index ratio

10-year yield/dollar ratio

GSCI commodity index

I believe that this is especially true for industrial commodities, but no longer has an industrial commodities index. If we were to stick with just copper and oil, then this would more or less seem to be the same argument made by Klombies, where he argues that dollar+bonds=copper + 3 x crude (what I call the Klombies Industrial Commodities Index, or KICI).

The reason behind this phenomenon is that although rising yields can be dangerous to commodity prices, lethal in fact, that when those rates do not keep pace with industrial commodities, this will weaken the dollar. Conversely, if commodities fall faster than yields, then the dollar will tend to strengthen. Gibson’s Paradox—although come to think of how resolutely Keynes (as I recall) described the phenomenon, it should probably be called Gibson’s Law—dictates that somebody must pay the piper. If yields are held down (or raised) by central banks (whether foreign or domestic), then the dollar will pay, and so the rise in commodities must be represented in dollar weakness and/or bond weakness.

This brings us to our second point, which is somewhat ironical at first, because it is another variation on the theme of Gibson’s Paradox. And, that is,

  • precious metals/industrial commodities = dollar/yields

Now, of these, I am by far most sure about the following equation, which I have talked about repeatedly in previous posts and already alluded to in this one.


  • gold/copper = dollar/10-year yield

I am not going to demonstrate that one again.

Now, for a number of reasons, I believe but am still unsure that the following equation more or less holds up:

  • silver/oil = dollar/3-month yield

silver/oil ratio

dollar index/3-month yield ratio

Using the three-month yield is especially troublesome, because it has gone so low that even a change of one basis point can be a statistically massive move. So, I am unable to use P&F charts to demonstrate all of the last decade’s movements, but you can see for yourself if there is a similarity or not since early 2008.

silver/oil ratio

dollar/3-month yield ratio

To give a slightly better idea of what we have in mind, here is a construction of the dollar/3m yield ratio from 1995-2008 (which is all I have data for at present) next to the gold/oil ratio which we can use as a kind of proxy for the silver/oil ratio, which is, in turn, presented just below for the period of 1965-2005 by flipping an oil/silver chart by upside down and inside out.

silver/oil ratio (modified from oil/silver chart)

It is not a perfect reflection, of course, but there does seem to be some type of relationship. Both the similarity between the gold/copper ratio and the silver/oil ratio over the last 30-40 years and between the silver/oil ratio and the three-month yield over the same period of time suggests to me that this relationship is not new. But, I do not have the data necessary to back it up.

silver/dollar ratio

oil/3myield ratio

oil/6myield ratio

I am not going to go into it right now, but I believe that both the gold/oil and silver/copper ratios will reflect a similar kind of relationship to those between precious metals and industrial commodities that we have already explored, although I am still not quite sure what the rules are governing gold/oil and silver/copper. If you have read my previous posts about my ‘Supersystem’, then you will know the vital importance of understanding oil/gold, but let’s just stick with the gold/copper and silver/oil equations tonight.

If you look at those two equations, you will see that they share a single common reference: the dollar. That permits us to combine the two equations into a single equation.

That is, since according to those equations,

  • dollar = (gold * 10yyield)/copper
  • dollar = (silver*3myield)/oil


  • (silver * 3myield)/oil = (gold * 10yyield)/copper


  • silver * copper * 3myyield = gold * oil * 10yyield


  • (silver * copper)/10yyield = (gold * oil)/3myield

and, most interestingly, I think,

  • yield curve spread = (silver * copper)/(gold * oil)

Again, I do not have the data to prove or test any of this, and I would have to suspect that the inclusion of so many variables would make the results a doubtful affair, but the eerie efficiency of my ‘Supersystem’ suggests that some such model as this must function.

The problem (for me) at the moment is that I have been holding that both oil/copper and gold/silver better represented the yield curve spread than did the reverse, but over the course of the last two years, the following two ratios seem to have the most to do with the yield curve, although it should be noted that this is a ratio of yields (10-year:6-month) rather than the yield curve spread itself.

10y/6m yield ratio

gold/oil ratio

Historically, none of these ratios alone has mirrored the yield curve.

In any case, let’s return to the simplest forms of our model.

  • yields/dollar = commodities
  • yields/dollar = industrial commodities/precious metals

As for the relationships between industrial commodities and precious metals (i.e., copper and oil, or silver and gold, respectively), we have noted before, following Klombies, that copper seems to lead oil in a commodity cycle. Silver seems to have the same relationship with gold.

If we were to be so bold as to try to come to a stricter definition using the unproven, elaborate version of our model, then,

  • oil/copper = (silver * 3my)/(gold * 10yyield)


  • copper/oil = (gold * 10yyield)/(silver * 3my)

This is counterintuitive, again, because it suggests that oil/copper is positively correlated with silver/gold and the yield curve, although neither perfectly. One more way of thinking about these problems is,

  • copper/oil ÷ gold/silver = yield curve

or even,

  • copper/gold ÷ oil/silver = yield curve

As counterintuitive as it is, it is possible, due to the relative volatility of the gold/silver ratio and the imperfect relationships they have with each other. But, our previous suspicion had been that the gold/copper ratio was a rough approximation of the 10-year rate and that the silver/oil ratio was something like the 3-month rate. This complex equation suggests the opposite.

The final consideration (for us at this moment, that is) is that the respective precious metal/industrial commodity ratios from 1980-2009 roughly fell along with interest rates and in that way appear to be positively correlated with rates, and yet, over the course of the intermediate term, it appears that they are negatively correlated, which is what Klombies more or less argues with respect to the 10-year rate and the gold/oil ratio (i.e., that they are negatively correlated).

It is hard to compare silver/oil or gold/copper and treasury rates without placing them on the same chart, which I am unable to do at the moment, so I will show you the gold/oil ratio as a proxy for these other ratios next to yields to demonstrate how precious metals/industrial commodities have this simultaneously positive and negative correlation with yields. Gold/oil is not the best example, because it is the most erratic of the commodity ratios, but you can nevertheless see a downward slope from the 1980s along with bond rates coinciding with an inverse relationship at a number of intermediate points.

gold/oil ratio vs treasury yields 1968-2009

I'm trying to improve the quality of my charts!

It is possible therefore that the complex equation of the commodity markets I have offered can incorporate this phenomenon, although there is plenty of reason to be skeptical without running the numbers and plotting them.

Any volunteers?


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