* ***** WARNING: I get into some math by the end of this article.*** *

*Introduction*

Maybe it’s me trying to channel Warren Buffett but I like to analyze simple companies, those with few inputs and a few outputs; I don’t like trying to figure out product mixes and what the next hot retail item will be (is Shrek more popular than Toy Story?). This is what makes mining stocks so fun.

A mining company is easy, they dig around and pull stuff out of the ground and then sell it. There are two questions, how much do they pull from the ground and at what price can they sell it out. Sure there may be added complexities, like what the cost of exploration is or if the company hedge its commodity exposure; but these concerns are ancillary.

*The Commodity Prices*

As seen in the chart below, there has been a recent run up in commodity prices: gold is at an all time high of over $1200, up over 35% in the last 18 months. In fact, over the last 18 months silver is up over 50%, aluminum is up over 30% and copper up over 100%.

*(this chart looks at the respective ETF which are designed to, and for the most part do, mirror the price movements in the underlying economy). *

*The Problem: *

However, there is something amiss. The mining companies, those dinging around and pulling these metals out of the ground have not seen a corresponding increase in their share prices. For example, across the same 18 month time Barrick Gold (NYSE: ABX) is up 25.5% while Kinross Gold Corporation (NYSE: KGC) is up only 6.5%, likewise Alcoa (Aluminum) (NYSE: AA) is up 47.5%.

If we believe that share price is based on earnings and growth, there are only three possible conclusions, (1) the assets, gold, copper, aluminum etc. are over valued (2) the share prices are under valued or (3) the output of these companies has decreased.

*The Strategy*

Based on the reports of the companies, scenario number three seems improbable. This leaves us with a very simple and profitable pairs trade. The strategy is to buy shares of the commodity producer (be it Alcoa, Kinross, etc) and short an equal dollar amount of the corresponding commodity ETF. This strategy will be profitable regardless of whether scenario (1) or (2) proves to be correct.

To be sure and taking gold as an example, if we accept scenario 1 then gold will fall from $1200 as will the GLD gold ETF. As in this scenario, Kinross or its peers are priced based on a lower commodity value you profit on your short of the ETF and not lose (significantly) on your long of the mining company. If we accept scenario 2 then if gold does not move or even continues to rise any loses on the short ETF will be made up on the increase in the shares of the mining company.

*Case Study*

I’ll focus a little more on Kinross and GLD, although this is where the math comes in I’ll leave it up to you to look at other mining companies, commodities and their ETFs.

In this case study the assumption is that for every one GLD shorted, approximately 6.6 shares of Kinross will be purchased.

The thesis is that a mining company’s value (or share price) should be highly related to the underlying commodity value. In other words, in this case study, as the price of gold goes up so should the share value of Kinross and as the value of gold decreases so should the value of Kinross. The following chart shows the change in the commodity price of gold from 2000 until May 2010 and the share price of Kinross over the same period.

We see from this chart that, except for a few periods, the relationship described above typically holds. We also see that any time that the relationship starts to become undone, e.g. the price increase of gold outpaces the price increase of the Kinross shares, eventually the gap disappears.

Looking at the right hand side of the above chart we see, as it did in 2004 and 2005 that the relationship between Kinross’s share price and the value of gold has began to diverge from the norm. Therefore, if the past is a predictor of the future the two charts should again converge, either though a decrease in the value of gold or an increase in the share price of Kinross.

Examining a ‘*normal*’ time period, post 9/11 (2003) and pre the 2008 market meltdown we see that the relationship between the Kinross share price and price of gold held fairly constant. A scatter plot of the share price and commodity value shows that relationship graphically. A line of best-fit/regression can be used to show the relationship numerically.

*(the fact that the points are tightly grouped around the best fit line indicates that from 2003 to 2008 the relationship of KGC and the price of Gold has held).*

The regression indicates that on average a one dollar increase in the price of gold will cause a 2.5cent increase in the share price of Kinross. Moreover, from 2003 to 2008, nearly 87% of the price of Kinross can be explained by the price of gold.

The regression provides us with a formula (Kinross’s share price=0.0251*the price of gold-3.3653) that has been 87% accurate between 2003 and 2008. Moreover, from 2008 until the market bottoms in February 2009 we find (by regressing the predicted share price on the actual share price) that the formula has had a lot of predictive power during the time period (the p-value on predicted share price is 0.006).

*(for those that like the statistics, I have included a copy of the ANOVA table)*

Conversely, from April 2009 until May 2010, the predicated share prices has been a less useful mechanism for determining the actual share price of Kinross (again, I have included the ANOVA table from the regression of the predicted share price on the actual share price from April 2009 until May 2010).

The above statistical analysis could be made more complex and perhaps more accurate. For example you may want to add lagged variables on the price of gold (the assumption being it takes time for Kinross’s share price to incorporate changes in the price of gold) or include in the regression the size of Kinross’s provable and probable reserves (which coincides with my initial statement that the value of a mining company is based on *how* much stuff is pulled from the ground in addition to the *price* of that stuff). However, for the purposes of this article it is suffice to say that a relationship that once existed no longer exists. Therefore, should the relationship return, an investor could profit.

**Conclusion**

Using the above formula, at the current gold price of approximately 1250, Kinross’s share price should be nearly $28 and not 18.70. Alternatively, inverting the formula would suggest that the price of gold should be nearer to $883. Something in-between these two extreme may be the right answer, however given the pairs strategy outlined above, it does matter whether it is the GLD, KGC or both that move; it simply matters that the relationship between the share price and the commodity price revert back to its historic norms.

I encourage you to take a look at other mining companies and their corresponding commodity prices. I also would warn you that before relying too heavily on the statistics you should also look to the fundamentals of the company to ensure that there is no obvious reason for the relationship to become undone.

**Disclosure: **I am not currently long any stock mentioned in this article.