Last week I submitted my first article on Seeking Alpha. I posted about the Gold Silver Ratio (GSR) and why the idea that it has to revert to a historical mean is nonsense. I went on to offer why this was so. Some disagreed with parts of my post but nobody took on the general thrust of the argument I made against GSR mean reversion. I admit some blame here as I could have packaged my argument a little better and made the case against mean reversion of the GSR the sole focus of my last article. Hopefully with a little more focus I can make my point more convincingly this time.

I want to start by pointing out that I am not selling anything. Last time I did state that I am gold only when it comes to precious metals and gave practical reasons for being so but I have no intention of selling you that position. Silver may very well be a good investment, but it won't be a good investment because the GSR has to revert to a historical mean.

I also want to point out that those who sell the GSR mean reversion theory are mostly in two camps, those who make money selling silver, and those who make money selling trading strategies. They both may be sincere in selling this theory, in that they themselves believe it, but they also have little incentive to re-examine their point of view in my opinion.

Put yourself in the position of someone who has sold silver as an investment for years and regularly promoted the notion of the GSR reverting to a historical ratio as a reason to invest in silver. If you came to the realization that GSR reversion is nonsense, how do you break that realization to the people who have followed your advice for years? Most people find admitting they were wrong a hard thing to do, but admitting you were wrong to people who put their money on the line based on your words seems even more daunting.

I will begin as in my last post by explaining the basics of mean reversion using the example of flipping a coin. If we flip a coin 4 times there are 16 possible results. Below is a list of those possible results.

4 heads: HHHH

3 heads: HHHT, HHTH, HTHH, THHH

2 heads: HHTT, HTTH, HTHT, THTH, THHT, TTHH

1 heads: TTTH, TTHT, THTT, HTTT

0 heads: TTTT

Our expected mean given a fair coin tells us that we should flip heads approximately 50% of the time. But from above we can see flipping 4 heads in a row is possible. Supposing the first time we do four flips we get a result of 4 heads(heads 100% of the time), there is only a 1/16 chance that over the next four flips we do not see a return toward the expected mean of 50%. This is the basic math behind mean reversion. Again I ask, why should we see this mean reversion happen in the ratio of two commodities?

In place of the mathematical certainty one gets if asking about how mean reversion works when flipping a coin, vagueness is offered by GSR traders. In my last post I quoted one such trader who likened mean reversion of the GSR to gravity. Others mention the relative ratio of the metals in the earth's crust, but we could have two commodities with identical supply, with one being useless and the other being useful. In such a case those commodities will not trade in line with their relative supply.

Now, while I do not wish to impose mathematical precision on proponents of GSR trading I do think it is fair to require them to offer up some logical argument for their position. I will lay out the logic of why they are wrong and would be happy to hear counter argument.

I think the following allegory highlights the logical flaws behind the notion that the GSR has to revert to a mean.

**The Tale Of The Island Traders**

Imagine a small island with plenty of farming and a vibrant market. On this island we have genetically modified animals, and the supply and demand for most animals has been stable for a long time, decades in fact. People are very happy with their diet!

The chicken/cow ratio happens to be 20:1, which records show is the historical mean. One cow costs twenty chickens. On this island the genetically modified cows and chickens are very resilient; they can be frozen and stored at almost no cost, as cheap as we might store metals in our world. People hoard surplus cows and chickens.

Unfortunately a new strand of virus hits the island and wipes out half of the chicken production for that year, and continues to do so year after year. People still demand the same amount of chickens and cows as before, except now the supply of chickens is continually half what it was before, and the chicken/cow ratio moves to 10:1. A cow now costs 10 chickens. A small group of armchair traders look at the chicken/cow ratio and see the historical mean is closer to 20:1. They holler in excitement to each other, "Reversion to mean! The chicken/cow ratio has got to revert to the mean!"

So the traders decide to sell their surplus chickens and buy some "undervalued" cows, some even sell their whole stash of "overvalued" chickens. They temporarily move the chicken/cow ratio to 12:1 but soon run out of chickens they are willing to make the trade with. After a while the new supply and demand fundamentals take hold again and the ratio settles at just over 10:1.

After many years the ratio never came back near that 20:1 ratio that the traders expected. Some traders realised their foolishness looking back and learned that supply and demand today and going forward are what matter.

Many more years passed on the island and the historical mean moved closer to 15:1. A new group of traders alerted by a passionate book writer saw that the current chicken/cow ratio was about 10:1, well below the historical mean of 15:1, and they began to cry like those that failed before them "Reversion to mean! The chicken/cow ratio has got to revert to the mean!"

**The Real World**

While the preceding tale does a lot to demonstrate the flaws of the GSR reversion notion I suspect some may need more convincing.

Another Seeking Alpha contributor, Andrew Hecht linked to my last article and incorrectly summarized my article as follows:

"The author argues that this historical relationship is nonsense."

Andrew went on to share the following advice:

"I believe that one ignores historical relationships between commodity prices within the same sector at their own peril."

My argument is not that the historical relationship is nonsense, my argument is trading based on the notion that the GSR has to revert to the mean is nonsense. And far from ignoring history I will use it to make my point and show how the traders in my simple allegory are not any different to those trading the GSR today.

One issue for GSR traders is how do they select the historical mean that they hope the GSR will revert back to? Someone looking to sell you some silver may be very keen to go back as far as possible in determining an average GSR. In a 2012 article submitted to Seeking Alpha titled '324 Years Of The Gold-To-Silver Ratio And $195 Silver' the author went back as far as 1687 in determining a mean GSR of about 27:1 to come up with an ambitious silver price target.

In Andrew Hecht's article that linked to my first post on this subject he shares the following:

"the long-term average of this relationship over the past four-plus decades is 55:1 or 55 ounces of silver value in each ounce of gold value, it closed on Friday at the 73.8:1 level. I have noticed over my years of trading in the precious metals markets that this relationship tends to revert to the mean over the long term."

Even if you think one of the above mean GSRs (27:1 or 55:1) is a better one to choose from, this very act of choosing a mean GSR shows that we are far away from the mathematical rigor the concept of mean reversion elicits in one's mind. On what criteria does a trader choose a mean GSR and when do they decide to move to a new mean GSR?

In the chart below I have marked the 55:1 ratio in black and a 40:1 ratio in green.

**Story Time**

In 1987 a "smart" trader who had watched the GSR since 1975(over 12 years) noticed that the average GSR over that period was about 40:1. He heard somewhere that "all things revert to the mean, just like gravity". Owning some gold and silver he decided to sell gold and buy silver in the hope that he could buy that gold back with less ounces of silver and increase his stock of both. Unfortunately the movement of the GSR did not go in his favor, and he ended up with a lot less gold and silver than he expected this "clever" strategy to yield.

Those looking for a mean reversion to a GSR of 55:1 today may have more data than the trader in that short story, but there is nothing to prevent them meeting the same fate. What happens to those traders looking for a mean reversion to 55:1 if the GSR continues to rise as in the amended chart below bringing the mean GSR to 70:1(blue line).

If the future plays out as in the chart above, when do the traders of the GSR decide to talk about a mean reversion to 70:1 instead of 55:1?

**Platinum**

Andrew Hecht also mentioned platinum in his article noting:

"Platinum is ten times rarer than gold, and it has more industrial applications on a per ounce produced basis. Therefore, it makes sense that platinum has historically traded at a premium to gold. The current discount is yet another piece of evidence that gold is expensive relative to other precious metal prices at its current price."

Not so long ago gold panners threw away nuisance pebbles, today we value those pebbles (platinum) a little differently. For thousands of years no amount of platinum could buy you gold. Supply and demand today and going forward are what matter, not a historical ratio.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.