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The Shadow Price of Gold



August 05, 2012 – Comments (10) | RELATED TICKERS: GLD

This may turn into a series of "what's gold worth?". As of now I have no definitive answers. My goal is to only look at some proposals which will largely be critical. Here's the first.

Some of you may have already seen this but if not here's a link to a brief description: The Shadow Price of Gold.

The shadow price of gold is defined by taking M0 (the monetary base) and dividing it by US gold reserves. The idea is that at one time the monetary base was backed by gold and so the "shadow price of gold" ought to reflect what gold is worth. 

There are two problems with this argument, one theoretical and one empirical.

The theoretical problem is that dollars are no longer convertible into gold. As a result the US government has no convertibility need to hold that gold. If the US government were to liquidate all of their gold, the shadow price of gold would be infinite but I fail to see any reason why the market price of gold would go to infinite as well. Alternatively, if the government were to begin purchasing significant amounts of gold, the shadow price of gold would decrease but I would suspect the spot price of gold to increase as supply would diminish. 

The only scenario I can think of is if the US currency was rejected by users and the result would be a currency collapse. But I don't know why the amount of gold held by the government would have any effect on that. After all, it makes no difference to me if the US government had 1 tonne of gold or 1 billion tonnes of gold. I can't convert dollars into gold so there's no practical difference to me. I certainly don't believe dollars are presently "backed" by gold.

One can reject these theoretical considerations if the shadow price of gold had some sort of predictive power. That's what the circle in the chart linked suggests. It looks as though the shadow price of gold tracked the spot price to some extent. The problem is that the axes on the chart make it somewhat deceptive. Here's a similar chart based on a log scale. (Note: I had to piecemeal data together from different source so it might not exactly match up. But it looks close enough to me to suggest that my data is somewhat reasonable.)

The next thing to look at is the ratio of the Shadow Price of gold to the spot price. 

As can be seen the shadow price has historically been higher than the spot price (with the exception of a brief period in the 1980's). 

As a result of both of these considerations, I find that the "shadow price of gold" fails to be a good judge of the value of gold. 

10 Comments – Post Your Own

#1) On August 06, 2012 at 8:55 AM, JaysRage (78.63) wrote:

I found this to be a quality read.   Thanks for putting this together.  I would like to point out that just because a relationship isn't linear, doesn't mean that there isn't a relationship that's worth monitoring.    If gold follows a loose log relationship to the "shadow value", that's worth noting.  

I understand that this relationship would still provide evidence that using the actual "shadow value", rather than the log("shadow value") will dramatically over-estimate the price of gold.  

Good work....I found it interesting.   

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#2) On August 06, 2012 at 10:31 AM, Valyooo (34.27) wrote:

Good blog, and good conclusion.  I used to use the shadow price as a predictive indicator.  Then oneday I realized, hey, nobody does the shadow price for sand dollars and sea shells, so I don't want to do it for gold either.


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#3) On August 06, 2012 at 5:55 PM, somrh (82.85) wrote:

JaysRage: I think it's fair to say there is a correlation between the two and models can be found. I actually found the power law relationship to have the highest correlation. After some rounding the model is (with G = spot price and S = shadow price)

G = 10 x SQRT(S)

The r^2 for this is about 0.57 which isn't too shabby. This model would put gold currently at around $1000.

However, I still have theoretical reservations for using something like this. An increase in M0 would increase S and therefore correlate with an increase in the price of gold. This seems to be more or less a reduction to an "inflation hedge" type argument for the price of gold.

The thing that bothers me, however, is that a decrease in gold reserves results in an increase in S and would therefore correlate with an increase in the price of gold. This part I have difficulty buying. If anything I would suspect that if gold reserves decrease then that would put downward pressure on the price of gold since there would be more "supply" in the market.

Personally I like to know that a relationship holds and to also know why a relationship holds before I use it. I'm still left with reservations as to why it might work on any other future data set (apart from the inflation argument which I hope to look at in another post). 

Valyooo, I hope you'll come up with some data on the shadow price of sea shells. They might presently be a bargain. 

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#4) On August 06, 2012 at 6:16 PM, somrh (82.85) wrote:

Quick follow-up.

The r^2 between the spot price of gold and M0 is 0.75 which seems to confirm my above hypothesis.

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#5) On August 06, 2012 at 9:48 PM, tomlongrpv (54.48) wrote:

Gold is intrisically of very limited value.  It is good for dentistry, jewelry and electronics.  As Watrren Buffet points out all the gold in the world would fit roughly iinto a baseball infield.  And at the prices that some think that lump of gold is "worth" you  could instead buy all of the farmland in the USA as well as several corporations the size of ExxonMobil and still have money left over.  The alternative assets you could buy would continue to produce income and useful things year after year while the owner of the gold would be left with a non-income producing lump no matter how many years went by.  As an "investment," gold is essentially a Ponzi scheme that depends on the presence of ever more fools to buy in to it;.  But it is a legal Ponzi scheme and the world's total population is continuing to grow and the political hysteria of the far-right with its survivalist message supports the scheme as well, so maybe it will work.  But I will choose other investments, thank you.



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#6) On August 07, 2012 at 12:14 AM, Melaschasm (< 20) wrote:

As long as the amount of gold held by the US government remains fairly constant, printing more money should maintain some correlation between the shadow price and the market price for gold.

If the quantity of gold held by the US government changes drastically, then the shadow gold formula will become meaningless.

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#7) On August 07, 2012 at 4:44 PM, somrh (82.85) wrote:


I too am of the opinion that gold is not an "investment", at least not in the Graham/Buffett sense. I tend to view it as a tangible asset that offers some level of "insurance" protection (particularly against inflation and hyperinflation). I hope to go more in depth on that in later posts.


I concur  (see my follow up post here). The gold reserves were at about 20K (metric tonnes) in 1950. They are currently just over 8K. Much of that was lost by the early 70's when Nixon finally closed the gold window. 

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#8) On August 09, 2012 at 10:41 AM, tomlongrpv (54.48) wrote:

It would be interesting to see a study of the various things that could be insurance against hyperinflation.  The kinds of societies that have suffered hyperinflation lately have not been the kinds of societies where one could easily maintain a large stockpile of gold in a safe condition.  (Imagine trying to do so in Zimbabwe.)  They have been societies where one might be better of with "insurance" consisting of ammunition, medical supplies, potable water and freeze-dried food.

 The risk of hyperinflation would seem to be tied to excessive stimulus by banks that control currencies.  We have seen exactly the opposite recently.  But were it to occur it would be interesting to see thoughts as to where investment should be directed.  Even fairly moderate inflation poses significant risks to many investments and might warrant a change in strategy.  But for me the insurance premium of owning gold is just too high relative to the risks its ownership supposedly addresses.

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#9) On August 10, 2012 at 3:14 PM, somrh (82.85) wrote:


I concur that would be an interesting study. 

One additional consideration is that in many cases hyperinflation events coincide with social breakdown. Currency may be rejected, governments may be overthrown, etc. If we have social breakdown, gold might not be of much value.

Trade requires a level of trust that might not be present. Without trade, gold would be worthless. (I sure ain't going to eat it.) So I suspect you're right that food, water, etc might be of more value in such a scenario. I think what investments you have are of little importance.

What meaning would "investments" have without functioning legal systems to protect "property rights"?

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#10) On August 11, 2012 at 1:54 PM, tomlongrpv (54.48) wrote:

Good last question.  In the event of social breakdown the only investments I can think of would be those in other countries that have not broken down that one could actually get to.  Not too practical for most of us.  Practically speaking gold and diamonds are "investments" only for people who live in countries likely to have their legal systems collapse and yet who have someplace they can flee to with their gold and diamonds that will value their gold and diamonds.  Such people are still probably better off opening up Swiss bank accounts if they can do so.

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