The gold model UPDATED July 18, 2008
There are three major changes in this revision of the gold model (the original article discussing the gold model can be found here, and I suggest you read it if you are not familiar with the model’s components). I changed the data for the money supply from M3 to the Actual Money Supply (AMS), a monetary aggregate that I have independently defined and calculated; I replaced the World Gold Council’s estimate of the total gold supply (all the gold ever mined) with a series of data compiled from historical resources and adjusted as described later in this article; and I moved away from a particular year as a starting date and used a mathematical formula to better “fit” the curve to the gold price. For June 2008, the model yields a theoretical gold price of $757 an ounce. This is substantially less than the current gold price, which is around $975 an ounce, and I will discuss the implications.
Actual money supply
After much deliberation I have come to believe that M3 overstates both the money supply and the inflation rate. The new money supply model that I use, AMS (link), is in my opinion much more accurate. From 1900 to 2007 the average annual compound increase in M3 is 7.09% while the average annual compound increase in AMS is 6.47%. The difference may not seem large, but 0.62% compounded over 108 years is the single largest contributor to the difference between the current theoretical gold value and the value given by the previous prototype of the model.
Gold supply data
Now that I have more accurate money supply data than M3, I also made an effort to obtain more accurate gold supply (the total of all past production) data. Reasonably good gold production data is available since 1492, when the Spaniards began shipping gold from the Americas; however, there is no consensus as to how much gold existed in 1492. The World Gold Council estimates that the gold supply as of December 2006 was 158,000 tonnes. If we subtract mine production from 1493 to 2006 from that gold supply figure we get an estimate of 17,665 tonnes as of 1492. James Turk, of GoldMoney (link), has done extensive research on gold production and supply and believes that, globally, there may only have been about 600 tonnes of gold in 1492. This makes a difference to the gold model as current mine production would be a higher percentage of the gold supply if there is less gold than the World Gold Council estimates, which would cause the theoretical gold price to be over-estimated.
Since I know James Turk has gone to some lengths to figure out the gold supply as of 1492, and I have no idea how the World Gold Council arrived at its estimates, I decided to use James’ figure for my own calculations from now on. Starting with 600 tonnes of gold supply in 1492, I added the annual gold production data of Adolf Soetbeer (1) for the years 1493 to 1899. I used the gold production data published by the US Geological Survey for the years 1900 to 2006 (link) and production data obtained from the World Gold Council’s website (link) since 2006.
Adjusting gold data for industrial use
I was content to use gross gold production as an estimate for gold inflation while I used M3 as a proxy for the money supply. Given the increase in accuracy of the data I am now using, I also decided to adjust the gold supply for gold that is unlikely ever to be recycled. Specifically, I have deducted from the gold supply the amount of gold used annually for industrial fabrication -- this includes dentistry but excludes all forms of jewelry manufacturing. Most of the scrap gold that is recycled each year comes from jewelry, and the amount retrieved from dentistry, electronics, or other industrial applications is very small.
The new gold supply data is thus 600 tonnes, plus annual mine production since 1493, less an estimate of the amount of gold used for industrial fabrication since 1900. I don’t know of any good data for industrial fabrication, other than the data supplied by GFMS. Unfortunately the data only goes back to 1968 and GFMS used to publish only Western World data. At the moment, global industrial fabrication is approximately equal to 18% of global mine production, according to GFMS. The average from 1968 to 2007, which is a mixture of Western World and global industrial demand, is just under 17% of global mine production, and the average from 1968 to 1971 is just under 15%. I don’t have any fabrication demand data for the period before 1968, but I doubt that a large percentage of annual gold production was used for either dentistry or other non-jewelry fabrication demand prior to 1945. I therefore decided to gradually reduce fabrication demand as a percentage of global mine production from 15% in 1969 to 5% in 1945, and kept it steady at 5% from 1945 to 1900. I made no adjustments to the pre-1900 gold supply data. Any error introduced by this adjustment of fabrication demand is probably less than the error introduced by not subtracting fabrication demand at all, and the error for the early years is significantly less than any potential errors in more current years, for which we have better data, simply because 92% of all the gold mined up until 2007 was mined since 1900.
The use of a lower gold supply in 1492 has resulted in a lower estimate of the current gold supply, which results in a higher gold inflation rate and thus a lower theoretical gold price. Subtracting fabrication demand from the gold supply, on the other hand, has slightly reduced the gold inflation rate and therefore slightly increased the theoretical gold price.
Finding the starting ratio
This model adjusts a starting ratio of the total dollar money supply to the global gold supply by their respective inflation rates to yield a time-series of gold prices. The problem is deciding which ratio to begin with: even though the gold price was fixed at $20.67 an ounce until 1934 and then at $35 an ounce until 1971, there was never a time when either of those gold prices was necessarily correct.
Consider that from the first $10 gold Eagle that was minted in 1795 the ratio of dollars to gold was fixed by the gold content of dollar coins. Until 1834 the gold content of a $10 Eagle was 0.5156 ounces. From this we can calculate that one ounce of gold was equal to $19.39. This ratio did not define the value of gold; rather it defined the value of a dollar in terms of gold. Changes to the gold content of US coins in 1834 and in 1837 meant that Eagles minted thereafter contained 0.48375 ounces of gold, re-setting the gold price to $20.67 an ounce. Again, there was never a physical ratio of dollars to gold that defined that value; it was defined because dollars were minted from gold. For all intents and purposes, dollars and gold were at the time the same thing, even though fiat currency was already making an appearance.
On the assumption that the market should be able to correctly price assets and currencies over a long period of time I decided to “fit” the theoretical gold model to the actual gold price between 1974 and 2007 and then work back to 1900 to see when the model suggests the market priced gold at $20.67 an ounce.
Volatility in the gold price can skew any attempt to obtain a proper fit but all we really need to know is the overall trend (slope) of the actual gold price. An analysis of the money supply always shows two inflection points which signify a pronounced change in the rate of inflation: one at approximately 1991 and the other around 1995. These inflection points are also visible in a chart of the gold price, and so I decided to calculate two actual gold price slopes: one from 1974 to 1990 and the second from 1996 to 2007, leaving the inflections intact. I then compared (2) the theoretical gold price to the modified actual gold price and adjusted the model’s starting point until the two were as close as possible. The chart below shows how the model fits with the modified actual gold price.
Putting the model to the test
The inflections in the actual gold price are entirely due to the free market’s pricing of gold in dollars whereas the inflections in the model are a result of a dramatic change in the relative inflation rates of dollars and gold during that period. The model shows (see chart below) that an ounce of gold was actually worth close to $20.67 in 1918 and then again in 1934. Since the gold price was fixed until 1971, physical gold was exchanged for dollars or vice versa depending on whether the gold price was overvalued or undervalued. From 1918 to 1930 gold was undervalued and dollars were overvalued, leading to gold hoarding and a massive increase in consumer spending and speculation with those overvalued dollars. Conversely, during the period from 1934 to 1943 gold was intentionally overvalued causing a massive transfer of gold from other countries into the US.
Even though the gold model is not based on the money supply in any particular year, it is entirely congruent, to the year, with movements in gold stock during the 20s, 30s and 40s. I discussed the two major discrepancies between the theoretical gold price and the actual gold price (from 1979 to 1984, and from 1996 to 2007) in the original gold model article (link
) and that analysis is still valid, so I will not repeat it here.
What the is model telling us
Now let’s look at the theoretical gold price compared to the actual gold price. While the lower theoretical gold price might be disappointing to some investors, I view it impartially. The model tells us only what the relative change in value between gold and dollars has been since 1900 -- it is not an attempt to predict next week, or next month’s gold price.
What this model does allow us to do is judge whether the gold price is under priced or over priced based on the relative inflation rates of gold and dollars. What we do with that information then becomes a subjective and personal matter.
When I constructed the first model in 2003 it showed that the gold price should have been trading for more than double what it was at the time. There was sufficient room for error and still more than enough margin left to make money. I also knew there would come a time when the gold price would exceed my model’s theoretical value -- that time has now come.
While this does not mean the gold price will now suddenly fall, or that the gold price could not go higher, it does indicate to me that the risk to reward ratio of buying gold has deteriorated. Fundamentally, gold is now over-valued by the market. The notion that gold is over-valued conforms to my belief that certain base metal prices, such as copper and aluminum are also over-valued. Oil is most likely over-valued in real terms as well, although it’s a much more complicated and emotionally charged commodity. I believed that gold would fare better than base metals and oil in the event of a price rout, but if gold is indeed also over-valued then that faith was misplaced.
Notwithstanding the above, we are facing very similar circumstances to those in the late 1970s: there is tension between the United States and Iran, there is concern about inflation, and confidence in the US dollar is failing. During 1979 and 1980 the gold price spiked in excess of its theoretical value and the same could happen at any time now. If we were to see the same magnitude of rise in the gold price as we saw then, gold could easily trade for $1,500 or more.
But we should not forget that in spite of gold’s spectacular rally in 1979 and 1980, the gold price fell hard afterwards and then traded sideways for years, until the theoretical price finally caught up with the market price. Assuming the model’s theoretical price is in the ballpark, we should not discount the possibility that the gold price could fall, or trade sideways, until the theoretical price has caught up again. Whether one should bet the gold price will spike as it did in 1980, or be more cautious, is entirely a personal and subjective matter. The theoretical gold price model tells us only what gold is worth relative to dollars, and not what the gold price is going to be next week.
I firmly believe that gold is money, and that it is the best form of money we have, but I have no emotional attachment to the price of gold. I also believe in the validity of analyzing the gold price on the basis of relative inflation rates, which is what this model does. The fact that the current theoretical gold price is $757 an ounce while the market price today (July 15, 2008) is $975 an ounce does not make me think the model is wrong. It makes me concerned that the gold price could fall and therefore I have adjusted my trading strategies accordingly.
What this model also demonstrates is that there is a causal relationship between inflation and prices. If the supply of dollars increases then dollars lose value, causing prices to rise. Similarly, if we increase the supply of gold then gold loses value meaning that gold buys less or, stated another way, the gold price falls. We can see from the charts above that merely adjusting for both the increase in the supply of dollars and the increase in the supply of gold resulted in a theoretical gold price that conforms very well with the observed gold price from 1974 to 2007, and when the gold price was fixed either at $20.67 or $35 an ounce, the over-valuation or under-valuation of gold caused transfers of gold to compensate for the changes in relative value between gold and dollars.
Today the gold price exceeds its theoretical value and that implies the US dollar has depreciated all it should. In fact, because the gold price exceeds its theoretical value it could imply that the US dollar has fallen too much. But the US still has a trade deficit of $696 billion for the twelve months up to and including April 2008. This trade deficit is no more sustainable than the gold price of $850 an ounce was in January 1980, and that means the dollar still has further to fall. If the dollar exchange rate declines the gold price will increase from its current levels and the gap between price and value will become even larger. The bottom line is that we should expect extreme volatility as several influences on the gold price now seem at odds with each other.
Next we can look at the current inflation rate to see what that portends for the gold price. The average year-over-year inflation rate for the first six months of 2008 is 8.56%. Assuming the inflation rate remains the same for the rest of 2008 and 2009 it would imply an average theoretical gold price of $776 for 2008 and an average theoretical gold price of $843 an ounce for 2009. As you can see, it will take a long time to catch up to the current gold price, unless the gold price falls, or the dollar’s inflation rate increases.
Then there is also the prospect of deflation, which we have not yet discussed, but is quite possible in the context of the current banking turmoil. If we do enter a period of dollar deflation, as occurred in the early 1930s, the theoretical gold price could actually decline. That is merely one of the reasons why I am paying a lot of attention to the Actual Money Supply and the Actual Inflation Rate at the moment.
(1) As published in the January 1910 edition of The Journal of Political Economy, Vol. 18, No. 1, pages 50-58.
(2) I used the sum of the square roots of the squares of the differences between the gold price and the model’s theoretical price to find the closest fit of the model to the actual gold price.
Paul van Eeden
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