I recently received
an e-mail asking about the price of gold. This person presented two
gold-pricing models in the body of the e-mail along with an estimate of what
price gold might command in the future in dollars.
the gist of what he wrote and provide an extended reply. He wrote
"We owe over 12
trillion dollars. At a $1000 per ounce gold price, that's 12 billion ounces
of gold. According to estimates, only 4–5 billion ounces of gold have
been produced since the beginning of time. This assumes either: a lot of Treasury
debt is going to be defaulted on OR the dollar price of gold is going much
higher than $1000. But how much higher? Does your analysis give you any
inkling about what a proper dollar price is for gold? I read there are 20
trillion dollars of currency circulating around the world converted back into
U.S. dollars. If there are 5 billion ounces, that's $4000 an ounce for all
the currency to be fully backed by gold or $2000 to be 50% backed."
The writer here has
given this matter some considerable thought and has come up with two very
different models. The first one compares U.S. Treasury debt to be paid in
dollars with ounces of gold and current gold price. The second one compares
all the currency in the world (converted into dollar terms) to all the gold in
the world. His serious thought and work deserve serious consideration.
There are many
competing models that aim at estimating the worth of gold, now and in the
future. They obviously give a range of different numbers. Bob Prechter has a
model that predicts gold below $700. Paul van Eeden, last I looked, thought
gold was fairly priced. Alf Field sees gold going to $6,000 or higher. The
e-mail writer’s model looks for gold at $2,000 and higher. Which model
or models should one choose? I’ll address only the two models that this
No gold pricing model
that comes up with a specific price for gold that I know of is complete. The
most important missing factor is something that is not quantifiable. That
factor is the degree of acceptance of the dollar in trade, exchange, and as a
store of value versus the degree of acceptance of gold. This factor is
qualitative. It depends on the behavior of those who use dollars and gold.
There is model risk
in all endeavors. In this case, it means that no matter how carefully we
think we understand pricing, we don’t fully understand all the factors
that drive pricing. If we did, the only downside risk would be in predicting
these factors, and the model would be worth more than gold. The fact is that
we do not know all the factors that influence the pricing of an asset. We
always have to bear model risk.
The writer is after a
"proper" price or "fundamental" price. What this means
concretely is a price toward which gold would gravitate if arbitrage or
equilibrium forces were at work long and effectively enough.
or demand is a key variable in gold’s pricing, any fundamental
price we come up with will only serve as an attractor to the actual price of
gold if we can identify arbitrage forces that induce people to trade toward
that price. I will come back to that after looking at the writer’s two
Model #1 relates U.S.
Treasury debt to the world supply of gold. This model says that if all the U.S. debt were paid in gold and if the US possessed all the gold in the world and paid off its debt
(in nominal terms), gold would have to be three times higher than at present.
This method is badly flawed. Why stop at U.S. government debt? Why not use
all debt? Why pay off the debt? And since the U.S. only has 1/20 or so of all
the world's gold, wouldn't the price be twenty times higher? A basic problem
with this model is that the gold price is not determined by the amount of
debt in the world or in the U.S. or issued by the U.S. government. The value
of the dollar in terms of gold is unaffected if the U.S. government issues a debt and then taxes citizens to pay it. It is unaffected if
someone obtains a mortgage loan and then repays it over time. I will say no
more about model #1. I won’t use it.
The writer’s model
#2 is better conceived. The total of all currencies (in dollar terms) is a
well-defined concept. The gold backing these currencies is a well-defined
concept. The currencies are liabilities of the issuers. They hold various
assets, including gold. Gold is what helps determine the acceptance of these
liabilities and their use as money. It is what gives them value.
mistakenly think that the paper dollars we use have nothing at all behind
them or that the currency is a 100 percent fiat or unbacked currency. It
should be understood that 100 percent pure fiat money does not last very
long. It goes to zero value as in Zimbabwe because people do not accept it
for long. The FED actually has 261.5 million ounces of gold that it carries
as an asset (auditing issues aside). Its bank notes are not pure fiat money.
What is true is that their wide use and acceptance depends on these notes
being made into legal tender. If that law were abolished, rival currencies
would have an easier time arising. It is also true that the FED is able to
issue its bank notes ad infinitum, which is another fiat element. This in
turn affects their acceptance, presumably lowering it.
Those matters behind
us, the model #2 comparison of the total of all currencies to the gold total makes
sense. The writer’s application of these ideas is flawed. Should we
compare all the gold, held by anyone anywhere to the currency total? Most
of that gold is not being used to back up the currency. A central bank issues
currency in a way that is analogous to Bank of America issuing stock. To
value the stock, we’d examine the assets of Bank of America, including
all of its branches. We would not get the total of all the branches of all
banks anywhere. We should use only the gold held by those central banks that
issue the currency in valuing the currency. They hold perhaps 20 percent of
all the above-ground gold. That means comparing total currency dollars to 0.8
to 1 trillion ounces of gold. That amount is a reasonable estimate of the
gold held by central banks.
The writer has a
second error. The total currency ounces is not $20 trillion. It is about $3.5
trillion. I think the writer here is perhaps using an estimate of all forms
of money, not just currency issued by central banks the world
over. He’s including demand deposits and time deposits in non-central
banks or some such construct. However, the latter deposits are not a
liability of the issuers of bank notes, which are the central banks. The
deposits used as money are a derivative money that is created when a
non-central bank makes a loan and creates a corresponding demand deposit. It
is true that this bank uses the currency of the central bank as a base for
making such loans and creating such deposits, but the backing for these
deposit liabilities is not gold. It is the loans the bank holds as its
If the reader sees
this matter differently than I do and wishes to use 20 trillion rather than
3.5 trillion, then this will raise the model price of gold by a factor of
20/3.5 = 5.7. Instead of getting $7,000 an ounce, the user of 20 trillion
will get $39,900 an ounce. You tell me if that is reasonable. I don’t
think it is. And I don’t think gold is the backing for all that
So then what we find
using model #2 and appropriate data inputs is $3.5 trillion currency/0.8
trillion ounces of gold = $4,375 per ounce; or we get $3,500 using the 1
trillion ounce figure. The mean of these two estimates is $3,938. This
assumes that every dollar of currency is 100 percent backed by gold. It
may be of interest to know that before the U.S. went off gold, the FED was
mandated by Congressional law to maintain 40 percent gold backing of the
dollar. At 40 percent backing, the estimate we are getting here is $1,575.
This method has the
flaw that every currency issued by central banks is not equally backed by
gold, as it assumes. In fact, the euro has a much larger backing than the
U.S. dollar. Clearly, the Zimbabwe currency will have a much higher gold
price in its local currency because its backing is zilch.
Model #2 also assumes
that these exchange rates are rates that will prevail indefinitely into the
future. Exchange rates change all the time, however. If the dollar
strengthens versus other currencies, this will cause the gold price in
dollars to decline, holding constant the world price of gold.
This is an important
economic fact that is verifiable and not clearly understood, and so I digress
slightly. The fact of the matter is that an identity holds. Let the term
forex stand for an index of foreign currencies. Then the domestic gold price
is $/gold oz = ($/forex) x (forex/gold oz). The term (forex/gold oz) is the world
price of gold. The term ($/forex) is the exchange rate between the dollar
and the world currency basket.
A stronger dollar
means that it takes fewer dollars to buy a unit of forex. This means that
$/forex is lower. This means that $/gold oz is lower, as long as the world
price of gold does not change. These statements can be verified using actual
Model #2 is not bad
at all. But I’d be strongly inclined to improve it by examining each
currency separately. When I do that with the U.S. dollar, I find that the 100
percent backing gold price estimate of $3,938 per ounce may get up to as high
as $7,151 an ounce.
For the U.S. data, the monetary base is currently $1.87 trillion. The monetary base changes every
week. Per ounce of gold held by the FED, this is $7,151. That represents 100
percent backing by gold. The dollar is now at less than 15 percent backing
(using gold at $1,050). This is the same low level it had in the late 1990s.
About half of the
monetary base is in place because of the FED’s extraordinary credit
expansion, and the permanence of that component is an open question. If the
extraordinary component of the monetary base is simply ignored, then the
backing percentage of the remainder is a much more respectable 28.6 percent. If
it were even 40 percent of this reduced amount, gold would be $1,400 an
ounce. If the backing were 40 percent of the total monetary base, gold would
Numbers such as these
surely give the impression that gold can go higher, but we knew that already.
Any asset can go higher. These numbers give the illusion of certainty and
necessity, or in other words they suggest that gold will go higher. But
the model has no reasoning in it to say why this has to happen, if it has to
happen at all.
The real problem of
the gold speculator is predicting the degree of acceptance or non-acceptance
of gold versus the dollar and its changes over time. Having an idea of
levels is nice, but we also need a model of what causes current levels to
change so that they eventually arrive at what we think is a level that will
prove to be an attractor for actual price.
The central question
is what incentives there are for those who use and accept dollars to
demand fewer dollars and demand more gold as time passes. It is the operation
of these incentives over time that will determine the price of gold, not the
numbers generated by models like the above.
The two major groups
of players in this drama are members of the public and the governments of the
world. A few short years ago, gold was $255 an ounce. Gold was not afforded a
high degree of acceptance. Dollars were accepted. This has changed
dramatically. Now gold is much higher.
The attempt to get
out of dollars en masse and into gold cannot lower the total supply of
dollars in the world unless the central banks contract that supply, and they
haven’t. Shareholders cannot lower the supply of shares of Bank of
America stock outstanding by intense selling. They can only make the price
fall to ration the existing supply at a lower price. In the same way, if
demand for gold is more intense, the existing supply will be rationed via a
higher price. The number of dollars in existence need not change any more
than the number of shares of Bank of America stock needs to change in order
to observe a price change.
Several major facts
lie behind this gold price rise, which has been, by the way, a rise in the
world price of gold. To recount these facts is to give a qualitative model
for gold price changes, not levels as in model #2. This is really model #3.
The first fact is
that the central banks have increased the supply of currencies (and bank
reserves), so that the gold backing per unit of currency issued has fallen. This
is of prime importance. In model #2, this causes the warranted price of gold
The second is that
the returns provided by investments in dollar-denominated securities have
declined. This too is of prime importance, but it is not in model #2. If safe
securities pay little or no interest and if there is price inflation
to boot, then holding currency or these safe securities is a losing
proposition. There is a very strong economic incentive to shift out of these
securities and into assets that maintain their value, such as gold. Gold is a
convenient asset for this purpose because it trades in a highly liquid and
low-cost market. As long as interest rates stay low, this factor operates to
pull funds out of safe securities and into gold.
The third factor is
that the banking system of the U.S. (and perhaps some other countries) is
insolvent. The loans that back the derivative money have been sliced in half
or more in value. The government guarantees are being called into play. This
results in more pressure upon the central bank to create credit for the
In addition, the FED
has responded to this pressure and to the worries of foreign debt holders
like China by making immense purchases of mortgage-backed securities. This
policy expands FED credits (the monetary base) and dilutes the dollar’s
backing as each week passes and more of these securities are absorbed by the
FED and paid for with newly-created FED money.
The deep recession
and the resulting government issuance of debt have the same effect of
pressuring the central bank. In the future, the immense debts that are in
prospect due to promises to pay off on programs like Medicare and Social
Security are going to pressure the government to inflate.
governments and central banks are discovering that their policy of piling up
dollar reserves has high costs that did not prevail when they began this
policy in the 1970s. Why did they not tell Nixon to kiss off when he closed
the gold window in 1971? Why didn't they play hard ball right there and then?
Why did they go along with this when it could hurt them directly and when it
was a repudiation? There are several reasons. They felt in a weak position. They
wanted to sell goods to the U.S., which was the big market. The U.S. applied various pressures. The U.S. was the big power with the big military that
operated as an umbrella over the non-Communist world. But the foreign
governments did not take much coercing at first. They liked the idea of
having some control over their own currencies. That was another reason they
went for the inconvertible dollar. They could have more power to manipulate
their own economies, or so they thought, until they discovered that the U.S.
dollar policy really called the tune. Furthermore, at that time, the gold
backing of the dollar was substantial, even if it was not convertible.
So they accepted
dollars that were not convertible into gold. What this acceptance did was to
relegate gold to a distinctly secondary and inferior status of
non-acceptance. Subsequently, the U.S. inflated merrily in the 1970s and gold
made a serious comeback due to public buying of gold, since the public is the
other major player that can turn away from dollars if it chooses. Gold ran up
far beyond even its 100 percent backed value. Very high U.S. interest rates scotched the gold bubble. Consequently, gold fell to an extremely large
discount to its fundamental value during an extremely long and tiring bear
market. Gold appeared to be almost entirely a relic. But even during this
period, gold was still a basic anchor to currency values. It was and is the
basic unit of account of the world’s monies, even though that important
role is not mentioned very often or emphasized. If gold were not present in
central bank reserve asset holdings, the paper currency system would not last
political economic matters have acted very slowly, this acceptance of the
inconvertible dollar has gone on now for almost 40 years. But that's long
enough for the relative strengths of the economies to change, and for foreign
governments to want more independence, both in terms of economic impact and
political power. They are now groping for a new relationship.
A number of things
are coming to a head among Russia, China, Brazil, and the Gulf states,
including their own growth, the FED's policies, the troubled US banking
system and economy, the extended US military positions, and the impossible
debt obligations of the US government for social programs. Other countries as
well have greater incentives to lower their acceptance of the dollar and
increase their acceptance of gold and/or other currencies that have higher
gold backing. This fourth factor is incipient but growing.
The preceding are
forces of arbitrage that make or induce abandonment of the
dollar. Their presence means that we can be more certain that this will
actually happen. Now let’s mention a few general considerations that
have less immediate but perhaps more long-run applicability.
One such force is the
incentive that a nation has to grow economically. Economic growth is
stimulated when the currency is stable, for then interest rates will tend to
be low and stable and businesses can undertake long-term investments with
greater assurance. Economic growth is also stimulated when a society eschews
a welfare and warfare state. And it is stimulated when property rights are
secure. The U.S. government has retarded this nation’s progress by
diminishing these policies that it once had in place before most of us were
If any major nation
or group of nations adopt these growth policies, they will grow relative to
the U.S. and then they will gain political power. If they even move in the
direction of these policies, they will grow stronger. That is a strong
inducement, based on solid grounds, to move away from the dollar. In other
words, political and economic competition at the level of the nation-state
can undermine the dollar. That may, if it happens, then force the U.S. to alter its policies.
Another such force is
rival privately-based currencies that are stable. Whatever enterprise or
group of enterprises that succeed in producing a private competing money
system with a stable money will be extremely profitable. This is not
unattainable, but it is very difficult given the privileged role of the
dollar as legal tender and in the nation’s payment systems. If this
happens, it will compete with the dollar. In fact, if another major nation
succeeds in constructing a stable gold-based currency, then this will provide
very significant competition to the dollar and impel other countries to move
toward gold as well.
A third force stems
from the domestic political economic policy. The U.S. federal government has
impossible dollar obligations and promises that it cannot meet in the next
ten to twenty years, short of a productivity miracle or two. Who is going to
pay these obligations? Some combination of scaling back, more borrowing,
reneging, and higher taxes is necessary, such as the value-added tax mentioned
by Speaker Pelosi only a few days ago. The wealth redistributions are going
to slow the economy and raise prices. The effect of all this is likely to be
increased pressure on the central bank to inflate.
There is a fourth
force, which is increased acceptance of gold as a component of diversified
investment portfolios. Gold has remained the world’s monetary unit of
account, even when it was very unpopular. It did not serve widely among many
people either in everyday exchange or as a store of value. That is changing.
By definition, the nonmonetary shocks to real economic activity are
uncorrelated with the monetary shocks that impact the price of gold. Hence,
over long periods gold’s price changes tend to show a low
contemporaneous correlation with the returns of stocks. As more and more
research has advertised the portfolio benefits of holding gold in a
portfolio, more and more investors are seeking it out. This requires bidding
gold away from other holders, which makes the price rise. That reduces the diversification
attractiveness, but the net result is still greater acceptance of gold as a
store of value.
bottom line? Gold’s price depends on the main factors mentioned above,
of which I place interest rates and monetary inflation of the currency as
the two of prime importance. I am not here speaking of changes in the money
supply, which have to do with the derivative monies produced by non-central
banks, and I am not speaking of changes in consumer prices or any set of
prices in the economy. I am speaking of that which is under the control of
the central bank, which is its inflation of its balance sheet liabilities. That
inflation, in turn, is affected by government policies and domestic political
The model prices of
gold are substantially higher than the present price. Gold looks very
attractive from that point of view. But there is a proviso. There is no
mathematical relation between the price of gold in the market and estimates
one obtains from a model, even a sound model. Over the years, the dollar has
been accepted and used while having widely varying amounts of gold backing,
no matter what a model like model #2 says. The degree of dollar acceptance
and backing varies through time, so that there is a large area of price
uncertainty of gold.
As people reduce
dollar acceptance, they demand more backing and they bid the price of the
dollar down in terms of gold, so that the gold price rises. As the gold price
rises, the value of any gold held by a central bank rises and this automatically
increases the backing. The market determines the dollar’s worth.
A model like that
relating currency to gold holdings gives levels of gold price. As
speculators, we need to judge the future acceptance of the dollar. Arithmetic
does not suffice. We need to judge changes in order to speculate
profitably in gold. We need to look for and judge real incentives that induce
people to leave the dollar and replace it with gold.
Michael S. Rozeff
Michael S. Rozeff is a retired Professor of Finance living in East
Amherst, New York. He publishes regularly his ideas and analysis on www.LewRockwell.com . Copyright © 2009