Gold's Fundamental Value

By: Michael_S_Rozeff

The estimate of gold's fundamental value reported in this article won't be much different from earlier estimates of mine or others. What's new here is a tad more insight into the assumptions that go into this estimate. Knowing this might alter one's confidence in the estimates, up or down. The perspective herein is definitely fundamental.

The United States has a gold stock of 261.5 million ounces. The first assumption is that the gold stock of the United States is what it says it is. One can adjust the estimates if one makes different assumptions about how much gold the United States has. I think the Treasury does in fact have in its possession the gold it claims to have.

The second assumption is that gold is Money. This means that gold retains its historical character as a highly marketable and liquid asset. It's globally acceptable.

The third assumption is that the gold stock is a monetary or money reserve. This means that the United States is not holding it for a strategic or industrial purpose. The Treasury of the United States holds it because it is Money. If it did not serve that purpose, that is, if the United States disposed of its gold stock, the State would lose a degree of control over its economy. That is why it keeps the gold.

The United States suspended redemption of Federal Reserve Notes (FRNs) for gold domestically in 1933 and internationally in 1971. Yet gold remains a reserve currency, not only in the United States but abroad. Suspension doesn't immediately destroy a paper currency. It removes one of its desirable features, which is convertibility into gold, but it doesn't destroy the value of that paper totally.

If gold is a reserve, against what is it a reserve? Against those persons who might hypothetically demand gold from the United States in exchange for Federal Reserve Notes (FRNs) or dollar-denominated United States Notes that they now hold - if they were given the chance. It's a hypothetical demand because the United States hasn't redeemed gold against its obligations since 1971.

Since there is an open market in gold, everyone now has the ability to redeem. The central banks that hold FRNs and dollars debts of the United States and other paper currencies as reserves had and have their reasons for doing so. Whatever these reasons, there are strong reasons for selling their dollar-denominated obligations for gold. For one thing, each one dollar's worth is backed by a few cents worth of gold. They can get more gold for their dollars by exchanging a dollar for a dollar's worth of gold. The average person in the United States isn't redeeming FRNs for gold in the open market. As long as they can buy bread and pay their bills in paper, FRNs and food stamps serve their purposes. Americans with wealth are different. They are increasingly more likely to redeem dollars for gold.

If gold is a reserve against hypothetical redemption, who might want to redeem? How far might such redemption carry? Let's think about specific sets of persons who hold dollar obligations who we think have reasons to convert the dollar-denominated obligations they hold into a different form of money, namely gold Money.

In two previous articles, I chose two sets of person and made two estimates of gold's fundamental value. Each set of persons holds an inventory of dollar-denominated paper or the equivalent obligations of the United States and Federal Reserve. Those persons were either (1) holders of the monetary base (FRNs + bank reserves), or (2) holders of bank deposits in the United States. I made two "Zero Discount Value" (ZDV) calculations for these two groups.

The ZDV is the implied market price of gold (in FRNs) such that each FRN is worth its weight in gold at that price when redeemed in gold from its issuer. At the ZDV, a person is indifferent between redeeming by sale in the open market and redeeming from the issuer (the United States and Federal Reserve.)

To understand this, take some easy numbers. Suppose those who hold the monetary base hold 20,000 FRNs. Suppose the issuers of the FRNs hold two ounces of gold to back the FRNs. Suppose the market price of gold in FRNs is 1,000 per ounce. Then 20,000 FRNs can buy 20 ounces of gold in the market. A hypothetical redemption from the issuers would fetch two ounces. A person has an incentive to redeem by sale in the open market, because he gets 20 ounces, not two. Only when the market price equals 10,000 FRNs per ounce does this incentive disappear. That price is the ZDV. The ZDV is the maximum market price at which gold should rationally sell if the issuers keep the supply at 20,000 FRNs.

The first article explained the meaning of the ZDV. The second article estimated a ZDV in the neighborhood of $7,500 an ounce, using the monetary base, and $11,090 and higher, using the whole banking system. The latter method is my preferred method. My guess is that bank assets are overstated by 30 percent. That implies a ZDV of $17,973.

In an article he wrote in late 2008, Brian Bloom used a different estimation method which I'll update now.

The implicit set of persons in his article is foreign central banks that hold dollar-denominated reserves. This makes sense as an alternative because in the good old days they could demand gold for these obligations.

The latest IMF data show that "allocated" U.S. dollar reserves are $2,828 billions. This is 62.1 percent of total reserves. Then there are "unallocated" reserves that total 3,520 measured in billions of dollars. I assume, as he did, that 62.1 percent of this is also held in dollars, which gives another $2,186 billions.

The sum total of U.S. dollar obligations (Treasury securities) held in central bank reserves is $2,828 + $2,186 billion = $5,014 billion.

The U.S. gold stock of 261.5 million ounces is worth about $314 billion at a price of $1,200 an ounce. The ZDV is $5,014,000/261.5 = $19,174 an ounce. This is not far from my banking system estimate of $17,973. Both of these should be rounded off because they are such iffy estimates. A ZDV of the mean of these or $18,600 is my estimate.

Another way of looking at is that the ratio of gold value held by the United States to potential claims on gold (if there were redeemability) is 314/5,014 = 6.3 percent. This is how much backing there is in gold Money against these obligations in paper money.

It's a fascinating fact that in August of 1931, just one month prior to Great Britain going off the gold standard, the Bank of England's gold reserve was 6.3 percent of the total demand deposit and note liabilities of the banking system. (See p. 10 of Elgin Groseclose's The Decay of Money (1962).)

In the olden days of the Federal Reserve, gold reserves of a minimum of 40 percent were legislated in the United States. The Bank of England had a ratio of 40 percent in July of 1914, before the inflation began. I take a 40 percent ratio as something reasonably realistic, meaning a price at which the desire to redeem paper for gold falls off substantially. In that case, we get 0.4 x $18,600 = $7,440.

If the market brings about a 40 percent implicit backing of the dollar by gold, by bidding up the price of gold, even without it being redeemable by the United States, but instead being redeemable in the market at that ratio, then we can expect a price of about $7,440. That's my bottom-line estimate of fundamental value of gold based on each method separately.

Actually, unless there is double-counting, it seems that the obligations against gold include both domestic banking and foreign central banking obligations. If that's correct, then we need to add the two estimates together, in which case, even at a 40 percent coverage, we get about $15,000.

Distrusted paper currencies do not usually go to zero right away. Sometimes they do, but usually the government has to print vast quantities of assignats, continentals, or whatever, before this happens. The British pound didn't go to zero after August 1931. It did get devalued several times, including in September 1931, but its trip downwards has taken decades. Governments sometimes fight the declines using exchange stabilization funds.

If these kinds of estimates are meaningful, we have a pretty good idea of gold's fundamental value. Backing of 6.3 percent is low. Backing of 40 percent is more normal. If mean reversion is the name of the game, then we have some idea where the gold price in dollars is likely to head, which is half the battle, but we don't know when. We also know that such trips are not one-way streets. Markets can do anything. The authorities can fight the rise in various ways. If the backing to gold goes up to 40 percent of ZDV of just one of these pools of funds, not both, that's a 6-fold rise. Over the following horizons, here are the continuously compounded annual rates of return (rounded off):

Why is gold so far below its fundamental value? Why is gold so cheap, even at $1,200 an ounce? The estimate depends on gold as Money as it was 75 years ago and more. The reason gold is so cheap is that governments disestablished it. Governments of the world stopped using gold as Money in order to be able to run monetary policies of their own choosing. Yet the major governments were unable to divorce their currencies entirely from gold. They still hold gold reserves. Markets take time because they depend on people acting, and people are now used to paper money, not gold. There is no routine payments and credit system in gold. Even when there was, silver was commonly used. Gold was for larger behind-the-scenes transactions.

Mean reversion isn't automatic. There have to be forces that impel governments into restoring gold for mean reversion to occur. Those forces are political-economic in nature. It may be the case that no nation becomes and remains an important commercial, mercantile, and industrial power unless it has a solid, honest. and stable money system. Gold affords such a system. Without gold or without a viable substitute for it - and what substitute is there - a nation's progress is thwarted.

Michael S. Rozeff [send him mail] is a retired Professor of Finance living in East Amherst, New York. He is the author of the free e-book Essays on American Empire.

© 2010 Copyright Michael S. Rozeff - All Rights Reserved
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