# Gold Arbitrage and Backwardation Part II (the Lease Rate)

In Part I, we discussed the concept of arbitrage. We showed why defining it as a risk-free investment that earns more than the risk-free rate of interest is invalid. There is no such thing as a risk-free investment, and in any case, economics must be focused on the acting man rather than theoretical constructs. We validated that arbitrage arises because the market is constantly offering incentives to the acting man in the form of spreads. Arbitrage is the act of straddling a spread. Arbitrage will tend to compress a spread. The spread will narrow, though not to zero because no one has any incentive to make it zero.

In this Part II, we look at the question: Is gold a currency? Professor Tom Fischer answers, “Yes, gold is a currency with the symbol XAU”[1]

Upon first reflection, one should become slightly uneasy about this logic. The question of what is a currency is essential to his argument about gold backwardation. We should not abdicate our responsibility to address this question, by deferring to the symbol naming committee at Bloomberg. Let’s look at the facts of reality to see what we may discover about this.

I should first disclose that I am president of the Gold Standard Institute USA. I have written many times to advance the understanding of why gold is money, most recently for Forbes.[2] That proposition is not under debate here.

Whether gold is a currency is a separate issue, and it’s key to Fischer’s argument in Why gold’s contango suggests central bank interference. It is important to keep the context firmly in mind. He contends that contango merely means that the rate of interest in gold is lower than the rate of interest in dollars, and further that the interest rate in gold should be higher than in dollars. Thus gold should normally be in backwardation. Therefore its historical contango is evidence of central bank manipulation. This chain of logic depends on gold being a currency in this context.

Deducing from definitions is always fraught with the possibility of error, and if one does it at all then one should be very careful to hold a consistent context. Consider the following reductio ad absurdum. Let’s define a box as a square container. Let’s define square as when someone is socially awkward and unpopular (this is an old-fashioned American expression that has been falling into disuse). Therefore it is awkward to buy products that come in boxes. There is a subtle logical error here which leads to an obviously absurd conclusion.

The error is that we switched contexts. No one proposition is false, but in the progression from proposition to proposition we changed the sense of the key concept. The result is an unsupported conclusion, where one thinks one has proved it.

We are trying to form conclusions about things as they exist in reality. We therefore cannot just manipulate symbols on paper. Those symbols have referents in reality that we must keep firmly in mind at all times. This becomes doubly—triply—a risk if we attempt to deduce from definitions. We cannot assume all characteristics of one thing that fits into our definition apply to other things that also fit into our definition.

Suppose we define currency as “a unit of exchange.” OK, the dollar is a unit of exchange. The dollar is printed in green too. Can we assume that all other currencies are printed in green? The dollar has a rate of interest. Can we assume that all other currencies have a rate of interest? What do we mean by a “rate of interest”, anyway? Are all rates in all currencies equivalent in all regards, regardless of how they are arrived at?

It is not in dispute that, in some contexts, gold is a currency. There are certainly transactions that take place today in which goods are exchanged for gold. Does this fact allow us, without further consideration and without context, to conclude that therefore gold backwardation is simply when the interest rate is higher in gold than in dollars? No way.

I have presented my theories of how the rate of interest is set in irredeemable currency[3] and how it is set under the gold standard.[4] The mechanisms are quite different and there is no reason to expect the spread between the rates to remain consistent, nor to expect any particular relationship between them.

It is not valid to philosophize, as Fischer does, that the rate of interest “should” be higher in gold because of tight credit conditions, or that it “should” be lower because of less inflation. Maybe, but a proper approach to monetary science demands that we find incentives and mechanisms by which the acting man will profit by moving the spread in the direction we suppose it ought to go.

The interest rate in irredeemable paper is unstable. It has spiked to dizzying heights, and it is now collapsing into the black hole of zero. If one wished to make assumptions, there is some reason to expect that the rate of interest in dollars should be higher during the rising cycle, especially as it spikes upwards, and lower during the falling cycle. Even this assumption is tricky because the complicating factor is that the rate of interest in dollars affects what happens in gold. A discussion of this interplay is outside the scope of this paper.

The reality is that we don’t have a gold standard today. We cannot assume that the rate of interest in gold is set today by the mechanisms I describe in In a Gold Standard, How Are Interest Rates Set (indeed it is not). To answer the question of how the gold interest rate is established today, we must look at who the actors are and the mechanics of what they do. Remember, we are not interested in floating abstractions such as definitions that do not refer to reality and the acting man. We want to know who does what, and what his incentives are, and contrast to the actors in a gold standard.

Although I have looked and inquired all over the world, I know of only two businesses that keep their balance sheets in gold. One is the fund I manage. I decided to keep the books in gold both because it’s appropriate to the nature of the fund, and to develop a case study on how to do it. Both of these reasons are way out of the mainstream.

The Perth Mint is the other, and they keep hybrid books for a simple reason. They have both cash costs and significant gold flows. They are specialists in the gold business. It is likely that a few other businesses of which I am not aware also keep their books in gold, but this is clearly a de minimis niche (if you keep your books in gold, I would love to hear from you).

This context is important because only a balance sheet denominated in gold can borrow in gold. Think about the typical case in the dollar world. For example, a chef borrows money to build out an attractive restaurant with posh décor and a hip bar where they plan to sell lots of expensive fancy mixed drinks. They spend some of those dollars to buy tiles, wood, mirrors, and light fixtures. They spend the rest to hire workers to build out the interior space to their design.

Businessmen and even economists do not normally think of the borrower as being “short” dollars. It’s easy to ignore because the borrower usually takes no currency exchange rate risk. He does not “sell” the money, and have to worry about “buying” it back at a later date at much higher prices. The enterprise is long a dollar income stream, and this is a perfectly suitable asset to match the short dollar loan.

Virtually every business and many individuals borrow in dollars, euros, pounds, yen, etc. Every business and most individuals keep their savings in those paper currencies. Savings, in this context, means that they are lenders. It is not possible to hold paper currency without being a creditor.

The extending and utilizing of credit in the dollar is exactly as one would expect of a widely used currency. Virtually everyone participates, with many on both sides simultaneously. It is therefore appropriate to speak of an interest rate in dollars.

What of gold? Why is lending gold called “leasing”? Who lends it? Who borrows it?

Gold lending might be called “leasing” to work around the legal tender laws. If it were legally structured as lending, then the borrower would be able to tender payment in dollars and the law and courts would consider the debt to be repaid. Clearly, no one would lend gold only to be repaid in dollars. Or worse yet, give the borrower a free option, to pay in whichever form is cheaper.

Another possible reason is the tax code. I am no tax expert, but I know that under U.S. law, the lessor does not incur capital gains if the market price of the leased property rises before the lease period is up. This is because the title to the property remains with the lessor. In a loan, a tax expert would have to opine, but the title may legally change hands and therefore there may be a capital gains tax if the price rises. This tax could easily exceed the interest, thus making a loan structure unfeasible.

I propose a third reason. Gold is not borrowed to finance business expansion or to buy machinery and real estate, much less consumer goods such as autos or a university education. Gold is not borrowed to finance purchase of long-term assets.

Businesses that specialize in gold, such as refiners, mints, and jewelers use gold leases, to enable them to carry[5] inventory or hedge inventory. These businesses operate on thin profit margins, and they cannot accept the risk of the gold price moving adversely to the dollar, in which their books are denominated.

I discussed the hedging of currency risk in detail in Theory of Interest and Prices in Paper Currency, so I will not repeat that material here. I will merely note that currency risk occurs when you are either long or short a currency that is not the numeraire of your balance sheet. If you are long the Japanese yen, and the yen drops relative to the dollar, then you incur losses. If you are short the euro and the euro rises, then you similarly take losses.

Those losses will often result in a margin call, which can drain the cash away from productive parts of the business. If they are large enough, then the firm can become insolvent. Businesses therefore buy hedges to protect themselves from these risks. The sellers of this protection themselves buy hedges. The buying and selling of hedges can go round and round, but there is no way for the risk to be eliminated. This lump stubbornly remains under the rug no matter how it’s pushed this way or that.

Consider the case of the coin shop. At any given time, it carries 100 gold Eagles in inventory so that it will be ready whenever a customer walks through the front door to buy gold. To manage the risk, it sells short a gold futures contract. With this hedge in place, it has no exposure to the gold price. The shop owner can sleep easily at night, knowing that so long as he can sell coins at X dollars above the spot price, he can be consistently profitable. He has no price risk.

Jewelry manufacturers and retailers are in the same position. Refiners, mints, and gold miners also have the same risks and needs. Thin margins do not mix with a volatile gold price, as measured in their native paper currency.

There is another way to look at these businesses’ use of gold. They are using gold as financing, similar in some ways to Real Bills. Recall that a Real Bill is used to finance inventory that is moving predictably towards the consumer. The baker doesn’t want to borrow money to buy the flour he carries. The Bill emerged out of the market spontaneously, as a solution to this problem. The Bill enables him to carry his inventory, without him having to have the capital to own it.

The baker’s issue was not volatile flour prices, but the cost of borrowing. Today, if there’s one thing central banks have achieved via their spigots that gush unlimited credit-effluent, it is that dirt-cheap credit flows to bakers, coin shops, and everyone else. It is not to avoid the cost of borrowing that they carry rather than own outright their gold. It is to avoid the risk of price movement.

The analogy to Real Bills is the use of self-liquidating clearing credit. This credit finances inventory that is moving towards the consumer, and it is extinguished by the sale of the inventory. It is not quite the same as the Real Bill, but compare and contrast to bonds. Bonds are used to buy plant or other long-term assets. The credit used to buy such assets is not liquidated by the sale of these assets, but amortized over years by the sale of products produced by operating the assets.

The gold “lease rate” is conceptually closer to the discount rate of Real Bills than the interest rate of bonds.

The opposite need occurs in other businesses. For example, look at the case of a business that seeks to arbitrage a differential between the gold lease rate and the dollar interest rate. They borrow gold and sell it to obtain dollars, which they invest at the LIBOR or use to buy Treasury bonds. This is also a thin spread. Unlike the coin shop, whose concern is a falling gold price, their concern is a rising gold price. This sort of business must buy a gold futures contract to hedge that risk. It would be suicidal for any business that leased gold and sold it unhedged. Sooner or later, the falling dollar—which would be experienced by this foolish business as a rising gold price—would sink them into bankruptcy. And that’s even assuming that the gold lessor of the gold would allow it.

There are other businesses that operate similarly in the gold market. And there are also arbitrageurs who straddle spreads in the gold market. For example, sometimes it is profitable to carry gold, and at other times to decarry it.

The point is that the gold lease rate is not set by the time preference of the marginal saver and the profit of the marginal entrepreneur. Savers who want to keep some of their surplus wealth in gold have only hoarding available to them. There is no such thing as a deposit account denominated in gold, paying interest in gold (if anyone is aware of such an account, please contact me).

The chief objection to holding gold expressed by most mainstream investors is, “gold has no yield”. This means that there is no investing in gold, only speculation on its price. Even the gold bugs whose motto is “the dollar will hyper-inflate soon” buy gold for their belief that its price will rise. They buy it as a speculative vehicle to get more of the dollars that they claim will soon be worthless.

The point of this discussion is that the cost of gold hedging, or alternatively, something akin to the gold discount rate, is a specialty niche. Unlike a bona fide interest rate, the gold lease rate does not emerge from the actions of either savers or entrepreneurs. Nor does it arise from the actions of the consumer and the retail industry in general, as the discount rate would in the gold standard.

The issue is not just the small number of participants or the total trading volume, but the fact that the trades which give rise to the gold lease rate today are a special case, unique to gold’s unnatural role under the worldwide regime of irredeemable paper.

It is interesting that the gold lease rate is not quoted directly. It is derived from two others things. It is calculated as: lease rate = LIBOR – GOFO. LIBOR is a dollar interest rate, and GOFO is the rate on a gold swap. No interest rate in the world has to be derived like this.

One should be careful not to try to read too much into the absolute level of the gold lease, or its spread to LIBOR. To wrap up this part of the discussion, let’s go back to Professor Fischer’s statement about the meaning of backwardation. He says that if gold is in backwardation, then that means that the gold lease rate is above the rate of interest in dollars.

I agree (with the entire discussion above as caveat), though I have one issue with that formulation. The correct definition of backwardation is when the bid on spot gold is greater than the ask on a gold futures contract. This is because backwardation in a commodity refers to when it is profitable to decarry it. This means one can sell the good in the spot market (on the bid) and buy it forward (at the ask). A positive decarry tends to correlate with negative GOFO, but not perfectly.[6] They are separate measurements. The positive decarry is the more accurate signal, not least because it is observable as a function of real market prices and is by definitional actionable. GOFO is calculated as a mean of quotes by six or more bullion banks’ reported rates, and if one wished to act on it one might find the real-world rate different enough to preclude profitable action.

Professor Fischer has published another paper[7] in the time that it has taken to me to write this second part. In this paper, he makes an error that illustrates my theme in this paper.

“The interest rate at which market participants can borrow gold without posting any collateral is called the gold lease rate (GLR). It is usually denominated relative to the Dollar amount of borrowed gold. For example, if the one year GLR was at 2% and gold spot was at USD 1,200, then someone could now borrow 1 oz of gold for one year, and they would have to return 1 oz of gold plus USD 24 in one year’s time. While GLR could also be expressed as a percentage of gold ounces that have to be returned, this is not commonly done. Nonetheless, it is obvious from this definition that GLR is the interest rate for borrowing gold.”

The error is very subtle. He says that if you borrow one ounce of gold then you can pay back the ounce plus \$24. However, \$24 is not equivalent to 2% interest in gold. 0.02 ounces is 2% interest. 0.02 ounces may work out to \$24, or less or far more.

The distinction between leasing and lending may not matter in many contexts. In this one—comparing the dollar interest rate to the gold lease rate—it does. If gold had a proper interest rate, then no lender would treat it repayment in gold as equivalent to repayment in dollars.

Today, gold is leased. It is leased by entities who keep their books in dollars. Repayment in dollars makes it simpler for them, and likely reduces their need to hedge. The lessor, in other words, wants a dollar income and happens to be using gold in this case to make it.

This is a good segue into the topic of gold’s dual nature. In this paper we have discussed gold as a currency. Gold is also a commodity, and analysis from that perspective may shed some more light on the topic.

In Part III, we discuss gold as a commodity.

[3] Theory of Interest and Prices in Paper Currency

[5] It is no coincidence that the same word, “carry”, is used to describe inventory on its way to the consumer, and also the position of buying gold spot and selling gold forward.

## 4 thoughts on “Gold Arbitrage and Backwardation Part II (the Lease Rate)”

1. dale

fascinating. but i am confused. there seems to be no risk-free rate on gold because there is gold government right? gold lease rate is just market rate,right?

1. Keith Weiner Post author

Dale,

There is no such thing as a risk-free return. If there is a return, there is a risk. Government can pass a law declaring their debt to be risk-free, and they may fool most of the people for a long time. But wishing does not make it so.

2. dale

Thanks Dr.Weiner! I see. I am doing binomial model on asset priced in gold and for risk-free rate ( there is none on gold?) i am using as a substitute Gold Lease Rate( since it is lowest counterparty risk rate between members of LBMA). does this make sense? thanks!

3. dale

but if there is no such thing as “no risk”, what are investors are supposed to do? 🙂 We count on government to use its powers or whatever and deliver that risk-free return, I guess, so we can sleep at night?