Gold Arbitrage and Backwardation Part I

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Professor Tom Fischer has written three papers[1][2][3] about gold backwardation and arbitrage. Across these three papers, he makes a case against the ideas of Professor Antal Fekete. I write this response solely on my own behalf. I do not speak on behalf of Fekete or his New Austrian school of Economics. I have two motivations for writing. First, I have written myself extensively about the gold basis and gold backwardation. Second, I have discussed my basis theory[4], and used it both to analyze market events (e.g. the crash of April 12 and 15, 2013)[5] and to make predictions, via the Monetary Metals Supply and Demand Report[6]. Additionally, I want to present a fuller treatment of certain topics.

The best place to begin is with Fischer’s discussion of arbitrage. Before addressing what he thinks is the flaw in Fekete’s definition, I want to look at an important point that Fischer makes. He says that one is not free to arbitrarily change or broaden a definition, in order to smuggle one’s conclusions. In Fekete’s Arbitrage Fallacy, Fischer writes:

“His mistake is akin to someone who has decided that the notion of “gold” was too narrow when only used for actual gold, so, to generalize and broaden the concept, any other metal should be called “gold” as well.”

Of course, I agree that this would indeed be an egregious error.

In each of his three papers on this topic, Fischer offers similar wording to define arbitrage, so let’s take the most complete one, also from Fekete’s Arbitrage Fallacy:

“…arbitrage in any currency is an investment that outperforms the risk-free rate of interest in that currency…”

There are two principles that students of the Austrian School will recognize right away. First, there is no such thing as a risk-free rate of interest. Non-Austrians are discovering this too, for example the European Central Bank. ECB executive board member, on Dec 9 Peter Praet, said:

“Appropriately treating banks’ holdings of sovereign debt according to the risk that they pose to banks’ capital makes it unlikely that the banks will use central bank liquidity to excessively increase their exposure to sovereign debt.”[7]

Banks have been borrowing from the central bank in order to buy the bonds of sovereign governments. The cost of borrowing from the ECB is lower than the interest rate on those sovereign bonds. They would appear to be performing arbitrage, as Fischer defines it.

But, as Mr. Praet reminds us, these bonds do pose risks. If the sovereign bond is risky, then what real instrument pays a risk-free yield?

The banks are not doing this because it has no risk. They are doing it because the ECB is offering dirt-cheap credit. In proposing its new regulations, the ECB is saying that it does not intend to stop offering subsidized credit. It just wants to impose restrictions on what banks can do with this credit or how much they can qualify for.

By the way, Fischer’s definition above does not state explicitly that the arbitrage investment is also supposed to be risk free. Later in the paper, he does state it:

“Yes, an arbitrage is risk-free, but it also needs to be better than the risk-free rate.”

There is no such thing as a risk-free investment either. Even the simple act of buying shares in New York for 99 and selling them a few milliseconds later in London for 100 has certain risks. Defining the unreal risk-free investment in terms of the unreal risk-free rate of interest is the finance equivalent of defining a dragon as a creature which preys upon unicorns.

The second principle—and this should not be controversial—is that the purpose of economics is to study human action. This was the title chosen by Ludwig von Mises, the greatest 20th century economist, for his greatest work.

The acting man is the proper focus of the economist. Whatever the merits of the notion of a risk-free interest rate, it has no relationship to actors in the economy. Indeed, it has no relationship to reality, and therefore it has no place in a proper theory of economics.

In teaching physics to new students, there is some merit to first studying frictionless surfaces, mass-less strings, and so on. Oversimplification is useful here, to allow the students to concentrate on learning basic principles first. More advanced students must deal with the complexity of the real world including strings that have mass.

There are two differences between positing a mass-less string and a risk-free rate of interest. The real string with mass is quite similar to the mass-less string, especially when the weights it ties together are orders of magnitude more massive. And the physics instructor makes it clear from the beginning that mass-less strings are just for novice students.

I do agree with Fischer on the principle that a proper definition for each concept is essential. Arbitrary definitions will not do, whether invented by a lone dissenting individual or by the consensus of an entire profession.

The opposite of arbitrary is objective, which means based in reality. All proper concepts are based in reality. Therefore, to properly form a concept, and hence define it, one must begin by looking at the various facts that give rise to it.

Ayn Rand wrote about concept formation:

“A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.”[8]

An example is the definition of chair. It’s a piece of furniture that you sit in. The definition does not include any mention of color, size, material, or number of legs. It must be broad enough to include every chair you will ever see in your life. At the same time, the definition must exclude all non-chairs such as tables, lamps, shelves, cars, and computers.

In Fischer’s example of a badly formed concept, gold is defined as all metals. All metals do share certain characteristics such as uniformity, divisibility, electrical and heat conductivity, etc. That is why we have the concept metal.

But we have the concept gold because gold is distinguished from all other metals. A definition of gold, which includes things such as zinc that do not possess its unique characteristics, is invalid. Such a definition is much too broad, and therefore unusable. It would cripple the thinking of anyone who accepted such a definition. Gold, iron, and zinc are all metals. Only gold is gold.

We’re now ready to build up to a proper concept of arbitrage. We will base our approach on something that exists in reality that’s performed by the acting man. Per our discussion of definitions, we must be thinking about what distinguishes arbitrage from all other kinds of actions.

Let’s look at certain principles described by Carl Menger, widely considered to be the founder of the Austrian School of economics. It is a fact that in all markets, there is not a single monolithic price. There is always a bid price and an ask price. Menger arrives at this by noting the problems in a then-popular notion. A certain quantity of one type of goods was assumed to be equivalent to another quantity of a different type of goods, if those goods were exchanged. In his book, Principles of Economics, Menger notes that if the goods were truly equivalent then any transaction could be reversed. But in reality, it does not work this way. If you buy 100 bushels of wheat at the grain market for 5 ounces of gold, then you cannot sell that wheat for 5 ounces unless the market moves upwards. Your loss is the bid-ask spread.

The bid and ask prices open up a whole new mode of thinking in economics. You can see that if you have wheat that you must sell then you must accept the bid price. If the wheat you provided to the bidder satisfies his demand, then this bidder will leave the market. The next-best bidder is the bidder below him. To sell something on the bid tends to cause the bid to drop. The opposite is true with buying at the ask price. It tends to lift the ask.

Consider the case of eggs offered in a farm town and bid in the city center. In this case, an actor can pick up and deliver the eggs. To do this, he must pay the ask price on eggs in the farm town, and be paid the bid in the city center. His profit is the city center egg bid minus the farm town egg ask.

In reality, it’s somewhat more complicated than this simple example. The would-be egg distributor must also buy fuel, a truck, and drivers’ wages in addition to eggs. He must pay the ask on all of these inputs.

The action of this egg-distributing actor will lift the ask price in the farm town and depress the bid price in the city center. As he scales up his activity (or his competitors do) the profit margin of this business will shrink. Will it go away entirely? No, the margin will never shrink to zero in the real world. It will shrink with each new competitor, until no new competitors are attracted to this business. More formally, we say that the marginal distributor walks away from this market; the spread is too small.

Marginality is another key idea introduced by Menger. Marginality provides an elegant and concise way to understand markets. If a bid ticks lower, then a marginal seller will leave the business of producing that good. If an ask ticks higher, then a marginal user of that good will either find a substitute or go out of business.

As markets developed, an actor appeared who was certainly not well understood at the time, and not well understood even today. The market maker stands ready to buy or sell. He makes a bid and an ask in the same good. In so doing, he narrows the bid-ask spread. He is the force that pulls down the ask if the bid is pressed, or pulls up the bid if the ask is lifted. Will the bid-ask spread ever be zero? No, it will compress until the marginal market maker walks away. Incidentally, each good has a different bid-ask spread, as a function of its liquidity (gold has the narrowest by far).

Now let’s move to a different kind of example, a consumer who buys apples every week. On the next visit to the grocer, he sees that pears are on sale. He switches his custom, refusing the apples and buying the pears instead. What will his action (along with the actions of many similar consumers) do? What will be the effect on apples? Without his buying, there is less pressure lifting the ask price. Instead, the apple merchant may have to dump apples on the consumer bid. In the pear market, his action lifts the ask.

The simple act of switching his custom is motivated by a certain kind of incentive offered by the market. And it will have a particular kind of effect on prices in the market.

We have looked at distributors, including those who buy multiple inputs to sell one output, market makers, and consumers who switch goods based on a sale. There are many other kinds of economic action that have something in common with these examples, but these few are sufficient. From them we can identify the essential. What do they have in common? What characteristic unites our examples and at the same time distinguishes them from all other kinds of action?

In my dissertation[9], I offered a definition of arbitrage as, “the act of straddling a spread in the markets.” In arbitrage, the acting man is offered an incentive to act, in the form of a spread. Whether this spread is used to earn a profit, or whether it is simply an inducement to try pears for a change, the spread is constantly signaling the incentives to take certain actions and to avoid taking others. There is also a feedback mechanism. The very act of taking the incentive—of straddling the spread—compresses it.

These are the two universal, absolute, immutable, and essential facts that give rise to the need for a broad concept of arbitrage. First, spreads signal an incentive to the acting man. Second, when an acting man takes the spread he causes it to become narrower; thus he reduces the incentive for the next actor to come along.

Arbitrage is what drives economic action and, therefore, it drives prices, changes to prices, spreads, and changes to spreads in markets.

Fischer asserts that arbitrage opportunities should all be arbitraged away. We can now refine this, and state with precision and clarity that every spread tends to compresses until the marginal actor is not attracted to straddle it. The spread does not go to zero.

It is not necessary to assert that everyone acts to straddle every spread offered; this would be impossible and is obviously false. It is sufficient, if we see an actionable spread, to predict that someone or many someone’s will take the arbitrage.

For those interested, a major part of my dissertation was to show that every attempt by the government to interfere with markets forces spreads to widen. This is why the presence of wide spreads today—with worldwide government intervention gone mad—does not invalidate the concept of arbitrage.

In Part II, I discuss Professor Fischer’s assertion that gold is a currency and hence conclusions may be drawn based on comparing its lease rate

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5 replies
  1. [email protected] says:

    Terrific read and look forward to part 2.

  2. jamesgl says:

    Keith… Thank you so very much for a clear, concise, and easy to read explanation and… A full set of definitions.

    I believe I now (Really for the first time) fully understand now what Is meant by arbitrage.

    Thanks again!


  3. Greg Jaxon says:


    Your definition of straddle admits situations that Dr. Fischer would probably exclude, for instance, your example of the apple consumer. Taking our “humans act” view, you’ve illustrated how spreads motivate the choice of action. The consumer’s ranked preferences for apples, pears, and cash sets up two bid prices. The shopkeeper similarly posts two ask prices. Each fruit then has a “spread” within the consumer’s world view – even if the shop is not functioning as an auction market, Austrians model each human actor as engaging in an internal auction. When the consumer goes short cash and long pears it is clearly the start of an arbitrage which is resolved as she derives more consumed utility per dollar than any of her other choices.

    This apparent overloading of terminology isn’t just something done solely for the symmetry or reductionism of it (although those aren’t bad reasons) This explanation exposes the key property of arbitrage: it is the action which, when taken, closes a spread.

    The consumer’s purchase “straddles” one of those spreads. For the individual consumer the act narrows the spread considerably, right down to the fruit’s diminishing marginal utility. The higher profit (in consumer utility) from “pears on sale” should exceed what the consumer has come to expect from her apple habit, but there is probably a greater risk that the pears are “on sale” for quality reasons.

  4. Keith Weiner says:

    Thanks for your comments.

    Greg: I agree with your assessment that a key to arbitrage is it narrows or closes a spread.

    I am somewhat amazed at how little has been said about the bid and the ask, and spreads in an economics context (traders get it more easily). Someone emailed me a while back and told me I was brilliant to come up with the idea of a separate bid and ask. He has studied Austrian economics! I wrote back and said thank you, but this comes straight from Menger.

    I think one could write a whole dissertation on arbitrage (this view of it, I am sure books have been written in mathematical finance). I don’t know why no one has.

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