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FEKETE’S “ARBITRAGE FALLACY” & REBUTTAL

The following is an essay is by Tom Fischer, a professor of financial

statistics at Wurzburg University in Germany.

Original at: http://www.safehaven.com/article/32088/feketes-arbitrage-

fallacy

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 By Tom Fischer; Tuesday 10th December, 2013

 In his essays touching on arbitrage in general and on backwardation in gold in particular, Antal E. Fekete has done

 something which is not very obvious to the untrained eye, but therefore possibly even more confusing and dangerous. Hismistake 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. I assume the reader would agree that

this would be a bad idea and might lead to confusion and a series of wrong conclusions as well. For instance - and Feketedoes something very similar which will be explained below - one could now be tempted to claim that, since it had alwaysbeen so, all "gold" should be yellow metal. But because some of the new "gold" apparently was not yellow, this was a sign of

 something in the "gold" market being foul. To be more specific, Fekete has abused the notion of "arbitrage" in his work on Austrian and "New Austrian" economics. In mathematical finance, "arbitrage" has a well-known and very precise meaning,which says, that it is a trading strategy that outperforms the risk-free rate of interest. In other words, arbitrage is a trade or strategy that is too good to be true. At some stage (references follow below), however, Fekete seems to have decided that

any(!) other economic transaction constituted an "arbitrage" as well. So, drawing the comparison to our example, any othermetal suddenly became "gold", too. Where this logic finally had to go wrong, will be explained in the remainder.

 Arbitrage: "money out of nothing" To expand on the generally accepted definition that arbitrage in any currency is aninvestment that outperforms the risk-free rate of interest in that currency, assume now that we can invest, but also borrow, atthe risk-free rate (as any borrower needs a lender, and vice versa). Under arbitrage conditions, this means that if an investordoes not have any capital to start with, she can borrow money at the risk-free rate and then outperform the loan's interest

using the arbitrage strategy. At the end, she pays back the loan while she can keep the profits she made on top of the risk-free return. She hence "made money out of nothing", or, as they say, she found a "free lunch".

 Arbitrage: independent of personal preferences An important property of arbitrage is that its existence does not depend on personal preferences or the "numeraire", that is the currency used to account for wealth. If an arbitrage opportunity is present, then it exists and is desirable for everyone, i.e. for all market participants. Since for everyone some money is betterthan none, all market participants would benefit from running the same arbitrage strategy if they could, independent of their particular personal preferences. Furthermore, if an arbitrage was present (or if it was not present) if we counted our wealth inDollars, it would also be present (or not present) if we counted our wealth, for instance, in ounces of gold, or any othercurrency or good. Hence, the numeraire does not matter.

 Arbitrage will be "arbitraged away" We had seen that arbitrage is a trade or strategy that, essentially, is too good to be true.Therefore, as professional "arbitrageurs" would seek out such strategies and would follow through with them, they shouldgenerally not exist, or not exist for long. As an example, a typical arbitrage is when a good can be bought and sold at two

different prices. Buying low and selling high at the same time is the arbitrage, but if everyone tries to do that, sellers and buyers will soon be overwhelmed by demand and supply, respectively, and prices will converge, such that any profits wouldfinally disappear. The arbitrage would "close" or "be arbitraged away". So, especially the property that arbitrage is desirable

for everyone independent of their personal preferences ensures that people will try to realize arbitrage and, in due course, thearbitrage will disappear.

 Fekete's arbitrage: barter, purchase, anything In his article "Disequilibrium Analysis of Price Formation. Disorder andcoordination in economics" (reference [1]), Fekete explains his own idea of arbitrage:

Whether recognized or not, arbitrage is the driving force of the market process. It is present in every market action, eventhough sometimes it may well be hidden. It is not generally recognized that barter -- a sale and a purchase 'telescoped' into asingle transaction -- is an instance of arbitrage. By the same token so is every purchase, since an explicit choice alwaysincorporates the implicit rejection of the nearest alternative. In Fekete's own words, "barter" is arbitrage and "every purchase" too, so essentially, any transaction or "every market action", as he formulates it. Given the earlier outlinedgenerally accepted meaning of arbitrage outside Fekete's and his disciples' work, this statement is absolutely wrong. Tosomeone trained in financial mathematics, it is comparable to the statement "gold is gold, and every other metal in the world

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is gold, too". So, to make a very clear distinction to the commonly used proper definition of arbitrage, we will call Fekete'sversion from now on a "Fekete-arbitrage". However, note that Fekete's "arbitrage" notion includes the proper standard notion(as it includes every market action, so it also includes proper arbitrage strategies). Therefore, we shall call a Fekete-arbitrage,that is not a proper arbitrage in the generally accepted sense, a "Fekete-only-arbitrage".

 Fekete-only-arbitrage cannot be "arbitraged away “According  to Fekete's definition, if someone buys herself lunch, i.e.exchanges cash for lunch and hence prefers lunch over cash, this constitutes an "arbitrage". I predict that this "arbitrage" willnot be "arbitraged away" anytime soon - unless we all wanted to starve ourselves around noon. Also, this someone's friend,who joins her over lunchtime, might have had her lunch already and would momentarily not have the slightest inclination to buy a second lunch. So, the friend clearly would prefer cash over food and, hence, would not transact. Buying lunchtherefore is no proper arbitrage, it is a Fekete-only-arbitrage. It is dependent on personal preference and will therefore never"close". We can also conclude that it is certainly not true that something in the "lunch market" is fishy just because thisFekete-only-arbitrage exists.

 Proper arbitrage in comparison Now, in contrast, consider a real arbitrage in the literal sense of a "free lunch". Our hungry protagonist would certainly pursue this arbitrage. However, so would her friend who is not hungry at all. Here is why: If thenot-so-hungry friend knew about where to get a delicious free lunch, she could offer any other hungry acquaintance, who didnot know of that free lunch opportunity, to get her a delicious lunch for a very competitive charge of, say, $5. The hungryacquaintance would happily agree. The not-so-hungry friend could now go and use that $5 for whatever she really wantedaccording to her own preferences, e.g. a subway ticket. So, the free lunch, as a proper arbitrage, would be pursued by thenot-so-hungry friend as well. It is independent of personal preference. What, however, would happen to a food place thatwas offering lunches to all and everyone for free? It would either go the way of the dodo, or it would have to charge realistic prices. The arbitrage, hence, would "close". However, if the free kitchen would stay open for a long time, then, quiteobviously, someone or something in the background would pay up for its actual costs. Some trickery in the "lunch market"could be assumed.

What should have been done Fekete should not have given the Fekete-only-arbitrages a new name, as they simply constitutemarket transactions due to differences in personal preference. Someone, just now, might prefer lunch over cash, but noteveryone does. In particular, if there exists a Fekete-only-arbitrage for one person, it does not mean that the same tradeconstitutes a Fekete-only-arbitrage for another person. In stark contrast to that, we had seen that proper arbitrage is desired by everyone at any time, as some money is always better than no money at all. The presence of Fekete-only-arbitrage istherefore a permanent state - it will not "close" or be "arbitraged away", as otherwise there would be no market transactionsat all.

What is the problem? The problem in Fekete's theory started to dawn on me when I repeatedly stumbled over claims that backwardation in gold futures meant arbitrage. The source of that fallacy, when I tried to trace it back, seemed to be Fekete.Having pointed out to more than one present or former Fekete disciple that backwardation did not at all imply arbitrage, Iwas told that I did not use the right notion of arbitrage, as they used Fekete's definition. This seemed a fair point, until I cameacross this piece of  text about the gold basis service on the feketeresearch.com web page - which I assume is authorized byFekete to use his name (reference [2]): 

The study and monitoring of the basis is always with one perversion in mind: being able to sell spot gold and replace it witha lower cost future - or 'actionable backwardation.' If the gold market moves to this state permanently, then 'risk-free' Dollarscan be made perpetually by deferring ownership of physical gold in favour of futures. 'Risk free' and 'permanent' are notstates that apply to any market on the whole, let alone with reference to the gold market. ' Risk free' and 'permanent' tend toget arbitraged away before anyone outside the market place notices. [Emphasis added.]

My first problem lies with the term "risk free". Yes, an arbitrage is risk-free, but it also needs to be better than the risk-free

rate. An "arbitrage" that makes 1%, if any bank account would return 2%, obviously is none. If this was overlooked, whichcould easily happen, then one might arrive at wrong conclusions. My second problem lies with the term "arbitraged away".Essentially, I had been blamed for not considering Fekete-only-arbitrage. But we have just arrived at the conclusion thatFekete-only-arbitrage cannot be "arbitraged away" at all. There was no doubt in my mind that backwardation did not meanarbitrage in the proper, generally accepted sense, and it does not have to go away for that reason. However, now I also hadshown that, although it was a Fekete-only-arbitrage, such supposed "arbitrages" still had no reason whatsoever to go away.Hence, Fekete's conclusion that backwardation in gold, since it supposedly made arbitrage possible, was an unnatural statethat had to be caused by a breakdown of the gold futures market and the default fears that come along with it, had beenfalsified.

Why gold backwardation is no arbitrage This article is not on the backwardation problem in particular, so in the following Iwill only briefly summarize why backwardation in gold does not imply arbitrage in the generally accepted sense. For furtherdetails, I would like to direct readers to my piece "Faux Gold Arbitrage" (reference [3]). The idea of the arbitrage proponentsis, as cited earlier (reference [2]): "being able to sell spot gold and replace it with a lower cost future [...]". In my own paper

on that topic, I wrote:

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The argument [...] goes as follows: Assume that someone owns gold today and that there is backwardation in the gold

market present in the sense that the spot price of gold today is higher than the forward price in, say, one year's time. Then,this person can sell gold today and simultaneously enter a forward contract, earn interest over one year, and buy back the

 gold at the end of that year at a cheaper price. The result is the same amount of gold, plus a cash profit consisting of theearned interest and the price differential between the sale and the purchase price. As this profit was risk-free, so theargument goes, this constituted an arbitrage, something which should not exist as it should be "arbitraged away".

 Here are, in summary, the reasons, why this logic is flawed:

1.  Counting wealth in Dollars, the strategy is not risk-free and hence not outperforming the risk-free rate, as the spot

 price of the gold at maturity could be much lower, and an over-all Dollar loss could be the consequence.

2.  Counting wealth in gold ounces, the strategy is risk-free, but no arbitrage, as the return over ounces equals exactlythe gold lease rate, which is the risk-free interest rate of gold, which would have had to be outperformed forarbitrage (recall here that arbitrage is independent of the numeraire). I call overlooking this fact the "change ofnumeraire" trap.

3.   Backwardation is omnipresent in currency markets, since, if one currency is in contango against the other, the

latter one is in backwardation against the former (mathematical fact). Hence, backwardation is caused bycontango. As a logical consequence, contango implies arbitrage too, if backwardation does, but not even Fekete seems to claim this. Of course, there is no arbitrage first place, as the forward curve can be explained by interestrate differentials.

4.   Apparently, no one arbitrages these foreign exchange backwardations away in practice either. With gold being acurrency with the symbol XAU and its own interest rate (the gold lease rate), the same argument applies to gold.

So, backwardation in gold cannot be arbitraged away - neither in the commonly accepted theory, nor in Fekete's theory, andalso not in practice. Any theories or any investment strategies based on this idea could therefore be flawed. Backwardation

in gold simply means that gold's interest rate is higher than that of the U.S.-Dollar. This is an interesting and rather seldom

occurrence, and the deeper reasons for it, and the possible implications of it, are open to interpretation and, maybe, speculation (see also my article "Why Gold's Contango Suggests Central Bank Interference"  on that topic; reference [4]). Ifthe gold forward market came under severe stress because of rising failure-to-deliver risk, it might well be the case that strong backwardation would be the consequence. I have no problem with this idea. However, arbitrage has nothing to do

with it, and backwardation in gold could very well exist outside extreme market situations, for instance, it could simply bethe consequence of a market expectation of falling gold prices.

Unsolicited advice to Fekete and other "New Austrian" economists If Fekete and his followers wanted to amend their

theories, they need to drop the idea that all market transactions caused by differences in personal preference should be called"arbitrage", as it is highly misleading and will greatly confuse researchers and economists who are used to the generallyaccepted definition of arbitrage, which has served very well. For their theories to become at least logically consistent, theywould also have to refrain from claiming that any market transaction constituted something like an arbitrage in the propersense, as this simply is not true and could lead to incorrect conclusions. As I wrote in my earlier mentioned paper "FauxGold Arbitrage" (reference [3]): "An arbitrageur does not need an economic theory or belief system. All she needs are pricesthat she can act on." So, arbitrage theory does not care about economic theory, be it Keynesian, Austrian, or "New Austrian",and this article is not on an economic or monetary issue. Scientifically, Fekete therefore has nothing to gain from not callingthings by their proper names. Similarly, using the established names would not take anything away from new economicideas he might have had. But if Fekete and his fellow "New Austrians" will not use the proper terms, or will continue usingthem improperly, they have a lot of credibility to lose. Months ago, while analyzing his theory, I contacted and repeatedlyincluded Antal E. Fekete in correspondence regarding the issues raised in this article, as I wanted to discuss them with him in person. Fekete once wrote (reference [5]): "Science has nothing to fear from an open debate. Feeling of insecurity ischaracteristic of a cult." To this day, I have not heard back from him.

References 

[1] Fekete, A. E.: Disequilibrium Analysis of Price Formation. Disorder and coordination in economics (January 01, 1999). Available at: www.professorfekete.com/articles/AEFDisequilibrium.pdf (retrieved: December 09, 2013)

[2]  www.feketeresearch.com/gold-basis-service2.php (retrieved: December 09, 2013)

[3] Fischer, T.: Faux Gold Arbitrage. BullionVault Gold News (September 02, 2013). Available at: goldnews.bullionvault.com/gold-arbitrage-backwardation-090220135(retrieved: December 09, 2013)

[4] Fischer, T.: Why Gold's Contango Suggests Central Bank Interference. SafeHaven (November 23, 2013). Available at:

www.safehaven.com/article/31904/why-golds-contango-suggests-central-bank-interference (retrieved: December 09, 2013)

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[5] Fekete, A. E.: Note (from September 09, 2005). In: Fekete, A. E.: Where Mises Went Wrong (September 16, 2005). Available at:  www.professorfekete.com/articles/AEFWhenMisesWentWrong.pdf (retrieved: December 09, 2013)

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Mr. Fischer first contacted the author around three months ago to enquirewithout prejudice (or as the author assumed) about Fekete's work on the

gold basis, its implications and Fekete’s stance on economics generally.

Having read similar lines of arguments presented by Mr. Fischer as in his

essay above, the author expressed his simple opinion that Mr. Fischer was

not taking heed of Menger's concept of marketability and subjectively

determined exchange. Furthermore, that there's no natural

correspondence between the name 'dollar,' or any fiat currency and 'gold.'

Mr. Fischer refused to accept this in correspondence and completelyignored reference to it and the mechanical implications from it.

Subsequent interaction with Mr. Fischer and the author has revealed

some form of bias against Fekete. Correspondence with Mr. Fischer has

included the phrases “ tremendous damage that Antal E. Fekete has done to

the sound money cause” and “ it is tragic that people have possibly spent

 years of their lives on this man’s fallacies.”  This certainly isn't the

demeanour of a supposed scientist who professed an open mind. One could

argue that Mr. Fischer's attitude to a professional mathematician such as

Fekete brings shame to his field of professional statisticians.

In the name of fairness and completion, someone unassociated with Fekete

or the author was asked to comment objectively on Mr. Fischer's essay.

With that in mind, the following essay was written by David van der

Linden. It independently summarises Mr. Fischer's somewhat simplistic

errors, as one is to infer from Mr. van der Linden's essay.

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Observational Errors of Dr. Tom Fischer’s article “Fekete’s Arbitrage Fallacy” David van der Linden

The following essay attempts to highlight a number of observational errors leading to Fischer’s

rejection of the New Austrian School of Economics’ theory on backwardation in the gold futures

market.

Fischer defines arbitrage as the outperformance of the risk free rate of interest[1]

. In general economic

theory, this definition describes a concept known as “economic profit”, different from entrepreneurial

profit. Here, entrepreneurial profit is the difference between a revenue flow and the factor costs of

production. Economic profit is the entrepreneurial profit divided by the invested capital, providing a

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measure for the profitability of a business compared to the “risk -free rate of interest”. Thus far,

Fischer’s definition of arbitrage applies to all profitable business. 

The idea of comparing the return on a transaction to a “risk -free rate of interest” is questionable. As

state credit is being depreciated on a nearly daily basis, with quantitative easing continuously pushing

interest rates lower, the “risk-free rate of interest” is most likely negative in real terms. This peculiarity

may lead to certain enterprise being classed as profitable according to the definition of “econ omic

profit”, while it does not outperform the constant currency depreciation. 

Fischer also allows his definition of arbitrage to apply to people who have no starting capital[1]

. The

claim is as follows: one can not only invest and outperform the “risk -free rate of interest”, but also

borrow against the same  rate of interest. Fischer overlooks the fact that interest rates are not

monolithic prices. Rates of interest according to Mengerian theory consist of a bid/offer spread.

Following Menger’s theory, Fekete synthesised the schools of time preference and productivity to

produce the only coherent theory of interest[2]

. Fekete’s theory states that the bid rate of interest is

derived from the marginal time preference, and the offered rate of interest is derived from marginal

productivity of capital. Lenders and borrowers act under different preferences, creating a bid offer

spread with a market maker acting in between the resulting spread.

This bid/offer spread denies the possibility of there being a single “risk-free rate of interest” which is

used to measure the profitability of an investment and the rate at which one borrows to finance the

investment. The rate of financing will undoubtedly be higher than the “risk-free” rate of return,

meaning that certain enterprise that was first considered profitable may now not be as profitable due

to the cost of borrowing being higher than the “risk-free rate of interest”. 

Fischer continues by announcing that the existence of arbitrage is independent of its numeraire[1]

.

That is to say, an arbitrage can be denominated in any currency. However, as mentioned before,

state credit is subject to manipulation and depreciation. An arbitrage denominated in dollars cannot be

compared to an arbitrage denominated in defined amounts of gold. The definition of one dollar can be

altered at any time, whereas the definition of one ounce of gold will remain exactly the same.

Denominating an arbitrage in measureless state credit ignores currency depreciation.

The crux of Fischer’s analysis is the statement that gold backwardation is no arbitrage[1]

. Gold

backwardation is a situation in which gold futures contracts trade at a discount to the gold spot “price”.

What many refer to as the “gold price” is in effect the exchange ratio of dollars to gold. When the “gold

price” is low the dollar trades high, and vice versa. The real price of gold (or said otherwise: the price

of money) is the rate of interest yielded by gold. Bearing in mind that the rate of interest is not a

monolithic price, but a bid/offer spread, gold’s rate of interest is most often noted as GOFO, or the

Gold Forward Offered Rate. Currently, backwardation in the gold futures market is paired with GOFO

rates that are higher than LIBOR (London Interbank Offered Rate). LIBOR is the prime interest rate

regarding fiat currencies worldwide. A GOFO quoted higher than LIBOR means that lending gold ismore profitable than lending dollars. This difference should lead to an increased supply of gold in

exchange for (fiat denominated) interest rate returns. A bullion clearing bank leases the offered gold

against an interest rate term, hedging the outstanding gold position with gold futures. An increased

activity in lending gold for an interest rate term (denominated in fiat) should push the futures market

into contango (gold futures at a premium to spot gold), as bullion banks require a larger amount of

futures to hedge their outstanding gold positions. This phenomenon is not visible in the gold futures

market, pointing to a reluctance for gold holders to lend out their gold for a fiat denominated return.

The high GOFO rate points to low readiness to lend gold and high readiness to borrow gold. Consider

that the desire to hold gold is the desire to hold gold over all other goods, including the nearest good

(other monetary units with similar marketability).

Fischer, on the other hand, looks at the gold backwardation arbitrage in terms of the exchange rate of

gold against the dollar. He states that the arbitrage would be a situation in which one buys gold

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futures at a discount to spot, which then mature into physical gold creating a profit, as physical gold

sells for more than the futures contracts. In Fischer’s view, this could not be arbitrage as the trade is

not risk free in dollar terms, and does not outperform the “risk-free rate of interest” in terms of gold

ounces, as the backwardation equals the gold forward rate. Fischer should however consider the

following: the holding of a gold future yields a rate of interest higher than the alternative rate of

interest (LIBOR).

The arbitrage that should take place in the gold futures market rests therefore not the difference in the

price of money (i.e. gold/silver) in the  present  and in the future, but rather on the price of fiat   in the

future and of gold  in the future.

Fischer also makes a point of denying that arbitrage is the driving force of any market, as posed by

Fekete. This analysis seems to flow naturally from the theories of Dr. Carl Menger. Menger suggested

that there are no economic equivalents (viewed objectively)[3]

. Consider the following; when a trade

takes place, two agents are driven by a desire to maximise their utility. If either of the agents were to

experience a decrease in their utility resulting from the trade, there will be no trade. However, as soon

as the trade is completed, there is no reason for either agent to return to the situation preceding the

exchange, unless a general change in the prevailing preferences has taken place.

Fischer gives an example of an agent buying a lunch, thereby exchanging cash for food. The agent’s

preferences are higher for food than for cash. Fischer argues that this type of exchange cannot be

arbitraged away, a necessary feature for an arbitrage. The seller of the lunch obviously experiences

an increase in utility from the exchange, as does the hungry customer. The arbitrage rests on the

preferences of the customer and the profitability for the entrepreneur. Should the preferences of the

customer change resulting in a lower demand for food, the price of food should drop. This is a natural

economic law. We can assume that as long as the exchange value of food for cash is lower than the

customer’s demand for food, the customer will happily continue the exchange. The demand curve

results from the consumer’s preferences, if the preferences change so will the demand curve. After

having eaten a first lunch, the customer may value food less rendering the price of a lunch higher than

the new demand. Buying a lunch now would result in negative consumer surplus, a decrease in utility

for the consumer. This change in preferences means the exchange will no longer take place, as there

is no longer a possible trade in which neither agent experiences a decrease in utility. One can no

longer speak of arbitrage.

Fischer calls arbitrage “money out of nothing” [1]

. New Austrian Economics recognises that

backwardation in the gold market as it currently exists comes from the realisation that exchanging

gold for fiat is exchanging money for nothing.

[1]: http://www.safehaven.com/article/32088/feketes-arbitrage-fallacy , Dr. Tom Fischer, Dec. 10th 2013

[2]: http://feketeresearch.com/upload/Analysis-of-The-Yield-Curve.pdf , Sandeep Jaitly, Sep. 24th 2012

[3]: Grundsätze der Volkswirtschaftslehre, Dr. Carl Menger, 1871

David van der Linden

December 16 th, 2013

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Mr. Fischer has been invited by the author to debate his charges against

Fekete with the author  –   as written communication had reached an

impasse. Mr. Fischer has refused on all occasions. Independent

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corroboration of Mr. Fischer’s observational errors has been forthcoming

with great elegance and brevity –  as Mr. van der Linden has shown.

Mr. Fischer should spend more time honing his social skills instead of

bringing shame to his university and professional statisticians generallywith his bigoted stance.

Sandeep Jaitly,

Fekete Research,

17th December 2012.