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Wednesday, November 3, 2010

From Arbitration to Arbitrage

Arbitrage happens when someone — an “arbitrageur” — profits from a price differential between markets for some good. He buys low in one market to sell high in another, and pockets the difference as risk-free profit. Etymologically, the word “arbitrage” is French, and refers to the decision of an arbitrator. The term was first used in English in its current sense early in the 18th century. At first sight it seems difficult to see how its meaning could drift so far from its original source. However, I can tell a little story that might shed some light on this.

According to Cicero (De Officiis, 1.33), Quintus Fabius Labeo (consul in 183 BC) was appointed by the Roman Senate to arbitrate a boundary dispute between the cities of Nola and Naples:

“[H]e took up the case and interviewed both parties separately, asking them not to proceed in a covetous or grasping spirit, but to make some concession rather than claim some accession. When each party had agreed to this, there was a considerable strip of territory left between them. And so he set the boundary of each city as each had severally agreed; and the tract in between he awarded to the Roman People. Now that is deceiving, not arbitrating [Decipere hoc quidem est, non iudicare].”

The same story is also related by Valerius Maximus (Facta et Dicta Memorabilia, 7.3.4), where he writes that “arriving at the scene, he [Labeo] advised both separately not to be greedy but to go backwards from the nodal point of the dispute [regredi a nodo controversiae] rather than forwards.”

Now, although it might not seem like it, this case bears a more than analogous relationship to arbitrage. Let us imagine that, instead of separate parties to a bargaining situation, we redescribe Nola and Naples as different markets for a single type of good. This case is somewhat unusual in that there happens to be only one token of that kind of good, namely, a specific tract of land lying between the two cities.

Let us further imagine that each market/city values that land at a certain price. In other words, each has a price in mind at which they are willing to part with the land. Unfortunately, when Labeo first appears on the scene, it seems that the land is — paradoxically — worth more to each party than the price at which the other is offering to purchase it. Nola thinks it is worth 1,000,000 denarii and would be willing to purchase it in exchange for some amount of money less than this, say 800,000 denarii. Same with Naples. In other words, each city would not pay more than 800,000 denarii for the land, but would not sell it for less than 1,000,000. Under these conditions, no bargain can be struck. There is a further and more obvious reason no bargain can be struck.

There is a theorem in economics called the Coase Theorem, which roughly states that, so long as property rights are well-defined and transaction costs are zero, parties will reach an efficient bargaining outcome. (Strictly speaking, this formulation of the theorem is grossly oversimplified, but it will do for our purposes.) Besides the fact that there is almost never such a thing as zero transaction costs, the obvious problem in this case is that there is an absence of defined property rights. A defined property right is precisely what they are bargaining for. And for this reason, neither party is sure whether it is playing the role of buyer or seller.

Here is where an arbitrator can come in and restore the conditions for efficient bargaining under the Coase Theorem. In effect, both parties give up their claims to some other party, namely the arbitrator. Under normal circumstances the latter, although he is now the “owner” of the land for purposes of bargaining, stands in a fiduciary relationship to the parties: rather than owning the land, he is more properly described as holding it in trust, and as such, he is not supposed to profit from it himself. The advantage to establishing this trust is that, for the purpose at hand, there is someone who can play the role of seller, while the two original parties become, in effect, bidders.

Once this new arbitrated bargaining structure was in place, Labeo, in the role of seller, accepted offers of purchase from the parties separately. It was exactly the circumstance that the parties were consulted separately that made them more akin to separate markets than to parties to a single transaction. In effect, it was a sealed auction. Cicero’s account says as much, and I think it must have been, because if either party caught wind that the other party was bidding so low (or rather, was willing to part with so much), they would have driven a harder bargain and asked for more. There must have been an information gap created by Labeo.

Obviously it differed from a normal sealed auction in that the auctioneer was privy to what was in the bid envelopes before they were opened. Indeed, Labeo was instrumental in helping the bidders to formulate their respective (inefficient) bids. Through what must have been his considerable powers of persuasion, he in effect convinced both parties to reduce their respective valuations of the land in question, leaving a differential which represented a profit to be pocketed by himself (on Rome’s behalf, of course).

Labeo effectively opened up a price differential between two markets for the same good, and made a risk-free profit as a result. If he had been bargaining in good faith in the role of trustee, he would have done his best to ensure an efficient outcome, which would have meant creating a price convergence between the two markets, so that there was no differential. In other words, he would have worked towards some optimal solution where each party was willing to purchase just so much of the land at just such a price as would ensure no surplus leftover for some third party to pocket. Labeo was an arbitrageur, not an arbitrator.

What makes arbitration and arbitrage similar is that both involve some agent who acts as go-between. In the former the go-between is a trustee who works to bring about market efficiency without profit to himself. In the latter the go-between takes advantage of market inefficiency rather than seeking to correct it. Thus, the difference between an arbiter and an arbitrageur is one of motivation.

The irony is that in economics, arbitrage can lead to long-run efficiency, because arbitrage activity acts as a signal to markets, alerting them to inefficient pricing, and leading to its correction. It would be as if after being burned by Labeo, Nola and Naples had a better understanding of what was at stake and what they lost. Armed with this new knowledge, if they were to do it over again, they would come to an agreement to split Labeo’s differential equally between, leaving no differential to be scooped up by a third party. Then they would both end up better off. Unfortunately, their’s was not a currency market; they won’t get another chance to do things right.

The trickery of Labeo aside, the profit margins in arbitrage are usually quite small and the opportunities presented tend to be rather fleeting. Once price information becomes available, markets adjust themselves quickly.

* * * *

The world is full of modern-day Labeos. They’re called real estate agents, and they work in pairs. One represents the seller of a home, and the other “represents” the prospective buyer. It’s supposedly a fiduciary relationship, at least in the sense that the two agents are supposed to be looking out for the interests of their respective principals. In reality, only the seller’s agent can be said to do so. Because they make their money from the percentage commission they receive from selling the house, both agents in reality represent the seller. They both have a vested interest in having the house sell for as high a price as possible, and thus in fleecing the buyer.

Unlike other kinds of arbitrageur, real estate agents don’t correct market valuations; they grossly inflate them. This is because they have an effective monopoly over whatever it is they do: if you wish to buy or sell a house, you must use their services, which means that although they distort prices, there is no real way the market can correct this unless buyers and sellers are allowed to interact directly with each other, thereby establishing non-collusive price signals to guide the market.

This monopoly may be breaking down, at least where I live. Real estate agents are now being forced to open up access to the Multiple Listing Service (MLS), meaning that they are about to lose their monopoly on access to the real estate market. In conjunction with this, I’ve noticed that a number of small firms have appeared on the scene whose aim is to make it easier for people to buy and sell homes without requiring the “services” of an agent. I predict that such developments, if allowed to continue apace, will lead to a moderation of prices and hopefully will someday make shelter more affordable in this city. I say “if allowed to continue apace” because there is a large lobby — guess who it’s funded by? — trying to put a stop to it.

Interestingly, the agent who “helped” us buy our home had the stones to tell us not to worry about what she was making in commission from our purchase, because we weren’t the ones paying it. She claimed that it was coming out of the seller’s pockets. She must truly have thought we were cretins, too stupid to figure out that the sellers would be paying the commission out of money that we had forked over to them in the first place. If the agents have done their jobs well, once the seller makes his end, he will be paying the commission out of the differential between selling price and the non-collusive market price.

Homework assignment: Can you find other examples of economic activity requiring a similar level of structural fraud and collusion? In a wry aside in The Selfish Gene, Richard Dawkins gives the example of divorce lawyers. The lawyers of both parties have a stake in not having the split settled quickly and amicably, as this would lead to a reduction of billable hours. This differs from the real estate case in that instead of both agents representing only one of the principals, they truly represent neither of them.

None of this is to say that there aren’t ethical lawyers and real estate agents out there who don’t operate in this unscrupulous way. However, I think it is useful to be aware of the underlying structure of such relationships, so that one doesn’t end up with an arbitrageur instead of an arbitrator.

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