posted
Does anyone (fugu, Jhai, other economists who live here that I don't know about) know of theory on how arbitrage situations are corrected in controlled markets? Say, for instance, that exchange rates were set by people, rather than algorithms or markets, who operated independently. It would be possible that three independent exchange rate setters could set rates that would open up opportunity for a triangle arbitrage. I'm interested in what method the independent rate setters would use to eliminate the arbitrage opportunity.
Maybe more realistically, on-line gaming sites set odds on various outcomes of events. If enough bookies set up enough odds independent of each other, they may (should?) create an arbitrage opportunity (sort of a distributed dutch book). In such a case, how do/would the bookies react to prevent arbitrage? One or more of them would have to change their odds, but what would govern the process? Is it done independently, or cooperatively? Is there a game theoretic model that could explain it?
Caveat: as is probably evident, I don't know much about arbitrage (or economic theory in general). It's conceptually related to some research I'm doing in fusing probability assessments, but being a non-economist I'm not familiar enough with the literature to know whether this problem has any relevance, and if so if there's theory already developed for it.
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posted
One option is that they don't eliminate the arbitrage. For instance, due to policy choices by the various gov'ts, there were large amounts of carry trade (a form of currency and interest rate arbitrage) involving Iceland and Europe, and Japan and India (among several places) recently. The gov'ts created and sustained this arbitrage opportunity as a side effect of policies they considered desirable.
Of course, then everyone with an arbitrage position that isn't hedged gets destroyed when the arbitrage opportunity is eliminated, such as happened recently with the aforementioned carry trade.
There isn't really a literature on how such 'controlled' situations might go about removing the arbitrage opportunity, other than by letting markets form that automatically handle them. If there are only a few players, one or more of those involved will need to adjust their rates to remove arbitrage. (edit: there is a literature on constructing markets that don't have arbitrage opportunities, but the occasional bit of arbitrage is probably a small price to pay for the ability to construct your market as you desire).
If bookies are creating arbitrage situations, then presumably the bookie(s) on the short end of the arbitrage situation will be losing money until they close it. If they don't close it, they'll have business problems, and won't be able to keep being a bookie. The issue will have self-corrected. This happens frequently in many markets, so it is often a reasonable solution.
You could provide tools to help bookies avoid creating arbitrage opportunities, of course, and that wouldn't be too hard, especially for any single offer. While detecting all arbitrage opportunities is difficult (and probably NP-complete for your market), detecting many possible ones should be relatively easy. Select various baskets of goods that might be on one side of an arbitrage via some simple heuristics, then check the appropriate other side of the arbitrage.
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Blayne Bradley
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posted
i remember in Mission Earth Jetero Heller was doing something similar to make large sums of money. Although he had the help of being able to see the near future of the stock market for commodities.
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posted
Not an economist, so I'm not sure if this formally counts as arbitrage, but your post reminds me of this.
In the Asian Financial Crisis of 1997, foreign hedge funds were both dumping HK dollars (which are pegged to the US dollar) and short-selling the stock market in order to make money by either breaking the peg or crashing the stock market. The HK government essentially stared them down and started buying up the stock market, in order to make them lose money.
More details here
quote: The HKMA was largely unprepared when speculators mounted their first attack in October 1997. Although the HKMA had intervened in the Hang Seng in July 1997 with a HK$1 billion purchase to stabilize the market, most analysts believed the Hong Kong economy was somehow immune to the Asian Financial Crisis contagion. During the currency attacks, speculators took out large short positions against the HK dollar with the aim of destabilizing the linked exchange rate. Powerful international hedge funds dumped $5 billion worth of borrowed Hong Kong dollars. These attacks activated the automatic adjusting mechanisms of the currency board and drove up interbank interest rates. The HKMA, sensing that currency speculators had been attempting to manipulate the market, raised interbank rates, at one point to an astronomical 280%. Speculators, many of whom were local banks, had to borrow locally to fund their short positions and also to maintain daily balances for normal bank operations. As a result, these speculators were forced to unwind their positions and incur heavy losses.
...
The situation had become much more complicated in the attack of August 1998. Speculators launched a coordinated and well-planned attack on the financial market. Over HK$30 billion were sold on August 5, 1998, chiefly through U.S. investment banks. Speculators took advantage of the built in mechanisms of the currency board to drive up interest rates, which subsequently applied downward pressure on stock prices. Intensively selling HK dollars over a short period had the right effect. This, combined with rumors and pressure on the government to delink the HK dollar to the US dollar and also rumors that the PRC would devalue the renmenbi, had catastrophic effects on the stock market. By pressuring the currency and selling stocks short, speculators anticipated profits from stock index futures contracts, even if they could not break the exchange rate link. This time, the HKMA was ready. Instead of absorbing the HK dollars, it got the Treasury to buy them. The government claimed that it needed the extra HK dollars because it planned to run a fiscal deficit of over HK$20 billion to fund its stimulus packages (Reyes, 250). Unlike in October of the preceding year, there was no change in the HK dollar balance in the banking system, so interbank rates climbed only three percentage points to 7.5%. Although limiting the interest rate effects on the Hang Seng, a far greater fear swept through the markets. This intervention had led analysts to believe that HK had dropped the peg. This rumor coupled with rumors from the Chinese central bank that the PRC was considering a devaluation, although both Beijing and Hong Kong issued denials, sent the Hang Seng to a five-year low on August 13 of 6,544 points. The HKMA was successful in routing the short-sellers, but the hedge funds were believed to have had over 20,000 Hang Seng Index futures contracts ready to expire in two weeks. The strike price was estimated to be between 8,000 and 9,000 points (Reyes, 51). The HKMA used official reserves to purchase stocks to ensure speculators did not profit.
posted
Thanks, fugu (and Mucus). I might bring this back up after I absorb what you've written.
One question: is there always a clear "loser" in an arbitrage situation. For instance, if we have intransitive preferences within a population for commodities A, B, C and someone smart comes in with A, exchanges it for B (plus profit), exchanges B for C (plus profit), exchanges C for A (plus profit) and walks away with A plus a guaranteed profit (or worse, does it all again), which exchangee is the loser, and should therefore adjust his preferences (assuming we want to close the arbitrage situation)?
In the case of the bookies, presumably they all set the odds the way they did in order to maximize their expected gain. It seems equivalent to me to the problem of intransitive preferences, and it's unclear to me why there's necessarily a clear loser.
Another thought, somewhat related, is that market solutions to arbitrage still depend on individuals changing their private valuations based on perceived imbalances. I wonder to what degree markets' ability to remove arbitrage opportunities is just an aggregated version of the bookie problem, depending essentially on someone blinking first. I guess I'm starting to think of these as sort of a game of multi-player chicken, where each player is trying to determine how valuable their individual preferences are relative to the net outflow of capital from the overall system. Does that make any sense at all?
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posted
Mucus: yeah, that's a classic run on the currency, which is basically a sort of arbitrage.
Senoj: there isn't always a clear loser in markets where status is equal (other than the people who are getting free money vs those who aren't), but in a betting market where there are bookies and people doing business with bookies, it is likely that one or more bookies will be the main loser in the arbitrage situation. That is, the arbitrage will essentially be a transfer from that set of bookies to the arbitrageurs.
For instance, if both sides of a two-side match winning will pay out three to one in some situation, then whichever bookie is the one making the bad odd (and one of them has to be) will in the long run be the one being arbitraged against.
In your example, all of the people along the line are having money extracted from them, because they could have made the trade themselves with less loss.
Yes, markets handle arbitrage by lots of tiny adjustments in how much things are valued. The length of arbitrage opportunities in the stock market has been studied, and most last a few minutes at most (partly due to the way the market makers make prices).
I wouldn't quite call it a game of chicken, but that's the basics. People are setting/accepting prices in attempts to maximize their own payouts, in a continuous grind towards the (evolutionary) Nash equilibria.
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posted
In your bookie example above you have to realize the event before you can know who the loser is. This is a little different than market based arbitrage, where the accumulation of lots of little interactions can lead to closing the arbitrage hole. In the 3-1 example, the two bookies would be clued into an arbitrage by high betting volumes. But prior to the outcome of the event becoming known, it's unclear which of the two stands to lose by the arbitrage; it takes a realization of the loss before the loss is attributable, which seems unacceptable. Instead, I'm sure they attempt to resolve it before it goes to trial, by either cooperatively or independently putting their odds into coherence.
Can you point me to any literature on the length of arbitrage opportunities in the stock market? It might contain some discussion of the dynamics, which is really what I'm trying to get to.
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posted
Yes, arbitrage on betting tends to have delayed payoffs. And both could insist they're offering the right odds. But anyone who consistently fails to approximate the odds correctly will lose money.
And it isn't like most bookies let their odds ride. Adjustments are, as you said, done based on volume and the like. If someone's taking your bet like crazy, there's probably a reason, and it probably means you need to make the side they're taking 'more expensive' by changing the odds. Unless you have outside reason for believing the odds are correct.
I don't think there generally will be a way to determine which side of the arbitrage is going to lose out until the event occurs. That's just the nature of betting markets. If both sides are going to insist their odds are correct, one of them is going to lose a lot of money.
You might also read the literature on prediction markets; they can be viewed as betting markets where, instead of naming a set of odds and letting people purchase as desired, you buy and sell based on the current odds implied by a price, based on your expectations of the payout. They get rid of the problem you're dissatisfied with because the price adjusts as demand adjusts.
Some references: Hedging Performance and Basis Risk in Stock Index Futures (Figlewski 1984) found that (way back in 1984) almost all the arbitrage opportunities were closed the following day. Direct Tests of Index Arbitrage Models (Neal 1996) looked at a lot of real arbitrage trades and found that between transaction costs and opportunity costs (such as the T-bill rate), stock index arbitrage basically never exists at a profitable level.
I know there's been something recent that found typical arbitrage holes lasted almost no time at all in the NYSE nowadays, but I can't find it right now.
A little more context might help understand what you're looking for, too.
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posted
Thanks, fugu. I'm off to a seminar (algorithmic applications of diffusion), but I'll come back to this afterwards. Thanks particularly for the references.
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