Arbitrage of prediction markets
I’ve noticed something very curious on Intrade markets for 2012 Republican Presidential Nominee—Ron Paul gets 3.5% of getting a nomination—a value that’s clearly (and spare me EMH here) wishful thinking of Ron Paul supporters more than any genuine estimate.
And this brings me to a question—if prediction markets overestimate chance of winning of some rare case, how can I profit from that? Naively if I know true chance is 1%, I win $3.5 99% of the time, and lose $97.5 1% of the time, for expected payoff of $2.5. But my maximum loss is 39x higher than my expected profit, and I won’t be getting any money out of it for three more years.
I’d need to bet significant amount to earn any money out of it, and that would require accepting 39x as high maximum loss. No reasonably prediction market would accept this kind of leverage without some collateral, nor could I get any reasonable loan for it at rates that would make this arbitrage profitable.
The only way I can think of would be convincing someone with plenty of money that I’m right, and have him provide me with collateral for some (probably very high) portion of the payoff. But if results depend on my ability to convince rich people, that’s not prediction market! None of this is a problem for people trying to artificially pump estimates for Ron Paul—they’ll just take the loss, and write it off as marketing expense.
None of these problems occur if some position is vastly overestimated, like 60% estimate if I know true value to be 40% - this would be a cheap bet—maximum loss of $40 for expected profit of $20, and people who want to pump it need to take about as much risk as people who want to bring it back to the true value, not a lot more.
I’m confused. Is there some nice way to arbitrage this, or is this an inherent weakness of prediction markets and we should only trust positions they pick as leaders, not chances of their long tail?
Intrade and IEM don’t usually pay interest on deposits, so for long term bets you can win the bet and still lose overall. The obvious solution is for them to pay such interest, but then they’d lose a hidden tax many customers don’t notice.
There are many details of Intrade that encourage a long-shot bias. These may be “hidden taxes,” good for Intrade’s bottom line, but I suspect that the long-shot bias is also, in itself, good for Intrade.
It’s nice that Intrade generates the positive externality of information, but if we want better information, it’s not surprising that we’d have to pay for it, such as providing other revenue streams than these hidden taxes.
That wouldn’t really fix the problem, as interests paid on deposits would be much smaller than interest you have to pay for loaning collateral.
Find another prediction market, or another person, willing to make the bet with you at the true (1%, say) odds. Then you buy one and hedge by selling the other. Arbitrage usually requires two different bets.
For instance, if you sell the Intrade prediction, but make a $1 bet at 99:1 odds that Paul will win the Republican nomination (god forbid), you win $3.50 - $1.00 when Paul loses, and $99.00 - $96.50 when he wins.
[Edited to fix math]
Arbitrage always requires more than one bet, but it usually requires more than two bets.
Another approach is to diversify. This is in fact how arbitrage is often used by hedge funds and the like—they attempt to identify many such opportunities which they believe (hope) are uncorrelated and spread their bets across them. On average they expect to make a positive return and they also are protected against the occasional low probability large loss. If they turn out to be wrong in their assumption of the various bets being independent you get an LTCM.
Hm, but isn’t bgrah449 using the strong definition of arbitrage, where you cannot lose, period?
Strike the word “strong.”
No.
I used the word ‘strong’ to emphasize one of the meanings of the word ‘arbitrage’. I’m not going to pull out my OED on you, but the strong definition of arbitrage is not the only definition, and isn’t even the most common use. Look at Wikipedia & Wiktionary; look at Google News or Google Books.
It’s fine to clarify what definition is meant when discussing technical details where that matter. To insist on only one definition in every use of the term is the sheerest fanaticism, nonsense on stilts, and merits every downvote it receives.
Is there no value in defending the definition of a word? Arbitrage originally meant expected profits with zero risk of loss. Now some people say they also want to use it to mean expected profits with non-zero risk of loss. Okay, then why not just say “expected profits” (or “edge” as traders would call it) since you’ve eliminated the distinction that makes the term meaningful in the first place? I mean, would you say that the AGI I’m building in my basement is “Friendly” just because I expect it to do good things, even though it also might paperclip the universe 2% of the time?
Pure arbitrage pretty much never exists. There is almost always non-zero risk of loss. Arbitrage transactions invariably have some execution risk, though with very liquid markets and electronic trading it may be arbitrarily small. Generally the liquid markets with the fastest trading are those that will offer the least arbitrage opportunities though so in reality greater profits almost always come at the cost of increased execution risk. It doesn’t seem a huge stretch to extend the concept to statistical arbitrage—you’re never really going from zero risk to risk, you’re just increasing from a very small risk to a larger risk and going from very reliable price correlations to less reliable ones.
There is value in clarifying which definition is being used. That is, I hope, what I’ve been doing here, in opposition to the notion that there is only one sense that can be used and so any clarification is nonsense.
And while strong arbitrage is nice in having 0 risk as opposed 0.1 risk or 0.11 risk, we experience no trouble in real life because some words can be made to overlap despite their average & typical uses. Expected profits or edges don’t necessarily cover the same mental ground; if I buy and hold indexes for 50 years, I might expect a profit, but few would call that arbitrage.
--Wittgenstein, Philosophical Investigations, 99
What you’re doing is purposefully diluting the word. “Arbitrage” as a word exists to talk about riskless profit. You’re trying to introduce risk to it, to what end?
You know, the first definition in the OED doesn’t even have anything to do with finance—it’s simply the decision of an arbitrator. The second is ‘exercise of individual judgement’. Only the third includes the commercial definition, and that (and its quotes from the 1800s on) speaks only of buying and selling in geographically disparate areas. Nothing about risk. Indeed, the 1882 quote goes ‘He cannot tell what the outcome will be… of this unfathomable arbitrage business.’
‘Arbitrage’ did not begin as the strong definition. It did not exist as finance at all. The strong definition is a 19th and 20th century technical addition to a word imported from the French. I am purposefully diluting it? How can I dilute something which was never pure to begin with?
Again, explain whether you are speaking descriptively or prescriptively when you say ‘arbitrage exists to talk about riskless profit’. If the former, you are manifestly wrong and have been wrong for the last 600 years according to the OED. If the latter, then why should we abandon all the other meanings?
You’re right—arbitrage as a word doesn’t exist to talk about riskless profit. Arbitrage as a financial term, however, exists to talk about riskless profit.
It would seem that taw was using the more general meaning and not the financial term.
If that is a once off 2% chance of failure then I’ll go with it and call it Friendly Enough For Me. Come to think of it I may be tempted by 2% per 1,000 years.
I’m virtually certain that you realize the implications; for instance, you’re saying you’re tempted by a 50% chance of paperclipping per 34,000 years. I’m less clear on how you could justify being tempted.
Start with assigning a very low probability on something better occurring. Then discount somewhat the extremely good options where you live billions of years, not valuing years on a linear scale. Then consider what you can do in 10,000 years with a super-intelligence backing you up. For example, it could build you a relativistic rocket and send you off fast enough that you are outside a future paper clipper’s future light cone. Possibly sending multiple copies of the human race out in various directions and with various planned durations of flight (given that you don’t know when Mostly Friendly is going to go nuts).
I haven’t done any maths on what the figures would need to be for me to actually choose that scenario. That’s why I say ‘may’. It is certainly worth considering seriously.
Good answer.
The Wikipedia article you cite is almost entirely uncited; the Wiktionary entry is clearly wrong. These don’t support your argument. (FWIW, the discussion page of the arbitrage article has several comments along the lines of, “This isn’t arbitrage.”)
Linking to Google search results is basically saying, “Go read a book.” It isn’t an argument; it’s just status posturing. “I don’t have to address your points.” Well, I’ll address them.
But first: How about this Google search?
Arbitrage is taking advantage of price differences in a market to make riskless profit. To the extent that someone describes a speculation strategy as “arbitrage,” they are trying to sell you something. If I told you something was “a sure thing,” and then it failed, would you change how you think about what “a sure thing” means or would you think, “When he says something is a sure thing, it isn’t always true”?
In general, I think you’re right about not being fanatical about definitions. But what was described, in the article and in the comment, is entirely the wrong use of the word “arbitrage.” Arbitrage is certainly not speculation (about as wrong a use of the word arbitrage as there is). Arbitrage is distinct from hedging, as well. Arbitrage is not a diversification tactic.
So I can’t help but conclude that your “a word can have many meanings” idea is just an applause light. Did I miss your alternative definition, of which mine is a subset, or was I just plain not squishy enough for your taste?
The problem is, what do you mean by the Wiktionary entry is clearly wrong? They seem pretty reasonable to this layman. Do you mean that they do not exclude every meaning including the possibility of loss? By what authority is this open-mindedness ‘wrong’? Did Jehovah in some obscure Numbers passage lay down this rule? Or is it just that you always use ‘arbitrage’ in the no-possible-loss sense, and so it’s incorrect for anyone else to use it any other way?
I hold to a descriptivist view of language; the use of a language is its meaning. If people use arbitrage in senses which allow loss, then arbitrage can mean techniques which allow loss. (Such techniques are a superset of techniques which don’t allow loss, so it’s fair to call the narrower no-loss definitions ‘strong’ definitions, along the lines of the Strong and Weak AI hypotheses, for example.) At that point, all I need to do is show that the other meanings are widespread. Wikipedia has it, and serves it up to ~1,600 viewers a day; Wiktionary probably adds a few hundred hits to that. The Google Books has hits that explicitly point out that they will henceforth use ‘arbitrage’ in its narrow sense; other books simply define it in a broad sense. The News hits demonstrate that the wider meanings are likewise in widespread use. (Your Google search has no relevance, any more than if I had instead said ‘bgrah449 is using the narrow definition of abitrage’, which ironically actually has a non-LW hit.)
I would disagree here. The article, perhaps, but the comment to which I was responding was clearly using the broader definitions: http://lesswrong.com/lw/1ia/arbitrage_of_prediction_markets/1b12
Long-Term Capital Management, from the popular history books I’ve read on them (and 1 or 2 academic articles long ago), did not believe it was an overall arbitrage. Arbitrages in the risk-free sense were taken when they found them, but much of their business was looking for mismatches which were not risk-free, but which they could exploit with leverage and hedge themselves against. They figured that they could only be killed by century-events or rarer. If they were just risk-free arbitraging, then they could never have been killed; if you can have losses on a risk-free arbitrage, an arbitrage in the narrow sense, then it’s not such an arbitrage, by definition.
Thus, bringing up the strategy of diversification, and LTCM in particular, only makes sense if mattnewport was thinking of arbitrage in the broader sense. (How can 100 risk-free arbitrages across the global economy be any safer than 100 risk-free arbitrages in just the USA? 100 0 = 100 0.) This was my original point: you and Blueberry both seemed (to me) to be discussing narrow/strong arbitrages, and mattnewport was putting forth a broad/weak arbitrage.
Ironically, ‘applause light’ can itself be an applause light.
For the record, I was indeed thinking of statistical arbitrage.
The Wiktionary entry is clearly wrong in that it isn’t a definition at all. The definition of “running” isn’t “what you do at a marathon.”
1,600 people a day doesn’t change the meaning of a word.
Statistical arbitrage is named thus because over an infinite time period, it is arbitrage.
Yes it does. Bgrah449, meet human language.
I don’t think so. I think “Statistical arbitrage” is marketing. As long as there is risk of ruin statistical arbitrage is still risky, even over infinite time. LTCM isn’t going to show a profit ever.
Pull out your OED on me. This is a subject I know. You are wrong.
For the benefit of the conversation, and posted without taking a position, here is the OED’s definition of arbitrage:
Here is the OED’s definition of Arbitration of Exchange:
ETA: One needs a subscription to follow those links.
I’d never really looked at Intrade before. It seems from a quick investigation that there’s a fairly major problem for anyone who wants to arbitrage this particular market (the 2012 Republican Presidential Nominee market) which makes for a rather inefficient market.
I pointed out in another comment that unless you believe Ron Paul supporters are more prone to wishful thinking than others that the biases should cancel out. If you look at the prices currently it appears that everyone’s supporters are prone to wishful thinking—the sum of all current market prices for all candidates is quite a bit over 100. It should be possible to arbitrage this by simply selling all the contracts. You get more than 100 coming in and never pay out more than 100.
Unfortunately it appears Intrade requires margin on the basis of your maximum possible loss and treats every bet in this market as independent! In other words if you sell against every candidate you have to meet a huge margin requirement even though you are not actually liable for more than a 100 payout in the worst case.
Am I missing something here or is this really the way Intrade works?
But what if the Constitution changed to allow co-presidents?
Not likely, but I thought I’d point out that I’ve been black-swanned on Intrade already. I bet on there being 50,000 swine flue cases by June 30, but then about a week before that deadline the CDC made a decision to stop updating its totals, pausing the count at a little under 50,000.
Even though the bet was written so that the CDC numbers were just being used as “best available”, Intrade decided at that point that those numbers would define the bet. So even though all other counts settled on a number well above 50,000 by June 30, the CDC was considered official and I lost the bet.
Intrade usually takes into account the fact that they’re mutually exclusive, and doesn’t require additional margin for additional candidates (I haven’t seen this documented anywhere, but it seemed to behave that way in the last election).
Still, Intrade’s margin rules aren’t as good as those of the big commodity futures exchanges. Interest rate futures have asymmetrical risk, but that doesn’t distort prices because little margin is required and they’re liquid enough that you can cut your losses before prices change too much.
Sum of bid prices is 135.5, sum of ask prices is 172.2. As there’s no other option, true sum should be less than 100, and obviously more-than-100 figure is nonsense.
That’s an even more obvious case of getting some money by correcting a prediction market, and again I don’t see how to do it without significant collateral.
You can’t do it at all; I’ve checked it out in previous cases. You have to be able to cover all possibilities and make a profit. So any combination that covers A and ~A will be more expensive to bet on than any return. No amount of leverage will correct this.
It appears to be possible in theory with the current 2012 Republican Presidential Nominee market. The current bids sum to quite a bit more than 100 so by selling contracts on every outcome you should receive more than 100 and you will never have to pay out more than 100 so you should have a guaranteed profit.
The problem is that the rules for this market say
which suggests to me that you would be required to put up margin to cover the possibility of losing every bet which is clearly not a possible outcome. That makes it impractical to take advantage of the arbitrage opportunity.
Liquidity might also be an issue in this case—you might not find buyers for all your contracts at the quoted market price.
You’re correct about Intrade’s requirement to front the money to cover your position in all cases until the contract ends or your sell it.
However:
That doesn’t follow. Even if the bids sum to more than a hundred, you have put up the other fraction of $10 for all of those n contracts. With a lot of the bids very low, then in order to cover all possibilities, you have to put up over $9 on many, and so it looks like you will have to front more than $10*(n-1), making it a loss from the beginning.
Yes, I ran the numbers in several cases like this in the ’08 election.
Aren’t you just restating the margin problem? The reason this strategy is impractical to implement is that you have to put up a lot of money to cover the payout on every contract you sell, even though at most one of them will pay out. The fact that Intrade don’t pay interest on deposits makes that a poor use of your money but you will get most of it back once the nominee is announced. You also get to keep the (100 + n) you got from selling the contracts and only pay out at most 100 leaving you with a profit of n.
Unless I’m misunderstanding something about the way Intrade works you will make a profit, but to do so you will have to tie up a relatively large amount of funds in a non-interest-paying Intrade account for the duration of the bets. With interest rates so low at the moment that’s not such an issue as it might be under more normal interest rates.
Horrible. If you can get access to it—use Betfair. It’s probably blocked in the states though.
No, you’d only lose $97.5 is if you believed Ron Paul has a 1% chance of being nominated on the day he got nominated.
Just sell Ron Paul at 3 points up to the limits of your linear utility of money, and set it to auto-buy the same number of Ron Paul shares if the price gets to 6 points.
Now from your perspective it’s a high chance of $3x and a low chance of -$3x.
This is great advice, many thanks. Auto-buy is supported by Intrade? So there’s no danger of the shares zooming past 6 points before I have a chance to buy them?
Of course the shares could get past 6 and then fall again—in fact they are most likely to—in which case you still lose overall. I’d probably use 9 rather than 6, since the irrational exuberance could conceivably go as high as 6.
If I’d known about this strategy when the right-wing bias on Intrade was rating Biden’s chances of stepping down as VP nominee at something like 4%, I would have been a lot more likely to try to profit from it.
what!? Why not?
Suppose the situation were that taw could make bets on the terms he wishes for—but only if he can convince 5 out of 9 rich people. How is this a market, and not some sort of bizarre committee or bureaucracy?
If I think I know a more efficient way to make a widget, I still need to convince somebody to put up the capital for my new widget factory.
It’s a weakness, but not inherent. The bid/ask spreads are wide enough to prevent you from making any Dutch book bet, no matter how much someone can back you.
As more people join prediction markets the bid/ask spreads will shrink, but so will the cases of inconsistent probabilities.
We could deal with some of these issues by expanding the market.
We could add one set of meta-contracts (really futures contracts), dealing with the price of Ron Paul contracts every X time period. So you could bet that the price of a Ron Paul contract would fall before Y date, alleviating the waiting issue you mentioned.
With regard to the lopsided risk factor, traditionally you would want to deal with this by insuring yourself, and the same possibility could apply here: if a very large firm were involved in the business, they could spread their insuring counter-bets across a large number of people (they would make the opposite bet to you, then pay you if your bet fell through and get paid if you won).
Since you are risk-averse, there is some potential margin between your risk tolerance and risk-neutrality that a firm with high capital could exploit for profit.
If you bet on future bets, there’s incentive to manipulate some bets.
Certainly—but as Robin Hanson points out, it’s precisely when people try to manipulate prices artificially that people are drawn into the markets to profit from those manipulators (and incidentally to prevent them).
I’m curious what your theory is for why Ron Paul supporters are especially prone to wishful thinking compared to supporters of other political candidates. Presumably you have some basis for deciding that Ron Paul supporters are either particularly prone to wishful thinking or more likely to express their wishful thinking on Intrade?
Where did taw say or imply that Ron Paul supporters are especially prone to wishful thinking compared to supporters of other political candidates?
(If he does think that they are particularly prone either to do it or to show it on Intrade, part of his “basis” might in fact be that 3.5% figure he quoted.)
It’s implied in his belief that the 3.5% probability is an over-estimate. He says that estimate is ‘clearly wishful thinking of Ron Paul supporters’. If that is true then Ron Paul supporters must either be more prone to wishful thinking than supporters of other candidates (if everyone was equally prone to wishful thinking then the biases should cancel out) or more likely to participate on Intrade. Either or both of these hypotheses may be true but I’m curious what the reasoning is.
Depending on taw’s theory to explain the Ron Paul bias he may be able to identify better arbitrage opportunities. If he believes that Ron Paul supporters are over-represented on Intrade for example then he should seek out other venues to place the other side of the bet to take advantage of the hedging opportunity described by Blueberry. Identify a venue where supporters of other candidates are over-represented and seek someone to take the bet at what he believes to be fair odds or at odds that underestimate Paul’s chances. Pocket the spread whoever wins.
He also suggests that Ron Paul supporters are trying to artificially pump estimates for Ron Paul and are willing to write off losses as a marketing expense. If this is more true for Ron Paul than it is for other candidates’ supporters then that suggests Ron Paul may have more dedicated supporters or wealthier supporters, both of which are tendencies that should in fact raise his probability of success given the nature of the US political system. Is he factoring that information into his own estimates?
Given your first paragraph, I think your question answers itself: his evidence is the 3.5% figure, which (for reasons unspecified) he considers an obvious overestimate.
There is something rather odd going on in this discussion, whose structure is as follows. A indicates belief in proposition p; B notices that p ⇒ q; B challenges A to supply evidence for q. This seems to presuppose that A’s belief in p is actually derived from a prior belief in q, since otherwise p would be the proposition to ask for evidence of; but when asked, B claims that s/he is only saying “A believes p, p ⇒ q, so A must believe q”. Which, by the by, is invalid if there’s any doubt about A’s agreeing that p ⇒ q. And, in this instance, there is plenty of scope for doubt about p ⇒ q: perhaps, for instance, Ron Paul supporters in general are no more prone to wishful thinking than anyone else, and no more prone to participate in Intrade, but there are one or two extremely determined and well-heeled ones.
The way I read his post it didn’t seem to me that he believed that the Intrade odds were an obvious overestimate for reasons unspecified. Rather it seemed that he proposed two possible reasons for the odds being overestimated. One was that the wishful thinking of Ron Paul supporters explained the overestimate, the other was that Ron Paul supporters were deliberately bidding up the market as a marketing exercise.
The weakness of the second explanation has already been pointed out. The first explanation is only an explanation at all if Ron Paul supporters are consistently more likely to be prone to wishful thinking than others. I was curious what taw’s reasons for believing that are.
It turns out that the explanation may be that all candidate’s supporters are prone to wishful thinking—we discussed in a separate thread the fact that Intrade appears to make it difficult to arbitrage consistent over-estimates of the odds of winning in this particular market. If that’s the case taw is probably right that the 3.5% is an overestimate for Ron Paul but was wrong to single out any one candidate as an example of a clear persistent overestimate in a prediction market.
The whole point of these markets is to prevent the kind of arbitrage you’re trying to figure out. You’re supposed to have skin in the game. That’s what makes them accurate.
You can’t arbitrage a single wrong opinion; you need two external differing opinions to start looking at arbitrage opportunities.
He just thinks that people are buying contracts at the wrong price and is frustrated because the particular setup of the InTrade market is such that a large collateral is required to bet against this particular kind of stupidity. He is trying to have an appropriate amount of skin in the game and not trying to arbitrage against InTrade.
(Edited)
It doesn’t strike me as very sporting to edit a post to make it sound like I didn’t address your point.
It is probably not the best title. Intrade do not try to discourage the kind of thing taw is talking about.
My reply to what used to be here was one of clear agreement with you and I marked the edit explicitly.
For the record, the edit was a remove “No, taw is trying to figure out a different kind of arbitrage”. A more correct statement would perhaps be “No, taw is trying to figure out a different kind of thing than what you are talking about and which isn’t really arbitrage at all”. But that is a distraction from the gist of your post, which I disagree with for the reason stated.
I will, of course, take more care to acknowledge contributions by name when I add edit notes. I erred too far on the side of brevity here.
From what I can tell, I’m being downvoted because taw doesn’t know what arbitrage means. This is happening on a site called “Less Wrong.” The Internet is a fantastic place.
No, you were downvoted for talking about what “[taw is] trying to figure out” and being wrong about it.
If this was your post then I (for one) would have voted you up.
(Now I am downvoting you Making a False Claim While Under the Influence of Petulance.)