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Arbitrage of prediction markets

6 Post author: taw 04 December 2009 10:29PM

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?

 

Comments (58)

Comment author: RobinHanson 05 December 2009 04:37:44AM 10 points [-]

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.

Comment author: Douglas_Knight 06 December 2009 05:24:23AM 3 points [-]

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.

Comment author: taw 05 December 2009 09:21:26AM 1 point [-]

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.

Comment author: Blueberry 04 December 2009 11:19:38PM *  8 points [-]

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]

Comment author: bgrah449 05 December 2009 03:46:32AM 1 point [-]

Arbitrage always requires more than one bet, but it usually requires more than two bets.

Comment author: mattnewport 04 December 2009 11:29:11PM 0 points [-]

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.

Comment author: gwern 05 December 2009 05:46:14PM 2 points [-]

Hm, but isn't bgrah449 using the strong definition of arbitrage, where you cannot lose, period?

Comment author: mattnewport 05 December 2009 01:23:10AM 6 points [-]

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?

Comment author: Nominull 05 December 2009 03:41:48AM 2 points [-]

But what if the Constitution changed to allow co-presidents?

Comment author: SilasBarta 05 December 2009 03:23:16PM *  17 points [-]

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.

Comment author: taw 05 December 2009 03:56:52AM 1 point [-]

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.

Comment author: SilasBarta 05 December 2009 03:18:51PM 2 points [-]

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.

Comment author: mattnewport 05 December 2009 11:29:38PM *  1 point [-]

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

This market is not linked to allow cross-margining of positions. You will be margined individually on each position, long or short.

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.

Comment author: SilasBarta 06 December 2009 12:35:59AM *  3 points [-]

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:

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.

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.

Comment author: mattnewport 06 December 2009 02:24:08AM 2 points [-]

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.

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.

Comment author: dilaudid 13 December 2009 03:52:46PM 0 points [-]

Horrible. If you can get access to it - use Betfair. It's probably blocked in the states though.

Comment author: pcm 05 December 2009 03:39:28AM 1 point [-]

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.

Comment author: Liron 05 December 2009 01:10:07AM 4 points [-]

I lose $97.5 1% of the time

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.

Comment author: ciphergoth 10 December 2009 01:17:41PM 0 points [-]

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.

Comment author: SilasBarta 05 December 2009 03:26:02PM 3 points [-]

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?

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.

Comment author: smoofra 04 December 2009 11:39:46PM 4 points [-]

But if results depend on my ability to convince rich people, that's not prediction market!

what!? Why not?

Comment author: gwern 05 December 2009 05:44:31PM 1 point [-]

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?

Comment author: smoofra 07 December 2009 06:01:16PM 2 points [-]

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.

Comment author: Technologos 05 December 2009 12:40:03AM *  0 points [-]

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.

Comment author: ChristianKl 05 December 2009 04:05:24PM 0 points [-]

If you bet on future bets, there's incentive to manipulate some bets.

Comment author: Technologos 06 December 2009 09:17:27PM 2 points [-]

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).

Comment author: mattnewport 04 December 2009 11:37:28PM *  0 points [-]

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?

Comment author: gjm 05 December 2009 12:21:47AM 0 points [-]

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.)

Comment author: mattnewport 05 December 2009 12:33:47AM *  0 points [-]

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?

Comment author: gjm 09 December 2009 12:02:29AM 1 point [-]

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.

Comment author: mattnewport 09 December 2009 02:10:30AM *  0 points [-]

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.