Sunday, April 10, 2016

Fee-Structure Distortions in Prediction Markets

Since the launch of the pioneering Iowa Electronic Markets almost thirty years ago, prediction markets have grown to become a familiar fixture in the forecasting landscape. Among the most recent entrants is PredictIt, which has been operating for about a year under a no-action letter from the CFTC.

Both IEM and PredictIt offer contracts structured as binary options: if the referenced event occurs, the buyer of the contract gets a fixed payment at the expense of the seller, and otherwise gets nothing. The price of the contract (relative to the winning payment) may then be interpreted as a probability; an assessment by the "market" of the likelihood that the event will occur. These probabilities can be calibrated against actual outcomes over multiple events, and compared with survey and model based forecasts. Comparisons of this kind have generally found the forecasting performance of markets to be superior on average to those based on more traditional methods.

But interpreting prices as probabilities requires, at a minimum, that the set of prices referencing mutually exclusive outcomes sum to at most one. This condition is routinely violated on PredictIt. For instance, in the market for the presidential election winner by party, we currently have:

Based on the prices at last trade, there is an absurd 108% likelihood that someone or other will be elected president. Furthermore, the price of betting against all three listed outcomes (by buying the corresponding no contracts) is $1.96, even though the payout from this bundle is sure to be $2.00. Since these contracts are margin-linked (the exchange only requires a trader to post his or her worst-case loss) the cost of buying this bundle would be precisely zero in the absence of fees, and this would be as pure an opportunity for arbitrage as one is likely to find.

On IEM, or the now defunct Intrade, such a pattern of pricing would never be observed except perhaps for an instant. The discrepancy would be spotted by an algorithm and trades executed until the opportunity had been fully exploited. Profits would be small on any given trade, but would add up quickly: the most active account on Intrade during the last presidential election cycle traded close to four million contracts for a profit of $62,000 with minimal risk and effort. This trader had a median holding period of zero milliseconds. That is, the trader typically sold multiple candidate contracts simultaneously (with the trades having identical timestamps) in a manner that could not possibly have been done manually.

Why don't we see this in PredictIt? The simple answer is the fee structure. Whenever a position is closed at a profit the exchange takes 10% of the gains; losing trades don't incur fees. Taking account of this fee structure, the worst-case outcome for a trader betting against all three outcomes in the example above would be a win by someone other than a major party nominee. In this case the trader would lose $0.95 and gain $0.99, incurring fees on the latter of around ten cents. The result would be a net loss rather than a gain, and hence no opportunity for arbitrage. Prices could remain at these levels indefinitely.

Still, algorithmic arbitrage can prevent prices from getting too far out of line with meaningful probabilities. The extent to which this happens depends on whether the events in question include some that are considered highly unlikely. In a market with only two possibilities (such as that referencing confirmation of Merrick Garland) price distortion will be lowest if both outcomes are considered equally likely. For instance, if the prices of the two contracts were each 53, betting against both would cost 94, and fees would be a shade above 5 no matter what happens. These prices could not be sustained, so the distortion would be at most 5%.   

But in the same market, prices of 99 and 10 for the two outcomes could be sustained, for a distortion of 9%. The cost of betting against both would be 91 but if the less likely outcome occurs, the fee would wipe out all gains. Hence no opportunity for arbitrage, and no pressure on prices to change. 

Given that PredictIt is operating as an experimental research facility with the purpose of generating useful data for academic research, this situation is unfortunate. It would be easy for the exchange to apply fees only to net profits in a given market, after taking account of all losses and gains, as suggested here. This does not require any change in the manner in which margin is calculated at contract purchase, only a refund once the market closes. If this is done, prices should snap into line and begin to represent meaningful probabilities. The decline in revenue would be partially offset by increased participation. And the transition itself would generate interesting data for researchers, consistent with the stated mission of the enterprise.


  1. Hi Rajiv,

    Your point on fees is a good one, but also that the fees are not so large that the implied probabilities would not still be ballpark if the only error were from the fees.

    That said, I was just thinking about and discussing some things that made me think of you, that you might be interested in, if I might note them here.

    I had a twitter exchange yesterday with Steve Waldman on the issue of Hillary's electability versus Bernie's:

    I think Hillary is far more electable, basically because Bernie is a self-proclaimed socialist, with a past of saying some extreme things, extreme to the general public. I think the multi-billion-dollar Republican attack machine would be very successful with this, much more successful than against Hillary, who they've exhausted everything they can find and manufacture over the last 25 years, and she's still heavily favored to beat them. For more on this, here is an article quoting the views of prominent political scientists:

    That said, I just took a look at the betting markets, at this site:

    Consider Hillary:

    – Unconditional probability of winning the general election: 69.2%
    – Probability of winning the nomination: 87.5%
    – Thus, assuming these events are independent (which they aren't; if she wins the nomination, then no big manufactured scandal got her, and her probability in the general is greater), the probability of winning, if she gets the nomination: 79.1% – Big, and this is an understatement due to the first two events not being independent. And yes, there is an implied fees issue, but it shouldn't distort the number *that* much.

    Now consider Bernie:

    – Unconditional probability of winning the general election: 12.5%
    – Probability of winning the nomination: 20%
    – Implied probability of winning the general if he gets the nomination: 62.5%

    So, 79.1% versus 62.5%, Hillary is substantially more electable according to these odds, but not by a giant margin. Do you think that an around 60% probability of Sanders winning the general election, if he's nominated, is quite at odds with top expert opinion, and/or reality? It seems too high to me.

    1. Richard, I have some issues with your baseline assumptions about who is more "electable," Hillary Clinton or Bernie Sanders. Unless the predictability of one candidate's electability over another is capable of being objectively determined in a methodologically valid manner, the validity of your analysis will be skewed by its many non-objective assumptions.

      For example, Clinton, too, has considerable baggage surrounding her past statements, such as her dehumanizing comments in a 1994 speech suggesting all urban black youths are "SuperPredators" who must be "brought to heel." This was raised in the public conscience only a few days ago, when former president Bill Clinton got into any ubly exchange with Black Lives Matters protesters.

      The Sanders campaign has demonstrated that the demographic affinity claimed and demonstrated by the Clinton campaign among black voters in the south does not translate to black voters under 30 or to black voters in any age cohort who identify themselves as liberal or progressive. Accordingly, there are a number of alternative scenarios in which Sanders' success in a general election will depend upon voter turnout, and the demographics of that turnout. One would have to predict voter turnout at a fairly fine-grained level to assess which candidate's "past statements" will be more resonant with actual general election voters.

      Also, your assumptions don't appear to take account of the growing public perception that Clinton's a chronic flip-flopper, shaping her public policy positions to match-up with her pollsters' determinations of what policy positions will attract more voters. Clinton has changed her fundamental positions on the minimum wage, the Trans Pacific Partnership, and fracking, to mention a few, all of which have, through polling, been determined to impact voter preferences.

      Furthermore, your assumptions about Clinton's electability run counter to the results of polling on the likelihood of voters in the general election to support Clinton or Sanders, respectively, in head-to-head match-ups against the remaining GOP challengers. In many of these polls, survey results showing Sanders winning by larger margins than Clinton; in some cases, quite large margins.

      Finally, your assumptions appear to give no credence whatsoever to polling among different voting demographics that find Clinton's "untrustworthiness" a significant impediment to voting for her in the general election, which goes directly to her electability.

      Similarly problematic is your assumption that Clinton's "baggage," such as the State Department email scandal, whether the State Department, under Clinton's leadership, should have been much better prepared for what happened at the American consulate in Benghazi, and whether the Clinton Foundation was involved in a pay-to-play scheme for favorable State Department decisions, including her approval of sales of U.S. weapons systems to Saudi Arabia, have been fully vetted in the public domain. There's substantial polling to support the contention that, despite being litigated in the media, few voters in the 2016 presidential election paid much attention to these issues at the time they were aired.

      If Donald Trump ends up being the GOP nominee, one can only imagine the frequency and intensity of the barrage of negative attack ads this expert manipulator of public perception will launch against Clinton, should she win the Democratic nomination.

      This all goes to say that, absent a meaningful and methodologically sound approach to objectively assess and reconcile the subjectivity of all such assumptions, I don't know how they can be taken into account in any predictive model that has any claim to accuracy.

  2. On the other hand, with all of his electability issues, Sanders would probably be going against a very vulnerable Trump, or a Cruz facing a Trump third party run, or revolt.

    Still, with the stakes so monumentally high this election, I'd really like the Democrats to put up their, I think, much more electable candidate.

  3. Richard, I saw your exchange with Steve and thought about chiming in but have so much on my plate right now and so little time. It's interesting to look at conditional odds: markets at the moment think Trump is more electable than Cruz (40% conditional on being nominated versus around one-third on PredictIt for example). I think this is roughly right, though I think Trump has been consistently underestimated throughout this campaign and I'd put his odds higher. Regarding Clinton and Sanders, polls at the moment favor sanders while markets favor Clinton as you have noted. One thing that Steve is perhaps not fully appreciating is that if Trump is the nominee the campaign will be as nasty and brutish as we have ever seen. Against Sanders you'll see ads with bread lines from the Soviet Union. Unfair, perhaps, but effective nonetheless. And against Clinton, if you think you've seen everything that can be thrown, just wait a few months. We have already seen a video from Trump featuring Cosby, Weiner, and Lewinsky. I think that this election will be closer than many seem to think, no matter who the nominees are, and we're in for a bumpy ride.

    1. First, I made a mistake in my comment, rushing it up:

      “assuming these events are independent (which they aren't; if she wins the nomination, then no big manufactured scandal got her, and her probability in the general is greater), the probability of winning, if she gets the nomination: 79.1% – Big, and this is an understatement due to the first two events not being independent”

      Basically, this would all be factored into the overall probability of winning the general election number, if it’s done correctly. So, probability of winning the general, given she wins the nomination, is just a straightforward backing out: 69.2%/87.5%.

      With regard to who’s more electable Cruz or Trump, it’s interesting that it’s not just their personal characteristics at all. If Cruz gets it, he’s at the disadvantage that he may well face a third party run from Trump, or at least a big angry reaction from the big niche of voters that strongly support Trump. This is a serious disadvantage, and Trump does not face as serious a threat of this kind.

      Yes, the slime thrown at Hilary will be beyond anything thrown at her before, or anyone before. But it does certainly make it much harder for the right that the public will have heard pretty much all of this already for the past 25 years, and Hillary is still standing strong, the strong favorite. With Bernie, by contrast, it will all be new, and much of it very surprising, or shocking: He’s an admitted socialist?! Quotes on him talking about expropriation?! Video clips of him from the 1970s.

      With control of the Supreme Court for a generation in the balance, the consequences are so monumental that I think electability dwarfs all for the Democratic nominee. The fate of the planet itself is very much at risk if we stop, and roll back, anti-global-warming measures and treaties with a Republican President, and a Republican Supreme Court severely blocking efforts for a generation. And this is not to mention tens of millions losing access to health care, Citizens United being overturned by a Democratic Supreme Court, versus extended much further by Republican control of the court for a generation, and so much else. Electability just dwarfs everything with the stakes this monumental and profound.

  4. Richard, I am in complete agreement with you about monumentality of the stakes. And while I don't concur entirely with your substantive reply, I very much appreciate your taking the time to respond.

    I think it would be an interesting academic challenge, as well as a worthwhile exercise in political punditry and outcome predictability to build a predictive model that could use secondary data to account for the variables raised in our exchange (e.g., controlling for differences in primary voting rules by state between closed and open primaries, so that primary results may be more accurately interpreted as predictive of outcomes in the general election).

    I would love to hear Rajiv's thoughts as to whether, and how, this might be done. Thanks again for your reply.


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