More on the Iowa Electronic Markets

That’s a cool analysis. I await the reactions of finance-types with interest. In the meantime, I will imagine the migraines you would give to “Bill Cleveland”:http://cm.bell-labs.com/cm/ms/departments/sia/wsc/ or “Ed Tufte”:http://www.google.com/search?q=edward+tufte&ie=UTF-8&oe=UTF-8 if you showed them any of those figures. Especially the second one.

You should really write this up as a paper.

In a way, I admire your dedication to the purity of the electoral process. But since I can’t vote in US elections, the question of who will win is at least as important to me as the question of who should win.

Plus there’s a chance to make a quid or two, which in the event of Bush winning, should at least buy some beer to cry into.

The Marshall Islands always votes with the US and Israel in the UN General Assembly on votes when nobody else does … maybe them?

I’d also hazard a guess at Kuwait.

Daniel, you need to go to the website and buy a copy of matlab forthwith, its much more straightforward and its graphics are a 1000X better than excel.

As someone who took Tufte’s seminar, I have to say that he would flunk you. I didn’t learn much in the way of statistics, but I learned to make my graphs purty. Too much chartjunk!

Alex: But a binary option that’s near the money has really weird vega; it shoots up then shoots back down again. And the way that IEM is set up, both contracts are almost always near the money.

I don’t understand what you mean by saying that the IEM bundles aren’t discounted; they pay off either $1 or nothing the day after the election. It’s not exactly hard for players in the market to do the discounting?

Andrew: How big do you think a market would have to be before it started to be efficient? (btw, your friends might not jump on pricing errors like this, but mine would like ferrets on a sausage. And the IEM are meant to be played by business school students!) Given that IEM is the oldest of its kind, how likely is it that any similar exercise would achieve that scale?

Interesting post. You are probably right about the difficulty of getting good market information out of a toy market.

d^2. With given conditions I’d become interested if the expected payoff were north of 1000. If credit cards were accepted (and you could set up accounts instantly), then I’d probably be willing to arbitrate the first time for 0 (i.e. just for boasting rights), but I’d probably need to make > 100 Usd per arbitrage before I become interested to help maintain market order (!). I’d expect my levels are on the low level, so I’d probably be one of the first to arbitrage.

Fascinating post, Daniel. I’d been struck by the lack of parity relation in the WTA contract, and I’d wondered it was a result of something like people using a probabilistic rather than arbitrage model, but this is just an excellent proof of it. A couple of things I wonder about:

1) Given what seems to be a deep-seated bias against short-selling, it seems to me that people who believe in a candidate’s chance of winning would be far more likely to register their view by buying their preferred candidate’s contract rather than selling the opponent’s. That makes me wonder whether the two markets (DEM04 and REP04) are in some sense self-contained (even though in theory they’re two sides of the same coin), and reflect the judgment of the market — informed, of course, by the price in the other market, which is why the relation stays close to 1 — of the candidate’s chances of winning.

2) What is the proper relation between the verdict of the vote-share market (which happens to be the market I’ve paid most attention to, even though it’s much smaller in dollar volume) and the verdict of the WTA market? In other words, if the VS market is predicting that Kerry is going to get 49% of the vote, is there a price in the WTA market that should follow from that?

3) I think abb1’s point about the possibility of manipulation is an interesting one, if only because the IEM has gotten so much more attention this year. On the other hand, if the markets are obeying a rough parity convention, that would seem to suggest that manipulation isn’t really at work.

Tufte would and should have a problem with the designers of Excel instead of the users of such product.

To sum: ‘You can’t polish a turd.’

Having said that, the more ‘meta’ we get from the actual person-pulling -the-lever-and-casting -the-vote, the less I put stock in the results. Sure, the fifteenth derivative of the obscure datum points to whatever, but until the new president is sworn in, all bets are off.

To me, all these models make no sense, because people don’t always vote rationally, so it is really impossible to tell. Does your model include Breslan? Zell Miller’s speech?

And really, you can toss all this away statistically by saying that the kind of people that are funded enough to play around with these things are generally the same people that vote republican. And since the money involved seems to fall under the threshold of ‘I will buy this because it is my TEAM! GO TEAM’ I really can’t put much stock into people really following a rational financial interest over the visceral.

I’m not sure whether this is still the case, but the prospectus (see “CONTRACT BUNDLES”) suggests that the IEM themselves will buy/sell you a bundle consisting of one BU|KERR and one KERR for 1$; this (together with the lack of interest earned on IEM cash a/cs pointed out by alex) might explain the violation of the parity rule.

(This also suggests an even easier arbitrage oppotunity: short the bundle of KERR and BU|KERR, invest the 1$ proceeds, and pay your $1 come election day. You pocket the interest on the $1.)

I know of at least one person attempting to manipulate the market. That $500 limit is really small.

The http://www.oddschecker.com/oddschecker/mode/o/card/cc8859x/odds/243698x/sid/377975>UK market is showing a similar picture as the US: odds lengthening on Kerry and shortening on Bush, with Bush a clear favourite.

Alex; but if you wanted to have a bet on KERR, say, you could finance it out of the proceeds of selling DEM04+REP04. The funds aren’t locked up, and even if they were, I can’t see how this would justify a negative time value of money. Also, I’m not sure what you mean by the “Black-Scholes no-arb criterion” – arbitrage free pricing is not a quirky assumption of B-S that can be relaxed, it’s a fundamental axiom of pricing and certainly necessary for markets to be considered efficient.

On the subject of vega; graph the function (actually, I’ve got a chart here so I’ll bear the laughter of the crowd and upload it). With 0.2 years to expiry, money rate 1.75%, strike price 0.5, vega goes from 0 to 0.8 to -1 to 0 as the price goes from 0.4 to 0.6.

Nnyhav: As I mentioned to Alex, people who are speculating in this market are presumably doing so with real money. If they’re accepting a zero interest rate to do so, that’s not efficient markets.

Furthermore, the distributional assumption is only going to make things worse. Any changes you make to the distribution to reflect the reality of the distribution of vote shares are going to tend to make the distro less leptokurtic, not more, which would imply even lower fair option premia and make the mispricing larger.

Lads: I just recalculated the spreadsheet on the assumption that the prevailing rate of interest for IEM purposes was zero, and it didn’t make much of a difference to the surface plot; the pricing anomaly is still there. As the bar chart suggests, we would need to find some principled justification for a negative nominal rate of interest (and, just to forestall convenience-yield type explanations about the price people are prepared to pay to be in the IEM action, we’d also need a theory of the fluctuations in that negative rate of return) in order to explain the problem in this way.

Matt is entirely right and illustrates both a) how important it is to be painstaking and punctilious in keeping track of the different contracts and b) in view of this, why I am uniquely ill-suited to the job.

Though the 4% implied probability that the electoral college will screw the American public looks like an overestimate to me … so maybe I will set the controls for the heart of Oxymoronia and declare it to be a “statistical arbitrage”.

Alex; the units on the horizontal scale are the price of the contract in dollars (from 0.02 to 1.0) and the vertical scale is the pure number which is vega. I used a vol of 0.2; if I put in your suggestion of 0.4 the range is plus 0.5 to minus 0.75, none of which seem trivial to me. Remember that vega of binary options changes dramatically with moneyness; as I say, the fact that the IEM binary contracts are almost always very near the money means that vega matters a lot more than one might think.

The implied interest rate from the package is shown in the bar chart on the fourth graph down; admittedly it’s drawn up based on closing prices rather than genuine contemporaneously tradable bids, but that’s as good as we’re going to get unless someone fancies writing a spider program to generate high-frequency data.

Or in other words (and I’ve just been playing around with this in a spreadsheet to see what happens), moving that vol assumption from 38% to 48% can make a 2 cent difference in the value of the WTA contract if the VS contract is trading between 0.495 and 0.51 – elsewhere, Alex is correct and it doesn’t make much odds. This strikes me as a region of interest since empirically, the VS contract does spend quite a lot of time in this range, and 2 cents difference is in this region the difference between favourite and underdog. It looks worth a bit more attention, though I agree that Alex is right that, further away from the money, vega is less important than I thought.

> Furthermore, the distributional assumption is only going to make things worse. Any changes you make to the distribution to reflect the reality of the distribution of vote shares are going to tend to make the distro less leptokurtic, not more, which would imply even lower fair option premia and make the mispricing larger.

d^2: You’re thinking too standard normal. If the distro is deformed in the manner I describe, the “in the money” tail is compressed, the “out of the money” expanded, making the latter appear more leptokurtic locally. (Volatility is no longer a scalar measure, becoming dependent on location of the mean.) The resulting asymmetry may or may not account for the apparent mispricing, but certainly reprices in the appropriate direction. It’s not meant to “reflect the reality of the distribution of vote shares” (suggesting some empirical parameterisation), only to reflect the reality of certain constraints thereon.

Daniel writes: … the IEM is not “efficient” in the financial economics sense of the term. … One can make all sorts of excuses about the amounts of money at stake, … but the plain fact of the matter is that the prices on IEM are not consistent with the time value of money. … That suggests to me that pricing here is being driven by a social convention that the prices ought to reflect people’s estimates of the probability of Kerry or Bush winning. … This suggests that James Surowiecki is right and Robin Hanson is wrong on the way in which “information markets” of this kind work. … for James Surowiecki, markets are just a handy way of organising information aggregation; voting and other ways of summarising crowd opinion might work just as well. Robin Hanson, on the other hand, appeared to be giving a much more particular role to markets as opposed to any other kind of social organisation. He commented that the reason why markets generated information was ” simple idea that anyone who notices a mistake in the price of a speculative market can make money by fixing that mistake.” To me, this seems like he’s committed to a view that efficiency in the sense of obeying parity conditions is the mechanism by which markets gather information.
… it seems to me that if markets like this work at all, they have to work under the Wisdom of Crowds model rather than the Theory of Sharks. And since all the big financial markets operate on the basis of “sharks” and arbitrage pricing, we need to separate them in our minds from toy markets like this; markets which don’t have a Hayekian reason to exist shouldn’t draw credibility from markets which do.

Why do you keep trying to put words in my mouth? Last time you said I misread Hayek, when I don’t discuss Hayek. Now you say I’m committed to the view that no one should ever find arbitrage opportunities in information markets. But I’ve never said any such thing. And I’m not even aware that James Surowiecki and I disagree on anything in this area. (Why not call me and talk, if you want to know what I think?)

Let me make an analogy. Private bounty hunters have an advantage over public police in having a stronger incentive to catch their targets. Does this mean bounty hunters always catch every target on the first day? Of course not. It just means that bounty hunters catch people faster and cheaper on average. Similarly, that fact that people can make money by fixing mistakes in information markets just gives those markets one advantage over mechanisms, like voting, which lack this feature. Not every mistake will be found and fixed – the effort to do this is often more than the reward offered.

Daniel writes: … if you believe in something like Robin’s view, then you would say that the maximally informative market prices are the most recent ones (because any difference between the prices and the state of the world is most likely to have been arbitraged away). … If you believe in something like James’ view, then you might say that a more informative view of the opinion of the crowd might be a moving average of, say, the last five days’ trading.

I’m open to the idea that a moving average might sometimes be more accurate, and even looked into that possiblity in our recent laboratory experiments. Even though these markets were very thin and inefficient, however, it still turned out that the last price was at least as accurate as moving averages.

Daniel writes: … A lot of the problem is that it simply isn’t profitable enough to arbitrage away the breaches of parity, unless you’re doing it just for the fun of proving a point. … even if it was the only problem, it appears to me to be a more or less insoluble one, unless we really believe that in the future we will live in a world where material proportions of peoples’ savings will be diverted away from productive enterprise and into these zero-sum games.

I have consistently proposed that information markets be subsidized by those who want the information. Subsidized markets are not zero-sum. If no one will pay to induce information on a topic, then we may well not get much information on that topic.

I think you are way off here. The prices of options may reflect supply and demand. The most obvious explanation of the price of the Kerry contract is that large numbers of people realize that the cost of a Bush victory is another four years of utter incompetence. These individuals are therefore taking the rational step of insuring themselves against a Bush victory.

The same effect is seen in insurance markets. I buy insurance on my house even though I neither expect nor desire the house to burn down. I pay substantially more for that contract than the probability of a total loss times the insured value.

I should also say, with regards to the moving-average/last-price question, that I think — as I argue in my book — that most of the time the market price in fact reflects the collective judgment of the crowd of investors. (The price of the last trade before market close probably doesn’t, but most of the time the two will be very close.) So I don’t think the distinctions between information markets, financial markets, parimutuel pools, or sophisticated voting systems are really all that important. In the terms Daniel sets out at the end, I think all markets are, roughly speaking, information markets. But Daniel — and most corporate-finance theorists — disagree with me on this, so I’ll be satisfied with the idea that the IEM, at least, is aggregating probabilistic forecasts.

The more substantive question has to do with Daniel’s implicit argument that in the absence of an opportunity for real profits, no one will invest any money in these markets. That may be the case, and one way around it is to subsidize them, as Robin Hanson suggests. But I’m unconvinced that the markets need to be real-money markets in order to aggregate useful information. A recent comparative study of the performance of the Newsfutures (which is a play-money market, with prizes for the best performers) and the Tradesports markets in NFL games found that the prices in the two markets were about equally good predictors of outcomes. (They were both, unsurprisingly, very good predictors.) Now, the NFL is perhaps a special case, since there’s lots of public information and there a lot of people who devote a lot of their free time to keeping up with the game. But it suggests that in at least some circumstances — certainly, I think, within many organizations — markets or other aggregating mechanisms can produce valuable forecasts even in the absence of the opportunity for material profits. (I think there do need to be rewards for good performance, but I think these could take a variety of forms.)

dsquared – if you write this up as a paper, you really ought to redo the graphs.

I suggest using little Bush heads and Kerry heads to mark the data points.

Here’s a “different version of the trend surface”:http://www.kieranhealy.org/files/misc/dem04.pdf. A bit more discussion “here”:https://www.crookedtimber.org/archives/002466.html

” one’s seen fit to equate it to neglecting the cost of Kerry?”

ba dum bum.

I re-read this post and I suspect more and more the question is being overcomplicated by unnecessary option analysis. I would bet a similar study of the market-settled package would yield a similar “negative carry” for the basic reason that newcomers to market tend simply to buy or bid one or the other contract instead of buying the package and selling an unwanted overpriced component. Hence the package is routinely priced 1 or 2 cents over parity purely by accident, yielding the observed ‘negative carry.’

DD: “[including bid-ask spreads does not] make a qualitative difference.”

-Well yes, if you don’t think there is a qualitative difference between borrowing a dollar at double digit negative interest rate and borrowing it at zero, as in your example.

Besides, as noted above, order depth is really so so. My feeling is that you would probably earn more as a market-maker than an arbitrageur on these betting exchanges.

Over at Catallarchy, I’ve blogged a comparison of markets and crowd polling as opinion aggregators. I think this explains why IEM is not efficient, and why Tradesports and similar markets still can be.