Here’s bit of bad news for my American Democrat friends; your candidate is dying on his arse in the Iowa Electronic Markets at the moment.
Here’s another bit of bad news; even at these prices, he’s still overvalued.
Note to readers. There is quite a lot of financial jargon in this post, because I’m dealing with quite a few issues that are only of interest to finance bods (and only marginally to them). The interesting stuff is toward the end.
I mean “Overvalued” in a technical sense here; given the prices of the other contracts trading on IEM, the “DEM04” contract on the winner-takes-all market should be priced significantly lower than the 0.454 which was its price as of the last trade when I was writing this.
I found out this little anomaly earlier this year, when I was playing around with get rich quick schemes and idly wondering whether I could put together a program-trading system that would dump large numbers of trades onto the IEM all at once and make a few of my enemies shit their pants. I assumed it was due to teething troubles as the market for the ‘04 Presidential race settled down, and that things would regularise soon enough.
The issue was, that I was working on some Visual Basic code to try and calculate the “implied volatility” of the vote-share market from the WTA market in order to compare it against the realised volatility. I’ve worked a bit with the Black-Scholes model for pricing binary options in the past, and I know that the sensitivity to volatility of this kind of option is a pretty badly-behaved function, so it didn’t surprise me that the implied volatility formula I’d ripped off from Paul Wilmott’s book didn’t seem to work. What did surprise me is that when I’d changed the code around, put in a more robust optimisation routine, corrected a few of my arithmetic errors and debugged, it still didn’t work. I was buggering around with this, off and on, for about two months, and nothing I could do could get it to work.
So I did what I ought to have done in the first place and drew a few pictures. Below, I’ve plotted a chart of volatility against price. The purple dots represent the Black-Scholes value of a binary call with 0.152 years to maturity (ie today’s date until the election) at an interest rate of 1.75% (CD rate), with a strike price of 0.50 (see footnote 3), with the underlying at 0.491 (the current quote for KERR in the vote-share market), for different assumptions about volatility. The blue dots are simply a horizontal line at 0.454, which is the current quote for DEM04 on the WTA market. “BS valuation” refers to “Black-Scholes“, you cheeky kids.
As you can see, the model value gets close to, but doesn’t reach the market value. In other words, there is no value for volatility which can be plugged into the Black-Scholes model and deliver the market price. Or to put it another way, the option is overvalued.
This isn’t a transient phenomenon, either. I put together a horrendous Excel spreadsheet which takes minutes to calculate, but which produces a line like the one above for every day of data in the life of the DEM04 contract. Below, I’ve plotted them as deviations from the market price of the option on the same day. As you can see, these curves typically don’t cross the x-axis; it’s the rule rather than the exception that the DEM04 contract is structurally overpriced.
So what’s going on here? Seasoned finance pros will already be champing at the bit, ready to tell me that the Black-Scholes model is a completely incorrect model to use in this context. Well, chaps, allow me to differ. Fair enough, if I was acting as a market maker in size for DEM04, I would probably want to use a more realistic model. But I simply don’t believe that B-S would give such wildly inaccurate prices; one of the good properties of the model is that it’s surprisingly robust. And further investigation of the data suggests that whatever’s going on here, it’s unlikely that we can explain this all away as “holes in Black-Scholes”.
For one thing, this is a phenomenon which is almost entirely one of the DEM04 contract. The REP04 contract prices perfectly well in a Black-Scholes framework, for the most part. This allows us to get another handle on the extent of the overpricing of DEM04; we can solve the model for the implied volatility of the BUSH|KERR vote-share contract (which must be the same as the volatility of the KERR contract) and plug this number into the valuation formula for DEM04. Below, I’ve charted this (careful; avert your eyes if you’re a Kerry supporter).
As you can see, the yellow line (reflecting the “fair value” of DEM04; I’ve put this on the right hand scale for some reason) is way below the blue line (its market value). Don’t pay too much attention to the frightening drop-off in fair value in the last few days; the REP04 winner-takes-all contract has risen much faster in value than the BUSH vote-share contract, a phenomenon which could only be justified by a sharp drop in implied volatility, which drastically reduces the fair value of DEM04.
In any case, don’t pay much attention to that chart at all because
it’s very badly drawn and poorly laid out it’s clear that any attempt to work on the basis of consistency between the DEM04 and REP04 prices is doomed to failure. The two markets are simply not consistent.
Why so sure? Well, they don’t obey a basic and obvious parity relation. Think about it this way. If you were to buy one DEM04 contract plus one REP04 contract, then you would have a portfolio which would pay out $1 for certain in November. How much would you be prepared to pay for this portfolio? Well, basically one dollar, minus the interest that you could have earned by not buying the portfolio and leaving the money in the bank. So in other words, the difference between the sum of the value of (DEM04 + REP04), and 1.00, is the implied rate of interest which one earns in the financial universe of the Iowa Electronic Market.
I’ve plotted this implied money rate below:
I hope it’s clear. In general, over the last three months, the Iowa Presidential Election Winner-Takes-All market has been pricing on the basis of a negative nominal interest rate. This is not consistent with most concepts of market efficiency.
(as an aside, really astute financial econometricians will right now be screaming about “bid-ask bounce”. The idea here is that the chart above has been plotted using closing prices. However, if the last trade of the day in DEM04 was a buy and the last trade in REP04 was a sell, you shouldn’t really just add them together without making an adjustment for the bid-ask spread in the IEM. This is a fair enough point, but I checked that it doesn’t make a qualitative difference. As I sit here typing, the WTA market has bids of 0.454 for DEM04 and 0.556 for REP04. That means you could sell one of each and get an interest-free loan of a buck.)
So what does this all mean?
Well first, on a practical note, it seems to me that if you want to back the Democratic candidate in the 2004 Presidential elections, you should do so by selling REP04 rather than buying DEM04, and vice versa; this way you take advantage of the fact that option premium is overvalued in DEM04 relative to REP04.
Second, on a more theoretical basis, to my mind this is, unless I have made a howler somewhere, more or less conclusive proof that the IEM is not “efficient” in the financial economics sense of the term. A market in which basic parity relations are not observed is not efficient. One can make all sorts of excuses about the amounts of money at stake, the restricted universe of traders, the fact that short-sellers on IEM do not have full use of funds, etc, but the plain fact of the matter is that the prices on IEM are not consistent with the time value of money.
Third, we can pick up some clues as to what’s going on here from the prices themselves. Although the parity relation does not hold, casually going through the numbers suggests to me that, most of the time, the mid-price of DEM04 plus the mid-price of REP04 adds up to 1, near enough. So there’s a sort of parity rule being enforced by the market participants. 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 isn’t how stock options are priced. Financial options are priced on the basis of Black-Scholes and similar models, via an arbitrage pricing argument. Donald Mackenzie studied the sociological process by which financial markets moved from a “probability-pricing” norm to an “arbitrage pricing” norm, and this doesn’t seem to have happened in the IEM (yet; I’ve not entirely given up on my program-trading operation!)
This suggests that James Surowiecki is right and Robin Hanson is wrong on the way in which “information markets” of this kind work. (Update: In comments below, Robin Hanson argues pretty convincingly that this is a pretty egregious caricature of his views. Sorry Robin.)In comments to my review of James’ book, the two of them outlined the difference in their views. James fundamentally thinks of markets as a way for people to “vote” and aggregate their views, with any predictive power they have coming from the fact that they’re a kind of crowd. In particular, 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.
This seems like a trival distinction, but it has big practical implications. In particular, 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. Personally, I’m still something of a sceptic about whether ‘toy’ markets of this kind really deliver the goods at all, and I must say that this exercise hasn’t exactly made me a believer. But 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.
I promise that this system was in profit when I stopped the experiment; I moved jobs and left all the files behind. My guess is that it would be in loss at the moment, since it seemed to be pretty structurally long Kerry.
Basically, the WTA contracts can be considered to be options (specifically “cash-or-nothing” binary options) written on the vote-share contracts with a strike price of 0.50. Option prices depend on the anticipated volatility of the underlying, so the “implied volatility” is the volatility number that you plug into the formula to make the model price consistent with the market price.
As discussed here, this is consistent with the contract specification. The Iowa vote-share market is for a two-horse race, and the “winner” for the purposes of the WTA contract is the winner of the Iowa VS market. The IEM actually paid out on Gore in 2000 for this reason.
As in, loosely speaking, the Bush contract is currently “in the money”, so volatility in the underlying hurts the binary option more than it helps.
Readers may think that this divergence between the vote-share and WTA contracts is unlikely to reflect a genuine decrease in uncertainty about the vote-share and may represent an investment opportunity. Since CT isn’t in the business of giving advice, readers who want to pursue that line of thought are on their own.
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. But I don’t think this is the only problem. And furthermore, 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 hereby claim the CT title for “Most Footnotes”
And “Most Gratuitous Self-Citations”.
In response to comments, here’s a quick plot of the sensitivity of the option to the volatility assumption (vega). This is plotting the first derivative of the value of the option with respect to volatility. If this doesn’t mean much to you, just laugh at the grotty Excel.