Sunday, November 05, 2006

Information and Prices

How exactly does new information get transmitted into the prices of financial assets once it becomes publicly available? To me this is one of the most interesting questions in the economics of finance. Sometimes the information has rather obvious price implications. For example, once Mark Warner announced that he would not be seeking the Democratic presidential nomination, the price of the contract 2008DEM.NOM.WARNER (which pays $10 if he is the eventual nominee) dropped rapidly from about $1.50 to practically zero, and has remained there since. It's perfectly obvious to everyone that this contract is very unlikely to pay anything at all.

Most of the time, however, new information is much harder to interpret. Today, for example, a new Mason-Dixon poll was released showing Lincoln Chafee up a point in the Rhode Island Senate race, the first time he has led in any poll since August. In fact, the two previous polls in the RCP list had him down by double digits. Clearly, the race there is tightening, and one would expect to see this reflected in the prices of the RI.SENATE06.DEM and RI.SENATE06.GOP contracts. But by how much should the prices change? In other words, to what extent should the new poll cause us to revise our beliefs concerning the likelihood of a Chafee victory?

Well, here's what actually happened to the price of RI.SENATE06.DEM (which pays $10 in the event of a Chafee loss to Whitehouse). The last trade before the new poll became public was at $9.39. Soon after the poll became public on the morning of November 5, the price dropped to $8.73. This was at 8:17 AM. By 9:38 the price was down to $8.00, by 10:08 to $7.50, by 10:22 to $6.70, and by 10:30 to $4.50. By 11:11 it was back up to $7.97, and has remained between $7.00 and $8:00 ever since:

The point is that nobody really knows what the "true" likelihood of a Chafee victory really is, and how exactly to adjust one's beliefs in the face of new information. The market aggregates the opinions of all participants, but does so in a noisy way that can sometimes involve a lot of volatility and overshooting. More interestingly, the process may be path-dependent, since trading alters the distribution of assets and cash holdings among participants, and hence the extent to which their individual beliefs are reflected in the eventual price.

Friday, October 13, 2006


Writing recently in Slate, John Dickerson argues:

"The most likely beneficiary of Warner's departure may be Bayh, who was competing for a similar sphere of donors and activists as a representative of the centrist wing of the Democratic Party. As a former governor of Indiana, Bayh can claim executive experience, just as Warner could, and offer the same hope that as a favorite son he could turn a red state into one the Democrats could count on."

As I noted yesterday, the initial market response to the Warner withdrawal was that Edwards would be the main beneficiary. But there's also some support for Dickerson's view. At around the same time as the price of the Warner contract was collapsing, the price of the Bayh contract jumped upwards:

Still, the rise in price here is small compared to the rise in the Edwards contract, and even the Clinton contract has gone up by more. It'll be interesting to see what happens over the next few days.

Thursday, October 12, 2006


At some point this morning it became clear the Mark Warner would not be seeking the Democratic presidential nomination for 2008. I'm not sure exactly when the first public announcement appeared, but here's a Reuters post stamped 9:55 AM.

As you might expect, the price of the Warner contract on Intrade (which would have paid $10.00 if he had been the nominee) collapsed rapidly from $1.50 to practically zero:

The price at 9:40 was $1.50; by 10:41 it was 11 cents. What's interesting about this is that the decline in price should have been matched by comparable increases in the prices of other contracts. Specifically, if the market believed that there was a 15% chance of a Warner nomination prior to the withdrawal, this probability should have been reallocated to other contenders once the announcement became public. This did not begin to happen for quite some time, and the process is still incomplete. The only contract to have risen significantly at this point is that for Edwards:

A sharp increase in price, from $0.81 to $1.28, took place during a ten minute interval starting at 11:33, about an hour after the collapse of the Warner contract. A couple of other contracts (Clinton, Bayh and Obama) have also seen modest increases but the main beneficiary of Warner's withdrawal seems to be Edwards.

Friday, October 06, 2006

Price Inconsistencies

In my last post I provided an example of price inconsistencies across contracts in the Iowa Electronic Markets. These discrepancies are usually pretty minor. But price inconsistencies across different exchanges can be quite large, which makes you wonder about the rationality of traders.

Here's a recent example. The IEM House06 market has two contracts (RH.hold06 and RH.gain06) which, taken together, are equivalent to the HOUSE.GOP.2006 contract on Intrade. In fact, IEM's RH.hold06 contract is dominated by Intrade's HOUSE.GOP.2006 contract, since the former expires at zero if the Republicans gain seats. So the price of RH.hold06 should never exceed that of HOUSE.GOP.2006.

But take a look at the prices of HOUSE.GOP.2006 on Intrade between 10/3 and 10/6:

At no point did it cost more that $4.90 for a contract that pays $10 if the Republicans keep the House. The average price was $4.52 on the 4th and $4.38 on the 5th, with almost $120,000 worth of contracts traded over those two days combined. Now take a look at the IEM prices on October 4 and 5:


To buy a set of contracts that are equivalent to HOUSE.GOP.2006 cost $5.36 on average on the 4th and $5.22 on the 5th. That's a price difference of more than 18%.

Why did traders on IEM pay so much more for contracts that they could have purchased on Intrade? I'm not really sure about this, but it's clear that the traders on these two markets are receiving different information, or processing it in different ways. Meanwhile, the stakes on IEM are too small to make it worthwhile for someone to engage in arbitrage across the two exchanges.

Thursday, October 05, 2006

Arbitrage in Prediction Markets

One of the interesting things about the IEM Congessional Control Markets is that there are lots of different ways in which to take a position on an event. So, for example, if you want to bet on the event that Democrats take control of the House, there are four ways to do it: (i) buy RH.lose06 in the House06 market, (ii) buy a fixed price bundle and then sell both RH.gain06 and RH.hold06 in the House06 market, (iii) buy both NH_RS06 and NH_NS06 in the Congress06 market, or (iv) buy a fixed price bundle and then sell both RH_RS06 and RH_NS06 in the Congress06 market. In a thick market with heavy trading and optimal behavior on the part of traders, these four different ways of entering the same position should cost the same. But these are thin markets with varying degrees of sophistication among participants, so prices across contracts and markets are sometimes not mutually consistent.

In fact, sometimes prices get so misaligned that there appears an opportunity for aribrtage: one can take a combination of positions that yields a sure profit (regardless of what happens in the election). Consider for instance the prices as of 7:30 CST this morning:
07:30:00 CST, Thursday, October 05, 2006.

Symbol Bid Ask Last
RH_RS06 0.445 0.460 0.430
RH_NS06 0.031 0.045 0.031
NH_RS06 0.300 0.315 0.320
NH_NS06 0.208 0.235 0.207

Symbol Bid Ask Last
RH.gain06 0.022 0.039 0.022
RH.hold06 0.516 0.534 0.520
RH.lose06 0.455 0.515 0.462

At these prices, a trader could bet on Republican loss of the house in the House06 market and simultaneously bet on Republicans maintaining control of the house in Congress06 for a sure profit. Selling RH.gain06 and RH.hold06 in the House06 market, and selling NH_RS06 and NH_NS06 in the Congress market has a total net cost of $0.954 per contract. Whathever happens on November 7, the positions in one market will expire at $1 while positions in the other will expire worthless. So you're buying $1 for a $0.954 on each set of contracts traded in this way.
Nobody is going to get rich looking for opportunities such as this, which is why it's so easy to find them. But this example is a nice way to see the logic underlying arbitrage based pricing relationships such as the put-call parity theorem.

Tuesday, October 03, 2006

Out of Hibernation

I think it's time to revive this blog after almost three years of hibernation. With the elections fast approaching, there's a lot of interesting activity on the prediction markets. I've been looking at Intrade and the Iowa Electronic Markets (Intrade is the same exchange as Tradesports, about which I've posted before).

What interests me about these markets is the manner in which their design affects the accuracy of their predictions. The prices in one market can be inconsistent with those in another market, sometimes even on the same exchange. This sets up opportunities for arbitrage, although the gains are typically pretty small. It also means that the markets sometimes make conflicting predictions, which raises the question of which market is more accurate on average. This is where market design and participation matter.

So what's been going on recently? Well, Intrade's SENATE.GOP.2006 contract (which pays if Republicans end up with 50 or more seats) has fallen from above 80 to around 75, which means that the Dems have about a one-in-four chance of taking the senate. The decline seems to be driven by Harold Ford's momentum in Tennessee: the TN.SENATE06.DEM contact now gives Ford an even chance of winning.

Meanwhile, thanks perhaps to this, the HOUSE.GOP.2006 contract (which pays if Republicans maintain control) has tumbled too, and now gives the Dems a slightly better than even chance of taking the House.