## Thursday, September 25, 2008

### Markets and Polls

A couple of weeks ago a strange thing happened on our electoral markets map. California turned red for a couple of hours. A few days later Michigan turned red as well. Neither of these states are about to vote republican, rather there were odd trades of Obama at a very low price in California and McCain at a high price in Michigan. Since we used the closing price the states were colored wrong until another trade occured.

So we adjusted our algorithm so that if the closing price is lower than the bid price (the price someone is willing to pay) we use the bid price instead. Also if the closing price is higher than the ask price (the price someone is willing to sell) we use the ask price. That seems to avoid the problems of rouge trades.

Which brings me to a controversial post at fivethirtyeight.com, a site that makes predictions based on poll numbers. Nate Silver notes that the prediction of Obama of the markets to win the presidency (about 58%) is much lower than his site's prediction (about 72%). Silver suggests the disparity is because of a rouge trader or traders that seem to be driving the price down and even buying Hillary stock.

I don't buy it. There is quite a bit of volume on these securities and the prices on Obama should bounce back quickly and in fact it does. The rouge trader cannot explain a difference of 14 points. The Hillary factor can be explained by the long-shot bias (people overweigh low probability events). The markets suggest that the probability that Hillary is president is about the same as McCain winning Illinois which sounds about right (even if they are both too high at around 4%).

I have a different theory: The race is tighter than the Silver analysis suggests. The polls can give you numbers about each state but not the correlation between them. Silver gives an explanation of how he handles the correlations in his simulations:

Our simulation accounts for this tendency by applying a similarity matrix, which evaluates the demographic relationships between different states by of a nearest-neighbor analysis as described here. Our process recognizes, for instance, that as the polling in Ohio moves, the polling in a similar state like Michigan is liable to move in the same direction. On the other hand, there may be little relationship between the polling movement in Ohio and that in a dissimilar state like New Mexico.
Silver admits he has little data to back up this claim. I believe the correlations are much tighter—that most of the states might move in the same direction depending on some future event or ad or gaffe or performance on the yet-to-be-held debates, that there is high future correlation even between Ohio and New Mexico.

The swing states are typically highly correlated and if the four states running about 50% (Nevada, Ohio, Virginia and New Hampshire) all go to McCain then the Electoral college ties and it would just take one other state (like New Mexico) to push it over.

The analysis of each state can be done well with polls and historical data and the market prices and polls for the individual states do not differ that much. But understanding the correlations between states is more guesswork and I trust the wisdom of the crowds over the wisdom of the one.

1. You are not addressing Nates's point, which had nothing to do with his or your predictions.

He was commenting that
(i) the Obama contract was trading at 52% on InTrade and at 61% on IEM and Betfair. Prima facie, it looked like a huge and very visible arbitrage opportunity
(ii) the trading and price movements for the Obama and Clinton contracts showed several large jumps (down for Obama, up for Clinton) that occurred in minutes and appeared to be synchronized.

Along the same lines, McCain prices show several large jumps, also apparently synchronized with Obama price drops.

All of this is consistent with a single bidder being occasionally active in the market. There is nothing wrong with that, but the apparent arbitrage is certainly suspicious.

2. As the other commentor said, Nate was not observing that 538 disagreed with intrade disagreed. Nate was observing that intrade disagreed with other online markets, IEM and Betfair.

3. Lance, I like your (unintended?) word-play of "rouge" vs. "rogue" :)

aravind

4. Anonymous at 1.

Nate made the mistake of not comparing like with like. The Intrade markets Nate was using as an example were the Intrade Contender Markets where betting takes place on Individuals rather than the Intrade 'Party as Winner' markets where the betting is on party victory. It might sound like a small issue - but's its not, with the Party markets being consistently higher than the Contender markets and much more in line with the Intrade State market behaviour.

Lance is right on State correlations being tight. If you look at a time motion plot of the weekly change in State probabilities vs. the actual Intrade probabilities of that State - and you do it for the key States, you can clearly see the dependency in action since June when I've been measuring it, especially with the movements that occurred through the convention period and since:

(The flash google gadget Under Battleground 131 about a third of the way down on that page)

The arbitrage is suspicious, and there are a lot of legacy contracts - particularly Clinton contracts - playing in the Intrade Contender markets and that does seem to be having a price anchoring effect of a few percentage points.

Which makes the Two Party Preferred Intrade markets a much better bet for analysis (pardon the pun).They have the drawback of being thinner, but the benefit of dealing with the actual presidential race as it is.

5. But there are comparable contracts at intrade and IEM, and I think they support Nate's point. Take a look at these graphs of the discrepancy between Intrade and IEM. It looks like there's been an unusually large difference in prices lately.

6. I had a basic question about the state numbers: Below are some volume numbers for some swing states.
Indiana: 111
Michigan: 1
Ohio: 210
New Hampshire: 28
Virginia: 169
North Carolina: 41
Florida: 164

Each contract is worth \$10, and the default contract size is 20 so even Ohio probably represents the opinion of 10 trades.

The odd trades you refer to indicate that there isn't a long queue of pending trades either, even in a state like Michigan. This seems like a seriously manipulable system. And the amounts involved don't seem large enough (\$6500 of trade in all the above states put together) to reasonably argue that arbitrage would be eliminated by smart traders.

Given all this, how much can one trust these numbers?

7. To further illustrate my point:
Florida is as swing as it gets, and is currently showing 58% Obama on the electoralmarkets.com.
Going to Intrade however, one sees:

Last 5 Trades (last update: Sep 28, 5:12:42 PM EDT)

Sep 28, 4:43:24 PM EDT 1 Lots @ 58
Sep 28, 4:37:25 PM EDT 1 Lots @ 55
Sep 28, 4:37:05 PM EDT 1 Lots @ 51
Sep 28, 4:36:53 PM EDT 14 Lots @ 50.9
Sep 28, 4:36:33 PM EDT 1 Lots @ 50

Today's volume: 196
Total volume: 4131

B Qty Bid Ask A Qty
6 51.0 54.0 30

Thus the number 58 came from two people having a 10 dollar bet at that rate.
(While I composed this post, the next trade of 5 lots happenned at 51!!)

This seems to me to be a very illiquid market. So one improvement to the website would be to take a (weighted) average of the last five trades to get a slightly more representative number.

--anon 6

8. Your discussion of correlation is very sensible, but it dances around a larger point (which Nate seems to have missed entirely): there is no reason why 538 and Intrade should agree, as they are predicting different things. They should only converge by Election Day.

Intrade is predicting the probability that a given candidate wins, and as Nate points out, it may not be doing the best job. 538, meanwhile, is predicting the outcome of an election held today. Given the current polls, it assigns a probability to how each state would vote in an election held today, then runs simulations to determine the probabilities of overall outcomes.

It's not immediately clear how 538 and intrade should relate. Certainly if 538 were predicting a 95% chance of victory for one candidate with months to go, intrade would not agree for two reasons.

1. Over many months, many folks would believe that there is more than a 5% chance some unforeseen even would dramatically shake things up.

2. Over many months, there's a very high chance that, if nothing else, the candidate trading at %95 will at least drift toward say %85 due to an unforeseen event.

In my opinion point 2 partially accounts for why intrade has trouble predicting probabilities close to 1 (i.e. it isn't purely explained by an irrational longshot bias)

9. Well here's the answer:

CQ Politics: Trader Drove Up Price of McCain ‘Stock’ in Online Market

An internal investigation by ... Intrade has revealed that a single investor’s purchases prompted "unusual" price swings that significantly boosted the prediction that Sen. John McCain will become president. ... Over the past several weeks, the investor has pushed hundreds of thousands of dollars into one of Intrade’s predictive markets for the presidential election, the company said, resulting in repeated monetary losses through a strategy that belies any financial motive. "The trading that caused the unusual price movements and discrepancies was principally due to a single 'institutional’ member on Intrade,” said the company’s chief executive, John Delaney, in a statement released Thursday. "We have been in contact with the firm on a number of occasions. I have spoken to those involved personally."

Also, eerac:

- I guess Nate has confidence in his model but the stronger point was that Intrade was the outlier here, disagreeing with the other betting sites.

- The probabilities here were not so close to 1 or 0. But I think intrade does have problems with such events, in part because transaction fees and opportunity costs mean that it's not worth investing in these cases (you could earn more by putting your money in a savings account).