Intrade, EMH and more Monte Carlos.
Posted by Possum Comitatus on June 30, 2008
All you folks that read the headline and wondered what the possible relationship between holographic Star Trek characters, Arnotts biscuits and betting markets could be, fear not.
In comments in the last post, Andrew Leigh raised the Efficient Market Hypothesis (EMH) as a good place to start for dealing with Intrade markets. For those that don’t know just what that is, it’s probably worth having a squiz at here.
For the sake of simplicity, we’ll just look at the three general forms of EMH, the strong form efficiency, the semi-strong form efficiency and the weak form efficiency – knowing which one applies to Intrade behaviour helps us enormously in trying to analyse the results.
So let’s do this via a process of elimination.
First up is the strong form efficiency which states (from the above link) that “Share prices reflect all information, public and private, and no one can earn excess returns.”.
The key here is the first bit, which as far as our Intrade analysis is concerned means that Intrade probabilities at any given time “reflect all information, public and private”.
The reason I used the Intrade results on election eve rather than election day itself in 2004 for calibrating our monte carlo sim is because of the massive volatility that occurred on election day in the Intrade markets – newstraders went haywire, making bets on every piece of dodgy exit polling that was released. Ironically the prices on election eve had it right, and prices on election day had it wrong for a good chunk of the time.
We know that Intrade prices don’t necessarily reflect “all information, public and private” at any given time, and we only have to look at the Intrade data on election day to see this. After the polls had closed in both Ohio and Florida, Kerry was actually ahead in the probabilities on Intrade. We can see this by borrowing a neat little chart of Intrade probabilities on Election day from Justin Wolfers and Eric Zitzewitz in their paper “Partisan Impacts on the Economy:Evidence from Predictions Markets and Close Elections” (2006).
By 9.00pm the polls had well and truly closed in the two key States of Ohio and Florida, private information was available to both Democrats and Republicans in Ohio and Florida by 9.00pm that told them who had won the election – yet the Intrade market did not reflect that private information, it simply continued to reflect the public information, the widespread broadcast of exit poll results that turned out to be erroneous (or actually just results that were within the margin of error of those exit polls). It wasn’t until after 10:00pm when political information started to leak to the media about the true state of affairs that the Intrade market reacted and pushed the Bush probability up beyond 50%, and did so rapidly. The same thing occurred in the Iowa Electronic Markets.
So we know that the strong form efficiency doesn’t always apply to Intrade – all private and public information is not reflected into the Intrade price at any given time, so we can reject the strong form efficiency.
We also know that weak form efficiency holds, since weak form efficiency simply tells us that the current Intrade price has all previous Intrade prices and trading volumes built into it. We expect Intrade prices to be serially correlated if they were weak form efficient and a quick peek at any Intrade political market or state shows that to be the case, for instance here’s the Democrat headline market and it’s correlogram:
It’s serially correlated up the wazoo – but interestingly it’s not exactly, statistically a basic random walk either (for the nerdy types that care for such things).
So the big question becomes, does the semi-strong form of efficiency hold?
Using a neat and simple Wiki definition, “Semi-strong-form efficiency implies that share prices adjust to publicly available new information very rapidly and in an unbiased fashion, such that no excess returns can be earned by trading on that information.”
We can certainly see that public information drove rapid adjustments to Intrade prices on election day in 2004, we also saw that private information didn’t impact upon price until it became public – so some degree of semi-strong form of efficiency would seem to apply.
This brings us to something that might be worth watching over the next few months in terms of the data. If we assume that there is a semi-strong form of efficiency operating in the Intrade markets, is the State by State market a stronger, weaker or similar level of that semi strong form compared to the headline markets?
Thanks to Caf, our Monte Carlo simulation at least partially adjusts for State non-independence – if we run those weekly simulations going back to April that gives us our implied State by State market probability, and compare that to the headline “Democrat as President” market probability we get something interesting:
We don’t have enough data yet to run any tests here (although we will eventually), but it looks as if the headline market could well be chasing the State market results – though, so saying, it could just be arbitrary at the moment, time will tell.
If our State market results can be demonstrated to be a leading indicator of the headline market, it will be evidence for the State markets containing a higher, more accurate level of information which takes time to flow through and be aggregated into the headline market – which, should that be the case, would be another piece of evidence backing the semi-strong form of efficiency argument.
Moving back to where our Monte Carlo sims stand at the moment, so far we are:
1. Turning our Intrade probabilities for each State into probability distributions with a mean of the implied probability for that State and a standard deviation now of 0.1. That let’s us treat probabilities not as true but as approximately true. As we approach the election, the standard deviation for those distributions will reduce, tightening up the Intrade probabilities to reflect greater certainty in the market of the implied probability being the true probability.
2. Thanks to Caf, for each iteration of the Monte Carlo sim, we generate a mean outcome M, uniformly distributed between 0.1 and 0.9. We use 0.1 and 0.9 to effectively cut the tails off the Intrade probabilities which we know aren’t accurate at the fringes. For each state election within a given iteration, we generate a value with mean M and a standard deviation of 0.01 (which we determined by using the 2004 election results as a calibration) to give us a call number. This call number for each state is compared to the randomly selected probability that we pull from our State probability distributions, and if our call number is greater than our State probability number we give the EV of a State to the Republicans, if it’s less than our State probability number we give it to the Democrats.
3.Each time we have an iteration, this process happens for all 51 electoral contests and we can sum the simulated number of Democrat Electoral College Votes. We repeat this process 100 000 times (which is now really stable at 100,000 iterations with this new method) to get a probability distribution of the Electoral College votes that the Democrats win in the simulation, which then allows us to calculate the probability of the State markets giving the Dems 270 ECVs or greater.
So the thing left to do is determine a process to reduce our standard deviation for the individual State probability distributions between now and the election, in such a way that it reflects the reduction in uncertainty in the markets that will occur during that period. I’m hunting through all sorts of data at the moment to see if I can find a good empirical basis for the shape of this reduction – but am always really open to any suggestions.
The US Election page on the Intrade data has had it’s weelkly update, this time applying the new simulation methodology.