Archives: September 2008
Thu Sep 25, 2008
Price Discrepancies and Presidential Election Odds
Nate over at FiveThirtyEight has observed a discrepancy between the prices for Obama over at Intrade (52.3 at the time of his writing) and at Betfair (61.7). I was pleased to see that he made none of the amateur errors I usually find when reading analyses of idea futures prices. Importantly, he recognizes that it is non-trvial to translate individual state odds into electoral vote victory odds.1
However, he misses one possible explanation for the price discrepancy between the two markets which would not involve an arbitrage opportunity. His key oversight rests in the following statement:
Right now, Obama is trading at 52.3 points. That is, Intrade implies that he has a 52.3 percent chance to become the next President.
In fact, one cannot directly infer probabilities from prices. I detailed many of the complicating factors during the last presidential election, but there is one which I did not discuss then and which is key here, and that is the possibility that the currency being traded may be correlated in value with the probability of the contract itself! Since Intrade pays out in dollars, and Betfair in pounds, this could theoretically be the explanation for the price discrepancy. Let me elaborate:
Suppose there is a contract which pays out if the value of the dollar declines by 10% (as determined by, say, the Consumer Price Index) in six months' time. Suppose further that it is widely agreed that the probability of this event occurring is 50%. What should the market price of this contract be? A naïve answer is $0.50, but in fact the answer is $0.45! This is because, conditional on the contract paying out, the currency with which it pays out has declined in value by 10%, so in today's dollars it is worth 0.9 x Probability = $0.45.
Now, if the market were in pounds, then there may be little to no correlation between the odds of the contract paying out and the value of the payout. In that case, you may see prices closer to £0.50.
Bringing this back to the matter at hand, it may be the case that Obama trades at a discount on Intrade relative to his odds of election if that event is perceived as having potentially negative consequences for the value of the U.S. dollar. There may be little to no expected effect on the value of the British pound, so Betfair does not see a similar discount. This would explain the price discrepancy in a way that allows no opportunity for arbitrage.
So, is this explanation correct? I don't know; I suspect there's something to it, simply because a Democratic White House can be expected to spend more than a Republican White House while Democrats control Congress, which would drive inflation. It may not be enough to account for an 18% difference (12% as of this writing), and Nate did note some other trade anomalies which might account for some of the discrepancy as well, but it is important to be aware of all possible causes before making assertions about market inefficiencies.
1. There are two naïve models for calculating victory odds from individual state odds, both of which are wrong:
The first methodology is to assign the electoral votes of each state to the candidate perceived as having an edge in that state (as determined by polls or market prices), and then to assign some sort of imprecise advantage to the candidate with a greater number of assigned electors. Besides its imprecision, the main problem with this approach is that it treats large advantages equivalently to small advantages, meaning that the expected sum of your electoral votes will be over-estimated if you have a slight edge in a large number of states (since you are unlikely to win all of those states), and conversely, under-estimated if you have a large edge in a small number of states.
The second methdology is to assume that each state is an independent variable and infer from the odds in those individual states the likelihood of every possible winning combination of electors, the sum of which gives you the winning odds for your candidate. The flaw here is simply that the results in each state are far from independent of each other, so you tend to way overestimate the degree to which the variables cancel each other out, and as a result, you overestimate the odds of the leading candidate.
The best known model turns out to be an idealized one which (for the sake of simplicity) treats as 0 the possibility that a candidate could win state A but not state B, if his probability of winning B was seen to be greater than A prior to the election. This model can be said to have "perfect correlation" between states, and yields a candidate's election likelihood as being equivalent to the likelihood of the Nth state in a list of all states ranked by likelihood, where that Nth state would be the one to put it over the top.
The first methodology is to assign the electoral votes of each state to the candidate perceived as having an edge in that state (as determined by polls or market prices), and then to assign some sort of imprecise advantage to the candidate with a greater number of assigned electors. Besides its imprecision, the main problem with this approach is that it treats large advantages equivalently to small advantages, meaning that the expected sum of your electoral votes will be over-estimated if you have a slight edge in a large number of states (since you are unlikely to win all of those states), and conversely, under-estimated if you have a large edge in a small number of states.
The second methdology is to assume that each state is an independent variable and infer from the odds in those individual states the likelihood of every possible winning combination of electors, the sum of which gives you the winning odds for your candidate. The flaw here is simply that the results in each state are far from independent of each other, so you tend to way overestimate the degree to which the variables cancel each other out, and as a result, you overestimate the odds of the leading candidate.
The best known model turns out to be an idealized one which (for the sake of simplicity) treats as 0 the possibility that a candidate could win state A but not state B, if his probability of winning B was seen to be greater than A prior to the election. This model can be said to have "perfect correlation" between states, and yields a candidate's election likelihood as being equivalent to the likelihood of the Nth state in a list of all states ranked by likelihood, where that Nth state would be the one to put it over the top.
