Fri, 04/29/2011 - 02:26 — Jinghao

For those of you who are not familiar with the website, it is a futures platform for predictions like elections. The idea is that through trade, the prices approximate the public's consensus on the approximate likelihood of something happening, like Trump winning the 2012 election.

Here are some consensus estimates for the 2012 Presidential election:

- President Obama has a 59.7% chance of being elected, suggesting the highest probability for a Republican win is 40.3%.
- Donald Trump has a 8.5% chance of becoming the Republican nominee, and a 5.7% chance of becoming elected. That means (through Bayes rule), if Donald Trump were nominated, Trump has a 67% chance of being elected.

The second fact reveals an interesting fact about the beliefs of people on Intrade. Somehow they believe that Trump has a good chance of winning if he were nominated. That encouraged me to research further to compose the following table:

Candidate | Pr(GOP Nominee) | Pr(Winner) | Pr(Winner|GOP Nominee)^{1} |
---|---|---|---|

Romney | 24.9% | 12.0% | 48.2% |

Pawlenty | 16.3% | 5.5% | 33.7% |

Mitch Daniels | 9.6% | 4.5% | 46.9% |

Huckabee | 7.8% | 2.7% | 34.6% |

Trump |
8.5% | 5.7% | 67.1% |

Bachmann | 6.3% | 1.4% | 22.2% |

Huntsman | 5.3% | 2.1% | 39.6% |

Palin | 5.0% | 1.7% | 34.0% |

Gingrich |
2.7% | 1.8% | 66.7% |

Ron Paul |
2.8% | 2.2% | 78.6% |

Interestingly, we see that the implicit belief is that among the Republican candidates, only Gingrich, Ron Paul and Trump have a good chance of defeating President Obama. Does that fit with your intuition?

If the GOP just wanted a GOP in the White House, it would try to pick the candidate with the highest posterior probability. Yet those candidates also have relatively low prior probability, suggesting that the GOP is not doing that (or the Intrade beliefs are wrong). What do you think?

Another interesting fact that surfaced was that the sum of each individual candidate winning totals to 100.6%, suggesting that there's an arbitrage opportunity. To exploit the arbitrage opportunity, you short $x of all of the candidates and invest that money somewhere else (Say, treasuries). As a result, you will gain 0.006x + returns from the treasuries (say, 2% on x for 1.5 years of investment) for sure, assuming your transactions do not meaningfully impact the price of the "shares".

Has anyone dabbled with Intrade? What do people think of these estimates? Are they pretty good, or do you think there is profit potential from statistical arbitrage?

^{1} I calculated the posterior probability using Bayes rule as follows: Pr(Winner|GOP Nominee) = Pr(Winner and GOP Nominee) / Pr(GOP Nominee) ≤ Pr(Winner) / Pr(GOP Nominee). The last equality follows from the fact that a candidate must be a GOP nominee (or a nominee of another party, which is highly unlikely) to be the winner.

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