Does anyone else find it very odd that MP.PETERS is trading at about $0.385 while VOTE.NZFIRST is trading at $0.36?

Winston Peters has two ways to get back into Parliament. The first is by winning Tauranga; the second, by getting 5% of the vote. MP.PETERS consequently should then be trading at a price equal to the sum of the probability of Peters winning Tauranga and the mass of the probability distribution of VOTE.NZFIRST that's above $0.50. We don't have a market on whether Peters will win Tauranga but I'd be shorting that market on any initial price above 20%. If his chances in Tauranga are about 20%, that means that 18.5% of the probability distribution on VOTE.NZFIRST is above $0.50. For those with less stats, that means that, if the prior analysis is right, NZ First has an 18.5% chance of bettering 5%. Assuming normality (always risky with this subject), that means that the standard error of the price estimate on VOTE.NZFIRST is about $0.156 [corrected]. I find that a bit high. If the standard error is 0.156, the 95% confidence interval is from $0.06 to $0.667 [corrected].

I could be way out on Winston's chances in Tauranga; if they're much higher, that tightens up the variance on VOTE.NZFIRST. Or, I could be way out in my distributional assumptions. Or, we could really just have a very high variance estimate of the true vote share for NZ First. If none of those are the case, though, either MP.PETERS is overpriced or VOTE.NZFIRST is underpriced.

Full disclosure: I shorted MP.PETERS after thinking this through as I find it more likely that MP.PETERS is overpriced than that either VOTE.NZFIRST is underpriced or that my prior assumptions are seriously out.

## Sunday, October 19, 2008

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## 8 comments:

Interesting post, but I think I disagree for two main reasons. The first relies on my rather hazy memory of stats; the second doesn't.

First, you seem to be assuming that the NZ First vote share and Winston Peters winning Tauranga are independent of each other. I'm not sure whether this is necessarily the case. But I'm also not sure that your analysis necessarily makes this assumption. Correct me if I'm wrong.

Secondly, and probably more importantly, I think you're probably underestimating Peters' chances of winning Tauranga. Given he only lost by around 700 votes in 2005, I'd say he has a better than 20% chance of winning, especially when you compare the relative profiles of Bob Clarkson and Simon Bridges.

I'm not sure whether you can do this, but, assuming independence, I'd be interested to know statistically what the market would rate Peters' chances in Tauranga (taking the two market probabilities we already have).

I was indeed assuming independence for simplicity on two measures that rather obviously have positive covariance. This, however, means that the correct price of MP.PETERS is lower than I'd have been guessing as you need to subtract the probability of both Peters' winning Tauranga and NZ.FIRST getting higher than 5% from the mass. Consequently, the case for shorting MP.PETERS is higher than I'd suggested.

I may well be underestimating Peters' chances in Tauranga. He was polling twenty points behind Bridges at the end of August, in the midst of the various scandals. It's entirely possible that he's recovered since then. I'd love to see some new polling on Tauranga.

We can't work backwards from the current prices to figure out Peters' actual chances in Tauranga without knowing the variance of the price estimate MP.PETERS. I used a guess on Peters' chances there to work out the standard error; I suppose one could guess at the variance to work out Peters' chances in Tauranga. I have more confidence in my guess at his chances in Tauranga than in my guess at what a sensible measure of the variance of the price estimate might be.

But what about the third way... if Ron Mark wins the Rimutaka seat?

If the chances of that one are decent, then I'm underestimating the proper price of MP.PETERS. On the other hand, if Mark is most likely to win Rimutaka if a rising swell for NZ First lifts both his chances and the chances of their beating 5%, then I'm not underestimating things by too much.

I'm short 175 and can't see myself moving to cover unless the price drops to about $0.30 or if VOTE.NZFIRST rises to about $0.45.

I know this is off-topic (and not necessarily addressed to the right person), but is there any particular reason why (for me at least), iPredict has been down nearly all day? This is not the first time I've experienced this.

Greg

I've had prices refreshing every half-hour or so while grading term papers and haven't had any problems with the site. So I don't think the problem is specific to iPredict.

Woe. HR must be on to it (absolutely nothing is coming up for me).

Cheers.

I think you are under-estimating the chances of Peters winning Tauranga. Last poll was 10th August, over a month ago.

Plus, don't forget the following facts from www.winstonpeters.com:

"Many commentators try to classify Winston but he is essentially in a class of his own. He is the last of the great New Zealand political characters who are “larger than life”. He is a devastating debater with lightning reflexes in the arena of Parliament. Some of his performances are pure theatre, according to even his most vocal critics."

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