Monday, October 20, 2008

More thoughts on Peters prices

Interesting discussion in the comments section on the prior post. Let's refine things a bit.

First, we can work out the standard deviation of the VOTE.NATIONAL price by looking at MAJ.NATIONAL. The point estimate price is $0.47 and the chances of their beating 50% are 26%. The Z score on the standard normal table for 24% (the area lying between the point estimate and $0.50 given that 50% lies above $0.47 and 26% lies above $0.50) is 0.645. Z = [x-mu / sigma], so 0.645 = [0.5 - 0.47]/sigma and sigma must then be 0.0465. So, we can be 95% sure that the actual National vote share will lie somewhere between 38% and 56%.

Now, there's no easy way of working from the standard error of VOTE.NATIONAL to that of VOTE.NZFIRST. A standard error of 4.65 percentage points is entirely wrong, but simply scaling it by the scale difference between the two markets also would be in error: we then could have arbitrarily-precise point estimates simply by increasing the payout per percentage point of the popular vote. Moreover, we should be less confident in the vote shares of the minor parties as compared to those of the major parties. I suppose that the best we can say is that the standard error of VOTE.NZFIRST should be higher than 0.465 percentage points: the scaled standard error for this market, or $0.0465.

Given that the standard deviation on the VOTE.NATIONAL market seems reasonably high, I'm less confident that the standard deviation on VOTE.NZFIRST is as tight as I was thinking initially. If the 95% CI on VOTE.NATIONAL runs from 38 to 56%, it's not that implausible that the 95% CI on VOTE.NZFIRST runs also over a pretty wide range.

For sake of argument, suppose that the standard error for VOTE.NZFIRST runs double the scaled value from VOTE.NATIONAL, so 0.093. If VOTE.NZFIRST is $0.37, then there's a 6% chance that VOTE.NZFIRST winds up above $0.50. If the standard error were triple that (scaled) from VOTE.NATIONAL, it would be a 15% chance. MP.Peters is trading at $0.39. What are Peters' chances in Tauranga given these prices? Somewhere between about 30-40%, depending on how you'd want to specify the covariance between VOTE.NZFIRST and Peters in Tauranga, and what estimate you'd like to use for the standard deviation of VOTE.NZFIRST.

I'm going to maintain my short position as I don't think it between 30-40% likely that Peters will win Tauranga.

Addendum I told you that it was overpriced! Tauranga.Peters opened at $0.24 and dropped within hours to $0.12.


Anonymous said...

I think it’s interesting to use the prices on iPredict to work out roughly how many seats each party will get (assuming Jim Anderton, Rodney Hide etc hold their electorates), and then form potential coalitions.

Based on my calculations, a National-Act-United Future coalition will hold a majority of four seats. This means John Key will be Prime Minister however small changes mean Helen Clark will be Prime Minister (depending on the support of the Maori Party).

Surely with such a small potential majority, uncertainty over coalition partners, and so on that this risk is not fully reflected in the price of PM.NATIONAL and it is overpriced in my opinion.

Crampton said...

Strange stuff: VOTE.NATIONAL went up from $0.46 to $0.48 while MAJ.NATIONAL dropped from 26% to 22%. This suggests that the variance of VOTE.NATIONAL has tightened up considerably: a Z score of 0.77 and consequently a sigma of 0.026: roughly half of the prior estimate!

There are a few problems in moving from the VOTE.XXX markets to composition of Parliament. First, the sum of all bids currently adds up to 104% of Parliament and I'm not seeing a market there on United Future. So all bids are scaled up from reality: folks ought be shorting the parties they think are overpriced rather than buying up the ones they prefer. Second, if Winston takes Tauranga (I'd say chances somewhere in the high 20s but I could easily be wrong), NZ First keeps its votes but otherwise we have to recalculate among the remaining votes. We don't currently have a market on United Future's vote share, so I'm not sure how I'd start working out the likelihood of the different coalition options. I would have started by saying UF is the residual, but the residual in this case is negative!