Thursday, October 23, 2008

Peters prices now internally consistent?

The introduction of PETERS.TAURANGA seems to have brought Peters prices closer into consistency with one another.

MP.PETERS: 0.3
VOTE.NZFIRST: 0.37
PETERS.TAURANGA: 0.18

Now,

MP.PETERS = probability (Vote.NZFirst>0.5) + Peters.Tauranga - [probability Vote.NZFirst >0.5 AND Peters.Tauranga]

We don't know the probability that Vote.NZ First > 0.5 and we don't know the joint probability of the last term. If we (obviously incorrectly) assume independence of the two terms, we can back out a biased measure of the probability that Vote.NZFirst > 0.5. Alternatively, we can take the limit case and say that Vote.NZFirst will definitely be above 0.5 if Peters wins Tauranga.

First, the independence case.

0.3 = p(V.NZ1>0.5) + 0.18 - p(V.NZ1>0.5)*0.18
0.12 = 0.82p(V.NZ1>0.5)
0.146 = p(V.NZ1 > 0.5)

Is it plausible that there's about an 18% chance that NZ First's vote share will be above 5%? Let's assume normality and look at our handy standard normal distribution. At a Z score of 1.05 we have the right mass in the upper tail. The implied standard deviation is then 0.13: 1.3 percentage points. That's still on the high side, with a 95% CI of 1% - 6.2%.

What happens if we take the limit case where NZ First's vote share definitely exceeds 5% in any state of the world in which Winston wins Tauranga? MP.Peters then reduces to being just the probability of NZ First getting 5% of the vote.

0.3 = p(V.NZ1>0.5) + 0.18 - 0.18
0.3 = p(V.NZ1>0.5)
Giving an implied standard deviation of 2.5% -- much too high.

If we make the obviously too-restrictive assumption of independence, we wind up with an upper-bound of plausibility estimate on the variance of VOTE.NZFIRST. If we relax that assumption, we move to far too high estimates of the variance (in my view). What would tighten things up? Either MP.Peters is still overvalued or PETERS.TAURANGA is undervalued or VOTE.NZFIRST is undervalued.

I'll consequently further short MP.Peters while going long on PETERS.TAURANGA and VOTE.NZFirst!

Update The latest polls have pushed up MP.Peters but haven't touched either Peters.Tauranga or VOTE.NZFirst. Very odd.

7 comments:

Anonymous said...

Very interesting. What is your assessment of the internal consistency of PM.Labour with the other political contracts? It seems to me that the PM.Labour contract should be trading at 0.50 or slightly above given the vote shares, 6 Maori seats and the likelihood that Maori side with Labour. Consequently I'm long PM.Labour (if nothing else its a hedge on being long taxable income under a Labour Govt in NZ!).

Anonymous said...

I agree and made a similar comment a few days ago. Even though National is likely to receive the most party votes, the way potential coalitions are shaping up indicates PM.Labour is underpriced and PM.National is overpriced.

Based on the iPredict prices and depending on the assumptions you make, at this stage, I think there will be a National-led coalition government however the majority will be very small, 2 or 3 seats – I think a fair price should be PM.National 0.55 or even less.

Dibbo said...

What concerns most about this pricing is that it illustrates how few NZers really understand how MMP works and,in particular, how the overhang seats distort the outcome. National need to hammer this home over the next 2 weeks else based on the poll that typically does the best job - the TV3 poll - they will be nowhere near Govt.

Crampton said...

Ok, some very rough numbers while my 8 month old naps:

ACT: 4 seats
Nat: 56 seats
UF: 1 seat
MAO: 6 seats (1 overhang)
LAB: 45 seats
GRN: 9 seats
PRG: 1 seat (1 overhang)

122 seat Parliament, 62 for majority. Both sides need Maori.

What happens if Winston makes it in? Sum of all prices then 104.5, have to scale back accordingly:

ACT: 4 seats
NAT: 54 seats
UF: 1 seat (1 overhang)
MAO: 6 seats (2 overhang)
NZ1: 5 seats
LAB: 44 seats
GRN: 9 seats
PRG: 1 seat (1 overhang)

124 seat parliament; 63 for Majority. Again, either side needs Maori.

Haven't time to work out distributions, but a quick look seems a lot more 50-50 than 70-30. You could say worse than that for National given that Maori's more likely to go with Labour, but there's a lot more of the distributional mass for National above the 50% mark than there is for Labour. Then again, the sum of (Labour + Green) will also be pretty high variance.

In any case, I'm going to go short PM.National. I think y'all are right here.

Crampton said...

Frustrating... I'm 647 short on Peters.Resign; I can't clear out that position to short PM.National or buy PM.Labour without throwing away huge amounts of money. There's no way that there's still a 10% chance that Peters will be fired before the election. Not with two investigations down, one to go, and he and Clark walking arm and arm at the county fair last week. I'm guessing that lots of folks have short positions on this one that they're trying to clear out to use elsewhere and that's what's keeping the price up.

Dibbo said...

Shorting Peters.Resign is a sure thing but it ties up too much capital and the price seems only likely to collapse close to the election. I dumped mine to free up funds to invest in contracts that are likely to move in the interim. I've been long Obama (still am) but dumping this for now also as a 10 cent moves is still a week away whereas PM.Labour could move 20 cents this week and 70 cents in the next two weeks. Unfortunately....

Crampton said...

Most of my Peters.Resign stake was bought when the price was well north of 50 cents. Have been covering bit by bit when prices haven't been too unreasonable.