And so is solved the mystery of the inconsistent prices

Prices in the vote share market have moved since my last posting and only partially because of my own trading. At current VS market prices (in combination with expectations on Dunne and Anderton where we have no markets, and overhang from the Maori seats where we do have a market), we're looking at

ACT 4
NAT 58
UF 1
MAO 6
LAB 44
GRN 9
PRG 1

That makes for a 63 seat National-Act-UF coalition in a 123 seat Parliament. That's substantially more than a 60 seat Maori-Labour-Green-Progressive coalition. Let's continue to assume that Maori opposes National on supply and confidence. Are the prices in the PM markets now consistent with the prices in the VS markets?

Again, we need to start by working out the standard deviation in the VS markets. We'll start by correcting an error that I'd made previously which meant that my prior estimates overstated National's chances of becoming government: the Majority.National market pays off based on whether National gets a majority of seats, not of the popular vote. This matters with overhang. If we were looking at a 120 seat Parliament, current prices would imply a standard deviation of 2.19 seats for National; at 123 seats, it's 5.46.

For the minor parties, I'll again benchmark against NZ First: 1.23 in the vote share market for 1.48 in the seats market.

The standard error of the seat share for the National coalition is then 5.66 seats.

What proportion of the distribution (63,5.66) lies above 61.5? About 60.4% of the distribution: about a 60.4% chance that we have a National-led government under these conditions.

Does that mean that PM.National is overstated? Not necessarily! I'd earlier given reason 4: that the Maori Party might not oppose National. If Maori either supports National or abstains on confidence and supply, we need the proportion of the distribution (63,5.66) that lies above 58.5, not 61.5: about 78.6%. If Maori abstains or supports National, National has a 78.6% chance of forming government. We now have some markets on what the Maori Party might do post election: those markets suggest about a 40% chance that Maori abstain on confidence and supply for a National-led government and a 20% chance that they join National in coalition. So, roughly a 60% chance that the Maori party does not oppose National. So taking the Maori Party into account, what's the chance that we have a National-led government? 71%. The current price in the PM market!

But we haven't accounted for that there's a 25% chance that Peters returns to Parliament. If Peters returns, we have a rather different configuration of Parliament:

ACT 4
NAT 56
UF 1
MAO 6
LAB 42
GRN 9
PRG 1
NZ1 5

and 124 seats: the Maori Party now get 2 by overhang rather than 1. 63 are needed for a majority.

ACT+NAT+UF = 61
LAB+GRN+PRG+NZ1 = 57

If Maori support National or abstain, National forms government; otherwise, Labour does. In the first case, we need to know the proportion of the National coalition vote that exceeds 59; in the second, 63. 63.68% and 36.32.

So, to take NZ First into account, we have a 75% chance (no NZ First) that the 71% probability was right and a 25% (NZ First) chance of a 52.7% likelihood of a National government: about 66% overall chance of a National-led government.

Overall, it might be the case that PM.National is overpriced. But if it is, it isn't by much. Given the chain of assumptions built into the analysis, I'd be reluctant now to short PM.National at 71%.

Does this mean I had things horribly wrong in the prior posts? Well, I did note that if the chances of the Maori party supporting National were higher than the chances of Peters returning to Parliament, then PM.National could be close to right. And, it looks at current prices like the chances of the Maori Party supporting National are more than double the chances of Peters returning to Parliament.

I'll be putting in buy orders to cover my prior PM positions a few places back in the order book!