At current prices, the markets are forecasting a 60% chance that 2009 temperatures will be above 2008 temperatures, with a 24% chance that 2009 temperatures will beat the 1998 high of a 0.546 degree anomaly. The 2008 anomaly was 0.324, so traders must reckon 60% of the temperature probability distribution lies above 0.324 and 24% lies above 0.546.

If you go to the underlying data series, which goes back to 1850, we find a mean change from year to year of close to zero (because of course it's anomaly relative to an average baseline) with a standard deviation of the year-on-year change of 0.115. So, in any given year, the next year's anomaly will fall within +/- 0.115 of the prior year's anomaly about 68% of the time. For the 2009 anomaly to be greater than 0.546 would require an increase equivalent to at least 1.93 standard deviations of the year-on-year change. A jump that large shouldn't happen more than about 2.5% of the time in a normally distributed series. You could try arguing that the variance of the series has increased, but the standard deviation of year on year changes over the last decade is almost identical to that of the whole 159 year series.

You might also well say that I ought to account for the warming trend. Let's try that. From 1980 through 2008, the average change in the anomaly has been 0.009483. We can add that to the 2008 temperature to get a prediction for 2009. The 2009 observation would need to be 1.83 SD above the expected temperature increase to beat the 1998 anomaly. We would expect that to happen 3.36% of the time.

I've included a graph with the underlying temperature series and bands showing changes 1.83 standard deviations above and below the prior year's observation. How often in the series' 158 year* history do we see the subsequent year's anomaly outside the 1.83SD band? 14 times. Or, 8.8% of the time, with 4.4% above the band and 4.4% below the band. That's a bit more than we'd expect from the standard normal distribution (6.7% of observations, 3.35% each side), but not a ton more. I've marked these with big red dots: 1863, 1865, 1877, 1879, 1890, 1916, 1930, 1954, 1957, 1964, 1974, 1977, 1997 and 1999. Those are years with temperatures that varied by more than 1.83 standard deviations of the normal year-on-year change from the prior year's observation. You'll probably need to click on the graph to enlarge it to see things properly.

I've been shorting this stock since it launched. I plan to continue shorting this stock. I'm not saying that 2009 can't be warmer than 1998, I just can't see how it's more than 20% likely to happen. I can't see that it's more than 10% likely to happen either. The analysis above should give an upper bound estimate of the likelihood of 2009 exceeding 1998: for a midpoint estimate, I'd not account for a warming trend and instead evaluate at the mean zero change. At what price would I start covering my shorts? Well, I think a fair price wouldn't be higher than $0.05, and I'm a bit risk averse.

Of course, feel free to follow the links provided in the stock description to get the underlying data and have your own play with it. I'm not doing anything high tech here.

*Yes, the series is 159 years long, but you can't look at the year-ahead for the most recent year. That's the one we're trading on!

Note: Post updated to provide analysis based on 1.83SD cutpoints (the upperbound case) rather than the midpoint case provided earlier.

## Monday, January 19, 2009

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## 10 comments:

Yup, i've been shorting it too.

But, can you stop telling everyone!! :D

Price is back up to 0.25...I'll keep shorting...

heh me too :)

With more people aware of global warming and being carbon neutral I think more people are actively doing something and that's why we see a decline since 1998. Also with the south island having snow and one of the coldest summers, and UK also having one of their coldest winters I'm picking it might be much colder than last year as well.

http://www.express.co.uk/posts/view/35266/Global-warming-It-s-the-coldest-winter-in-decades

I hadn't even thought of trading these contracts. But having seen Crampton's analysis I have to agree that the pricing is very rich. A nice safe short to have in the book. i'd be grateful for more on the bid above 0.20 please.

Incidentally, the other safe short is King to be removed as Deputy Leader of Labour. There is no way the party will change the leadership in Year 1, so as I see it the market is presently saying that there is a 28% chance that she kicks the bucket!

I'm wondering how much of it is people discounting over the whole year that we'd have to wait for it to pay out: I personally wouldn't short it for less than 0.15 because that would represent an expected return of ~10% using a 5% chance of it being higher than 1998.

Does this make sense?

Bob, I'd be with you except for that lots of other stocks with long duration seem to trade well. The sum of all bids in the 2011 election markets was about $1 even before the bundle option came in, for example.

I wonder how many of you have noticed that the dember 2008 data is not in the series yet, making 2008 look lower than it probably will be...

Why do you think it's not in the series? It lists 2008-12 as the end period for the series; there's an entry of 0.307 as the December temperature anomaly. I see no reason to think the series incomplete.

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