Tuesday, June 21, 2005

Predicting climate change (3)

Time to look at another claim on the FX market. This time it's the turn of SLv1, the probability of a 1m rise in sea level by 2030 (compared to 1994, the claim's launch date). This is currently priced at about $0.19, indicating that the market thinks there is a 19% probability of this rapid sea level rise occurring. But what do the experts think?

Firstly, there is no way that thermal expansion alone could generate such a rapid rise in sea level. The only mechanism that could hypothetically cause such a rapid rise would be the collapse of a major ice sheet, and the West Antarctic Ice Sheet (WAIS) is the most (only?) credible candidate for that. A quick google quickly found this paper which discusses the subject in depth. The paper estimates the risk of collapse at about the 5% level over the next 200 years - and note that their definition of "collapse" is anything over 1cm sea level rise per year, which is still a long way way short of the 4cm/year required for the claim to come true (in terms of the claim, the post-1994 sea level rise is small enough to ignore). It doesn't take a genius to work out that 1m by 2030 simply isn't going to happen, unless all the scientists have completely overlooked some massive part of the problem. Since these are the same scientists (roughly speaking) who first considered the problem, and without whose investigations the FX claim would never have been set up, it seems more than a little ridiculous that the market traders think the scientists are so badly wrong. Prediction markets have their place in aggregating information, but the only justification for such a high price is that someone somewhere is assuming the existence of a whole new aspect to the problem that has not yet even been proposed (AFAIK).

So that makes 3 claims relating to climate change (first two here and here) where the market is substantially more alarmist than the scientific consensus. I'll have more to say about what I think about the causes and implications of this later.


Anonymous said...

I disagree that a price of 19 for the Yes claim is the same thing as a 19% chance that the statement is true. For example, look at:


The claim will be true (pay 1 to Yes holders) in 2015. The current price of a No is 5, and the No will be valueless in 2015. But until then, there is speculative value in a No. If I buy at 5, I would do so to hope to sell at 6. Or 7. Or 10.

Another way to look at this is that one hopes to get a return on
investment. Even a very safe investment will require a return, or why would I bother? A Yes for T2015 costs 95 currently, so for a
completely secure investment the FX market is currently offering 0.5% to 2015.

If that same rate of return is projected to 2030, then roughly 13 of the price for the Yes is from this minimum expected return even if a NO was a sure thing.

But a No on 1 meter rise by 2030 is not a sure investment. There is a change that you might lose, and maybe well before 2030. As a result, the expected average return, even after taking into account the risk, will need to be higher. How much higher would depend on the level of risk, and that's harder to project.

So what does the FX market price of 19 for SLv1 really mean? Most of the price is the minimum expected return. Some of the price is risk, and some is higher expected return in the presence of risk.

Is this fairly priced? That's harder to say. I'm short (that is I hold No's for this claim), so I do think it is overpriced. But it's not much overpriced. My opinion is that 14 - 16 would be close to fair price.

Phil Hays

James Annan said...

Well, my point would perhaps have been stronger at a price of $0.32, which it was a few months ago :-)

Longshot bias is a common phenomenon, and people on FX clearly choose "irrational" bets (eg the "true" claims) for the thrill of trying to find a bigger fool. But I can't see these effects generating a price as high as the $0.20 that Slv1 is currently trading at - that is not a longshot price!

You are right that the return on the $0.80 "No" is not very high given the 25 year time scale. But the return on the "Yes" is an expected loss of 4% per year (assuming a linear decline), with some variance due to volatility. Remember that the FX market is strictly zero-sum, the claims with guaranteed positive gain only exist because enough players are prepared to pay money for the thrill of the chase.

I repeat: the probability of a 1m rise in sea level by 2030 is negligible. This claim might as well be called "False in 2030".

Anonymous said...

What price should a "99+% chance of false in 2030" claim have as a longshot price? By extrapolation from the claim T2015, I've suggested around 14 to 16. If you disagree, what price would you expect and why?

The expected loss of a yes claim (on a false in 25 years) is 4% a year, regardless of the price, so that doesn't help. To go long on the yes on a "False in 25 year" claim is to count on some variance due to volatility to enable selling at a profit: The question is: how much variance is expected?

That is a question of economics not of sea level change.

Phil Hays

James Annan said...

I think the standard "longshot bias" explanation depends on the investor overestimating the true odds, which clearly does not apply in the case of a claim with a pre-determined outcome.

I'm not sure what theory applies for this level of irrational purchasing where the asset is known to be intrinsically worthless, but your extrapolation to estimate the "expected" price clearly fails eventually, since there can be no justification for a No price of >$0.50 for a true claim of any duration (at this point, the Yes has more volatility as well as the gradual drift towards $1).

In any case, I'm sure you would agree that the earlier price of $0.32 (at which point I joined FX and started pushing the price down) is a long way removed from your extrapolated estimate of $0.13-$0.14 and can only be explained by a substantial overestimate of the risk of 1m of sea level rise.

Anonymous said...

FX is a game. As a game, it does not have any fixed goals, but leaves that up to the players. If your goal is to get on the Fx "Top 10 Players by Score", then this goal can't be reached by buying a long term position returning a sure 1% per year. A player would need better than a 10% per year return to match what the current #10 on the list has done. There are two ways to do this that I can see:

1. Take short term positions that are risky, and make the correct calls. For example, sell MJ06 while the jury was out. Buy Bush04 on November 1.

2. Trade. Take a position, and then unwind the position after the price has moved, hopefully for your profit. For example, I'm no longer short C02LVL. The price probably isn't going to move that much more, and if it did I might take a position again. I got 12% for a month, I'll let others get 12% over the next 25 years. Unless, of course, I can see another way to trade it.

I'm not sure how any fixed theory of how to profit from trading can exist. If there was such a theory, it would seem to me to make a user of such a theory to have predictable actions. If I can predict what other traders will do, I should be able to figure out a way to profit from their actions.

I agree that a long enough term claim in the FX game is only useful as a trading item, and not as a buy_and_hold investment. As such, the most likely price will approach 50 as the term increases, regardless of the eventual payoff, as that is where the buy and sell sides are matched.

I don't understand how or why you claim a limit on the price. A True_in_3535 claim would be just as likely to trade above 50 as below 50, as the eventual payoff is so far off as to not be a significant factor.

I do not agree that a price of 32 for SLv1 is proof positive of a group overestimate of the risk of 1m of sea level rise. I see it as just as likely to be the result of trading games. How could we tell the difference?

Phil Hays

James Annan said...

It seems a bit convenient to claim that since it is only a game, the prices have no meaning. It is those who are trying to win who will make money and therefore have the strongest influence in the marketplace. Moreover, it is clear that the prices do generally relate to the payoff in a reasonable (albeit imperfect) way - have a look here.

As for the price of a true claim never falling below $0.50, that seems obvious since a speculator will always prefer the cheaper side of a random bet (cos it amplifies the volatility). It is not just the absolute return on one side of the bet that counts, but the return relative to the other side of the bet. People buying Slv1 at $0.32 are only getting double the volatility they would get with selling at $0.68 and are paying a premium in terms of an expected loss of 4% pa versus a gain of 2% pa. I am not sure what drives the relationship between expected loss and equilibrium volatility ratio, but this seems way out of line with the rest of the market unless people really do think it has a significant chance of coming true.

Anonymous said...

James, regarding your comment that a WAIS collapse is probably the only available mechanism for a 1m sea level rise by 2030 but that this is exceedingly unlikely, remember that only a partial collapse would be needed and that the recent small collapses on the peninsula were a "surprise" to the Antarctic experts. The difficulty with all of these potential climate change tipping points is they seem to be impossible to predict with any precision and that no climate scientist would want to be caught making a prediction that would have a chance of being disproven within that scientist's lifetime. From the point of view of risk assessment, this seems a little too conservative.

Anonymous said...

I think you have missed the main point of my comments. I'm not disagreeing with your statement that FX prices do provide some information about the true odds of events. I am saying that the amount of information decreases with an increase in the time left on the prediction due to the decreasing rate of return for being correct, and we can measure this effect to an extent with the True claims, and to a lesser extent with claims with only a tiny change of being true (or false).

This might be changed somewhat if it was real money, but with real money long term investments paying 0.5% are usually not attractive, and nearly even odds bets can be more attractive. In the context of the game, it might be changed more if there was a larger return for holding a position for a longer time period. A practical test of such rules would be that under such rules a No on a True claim would sell for ~0 regardless of the term. This is not the state of the FX exchange rules, as the No tickets on True claims being traded shows.

I agree that speculator will always prefer the cheaper side of a random bet. But a speculator will need volatility. If the price of a True_in_3535 claim goes to 50 and stays there, it will not be traded. After all, 51 and 49 are not all that different in terms of being cheaper. It seems obvious to me both that a very long term claim will average price near 50, and to be traded, it will need some volatility. Does this not imply that it will trade on both sides of 50?

As for sea level increasing by one meter by 2030, I'm sure that there is a range of opinion. However, there isn't any practical difference in how it would be traded between my opinion (~1% risk), your opinion (~0 risk) and someone who thought it was a significant risk (~10%). All three opinions could lock in a tiny return on investment by buying NO tickets at the current prices. But why lock in a tiny return on investment? What would the motivation be?

James Annan said...

Phil, I don't disagree with everything you say, but I do think you in turn are missing the point that the market price does not depend solely on the (very low) return on the Y coupon (for a known true claim). Instead, it is the relationship between the returns on Y and N that counts. For a 25 year time scale, the N returns a 4% pa expected loss, and even if the gain on the Y is negligible, the only possible reason for buying N at any price is if the investor hopes to ride the volatility (which potentially gives large returns as the N price approaches 0, of course).

Even for a 200 year claim, the N price will only ever go to $0.51 if someone decides they would rather buy N at $0.51 than Y at $0.50. Given that the latter has a larger gain due to volatility as well as the (negligible) gain advantage, I can't see why any players could possibly want to do that. Of course, there are probably some truly stupid players :-)

Perhaps what we need is a "True 2030" claim to provide a benchmark - extrapolating out from 10 years is probably a bit unreliable.

Anonymous said...

Market price does depend (almost) solely on the return on the Yes ticket if the remaining term is short enough. If the term is somewhat longer, then it is more complex. If the term is long enough, then the expected return on the Yes ticket has almost nothing to do with the expected price. The amount of information in the price as to the truth of the claim decreases with an increase in the time left on the prediction due to the decreasing rate of return for being correct, and the decreasing cost of being wrong.

Expected volatility is not just a function of the price, it is a function of the orders in the book. Look at the book for Slv1. Notice that a player is offering to buy back the 972 tickets he is short at 17. If I was to try to move the price below 17, I'd need to spend about 825.62. To move the price up by the same amount, I'd need to spend about 9.60. While this is partly due to the price, look at the number of tickets: 1034 vs 49.

As for a benchmark to compare to, a "True in 2030" would be one, however a "99% chance of True in 2030" might be a better match.