Friday, July 27, 2012

Betting on Krugman's Dice

Aside from an incorrect (or maybe just wildly oversimplified) statement that "...even a fairly modest rise in average temperatures translates into a much higher frequency of extreme events...", Paul Krugman recently wrote an interesting commentary on global warming, that a gambler wagering on climate change could no longer rationally assume a fair bet either way.

These bets are not so hypothetical.  Much like credit default swaps serve to allow investors to match the exposure of various credit risks, weather insurance and derivatives transactions can help us understand the dollars and cents of risks of climate change and potential actions in response to changes.  (Please insert here the disclaimer that I am not advertising insurance or derivatives sales.  Also insert the self promotional plug: If you want such protection, contact Metar Weather.)

Here's an interesting example.  This plot shows the annual snowfall at LaGuardia Airport from 1949 to 2012. To the casual observer, it show be pretty clear the volatility of this time series is not stable.  It looks more volatile recently. 

The statistics are striking.  If we break the series into two periods: 1949-1990, and 1991-2012 you probably cannot eyeball the differences.  The Average snowfall actually rises by five inches.  But, the standard deviation (a measure of volatility) nearly doubles, rising from about 12 to a bit over 20.  So, in a simple sense, there's more snow, on average, but snowfall has become riskier.

But, there's more.  Let's consider the skewness of the series. (This is the measure of how much more likely outlier events happen in one direction or another.  A positive skew means outliers are more likely to the upside than the downside.)  In the early period, the skewness is about 1.1, while in the latter it has dropped to 0.7.

So what the heck does this have to do with Krugman's dice??  Suppose you wanted to place a bet on snowfall at LaGuardia.  Say that there will be at least 12" of snow in the next year.  Well, the price has changed.  The price has changed definitively.  Krugman's dice aren't theoretical.

(And, no, I cannot tell you the prices.  I suspect that would definitely put me over the line into selling insurance or derivatives on my blog, which I will not do!)