Sunday 9 November 2014

GDP-Derivatives: A Global Risk Management Tool; What do we mean by "invariance up to isomorphism"

Economic statistics are compiled and written by bureaucrats who get fired only if they show they haven't been doing any work, so is it any surprise that their figures should be revised?

http://www.nytimes.com/2014/11/07/business/economy/doubting-the-economic-data-consider-the-source.html?partner=rss&emc=rss&_r=2

One of the problems in financial engineering is getting a set of figures that the world can agree on. This is what I call the problem of finding the invariance.  One way to think about Category Theory is that it's all about finding invariance at the level of isomorphism, or more forcefully, of finding what is uniquely true and accurate because it is indicated by gestural arrows that point directly at it.  At a visceral level, notice how when we point at something saying that "it's right there", we are in a state of "understanding is not merely a pointing but an extension of the pointing as part of the activities of the world."  Category Theory at the level of functoriality tells us "it's all about the pointing" so the object itself is not at necessary, or again, to put it more forcefully, the object is completely defined by the infinite number of pointings that we have of that object, so the substantiality of the object disappears!  We don't need the object at all, because now we know it completely in its infinite possibilities of being.  This sounds very abstract (and it is) but in everyday life, we do this "gestural understanding" all the time, whenever we eat, sleep, converse, enjoy a drink...all of these "things" are invariances at the level of isomorphism.  But the problem of government statistics...

is that they get revised and so we have tremendously long time-lags in response to "certainties of announcements" that affect our buying and selling decisions.

In 1999, I had worked with an ex-Merrill Lynch derivatives trader to create a "GDP-derivative" which basically would allow you to take take bets on the GDP of any nation in the world.  Of all the derivatives that could help humanity manage its "spaceship resources", I thought a GDP derivative would be the best.  It would mean essentially that a globally active company (or any other legal entity including a state) could manage its risk.  So, if say you wanted to hedge Brazilian GDP risk, you could.  The conceptual design for this product was pretty EZ.  All you have to do is think "swap", i.e., the cash flows of a buyer and seller in relation to the data regarding the GDP figure.  For 'proving out' the instrument, we just made a table of natural buyers versus sellers, and listed the sectors underneath each heading, and thought through which companies would be "natural buyers and sellers" given different scenarios of "expected GDP".  Anyone doing a masters level course on quantitative finance should be able to knock up this model in a leisurely afternoon.

Anyway, the problem we had was the "revisions" on GDP data.  Since these numbers came out 6 to 18 months after the first announcement, it became difficult to "match up" reality.   In the language I use today, I'd say, "We couldn't get a simple isomorphism and therefore, no invariance."  Without an invariance (an agreement on the GDP-figures), our model would not work.  Of course, that was back then, before we had Google data.  Now, I'm pretty sure we could crunch up our own GDP-index in order to create the GDP-derivative.  Then it's a matter of selling and marketing...     

No comments:

Post a Comment