23.11.08

TAKE IT TO THE LIMIT. Neo-Neocon comments on a Vanity Fair investigation of the asset-valuation models that assured hedge fund managers of the optimality of option valuation, tranched mortgage securities, and other potentially useful yet dangerous investment strategies. Neo's summary: alchemy. The reality is more troubling.
The quants’ Value at Risk models had implied that the loss the firm suffered in August 1998 was so unlikely that it ought never to have happened in the entire life of the universe. But that was because the models were working with just five years of data. If they had gone back even 11 years, they would have captured the 1987 stock-market crash. If they had gone back 80 years they would have captured the last great Russian default, after the 1917 revolution. [Salomon Brothers arbitrage manager John] Meriwether himself, born in 1947, ruefully observed, “If I had lived through the Depression, I would have been in a better position to understand events.” To put it bluntly, the Nobel Prize winners knew plenty of mathematics but not enough history.
Although they didn't fully grasp the mathematics. Look at the option pricing formula: one key variable goes to zero as time goes to infinity. Such convergence is useful in several areas of statistical inference, often under the label asymptotic distribution theory. (I picked a relatively straightforward result. It can get much messier.)

The problem, in practice, is that the small-sample properties of these estimators can be very different from the limiting properties. And small samples can be very large. It was either John Allen Paulos or Martin Gardner who reported a conversation with a mathematically sophisticated nephew who explained, roughly, that a million is a very large number, but a long way from infinity, and a trillion (as in the government budget at the time) is much larger, but no closer to infinity, and a google a long way from a trillion, but still no closer to infinity. That said, a model with a bit of memory of the Russian default at the beginning of Communism might be better equipped to handle a Russian default at its end.

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