Sunday, August 30, 2009

Heraclitus and a Quant

I have always been fond of the pre-Socratics. Perhaps because, since we have only fragments, we can extrapolate in whatever direction suits our fancy. Perhaps because virtually all of them worked on the frontiers of both fledgling science and fledgling philosophy and thus tended to be bold.

Heraclitus “the obscure” was one of the most profound. Some of the recorded fragments are well known, such as “The path up and down is one and the same.” It’s a cheap shot to say that Heraclitus never experienced the financial markets where the path up is radically different from the path down. He was “testing” the concept of the unity of opposites both scientifically and philosophically.

But Heraclitus, who believed in the dominance of change in the world, did address the basic flaw of all risk management: “If one does not expect the unexpected one will not find it out, since it is not to be searched out, and difficult to compass.” (These translations, by the way, all come from Kirk and Raven’s The Presocratic Philosophers.)

Of course the most famous fragment is that you can’t step twice into the same river. Fleshed out, in another fragment, “Upon those that step into the same rivers different and different waters flow. . . . It scatters and . . . gathers . . . it comes together and flows away . . . approaches and departs.”

So what’s the point of this rumination? Or, better, what sent me back to Heraclitus? An important cautionary note from one of the early quants, best known to people outside the financial world as the man who beat the dealer in blackjack. “Here are some of the things we learned about building successful quantitative models in finance. Unlike blackjack and gambling games, you only have one history from which to use data (call this the Heraclitus principle: you can never invest in the same market twice). This leads to estimates rather than precise conclusions.”(“A Perspective on Quantitative Finance: Models for Beating the Market” by Ed Thorp, from The Best of Wilmott, vol. 1 [Wiley, 2004], p. 36) And, Heraclitus would add, the potential to be blindsided by the unexpected.

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