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Daily Speculations The Web Site of Victor Niederhoffer & Laurel Kenner Dedicated to the scientific method, free markets, deflating ballyhoo, creating value, and laughter; a forum for us to use our meager abilities to make the world of specinvestments a better place. |
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2/6/2005
Professor Ross Miller Considers Taleb/Niederhoffer
This week I will be covering the Gladwell article on NNT/Chair in my derivatives for graduate accounting students class.
In a recent communiqué NNT reiterates that he believes volatility to be "undefined."
To quote him precisely and in context: "By saying 'weakly correlated' I know I may be saying something lacking in rigor. 'Volatility' is necessarily a Gaussian concept; we do not even know how to measure it the weights are Norm L2 (meaning that observations are weighed by themselves, so large observations weigh more than smaller ones). In a power law environment, with exponent a<2 (or a Multifractal process with about any a), volatility is undefined but the fatness of tails can be known, measured by a and some degree of asymmetry. Hopefully in the victory of Mandelbrot paradigm we will not talk about such thing as volatility but tail exponent."
NNT is, however, himself lacking in rigor. He uses "undefined" when referring to volatility when the right word is "unbounded" or what a layman would call "infinite."
It is noted by Gladwell that NNT worships Karl Popper.
Here's the conundrum: Any amount of finite data will lead to the empirical conclusion of a finite volatility. To fit NNT's "theory" into a Popperian framework requires that it be refutable. That, however, would require unbounded data to test this hypothesis EMPIRICALLY. (Note: The infeasible alternative is to know the distribution-generating process a priori, but only Plato can do that and he's dead and no one can find the keys to his cave.)
It is left as an exercise for the reader to show that if NNT is correct (empirical proof or not), not only does any calculation involving volatility become "incorrect," so does any calculation involving returns--completely invalidating all forms of "counting."