Enthusiasms (odd): December 2004 Archives

Well-seasoned Stock (Market)

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That's kurtosis, which is neither ketosis, thankfully, nor kenosis.

Let's face it. One of the reasons you stop by here is that you want to see what oddity I will trot out next, what quirky thing presented itself to my warped imagination as a thing of interest.

Well today we have Kurtosis and Mandelbrot's analysis of the stock market.

from The (Mis)Behavior of Markets
Benoit Mandelbrot and Richard L. Hudson

Statisticians like to condense a lot of confusing information into one clear talking point, and so they have devised a single number to measure what we have been discussing--how closely real data fit the ideal bell curve. They call it kurtosis, for the Greek kyrtos, or curved. But we can think of it as how much "spice" is in the statistical broth. A perfect, unseasoned bell curve has a kurtosis of three. A hot, fait-tailed curve of the sort we have been finding would have a higher spice number, while a curve that had been boiled into a dull paste would have a lower number. According to a 2003 book by Wim Schoutens, a Catholic University of Leuven mathematician, the daily variaiton in another common U.S. stock-market index, the Standard&Poor's 500, had a kurtosis of 43.36 between 1970 and 2001. This is, by the bland standard of the statistical kitchen, a five-alarm chili. If you throw out the spiciest data point, the October 1987 crash, you still get an uncomfortably hot dish: a kurtosis of 7.17. The high-tech NASDAQ index: 5.78. The French CAC-40: 4.63. All are above the Gaussian norm of three.

Hope that whipped up the Holiday appetite dulled from too many sweets and too much turkey. Get out your stock (market) pot and boil yourself up some Kurtosis of 1987!

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This page is a archive of entries in the Enthusiasms (odd) category from December 2004.

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