Mandelsbrot’s infinite-variance price model implies infinitely expected stock prices

Evidence

For all the apparent technicality of the issue of infinite variance, Levy distributions had aroused strong passions. One mathematically sophisticated interviewee, Oldrich Vasicek, told me that he thought that Mandelbrot “must just have pulled everybody’s legs the whole time… I just cannot believe he would actually take it [Levy distributions with infinite variance] seriously himself… It has consequences so brutal that nobody would be able to live with that.” If the logarithm of a stock price varied according to a Levy process with infinite variance, as Mandelbrot had hypothesized, then the expected value of the price itself would be infinite. “So you’d be saying with straight face that you have an infinite expectation for tomorrow’s Xerox price.” — Donald MacKenzie, An Engine, Not a Camera, 517

Categorization

• CANDY: The absurd-but-true implication that an infinite-variance Levy process means an infinite expected price for tomorrow’s Xerox stock is a great cocktail-party physics/econ fact.
• XREF: connects to: Stock price changes are modeled with thin-tailed lognormal distributions, not fat-tailed ones — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 138