[danm]

Actually, I believe his point is that the probability distribution is from the Cauchy Distribution, where the mean, the variance, and the kurtosis are all undefined. In fact, you're providing an example of exactly what he writes about in believing that the tools being taught in "freshman econometrics" apply to the sort of randomness you encounter in the real world. Certainly Mandelbrot has had some things to say about this topic as well.

When basic financial tools and theories are based on assumptions that are Just Plain Wrong, it makes you question the gigantic stack that has been built on top of them.

It's easy enough to dismiss this stuff as worrying about edge cases, but these edge cases occur more often than the theory dictates, and unfortunately, people underestimate their impact.

[mediaman]

You're right about him preferring a Cauchy distribution vs. a leptokurtotic distribution, I was mistaken.

Taleb argues that these tools aren't being used in the real world, but all the evidence in places like the options market seems to indicate otherwise: options get way more expensive (from a lognormal perspective) the deeper in/out of the money they are, primarily because there are fat tails already being modeled into the price. And given that options market data, it's tough to see how going long on Black Swans will fetch a good Sharpe ratio--which wouldn't be the case if it were true that everyone were slaves to normal distributions.

[bhewes]

Yeah what you described is called the volatility smile.

I would say going long on Black Swans is more of an insurance policy unless you are a VC. As the Taleb advised Universa Investments L.P. sells itself as "an investment management firm that specializes in hedging tail risks for its clients. Universa has a focused investment approach employing positively-skewed payoffs, empirical and fundamental-based option valuation, and order flow trading."