Outside the Platonic world of financial models, assuming the underlying distribution is a scalable "power law", we are unable to find a consequential difference between finite and infinite variance models -a central distinction emphasized in the econophysics literature and the financial economics tradition. While distributions with power law tail exponents α>2 are held to be amenable to Gaussian tools, owing to their "finite variance", we fail to understand the difference in the application with other power laws (1<α<2) held to belong to the Pareto-Levy-Mandelbrot stable regime. The problem invalidates derivatives theory (dynamic hedging arguments) and portfolio construction based on mean-variance. This paper discusses methods to deal with the implications of the point in a real world setting.
['Nassim Nicholas Taleb']
Finiteness of Variance is Irrelevant in the Practice of Quantitative Finance