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Finiteness of Variance is Irrelevant in the Practice of Quantitative Finance

Complexity, Vol. 14, Issue 3, pp. 66–76, January/February 2009

12 Pages Posted: 9 Jun 2008 Last revised: 16 Nov 2012

Nassim Nicholas Taleb

NYU-Tandon School of Engineering

Date Written: June 9, 2008

Abstract

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-Lévy-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.

Keywords: Portfolio theory, power laws, option pricing, fat tails, risk management

JEL Classification: D8, G11, G12, G13, N00

Suggested Citation

Taleb, Nassim Nicholas, Finiteness of Variance is Irrelevant in the Practice of Quantitative Finance (June 9, 2008). Complexity, Vol. 14, Issue 3, pp. 66–76, January/February 2009. Available at SSRN: https://ssrn.com/abstract=1142785 or http://dx.doi.org/10.2139/ssrn.1142785

Nassim Nicholas Taleb (Contact Author)

NYU-Tandon School of Engineering ( email )

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