Finiteness of Variance is Irrelevant in the Practice of Quantitative Finance
Nassim Nicholas Taleb
New York University-Poly School of Engineering
June 9, 2008
Complexity, Vol. 14, Issue 3, pp. 66–76, January/February 2009
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.
Number of Pages in PDF File: 12
Keywords: Portfolio theory, power laws, option pricing, fat tails, risk management
JEL Classification: D8, G11, G12, G13, N00
Date posted: June 9, 2008 ; Last revised: November 16, 2012
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