Finiteness of Variance is Irrelevant in the Practice of Quantitative Finance

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.

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

working papers series