PORTFOLIO THEORY FOR "FAT TAILS"

D. Sornette, J. V. Andersen and P. Simonetti
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D. Sornette: Institute of Geophysics and Planetary Physics and Department of Earth and Space Science, University of California, Los Angeles, California 90095, USA;
J. V. Andersen: Nordic Institute for Theoretical Physics, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
P. Simonetti: Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2000, vol. 03, issue 03, 523-535

Abstract: We introduce a faithful representation of the heavy tail multivariate distribution of asset returns, as parsimonious as the Gaussian framework. Using calculation techniques of functional integration and Feynman diagrams borrowed from particle physics, we characterize precisely, through its cumulants of high order, the distribution of wealth variations of a portfolio composed of an arbitrary mixture of assets. This approach makes quantitative and rigorous the well-known fact that minimizing the variance, i.e. the relatively "small" risks, often increases larger risks as measured by higher normalized cumulants and the Value-at-Risk.

Date: 2000
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DOI: 10.1142/S0219024900000504

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